ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 The flux calibration sources. were PIS 63s and/or PISS 293: phase referencing took place with respect to QSO D2243-123., The flux calibration sources were PKS $-$ 638 and/or PKS $-$ 293; phase referencing took place with respect to QSO B2243-123.3 Since the orbital period of 9) STOd. is very. close. to 2 davs (1.94 daws) it is cillicult to obtain grouncd-based observations which cover the whole orbit [rom one site., Since the orbital period of GJ 876d is very close to 2 days (1.94 days) it is difficult to obtain ground-based observations which cover the whole orbit from one site.4 In order to do this we obtained (wo I0-hour observations within two days ancl repeated. this eighteen days later (see Table 1), In order to do this we obtained two 10-hour observations within two days and repeated this eighteen days later (see Table 1).5 We determined. the orbital phase of cach observation using the ephemeris of Rivera (2005) for CJ ST6cl (assuming = 907). which defined ὁ=0.0 as the transit epoch and has uncertainty 0.03 eveles.," We determined the orbital phase of each observation using the ephemeris of Rivera (2005) for GJ 876d (assuming $i=90^{\circ}$ ), which defined $\phi=0.0$ as the transit epoch and has uncertainty 0.03 cycles."6 La Table 3 we show the phase coverage of our observations: we obtained coverage for of the orbital period., In Table 3 we show the phase coverage of our observations; we obtained coverage for of the orbital period.7 However. we did. not. detect radio emission at any of these epochs. individually or combined into a single image.," However, we did not detect radio emission at any of these epochs, individually or combined into a single image."8 Phe 36 upper limit to the tux density in the combined image was 1225., The $3\sigma$ upper limit to the flux density in the combined image was $\mu$ Jy.9halos in theerternal absorption (Aharonian. Coppi Vools 19€dt).,"halos in the absorption (Aharonian, Coppi Voelk 1994)."10 Such an extended halo due τοπα absorptioi nw be of very long variable timescale at lcust o105 yr (corresponding to one mean free path) SCC equation (21)., Such an extended halo due to absorption may be of very long variable timescale at least $\sim 10^3$ yr (corresponding to one mean free path) [see equation (24)].11" IHowever if the absorption works in the ceural cneine. the time-depeudentsvuchrotrou selfCompton model inchiding pair cascade (Wang. Zhnoi Cheng 2010) could predict the interesting spectrum and helt curves, Which iav interpret the variations of PISS 2155-301 (Urry et al 1997)."," However if the absorption works in the central engine, the time-dependentsynchrotron self-Compton model including pair cascade (Wang, Zhou Cheng 2000) could predict the interesting spectrum and light curves, which may interpret the variations of PKS 2155-304 (Urry et al 1997)."12" The other radiative properlos of such ai extended pair halo are uceded to be stuied in order to distinguish the absorption from the οἱ onc,", The other radiative properties of such an extended pair halo are needed to be studied in order to distinguish the absorption from the one.13ο is up and East is deft in all figures.,North is up and East is left in all figures.14 Figure S spectacularly displavs. the SUISHoοσο ratio throughout he whole FOV (see caption).," Figure 8 spectacularly displays the $\frac{[\textnormal{N}\,\textsc{ii}]\,\lambda6584}{\textnormal{H}{\alpha}\,\lambda6563}$ ratio throughout the whole FOV (see caption)."15 Red emphasizes regions dominated by while bluer shades. pinpoint a stronger emission of the IN extsceii] AGDS4 X. transition. (with. respect to. the. redder areas)., Red emphasizes regions dominated by while bluer shades pinpoint a stronger emission of the $[$ $]$ $\lambda$ 6584 $\mbox{\AA}$ transition (with respect to the redder areas).16 Phree stars with strong lines are detected. (the hird being barely perceptible very close to the center of he figure)., Three stars with strong lines are detected (the third being barely perceptible very close to the center of the figure).17 At the position of all other stars. bad: pixels were removed. ancl replaced by mean values. statistically representing the surrounding nebular-gas content.," At the position of all other stars, bad pixels were removed and replaced by mean values statistically representing the surrounding nebular-gas content."18" “This igure is particularly useful to describe tonizecl features in our FOV,", This figure is particularly useful to describe ionized features in our FOV.19 The Five College Radio Astronomy Observatory(CIAO) CO(I1-0) survey. of the 25 Galactic cquacrant (leverοἱaL.1998) has revealed very faint emission corresponding to tenuous molecular material at the position of the bright. central ionized structure in Figures 3 to 7.," The Five College Radio Astronomy Observatory(FCRAO) CO(1-0) survey of the $^{\mbox{\scriptsize{nd}}}$ Galactic quadrant \citep{Hey1998} has revealed very faint emission corresponding to tenuous molecular material at the position of the bright, central ionized structure in Figures 3 to 7."20 This suggests the presence of a large molecular fragment. surrounded. by the most massive stars of the Alelotte 15 cluster. that has undergone almost full erosion. by. the UV [lux and stellar winds of the nearby ionizing sources.," This suggests the presence of a large molecular fragment, surrounded by the most massive stars of the Melotte 15 cluster, that has undergone almost full erosion by the UV flux and stellar winds of the nearby ionizing sources."21 Figure S reveals the fibunentarv nature of the central structure., Figure 8 reveals the filamentary nature of the central structure.22 These filaments most likely trace out the spatial disposition. on the plane of the sky. of the eroded (sometimes fully ionized) molecular envelopes.," These filaments most likely trace out the spatial disposition, on the plane of the sky, of the eroded (sometimes fully ionized) molecular envelopes."23 The central structure is surrounded. by dilfuse tonizecd material likely associated to photoevaporated [Lows kinematically in agreement with the Champagne phase (Lagrois&Joncas2009a)., The central structure is surrounded by diffuse ionized material likely associated to photoevaporated flows kinematically in agreement with the Champagne phase \citep{Lag2009a}.24. One of these Hows (displaving blue shades in Figure S) is particularly welldefined. propagating from the bottom-center of our FOV approximately toward the upper-left corner of Figure S.," One of these flows (displaying blue shades in Figure 8) is particularly well-defined, propagating from the bottom-center of our FOV approximately toward the upper-left corner of Figure 8."25 West of the central structure. the spatial arrangement of the nebular eases is extremely complex.," West of the central structure, the spatial arrangement of the nebular gases is extremely complex."26 Ionized. filaments are still perceptible although the contrast with the dilfuse surroundings is not as clear., Ionized filaments are still perceptible although the contrast with the diffuse surroundings is not as clear.27 Toward the western boundary of Figure S. even the emission appears darker. obscured by interstellar dust.," Toward the western boundary of Figure 8, even the emission appears darker, obscured by interstellar dust."28 Shock excitation in the vicinity of the bright. central ionizecl structure. displaved in Figures 3 to S. will be largely discussed and investigated in 8 5.2.1.," Shock excitation in the vicinity of the bright, central ionized structure, displayed in Figures 3 to 8, will be largely discussed and investigated in $\S$ 5.2.1."29 Toward the south-castern portion of our FOV. a small CO fragment is clearly detected in the FOCRAO survey at the svstemic velocity of the 11805 region. (see CO contours in Figures 3 to 7).," Toward the south-eastern portion of our FOV, a small CO fragment is clearly detected in the FCRAO survey at the systemic velocity of the 1805 region (see CO contours in Figures 3 to 7)."30 Hs ionized counterpart is revealed by a hin. rounded ionization front especially visible in the lower-eft corner of Figure δ (see also Figure 190)).," Its ionized counterpart is revealed by a thin, rounded ionization front especially visible in the lower-left corner of Figure 8 (see also Figure )."31 This specilic shape of the ionization front results [rom the vast majority of the ionizing sources in Melotte 15 being located behind he molecular clump., This specific shape of the ionization front results from the vast majority of the ionizing sources in Melotte 15 being located behind the molecular clump.32 This was kinematically confirmed. in Lagrois&Joncas(2009a).. by the detection. of an accelerated. ionized outllow moving away from the observer (sce §& 5.2.2.1).," This was kinematically confirmed, in \citet{Lag2009a}, by the detection of an accelerated ionized outflow moving away from the observer (see $\S$ 5.2.2.1)."33 This flow eventually collicles or simply coincides in lines-ol-sieht with the south-central/north-cast low mentioned in the previous paragraph., This flow eventually collides or simply coincides in lines-of-sight with the south-central/north-east flow mentioned in the previous paragraph.34 This results in particularly complicated kinematical motions in central 11805. with non-thermal line widths. approaching he supersonic regime ( 110 km 1j according to resolution observations (Lagrois&Joncas2009a)., This results in particularly complicated kinematical motions in central 1805 with non-thermal line widths approaching the supersonic regime $\sim$ 10 km $^{-1}$ ) according to high-resolution observations \citep{Lag2009a}.35. In the same area of Figure 8 (see also Figure 19c)). a cvlindrical. cigar-like feature appears to be associated with an isolated star with strong lines (see above).," In the same area of Figure 8 (see also Figure ), a cylindrical, cigar-like feature appears to be associated with an isolated star with strong lines (see above)."36 The feature has bright and rims but is almost completely eas-deprived near its center., The feature has bright $^{+}$ and $^{+}$ rims but is almost completely gas-deprived near its center.37 This structure as well as the rounded. ionization [ront found in the lower-lelt corner. of Figure 8S will be discussed in 58 5.2, This structure as well as the rounded ionization front found in the lower-left corner of Figure 8 will be discussed in $\S$ 5.2.2.38 ligure 9 was processed identically to Figure S and displays the SUEESDEYSENINNGTIGIGTAL ratio (where the numerator is he sum of both lines of the S extscii]doublet).," Figure 9 was processed identically to Figure 8 and displays the $\frac{[\textnormal{S}\,\textsc{ii}]\,\lambda\lambda6716, 6731}{[\textnormal{N}\,\textsc{ii}]\,\lambda6584}$ ratio (where the numerator is the sum of both lines of the $[$ $]$ doublet)."39" Again, blueshadesidentifynilrogen richzoneswhileredareasindicatethatasizeableroleisplayedbgsul furintheor κο) "," Again, blue shades identify nitrogen-rich zones while red areas indicate that a sizeable role is played by sulfur in the overall gas emissivity."40clearly dominates over S extsci, One immediately notices the complexity of the chemical properties in 1805.41i]wehereHo is the brightest. weaker zones (in integrated intensity) show an important increase of the relative contribution of the sulfur material.," While $[$ $]$ clearly dominates over $[$ $]$ where is the brightest, weaker zones (in integrated intensity) show an important increase of the relative contribution of the sulfur material."42 In. particular. he reacer’s attention is directed toward the north-eastern ilament of the bright. central structure described: above.," In particular, the reader's attention is directed toward the north-eastern filament of the bright, central structure described above."43 Series of small. quasi-circular blobs are found.," Series of small, quasi-circular blobs are found."44 The. top hree reveal two nitrogen-dominated. features (in blue) and one with a stronger relative contribution in. S extsciil(inred)., The top three reveal two nitrogen-dominated features (in blue) and one with a stronger relative contribution in $[$ $]$ (in red).45"IEneestigalinglheircorrespondingspectrum. ihe feriscr] intensity remains roughly constant from one blob o another while the Ν ferastrongallenualionalonglheline οἱ sighlofthesvedder""onctwhicherplainstherelativelypoorcontributionofniti"," Investigating their corresponding spectrum, the $[$ $]$ intensity remains roughly constant from one blob to another while the $[$ $]$ lines suffer a strong attenuation along the line-of-sight of the “redder” one (which explains the relatively poor contribution of nitrogen towards it)."46i , This behavior is not generalized to our whole FOV although similar features can be found here and there.47The supernova remnant 11B3 (see Figure 1) is located oo far away from our FOV to have had a sizeable impact on the chemical properties in central 11805., The supernova remnant HB3 (see Figure 1) is located too far away from our FOV to have had a sizeable impact on the chemical properties in central 1805.48 Alternatively. we can argue that the old. large molecular cloud. that gave mth to Alelotte 15 roughly 2.5 Myr ago. may have had an inhomogeneous distribution of its chemical compounds.," Alternatively, we can argue that the old, large molecular cloud, that gave birth to Melotte 15 roughly 2.5 Myr ago, may have had an inhomogeneous distribution of its chemical compounds."49 Old supernovae in 11805. whose non-thermal emission has vanished since. could also be held responsible.," Old supernovae in 1805, whose non-thermal emission has vanished since, could also be held responsible."50 We reiterate that the 11505 region was most likely formecl by a succession of different star clusters (see § 2) ie. although no indication for supernova remnants is currently. found inside the large region. it is highly probable that he inner zones of 11805 were. at some time in the past. disturbed by supernova events associated to. previous generations of massive stars.," We reiterate that the 1805 region was most likely formed by a succession of different star clusters (see $\S$ 2) i.e., although no indication for supernova remnants is currently found inside the large region, it is highly probable that the inner zones of 1805 were, at some time in the past, disturbed by supernova events associated to previous generations of massive stars."51" These stars could have had an intrinsic inhomogeneity in their inner nitrogen distribution. which eventually led to an anisotropic dispersion of these chemical compounds. products of the CNO evele. as cach stellar object. reached the end. of its life (ee. see the works by AlacAlpineefa£,(2007).. MacAlpine&Satterfield. (2008).. and Charleboisefaf(20100). on the Crab nebula)."," These stars could have had an intrinsic inhomogeneity in their inner nitrogen distribution which eventually led to an anisotropic dispersion of these chemical compounds, products of the CNO cycle, as each stellar object reached the end of its life (e.g., see the works by \citet{Mac2007}, \citet{Mac2008}, and \citet{Cha2010} on the Crab nebula)."52 Line ratios. in the literature. usually correspond. to ratios xtween two (or more) line Uuxes.," Line ratios, in the literature, usually correspond to ratios between two (or more) line fluxes."53 For à given emission ine. the line Hux is proportional to the product. between its peak intensity and its width as returned by the Gaussian it.," For a given emission line, the line flux is proportional to the product between its peak intensity and its width as returned by the Gaussian fit."54 In this work. the relatively low spectral resolution used (μου & 3) is roughly a factor 10 to 20 greater than typical non-thermal velocity [üctuations. along the line-of-sight. ound in 11805 using high-resolution observations of the kinematics (Lagrois&Joncas 2009a)..," In this work, the relatively low spectral resolution used (see $\S$ 3) is roughly a factor 10 to 20 greater than typical non-thermal velocity fluctuations, along the line-of-sight, found in 1805 using high-resolution observations of the $^{+}$ kinematics \citep{Lag2009a}. ."55 Hlence. in this work. the width of each emission line is entirely. dominated w the instrumental response and the returned. widths are very similar. from one ion to another. independently: of he position in the FOV.," Hence, in this work, the width of each emission line is entirely dominated by the instrumental response and the returned widths are very similar, from one ion to another, independently of the position in the FOV."56 Therefore. line ratios. in the," Therefore, line ratios, in the"57one can pul dp+7/2. n or p) is divided into » bins.,"one can put $\delta_D+\pi/2$ , $\eta$ or $p$ ) is divided into $n$ bins."58 We use »=36 bins of equal width., We use $n=36$ bins of equal width.59 We repeated our analvses using also different values of bin's width: no significant difference appeared among results., We repeated our analyses using also different values of bin's width; no significant difference appeared among results.60 The 4 lest vields (he critical value of 49.8 for 35 degrees ol freeclom (at the significance level a=0.05)., The $\chi^2$ test yields the critical value of $49.8$ for $35$ degrees of freedom (at the significance level $\alpha=0.05)$.61" If deviation [rom isotropy is a slowly varying function of the 9 angle one can use the Fourier test (ILawlev&Peebles1975):: where .N, - the munber of galaxies within k-th angular bin and ας Noy - the expected number of galaxies per bin."," If deviation from isotropy is a slowly varying function of the $\theta$ angle one can use the Fourier test \citep{h4}: where $N_k$ - the number of galaxies within k-th angular bin and as $N_{0,k}$ - the expected number of galaxies per bin."62" If theoretical probability function p, is uniform (1e Noy. are equal. as il is in the cases of the η and p angles) or svimietric with respect to the value @=7/2 (i.e. with respect lo value 05=0 in the case of 05 angle) we obtain thefollowing expressions for the A;, coellicients: with the standard deviation given by the expressions: The probability that the amplitude"," If theoretical probability function $p_k$ is uniform (i.e $N_{0,k}$ are equal, as it is in the cases of the $\eta$ and $p$ angles) or symmetric with respect to the value $\theta=\pi/2$ (i.e. with respect to value $\delta_D=0$ in the case of $\delta_D$ angle) we obtain thefollowing expressions for the $\Delta_{i1}$ coefficients: with the standard deviation given by the expressions: The probability that the amplitude"63eround-based aud HST data. and Section { gives tlie results.,"ground-based and HST data, and Section \ref{section:results} gives the results."64 The paper eucs with a discussion aud summary of our results and their implications for spiral galaxy GC systems aud galaxy. formation models., The paper ends with a discussion and summary of our results and their implications for spiral galaxy GC systems and galaxy formation models.65 linages of NGC 7811 were obtained in 1995 December and 1999 October with the 3.5 in WIYN at Witt Peak National Observatory., Images of NGC 7814 were obtained in 1998 December and 1999 October with the 3.5 m WIYN at Kitt Peak National Observatory.66" The detector used was a 2018x2018 CCD (S2IsB). which has 0.196""-pixels aud a field-of-view 6.7’ on a side when mounted on WIYN."," The detector used was a 2048x2048 CCD (S2KB), which has $\arcs$ -pixels and a field-of-view $\arcm$ on a side when mounted on WIYN."67 To observe as much of the galaxy halo aud GC system as possible. we positioned the center of NGC 7811 in oue corner of the CCD. which gives us radial coverage to 9. or ~35 kpe.," To observe as much of the galaxy halo and GC system as possible, we positioned the center of NGC 7814 in one corner of the CCD, which gives us radial coverage to $\sim$ $\arcm$, or $\sim$ 35 kpc."68 To help separate GCs [roin contaminating[eJ objects (foregrounde stars aud backgrouudD> egalaxies). imagesDm were obtained in three broadbaud filters (BVR).," To help separate GCs from contaminating objects (foreground stars and background galaxies), images were obtained in three broadband filters (BVR)."69 Multiple exposures were taken in each filter auc the telescope was dithered between exposures to facilitate cosmic ray removal., Multiple exposures were taken in each filter and the telescope was dithered between exposures to facilitate cosmic ray removal.70 Total integration times were 7200 s (four exposures) iu B. 5100 s (lee exposures) in V. aud 2100 s (tliree exposures) in Zt.," Total integration times were 7200 s (four exposures) in $B$, 5400 s (three exposures) in $V$ and 5400 s (three exposures) in $R$."71 One B-baucl. oue V-baud. aud the three Zt-band frames were taken under photometric coucitious. aud the rest of the images were taken ou mostly clear. but not photometric. nights.," One $B$ -band, one $V$ -band, and the three $R$ -band frames were taken under photometric conditions, and the rest of the images were taken on mostly clear, but not photometric, nights."72 Staudard star fields (Lauclolt 1992) were observed durius one night in 1999 October for use in the photometric calibration., Standard star fields (Landolt 1992) were observed during one night in 1999 October for use in the photometric calibration.73 The errors on the zero-point coustauts ranged from 0.003 to 0.002 magnitudes. indicating that the night was iucdeed photoimetric.," The errors on the zero-point constants ranged from 0.003 to 0.005 magnitudes, indicating that the night was indeed photometric."74 Preliminary reductions (overscan aud bias level subtraction. flat-field division) of the WIYN images were accomplished using standard tasks.," Preliminary reductions (overscan and bias level subtraction, flat-field division) of the WIYN images were accomplished using standard tasks."75 Sky subtraction was performed on the iucdividual inages taken in each filter before they were scaled to a common flux level aud combined., Sky subtraction was performed on the individual images taken in each filter before they were scaled to a common flux level and combined.76 The background level was restored to the combined images aud {μον were aligned aud flipped to a north-up. east-left orientation.," The background level was restored to the combined images and they were aligned and flipped to a north-up, east-left orientation."77" The resolution (point-spread. Fuuction FWHM) of the combined images is 1.0"" in B. 1.0"" in V. aud 1.3"" in R. In addition to the WIYN data. we also made use of data from the HST [or this study."," The resolution (point-spread function FWHM) of the combined images is $\arcs$ in B, $\arcs$ in V, and $\arcs$ in R. In addition to the WIYN data, we also made use of data from the HST for this study."78 Two Wide-Field aud Planetary Camera 2 (WEPC2) data sets were available in the archive., Two Wide-Field and Planetary Camera 2 (WFPC2) data sets were available in the archive.79 Lnages [rom program GO.5297 (PI: Regan) were positioned with the ceuter of the galaxy on the PC chip. aud images from program GO.G685 (PLE Huizinga) were positioned away [rom the galaxy. center. to include inore of the halo.," Images from program GO.8597 (PI: Regan) were positioned with the center of the galaxy on the PC chip, and images from program GO.6685 (PI: Huizinga) were positioned away from the galaxy center, to include more of the halo."80 The former. which we will call the galaxy. pointing. consisted of two," The former, which we will call the galaxy pointing, consisted of two"81(2-4)).,\ref{sigma}) ).82" In Figure 1 we set σι=1 where o,=(oo9/1cen?g!) and ey=(09/100kins+),", In Figure \ref{bhalpha} we set $\sigma_1v_{100}^a=1$ where $\sigma_1 \equiv \left(\sigma_0/1 \ \mathrm{cm}^2 \ \mathrm{g}^{-1}\right)$ and $v_{100} \equiv \left(v_0/100 \ \mathrm{km} \ \mathrm{s}^{-1}\right)$.83 The characteristic density. radius. and velocity dispersion. py. ry. and v; have been calculated from the dark halo concentrations using the routine mace publicly available by Eke. Navarro. Steinmetz (2001) (hereafter ENS). and described in Appendix A. Once (he accretion radius extends into the optically thin region of the dark halo the (hud approximation is no longer valid.," The characteristic density, radius, and velocity dispersion, $\rho_s$, $r_s$, and $v_s$ have been calculated from the dark halo concentrations using the routine made publicly available by Eke, Navarro, Steinmetz (2001) (hereafter ENS), and described in Appendix A. 	Once the accretion radius extends into the optically thin region of the dark halo the fluid approximation is no longer valid."84 The subsequent slow growth of the black hole proceeds as dark matter particles are scattered into the loss cone., The subsequent slow growth of the black hole proceeds as dark matter particles are scattered into the loss cone.85 This phase of growth was treated bv Ostriker (2000) for a velocity independent cross section., This phase of growth was treated by Ostriker (2000) for a velocity independent cross section.86 Loss cone accretion can grow black holes comparable to eqn. (2)) (, Loss cone accretion can grow black holes comparable to eqn. \ref{Mbh}) ) (87for a general velocity. dependent συ).,for a general velocity dependent $\sigma_{DM}$ ).88 However. this assumes a cuspy profile extends into the innermost regions of the halo for a Hubble Gime. whieh will not be the case if halos are significantlv. flattened by heat transfer during that same (ime interval.," However, this assumes a cuspy profile extends into the innermost regions of the halo for a Hubble time, which will not be the case if halos are significantly flattened by heat transfer during that same time interval."89 Conversely. accretion [rom the optically thick region of the halo grows black holes nearly instantaneously in comparison (o cosmological (imescales. as we will see in (he next section.," Conversely, accretion from the optically thick region of the halo grows black holes nearly instantaneously in comparison to cosmological timescales, as we will see in the next section."90 Since we have neglected the optically thin phase of growth and also any contribution to the mass from barvons. equ. (2))," Since we have neglected the optically thin phase of growth and also any contribution to the mass from baryons, eqn. \ref{Mbh}) )"91 should be regarded as a lower limit when compared to observations., should be regarded as a lower limit when compared to observations.92 Finally. it should be noted Chat the black hole mass calculated here is that grown from a single dark halo.," Finally, it should be noted that the black hole mass calculated here is that grown from a single dark halo."93 We will consider the effect of the dark halo merger history on this estimate in 86., We will consider the effect of the dark halo merger history on this estimate in 6.94 From Figure 1 it is apparent that the black hole mass in equ. (2)), 	From Figure \ref{bhalpha} it is apparent that the black hole mass in eqn. \ref{Mbh}) )95 may be very sensitive to the value of the inner profile exponent a., may be very sensitive to the value of the inner profile exponent $\alpha$.96 It is thus prudent to determine how physical processes not considered above might alter the inner profile., It is thus prudent to determine how physical processes not considered above might alter the inner profile.97 In what follows we consider the effect of the accretion flow and heat transfer., In what follows we consider the effect of the accretion flow and heat transfer.98 If. to lowest order. we take the accretion {ο be spherical. (hen. in the inner regions r«r.ry. gravitv clominates over pressure and the particles are in [ree fall with the radial velocity vu9 ο," 	 	If, to lowest order, we take the accretion to be spherical, then, in the inner regions $r \ll r_c \ll r_s$, gravity dominates over pressure and the particles are in free fall with the radial velocity $u\propto r^{-1/2}$."99" M=const. implies pxr ον, "," Then $\dot{M} = \mathrm{const}$, implies $\rho \propto r^{-3/2}$ ."100"This density profile will interpolate smoothly with the most probable value of the inner profile slope a=13402 al r~r,..", This density profile will interpolate smoothly with the most probable value of the inner profile slope $\alpha = 1.3 \pm 0.2$ at $r\sim r_c$.101 Now consider (he effect of heat transfer., 	 	Now consider the effect of heat transfer.102 We have just seen that (xr1/2 or Txr Ffor r<r... so that the inner regions of the flow are dvnamically hot.," We have just seen that $u\propto r^{-1/2}$ or $T\propto r^{-1}$ for $r\ll r_c$, so that the inner regions of the flow are dynamically hot."103 Also the censity profile in eqn. (2)), Also the density profile in eqn. \ref{NFW}) )104 produces a temperature inversion. so that heat will flow Irom the outer halo inward flattening the inner profile.," produces a temperature inversion, so that heat will flow from the outer halo inward flattening the inner profile."105" We are thus led toconsider how heat flow outward from the accretion flow r«r. and inward from the outer halo rX»r, alters the density profile near (he temperature minimunm al r7r..", We are thus led toconsider how heat flow outward from the accretion flow $r \ll r_c$ and inward from the outer halo $r \gg r_c$ alters the density profile near the temperature minimum at $r \sim r_c$.106 Taking note of the fact that the transport behavior differs under optically thick and thin conditions. we consider(hese cases separately.," Taking note of the fact that the transport behavior differs under optically thick and thin conditions, we considerthese cases separately."107 Figure 2.. presents a cartoon (o illustrate the density. and," Figure \ref{cartoon}, , presents a cartoon to illustrate the density and"108features of the groups: in particular. the forward motion of the leading part is usually faster than the receding motion of the following part and this. combined with the well-known tilt of the group axes. may cause an intrinsic equatorward shift. which 15 not a direct consequence of the Coriolis effect.,"features of the groups; in particular, the forward motion of the leading part is usually faster than the receding motion of the following part and this, combined with the well-known tilt of the group axes, may cause an intrinsic equatorward shift, which is not a direct consequence of the Coriolis effect."109 Using groups as tracers could therefore modify (enlarge) the covariance values., Using groups as tracers could therefore modify (enlarge) the covariance values.110 However. the use of single sunspots can modify our analysis results because of the intrinsic (non-Cortolis) sunspot-group rotation.," However, the use of single sunspots can modify our analysis results because of the intrinsic (non-Coriolis) sunspot-group rotation."111 Furthermore. it appears impossible to isolate a Coriolis-effect component in the correlations.," Furthermore, it appears impossible to isolate a Coriolis-effect component in the correlations."112 To avoid the impact of the effect mentioned by Leighton. some selection criteria were used.," To avoid the impact of the effect mentioned by Leighton, some selection criteria were used."113 A morphological shift is typical of the growing phase of sunspot-group development and is almost insignificant about the maximum phase. when a group reaches its maximal area and extension: for a while spot emergence and disappearance are insignificant and the group can be considered an individual entity.," A morphological shift is typical of the growing phase of sunspot-group development and is almost insignificant about the maximum phase, when a group reaches its maximal area and extension: for a while spot emergence and disappearance are insignificant and the group can be considered an individual entity."114 In the first approach. we considered only active regions that exhibited maximal area on the visible solar dise and data for a maximum of three days prior to and after the maximal area. depending on observability.," In the first approach, we considered only active regions that exhibited maximal area on the visible solar disc and data for a maximum of three days prior to and after the maximal area, depending on observability."115 This selectior should not affect our results because our aim is not to determine the absolute value of the correlations but instead their temporal variation., This selection should not affect our results because our aim is not to determine the absolute value of the correlations but instead their temporal variation.116 Correlations between longitudinal an latitudinal motions were computed using the formula: This formula illustrates the correlation between the AZ; and AB; values. the diurnal longitudinal and latitudinal shifts of a given sunspot group. respectively. for the period about which it exhibits its maximal area.," Correlations between longitudinal an latitudinal motions were computed using the formula: This formula illustrates the correlation between the $\Delta L_{i}$ and $\Delta B_{i}$ values, the diurnal longitudinal and latitudinal shifts of a given sunspot group, respectively, for the period about which it exhibits its maximal area."117 The diurnal shifts are differences between the daily positions of sunspot groups taken from the DPD catalogue., The diurnal shifts are differences between the daily positions of sunspot groups taken from the DPD catalogue.118 Since the observations were completed at different moments of the days the diurnal shifts are normalised to temporal differences of 24 hours., Since the observations were completed at different moments of the days the diurnal shifts are normalised to temporal differences of 24 hours.119 The (AL.AB) covariance has been used for this type of analysis. which ts the numerator of the above formula: its dimension ts velocity squared and it can be considered to be a measure of the Reynolds stress.," The $\langle\Delta L,\Delta B\rangle$ covariance has been used for this type of analysis, which is the numerator of the above formula; its dimension is velocity squared and it can be considered to be a measure of the Reynolds stress."120 The covariance is a suitable tool for studying the magnitude of the effect for the aforementioned theoretical reasons. for studying the temporal behaviour of the effect. however. a normalised quantity. the correlation coefficient. appears to be more informative.," The covariance is a suitable tool for studying the magnitude of the effect for the aforementioned theoretical reasons, for studying the temporal behaviour of the effect, however, a normalised quantity, the correlation coefficient, appears to be more informative."121 For similar reasons no correction was made for differential rotation., For similar reasons no correction was made for differential rotation.122 On the one hand. the rotation profile exerts similar influence during the cycle and therefore does not modify the temporal profile of the correlations.," On the one hand, the rotation profile exerts similar influence during the cycle and therefore does not modify the temporal profile of the correlations."123 On the other hand. the differential rotation profile varies with depth and it ts not obvious which depth should be applied.," On the other hand, the differential rotation profile varies with depth and it is not obvious which depth should be applied."124 In any case. it appears informative not to burden the results with ambiguous modifications but to follow a normalised parameter with respect to a steady. rotating frame.," In any case, it appears informative not to burden the results with ambiguous modifications but to follow a normalised parameter with respect to a steady, rotating frame."125 By using the above procedure. we attempt to find the curve of latitudinal dependence of the (AL.AB) correlations.," By using the above procedure, we attempt to find the curve of latitudinal dependence of the $(\Delta L, \Delta B)$ correlations."126 The first step provides the curve obtained over the entire solar cycle., The first step provides the curve obtained over the entire solar cycle.127 In the second step. individual curves are plotted on a yearly basis to follow any eventual connection with the cycle phase.," In the second step, individual curves are plotted on a yearly basis to follow any eventual connection with the cycle phase."128 If some deviations are obtained from the patterns expected on the basis of the Coriolis effect. then these may be signatures of the impact of a changing velocity field.," If some deviations are obtained from the patterns expected on the basis of the Coriolis effect, then these may be signatures of the impact of a changing velocity field."129 A correlation coefficient was computed by using the above formula for each selected sunspot group (by following it from the first selected day to the last one) in each 5° wide latitudinal stripe and the derived values were averaged within the stripes in both hemispheres., A correlation coefficient was computed by using the above formula for each selected sunspot group (by following it from the first selected day to the last one) in each $5^{o}$ wide latitudinal stripe and the derived values were averaged within the stripes in both hemispheres.130" Figure 1. shows the latitudinal distribution of the (AL.AB) correlation coetficient for the years 1986-1998, along with the numbers of considered groups within the 5° latitudinal stripes."," Figure \ref{8456fig1} shows the latitudinal distribution of the $(\Delta L, \Delta B)$ correlation coefficient for the years 1986-1998, along with the numbers of considered groups within the $5^{o}$ latitudinal stripes."131 The derived latitudinal distribution is similar. to. that published by Pulkkinen and Tuominen (1998)) (if one takes into account the differences in. coordinate. definitions). and Latushko (1993))., The derived latitudinal distribution is similar to that published by Pulkkinen and Tuominen \cite{pulkkinen}) ) (if one takes into account the differences in coordinate definitions) and Latushko \cite{latushko}) ).132 The most interesting feature can be seen in the temporal behaviour., The most interesting feature can be seen in the temporal behaviour.133 Figure 2. shows the plots of the latitudinal distributions of correlations for each of the 13 years separately., Figure \ref{8456fig2} shows the plots of the latitudinal distributions of correlations for each of the 13 years separately.134 The phase of cycle 22 can be traced by comparing the panels of each year with the cycle shape plotted in Fig. 3.., The phase of cycle 22 can be traced by comparing the panels of each year with the cycle shape plotted in Fig. \ref{8456fig3}.135 It is conspicuous that the most unanimous monotone latitudinal distribution is found in the maximum year. 1989 and one year before. 1955.," It is conspicuous that the most unanimous monotone latitudinal distribution is found in the maximum year, 1989 and one year before, 1988."136 The years of increasing activity show a similar trend. with larger scatter because of number statistics apart from the years at the end of the declining phase. which exhibit stochastic patterns.," The years of increasing activity show a similar trend, with larger scatter because of small-number statistics apart from the years at the end of the declining phase, which exhibit stochastic patterns."137 The distribution can, The distribution can138"mode (by which the power spectrum. estimate shoulc be divided): where m=(m,.my.ms) is a vector of integers. At=GOLIυπ In Equation 14.. PUR) is the underlying ποσο] power spectrum.","mode (by which the power spectrum estimate should be divided): where $\vec{m} = (m_x,m_y,m_z)$ is a vector of integers, $\vec{k'} =139(k_x',k_y',k_z') = (k_x + m_x k_{{\rm Nyq},x}, k_y + m_y k_{{\rm140 Nyq},y}, k_z + m_z k_{{\rm Nyq},z})$ and In Equation \ref{eqpkngpcorr}, $P(\vec{k})$ is the underlying model power spectrum."141 Given that this is initially unknown. we proceed by an iterative approach: we assume a f[iducial cosmological model. compute the correction. factor. [it cosmological parameters to the power spectrum. re-caleulate the correction factor. and then repeat the parameter fit.," Given that this is initially unknown, we proceed by an iterative approach: we assume a fiducial cosmological model, compute the correction factor, fit cosmological parameters to the power spectrum, re-calculate the correction factor, and then repeat the parameter fit."142 Phe magnitude of the correction is typically 2% at scale &s0.2h |l.," The magnitude of the correction is typically $2\%$ at scale $k \approx 0.2 \, h$ $^{-1}$."143 The spatially-varving selection function WCF) has two ellects on the process of power spectrum estimation., The spatially-varying selection function $W(\vec{x})$ has two effects on the process of power spectrum estimation.144" Firstly the expectation value of Equation 13. is the underlving power spectrum DU) convolved with the survey selection function: The numerator of Equation 16/— is summed. over the eric points j in Fourier space lor which the Fast Fourier “Transform of WO"") is caleulated. sspacec by (AK.Ab,ARS)=(2r/h..2a/hy.2a/b.)."," Firstly the expectation value of Equation \ref{eqpkest} is the underlying power spectrum $P(\vec{k})$ convolved with the survey selection function: The numerator of Equation \ref{eqpkconv} is summed over the grid points $\vec{k'}$ in Fourier space for which the Fast Fourier Transform of $W(\vec{x})$ is calculated, spaced by $(\Delta k_x,145\Delta k_y, \Delta k_z) = (2\pi/L_x, 2\pi/L_y, 2\pi/L_z)$."146 lor. reasons of computing speed when fitting models. we re-cast this equation as a matrix multiplication in Fourier bins of width Ak=0.01h ?: We determine the convolution matrix M;; by evaluating the full sum of equation 16. for α set of unit vectors. [for bin i: Secondlv. the estimates of the power in different Fourier modes & become correlated.," For reasons of computing speed when fitting models, we re-cast this equation as a matrix multiplication in Fourier bins of width $\Delta k147= 0.01 h$ $^{-1}$: We determine the convolution matrix $M_{ij}$ by evaluating the full sum of equation \ref{eqpkconv} for a set of unit vectors, for bin $i$: Secondly, the estimates of the power in different Fourier modes $\vec{k}$ become correlated."148 Lowe average the estimates of Equation 13. into bins in Fourier space. labelling the bins by ἐς the covariance between bins 7 and j is given by (FINI. equation 2.5.2) where & ancl A’ are. pairs of Fourier modes Wing in bins / ancl j. P? is the characteristic power spectrum amplitude in bins £ and j defined below. and the functions QU) and SU) are given by FIND equations 2.2.3 and 2.2.5: In deriving Equation 20. it is assumed that the power spectrum factor 2 which appears is effectively constant over Fourier separations kok which procuce correlated estimates.," If we average the estimates of Equation \ref{eqpkest} into bins in Fourier space, labelling the bins by $i$ , the covariance between bins $i$ and $j$ is given by (FKP, equation 2.5.2) where $\vec{k}$ and $\vec{k'}$ are pairs of Fourier modes lying in bins $i$ and $j$, $P$ is the characteristic power spectrum amplitude in bins $i$ and $j$ defined below, and the functions $Q(\vec{k})$ and $S(\vec{k})$ are given by FKP equations 2.2.3 and 2.2.5: In deriving Equation \ref{eqpkcov} it is assumed that the power spectrum factor $P$ which appears is effectively constant over Fourier separations $\vec{k}-\vec{k'}$ which produce correlated estimates."149 For our datasets the Fourier. transform of the selection function. Woo. is sullicicntly compact around &=0 that this is à valid approximation.," For our datasets the Fourier transform of the selection function, $\tilde{W}(\vec{k})$, is sufficiently compact around $k=0$ that this is a valid approximation."150 We evaluated Equation 20 for each survey region by a direct. summation over Fouricr modes in the EIE erid., We evaluated Equation \ref{eqpkcov} for each survey region by a direct summation over Fourier modes in the FFT grid.151 Equation 20. depends on the uncderlving power spectrum. which is initially unknown. in le same manner as equation I4..," Equation \ref{eqpkcov} depends on the underlying power spectrum, which is initially unknown, in the same manner as equation \ref{eqpkngpcorr}."152 We again used an iterative pproach whereby we initially usec a default model power spectrum to make this calculation. and then replaced it using 1e fitted parameters.," We again used an iterative approach whereby we initially used a default model power spectrum to make this calculation, and then replaced it using the fitted parameters."153 In order to facilitate comparison with other studies it is useful to take the limit of these equations in the case where vw selection [function is constant. W(r)=L1/£N..," In order to facilitate comparison with other studies it is useful to take the limit of these equations in the case where the selection function is constant, $W(\vec{x}) = 1/N_c$."154 The »ower spectrum estimator of Equation 13. becomes and the covariance matrix in Equation 90 reduces to a diagonal matrix with entries: where Np is the number of Fourier modes bing in bin ἐν, The power spectrum estimator of Equation \ref{eqpkest} becomes and the covariance matrix in Equation \ref{eqpkcov} reduces to a diagonal matrix with entries: where $N_{\vec{k}}$ is the number of Fourier modes lying in bin $i$.155 Equation 240 clarifies that there are two sources of error in an estimate of the power spectrum: cosmic variance ancl shot noise. represented by the two terms inside the bracket.," Equation \ref{eqpksimperr} clarifies that there are two sources of error in an estimate of the power spectrum: cosmic variance and shot noise, represented by the two terms inside the bracket."156 In this Section we calculate the distortion in the galaxy power spectrum. created. by the types of redshift) bLuncer described in Section 2.7.., In this Section we calculate the distortion in the galaxy power spectrum created by the types of redshift blunder described in Section \ref{secbadz}.157" In order to eain intuition we beein with a simple model using the ~Hat-sky approximation"" which supposes that galaxies are scattered in position along a single axis of the cuboid (which. we take as the τανκ).", In order to gain intuition we begin with a simple model using the “flat-sky approximation” which supposes that galaxies are scattered in position along a single axis of the cuboid (which we take as the $x$ -axis).158 Defining 9(.F) as the galaxy overdensity in the cell at position Ko—Grog.z). the galaxy number distribution is given by where WOOF) is the selection. function. normalized as above.," Defining $\delta(\vec{x})$ as the galaxy overdensity in the cell at position $\vec{x} = (x,y,z)$, the galaxy number distribution is given by where $W(\vec{x})$ is the selection function normalized as above."159 We now suppose that a fraction f of galaxies are scattered in position along the w-axis such that their final J-position is drawn from a probability cüstribution. (Cr) (Le. as described by Equation 7for our data).," We now suppose that a fraction $f$ of galaxies are scattered in position along the $x$ -axis such that their final $x$ -position is drawn from a probability distribution $V(x)$ (i.e., as described by Equation \ref{eqnzfit} for our data)."160 This process creates a scattered galaxy number cistribution given by where the normalization constant Ny can be caleulated by requiring that SOF)= f{N.Equations 25 and 26 have Fourier transforms where we have defined the convolved density Ποιά, This process creates a scattered galaxy number distribution given by where the normalization constant $N_1$ can be calculated by requiring that $\sum_{\vec{x}} S(\vec{x}) = f N$ .Equations \ref{eqnx} and \ref{eqsx} have Fourier transforms where we have defined the convolved density field161Tn this paper we compare (approximate) analytical expressions for the expansion of a PWN in a supernova relnnant with lycrodvuamical παος carried out with the Versatile Advection Code (VAC).,In this paper we compare (approximate) analytical expressions for the expansion of a PWN in a supernova remnant with hydrodynamical simulations carried out with the Versatile Advection Code (VAC).162 We confirm earlier analytical results (Revuolds Chevalier. 1981: Chevalier Frausson. 1992) which state that the PWN is expanding supersonicallv when it is moving throug1 the reely expanding ejecta of the SNR.," We confirm earlier analytical results (Reynolds Chevalier, 1984; Chevalier Fransson, 1992) which state that the PWN is expanding supersonically when it is moving through the freely expanding ejecta of the SNR."163 Due to deceleration of the expanding SNR ejecta by the interstellar iuediuu (ISMD. a reverse shock propagates back to the ceuter of he SNR (e.g. Melsoe. 197E Cioffi et al.," Due to deceleration of the expanding SNR ejecta by the interstellar medium (ISM), a reverse shock propagates back to the center of the SNR (e.g. McKee, 1974 Cioffi et al."164 1988))., 1988)).165 Due to the oyesence of reverberations of the reverse shock. in the SNR the expansion of the PWN eoes through am uuseady yhase when this reverse shock hits the οσο of the PNW.," Due to the presence of reverberations of the reverse shock in the SNR, the expansion of the PWN goes through an unsteady phase when this reverse shock hits the edge of the PNW."166 After these reverberations lave decaved. the expansion of he PWN through the ejecta of the SNR progenior star continues subsonicaIv with the PWN aliiost in pressure equilibrium with the interior of the SNR.," After these reverberations have decayed, the expansion of the PWN through the ejecta of the SNR progenitor star continues subsonically with the PWN almost in pressure equilibrium with the interior of the SNR."167 This paper is organised as follows., This paper is organised as follows.168 Iu seclous 2 and 3 we discuss t1ο aforemientioued two stages of the PWN/SNR system., In sections 2 and 3 we discuss the aforementioned two stages of the PWN/SNR system.169 lu section 1 the hvadrodyιαπσα] s«umnuulatious will be prescuted and compared with the analytical expressions frou section 2 and 3., In section 4 the hydrodynamical simulations will be presented and compared with the analytical expressions from section 2 and 3.170 Tn the carly stage of the evolution of a PWN. the SNR consists mostly of the stellar ejecta expanding freely iuto he iuterstellar iuediu.," In the early stage of the evolution of a PWN, the SNR consists mostly of the stellar ejecta expanding freely into the interstellar medium."171 The PWN expands iuto these ejecta., The PWN expands into these ejecta.172 The sound velocity in the interior of the SNR is uuch smaller than the expansion velocity of the PWN., The sound velocity in the interior of the SNR is much smaller than the expansion velocity of the PWN.173 The supersonic expansion of the PAWN results in a shock wropagating iuto the ejecta (sce figure 1)., The supersonic expansion of the PWN results in a shock propagating into the ejecta (see figure 1).174 Au analytical equation for the radius of this shock cau ve derived for a constaut spindown Iuuinositv., An analytical equation for the radius of this shock can be derived for a constant spindown luminosity.175 Usine this solution. the assuuption of supersouic expansion will be checkedp," Using this solution, the assumption of supersonic expansion will be checked."176osteriori For simplicity we assune that the ejecta have a unitorm density. and a linear velocity profile as a function of radius. pati (Ge). with Ry=Vor the radius of the trout of the ejecta.," For simplicity we assume that the ejecta have a uniform density, = , and a linear velocity profile as a function of radius, (r)= = ( ) , with $R_{\rm ej}=V_0t$ the radius of the front of the ejecta."177 The value of Vy is deteriunued by the requirement that the kinetic energy of the ejecta equal the total mechanical cherey £y of the SNR: Ey = ο =Male , The value of $V_0$ is determined by the requirement that the kinetic energy of the ejecta equal the total mechanical energy $E_{0}$ of the SNR: 	E_0 = ( r^2 r =.178This vields:I, This yields:.179E We asstune that the stellar ejecta swept up by the strong shock which bounds the PWN collect in a thin shell. and that this material nioves with the post-slock velocity.," We assume that the stellar ejecta swept up by the strong shock which bounds the PWN collect in a thin shell, and that this material moves with the post-shock velocity."180" Neglecting the contribution of the thermal energy we cau write the total (ποιο) cuerey of this shell. £44. as: Eautf)- Ma) IRE where AL) y, is the ejCa Düass swept up by tje pulsar wind nebula."," Neglecting the contribution of the thermal energy we can write the total (kinetic) energy of this shell, $E_{\rm shell}$, as: }(t)= (t) (t) + )^2, where (t) )^3 is the ejecta mass swept up by the pulsar wind nebula."181 Iu deriving the post-shock velocity. we assuned that the ejecta have as an ideal norelativistic gas with adiabatic licat vatlo τα=5/3 aid used the IIugoniot inip conditions for a strong shock.," In deriving the post-shock velocity, we assumed that the ejecta behave as an ideal non-relativistic gas with adiabatic heat ratio $\gamma_{\rm ej} = 5/3$ and used the Rankine-Hugoniot jump conditions for a strong shock."182 The interior of the PWN is «onmüinated bv thermal energv., The interior of the PWN is dominated by thermal energy.183 The sound speed in a reaistic PWN is close to the speed o: licht e. while the expanzion velocity is mach less thane.," The sound speed in a realistic PWN is close to the speed of light $c$, while the expansion velocity is much less than $c$."184 Perturbationsiu the pressure will be sinootled out rapidly.on a sound crossing tiue ty~Rivenfe. nanch less than t1c expansion fine scale Tos2Dufpw ," Perturbationsin the pressure will be smoothed out rapidly,on a sound crossing time $t_{\rm s} \sim R_{\rm pwn}/c$, much less than the expansion time scale $t_{\rm exp} \sim R_{\rm pwn}/\dot{R}_{\rm pwn}$."185Therefore. we can assume a nearly ποτ pressurefi P in the PWN.," Therefore, we can assume a nearly uniform pressure $P_{\rm pwn}$ in the PWN."186 The internal energv ο the PWN then equals 5p:, The internal energy of the PWN then equals ^3.187: Ποιο we take tpn1/3 because the pulsu wind uebula material is relativistically hot., Here we take $\gamma_{\rm pwn} =4/3$ because the pulsar wind nebula material is relativistically hot.188" The pressure of the interior of the PWN iust roughly equal the pressure in the shocked ejecta just dowustream of the outer shock ofNS pulsu wind nebula at Z: ptt) (Patt κ}, ", The pressure of the interior of the PWN must roughly equal the pressure in the shocked ejecta just downstream of the outer shock ofthe pulsar wind nebula at $R_{\rm pwn}$ : (t) - )^2 .189Combining these relations viclds:, Combining these relations yields: =190Clusters of galaxies contain a conspicuous amount of gas classified as intracluster medium (ICM).,Clusters of galaxies contain a conspicuous amount of gas classified as intracluster medium (ICM).191 The dominant baryonic component of the ICM is represented by the ray emitting thermal plasma. amounting to about of the total gravitational mass of the cluster (?)..," The dominant baryonic component of the ICM is represented by the X-ray emitting thermal plasma, amounting to about of the total gravitational mass of the cluster \citep{2005xrrc.procE8.02F}."192 Additional nonthermal components of the ICM. not obviously associated with individual radio galaxies. have been detected in several clusters.," Additional nonthermal components of the ICM, not obviously associated with individual radio galaxies, have been detected in several clusters."193 ? classify them ashalos: centrally located. Mpe-scale. low surface brightness. steep-spectrum radio sources with a regular morphology.relics: elongated. steep-spectrum radio sources often found at the periphery of clusters. andmini-halos: diffuse. moderately large (~S500 kpe) radio sources surrounding powerful central dominant (cD) radio galaxies in cooling core clusters.," \citet{fergiov}194 classify them as: centrally located, Mpc-scale, low surface brightness, steep-spectrum radio sources with a regular morphology,: elongated, steep-spectrum radio sources often found at the periphery of clusters, and: diffuse, moderately large $\sim500$ kpc) radio sources surrounding powerful central dominant (cD) radio galaxies in cooling core clusters."195 The existence of these extended nonthermal features in galaxy clusters prove there are large-scale magnetic fields in them., The existence of these extended nonthermal features in galaxy clusters prove there are large-scale magnetic fields in them.196 Their study ts therefore the key to any comprehensive description of the ICM., Their study is therefore the key to any comprehensive description of the ICM.197 Because they are the result of the synchrotron process. halos and relics are generally intrinsically polarized. assuming ordered nagnetic fields.," Because they are the result of the synchrotron process, halos and relics are generally intrinsically polarized, assuming ordered magnetic fields."198 While radio relics are indeed highly polarized (20-40%)). radio halos generally do not show any significant. polarization (?)..," While radio relics are indeed highly polarized ), radio halos generally do not show any significant polarization \citep{fergiov}."199 This is thought to come from internal depolarization along the line of sight and/or beam depolarization. given the low resolution needed for detecting these sources.," This is thought to come from internal depolarization along the line of sight and/or beam depolarization, given the low resolution needed for detecting these sources."200 The study of the polarization associated with halos and relics ts a powerful diagnostic tool that can be used to constrain the strength and geometry of magnetic fields in clusters., The study of the polarization associated with halos and relics is a powerful diagnostic tool that can be used to constrain the strength and geometry of magnetic fields in clusters.201 Important complementary information on cluster magnetic fields along the line of sight can also be derived through the study of the rotation measure distributions observed towards background and cluster radio sources. since their polarized emission experiences Faraday rotation while crossing the magnetized ICM.," Important complementary information on cluster magnetic fields along the line of sight can also be derived through the study of the rotation measure distributions observed towards background and cluster radio sources, since their polarized emission experiences Faraday rotation while crossing the magnetized ICM."202 These studies have determined values for cluster magnetic fields of a few µα (forareviewsee?.andreferences therein)..," These studies have determined values for cluster magnetic fields of a few $\mu$ G \citep[for a review203see ][and references therein]{carilli}."204 In addition. stronger magnetic fields are detected in the innermost regions of cooling core clusters. where RM values of several hundreds of rad m (?) up to a few thousand rad m7 (?) have been An important technique recently developed to analyze and interpret polarization data is RM-synthesis (?)..," In addition, stronger magnetic fields are detected in the innermost regions of cooling core clusters, where RM values of several hundreds of rad $^{-2}$ \citep{2001ApJ...547L.111C} up to a few thousand rad $^{-2}$ \citep{vogt} have been An important technique recently developed to analyze and interpret polarization data is RM-synthesis \citep{br2005}."205 By separating the polarized emission as a function of Faraday depth. this technique can give important information on the 3-dimensional structure of clusters of galaxies.," By separating the polarized emission as a function of Faraday depth, this technique can give important information on the 3-dimensional structure of clusters of galaxies."206 Such investigations become progressively more difficult to carry out at low frequencies. where instrumental (1.06. beam and bandwidth depolarization) and astrophysical effects (depolarization occurring inside and outside the radio source) may reduce the observed polarized emission.," Such investigations become progressively more difficult to carry out at low frequencies, where instrumental (i.e. beam and bandwidth depolarization) and astrophysical effects (depolarization occurring inside and outside the radio source) may reduce the observed polarized emission."207 is a nearby (z=0.0806.?) rich cluster. which has been studied at several wavelengths.," is a nearby \citep[z=0.0806,][]{struble} rich cluster, which has been studied at several wavelengths."208ROSAT X-ray observations indicate that is à non-cooling core cluster that has recently undergone a merger (?????)..," X-ray observations indicate that is a non-cooling core cluster that has recently undergone a merger \citep{burns1995,1998ApJ...492...57D,fer,miller,sakelliou}."209 Optical studies of reveal the presence of kinematical substructures in the form of several associated groups (?).., Optical studies of reveal the presence of kinematical substructures in the form of several associated groups \citep{2003ApJS..149...53Y}.210 This result. together with the high ratio of velocity dispersion to X-ray temperature (6.3keV:?).. indicates a non-relaxed system.," This result, together with the high ratio of velocity dispersion to X-ray temperature \citep[6.3211keV;][]{horner}, indicates a non-relaxed system."212 At radio wavelengths. hosts a diffuse radio halo. a relic source. and seven extended head-tail radio galaxies.," At radio wavelengths, hosts a diffuse radio halo, a relic source, and seven extended head-tail radio galaxies."213 On the basis of their morphological properties at low frequency. they are named Goldfish. Double. Original TRG. Sidekick. Bean. Beaver. and Embryo (?)..," On the basis of their morphological properties at low frequency, they are named Goldfish, Double, Original TRG, Sidekick, Bean, Beaver, and Embryo \citep{har}."214 The former 4 radio galaxies He near the cluster center. while the others are located at a large projected distance: the Embryo and the Beaver lie at 1.5 Mpe: the Bean at ~ 3.5 Mpe.," The former 4 radio galaxies lie near the cluster center, while the others are located at a large projected distance: the Embryo and the Beaver lie at 1.5 Mpc; the Bean at $\sim$ 3.5 Mpc."215 Most of these radio galaxies have a narrow angle tail (ΝΑΤ.2) morphology. which suggests a strong interaction between the plasma ejected by the parent galaxy and the ICM.," Most of these radio galaxies have a narrow angle tail \citep[NAT,216][]{1976ApJ...203L.107R} morphology, which suggests a strong interaction between the plasma ejected by the parent galaxy and the ICM."217 Moreover. their tails show a random orientation. with respect to the cluster center. suggesting that they are in random orbits inside the cluster (?)..," Moreover, their tails show a random orientation with respect to the cluster center, suggesting that they are in random orbits inside the cluster \citep{fer}."218 Sensitive Westerbork. Synthesis Radio Telescope (WSRT), Sensitive Westerbork Synthesis Radio Telescope (WSRT)219Cepheicl variables constitute one of the most. important primary distance calibrators.,Cepheid variables constitute one of the most important primary distance calibrators.220 Indeed. they obey a Period-Luminosity (PL) relation: from which the absolute magnitude. £A can. be determined. just. from the measurement of the period. provided that the slope ὁ and the zero-point p are known.," Indeed, they obey a Period-Luminosity (PL) relation: from which the absolute magnitude $\langle M_V \rangle$ can be determined just from the measurement of the period, provided that the slope $\delta$ and the zero-point $\rho$ are known."221 The slope of the PL relation seems very well established from grounc-basecl observations in the Large. Magellanic Cloud (LMCO because the population incompleteness bias pointed out for more distant. galaxies (Lanoix et al., The slope of the PL relation seems very well established from ground-based observations in the Large Magellanic Cloud (LMC) because the population incompleteness bias pointed out for more distant galaxies (Lanoix et al.222 1999a) seems negligible in the LMC., 1999a) seems negligible in the LMC.223 The slope of the PL relation is easier to obtain from an external galaxy because. all Cepheids being at the same distance. the slope can be determined. by using apparent. magnitudes. instead: of absolute magnitudes.," The slope of the PL relation is easier to obtain from an external galaxy because, all Cepheids being at the same distance, the slope can be determined by using apparent magnitudes instead of absolute magnitudes."224 A reasonable value for the photometric V-band is 0=2.77£0.08 (see for instance Cieren οἱ al., A reasonable value for the photometric V-band is $\delta = -2.77 \pm 0.08$ (see for instance Gieren et al.225 1905. Tanvir 1997. Caldwell Laney 1991. Alacore Freedman: 1991).," 1998, Tanvir 1997, Caldwell Laney 1991, Madore Freedman 1991)."226 In the present study we will adopt this value and will discuss further the effect of a change of it., In the present study we will adopt this value and will discuss further the effect of a change of it.227 The establishment of the zero-point still remains a major goal., The establishment of the zero-point still remains a major goal.228 “Today. thanks to the HIPPABCOS satellite the trigonometric parallaxes of galactic Cepheids are accessible. allowing a new determination of p.," Today, thanks to the HIPPARCOS satellite, the trigonometric parallaxes of galactic Cepheids are accessible, allowing a new determination of $\rho$."229 After. the first release of LILPPARCOS data. a calibration of the Cepheid PL relation was published by Feast Catehpole (1997. hereafter. FC).," After the first release of HIPPARCOS data, a calibration of the Cepheid PL relation was published by Feast Catchpole (1997, hereafter FC)."230 This work gave a distance for the LMC galaxy larger than the one generally assumed., This work gave a distance for the LMC galaxy larger than the one generally assumed.231 Lowever. some papers (Macdore Freedman 1998. Sandage Tammann 1998) argued that this calibration is only brighter than previous ones at the level of <0.1 mag.," However, some papers (Madore Freedman 1998, Sandage Tammann 1998) argued that this calibration is only brighter than previous ones at the level of $\le 0.1$ mag."232 An independent study of the calibration of the PL relation, An independent study of the calibration of the PL relation233" z0.l ?)) ~ (??). (~60%:2?) (~27-42%,??).."," $\lesssim$ \citealt{Burgasser2007b}) $\sim$ \citep{Basri2006, Joergens2008} \citep[$\sim$60\%;][]{Duquennoy1991} \citep[$\sim$27--42\%;][]{Fischer1992,234 Reid1997}."235 ~4-5 ~30 (??).. ~1," $\sim$ $\sim$ \citep{Duquennoy1991, Fischer1992}."236" (e.g..22).. ? 10/7? ~300 10!"" the same formation process(es) may not be responsible for the two populations."," $\sim$ \citep[e.g.,][]{Lepine2007a, Dhital2010}, \citet{Close2003} $10^{42.5}$ $\sim$ $10^{40}$ the same formation process(es) may not be responsible for the two populations."237 It is now generally believed that most stars form in multiple systems via fragmentation of the protostellar cloud. with single stars being the result of decay of unstable multiples (e.g..?)..," It is now generally believed that most stars form in multiple systems via fragmentation of the protostellar cloud, with single stars being the result of decay of unstable multiples \citep[e.g.,][]{Kroupa1995a}."238 The most favored process is gravoturbulence where the fragmentation is the result of a combination of turbulent gas flows and gravity., The most favored process is gravoturbulence where the fragmentation is the result of a combination of turbulent gas flows and gravity.239 Hydrodynamical simulations have shown that when turbulent gas flows in protostellar clouds collide. they form clumps that are gravitationally unstable and. hence. collapse forming multiple stellar embryos (e.g..222? )..," Hydrodynamical simulations have shown that when turbulent gas flows in protostellar clouds collide, they form clumps that are gravitationally unstable and, hence, collapse forming multiple stellar embryos \citep[e.g.,][]{Caselli2002, Goodwin2004a, Goodwin2004b, Bate2009}."240 Within a few freefall times. most of these embryos are ejected due to mutual dynamical interactions. preferentially the ones with lower masses.," Within a few freefall times, most of these embryos are ejected due to mutual dynamical interactions, preferentially the ones with lower masses."241 To then explain the observed distributions of VLM binaries separations. two explanations have been proffered.," To then explain the observed distributions of VLM binaries separations, two explanations have been proffered."242" The first so-called “ejection hypothesis"" suggests that most VLM binaries. unlike the more-massive stellar systems. are the result of the ejected embryos (?).."," The first so-called “ejection hypothesis” suggests that most VLM binaries, unlike the more-massive stellar systems, are the result of the ejected embryos \citep{Reipurth2001}."243 The wider systems get disrupted. explaining the overall rarity of VLM and BD binaries.," The wider systems get disrupted, explaining the overall rarity of VLM and BD binaries."244 The second is preferential accretion within the first 0.1 Myr (~1 freefall time). making VLM systems tighter and more equal-mass.," The second is preferential accretion within the first 0.1 Myr $\sim$ 1 freefall time), making VLM systems tighter and more equal-mass."245 As a result. even VLM distributions that initially may have looked similar to that of higher mass stars are transformed and look like the observed VLM distributions (?).," As a result, even VLM distributions that initially may have looked similar to that of higher mass stars are transformed and look like the observed VLM distributions \citep{Bate2009}."246 However. neither hypothesis explains why ~10% of observed VLM binaries are wider than 100 AU.," However, neither hypothesis explains why $\sim$ of observed VLM binaries are wider than 100 AU."247 Two other theories on VLM/BD formation. disk fragmentation (e.g..2?) and photoablation (2).. require massive stars to trigger the process and cannot explain the existence of VLM binaries in the field.," Two other theories on VLM/BD formation, disk fragmentation \citep[e.g.,][]{Watkins1998a, Watkins1998b} and photoablation \citep{Whitworth2004}, require massive stars to trigger the process and cannot explain the existence of VLM binaries in the field."248 To resolve the differences between observational and numerical results and to distinguish betweenthevarious formationscenarios. a larger sample of VLM binaries—very wide systems that are most susceptible to dynamical effects—is needed.," To resolve the differences between observational and numerical results and to distinguish betweenthevarious formationscenarios, a larger sample of VLM binaries---especiallyvery wide systems that are most susceptible to dynamical effects—is needed."249the SED fitting by Iartaltepeetal.(901011: 110 of these pass our ACN aud uncertainty criteria.,the SED fitting by \citet{Kartal10}; 410 of these pass our AGN and uncertainty criteria.250 However. the 160 jan detections for these cones are of low significance: 6/110 ealaxies )) ave below 5 o where the σ value iucludes the confusion noise of 10 niJw for the survey (Fraveretal.2009).," However, the 160 $\micron$ detections for these sources are of low significance: 236/410 galaxies ) are below 5 $\sigma$ where the $\sigma$ value includes the confusion noise of 10 mJy for the survey \citep{Frayer09}."251. Although a consistent lis obtained if a stacked 160 you flux is used for SED fitting. iucludiug these fluxes iu the individual fits results in values typically high by 0.2 dex Csartaltepe 2010).," Although a consistent is obtained if a stacked 160 $\micron$ flux is used for SED fitting, including these fluxes in the individual fits results in values typically high by 0.2 dex \citep{Kartal10}."252. This problem is consistent with ους&Turner (1998).. who show that detections below |Ὁσ are biased towardsbrighter fluxes than their true values: see their =2: this effect is conunonly kuown as the Eddington bias.," This problem is consistent with \citet{Hogg98}, who show that detections below $4-5 \sigma$ are biased towards brighter fluxes than their true values; see their Figure 2; this effect is commonly known as the Eddington bias."253 FigureWe therefore exclude the 160 jnu-detected objects., We therefore exclude the 160 $\micron$ -detected objects.254 After applying the cuts discussed at the ]egiuniue of this section. we have 751 sources left.," After applying the cuts discussed at the beginning of this section, we have 751 sources left."255 These sources have redshifts ranging from +=0.07 to 1.51 with à mean and median redshift of 0.52 and 0.13.," These sources have redshifts ranging from $z =2560.07$ to $1.81$ with a mean and median redshift of 0.52 and 0.43."257" The huuinosity of this snbsaurple ranges fon oof 10°? to 1042?;E, aud the mean aud median js ave 10153 aud Lott?L2 vespectively."," The luminosity of this subsample ranges from of $10^{9.5}$ to $10^{12.5}$ and the mean and median s are $10^{11.1}$ and $10^{11.2}$, respectively."258 The comparison with cestimated frou the 21 juu fluxes alone indicates au average scatter of 0.25 dex relative to the assigned yvalues., The comparison with estimated from the 24 $\micron$ fluxes alone indicates an average scatter of $0.25$ dex relative to the assigned values.259 Some fraction of this scatter must arise in the assenienut of bby Iuwtaltepeetal.(2010): the median huminositv uncertaintv within their workis 0.23dex., Some fraction of this scatter must arise in the assignment of by \citet{Kartal10}; the median luminosity uncertainty within their work is 0.23 dex.260 That is. the 21 μπα ο] calculation agrees with their aulti-waveleneth fits virtually within the interual scatter of these fits.," That is, the 24 $\micron$ -only calculation agrees with their multi-wavelength fits virtually within the internal scatter of these fits."261 We quantify the contribution of uncertainties intrinsic to the new indicator in this test by couducting a Monte Carlo experiment to determine the scatter that must arise from our estimation of Ikartaltepeetal.(2010). Inuinosities.," We quantify the contribution of uncertainties intrinsic to the new indicator in this test by conducting a Monte Carlo experiment to determine the scatter that must arise from our estimation of \citet{Kartal10}262 luminosities."263 We simulate a sample (η 105) with a scatter of 0.23 dex and reaucasure the values. introducing measurement errors in the process. which shows that an uncertaiuty of ~O.1 dex associated with the new indicator will broaden the intrinsic scatter of the Nartaltepeetal.(2010) siuuple to the 0.25 dex measured.," We simulate a sample $n = 10^4$ ) with a scatter of 0.23 dex and re-measure the values, introducing measurement errors in the process, which shows that an uncertainty of $\sim$ 0.1 dex associated with the new indicator will broaden the intrinsic scatter of the \citet{Kartal10} sample to the 0.25 dex measured."264 This result is consistent with the 0.150.13 dex scatter found in Section ?7.. labelsecinudicatoresfseimnina, This result is consistent with the $0.12-0.13$ dex scatter found in Section \ref{sec:indicator_testindiv}.265rgM ctestedthencw210)nmiidie 10HfarL...the ⇁ mancasurcincatsofscccisaimplesof. . galawaicesscelecte .Í istehatreso, We tested the new 24 $\micron$ indicator on far-IR measurements of seven samples of galaxies selected withvarious techniques.266l riesdeirήtho mid-IR depth! onπας Dbecouies ep dat 500402: (2)200gula ciesin N sclectedatlüü- 500402: ()751galaciesinILDECOS MOSsclectt MNMMis brightyalacies fromBRicectal.(2010): Fiee2 lan Kartaltedy|«illiPE;saineimsm brightlenscdgalacies fromRujopakariveial:(5)i2012):: (G)sfac οList / dep ae«n COnSCGI ns μι] ond ," These include (1) 91 galaxies in ECDFSselected at $250-500$ $\micron$; (2) 200 galaxies in HDFN selected at $100-500$ $\micron$; (3) 751 galaxies in COSMOS selected at 70 $\micron$ \citep{Kartal10}; (4) 16 far-IR-bright galaxies from \citet{Rex10}; (5) five 24 $\micron$ -bright lensed galaxies from \citet{Rujopakarn12}; (6) stacked photometry of 35,000 galaxies in COSMOS selected at 24 $\micron$ from \citep{Lee10}; (7) stacked photometry of 3172 galaxies in the ECDFS selected at 3.6 and 4.5 $\micron$ ."267All of these tests indicate that the new indicator has clinunated the svstematic overestimation of to musinatchine of SED templates. which is caused by citethe nüsassiguiieut of the SEDs of compact local U/LIRGs to the extended U/LIRGs at high + at the same LUIIB).," All of these tests indicate that the new indicator has eliminated the systematic overestimation of due to mismatching of SED templates, which is caused by the misassignment of the SEDs of compact local U/LIRGs to the extended U/LIRGs at high $z$ at the same ."268. For star-forming galaxies at 0.0<2.8. the new imdiceator vields cestimates consistent withHerschel far-IR ucasuremeuts with au average aerecment of 0.021.03 dex aud a lc scatter of 0.150.13 dex.," For star-forming galaxies at $0.0 < z < 2.8$, the new indicator yields estimates consistent with far-IR measurements with an average agreement of $0.02-0.03$ dex and a $1-\sigma$ scatter of $0.12-0.13$ dex."269 Based on the samples in ECDFS and IIDEN. we estimate that the fraction of compact merecr-trigeered U/LIRGs bevoud the local Universe to be ~10% (more discussion in Section ??)).," Based on the samples in ECDFS and HDFN, we estimate that the fraction of compact merger-triggered U/LIRGs beyond the local Universe to be $\sim$ (more discussion in Section \ref{sec:discuss_sfmodes}) )."270 We tabulate the luminosities of the recomended ROO SED templates to describe stir-foruüug galaxies οἼνοιι their observed 21 jun fluxes and redshifts in Table 3.., We tabulate the luminosities of the recommended R09 SED templates to describe star-forming galaxies given their observed 24 $\micron$ fluxes and redshifts in Table \ref{table_fluxztemplate}.271" Even at the brght-eud of the fux rauge at hieh-: (c.e.. fo,=3.01nJy at 2=2.8. which correspouds to oof 2«Lot! £4). the appropriate ROO templates are those of local LIRGs with oof no more than «LottE..."," Even at the bright-end of the flux range at $z$ (e.g., $f_{24} = 3.0$ mJy at $z = 2.8$, which corresponds to of $2 \times 10^{14}$ ), the appropriate R09 templates are those of local LIRGs with of no more than $5 \times 10^{11}$."272 In fact. it is evideut from the table that most IR-huuinous star-forming galaxies at O<2<2.8 exhibit spectral characteristics of local ealaxies with iin the range of 10103410H Finally. SFRs can be determined by making use of the relationship between aand the rest-frameu).. and subsequenutlv the rest-frame aud SER. originally given bv Rickeetal.(2009).," In fact, it is evident from the table that most IR-luminous star-forming galaxies at $0 < z < 2.8$ exhibit spectral characteristics of local galaxies with in the range of $10^{10} - 3 \times 10^{11}$ Finally, SFRs can be determined by making use of the relationship between and the rest-frame, and subsequently the rest-frame and SFR, originally given by \citet{Rieke09}."273. The introduction of the stretching factor. which effectively re-normalizes the SED templates. requires a modification of the relationship between aandμι).," The introduction of the stretching factor, which effectively re-normalizes the SED templates, requires a modification of the relationship between and."274".. The original fit as given in equation AG of Riekeet1al.(2009). is The imodi&Bed relationship is obtained bw re-fitting equation 6 with the stretching factor. 5;. multiplving both aud ffor cachL(21 template ἐν,"," The original fit as given in equation A6 of \citet{Rieke09} is The modified relationship is obtained by re-fitting equation \ref{eq6} with the stretching factor, $S_i$, multiplying both and for each template $i$."275" The re-fitted relation allows tto be calculated by substituting L(TIB), (from equation 5)) iu the followiug.", The re-fitted relation allows to be calculated by substituting $L({\rm TIR})_{{\rm new}}$ (from equation \ref{eq5}) ) in the following.276 To determine the SFR from the rest-framejnu).. the calibration given by Rickeetal.(2009) remains valid.," To determine the SFR from the rest-frame, the calibration given by \citet{Rieke09} remains valid."277 However. that calibration has a term that corrects for a decrease in cem above for=o," However, that calibration has a term that corrects for a decrease in ratio above $= 10^{11}$."278 Since the correction is motivated bv an increase of optical depth at high reveuts παnnm from SHEescaping DESDUC op sigimfcant dit ensuno the geonetry the galaxy.," Since the correction is motivated by an increase of the optical depth at high that prevents the mid-IR emission from escaping, the threshold at which optical depth becomes significant depends directly on the geometry of the galaxy."279 Iu Ht the extended. ofstructure of. the li ilii]afDANT PAfida lower Hie optic bs for a given aand the luminosity threshold where the optical depthVAτοπ] apply has tobe scaled wpby a stretching factor as well.," In the same way that the extended structure of the galaxy beyond the local Universe affects the IR-emitting environment, the optical depth will consequently be lower for a given and the luminosity threshold where the optical depthshould apply has tobe scaled up by a stretching factor as well."280 The5; corresponding to the original threshold is 12.6. (referring to Table 1)). vielding an IR huuinosity +weshold of 1.3«10127 £2... which is equivalent to oof 1.6«1044 EL...," The $S_i$ corresponding to the original threshold is $\times$ (referring to Table \ref{table_si}) ), yielding an IR luminosity threshold of $1.3 \times 28110^{12}$ , which is equivalent to of $1.6 \times 10^{11}$ ."282 Therefore the relationship between SFR and ((from Equation 7)) is giveu by, Therefore the relationship between SFR and (from Equation \ref{eq7}) ) is given by283Galaxy redshift surveys show that ealaxics are not clistrioited: uniformly.,Galaxy redshift surveys show that galaxies are not distributed uniformly.284 Instead. they form. à. complicated HelWweok around large regions that are almost empty. so-caller voids.," Instead, they form a complicated network around large regions that are almost empty, so-called voids."285 One of the most [famous voids. in the region of 30011es. has a diameter of ~505. Mpc. and was found by ]xirsciner et al Subsequent larger redshift surveys [oun more anc more voids (for example Geller Luehra 1989. da Costa οἱ al 1994. Shechtman et al 1996. Einasto et al 19t7. Plionis Basilikos 2002).," One of the most famous voids, in the region of Boöttes, has a diameter of $\sim 50h^{-1}$ Mpc, and was found by Kirschner et al Subsequent larger redshift surveys found more and more voids (for example Geller Huchra 1989, da Costa et al 1994, Shechtman et al 1996, Einasto et al 1997, Plionis Basilikos 2002)."286 These surveys allowed stuclies of the properties of voids and of void. galaxies (Einasto οἱ al 1994. Lindner οἱ al 1995 ancl 1996. ELAct et al 19t97. Mülller et al 2000). but only recently have galaxy surveys become large enough to vield sullicient sample sizes for svstematie studies (Llovle Vogeley 2002. 2004: Rojas et al 2003: Croton ct al 2004).," These surveys allowed studies of the properties of voids and of void galaxies (Einasto et al 1994, Lindner et al 1995 and 1996, El–Ad et al 1997, Mülller et al 2000), but only recently have galaxy surveys become large enough to yield sufficient sample sizes for systematic studies (Hoyle Vogeley 2002, 2004; Rojas et al 2003; Croton et al 2004)."287 L‘or similar reasons. voids in cosmological Nobody simulations have also been less wellstudied.," For similar reasons, voids in cosmological N–body simulations have also been less well–studied."288" Lark simulations of Cold Dark Matter (CDM) universes showed that large empty regions were generic (Icke 1984. Davis et al 1985). and Larger more recent simulations (e.g.. Jenkins et al 1998) have provided a clearer picture of the ""void hierarchy? (Van de Weveacrt Van lxampen 1993. Sheth Van ce Weveacrt 2004)."," Early simulations of Cold Dark Matter (CDM) universes showed that large empty regions were generic (Icke 1984, Davis et al 1985), and larger more recent simulations (e.g., Jenkins et al 1998) have provided a clearer picture of the `void hierarchy' (Van de Weygaert Van Kampen 1993, Sheth Van de Weygaert 2004)."289 Detailed studies of the properties of voids in the dark matter istribution are now becoming increasinglv common (Little Meinberg 1994. Gardner 2001. Schmidt et al 2001. Gottlóbber et al 2003. Patiri et al 2004).," Detailed studies of the properties of voids in the dark matter distribution are now becoming increasingly common (Little Weinberg 1994, Gardner 2001, Schmidt et al 2001, Gottlöbber et al 2003, Patiri et al 2004)."290 oebles (200) noted that the properties of CDM. voids and of the galaxies inside them: formed. a strong test. for CDA., Peebles (2001) noted that the properties of CDM voids and of the galaxies inside them formed a strong test for CDM.291 Subsequently. Mathis White (2002) and Benson et al (2003) investigated properties of voids in semianalytical models where mock galaxies are placed in darkmatter only simulations following physically motivated recipes.," Subsequently, Mathis White (2002) and Benson et al (2003) investigated properties of voids in semi–analytical models where mock galaxies are placed in dark–matter only simulations following physically motivated recipes."292 One of the problems with voids and with studies of voids is that there is little agreement on how to define a void in the galaxy istribution., One of the problems with voids and with studies of voids is that there is little agreement on how to define a void in the galaxy distribution.293 Are voids regions which are completely devoic of galaxies?, Are voids regions which are completely devoid of galaxies?294 Or can there be galaxies inside a void?, Or can there be galaxies inside a void?295 LW ves. how do void galaxies differ from their cousins that populate denser environments?," If yes, how do void galaxies differ from their cousins that populate denser environments?"296 And what is the spatial distribution o [void galaxies within voids?, And what is the spatial distribution of void galaxies within voids?297 Are they scattered. throughout the void interior. or do they tend to pile up around the ecgosT," Are they scattered throughout the void interior, or do they tend to pile up around the edges?"298TD 1n models of gaaxy formation within the context. of hicrarchica clustering. the galaxy distribution is determined," In models of galaxy formation within the context of hierarchical clustering, the galaxy distribution is determined"299"(Rectoretal.,1999) is adopted, the source still has unusual properties due to its unusual for BL Lacs radio morphology and host galaxy (lenticular, instead of a giant elliptical) 1973)..","\citep{rector} is adopted, the source still has unusual properties due to its unusual for BL Lacs radio morphology and host galaxy (lenticular, instead of a giant elliptical) \citep{nilson}."300 In FR I radio galaxies and BL Lacs the VHE eemission is most probably produced in the innermost part of the jet that is ejected by the supermassive black hole., In FR I radio galaxies and BL Lacs the VHE emission is most probably produced in the innermost part of the jet that is ejected by the supermassive black hole.301" For IC 310, it is not clear a priori if the eemission is powered by the same mechanism."," For IC 310, it is not clear a priori if the emission is powered by the same mechanism."302 An alternative possibility is that y-rays are produced at the bow shock formed in interaction of relativistic outflow from the fast moving galaxy with the intracluster medium., An alternative possibility is that s are produced at the bow shock formed in interaction of relativistic outflow from the fast moving galaxy with the intracluster medium.303" In this respect, the — Perseus cluster system might be similar to a much smaller scale PSR B1259-63 system, in which eemission is produced at the bow shock formed in interaction of relativistic outflow from a pulsar moving through a dense wind of a companion star (Tavani&Arons,1997)."," In this respect, the – Perseus cluster system might be similar to a much smaller scale PSR B1259-63 system, in which emission is produced at the bow shock formed in interaction of relativistic outflow from a pulsar moving through a dense wind of a companion star \citep{tavani97}."304. Angular resolution of ttelescopes is only marginally sufficient to resolve the bow shock surface in the IC 310 — Perseus cluster system., Angular resolution of telescopes is only marginally sufficient to resolve the bow shock surface in the IC 310 – Perseus cluster system.305" The angular length of the ""tail"" of the bow shock visible in the radio band is ~15’."," The angular length of the ""tail"" of the bow shock visible in the radio band is $\sim 15'$."306" The uncertainty of the source position is ~4’, which is smaller than the length of the tail."," The uncertainty of the source position is $\sim 4'$, which is smaller than the length of the tail."307" The data indicate that most of the eemission is produced in the ""head"" part of the source (see Fig. 3))."," The data indicate that most of the emission is produced in the ""head"" part of the source (see Fig. \ref{fig:ROSAT+radio}) )."308" At the same time, the angular resolution is not sufficient to distinguish between emission from the ""head"" of the bow shock and the emission from the base of the jet near the supermassive black hole, which powers the source activity."," At the same time, the angular resolution is not sufficient to distinguish between emission from the ""head"" of the bow shock and the emission from the base of the jet near the supermassive black hole, which powers the source activity."309" The crucial test, which would allow to distinguish between the two mechanisms would be the (non) detection of variability of eemission from the source."," The crucial test, which would allow to distinguish between the two mechanisms would be the (non) detection of variability of emission from the source."310" Indeed, in the BL Lac type models the eemission is expected to be variable at different timescales, down to the timescale of light-crossing of the central supermassive black hole."," Indeed, in the BL Lac type models the emission is expected to be variable at different timescales, down to the timescale of light-crossing of the central supermassive black hole."311" On the other hand, if the observed eemission is produced at the bow-shaped contract surface between the AGN outflow and the intracluster medium, the ssource has —kpc scale size."," On the other hand, if the observed emission is produced at the bow-shaped contract surface between the AGN outflow and the intracluster medium, the source has $\sim$ kpc scale size."312 This means that the eemission could not be variable on timescales much shorter than ~10? yr., This means that the emission could not be variable on timescales much shorter than $\sim 10^3$ yr.313" Variability of the ssignal from ccould not be studied withFermi, which has detected only five y-rays from the source at energies above 30 GeV. We verified that the five detected events did not come within a narrow time window, which would indicate the possibility of a strong flare from the source."," Variability of the signal from could not be studied with, which has detected only five s from the source at energies above 30 GeV. We verified that the five detected events did not come within a narrow time window, which would indicate the possibility of a strong flare from the source."314 The presence or absence of variability of the VHE eemission from ccould be readily verified in observations with ground based ttelescopes., The presence or absence of variability of the VHE emission from could be readily verified in observations with ground based telescopes.315" A previous observation of the region around Perseus cluster with Whipple telescope has resulted in an upper limit one the source flux (Perkinsetal.,2006).", A previous observation of the region around Perseus cluster with Whipple telescope has resulted in an upper limit one the source flux \citep{perkins06}.316". However, this upper limit is comparable to theFermi measurement of the source flux, so that no conclusion about the presence or absence of long-term variability of the source could be drawn from the comparison of Whipple and observations."," However, this upper limit is comparable to the measurement of the source flux, so that no conclusion about the presence or absence of long-term variability of the source could be drawn from the comparison of Whipple and observations."317" It is clear that observations of the source with the new generation of ground-based ttelescopes VERITAS or MAGIC (the source is in the northern hemisphere, not easily accessible for HESS) would give much higher signal statistic at energies above 100 GeV, so that the hypothesis of the flux variability could be easily"," It is clear that observations of the source with the new generation of ground-based telescopes VERITAS or MAGIC (the source is in the northern hemisphere, not easily accessible for HESS) would give much higher signal statistic at energies above 100 GeV, so that the hypothesis of the flux variability could be easily."318"tested"".", From Fig.319 From Fig.3 is is immediately clear that not every head-tail radio galaxy in the Perseus cluster emits in the VHE bband at the sensitivity level., \ref{fig:ROSAT+radio} is is immediately clear that not every head-tail radio galaxy in the Perseus cluster emits in the VHE band at the sensitivity level.320" The image of the cluster, shown in this figure, includes another prototypical head-tail galaxy, NGC 1265."," The image of the cluster, shown in this figure, includes another prototypical head-tail galaxy, NGC 1265."321" This source is clearly identified in the radio band, but, contrary to310,, does not show significant X-ray and VHE eemission."," This source is clearly identified in the radio band, but, contrary to, does not show significant X-ray and VHE emission."322" A comparison of the physical parameters of aand NGC 1265 (e.g. velocity through the intracluster medium, overall power of relativistic outflow etc.)"," A comparison of the physical parameters of and NGC 1265 (e.g. velocity through the intracluster medium, overall power of relativistic outflow etc.)"323 could help to clarify the conditions under which particle acceleration and VHE eemission in this type of sources occurs., could help to clarify the conditions under which particle acceleration and VHE emission in this type of sources occurs.324Sequence; Bamberg. Germany. August 11-13. 2010).,"; Bamberg, Germany, August 11-13, 2010)."325 The role of planets in PN shaping is topical in this context., The role of planets in PN shaping is topical in this context.326 In 2 we explain the PN shaping framework laid out by ?.., In \ref{sec:Soker1997} we explain the PN shaping framework laid out by \citet{Soker1997}. .327 In 23. we discuss new results in the field of PN 3.1)) and planets 3.2)). which allow us to reassess the work of ? in8 4..," In \ref{sec:newresults} we discuss new results in the field of PN \ref{ssec:PNresearch}) ) and planets \ref{ssec:exoplanetsresearch}) ), which allow us to reassess the work of \citet{Soker1997} in \ref{sec:reframingSoker1997}."328 In 7 we present some argunmenis regarding the detection of naked central stars. while in 8. we conclude.," In \ref{sec:nakedCS} we present some arguments regarding the detection of naked central stars, while in \ref{sec:Summary} we conclude."329 Soker (1997) presented a classification of 453 PN. based on the morphological svstems ol ? and ?.. with the aim of distinguishing between the role of stellar. ancl substellar companions.," Soker (1997) presented a classification of 458 PN, based on the morphological systems of \citet{Schwarz1993} and \citet{Corradi1995}, with the aim of distinguishing between the role of stellar and substellar companions."330 ? further classified elliptical PN into those with large and small departure from sphericity., \citet{Soker1997} further classified elliptical PN into those with large and small departure from sphericity.331 He divided PN morphologies into four categories and flanked each category with (he physical process most likely (o give rise to that shape using a series of observational argunments. (, He divided PN morphologies into four categories and flanked each category with the physical process most likely to give rise to that shape using a series of observational arguments. (3321) Spherical PN are formed by progenitors that did not have a companion. or did not interact with their companion.,"1) Spherical PN are formed by progenitors that did not have a companion, or did not interact with their companion."333 Some departure from sphericity (hough no axi-svimmietrvy) mav be expected if the companion separation is large. but still interacting in some wav wilh (he primary ancl the PN is formed over a span of time comparable will the orbital period. (," Some departure from sphericity (though no axi-symmetry) may be expected if the companion separation is large, but still interacting in some way with the primary and the PN is formed over a span of time comparable with the orbital period. ("3342) Bipolar PN are formed by a close stellar companion that avoided a common envelope phase. or that entered (he common envelope only late in (he evolution.,"2) Bipolar PN are formed by a close stellar companion that avoided a common envelope phase, or that entered the common envelope only late in the evolution."335 The stellar companion accretes a substantial fraction of the AGB wind. and blows two opposite jets that shape the nebula into a bipolar structure.," The stellar companion accretes a substantial fraction of the AGB wind, and blows two opposite jets that shape the nebula into a bipolar structure."336 Point svnuuetric structures are also possible due to precession of the accretion disk around the companion. (, Point symmetric structures are also possible due to precession of the accretion disk around the companion. (3373) Elliptical PN with laree departure from sphericity ave formed by stellar companions in a common envelope.,3) Elliptical PN with large departure from sphericity are formed by stellar companions in a common envelope.338 The companion in the envelope does not blow strong jets (or blows no jets al all). but the interaction with the envelope ensures high equatorial mass loss (hat leads to an expanding ring structure. (," The companion in the envelope does not blow strong jets (or blows no jets at all), but the interaction with the envelope ensures high equatorial mass loss that leads to an expanding ring structure. ("3394) Elliptical PN with small departure [rom sphericity are formed. by a substellar companion (a brown dwarf or a planet) that spins-up theenvelope of the AGB progenitor.,4) Elliptical PN with small departure from sphericity are formed by a substellar companion (a brown dwarf or a planet) that spins-up theenvelope of the AGB progenitor.340 Weak jets max be present., Weak jets may be present.341only to capture the shocks that form when the gas orbits in the non-axisvnunetric potential. but also to properly. model the loss of angular momentum and hence the resulting radial inflow of the gas due to the strong shear in the underlying cilferentiallv rotating disk.,"only to capture the shocks that form when the gas orbits in the non-axisymmetric potential, but also to properly model the loss of angular momentum and hence the resulting radial inflow of the gas due to the strong shear in the underlying differentially rotating disk."342 Slvz et al. (, Slyz et al. (3432002) showed that if an isothermal gas is initialized to be in centrifugal equilibrium within a purely axisvmmetric galactic potential. simulation with the DCGIx scheme produces the steady-state Navier-Stokes solution to a high degree of accuracy.,"2002) showed that if an isothermal gas is initialized to be in centrifugal equilibrium within a purely axisymmetric galactic potential, simulation with the BGK scheme produces the steady-state Navier-Stokes solution to a high degree of accuracy."344 The tests were carried out for parameters which are relevant for galaxy studies: an asvinptotically Hat rotation curve with Caax= 220 .a sound speed of e= 10. i.c. a highly supersonic (Mach = 20) shear How throughout most of the disk.," The tests were carried out for parameters which are relevant for galaxy studies: an asymptotically flat rotation curve with $v_{\rm max} = $ 220, a sound speed of $c_{\rm s} = $ 10, i.e. a highly supersonic (Mach $\approx$ 20) shear flow throughout most of the disk."345 The success of DGI in giving viscous radial [lows on the order of 1. in a disk rotating differentially at 220. is a technical success which insures that when studying the kinematics of the gas in a ealactic disk. with a decent eric resolution. one does not have to worry about artificial dissipation.," The success of BGK in giving viscous radial flows on the order of 1 in a disk rotating differentially at 220 is a technical success which insures that when studying the kinematics of the gas in a galactic disk, with a decent grid resolution, one does not have to worry about artificial dissipation."346 The number of grid. cells. i.e. the spatial resolution of a simulation. is one of the parameters whose variation we study in this paper.," The number of grid cells, i.e. the spatial resolution of a simulation, is one of the parameters whose variation we study in this paper."347 In addition to the dissipation introduced by the BCI algorithm. there is the inevitable dissipation arising [rom the fact that the code only saves cell averages at the end of each iteration.," In addition to the dissipation introduced by the BGK algorithm, there is the inevitable dissipation arising from the fact that the code only saves cell averages at the end of each iteration."348 Hence the larger the cells. the less information the code retains.," Hence the larger the cells, the less information the code retains."349 To keep this numerical dissipation which is proportional to the cell. dimensions at à constant value throughout the grid. we perform. our simulations on an evenly spaced: Cartesian grid.," To keep this numerical dissipation which is proportional to the cell dimensions at a constant value throughout the grid, we perform our simulations on an evenly spaced Cartesian grid."350 Our runs in Paper L were performed on a 201 201 grid giving a resolution clement of about 115 pe on a side., Our runs in Paper I were performed on a 201 $\times$ 201 grid giving a resolution element of about 115 pc on a side.351 For comparison. in this paper we look at runs done at half (101 101) and double that resolution (401. 401).," For comparison, in this paper we look at runs done at half (101 $\times$ 101) and double that resolution (401 $\times$ 401)."352 There are three other parameters we explore in our modeling., There are three other parameters we explore in our modeling.353 As already. stated in the introduction and described in Paper LE. for our numerical investigation of the solutions for gas Dow in the gravitational potential of NGC 4254 we use a potential derived: from. observations.," As already stated in the introduction and described in Paper I, for our numerical investigation of the solutions for gas flow in the gravitational potential of NGC 4254 we use a potential derived from observations."354 The niass-to-light ratio corrected A'-band image provides us with a stellar density map from which we compute the form ofthe non-axisvmametrie component ofthe gravitational potential. and the rotation curves [rom observed. long-slit. H-alpha kinematies give us a measurement of the total gravitational potential of the galaxy.," The mass-to-light ratio corrected $K$ -band image provides us with a stellar density map from which we compute the form of the non-axisymmetric component of the gravitational potential, and the rotation curves from observed long-slit H-alpha kinematics give us a measurement of the total gravitational potential of the galaxy."355 By assuming an axisvmmetric isothermal profile for the dark halo we construct a series of potentials of dilferent values. for the strength of the stellar contribution. f4 (ef," By assuming an axisymmetric isothermal profile for the dark halo we construct a series of potentials of different values for the strength of the stellar contribution, $f_{\rm d}$ (cf."356 eqns., eqns.357 9 and. 10. Paper D). which all match the observed: rotation curve.," 9 and 10, Paper I), which all match the observed rotation curve."358 Constraining the parameter fy is our main scientific objective., Constraining the parameter $f_{\rm d}$ is our main scientific objective.359 Note that we do not work with a self-consistent model., Note that we do not work with a self-consistent model.360 We dynamically follow the eas. neglecting its sell-eravity. in a fixed external potential which represents the combined gravitational effect of stars and dark matter.," We dynamically follow the gas, neglecting its self-gravity, in a fixed external potential which represents the combined gravitational effect of stars and dark matter."361" Another parameter which plavs the most important role in shaping the eas morphology in our simulations is the pattern speed. ,. of the external potential."," Another parameter which plays the most important role in shaping the gas morphology in our simulations is the pattern speed, $\Omega_{\rm p}$, of the external potential."362 We assume the entire potential rotates rigidlv with the same pattern προσ and we perform the simulations in this rotating reference frame., We assume the entire potential rotates rigidly with the same pattern speed and we perform the simulations in this rotating reference frame.363 We choose the direction of pattern and. gas rotation to be clockwise so that inside corotation the eas enters the spiral arms from the concave side., We choose the direction of pattern and gas rotation to be clockwise so that inside corotation the gas enters the spiral arms from the concave side.364" Figure 1. shows how the locations of the resonances change with the different Q), that we use.", Figure \ref{resonances} shows how the locations of the resonances change with the different $\Omega_{\rm p}$ that we use.365 We keep away from the dillieult. question of how the spiral formed. and we do not look for time-dependent solutions.," We keep away from the difficult question of how the spiral formed, and we do not look for time-dependent solutions."366 Instead we study only steady or equasi-steacdy Lows in NGC 4254's fixed external gravitational potential., Instead we study only steady or quasi-steady flows in NGC 4254's fixed external gravitational potential.367 In the time-indepenclent case. the gas How must satisfy: where «t is the potential of the combined centrifugal and. gravitational forces.," In the time-independent case, the gas flow must satisfy: where $\Phi$ is the potential of the combined centrifugal and gravitational forces."368 This svstem of equations must be completed by an equation of state and. this introduces the last parameter of the problem: the gas sound speed., This system of equations must be completed by an equation of state and this introduces the last parameter of the problem: the gas sound speed.369 Because we do not know the elective equation of state of interstellar matter. the simplest thing to do is to assume an isothermal equation of state p—Ap. whereAK —ce7/5.2 5 being the ratio of specific heats of the gas. and ὃς is its constant sound speed.," Because we do not know the effective equation of state of interstellar matter, the simplest thing to do is to assume an isothermal equation of state $p = K \rho$ , where $= {c_{\rm s}}^{2}/\gamma$, $\gamma$ being the ratio of specific heats of the gas, and $c_{\rm s}$ is its constant sound speed."370 To studs how the gas Low responcds to changes in ὃς. we simulate the gas with sound speeds of 10. 15. 20 and 30," To study how the gas flow responds to changes in ${c_{\rm s}}$, we simulate the gas with sound speeds of 10, 15, 20 and 30."371 Since the scale height of gas and stars in a typical non-interacting late tvpe disk galaxy is about 1/40 to 1/75 the diameter of the visible galactic disk (¢.g.. Schwarzkopf Dettmar 2000). we restrain this study to. two-cimensions.," Since the scale height of gas and stars in a typical non-interacting late type disk galaxy is about 1/40 to 1/75 the diameter of the visible galactic disk (e.g., Schwarzkopf Dettmar 2000), we restrain this study to two-dimensions."372 Alore specifically we approximate the disk as a thin sheet. and only compute the gas [ow in the two dimensions of the disk plane.," More specifically we approximate the disk as a thin sheet, and only compute the gas flow in the two dimensions of the disk plane."373 Alternatively. one can view this approximation as an integration over the disk thickness perpendicular to the plane. and our physical variables as mean values in this direction.," Alternatively, one can view this approximation as an integration over the disk thickness perpendicular to the plane, and our physical variables as mean values in this direction."374 Table 1. summarizes the parameters we use for the simulations and indicates the parameters of our. fiducial simulation in boldlace., Table \ref{SimuParam} summarizes the parameters we use for the simulations and indicates the parameters of our fiducial simulation in boldface.375 We initialize the gas density profile to be exponential with a scale length which is on the order of the observed. disks stellar scale length. namely 3.86 kpe.," We initialize the gas density profile to be exponential with a scale length which is on the order of the observed disk's stellar scale length, namely 3.86 kpc."376 Upon estimating the total mass of the ealaxy [rom the observed rotation curves. we set the mass of the gaseous disk to be 5 per cent of this total mass.," Upon estimating the total mass of the galaxy from the observed rotation curves, we set the mass of the gaseous disk to be 5 per cent of this total mass."377 The gas is therefore moving in a potential produced by a mass much. greater than itself which means that. even in the densest regions (spiral armis). the neglect of its self-eravity will translate into à modest unclerestimate of its density (Berman. Pollard and Hockney. 1979).," The gas is therefore moving in a potential produced by a mass much greater than itself which means that, even in the densest regions (spiral arms), the neglect of its self-gravity will translate into a modest underestimate of its density (Berman, Pollard and Hockney 1979)."378 As [or the initial dvnamics of the gaseous disk. the simulations begin. with the gas llowing on circular orbits in inviscid centrifugal equilibrium with respect to the axisvmmetric gravitational potential which best fits theobserved rotation curves.," As for the initial dynamics of the gaseous disk, the simulations begin with the gas flowing on circular orbits in inviscid centrifugal equilibrium with respect to the axisymmetric gravitational potential which best fits theobserved rotation curves."379 The non-axisvmmoetric, The non-axisymmetric380of outflows of two luminous YSOs and find a change in slope al a break-point velocity of 10 L|,of outflows of two luminous YSOs and find a change in slope at a break-point velocity of 10 $^{-1}$.381 They suggest that the high velocity (|Ar>lO 1) gas maw drive the low velocity (JAv<10 +) gas., They suggest that the high velocity $|{\Delta}v|>10$ $^{-1}$ ) gas may drive the low velocity $|{\Delta}v|<10$ $^{-1}$ ) gas.382 With the assumption of the optically thin SiO thermal emission in LTE. we derive the mass-velocity diagrams for (he $jO outflows lor the two sources (see Fig. 9)).," With the assumption of the optically thin SiO thermal emission in LTE, we derive the mass-velocity diagrams for the SiO outflows for the two sources (see Fig. \ref{mv}) )."383 Since the SiO emission is dominantily redshifted in [18264 and blueshifted in 123151. we derive the mass-velocitv. relations in the corresponding wings for the two sources.," Since the SiO emission is dominantly redshifted in I18264 and blueshifted in I23151, we derive the mass-velocity relations in the corresponding wings for the two sources."384 The redshifted emission in 118264 is mostly attributed to the SE outflow., The redshifted emission in I18264 is mostly attributed to the SE outflow.385 So Fig., So Fig.386 9aa represents (he mass-velocity relationship of the HIC: of the SE outflow and can be fitted by a broken power law with the index steepening from 4=0.360.05 to 45=L.52:0.3 at Av=10 |," \ref{mv}a a represents the mass-velocity relationship of the HC of the SE outflow and can be fitted by a broken power law with the index steepening from ${\gamma}_1=0.36\,{\pm}\,0.05$ to ${\gamma}_2=1.5\,{\pm}\,0.3$ at ${\Delta}v=10$ $^{-1}$."387 The mass distribution in the velocity channels of the VIIC of the SE outflow has large scatters and can hardly be described by a linear fit., The mass distribution in the velocity channels of the VHC of the SE outflow has large scatters and can hardly be described by a linear fit.388 Similarly. the blueshilted lobe of the SiO outflow in 123151 is also fitted by a broken power law with 54=0.90.1 for |Av<10 and 5»=342 for Ne>10 !.," Similarly, the blueshifted lobe of the SiO outflow in I23151 is also fitted by a broken power law with $\gamma_1=0.9\,{\pm}\,0.1$ for $|{\Delta}v|<10$ $^{-1}$ and $\gamma_2=3\,{\pm}\,2$ for $|{\Delta}v|{\geq}10$ $^{-1}$."389 From three dimensional simulations of a dense molecular jet penetrating a dense molecular medium. Smithetal.(1997) predict the change in slope αἱ high velocities due to a. jet-bow shear laver consisting of molecules which survived the jet terminal shock.," From three dimensional simulations of a dense molecular jet penetrating a dense molecular medium, \citet{Smith97} predict the change in slope at high velocities due to a jet-bow shear layer consisting of molecules which survived the jet terminal shock."390 Models of material being accelerated by jet-diiven bow shocks (Downes1999). have reproduced a power law relationship between mass and velocity with 5 increasing with decreasing molecular abundance in the jet., Models of material being accelerated by jet-driven bow shocks \citep{Downes99} have reproduced a power law relationship between mass and velocity with ${\gamma}$ increasing with decreasing molecular abundance in the jet.391 However. Downes&Rav(1999) eive an upper limit of 3.75 for 5. which is much less (han the observed values.," However, \citet{Downes99}392 give an upper limit of 3.75 for ${\gamma}$, which is much less than the observed values."393 Therefore the physical origin is still unclear for (he broken power law of the mass-velocity diagrams., Therefore the physical origin is still unclear for the broken power law of the mass-velocity diagrams.394 The SiO in the gas phase of molecular outflows can be produced through the sputtering of Si-bearing material in grains. where the sputtering is driven by neutral particle impact on charged grains in shocks (Schikeetal.1997).," The SiO in the gas phase of molecular outflows can be produced through the sputtering of Si-bearing material in grains, where the sputtering is driven by neutral particle impact on charged grains in shocks \citep{Schike97}."395. In Fig., In Fig.396 τας. the jet-like SE outflow in 118264 coincides well with the IIPCO — structure extending to the southeast. suggesting the SiO emission in (his region may arise [rom (he interaction between the shocks driven by the jet or wind from the central (proto)star and the dense ambient gas clump.," \ref{hcoint}a a, the jet-like SE outflow in I18264 coincides well with the $^{13}$ $^+$ structure extending to the southeast, suggesting the SiO emission in this region may arise from the interaction between the shocks driven by the jet or wind from the central (proto)star and the dense ambient gas clump."397 Such an interaction mainlv exists in the redshifted lobe since the SiO emission is clominantly redshifted., Such an interaction mainly exists in the redshifted lobe since the SiO emission is dominantly redshifted.398 In Fie., In Fig.399 I0aa. the SiO line at the downstream peak of the HC of the SE outflow. (denoted as the southern cross in Fie.," \ref{profile}a a, the SiO line at the downstream peak of the HC of the SE outflow (denoted as the southern cross in Fig."400 3bb) shows a prolile with a steep decrease Cowarcl the svstenic velocity and a gradual redshilted wing. which suggests the SiO enhancement arising from the quiescent material accelerated by the shock when (he jet or wind impinges into the dense ambient gas.," \ref{sioint1}b b) shows a profile with a steep decrease toward the systemic velocity and a gradual redshifted wing, which suggests the SiO enhancement arising from the quiescent material accelerated by the shock when the jet or wind impinges into the dense ambient gas."401 We have checked the corresponding single-dish SiO spectrum. and find. (hat such a profile also exists., We have checked the corresponding single-dish SiO spectrum and find that such a profile also exists.402 So (he steep decrease towiud (he svstemic velocity can not be due to the missing short spacings., So the steep decrease toward the systemic velocity can not be due to the missing short spacings.403 This kind of SiO proliles aud interactions have been observed, This kind of SiO profiles and interactions have been observed404"at least, the mean HOD is therefore a good choice of weight function.","at least, the mean HOD is therefore a good choice of weight function."405 We will examine other galaxy classes below., We will examine other galaxy classes below.406" To examine the impact of item (iii), the stochasticity of the HOD, on mass-estimator performance, we populate the halos in the Millennium simulation with LRGs as per the HOD prescription."," To examine the impact of item (iii), the stochasticity of the HOD, on mass-estimator performance, we populate the halos in the Millennium simulation with LRGs as per the HOD prescription."407" We place central galaxies in the specified fraction of halos, plus a Poisson-distributed number of satellite galaxies in the halos which host a central galaxy."," We place central galaxies in the specified fraction of halos, plus a Poisson-distributed number of satellite galaxies in the halos which host a central galaxy."408 The red triangle in Figure 9 shows the stochasticity E vs the number density of LRGs., The red triangle in Figure \ref{evsn} shows the stochasticity $E$ vs the number density of LRGs.409 We find stochastically occupied halos achieve a factor of two higher (worse) E than the deterministic weighting by the mean HOD., We find stochastically occupied halos achieve a factor of two higher (worse) $E$ than the deterministic weighting by the mean HOD.410" While the stochastic LRG HOD requires ~3x as many redshifts to reach E=0.5 as an ideal survey would require, it is similar to what one would predict from an optimal survey if the biased-Poisson model were a correct description of halo stochasticity (dashed black line)."," While the stochastic LRG HOD requires $\approx 3\times$ as many redshifts to reach $E=0.5$ as an ideal survey would require, it is similar to what one would predict from an optimal survey if the biased-Poisson model were a correct description of halo stochasticity (dashed black line)."411" The green solid curve in Figure 9 shows the result of weighting the halos by the number of galaxies drawn from HODs with varying minimum galaxy luminosities, from ?).."," The green solid curve in Figure \ref{evsn} shows the result of weighting the halos by the number of galaxies drawn from HODs with varying minimum galaxy luminosities, from \citet{Zehavi10}."412" The behavior is similar to the LRG HOD: even though the mean number of galaxies per halo looks like the optimal weight, using the actual number of galaxies as weight results in larger E."," The behavior is similar to the LRG HOD: even though the mean number of galaxies per halo looks like the optimal weight, using the actual number of galaxies as weight results in larger $E$."413 The randomness in the number of galaxies in each halo introduces additional stochasticity that degrades the mass estimator., The randomness in the number of galaxies in each halo introduces additional stochasticity that degrades the mass estimator.414" If galaxies are to be used to provide optimal reconstructions of the mass, then they must themselves be weighted in some way so as to reduce the stochasticity in the weight applied to halos of a given mass."," If galaxies are to be used to provide optimal reconstructions of the mass, then they must themselves be weighted in some way so as to reduce the stochasticity in the weight applied to halos of a given mass."415 Determining the optimal mark is an interesting problem for the future., Determining the optimal mark is an interesting problem for the future.416" Formalism for treating this more general problem has been developed in ?),, and can be used directly, but is beyond the scope of this work."," Formalism for treating this more general problem has been developed in \citet{Sheth05}, and can be used directly, but is beyond the scope of this work."417" Our results suggest that it is interesting to study how best to supplement the spectroscopic galaxies with a larger, deeper photometric-redshift sample."," Our results suggest that it is interesting to study how best to supplement the spectroscopic galaxies with a larger, deeper photometric-redshift sample."418 The spectroscopic galaxies can be weighted by the number of photo-z galaxies consistent with sharing the same halo., The spectroscopic galaxies can be weighted by the number of photo-z galaxies consistent with sharing the same halo.419 The deeper photo-z catalog potentially has lower stochasticity in halo mass estimates., The deeper photo-z catalog potentially has lower stochasticity in halo mass estimates.420" We have seen that the mean HODs for LRGs and luminosity-selected galaxies are good approximations to the optimal weight, but the stochasticity in halo occupation degrades E for a given source density n."," We have seen that the mean HODs for LRGs and luminosity-selected galaxies are good approximations to the optimal weight, but the stochasticity in halo occupation degrades $E$ for a given source density $n$."421" Galaxy redshift surveys based on emission line detection will likely result in substantially different halo weightings, so we investigate the mass-reconstruction performance of such a survey relative to an LRG survey or optimal weighting."," Galaxy redshift surveys based on emission line detection will likely result in substantially different halo weightings, so we investigate the mass-reconstruction performance of such a survey relative to an LRG survey or optimal weighting."422 We model the emission-line sample by starting with the mean HOD for blue galaxies given by equations (10) and (11) and Table 4 in (?):: where Mg=7x10?! and ag=0.8 ?).., We model the emission-line sample by starting with the mean HOD for blue galaxies given by equations (10) and (11) and Table 4 in \citep{Zehavi05}: where $M_B = 7\times10^{13} h^{-1}M_{\odot}$ and $\alpha_B=0.8$ \citep[following][]{Sheth01}. .423 This is plotted as the cyan Moline in Figure 1.., This is plotted as the cyan line in Figure \ref{wvsm}.424" There is a bump in the number of blue galaxies between M!Μο to ~M?h!Mo, which is very different from the optimal weight."," There is a bump in the number of blue galaxies between $\sim M^{11}~h^{-1}M_{\odot}$ to $\sim M^{12}~h^{-1}M_{\odot}$, which is very different from the optimal weight."425 The outcome of E from weighting halos in the Millennium simulation according to galaxy counts drawn from this HOD is shown in the blue triangle of Figure (9))., The outcome of $E$ from weighting halos in the Millennium simulation according to galaxy counts drawn from this HOD is shown in the blue triangle of Figure \ref{evsn}) ).426" Although the blue galaxy sample achieves lower E than the LRG does, notice that it requires 100x more redshifts, i.e., is 100x more costly than an optimally weighted sample."," Although the blue galaxy sample achieves lower $E$ than the LRG does, notice that it requires $100\times$ more redshifts, i.e., is $100\times$ more costly than an optimally weighted sample."427" If we were to under-sample the blue galaxies—e.g. by obtaining redshifts for ten percent, or one percent of the sample with the brightest emission lines—then E would rise to 0.54 and 0.86, respectively, if the sub-sampling rate is independent of halo properties."," If we were to under-sample the blue galaxies—e.g. by obtaining redshifts for ten percent, or one percent of the sample with the brightest emission lines—then $E$ would rise to 0.54 and 0.86, respectively, if the sub-sampling rate is independent of halo properties."428" Clearly, emission line samples are a very inefficient way to reconstruct the mass, although this disadvantage is countered by the fact that emission lines canbe much stronger and easily detected relative to LRG absorption features."," Clearly, emission line samples are a very inefficient way to reconstruct the mass, although this disadvantage is countered by the fact that emission lines canbe much stronger and easily detected relative to LRG absorption features."429 Optimization of a survey would need to weigh these effects., Optimization of a survey would need to weigh these effects.430The results of the previous section suggest an overall shallower slope than the Tonry slope determined for red colours. accompanied by a significant cosmic scatter.,"The results of the previous section suggest an overall shallower slope than the Tonry slope determined for red colours, accompanied by a significant cosmic scatter."431 The question is whether this is created by a single relation with some scatter as in case B) (see also Met et al. 2005)).," The question is whether this is created by a single relation with some scatter as in case B) (see also Mei et al. \cite{Mei05}) ),"432 or by a two-branch solution as in case D) (Jerjen et al. 20010)., or by a two-branch solution as in case D) (Jerjen et al. \cite{Jerjen01}) ).433" Case D) contains the implicit assumption that a) the relation between M, and (V—D) broadens up significantly at blue colours: b) the age-metallicity distribution of the galaxies vestigated is broad; and c) the investigated galaxies consist of two distinct populations: an old. metal-poor one plus an intermediate age. more metal-rich one."," Case D) contains the implicit assumption that a) the relation between $\overline{M}_I$ and $(V-I)_0$ broadens up significantly at blue colours; b) the age-metallicity distribution of the galaxies investigated is broad; and c) the investigated galaxies consist of two distinct populations: an old, metal-poor one plus an intermediate age, more metal-rich one."434 Such a bimodality 1 stellar populations is known from the colour distribution of globular cluster systems (e.g. Peng et al. 2005.. ," Such a bimodality in stellar populations is known from the colour distribution of globular cluster systems (e.g. Peng et al. \cite{Peng05}, ,"435Patig 2000.. Harris et al. 2005..," Kissler-Patig \cite{Kissle00}, , Harris et al. \cite{Harris05},"436. Dirsch et al. 2003)).," Dirsch et al. \cite{Dirsch03}) ),"437 but it has ot been found for bright dEs (e.g. Geha et al. 2003..," but it has not been found for bright dEs (e.g. Geha et al. \cite{Geha03},"438 Held Mould 1994))., Held Mould \cite{Held94}) ).439 In order to support a two-branch calibration n the sense of the Jerjen papers — as opposed to an overall shallower relation with some intrinsic scatter — there have to be two well separated galaxy populations in the M;-(V—/)o To investigate this. we test the distance distribution i the different calibration cases for bimodality.," In order to support a two-branch calibration in the sense of the Jerjen papers – as opposed to an overall shallower relation with some intrinsic scatter – there have to be two well separated galaxy populations in the $\overline{M}_I$ $(V-I)_0$ To investigate this, we test the distance distribution in the different calibration cases for bimodality."440 We use KMM (e.g. Ashman. Bird. Zepf 1994)) in homoscedastic mode to quantify the probability with which a double-peaked Gaussia distance distribution is preferred over a single-peaked one.," We use KMM (e.g. Ashman, Bird, Zepf \cite{Ashman94}) ) in homoscedastic mode to quantify the probability with which a double-peaked Gaussian distance distribution is preferred over a single-peaked one."441 This ts certainly a very crude estimator. but the measurement uncertainties and low numbers do not allow for more detailec considerations.," This is certainly a very crude estimator, but the measurement uncertainties and low numbers do not allow for more detailed considerations."442 The confidence levels with which a bimodal Gaussian is preferred over a unimodal one are the following: for case A). for case B). for case C). anc for case D).," The confidence levels with which a bimodal Gaussian is preferred over a unimodal one are the following: for case A), for case B), for case C), and for case D)."443 The strongest case for a double-peakec distribution is case B). yielding one main peak with 12 galaxies and a secondary one with five.," The strongest case for a double-peaked distribution is case B), yielding one main peak with 12 galaxies and a secondary one with five."444 These five galaxies are the ones below the long dashed line in Fig. 9.., These five galaxies are the ones below the long dashed line in Fig. \ref{VImbar}.445 The fact that the probabilities for cases B) and D) are so different i5 consistent with a proper two-branch calibration as opposed to a unimodal one with broad scatter., The fact that the probabilities for cases B) and D) are so different is consistent with a proper two-branch calibration as opposed to a unimodal one with broad scatter.446 However. the confidence level for case B) is only 1.56. and therefore this finding is still of indicative nature.," However, the confidence level for case B) is only $\sigma$, and therefore this finding is still of indicative nature."447 We note that the SBF S/N and also the amount of background fluctuations BG is not a function of distance modulus., We note that the SBF S/N and also the amount of background fluctuations $BG$ is not a function of distance modulus.448 Both entities are indistinguishable between SBF-bright and SBF-faint Are there any other differences between dEs belonging to the bright and faint 77; part of case D)?, Both entities are indistinguishable between SBF-bright and SBF-faint Are there any other differences between dEs belonging to the bright and faint $\overline{m}_I$ part of case D)?449 The difference i mean colour (V—[) between SBF-faint and bright dEs is insignificant. being -0.015 + 0.028 mag.," The difference in mean colour $(V-I)$ between SBF-faint and bright dEs is insignificant, being -0.015 $\pm$ 0.028 mag."450 However. the meal V-band total luminosity of the SBF-faint sample is 1.6 + 0.5 mag brighter than that of the SBF-bright sample. accompanied by a | mag brighter mean central surface brightness and larger exponential scale length.," However, the mean $V$ -band total luminosity of the SBF-faint sample is 1.6 $\pm$ 0.5 mag brighter than that of the SBF-bright sample, accompanied by a 1 mag brighter mean central surface brightness and larger exponential scale length."451 An obvious conclusion from this finding is that the lower luminosity and smaller dEs i1 Fornax have in comparison to their brighter counterparts a younger integrated age and somewhat higher metallicities. see Fig. l..," An obvious conclusion from this finding is that the lower luminosity and smaller dEs in Fornax have in comparison to their brighter counterparts a younger integrated age and somewhat higher metallicities, see Fig. \ref{twobranch}."452 This may imply that the Fornax dwarf galaxy populations were built up in subsequent events. where the most recent events produced less massive dwarf galaxies than at earlier times.," This may imply that the Fornax dwarf galaxy populations were built up in subsequent events, where the most recent events produced less massive dwarf galaxies than at earlier times."453 The significant bimodality in 71; is in that context consistent with at least two separate dwarf formation episodes in We finally note that the average projected radial distance to NGC 1399 is indistinguishable for both samples. indicating that both groups are not distributed in a significantly different fashion.," The significant bimodality in $\overline{m}_I$ is in that context consistent with at least two separate dwarf formation episodes in We finally note that the average projected radial distance to NGC 1399 is indistinguishable for both samples, indicating that both groups are not distributed in a significantly different fashion."454 Due to theintrinsicfaintness of the investigated dEs.," Due to theintrinsicfaintness of the investigated dEs,"45528 Tv1...,28 $\mu$.456 For a spectral index of Os. the T.E CUIZ observations are ~LO times more sensitive.," For a spectral index of $-0.8$, the 1.4 GHz observations are $\sim 10$ times more sensitive."457 We restrict our conrparison to a 1.1 degree radius circular area to avok he noisy edge of the deep 1.1 GIIz survey., We restrict our comparison to a 1.4 degree radius circular area to avoid the noisy edge of the deep 1.4 GHz survey.458" For all of the 399 sources detected at 153 MITz we find a counterpart iu he 1.£ CdIz map (383 sources were automatically matches within a 25"" search radius. while the remaining fraction of sources with complex morphology were confine nanuallvj)."," For all of the 399 sources detected at 153 MHz we find a counterpart in the 1.4 GHz map (383 sources were automatically matched within a $25\arcsec$ search radius, while the remaining fraction of sources with complex morphology were confirmed manually)."459 We could not match the full CAIRT area. mt considering that our source extraction is based ou οσα]. noise and that the false detections only appearec ο Occur near à few bright sources. we estimate that the contamination of our complete catalog over the full survey area is <Ol percent.," We could not match the full GMRT area, but considering that our source extraction is based on local noise and that the false detections only appeared to occur near a few bright sources, we estimate that the contamination of our complete catalog over the full survey area is $< 1$ percent."460 For au estinate of the astrometric unucertaimtfyv. we compare the source positions in the GAIRT 153 MITIZ catalog against catalog source positions frou the deep WSRT 1.1 GIIz map of ?..," For an estimate of the astrometric uncertainty, we compare the source positions in the GMRT 153 MHz catalog against catalog source positions from the deep WSRT 1.4 GHz map of \citet{devries2002}."461" For our position comparison. we ouly use sources whose flux profile is accurately described bv a single gaussian. aud whose peak flux 5, is at least Loo,"," For our position comparison, we only use sources whose flux profile is accurately described by a single gaussian, and whose peak flux $S_p$ is at least $10\,\sigma^{}_\mathrm{L}$."462" This bypasses most of the position errors that arise from low signal-to-noise (S/N. or 5,/0,). differeut erouping of eaussiaus and spectral variations across sources."," This bypasses most of the position errors that arise from low signal-to-noise (S/N, or $S_p / \sigma^{}_\mathrm{L}$ ), different grouping of gaussians and spectral variations across sources."463" Using a search radius of 10"". we cross-match 126 sources m both catalogs."," Using a search radius of $10\arcsec$, we cross-match 126 sources in both catalogs."464 From this. we measure a small iiezui position offse in RA aud DEC of (An.A0)=(0.117. 0.097).," From this, we measure a small mean position offset in RA and DEC of $(\Delta\alpha,\Delta\delta) = (0.11\arcsec,0.09\arcsec)$ ."465 We correct the catalog positious for this sun offset., We correct the catalog positions for this small offset.466" The estimated RAIS scatter around this offse isoy=1.32"""," The estimated RMS scatter around this offset is $\sigma^{}_{\alpha,\delta} = 1.32\arcsec$."467" The S/N-independent part of the »ositional uncertainty of 16 1.E GIIz sources is 0.11"" (?2).. jerefore we derive au absolute astrometric uucertaimtv for ιο 153 MIIz sources of |3|"","," The S/N-independent part of the positional uncertainty of the 1.4 GHz sources is $0.44\arcsec$ \citep{devries2002}, therefore we derive an absolute astrometric uncertainty for the 153 MHz sources of $1.24\arcsec$."468 We quadratically add this o the calculated (S/N-depeudeut) position accuracies iu 1ο 153 MITz source catalog (see Section 3.1))., We quadratically add this to the calculated (S/N-dependent) position accuracies in the 153 MHz source catalog (see Section \ref{sec:bootes_bdsm}) ).469 The uncertainty of the flux scale trausferred from the calibrator 3C 286 to the target fiek is influenced we oseveral factors: (1) the quality of the calibrator observational data. 1) the accuracy of calibrator source uodel. aud Gil) the difference iu observing conditions vetween the calibrator and target field.," The uncertainty of the flux scale transferred from the calibrator 3C 286 to the target field is influenced by several factors: (i) the quality of the calibrator observational data, (ii) the accuracy of calibrator source model, and (iii) the difference in observing conditions between the calibrator and target field."470 Because of the relatively large uncertaüutv in the fiux scale at low requencies. we discuss iu some detail the isses that influence these factors.," Because of the relatively large uncertainty in the flux scale at low frequencies, we discuss in some detail the issues that influence these factors."471 The quality of the calibrator data 1s most roticeably affected by RFI ux w ionospheric phase rotations., The quality of the calibrator data is most noticeably affected by RFI and by ionospheric phase rotations.472 The repeated observation of 3C 286 every ~15 minutes duiug the observing euabled us to monitor these effects over time., The repeated observation of 3C 286 every $\sim 45$ minutes during the observing enabled us to monitor these effects over time.473" The mild fluctuations in the initial (hor interval) calibration gain phases at the start of the data reduction showed that the ionosphere was very calin during both observing niehts. therefore we exclude the possibility of diffraction or focussing effects (ο,ος,7)."," The mild fluctuations in the initial (short interval) calibration gain phases at the start of the data reduction showed that the ionosphere was very calm during both observing nights, therefore we exclude the possibility of diffraction or focussing effects \citep[e.g.,][]{jacobson1992a}."474 Apparent flux loss due to ionospheric pliase rotations was preveuted by applving the (short interval) gain phase corrections before baudpass- aud amplitude calibration (see Section 2.2))., Apparent flux loss due to ionospheric phase rotations was prevented by applying the (short interval) gain phase corrections before bandpass- and amplitude calibration (see Section \ref{sec:bootes_dr}) ).475 REI was continuously preseut during both obscrving sessions., RFI was continuously present during both observing sessions.476 This mainly consisted of persisten REI over the full band. most noticeably on the shortest (centra square and ucighbouring ari antenna) baselimes. aux of nore sporadic events on longer baselimes during one or more time stamps and/or narrow frequency ranges.," This mainly consisted of persistent RFI over the full band, most noticeably on the shortest (central square and neighbouring arm antenna) baselines, and of more sporadic events on longer baselines during one or more time stamps and/or narrow frequency ranges."477" The sporadic events were relatively easy to recognize auc excise, but for the persistent RFT this is much more difficult due o a lack of coutrast between healthy iik affected data on a single baseline."," The sporadic events were relatively easy to recognize and excise, but for the persistent RFI this is much more difficult due to a lack of contrast between healthy and affected data on a single baseline."478 Some of the shortest. most affectoc baselines were removed cxupletely.," Some of the shortest, most affected baselines were removed completely."479 Ou longerC» baseliues. ]xxwisteut REI frou quasi-stationarv sources can average out due to fringe racking (?7).. but does add noise.," On longer baselines, persistent RFI from quasi-stationary sources can average out due to fringe tracking \citep{athreya2009}, but does add noise."480 Large magnitude REI amplitude errors in the visibilitics may result in a suppression of the eain aüuplitude corrections., Large magnitude RFI amplitude errors in the visibilities may result in a suppression of the gain amplitude corrections.481 Because these effects are hard to quantity. we adopt an ad-hoc 2 percent amplitude error due to RET.," Because these effects are hard to quantify, we adopt an ad-hoc 2 percent amplitude error due to RFI."482the large-scale magnetic field. is zero.,"the large-scale magnetic field, is zero."483 Exceptions are the simulations of Machidaetal.(20062):Price&Bate(2007):Llennebelle&Ciardi (2009).. which however focused mostly on the core ancl disc dynamics.," Exceptions are the simulations of \cite{machida_evolution_2006,price_impact_2007,hennebelle_disc_2009}, which however focused mostly on the core and disc dynamics."484 Here we present simulations of the collapse of pre-stellar. dense. cores with misaligned initial configurations (a—Οἱ 907). and show that the angle o ds fundamental in determining not only the properties of the outllow. but also the mass accretion onto the core.," Here we present simulations of the collapse of pre-stellar dense cores with misaligned initial configurations $\alpha=0^{\circ}-90^{\circ}$ ), and show that the angle $\alpha$ is fundamental in determining not only the properties of the outflow, but also the mass accretion onto the core."485 In particular we observe the gradual decrease in the mass ejection with increasing angle a. until its total suppression for nearly perpendicular configurations.," In particular we observe the gradual decrease in the mass ejection with increasing angle $\alpha$, until its total suppression for nearly perpendicular configurations."486 We follow numerically the gravitational collapse of dense pre-stcllar cores. up to. and including the formation of the first (or acliabatie) core.," We follow numerically the gravitational collapse of dense pre-stellar cores, up to, and including the formation of the first (or adiabatic) core."487 The numerical simulations were performed. with Ramses (Teyssier2002:Fromangοἱal. 2006).. an adaptive mesh refinement code which uses a Godunov-tvpe scheme and. constrained. transport. το solve the ideal MIID. equations.," The numerical simulations were performed with Ramses \citep{teyssier_cosmological_2002,fromang_high_2006}, an adaptive mesh refinement code which uses a Godunov-type scheme and constrained transport to solve the ideal MHD equations."488 Throughout the simulations the Jeans length is resolved: with at least 10 cells. and a ΗΕ solver is emploved.," Throughout the simulations the Jeans length is resolved with at least 10 cells, and a HLLD solver is employed."489" The initial conditions consist of a one solar mass core whose density profile resembles the observec cores. and is given by alr)=n,[1|Gr where ro~1000 AU is the inner cloud. radius."," The initial conditions consist of a one solar mass core whose density profile resembles the observed cores, and is given by $n(r)=n_{c}/\left[1+(r/r_{0})^{2}\right]$ where $r_{0}\sim1000$ AU is the inner cloud radius."490 This rar]isotherma cloud (Z£~10 IX) is placed. inside à warn and dilfuse medium in pressure equilibrium with the cloud. edge. with a contrast of 10 between central. n=8S«10 em.7. anc edge densities.," This isothermal cloud $T\sim10$ K) is placed inside a warm and diffuse medium in pressure equilibrium with the cloud edge, with a contrast of 10 between central, $n_{c}=8\times10^{6}$ $^{-3}$, and edge densities."491 Phe cloud is initially in solid body rotation and threaded by a uniform magnetic field along the z-axis. whose intensity is proportional to the column density of the cloud.," The cloud is initially in solid body rotation and threaded by a uniform magnetic field along the $z$ -axis, whose intensity is proportional to the column density of the cloud."492 The rotation axis is in the or2 plane aux makes an angle a with respect to the magnetic field., The rotation axis is in the $x-z$ plane and makes an angle $\alpha$ with respect to the magnetic field.493 For ease of presentation we define. in addition to the Cartesian coordinates (Gr.jg.2). evlindrical coordinates (στὡ.Z) with Z parallel to the initial rotation axis.," For ease of presentation we define, in addition to the Cartesian coordinates $(x,y,z)$, cylindrical coordinates $(\varpi,\phi,Z)$ with $Z$ parallel to the initial rotation axis."494 ALL simulations are characterized by four. parameters: the ratio of rotational over gravitational energy ( 0.03). the ratio of thermal over eravitational energy (22 0.25). the degree of magnetization fr. and the angle a.," All simulations are characterized by four parameters: the ratio of rotational over gravitational energy $\simeq0.03$ ), the ratio of thermal over gravitational energy $\simeq0.25$ ), the degree of magnetization $\mu$, and the angle $\alpha$."495 Only the ellects of cillerent ji. the mass-to- over critical mass-to-Iux ratio. and à are investigated in this work.," Only the effects of different $\mu$, the mass-to-flux over critical mass-to-flux ratio, and $\alpha$ are investigated in this work."496 The general outllow formation and dynamics are presented in Figure 1.., The general outflow formation and dynamics are presented in Figure \ref{figure1}.497 As the initially spherical. magnetized pre-stellar core. undergoes. gravitational collapse it Lattens preferentially along the magnetic field. lines. producing a dvnanically-collapsing. magnetized clise-like structure. orpscudo-dise.," As the initially spherical, magnetized pre-stellar core undergoes gravitational collapse it flattens preferentially along the magnetic field lines, producing a dynamically-collapsing, magnetized disc-like structure or."498. Following the isothermal collapse phase. an adiabatic core with densities Z101 and a radius ~10.20 AU. forms at the centre of the infalling envelope.," Following the isothermal collapse phase, an adiabatic core with densities $\gtrsim10^{10}$ and a radius $\sim10-20$ AU, forms at the centre of the infalling envelope."499 The ensuing build-up of a centrifugally supported dise (or simply dise)). with characteristic diameters 50200 AU. depends on the cllicieney of magnetic torques to remove angular momentum from the pseudo-disc.," The ensuing build-up of a centrifugally supported disc (or simply ), with characteristic diameters $\sim50-200$ AU, depends on the efficiency of magnetic torques to remove angular momentum from the pseudo-disc."500 In Hennebelle&Ciarei(2000) it was argued that the magnetic braking elliciency is proportional tof 7. where the characteristic scale-height h of the disc is in turn determined by the angle a between the initial magnetic field and rotation axis.," In \cite{hennebelle_disc_2009} it was argued that the magnetic braking efficiency is proportional to $h^{-1/2}$, where the characteristic scale-height $h$ of the disc is in turn determined by the angle $\alpha$ between the initial magnetic field and rotation axis."501 Increasing their nusalignment produces thicker pseudo-dises which are Less clliciently braked by the magnetic field. ancl thus. lead more easily to the formation of centrifugally supported discs.," Increasing their misalignment produces thicker pseudo-discs which are less efficiently braked by the magnetic field, and thus lead more easily to the formation of centrifugally supported discs."502" In general we find that outllows are launched. for all angles @ὉSO"" independently of the existence of a centrifugally supported. disc.", In general we find that outflows are launched for all angles $\alpha\lesssim80^{\circ}$ independently of the existence of a centrifugally supported disc.503 However when a90° the ejection of matter is essentially. suppressed. even when a disc is present.," However when $\alpha\sim90^{\circ}$ the ejection of matter is essentially suppressed, even when a disc is present."504 The remaining outward motions observed in the perpendicular configuration are particularly interesting because mass ejection does not. produce either à magnetic cavity. or a jet.," The remaining outward motions observed in the perpendicular configuration are particularly interesting because mass ejection does not produce either a magnetic cavity, or a jet."505 In fact. mass is not launched [rom the core. but the traces dense regions of the disc which are at a large radi [rom the core (~200 AU) and are being radiallv expelled by the highly twisted magnetic field.," In fact, mass is not launched from the core, but the traces dense regions of the disc which are at a large radii from the core $\sim200$ AU) and are being radially expelled by the highly twisted magnetic field."506 The outllowing gas propagates perpendicularlv to the rotation axis (see Figure 2)) and in the plane of the disc. with racial ejection and azimuthal speeds. ez80.," The outflowing gas propagates perpendicularly to the rotation axis (see Figure \ref{figure2}) ) and in the plane of the disc, with radial ejection and azimuthal speeds, $v_{\varpi}\approx v_{\phi}$."507" For a=SO the formation of bipolar outllow begins as he magnetic field lines. connecting the outer regions of the cloud to its rapidly. rotating inner regions. undergo strong shear which results in a significant azimuthal component (D,,) of the magnetic field being generated. close to the acliabatic core and. dise (if present)."," For $\alpha\lesssim80^{\circ}$ the formation of bipolar outflow begins as the magnetic field lines, connecting the outer regions of the cloud to its rapidly rotating inner regions, undergo strong shear which results in a significant azimuthal component $B_{\phi}$ ) of the magnetic field being generated close to the adiabatic core and disc (if present)."508 The growing magnetic »essure gradient accelerates the plasma. inflating bi-polar magnetic cavities within the infalling envelope.," The growing magnetic pressure gradient accelerates the plasma, inflating bi-polar magnetic cavities within the infalling envelope."509 At this stage rw ratio of MIID. Povnting to kinetic flux magnitudes. P=IPape? where ey is the component ofthe velocity »vpendicular to the magnetic field. and. the plasma-:. defined as the ratio of the thermal to magnetic pressure. are typically P~210. and 3~10%0.1 in the magnetic Ανν.," At this stage the ratio of MHD Poynting to kinetic flux magnitudes, $\Gamma = v_{\perp}B^{2}/2\pi\rho v^{3}$, where $v_{\perp}$ is the component of the velocity perpendicular to the magnetic field, and the $\beta$ , defined as the ratio of the thermal to magnetic pressure, are typically $\Gamma \sim 2-10$, and $\beta\sim10^{-3} - 0.1$ in the magnetic cavity."510" Such “magnetic tower"" structure is similar to that described by Lynden-Bell(2003). and re-produced in scaled laboratory experiments by Lebedev.ctal.(2005)... ancl it is inflated by the magnetic field. and is not. mechanically-riven by wide-angle winds."," Such “magnetic tower” structure is similar to that described by \cite{lynden-bell_discs_2003} and re-produced in scaled laboratory experiments by \cite{lebedev_magnetic_2005}, and it is inflated by the magnetic field and is not mechanically-driven by wide-angle winds."511" At the base of the cavity the continuous generation of £4, provides the Povnting [lux powering an outllow which originates from the core and a region extending several AU around it.", At the base of the cavity the continuous generation of $B_{\phi}$ provides the Poynting flux powering an outflow which originates from the core and a region extending several AU around it.512" Depending on the ejection ellicienev. which is measured by the ejection index £&c—dlInAM,fdinwz with M, the mass accretion rate through the disc. this outflow can be described as either centrifugallv or magnetic pressure driven (Ferreiraletierο"," Depending on the ejection efficiency, which is measured by the ejection index $\xi=d\ln\dot{M}_{a}/d\ln\varpi$ with $\dot{M_{a}}$ the mass accretion rate through the disc, this outflow can be described as either magneto-centrifugally or magnetic pressure driven \citep{ferreira_magnetized_1995}."513 As we shall see in the next section. the ejection clliciency increase in time and both launching regimes are attained during the simulations.," As we shall see in the next section, the ejection efficiency increase in time and both launching regimes are attained during the simulations."514" The collimation of this “cise” wind into a jet depends on the radial distribution of currents (c.g. Pudritzctal. 2006)). ancl therefore on the width of the magnetic cavity itself. which takes up the “return current” and the magnetic stresses associated with the £5, component of the magnetic field (e.g. Spruit 2000))."," The collimation of this “disc” wind into a jet depends on the radial distribution of currents (e.g. \citealt{pudritz_controllingcollimation_2006}) ), and therefore on the width of the magnetic cavity itself, which takes up the “return current” and the magnetic stresses associated with the $B_{\phi}$ component of the magnetic field (e.g. \citealt{spruit_theory_2009}) )."515 Llowever. the collimation of the magnetic tower depends in turn on the distribution of gas and magnetic Ποιά in the surrounding environment. which is swept up into a shock laver delineating the walls of the expanding magnetic tower.," However, the collimation of the magnetic tower depends in turn on the distribution of gas and magnetic field in the surrounding environment, which is swept up into a shock layer delineating the walls of the expanding magnetic tower."516 Therefore the medium through which the magnetic tower expands plavs as well an important role on the overall collimation of the outflow., Therefore the medium through which the magnetic tower expands plays as well an important role on the overall collimation of the outflow.517 Figure 2 shows theoutflows’ three-dimensional structure for cdillerent. a. indicating that increasing the misalignment leads to the," Figure \ref{figure2} shows theoutflows' three-dimensional structure for different $\alpha$ , indicating that increasing the misalignment leads to the"518the close encounters happen when the planetesimals are on eccentric orbits. the relative velocities involved are higher. and the inclinations resulting from the scattering events are much greater than for figure 6aa. During this simulation. of the bodies were accreted by the central star. and by the migrating planet.,"the close encounters happen when the planetesimals are on eccentric orbits, the relative velocities involved are higher, and the inclinations resulting from the scattering events are much greater than for figure \ref{fig:all_BW}a a. During this simulation, of the bodies were accreted by the central star, and by the migrating planet."519 If we increase the planet mass even further. the capture probability reaches almost unity. and the vast majority of planetesimals get stuck in a resonance far away from the planet.," If we increase the planet mass even further, the capture probability reaches almost unity, and the vast majority of planetesimals get stuck in a resonance far away from the planet."520 As they are dragged along and their eccentricities go up. they are protected from a close encounter with the planet for some time. since they are so far away.," As they are dragged along and their eccentricities go up, they are protected from a close encounter with the planet for some time, since they are so far away."521 It turns out. almost all these bodies will reach e>>0.9. and are accreted by the central star before they have time to be scattered by the migrating planet.," It turns out, almost all these bodies will reach $e\gg0.9$, and are accreted by the central star before they have time to be scattered by the migrating planet."522 An example of this scenario is shown in figure 5.., An example of this scenario is shown in figure \ref{fig:epumping}.523 This means. that in the systems where you would expect to find the highest relative velocities (and therefore the highest inclinations) the majority of the planetesimals are actually lost to the central object.," This means, that in the systems where you would expect to find the highest relative velocities (and therefore the highest inclinations) the majority of the planetesimals are actually lost to the central object."524 A way to get around this. might be to put an additional. stationary planet close to the central star. which will scatter the highly excited planetesimals before they come too close to the central object.," A way to get around this, might be to put an additional, stationary planet close to the central star, which will scatter the highly excited planetesimals before they come too close to the central object."525 This planet could not be too massive. as this would lead to it ejecting the planetesimals on hyperbolic orbits.," This planet could not be too massive, as this would lead to it ejecting the planetesimals on hyperbolic orbits."526 In this study we have restricted ourselves to single-planet systems. but the study of stellar systems with multiple planets. one of which is migrating. might be very interesting indeed.," In this study we have restricted ourselves to single-planet systems, but the study of stellar systems with multiple planets, one of which is migrating, might be very interesting indeed."527 Another way to protect the planetesimals from accretion by the central star would be to introduce a gas drag. which would dampen the eccentricities.," Another way to protect the planetesimals from accretion by the central star would be to introduce a gas drag, which would dampen the eccentricities."528 The effect of gas of the results is further discussed in section??.., The effect of gas of the results is further discussed in section\ref{sec:discussion}.529 From section ??. we know that the capture probability also depends on the migratior rate of the planet., From section \ref{sec:rescap} we know that the capture probability also depends on the migration rate of the planet.530 We have therefore conducted a small parameter study. where the migration rate and planet mass have been varied.," We have therefore conducted a small parameter study, where the migration rate and planet mass have been varied."531 In total we carried out 12 simulations with the planet-mass ranging from 0.1—20Mnop and € between 7.3x107—7.3x107°AUνι].," In total we carried out 12 simulations with the planet-mass ranging from $0.1-20M_{\rm Nep}$ and $\xi$ between $7.3\times10^{-4}-7.3\times10^{-6}\rm \, AU\,yr^{-1}$."532 Table | shows the characteristics of planetesimal populations after migration has taken place. as well as the fraction of planetesimals which have bee! lost during the integration.," Table \ref{table:simulations} shows the characteristics of planetesimal populations after migration has taken place, as well as the fraction of planetesimals which have been lost during the integration."533" Both higher planet mass and lower migration rate appear to ensure high average inclinations,", Both higher planet mass and lower migration rate appear to ensure high average inclinations.534 This is the case because: 1) massive planets are more capable of scattering planetesimals into highly-inclined orbits (see section ??)). and 2) relatively massive planets and low migration rates increase the probability of resonance capture. allowing for more eccentricity-pumping and a higher relative velocity between the planetesimal and the planet during the close encounter.," This is the case because; 1) massive planets are more capable of scattering planetesimals into highly-inclined orbits (see section \ref{sec:scattering}) ), and 2) relatively massive planets and low migration rates increase the probability of resonance capture, allowing for more eccentricity-pumping and a higher relative velocity between the planetesimal and the planet during the close encounter."535 However. if the combination of migration rate and planet mass causes the planetesimals to get stuck in a resonance too far. they are likely to be lost to the central star before having a close encounter with the migrating planet.," However, if the combination of migration rate and planet mass causes the planetesimals to get stuck in a resonance too far, they are likely to be lost to the central star before having a close encounter with the migrating planet."536 Section ?? has left us with populations of planetesimals and constraints on their orbital parameters., Section \ref{sec:simulations} has left us with populations of planetesimals and constraints on their orbital parameters.537 Section ?? will calculate the time scales on which these planetesimals should collide and form dust. and section ?? will estimate the total mass and surface area of the dust size distribution resulting from the collisional cascade.," Section \ref{sec:colltimes} will calculate the time scales on which these planetesimals should collide and form dust, and section \ref{sec:dsd} will estimate the total mass and surface area of the dust size distribution resulting from the collisional cascade."538 Suppose we have N planetesimals of radius R. mass i and a geometrical cross-section for collisions of ej=4xR. flying around in some volume V.," Suppose we have $N$ planetesimals of radius $R$ , mass $m$ and a geometrical cross-section for collisions of $\sigma_{\rm coll} = 4\pi R^2$, flying around in some volume $V$."539 We can define the sweeping time as whereVeoll collveo is. the collision.uU velocity. between. the planetesimals., We can define the sweeping time as where $v_{\rm coll}$ is the collision velocity between the planetesimals.540 Since the populations from table | show pretty eccentric orbits. the collision velocity will vary a lot between collisions. but for the purpose of this calculation we estimate it as with 7 between 0.5 and 2.," Since the populations from table \ref{table:simulations} show pretty eccentric orbits, the collision velocity will vary a lot between collisions, but for the purpose of this calculation we estimate it as with $\eta$ between 0.5 and 2."541 For two nearly circular orbits η is determined by the vertical component of the individual velocities (2).., For two nearly circular orbits $\eta$ is determined by the vertical component of the individual velocities \citep{dominik03}.542 But since the orbits in our populations are eccentric and randomly oriented. 17 will lie closer to. V2.," But since the orbits in our populations are eccentric and randomly oriented, $\eta$ will lie closer to $\sqrt{2}$ ."543 If we assume the volume is wedge-shaped and lies between an Inner and an outer radius. 7j and roy. and has a normalized height of ή=H/r. we can write it às where h=tanq.," If we assume the volume is wedge-shaped and lies between an inner and an outer radius, $r_{\rm in}$ and $r_{\rm out}$, and has a normalized height of $h=H/r$, we can write it as where $h=\tan{i_{\rm max}}$."544 We have to think carefully about 7j; and rou., We have to think carefully about $r_{\rm in}$ and $r_{\rm out}$.545 One might insert the minimum and maximum values of the semi-major axis found in the resulting populations. but this is not correct since most comets are on pretty eccentric orbits.," One might insert the minimum and maximum values of the semi-major axis found in the resulting populations, but this is not correct since most comets are on pretty eccentric orbits."546 On the other hand. choosing rou to be equal to eal+Cmax) will increase the volume drastically even though only one planetesimal is able to get to ray.," On the other hand, choosing $r_{\rm out}$ to be equal to $a_{\rm max}(1+e_{\rm max})$ will increase the volume drastically even though only one planetesimal is able to get to $r_{\rm out}$."547 It makes more sense to define something like where (ag) and (e) can be taken from table {.., It makes more sense to define something like where $\langle a\rangle$ and $\langle e\rangle$ can be taken from table \ref{table:simulations}.548" We approximate c,~Via). which is found to work well for most populations in table Τ.."," We approximate $\sigma_{a} \sim \sqrt{\langle a\rangle}$, which is found to work well for most populations in table \ref{table:simulations}."549 The collision time for the comets will become with N'the number of bodies being constrained by the total mass of the population M where p denotes pethe density of the planetesimal material., The collision time for the comets will become with the number of bodies being constrained by the total mass of the population $M$ where $\rho$ denotes the density of the planetesimal material.550 We can now calculate the collision time scale for different populations., We can now calculate the collision time scale for different populations.551 A promising case for creating a halo-like structure appears tobe M2. which has high inclinations but is.still located relatively close to the star.," A promising case for creating a halo-like structure appears tobe M2, which has high inclinations but isstill located relatively close to the star."552 From table 1. we find (a)=8.61 AU. (e)=0.538 and fay= 35.257.," From table \ref{table:simulations} we find $\langle a\rangle=8.61$ AU, $\langle e\rangle=0.538$ and $i_{\rm max}=35.25^{\circ}$ ."553 For this specific configuration of comets. the collision time becomes," For this specific configuration of comets, the collision time becomes"554expansion is We are now interested in comparing this Gime to the lifetime of a star.,expansion is We are now interested in comparing this time to the lifetime of a star.555" The lifetime can be expressed in terms of (he efficiency of generating enereyv [rom nuclear reactions. e. and the fraction of the Edclington Inminosity ad which the star radiates energy. 6,"," The lifetime can be expressed in terms of the efficiency of generating energy from nuclear reactions, $\epsilon$, and the fraction of the Eddington luminosity at which the star radiates energy, $\ell$."556" The Eddington luminosity of a star of mass M is given by where jf, is the mean mass per electron (71.2, for the fully ionized primordial mixture ol hvdrogen and helium).", The Eddington luminosity of a star of mass $M$ is given by where $\mu_e$ is the mean mass per electron $ \simeq 1.2 m_p$ for the fully ionized primordial mixture of hydrogen and helium).557 The stellar lifetime is llence. the ratio of the age of the universe to the stellar lifetime when the cosmic acceleration starts is This solves. at least in part. the coincidence problem: the ratio of (he age of (he universe to the stellar lifetime does not depend on the extremely small values of the particle masses (vellecting the weakness of eravitv when we use Planck units).," The stellar lifetime is Hence, the ratio of the age of the universe to the stellar lifetime when the cosmic acceleration starts is This solves, at least in part, the coincidence problem: the ratio of the age of the universe to the stellar lifetime does not depend on the extremely small values of the particle masses (reflecting the weakness of gravity when we use Planck units)."558 It is (erefore not so surprising that Che (wo times turi out to be comparable. even though they still depend on (quantities that are far [rom unity: the ratio of the electron to proton mass. the fine-structure constant. the efficiency. of nuclear reactions. and the fraction of the Edclington Iuminosity at which a certain star radiates.," It is therefore not so surprising that the two times turn out to be comparable, even though they still depend on quantities that are far from unity: the ratio of the electron to proton mass, the fine-structure constant, the efficiency of nuclear reactions, and the fraction of the Eddington luminosity at which a certain star radiates."559 The fraction ( is close to unitv for massive stars. it is 6=101 for the Sun. and drops to 6~10.* for the lowest mass stars that are still able to ignite nuclear reactions.," The fraction $\ell$ is close to unity for massive stars, it is $\ell = 10^{-4.6}$ for the Sun, and drops to $\ell \sim56010^{-7}$ for the lowest mass stars that are still able to ignite nuclear reactions."561 The conjecture proposed by Afshordi (2010) that the invisible tension in the universe arises [rom a gravitational aether (hal acquires a negative pressure from (he existence of astrophysical black holes implies (hat (his invisible tension scales as my., The conjecture proposed by Afshordi (2010) that the invisible tension in the universe arises from a gravitational aether that acquires a negative pressure from the existence of astrophysical black holes implies that this invisible tension scales as $m_p^{-6}$.562 This provides an automatic explanation for why (he acceleration of (he expansion of the universe is starting, This provides an automatic explanation for why the acceleration of the expansion of the universe is starting563It is our unhappy luck that even though we live in three dineusions. we are forced oO view inost of the Universe as a two ciumenusional projection with oulv one dimension of velocity information.,"It is our unhappy luck that even though we live in three dimensions, we are forced to view most of the Universe as a two dimensional projection with only one dimension of velocity information."564 As such. we know very little about the moticmus of the thiugs around us in any direction other than radialv outward.," As such, we know very little about the motions of the things around us in any direction other than radially outward."565 A inore colmprehcusive view of motions in the Universe woul xovide a unique probe iuo the history aud future of he things around us., A more comprehensive view of motions in the Universe would provide a unique probe into the history and future of the things around us.566 Iudeed. wihin the Milkv Wav. he IIIPPARCOS (Perrvinan&ESA1997) aud near-uture GATA (Perrvinan2402). nmüssious have brough about a rebirth in the ancieit field of astrometry. pushine accuracies for direct propor motion measurements cowl first to imas/vear precison aud then on to tens of pas/vyoar.," Indeed, within the Milky Way, the HIPPARCOS \citep{perryman97} and near-future GAIA \citep{perryman02} missions have brought about a rebirth in the ancient field of astrometry, pushing accuracies for direct proper motion measurements down first to mas/year precision and then on to tens of $\mu$ as/year."567 The prospect of illious of stars with full G-D jnse-pajce motion known for au appreciable Yaction of: the Galaxy has allowed astrouoimners to xopose ucasurnug Galactic structure (c.g. and recovering Galactic history (c.g.Heli&deZeeweWwJOO} iu uupreceeuted detail., The prospect of billions of stars with full 6-D phase-spa<ce motion known for an appreciable fraction of the Galaxy has allowed astronomers to propose measuring Galactic structure \citep[e.g.][]{johnston99} and recovering Galactic history \citep[e.g.][]{helmi00} in unprecedented detail.568 Similar measureueuts of the full phase-space positions of objects throughout aud bevoud the Local Group would allow an analogous recoustruction of the masses and wast interaction of these ojects and test the existence Mf large-scale flows in the Universe (seeShavaetal.2003.foraninvestisatioionLocalCroup scales)., Similar measurements of the full phase-space positions of objects throughout and beyond the Local Group would allow an analogous reconstruction of the masses and past interaction of these objects and test the existence of large-scale flows in the Universe \citep[see][for an investigation on Local Group scales]{shaya03}.569 Cosmological sinilations of structure formation suggest iat the peculiar velocity cistribution of galaxy clusters jas τοῦποπαare spread of Tee~ 500 Ikan/s (Sheth&Diaferio 2001).. correspowing to proper motion scales or Galaxy clusters at distaice d. frou us of At first sight. this sugeestsOO that the next generation of astrometric missions would have sufficient precision to detect these transverse motions.," Cosmological simulations of structure formation suggest that the peculiar velocity distribution of galaxy clusters has root-mean-square spread of $\sigma_{\rm pec} \sim$ 500 km/s \citep{sheth01}, corresponding to proper motion scales for galaxy clusters at distance $d$ from us of At first sight, this suggests that the next generation of astrometric missions would have sufficient precision to detect these transverse motions."570 However. prospects for direct measurements remain dim both because individual ealaxies are extended aud galaxy clusters have larec internal velocity dispersious.," However, prospects for direct measurements remain dim both because individual galaxies are extended and galaxy clusters have large internal velocity dispersions."571 As an alternative to direct uxasuremaents of propor motions of nearbystellar clusters. Galactic astronomers have traditionally cuyploved a ireat ecomctrical trick that allows them to infer the motion of an object in three-dinieusious frou linc-of-ieht velocities alone.," As an alternative to direct measurements of proper motions of nearby clusters, Galactic astronomers have traditionally employed a neat geometrical trick that allows them to infer the motion of an object in three-dimensions from line-of-sight velocities alone."572 The method relies on the fact that the projection of the transverse inmotion iuto the linc-ofsight will induce a eracdicut in the average line-of-sielt velocities 1ieasured across anv extended object al effect known as known “perspective rotation” (hereafterPRFeastοἳal. 1961).., The method relies on the fact that the projection of the transverse motion into the line-of-sight will induce a gradient in the average line-of-sight velocities measured across any extended object — an effect known as known “perspective rotation” \citep[hereafter PR ---][]{1961Feast}.573 PR has been used to verify iieastrelents of the proper motion of the elobular cluster Omega Centauri (Merrittetal.1997).. as well as the «istance to the Large Magellanic Cloud (Could2000...," PR has been used to verify measurements of the proper motion of the globular cluster Omega Centauri \citep{1997Merritt}, as well as the distance to the Large Magellanic Cloud \citep{2000Gould}."574 Most receutlv. hkapliughat&Strigari(2008) poiuted out tji there are now suffiicicut spectra takeri for stars in nearby dwarf spheroidal galaxies for a pi‘ecision of ~ LOO kms iu tangential velocity estimates to be possible.," Most recently, \citet{2008Kaplinghat} pointed out that there are now sufficient spectra taken for stars in nearby dwarf spheroidal galaxies for a precision of $\sim$ 100 km/s in tangential velocity estimates to be possible."575" Walkeretal.(2008). subsequently verifed this asserjon with estimates for the motion of Forax, and Cariii flat agreed with prior astrometric mie:wsurments aud the first hrec-dimensional niecasuremoeut o ‘the motion of Sextaus.", \citet{walker08} subsequently verified this assertion with estimates for the motion of Fornax and Carina that agreed with prior astrometric measurments and the first three-dimensional measurement of the motion of Sextans.576 Thev also made estimates for Scitilptors proper motion hat disagreed with prior work his disagreement could ο explained as coutamination w Sculptors intrinsic rotatiou., They also made estimates for Sculptor's proper motion that disagreed with prior work — this disagreement could be explained as contamination by Sculptor's intrinsic rotation.577 To date. M31 is the most distant object that PR js been neasured for (usingfjeline-ofsightveloci-&Cuhathakurta2008) and this study represents over au order-ofanaenitude leap i ithe cistauce to which such aieasurement had been attempted.," To date, M31 is the most distant object that PR has been measured for \citep[using the line-of-sight velocities of 17 of its satellite galaxies, see][]{2008VanDerMarel} — and this study represents over an order-of-magnitude leap in the distance to which such a measurement had been attempted."578 However. there is no limit iu principle to the distance of objects for which this technique could prove useful.," However, there is no limit in principle to the distance of objects for which this technique could prove useful."579 Iudeed. may nearby clusters of galaxies have angular sizes of the sale order-ofinagitucde as M31s satellite svstem. witli mcasurements of line-ofsight velocities of huudreds of," Indeed, many nearby clusters of galaxies have angular sizes of the same order-of-magnitude as M31's satellite system, with measurements of line-of-sight velocities of hundreds of"580With these assumptions in hand. I proceed (o describe the interaction of the jets with the surrounding inflowing gas. as was done in Paper 2.,"With these assumptions in hand, I proceed to describe the interaction of the jets with the surrounding inflowing gas, as was done in Paper 2."581 If the jets penetrate through the surrounding gas they will be eollimated bv that gas. and. two narrow collimated fast jets will be formed. similar to the flow structure in the simulations of Sutherland Bicknell (2007) for ACN jets. and of MacFadven οἱ al. (," If the jets penetrate through the surrounding gas they will be collimated by that gas, and two narrow collimated fast jets will be formed, similar to the flow structure in the simulations of Sutherland Bicknell (2007) for AGN jets, and of MacFadyen et al. ("5822001) for CCSN.,2001) for CCSN.583 If. on the other hand. the jels cannot penetrate the surrounding eas (μον will deposit their enerey in the inner region.," If, on the other hand, the jets cannot penetrate the surrounding gas they will deposit their energy in the inner region."584 Two hot bubbles (that mieht merge to one almost spherical bubble) will be formed that will accelerate (he surrounding gas and form a SMW outflow. as was studied in Paper 1.," Two hot bubbles (that might merge to one almost spherical bubble) will be formed that will accelerate the surrounding gas and form a SMW outflow, as was studied in Paper 1."585 The conditions for the jets not to cool are derived in section 3.1.. while the conditions for the jets nol to penetrate the surrounding gas but rather form a 9MW outflow are derived insection 3.2..," The conditions for the jets not to cool are derived in section \ref{subsec:cooling}, while the conditions for the jets not to penetrate the surrounding gas but rather form a SMW outflow are derived insection \ref{subsec:pen}."586 Based on the results of Itoh et al. (, Based on the results of Itoh et al. (5871989. 1996). IXohri et al. (,"1989, 1996), Kohri et al. ("5882005). ancl the approximate equation eiven by MacFadyen Wooslev (1999). I approximate (he neutrino cooling rate by ] will consider first the possibility that the narrow jets are shocked within the convective region al r~50—200km [found in the simulations of Ott et al. (,"2005), and the approximate equation given by MacFadyen Woosley (1999), I approximate the neutrino cooling rate by I will consider first the possibility that the narrow jets are shocked within the convective region at $r \sim 50-200 \km$ found in the simulations of Ott et al. ("5892009).,2009).590" Taking a mass of ~Q.1AZ. to be shocked inside a radius of <100km. and reside inside two bubbles that occupypart of the spherical volume. V.ον10?!em. the density is p,~LOMοem?."," Taking a mass of $\sim 0.1 M_\odot$ to be shocked inside a radius of $<100 \km$, and reside inside two bubbles that occupypart of the spherical volume, $V \sim 10^{21} \cm^3$, the density is $\rho_b \sim 10^{11} \g \cm^{-3}$."591 The total energv carried by neutrinos in a time M is where .M is given in seconds., The total energy carried by neutrinos in a time $\Delta t$ is where $\Delta t$ is given in seconds.592 The infalling gas is accelerated to a velocity of ~10!kms1 and the relevant interaction radius is ~10km., The infalling gas is accelerated to a velocity of $\sim 10^4 \km \s^{-1}$ and the relevant interaction radius is $\sim 10^3 \km$.593 Therelore. M~0.1s.," Therefore, $\Delta t \sim 0.1 \s$."594 to be negligible compared with the jets’ energv ~10?!erg. the temperature of the shocked jets should be T<4x10!K.," to be negligible compared with the jets' energy $\sim 10^{51} \erg$, the temperature of the shocked jets should be $T \la 4 \times 10^{10} \K$."595 This limits the pre-shock jets’ velocity. (assiumning the material was already. disintegrated to nucleons) to e;Zi5x10!kms ο., This limits the pre-shock jets' velocity (assuming the material was already disintegrated to nucleons) to $v_f \la 5 \times 10^4 \km \s^{-1}$ .596 This velocity is too low for the mechanism. proposed here., This velocity is too low for the mechanism proposed here.597Two different problems in the context of mass loss in late stages of stellar evolution are investigated.,Two different problems in the context of mass loss in late stages of stellar evolution are investigated.598 In the first case the primary's extended envelope fills its Roche lobe and the gas flows in a narrow stream towards the secondary., In the first case the primary's extended envelope fills its Roche lobe and the gas flows in a narrow stream towards the secondary.599 This could be the case when the is in , This could be the case when the companion is in periastron.600We also use this model to test ourcompanion numerical model., We also use this model to test our numerical model.601periastron. Mass transfer in the second model is driven by a massive wind that is captured by a detached companion star., Mass transfer in the second model is driven by a massive wind that is captured by a detached companion star.602" This is an important mechanism for the formation of accretion disks in detached binaries, symbiotic stars and massive X-ray binariesinteracting ?2).."," This is an important mechanism for the formation of accretion disks in detached interacting binaries, symbiotic stars and massive X-ray binaries \citep[see e.g.][]{1984Obs...104..152L,2004MNRAS.350.1366S}."603 We follow the gas flow in the orbital plane of the system using 2-dimensional hydrodynamical simulations that allows us to resolve the large density contrasts close to the secondary., We follow the gas flow in the orbital plane of the system using 2-dimensional hydrodynamical simulations that allows us to resolve the large density contrasts close to the secondary.604 We limit our wind accreting model to the orbital plane of the binary system where the wind is focused forming an equatorial outflow that has a significant density enhancement compared with the regions further polewards (?).. , We limit our wind accreting model to the orbital plane of the binary system where the wind is focused forming an equatorial outflow that has a significant density enhancement compared with the regions further polewards \citep{2008A&A...484L...9W}. .605In Fig. D].," In Fig. \ref{fig:roche},"606 we show a diagram of the Roche potential in the equatorial for a mass ratio q=1., we show a diagram of the Roche potential in the equatorial plane for a mass ratio $q=1$.607" planeThe basic equations of hydrodynamics describing the evolution of the density and velocity field are: where p is the density in the orbital plane, v the velocity of the fluid, p the pressure and Φ the gravitational potential."," The basic equations of hydrodynamics describing the evolution of the density and velocity field are: where $\rho$ is the density in the orbital plane, $\mvect{v}$ the velocity of the fluid, $p$ the pressure and $\Phi$ the gravitational potential."608 Both stellar gravity potentials were approximated as point masses., Both stellar gravity potentials were approximated as point masses.609 To avoid numerical problems close to the stars the potential is softened using the function: where the ε was set to 0.01 units in our simulations with smoothingstandardlength resolution., To avoid numerical problems close to the stars the potential is softened using the function: where the smoothing length $\epsilon$ was set to 0.01 length units in our simulations with standard resolution.610 The unit of length in our calculations corresponds to the separation between the stars., The unit of length in our calculations corresponds to the separation between the stars.611 In our higher resolution simulations the number of grid zones in the accretion was ~200., In our higher resolution simulations the number of grid zones in the accretion region was $\sim 200$.612 The surface of the compact accretor was not regionresolved in our models., The surface of the compact accretor was not resolved in our models.613" Our code is based on (?),, which is a fully parallel block-structured Adaptive Mesh Refinement (AMR) implementation of the Piecewise Parabolic Method (PPM) (??) in its original Eulerian form?."," Our code is based on \citep{2000ApJS..131..273F}, which is a fully parallel block-structured Adaptive Mesh Refinement (AMR) implementation of the Piecewise Parabolic Method (PPM) algorithm \citep{1984JCP...54..115,1984JCP...54..174} in its original Eulerian form."614. The code has algorithmbeen extensively tested in various compressible flow problems with astrophysical applications (seee.g.??)..," The code has been extensively tested in various compressible flow problems with astrophysical applications \citep[see e.g.][]{2002ApJS..143..201C,2006MNRAS.370..529D}."615" For numerical convenience we introduce dimensionless units, where the binary separation d is taken as the unit of length."," For numerical convenience we introduce dimensionless units, where the binary separation $d$ is taken as the unit of length."616 The unit of time is calculated from the orbital angular frequency C of the system., The unit of time is calculated from the orbital angular frequency $\Omega_{\mathrm{b}}$ of the system.617" The orbital period of the system is then defined by Each simulation was run for about 10 orbital periods, when the system has reached a quasi-equilibrium state."," The orbital period of the system is then defined by Each simulation was run for about 10 orbital periods, when the system has reached a quasi-equilibrium state."618 The evolutionary time of the results discussed in Section] will be given in units of Py., The evolutionary time of the results discussed in Section \ref{sec:results} will be given in units of $P_{\mathrm{b}}$.619 We normalize all physical quantities for numerical convenience., We normalize all physical quantities for numerical convenience.620 The gravitational constant G is set to one as is done frequently in relativistic calculations., The gravitational constant $G$ is set to one as is done frequently in relativistic calculations.621 Eq., Eq.622" 6, can be considered as a normalization condition for the unit of mass to be the sum of the stellar masses M=MA+Mg.", \ref{eq:kepler} can be considered as a normalization condition for the unit of mass to be the sum of the stellar masses $M = M_{\rm A} + M_{\rm B}$.623 Our implementation of the code uses polar coordinates and was run in both the coordinate system corotating with the angular speed of the system and in the inertial frame., Our implementation of the code uses polar coordinates and was run in both the coordinate system corotating with the angular speed of the system and in the inertial frame.624" In addition to the usual hydrodynamic quantities, our model includes the gravity of both stars, and the Coriolis and centrifugal forces."," In addition to the usual hydrodynamic quantities, our model includes the gravity of both stars, and the Coriolis and centrifugal forces."625 The code is based on release 2.5 of with customized modules for the equation of state and gravity forces that explicitly conserve angular momentum transport (?)., The code is based on release 2.5 of with customized modules for the equation of state and gravity forces that explicitly conserve angular momentum transport \citep{1998A&A...338L..37K}.626 This is particularly important when large density gradients are present in the wind., This is particularly important when large density gradients are present in the wind.627 The Coriolis forces were treated conservatively as described by ?.., The Coriolis forces were treated conservatively as described by \citet{1998A&A...338L..37K}.628 A Courant number of 0.7 was used in the simulations., A Courant number of 0.7 was used in the simulations.629" We use an equation of state for an ideal gas with ratio of specific heats between y=1—5/3 to represent more realistic cases that include radiative cooling, and a modified isothermal Riemann solver ported from the AMRA code (?).. "," We use an equation of state for an ideal gas with ratio of specific heats between $\gamma = 1-5/3$ to represent more realistic cases that include radiative cooling, and a modified isothermal Riemann solver ported from the AMRA code \citep{2001CPC..138..101}. ."630"We ignore magnetic fields, radiation transfer or explicit Navier-Stokes viscosity in our models."," We ignore magnetic fields, radiation transfer or explicit Navier-Stokes viscosity in our models."631 has a small numerical viscosity that has been estimated by ?.., has a small numerical viscosity that has been estimated by \citet{2007A&A...471.1043D}.632 Non-axisymmetric effects on the tidally enhanced wind may be caused by magnetic fields., Non-axisymmetric effects on the tidally enhanced wind may be caused by magnetic fields.633 It is likely that stellar winds in AGB stars are primarily radial since the extended envelope cannot have significant rotation (?).., It is likely that stellar winds in AGB stars are primarily radial since the extended envelope cannot have significant rotation \citep{2002MNRAS.329..204S}.634 The MHD collimation of the wind is a very efficient mechanism and can be more important than gravitational focusing (??)..," The MHD collimation of the wind is a very efficient mechanism and can be more important than gravitational focusing \citep{2000ApJ...544..336G,2001ApJ...560..928G}."635" However, MHD effects are not included in our calculations since there are presently no constraints on the magnetic fields in symbiotic systems."," However, MHD effects are not included in our calculations since there are presently no constraints on the magnetic fields in symbiotic systems."636" At the AGB phase, it is unlikely that a globally ordered magnetic field strongly affects the dynamics of the wind."," At the AGB phase, it is unlikely that a globally ordered magnetic field strongly affects the dynamics of the wind."637 The formation of an accretion disk can be affected by accretion onto the secondary., The formation of an accretion disk can be affected by accretion onto the secondary.638 In the case of a reflecting boundary the stream bounces off the stellar surface and orbits the accretor., In the case of a reflecting boundary the stream bounces off the stellar surface and orbits the accretor.639" However, if no mass is allowed to accrete onto the the orbiting disk continues to increase as the simulation secondarycontinues."," However, if no mass is allowed to accrete onto the secondary the orbiting disk continues to increase as the simulation continues."640 We use a mechanism that allows us to remove gas from the vicinity of the secondary., We use a mechanism that allows us to remove gas from the vicinity of the secondary.641 The accretion is accounted for by removing some mass from the region defined |r—rg|<rac and adding it to the mass of the star to calculateby the gravitational forces., The accretion is accounted for by removing some mass from the region defined by $|\mathbf{r}-\mathbf{r}_\mathrm{B}|< r_\mathrm{acc}$ and adding it to the mass of the star to calculate the gravitational forces.642 The goal was to obtain a quasi-stable configuration and to be able to estimate the accretion rate onto the accretor., The goal was to obtain a quasi-stable configuration and to be able to estimate the accretion rate onto the accretor.643 The size of the accretion region gcc is defined as a fraction of the Hill radius of the mass accretor., The size of the accretion region $r_\mathrm{acc}$ is defined as a fraction of the Hill radius of the mass accretor.644" In most of our simulations the accretion radius 1S acc=0.1Rp, where Ry is the Hill radius of the secondary The mass is removed from the disk after each time step using the expression (?) where is a constant fractionof the order unity, At denotes the timestepf and pay is the average densityin the region"," In most of our simulations the accretion radius is $r_\mathrm{acc} = 0.1 R_\mathrm{H}$, where $R_\mathrm{H}$ is the Hill radius of the secondary The mass is removed from the disk after each time step using the expression \citep{2002A&A...387..550G}645 where $f$ is a constant fractionof the order unity, $\Delta t$ denotes the timestep and $\rho_\mathrm{av}$ is the average densityin the region"646"where τμ is (he Bond albedo. £L, the parent stellar Iuminosity. and d (he distance from the parent star.","where $A_B$ is the Bond albedo, $L_*$ the parent stellar luminosity, and $d$ the distance from the parent star."647 The factor e is a crude. first-order. correction in (he case where an atmosphere is assumed (lor zero-atmosphere e=1).," The factor $\epsilon$ is a crude, first-order, correction in the case where an atmosphere is assumed (for zero-atmosphere $\epsilon =1$ )."648 It incorporates the infrared optical depth. and for a present-day Earth-tvpe atmosphere εν0.62 (e.g. MeGulffie&ILenderson-Sellers(2005))).," It incorporates the infrared optical depth, and for a present-day Earth-type atmosphere $\epsilon \simeq 0.62$ (e.g. \citet{mcguffie05}) )."649 The fast-rotating approximation should be a Lair one when applied to moons of giant planets aligned wilh the system orbital plane. since while they should have svnchronous spin-orbits (as is (he case for the Galilean satellites) the combination of their orbital period with that of their host planet will (vpically result in rapidly chaneine. and generally unilorm insolation across (he moon surfaces.," The fast-rotating approximation should be a fair one when applied to moons of giant planets aligned with the system orbital plane, since while they should have synchronous spin-orbits (as is the case for the Galilean satellites) the combination of their orbital period with that of their host planet will typically result in rapidly changing, and generally uniform insolation across the moon surfaces."650" For moon svstems al significant inclination {ο the svstem plane there is the potential for much more static stellar insolation. we have not considered this situation. but note that the slow-rotating Zi, is only a [actor of V2 larger than that for a [ast-rotating body."," For moon systems at significant inclination to the system plane there is the potential for much more static stellar insolation, we have not considered this situation, but note that the slow-rotating $T_{eq}$ is only a factor of $\sqrt{2}$ larger than that for a fast-rotating body."651 We have also examined (he potential eclipse. or shadowing. times of moons by the host planet. assuming all moon orbits lie in the planetary svstem plane.," We have also examined the potential eclipse, or shadowing, times of moons by the host planet, assuming all moon orbits lie in the planetary system plane."652 These range from e12% to ~Q.1 of the total moon orbital period. for close-in (a7POP ) and outer (a2)ouler moons respectively.," These range from $\sim 12$ to $\sim 0.1$ of the total moon orbital period, for close-in $a_s^{inner}$ ) and outer $a_s^{outer}$ ) moons respectively."653 In (he case of close-in moons (as defined by Equation 1) the actual shadow time is typically ~20 minutes. compared to 5 hours for the outermost allowed moons in the saniple.," In the case of close-in moons (as defined by Equation 1) the actual shadow time is typically $\sim 20$ minutes, compared to $\sim 5$ hours for the outermost allowed moons in the sample."654 We therefore ienore this effect in considering the first-order. long terim. impact of stellar insolation on moon and satellite svstems.," We therefore ignore this effect in considering the first-order, long term, impact of stellar insolation on moon and satellite systems."655 A major source of uncertainty is whether or not an atmosphere is included in the estimation of surface conditions., A major source of uncertainty is whether or not an atmosphere is included in the estimation of surface conditions.656 Since we are first concerned here with the potential vacuum sublimation of surface volatiles. and the impact on moon characteristics. we assune conditions aud set e=1.," Since we are first concerned here with the potential vacuum sublimation of surface volatiles, and the impact on moon characteristics, we assume zero-atmosphere conditions and set $\epsilon=1$."657 Stellar Iumninosiüies are compiled [ον our exoplanet sample [rom the on-line catalog ancl sources described in 82., Stellar luminosities are compiled for our exoplanet sample from the on-line catalog and sources described in 2.658 Where luminosities are not directly available we have estimated them using the reported optical magnitudes and distances., Where luminosities are not directly available we have estimated them using the reported optical magnitudes and distances.659" The total range is 0.29<L,/L.4.59 with a mean of 1.66L.."," The total range is $0.29 <660\rm{L}_*/\rm{L}_{\odot} < 4.59$ with a mean of $1.66$ $_{\odot}$."661" We then compute the orbital ranges for T,«110 IK. 110 WW. 2173«T,,<373 kk. and T;,>373 Ik. assuming albedo's of either sly=0.63. commensurate with that of Europa. or 0.3 commensurate with that of a mixed surface. such as the Earth."," We then compute the orbital ranges for $T_{eq}<170$ K, $170$ $<T_{eq}<273$ K, $273<T_{eq}< 373$ K, and $T_{eq}>373$ K, assuming albedo's of either $A_B=0.68$, commensurate with that of Europa, or $0.3$ commensurate with that of a mixed surface, such as the Earth."662" As described above. we have not included the effect of an atmosphere on T;,."," As described above, we have not included the effect of an atmosphere on $T_{eq}$."663 The orbital parameters (αμ. ο. P) of the sample exoplanets are used to evaluate the amount of time each planet spends within a given zone. ancl to evaluate time averaged fluxes and temperatures.," The orbital parameters $a_p$, $e$, $P$ ) of the sample exoplanets are used to evaluate the amount of time each planet spends within a given zone, and to evaluate time averaged fluxes and temperatures."664 In both cases we are effectively. assuming no time latency in reaching an, In both cases we are effectively assuming no time latency in reaching an665this function. which is dominated by the convolution with the redshift error distribution.,"this function, which is dominated by the convolution with the redshift error distribution."666" Given this probability distribution in the 7 direction. the amplitude of ή) can be estimated by fitting a scaled version of our model «ήν.7) to the data at the r, value of interest."," Given this probability distribution in the $\pi$ direction, the amplitude of $w(r_p)$ can be estimated by fitting a scaled version of our model $\xi(r_p,\pi)$ to the data at the $r_p$ value of interest."667" In practice. our model £(7,.7) will not be exact. and we considered the following compromise procedure for estimating w(r,) so that the result is robust."," In practice, our model $\xi(r_p,\pi)$ will not be exact, and we considered the following compromise procedure for estimating $w(r_p)$ so that the result is robust."668" For each +,, value. we fit the amplitude of the (convolved) model ερconst.7) to the data."," For each $r_p$ value, we fit the amplitude of the (convolved) model $\xi(r_p={\rm const},\pi)$ to the data."669" We then integrate the data for £(r,.x) out to z=10075!Mc. from which point on we integrate the convolved model out to infinity (see Fig. 4)."," We then integrate the data for $\xi(r_p,\pi)$ out to $\pi=100\mpcoh$, from which point on we integrate the convolved model out to infinity (see Fig. \ref{fitdata}) )."670 This combines the exact measurement of ο) within Tyas=10071Me with an estimate of the missing signal at larger 7., This combines the exact measurement of $w(r_p)$ within $\pi_{\rm max}=100\mpcoh$ with an estimate of the missing signal at larger $\pi$.671 Since this correction is typically of the overall signal. we do not need to estimate it very accurately.," Since this correction is typically of the overall signal, we do not need to estimate it very accurately."672 In practice. the results from the 2-stage procedure were very similar to the direct fitting method.," In practice, the results from the 2-stage procedure were very similar to the direct fitting method."673" This process is performed separately for the red and blue galaxy samples. using the appropriate pairwise error distributions and the final best-fitting halo-model &(r,.7) for the unconvolved prediction."," This process is performed separately for the red and blue galaxy samples, using the appropriate pairwise error distributions and the final best-fitting halo-model $\xi(r_p,\pi)$ for the unconvolved prediction."674 The width of the convolved model in Fig., The width of the convolved model in Fig.675 4 suggests that the redshift errors yielded by the object classification scheme. which we used for the calculation of the pairwise error distribution. may be slightly overestimated.," \ref{fitdata} suggests that the redshift errors yielded by the object classification scheme, which we used for the calculation of the pairwise error distribution, may be slightly overestimated."676 In order to estimate the effect on the projected correlation function. we tried repeating the analysis with redshift errors scaled to SO6c of the values given in the object catalogues.," In order to estimate the effect on the projected correlation function, we tried repeating the analysis with redshift errors scaled to $80$ of the values given in the object catalogues."677 This scaling gives the best fit to the data; however. the resulting changes to «(rn) were small compared to the random errors.," This scaling gives the best fit to the data; however, the resulting changes to $w(r_p)$ were small compared to the random errors."678 The mean galaxy density is determined from the observed galaxy counts in each field. which does not necessarily represent the the true density (Groth&Peebles1977).," The mean galaxy density is determined from the observed galaxy counts in each field, which does not necessarily represent the the true density \citep{GrothPeebles77}."679. The estimator will be on average biased low with respect to the true correlation by a constant 7: where ην) is the true projected correlation function. iyCGny) the measurement.," The estimator will be on average biased low with respect to the true correlation by a constant ${\cal I}$: where $w_t(r_p)$ is the true projected correlation function, $w_m(r_p)$ the measurement."680 The integral constraint Z is given where 5 is the physical area corresponding to the solid angle of the field at the redshift under consideration., The integral constraint ${\cal I}$ is given by where $S$ is the physical area corresponding to the solid angle of the field at the redshift under consideration.681" For the calculation of the integral constraint. we assume that the three dimensional correlation function ¢{7) ts to first approximation a power law: Then the evaluation of equation 7 yields where C is a numerical factor. which depends only on the slope 5: If the correlation function is given by equation (13)). the measurement yields The true amplitude Cr, is not known. but Z/(Cr5) can be estimated by performinga Monte Carlo integration (where we use the mean of the pair counts (2?) at a projected distance +, of the four fields): The true value of Cy, can be estimated by fitting equation (16)) to the data. taking the value of Z/(Cyr,) from equation (07)."," For the calculation of the integral constraint, we assume that the three dimensional correlation function $\xi(r)$ is to first approximation a power law: Then the evaluation of equation \ref{projection} yields where $C$ is a numerical factor, which depends only on the slope $\gamma$: If the correlation function is given by equation \ref{wrp}) ), the measurement yields The true amplitude $C r_0^\gamma$ is not known, but ${\cal I}/(C r_0^\gamma )$ can be estimated by performinga Monte Carlo integration (where we use the mean of the pair counts $\langle682RR\rangle$ at a projected distance $r_p$ of the four fields): The true value of $C r_0^\gamma$ can be estimated by fitting equation \ref{integconstfit2}) ) to the data, taking the value of ${\cal I}/(C683r_0^\gamma)$ from equation \ref{integconstfit3}) )."684 This value. multiplied by the fitted amplitude C7. yields the integral constraint Z.," This value, multiplied by the fitted amplitude $C r_0^\gamma$, yields the integral constraint ${\cal I}$."685" The measurement can then be corrected for the integral constraint by adding Z to «5,(75).", The measurement can then be corrected for the integral constraint by adding ${\cal I}$ to $w_m(r_p)$.686 This method yields estimates of J=0.1175.1Mpe for the red galaxiesand Z=0.33h+Mpe for the blue galaxies., This method yields estimates of ${\cal I}=0.14 \mpcoh$ for the red galaxiesand ${\cal I}=0.33\mpcoh$ for the blue galaxies.687" These values are negligible in comparison with the observed data for +,Z520h1 Mypc. demonstrating that the fields are large enough to deliver a fair sample."," These values are negligible in comparison with the observed data for $r_p \la 20\mpcoh$ , demonstrating that the fields are large enough to deliver a fair sample."688 As a cross-check. note that we expect Z=20057 (since we integrated over Ax=2005.1 Nc). where a? is the fractional variance in galaxy numbers between different realizations of our survey.," As a cross-check, note that we expect ${\cal I}=200 \sigma^2$ (since we integrated over $\Delta \pi=200\mpcoh$ ), where $\sigma^2$ is the fractional variance in galaxy numbers between different realizations of our survey."689 With three fields. σ should be \/3 times smaller than the field-to-field rms variation. so our figures for Z suggest and expected scatter in the numbers of galaxies per field for red and blue galaxies respectively.," With three fields, $\sigma$ should be $\sqrt{3}$ times smaller than the field-to-field rms variation, so our figures for ${\cal I}$ suggest and expected scatter in the numbers of galaxies per field for red and blue galaxies respectively."690 This agrees well with the numbers in Table 1., This agrees well with the numbers in Table 1.691 Finally. there is the crucial issue of setting realistic error bars on our correlation estimates.," Finally, there is the crucial issue of setting realistic error bars on our correlation estimates."692 The three COMBO-17 fields measure ~31«307 each and are thus large enough to carry out a jack-knife analysis., The three COMBO-17 fields measure $\sim 31'\times 30'$ each and are thus large enough to carry out a jack-knife analysis.693 We divide each field into four quadrants. and then calculate the correlation function ο) (neluding the integral constraint) for twelve realisations of the data. each time omitting one of the quadrants.," We divide each field into four quadrants, and then calculate the correlation function $w(r_p)$ (including the integral constraint) for twelve realisations of the data, each time omitting one of the quadrants."694 The variance in e 18 then given approximately by where V=12 is the number of realisations of the data (e.g. Serantonetal. 2002))., The variance in $w$ is then given approximately by where $N=12$ is the number of realisations of the data (e.g. \citealp{Scranton02}) ).695 In order to check for cross-correlations between the data points. we can extend the jack-knife method in the obvious way to estimate the covariance between different bins. OF.," In order to check for cross-correlations between the data points, we can extend the jack-knife method in the obvious way to estimate the covariance between different bins, $\sigma^2_{ij}$ ."696 The naturalway to express this is as a correlation coefficient matrix: rjστι σσ., The naturalway to express this is as a correlation coefficient matrix: $r_{ij}\equiv\sigma^2_{ij}/\sigma_{i}\sigma_{j}$ .697 Results in this form are presented below., Results in this form are presented below.698Denote by X the horizoutal lift of £.,Denote by $X$ the horizontal lift of $\xi$.699 We thus have the following objects ou P: oo. a. x: E. X.," We thus have the following objects on $P$ : $\overline{\beta}$ , $\overline{\alpha}$, $\overline{\omega}$; $E$, $X$."700 Iu canonical coordinates Ds.ρε on xHU) for each ©C M. we have where aud Also The quantities JJ. zZ. aud α ecnerate a closed. nowhere vanishing l-forimi with Denote by £g the raisiug operator for 9.," In canonical coordinates $\{s, x^0, x^i, p_i \}$ on $\pi^{-1} (U)$ for each $U\subset M$ , we have where and Also The quantities $\overline{\beta}$, $\overline{\omega}$, and $\overline{\alpha}$ generate a closed, nowhere vanishing 1-form and a pre-symplectic form with Denote by $\sharp_{\overline{\Omega}}$ the raising operator for $701 \overline{\Omega}$ ."702 Then. aud These quantities therefore do uot generate a new vector field on P? independent of £ aud X.," Then, and These quantities therefore do not generate a new vector field on $P$ independent of $E$ and $X$."703 Using the representation of 3. a. 6. E aud X dn canoulcal coordinates. we easily derive the following relations: We now asstune furthermore that the Liouville field £ is complete.," Using the representation of $\overline{\beta}$, $\overline{\omega}$, $\overline{\alpha}$, $E$ and $X$ in canonical coordinates, we easily derive the following relations: We now assume furthermore that the Liouville field $\xi$ is complete."704 Then NX is also complete., Then $X$ is also complete.705 With thisasstuuption. the fields £ and X generate a C(1)X action on P.," With thisassumption, the fields $E$ and $X$ generate a $U(1)\times \R$ action on $P$."706" Since Lo and X are everywhere linearly independent. the orbits of this action are Stο, that is. evlinders. or T?=St.St."," Since $E$ and $X$ are everywhere linearly independent, the orbits of this action are $S^1 \times707\R$, that is, cylinders, or $T^2 = S^1 \times S^1$."708 Each orbit projects onto a correspouding orbit of€iu A.The 1-fonuu @ is closedaud nowhere zero., Each orbit projects onto a corresponding orbit of $\xi$in $M$.The 1-form $\overline{\theta}$ is closedand nowhere zero.709 Ittherefore defines a foliation CF] on P.Let Fhe a leat of (F1., Ittherefore defines a foliation $\{ F \}$ on $P$ .Let $F$ be a leaf of $\{ F \}$ .710 The F clearly is a Pfaffian manifold with Of-n|r. ," The $F$ clearly is a Pfaffian manifold with $\overline{\alpha}_F = \overline{\alpha}711|_F$ "712an accurate offset between the burst and the centroid of the host. as well as constrain the size of the radio emitting region refsec:offset)).,"an accurate offset between the burst and the centroid of the host, as well as constrain the size of the radio emitting region \\ref{sec:offset}) )."713 Very Large Array Inc.)) observations of were initiated. on 1998. July 4.40 UT at 4.86 GHz.," Very Large Array ) observations of were initiated on 1998, July 4.40 UT at 4.86 GHz."714 ΑΙ observations were obtained in the standard continuum mode with 250 MHz contiguous bands., All observations were obtained in the standard continuum mode with $2\times 50$ MHz contiguous bands.715 We used the extra-galactic sources J2330+110. 10010109 and J00224061 for phase calibration and 3C48 (JO137+331) and 3C147 (J0542+498) for flux calibration.," We used the extra-galactic sources J2330+110, J0010+109 and J0022+061 for phase calibration and 3C48 (J0137+331) and 3C147 (J0542+498) for flux calibration."716 We used the Astronomical Image Processing System (AIPS) for data reduction., We used the Astronomical Image Processing System (AIPS) for data reduction.717 The fluxes presented here are the values measured on the images at the position of the source., The fluxes presented here are the values measured on the images at the position of the source.718 Late-time observations (time after the burst. ¢>350 days) were co-added over a period of a few to thirty days in order to increase the overall sensitivity of each detection.," Late-time observations (time after the burst, $t\gtrsim 350$ days) were co-added over a period of a few to thirty days in order to increase the overall sensitivity of each detection."719 This is appropriate since the expected change in the flux density from the afterglow over a few days. several hundred days after the burst. is negligible relative to the associated errors in the measurements.," This is appropriate since the expected change in the flux density from the afterglow over a few days, several hundred days after the burst, is negligible relative to the associated errors in the measurements."720 A log of the late-time observations and the flux density measurements are summarized in Table ].. and the lightcurves are shown in Figure 1..," A log of the late-time observations and the flux density measurements are summarized in Table \ref{tab:vla}, and the lightcurves are shown in Figure \ref{fig:radiolc}."721 A summary of the early radio data. as well as broadband modelingis given in Berger et al. (2001).," A summary of the early radio data, as well as broadband modelingis given in Berger et al. \nocite{b+01}) )."722 From Figure l.. we see that the late-time (t>350 days) radio lighteurves do not exhibit the customary power-law decay expected of afterglows but instead show flattening.," From Figure \ref{fig:radiolc}, we see that the late-time $t\gtrsim 350$ days) radio lightcurves do not exhibit the customary power-law decay expected of afterglows but instead show flattening."723" From the early broadband data we know that the afterglow spectrum peaked at frequency. 1/4,~4«101 Hz atr=1.2 days (Vreeswi]ketal. 1999))."," From the early broadband data we know that the afterglow spectrum peaked at frequency, $\nu_m\sim 4\times 10^{12}$ Hz at $t=1.2$ days \cite{vgo+99}) )."724 If the explosion was spherical then we expect τηX(7 (Sari.Piran&Narayan1998:; Chevalier 20000)., If the explosion was spherical then we expect $\nu_m\propto t^{-3/2}$ \cite{spn98}; \cite{cl00}) ).725 Thus the radio afterglow ts expected to decay fort>70 days after the burst., Thus the radio afterglow is expected to decay for $t>70$ days after the burst.726 If the ejecta were collimated (opening angle. 7;). then we expect a more rapid decay. ήXf. once the bulk Lorentz factor. Τ. of the flow falls below 0;. Τίς07! (Sart.Piran&Halpern 1999)).," If the ejecta were collimated (opening angle, $\theta_j$ ), then we expect a more rapid decay, $\nu_m\propto t^{-2}$, once the bulk Lorentz factor, $\Gamma$, of the flow falls below $\theta_j$, $\Gamma(t)\lesssim \theta_j^{-1}$ \cite{sph99}) )."727 In this case. we expect the radio afterglow to start decaying at even earlier times. and the flux will decay faster relative to a spherical explosion.," In this case, we expect the radio afterglow to start decaying at even earlier times, and the flux will decay faster relative to a spherical explosion."728 In either case. we expect the radio afterglow to decay by at least a factor of three over the time span under consideration. 350«f£<1000 days.," In either case, we expect the radio afterglow to decay by at least a factor of three over the time span under consideration, $350<t<1000$ days."729 We can clearly see from Figure ] that this decay is not taking place. and the flux instead remains constant over a period of approximately 650 days.," We can clearly see from Figure \ref{fig:radiolc} that this decay is not taking place, and the flux instead remains constant over a period of approximately 650 days."730 This behavior is similar to the flattening observed in the optical/NIR lightcurves of several GRBs (including 980703)). when the emission from the afterglow decays below the level of emission from the host galaxy.," This behavior is similar to the flattening observed in the optical/NIR lightcurves of several GRBs (including ), when the emission from the afterglow decays below the level of emission from the host galaxy."731" Furthermore. the afterglow spectrum 1s expected to be a power law. F,,1/7. where J2(p- D)/2and p is the power law index of the Lorentz factor distribution of the shocked electrons. N(5)d5x5ας for 5>σα (Sart.Piran&Narayan 1998))."," Furthermore, the afterglow spectrum is expected to be a power law, $F_\nu\propto \nu^{-\beta}$, where $\beta=(p-1)/2$ and $p$ is the power law index of the Lorentz factor distribution of the shocked electrons, $N(\gamma)d\gamma \propto \gamma^{-p}d\gamma$ for $\gamma > \gamma_{\rm min}$ \cite{spn98}) )."732 From the observations of many afterglows. we note that p is in the range 2.2—2.6 and thus we expect ./j~0.7.," From the observations of many afterglows, we note that $p$ is in the range 2.2–2.6 and thus we expect $\beta\sim 0.7$."733 However. the observed spectral index m the range 1.43-8.46 GHz is much lower. ./=0.32£0.12.," However, the observed spectral index in the range 1.43–8.46 GHz is much lower, $\beta=0.32\pm 0.12$."734 We thus conclude that there exists a steady source of emission other than the afterglow., We thus conclude that there exists a steady source of emission other than the afterglow.735 One possible explanation for this component is emission from an active galactic nucleus (AGN)., One possible explanation for this component is emission from an active galactic nucleus (AGN).736 It has been noted in surveys of the Hubble Deep Field (HDF). its flanking fields. and the Small Selected Area 13 (SSAI3) that approximately of the radio sources are AGN with spectral indices of about 0.3 (Richardsetal.1999:; Richards2000:: Barger.Cowie&Richards20005).," It has been noted in surveys of the Hubble Deep Field (HDF), its flanking fields, and the Small Selected Area 13 (SSA13) that approximately of the radio sources are AGN with spectral indices of about 0.3 \cite{rfk+99}; \cite{r00}; \cite{bcr00}) )."737 Windhorst et al. (, Windhorst et al. (7381993) found a similar result in their survey of two 7’«7' fields at 8.44 GHz.,1993) found a similar result in their survey of two $7'\times 7'$ fields at 8.44 GHz.739 Thus. there is a modest probability that the emission from the host of is due to an AGN.," Thus, there is a modest probability that the emission from the host of is due to an AGN."740 We consider the AGN hypothesis unlikely based on the radio data and optical spectroscopy., We consider the AGN hypothesis unlikely based on the radio data and optical spectroscopy.741 First. optical spectra of the source obtained by Djorgovski et al. (," First, optical spectra of the source obtained by Djorgovski et al. ("742"1998) show no evidence for an unobscured AGN: high-ionization lines such as Mg IL A2799, |NeVJA3346. and [NeV]A3426 are absent. and the [OIIIJA4959 to / ratio is approximately 0.4. much lower than [OIIL[/H.7>1.3 for AGN (Rola.Terlevich&1997)).","1998) show no evidence for an unobscured AGN: high-ionization lines such as Mg II $\lambda 2799$, $\lambda 3346$, and $\lambda 3426$ are absent, and the $\lambda 4959$ to $\beta$ ratio is approximately 0.4, much lower than ${\rm [OIII]/H}\beta>1.3$ for AGN \cite{rtt97}) )."743 Another way to discriminate between AGN and star-forming galaxies is to correlate the [OIL] equivalent width (EW) with continuum color (Dressler&Gunn1982))., Another way to discriminate between AGN and star-forming galaxies is to correlate the [OII] equivalent width (EW) with continuum color \cite{dg82}) ).744 Kennicutt (1992) showed that AGN have redder colors for similar [OIL] EW. relative to normal galaxies.," Kennicutt (1992) showed that AGN have redder colors for similar [OII] EW, relative to normal galaxies."745 Using the spectrum presented in Djorgovski et al. (, Using the spectrum presented in Djorgovski et al. (746"1998) we evaluate the color index. (41-50)=2Slog[£,(5000)f.(1100)] CKennicutt1992)). and find it to be Ox0.1: an AGN/ with the same [OIL] EW would have a value =>0.3 (Kennicutt 1992)).","1998) we evaluate the color index, $(41-50)\equiv 2.5{\rm747log}[f_\nu(5000{\rm \AA})/f_\nu(4100{\rm \AA})]$ \cite{k92}) ), and find it to be $0\pm 0.1$; an AGN with the same [OII] EW would have a value $\gtrsim 0.3$ \cite{k92}) )."748 Finally. Rola. Terlevich Terlevich (1997)) found that for a sample of emission-line galaxies at zo0.8. the color index between the continuum underlying the H./ and [OI]A3727 lines is =0.4 for all AGN in their sample.," Finally, Rola, Terlevich Terlevich \nocite{rtt97}) ) found that for a sample of emission-line galaxies at $z\sim 0.8$, the color index between the continuum underlying the $\beta$ and $\lambda 3727$ lines is $\ge 0.4$ for all AGN in their sample."749 Using the spectrum of Djorgovski et al. (, Using the spectrum of Djorgovski et al. (7501998) we find that this color index is approxmiately zero.,1998) we find that this color index is approxmiately zero.751 A second. but less persuasive argument against an AGN origin is the apparent absence of significant radio variability over the 650 day monitoring period (see Figure 2)).," A second, but less persuasive argument against an AGN origin is the apparent absence of significant radio variability over the 650 day monitoring period (see Figure \ref{fig:fluc}) )."752 The radio cores of most. but not all. low-luminosity AGN show variability exceeding the observed levels (Falckeetal. 2000)).," The radio cores of most, but not all, low-luminosity AGN show variability exceeding the observed levels \cite{flb+00}) )."753 We thus conclude that the radio emission seen from the host of is unlikely to be due to AGN activity., We thus conclude that the radio emission seen from the host of is unlikely to be due to AGN activity.754 However. star-forming galaxies exhibit radio emission arising from their supernova remnants (SNRs) and HII regions.," However, star-forming galaxies exhibit radio emission arising from their supernova remnants (SNRs) and HII regions."755 In the next section we show how the observations. the radio spectral index. and the optical spectrum. are consistent with the hypothesis that the radio emission is related to star formation.," In the next section we show how the observations, the radio spectral index, and the optical spectrum, are consistent with the hypothesis that the radio emission is related to star formation."756 Star formation is traced by optical. far-IR. sub-mm. and radio emission.," Star formation is traced by optical, far-IR, sub-mm, and radio emission."757 In the following we will use the radio data to estimatethe SER in the host galaxy of980703.. and then compare the results with the SFR derived from optical indicators. and with radio surveys at a similar redshift range in order to place the host of in a larger context.," In the following we will use the radio data to estimatethe SFR in the host galaxy of, and then compare the results with the SFR derived from optical indicators, and with radio surveys at a similar redshift range in order to place the host of in a larger context."758" Using all the measurements in Table |.. we find the following weighted-average flux densities for the host galaxy of 980703:: Fy.s46=39.34.9 py. Faso=42.148.6 py. and F,,43=68.0+£6.6 jJy."," Using all the measurements in Table \ref{tab:vla}, , we find the following weighted-average flux densities for the host galaxy of : $F_{\nu,8.46}=39.3\pm 4.9$ $\mu$ Jy, $F_{\nu,4.86}=42.1\pm 8.6$ $\mu$ Jy, and $F_{\nu,1.43}=68.0\pm 6.6$ $\mu$ Jy."759 From the redshift of 980703.. 5=0.966 (Djorgovskietal. 1998)). and the cosmological," From the redshift of , $z=0.966$ \cite{dkb+98b}) ), and the cosmological"7601997)).,).761 To make (hat possible. Starch comparisons have been used (ο build up a system of stancard-star data on a uniform zero point.," To make that possible, Sturch comparisons have been used to build up a system of standard-star data on a uniform zero point."762 That svstem is based on measurements of the llvades and Coma. lor whieh extant data (Crawlord 1969)) turn out to share a common zero point.," That system is based on measurements of the Hyades and Coma, for which extant data \citealt{cp66,cb69}) ) turn out to share a common zero point."763 The IHLvades-Conma paper (see 1992)) and three others produced by the project ave listed in Table 1., The Hyades-Coma paper (see \citealt{tj92}) ) and three others produced by the project are listed in Table 1.764 Joner&Tavlor have presented comparable results for the Pleiades. and Joneretal.(1995). have added an auxiliary paper on the photometry of Gronbech&Olsen(1976.1977).," \citet{jt07} have presented comparable results for the Pleiades, and \citet{jtpj95} have added an auxiliary paper on the photometry of \citet{go76,go77}."765. Relative to the Ivacles-Coma svstem. ollsets have been detected for M61. Praesepe. aud NGC 752.," Relative to the Hyades-Coma system, offsets have been detected for M67, Praesepe, and NGC 752."766 For the latter two clusters. all but one of the derived values of M] (with M being a mean residual: see and Table 6 of Joner&Tavlor 2007..)," For the latter two clusters, all but one of the derived values of $|M|$ (with $M$ being a mean residual; see and Table 6 of \citealt{jt07}. .)"767 To date. data Irom the project have been used in zero point tests and color-color diagnosis (see. for example. Anthony-Twarog&Twarog2006 and Ixiunan1998.. respectively).," To date, data from the project have been used in zero point tests and color-color diagnosis (see, for example, \citealt{att06} and \citealt{k98}, respectively)."768 Use of project results to establish cluster measurements as stancdardestar data is also possible (see. [or example. Appendix D of Joner&Taylor1995)).," Use of project results to establish cluster measurements as standard-star data is also possible (see, for example, Appendix B of \citealt{jt95}) )."769 To grasp tlie overall results of (he zero point projects. suppose first that the Baconian standard (recall 82.3) were to prevail throughout the photometric discipline.," To grasp the overall results of the zero point projects, suppose first that the Baconian standard (recall 2.3) were to prevail throughout the photometric discipline."770 As one outcome. statistical analvsis would be applied dependable to photometric data sets. and the results would take precedence over all contrary. axioms about the alleged character of the data (see 83.8).," As one outcome, statistical analysis would be applied dependably to photometric data sets, and the results would take precedence over all contrary axioms about the alleged character of the data (see 3.8)."771 A second outcome would be increased caution about gauging photometric cualitv., A second outcome would be increased caution about gauging photometric quality.772 Too often. discourse among photometric astronomers takes place in an eve-smarting haze of skepticism about the quality of published photometry.," Too often, discourse among photometric astronomers takes place in an eye-smarting haze of skepticism about the quality of published photometry."773 Inventing poorly supported. ancl often specious criticisms of such data is a widespread practice (see. for example. objections discussed in 83.3 and a class of eriticisms diagnosed in 87 of Tavlor&Joner 2005)).," Inventing poorly supported and often specious criticisms of such data is a widespread practice (see, for example, objections discussed in 3.8 and a class of criticisms diagnosed in 7 of \citealt{tj05}) )."774 After the changeover to the Daconian standard. a lesson taught by photometric zero points would attract notice.," After the changeover to the Baconian standard, a lesson taught by photometric zero points would attract notice."775 It would be acknowledged that maximum values of |.V| can be about 86 mnmag (see Table 3 of Stetsonetal. 2004)). 40GO mmag (see 4.1 and 6). 25 manage (see section 5). and <0.9zx1.0 munag (see 83.3).," It would be acknowledged that maximum values of $|M|$ can be about 86 mmag (see Table 3 of \citealt{smv04}) ), 40–60 mmag (see 4.1 and 6), 25 mmag (see section 5), and $\leq 0.9 \pm 1.0$ mmag (see 3.3)."776 In response. there would be no generalizations about any alleged limit to zero point coherence (see notably Sletsonetal.2003. and 83 of Stetsonetal. 2004)).," In response, there would be no generalizations about any alleged limit to zero point coherence (see notably \citealt{sbg03} and 3 of \citealt{smv04}) )."777 Instead. particular data sets would be emuged solely on (their particular merits ancl demerits.," Instead, particular data sets would be gauged solely on their particular merits and demerits."778 Yet another result would be a reluctance to “block the road of inquiry” (to quote Charles, Yet another result would be a reluctance to “block the road of inquiry” (to quote Charles779"We model the evolution of a periodic. cubical region of a critical density Linstein-cle Sitter universe (Q=1. , 0).","We model the evolution of a periodic, cubical region of a critical density Einstein-de Sitter universe $\Omega=1$ , $\Omega_\Lambda=0$ )."780 We use a simulation code based on a hierarchical P3AL implementation. (Couchman 1991) for eravity and smoothed particle hvdrodynamiecs (Lucey LOTT. Cingold Monaghan 1977. see Monaghan 1992 for a review) for νοτονπαμίσος (Pheuns 1998)," We use a simulation code based on a hierarchical P3M implementation (Couchman 1991) for gravity and smoothed particle hydrodynamics (Lucy 1977, Gingold Monaghan 1977, see Monaghan 1992 for a review) for hydrodynamics (Theuns 1998)."781 The comoving size of the simulation box is L/(2h)Alpe.. where the Hubble constant today is written as Lig=1007 km s.| +.," The comoving size of the simulation box is $L/(2h)$, where the Hubble constant today is written as $H_0=100 h$ km $^{-1}$ $^{-1}$."782 We will assume fp=0.5 throughout and. describe simulations with £L=5.5 and 22.22\pe., We will assume $h=0.5$ throughout and describe simulations with $L=5.5$ and $22.22$.783. A fraction Qgh-=0.0125 — he matter density is assumed to be baryonic. consisten with limits from nucleo-svnthesis (Walker 1991. bu note the continuing debate on the cleuterium abundance derived. from. quasar spectra which might favour higher values Qeh?=0.019. see Durles Tytler L997 zux references therein)," A fraction $\Omega_Bh^2=0.0125$ of the matter density is assumed to be baryonic, consistent with limits from nucleo-synthesis (Walker 1991, but note the continuing debate on the deuterium abundance derived from quasar spectra which might favour higher values $\Omega_B h^2=0.019$, see Burles Tytler 1997 and references therein)."784 Vhe rest of the matter is assumed. to rc in the form of cold dark matter., The rest of the matter is assumed to be in the form of cold dark matter.785 To generate initia conditions for the simulations at the starting redshift 2=50 we use the fit to the cold dark matter linear transfer function rom Bardeen (1986) ancl normalise it such that the incarly extrapolated: value of ax=0.7 at the present clay., To generate initial conditions for the simulations at the starting redshift $z=50$ we use the fit to the cold dark matter linear transfer function from Bardeen (1986) and normalise it such that the linearly extrapolated value of $\sigma_{8}=0.7$ at the present day.786 These simulations use 64 particles of either species hence he gas mass resolutions are 1.5«10341. and 2.2«107A. or L=2:22 and L= 5.5Mpoe. respectively.," These simulations use $64^3$ particles of either species hence the gas mass resolutions are $1.5\times 10^8 M_\odot$ and $2.2\times 10^6787M_\odot$ for $L=22.22$ and $L=5.5$ Mpc, respectively."788 Gas in these simulations is ionized and. photo-heated » an imposed uniform. background. of ionizing photons assumed to originate from quasars as computed by Llaarelt Macau (1996)., Gas in these simulations is ionized and photo-heated by an imposed uniform background of ionizing photons assumed to originate from quasars as computed by Haardt Madau (1996).789 This (ux is redshift dependent. mimicking he evolution of the quasar luminosity function.," This flux is redshift dependent, mimicking the evolution of the quasar luminosity function."790 Gas can also cool by interacting with microwave background photons and hrough collisional cooling., Gas can also cool by interacting with microwave background photons and through collisional cooling.791 The detailed rates for all these orocesses as a function of temperature are taken from Cen (1992) with some minor moclifications., The detailed rates for all these processes as a function of temperature are taken from Cen (1992) with some minor modifications.792 We assume ionization equilibrium: throughout and use a helium abundance of )=0.24 by mass., We assume ionization equilibrium throughout and use a helium abundance of $Y=0.24$ by mass.793 We have compared in detail the results rom our code against the published. results of (Llernquist 1996. Croft 1997) and find excellent agreement (see Theuns 1998 for more details of these comparisons and for a description of our code and. cooling rales).," We have compared in detail the results from our code against the published results of (Hernquist 1996, Croft 1997) and find excellent agreement (see Theuns 1998 for more details of these comparisons and for a description of our code and cooling rates)."794 The elective mean optical depth 7 from the simulations. with this set of parameters. is significantlv. lower than the observed. value.," The effective mean optical depth $\bar\tau$ from the simulations, with this set of parameters, is significantly lower than the observed value."795 Consequently. we have reduced. the amplitude ΕΕ of the ionizing radiation given by Haardt Macau (1996) by a factor of two.," Consequently, we have reduced the amplitude $\Gamma_\H$ of the ionizing radiation given by Haardt Madau (1996) by a factor of two."796 Llere. Fu is the amplitude of the radiation spectrum. at the hydrogen Lyman edge.," Here, $\Gamma_\H$ is the amplitude of the radiation spectrum at the hydrogen Lyman edge."797 Since r scales approximately as 7x(Qgh?y?hy (Rauch 1997). we would obtain the same results by keeping the original value of Εμ from. Haardt Macau but. increase Oh? [rom 0.0125 to 0.0177. which is still well within the range allowed by nucleo-synthesis.," Since $\bar\tau$ scales approximately as $\tau\propto (\Omega_B h^2)^2/h \Gamma_\H$ (Rauch 1997), we would obtain the same results by keeping the original value of $\Gamma_\H$ from Haardt Madau but increase $\Omega_B h^2$ from 0.0125 to 0.0177, which is still well within the range allowed by nucleo-synthesis."798 At several output times we compute simulated spectra along lines of sight through the simulation box., At several output times we compute simulated spectra along lines of sight through the simulation box.799 Each spectrum is convolved with a Caussian with FWILAL = 58 km 5. then re-sampled. onto pixels of width 3 km s! to mimic the instrumental profile and characteristies of the IIS spectrograph on the Ixeck telescope.," Each spectrum is convolved with a Gaussian with FWHM = 8 km $^{-1}$, then re-sampled onto pixels of width 3 km $^{-1}$ to mimic the instrumental profile and characteristics of the HIRES spectrograph on the Keck telescope."800 Artificial noise is introduced by adding a Gaussian random signal with zero mean. and standard deviation o=0.02 to every pixel a SNIUof 50 for pixels at the continuum).," Artificial noise is introduced by adding a Gaussian random signal with zero mean, and standard deviation $\sigma=0.02$ to every pixel a SNR of 50 for pixels at the continuum)."801 The absorption lines in these mock observations are then fitted with Voigt profiles using an automated version of ΜΟΙ (Carswell 1981)., The absorption lines in these mock observations are then fitted with Voigt profiles using an automated version of VPFIT (Carswell 1987).802 We show in figure examples of simulated spectra at 2=3. 2.1 0.5 for the £=22.22 Alpe lower resolution simulation.," We show in figure \ref{fig:spectra} examples of simulated spectra at $z=3$, 2, 1 0.5 for the $L=22.22$ Mpc lower resolution simulation."803 Fluctuations in neutral hydrogen. density. caused. by gas tracing dark matter potential wells. produce absorption features similar to those in observed spectra.," Fluctuations in neutral hydrogen density, caused by gas tracing dark matter potential wells, produce absorption features similar to those in observed spectra."804At low redshifts. there are large regions of the spectrum with very low absorption.,"At low redshifts, there are large regions of the spectrum with very low absorption."805 These regions are separated. by prominent absorption features. most of which are just a single strong," These regions are separated by prominent absorption features, most of which are just a single strong"806"Apart from the complex dynamics of the whole system. the planet iis a ""standard"" hot Jupiter.","Apart from the complex dynamics of the whole system, the planet is a ""standard"" hot Jupiter."807 It orbits a metal-rich star. which accounts for the observed increase in the incidences of hot Jupiters with the metallicity of the host star 2007)..," It orbits a metal-rich star, which accounts for the observed increase in the incidences of hot Jupiters with the metallicity of the host star \citep{2007ARA&A..45..397U}."808 The period of is longer than the 3-4 days typical value. but considering the eccentricity of its orbit. its periastron distance is typical of hot Jupiters.," The period of is longer than the 3-4 days typical value, but considering the eccentricity of its orbit, its periastron distance is typical of hot Jupiters."809 The orbit misalignment of the planet with the stellar rotation axis of is measured with the B parameter., The orbit misalignment of the planet with the stellar rotation axis of is measured with the $\beta$ parameter.810 The true angle between the axes of the stellar and planetary orbits is usually called w and is statistically related to 8 through sin7 (unknown) and the orbital inclination (7) (see Fabrycky&Winn(2009) for details)., The true angle between the axes of the stellar and planetary orbits is usually called $\psi$ and is statistically related to $\beta$ through $\sin I$ (unknown) and the orbital inclination $i$ ) (see \cite{2009ApJ...696.1230F} for details).811 When P deviates significantly from zero. this provides us with a lower limit to the v.," When $\beta$ deviates significantly from zero, this provides us with a lower limit to the $\psi$."812 When £ ts beyond 90°. the orbital spin has the opposite direction to the stellar rotation provided that the orbit does not transit the star between its pole and its limb.," When $\beta$ is beyond $^\circ$, the orbital spin has the opposite direction to the stellar rotation provided that the orbit does not transit the star between its pole and its limb."813 According to 99 from Fabrycky&Winn(2009).. this condition is met when />3.6 degree.," According to 9 from \cite{2009ApJ...696.1230F}, this condition is met when $I>3.6$ degree."814 By combining Vsin/. with the estimated age of the star. one can exclude such a small / angle.," By combining $V\,sin\,I,$ with the estimated age of the star, one can exclude such a small $I$ angle."815 Interpreted with the large 8 value. we can conclude that a true retrograde orbit is the most likely scenario forWASP-Sb.," Interpreted with the large $\beta$ value, we can conclude that a true retrograde orbit is the most likely scenario for."816. The origin of the unusual shape and orientation of the orbit of us possibly related to the Kozai mechanism (Kozat1962;Wu&Murray2003) or the outcome of a violent dynamical interaction history.," The origin of the unusual shape and orientation of the orbit of is possibly related to the Kozai mechanism \citep{1962AJ.....67..591K, 2003ApJ...589..605W} or the outcome of a violent dynamical interaction history."817 The evidence of two other bodies and a possible series of secular effects (Takedaetal.2008) make the ssystem unique and interesting for additional dynamical studies and a test case for formation scenarios of hot Jupiters that constitute an alternative to the dise-migration mechanism., The evidence of two other bodies and a possible series of secular effects \citep{2008ApJ...683.1063T} make the system unique and interesting for additional dynamical studies and a test case for formation scenarios of hot Jupiters that constitute an alternative to the disc-migration mechanism.818The lines in Fig. (,The lines in Fig. (819"2) show the predicted change in the power spectrum of theLy-a forest transmitted flux, Pp(k), as M, is varied.","2) show the predicted change in the power spectrum of the$\alpha$ forest transmitted flux, $P_F(k)$ , as $M_{\pbh}$ is varied."820 The points with error bars are Pr(k) measured by Croft et al. (, The points with error bars are $P_F(k)$ measured by Croft et al. (8212002) using their fiducial sample (Z= 2.72).,2002) using their fiducial sample $\bar{z}=2.72$ ).822 The predictions were made using the large set of numerical simulations and the interpolation code described in McDonald et al. (, The predictions were made using the large set of numerical simulations and the interpolation code described in McDonald et al. (8232003).,2003).824" We have not yet performed fully hydrodynamic simulations using PBH power spectra, so our result is based entirely on hydro-PM simulations (e.g., Gnedin Hui 1998; McDonald, Miralda-Escudé,, Cen 2002; McDonald 2003)."," We have not yet performed fully hydrodynamic simulations using PBH power spectra, so our result is based entirely on hydro-PM simulations (e.g., Gnedin Hui 1998; McDonald, Miralda-Escud\'e,, Cen 2002; McDonald 2003)."825 The curves we show are smooth because the power spectra computed from the simulations have been compressed into the parameters of an analytic fitting formula., The curves we show are smooth because the power spectra computed from the simulations have been compressed into the parameters of an analytic fitting formula.826 The background cosmological model used in Fig. (, The background cosmological model used in Fig. (827"2) is assumed to be flat with a cosmological constant, Q,,,,=0.26, Qy=0.04, h—0.72, and n—0.9 (this value of n is close to the best fit found by Croft et al.","2) is assumed to be flat with a cosmological constant, $\Omega_{\cdm}=0.26$, $\Omega_b=0.04$, $h=0.72$, and $n=0.9$ (this value of $n$ is close to the best fit found by Croft et al."828 2002 for our model)., 2002 for our model).829" The Ly-a forest model assumed in the simulation is controlled by 3 the mean transmitted flux fraction in the forest, F, parameters:and the parameters, Ti4 and y—1, of a power-law temperature-density relation for the gas in the IGM, T=T14(A/1.4)-1, where A is the density of the gas in units of the mean density (see McDonald 2003 for a demonstration of the effects of these parameters on the flux power spectrum)."," The $\alpha$ forest model assumed in the simulation is controlled by 3 parameters:the mean transmitted flux fraction in the forest, $\bar{F}$, and the parameters, $T_{1.4}$ and $\gamma-1$, of a power-law temperature-density relation for the gas in the IGM, $T=T_{1.4}(\Delta/1.4)^{\gamma-1}$, where $\Delta$ is the density of the gas in units of the mean density (see McDonald 2003 for a demonstration of the effects of these parameters on the flux power spectrum)."830 The allowed range of each of these parameters has been by independent observations., The allowed range of each of these parameters has been constrained by independent observations.831 We use the measurement constrainedF'=0.746+0.018 from McDonald et al. (, We use the measurement $\bar{F}=0.746\pm0.018$ from McDonald et al. (8322000) and the measurements T1.4=20500+2600 K and 4—1=0.44:0.2 from McDonald et al. (,2000) and the measurements $T_{1.4}=20500\pm 2600$ K and $\gamma-1=0.4\pm0.2$ from McDonald et al. (8332001).,2001).834" To obtain these values at z—2.72, we interpolated between the redshift bins used by McDonald et al. ("," To obtain these values at $z=2.72$, we interpolated between the redshift bins used by McDonald et al. ("835"2000, 2001).","2000, 2001)."836" We subtracted of the potential continuum fitting bias they discuss from F’, and add the same number in quadrature to their error on F."," We subtracted of the potential continuum fitting bias they discuss from $\bar{F}$ , and add the same number in quadrature to their error on $\bar{F}$ ."837 We add 2000 K in quadrature to the error bars on 714 to help absorb any systematic errors., We add 2000 K in quadrature to the error bars on $T_{1.4}$ to help absorb any systematic errors.838 To produce Fig. (, To produce Fig. (839"2), we fixed these a forest parameters to their measured values, and fixed the normalization of the initially adiabatic component of the linear power spectrum, og, to the value that gives the best fit when M,,,,=0.","2), we fixed these $\alpha$ forest parameters to their measured values, and fixed the normalization of the initially adiabatic component of the linear power spectrum, $\sigma_8^*$, to the value that gives the best fit when $M_{\pbh}=0$."840 It is not surprising to see that the a forest power increases dramatically as the white noise power from the PBHs becomes significant on the observed scales., It is not surprising to see that the $\alpha$ forest power increases dramatically as the white noise power from the PBHs becomes significant on the observed scales.841 Fig. (, Fig. (842"2) is not sufficient to place constraints on M, because we have not varied any of the other parameters to see if the predicted power can be adjusted to match the observations.",2) is not sufficient to place constraints on $M_{\pbh}$ because we have not varied any of the other parameters to see if the predicted power can be adjusted to match the observations.843" To obtain an upper limit on the PBH mass we compute y?(M,,,,,), minimizing over the amplitude of the linear power and the three Ly-a forest parameters, to the observational constraints described above on PF, subjectTi4, and Υ—1."," To obtain an upper limit on the PBH mass we compute $\chi^2(M_{\pbh})$, minimizing over the amplitude of the linear power and the three $\alpha$ forest parameters, subject to the observational constraints described above on $\bar{F}$, $T_{1.4}$, and $\gamma-1$."844 We follow Croft et al. (, We follow Croft et al. (8452002) in using only Pr(k) points with k«0.04 s/km.,2002) in using only $P_F(k)$ points with $k<0.04$ s/km.846" Defining an upper limit by x?(M,4)—x7(0)=4, we find M,«17000 Mo."," Defining an upper limit by $\chi^2(M_{\pbh})-\chi^2(0)=4$, we find $M_{\pbh}<17000 \msun$ ."847 Fig. (, Fig. (8483) shows how this limit is obtained.,3) shows how this limit is obtained.849" The temperature-density relation parameters play no role, but F is important."," The temperature-density relation parameters play no role, but $\bar{F}$ is important."850" As M,,,,,, increases, the best fit value of F also increases until this trend is halted by external constraint on F."," As $M_{\pbh}$ increases, the best fit value of $\bar{F}$ also increases until this trend is halted by the external constraint on $\bar{F}$."851" The effect of the increase in F is theto reduce Pr(k) (McDonald 2003), counteracting the increase in power due to M,PBH*"," The effect of the increase in $\bar{F}$ is to reduce $P_F(k)$ (McDonald 2003), counteracting the increase in power due to $M_{\pbh}$."852" Finally, the unconstrained parameter og also increases with M,,,,,,BH? further decreasing the power on small scales while increasing Pr(k) on large scales (see McDonald 2003; this freedom to adjust the tilt of Pr(k) is significant — with og fixed we find M,,,,<5800Mo)."," Finally, the unconstrained parameter $\sigma_8^*$ also increases with $M_{\pbh}$, further decreasing the power on small scales while increasing $P_F(k)$ on large scales (see McDonald 2003; this freedom to adjust the tilt of $P_F(k)$ is significant – with $\sigma_8^*$ fixed we find $M_{\pbh}<5800853\msun$ )."854 Fig. (, Fig. (855"3) may at first appear unconvincing to the reader unfamiliar with the Ly-o forest; however, the result is ultimately simple to understand.","3) may at first appear unconvincing to the reader unfamiliar with the $\alpha$ forest; however, the result is ultimately simple to understand."856 In Fig. (, In Fig. (857"1) we see that the white noise power begins to dominate on the scales to which the Ly-a forest is sensitive when M,,,,,~10000M5 (note that 1 comoving Mpc/h — 108 km/s at z—2.72 in our model).",1) we see that the white noise power begins to dominate on the scales to which the $\alpha$ forest is sensitive when $M_{\pbh}\sim 10000 M_\odot$ (note that 1 comoving Mpc/h = 108 km/s at $z=2.72$ in our model).858" As M,,, increases there is simply too much power on the scale of the Ly-o forest to produce the observed level of fluctuations.", As $M_{\pbh}$ increases there is simply too much power on the scale of the $\alpha$ forest to produce the observed level of fluctuations.859 Increasing F can cancel some of the effect but the size of the increase is limited because F' is directly observable., Increasing $\bar{F}$ can cancel some of the effect but the size of the increase is limited because $\bar{F}$ is directly observable.860 A factor of ~2 relaxation in the upper bound seems unlikely but not inconceivable., A factor of $\sim 2$ relaxation in the upper bound seems unlikely but not inconceivable.861" For example, if we arbitrarily increase the error bar on F to £0.03, the limit we derive is M,,,,«41000Mo."," For example, if we arbitrarily increase the error bar on $\bar{F}$ to $\pm 0.03$, the limit we derive is $M_{\pbh}<41000 M_\odot$."862 The limit is Λι<37000Mo if we arbitrarily decrease the predicted Pr(k) by for all models., The limit is $M_{\pbh}<37000 M_\odot$ if we arbitrarily decrease the predicted $P_F(k)$ by for all models.863" The assumed value of n has no effect on the result (we obtain M,4,,«18000Mo using n= 1).", The assumed value of $n$ has no effect on the result (we obtain $M_{\pbh}<18000 M_\odot$ using $n=1$ ).864" Finally, we remind the reader that the Ly-o forest only constrains the power spectrum in km/s units at z= 2.72."," Finally, we remind the reader that the $\alpha$ forest only constrains the power spectrum in km/s units at $z=2.72$ ."865" Equation (8)and our assumed cosmological model were used to compute M,,,.", Equation (8)and our assumed cosmological model were used to compute $M_{\pbh}$ .866" So, apart from the Poisson noise, is thereanydifference between the gravitational clustering of the conventional CDM (WIMP particles) and PBHs?"," So, apart from the Poisson noise, is thereanydifference between the gravitational clustering of the conventional CDM (WIMP particles) and PBHs?"867 The answer is yes., The answer is yes.868" The collisional relaxation time for a gravitational system is of the order of the number of particles, times the dynamical time of the system."," The collisional relaxation time for a gravitational system is of the order of the number of particles, times the dynamical time of the system."869" Therefore, one expects the relaxation related effects, e.g. evaporation and core"," Therefore, one expects the relaxation related effects, e.g. evaporation and core"870herefore expect a significant time evolution of the observed structure within a few 10 vr.,therefore expect a significant time evolution of the observed structure within a few $10^7$ yr.871 In this context. the static model based on the epicvelic approximation presented. in Sect.," In this context, the static model based on the epicyclic approximation presented in Sect."872 4.4. should be used. with caution. ancl can only serve as a guideline for future full hyerodynamical simulations.," \ref{sec:bar} should be used with caution, and can only serve as a guideline for future full hydrodynamical simulations."873 The gaseous response to a tumbling bar for a potential with a single ILIt was examined by Fukuda. Wada Llabe (1998) via numerical simulations.," The gaseous response to a tumbling bar for a potential with a single ILR was examined by Fukuda, Wada Habe (1998) via numerical simulations."874" Their corresponding run ""Bh indeed. produces trailing spiral shocks resembling the ones we observe in NGC 2974."," Their corresponding run ""Bb"" indeed produces trailing spiral shocks resembling the ones we observe in NGC 2974."875 Their simulations suggest that fueling is rather inellicient in this, Their simulations suggest that fueling is rather inefficient in this876by stacking different homogeneous layers.,by stacking different homogeneous layers.877 As described in Sect., As described in Sect.878" 2.1, our model atmospheres consist of 40 layers."," 2.1, our model atmospheres consist of 40 layers."879" As described in detail by e.g. deHaanetal.(1987),, the doubling-adding method makes use of the fact that if one knows the reflection and transmission properties of two adjacent atmospheric layers, one can straightforwardly calculate these properties for the combined layer."," As described in detail by e.g. \citet{deh87}, the doubling-adding method makes use of the fact that if one knows the reflection and transmission properties of two adjacent atmospheric layers, one can straightforwardly calculate these properties for the combined layer."880" For each atmospheric layer, the calculation of its reflection and transmission properties starts with calculating them analytically for a horizontal slice of the layer with a very small optical thickness."," For each atmospheric layer, the calculation of its reflection and transmission properties starts with calculating them analytically for a horizontal slice of the layer with a very small optical thickness."881" Then, using the so-called 'doubling'-equations (seedeHaanetal.1987),, the properties of a layer with twice the inital optical thickness are calculated."," Then, using the so-called 'doubling'-equations \citep[see][]{deh87}, the properties of a layer with twice the inital optical thickness are calculated."882 This is repeated until the required optical thickness is reached., This is repeated until the required optical thickness is reached.883 The reflection and transmission properties of the whole atmosphere are calculated by combining the properties of the individual layers using the ’adding’-equations (seedeHaanetal.1987)., The reflection and transmission properties of the whole atmosphere are calculated by combining the properties of the individual layers using the 'adding'-equations \citep[see][]{deh87} .884" We use a special version of the doubling-adding algorithm, namely the so-called ""internal sources’ algorithm of Waubenetal. (1994), which fully includes multiple scattering of thermal radiation emitted by the planet's atmosphere."," We use a special version of the doubling-adding algorithm, namely the so-called 'internal sources' algorithm of \citet{wau94}, which fully includes multiple scattering of thermal radiation emitted by the planet's atmosphere."885" In this version, the temperature of each atmospheric layer (see Fig."," In this version, the temperature of each atmospheric layer (see Fig."886 1) determines the amount of thermal radiation that is emitted in the layer., 1) determines the amount of thermal radiation that is emitted in the layer.887 The emission itself is isotropic., The emission itself is isotropic.888" However, scattering of this radiation within the atmospheric layer and/or within other layers will influence the angular distribution of the radiation as it emerges at the top of the atmosphere."," However, scattering of this radiation within the atmospheric layer and/or within other layers will influence the angular distribution of the radiation as it emerges at the top of the atmosphere."889 We calculate the emerging thermal radiation along twenty angles between 0° (towards the zenith) and 90° (parallel to the atmosphere)., We calculate the emerging thermal radiation along twenty angles between $^\circ$ (towards the zenith) and $^\circ$ (parallel to the atmosphere).890" Note that since our atmospheric layers are horizontally homogeneous, the emerging thermal radiation is independent of the azimuth angle."," Note that since our atmospheric layers are horizontally homogeneous, the emerging thermal radiation is independent of the azimuth angle."891" Next, assuming the model planet is locally plane-parallel (thus that the mean-free path of the photons is small enough to ignore atmospheric curvature), we calculate disc-averaged thermal emission spectra by integrating the locally emitted spectra over the disc as follows The cosine of the emission angle (u) is included in the integration to account for the spherical shape of the planet."," Next, assuming the model planet is locally plane-parallel (thus that the mean-free path of the photons is small enough to ignore atmospheric curvature), we calculate disc-averaged thermal emission spectra by integrating the locally emitted spectra over the disc as follows The cosine of the emission angle $\mu$ ) is included in the integration to account for the spherical shape of the planet."892" To calculate the scattering and absorption of radiation with wavelength 2 within each atmospheric layer, the doubling-adding algorithm needs to know for each layer and at the given A: its extinction optical thickness (the sum of the scattering and absorption optical thicknesses), and the single-scattering albedo (the ratio of the scattering optical thickness to the extinction optical thickness) and the scattering phase of the mixture of particles and gas molecules in the layer."," To calculate the scattering and absorption of radiation with wavelength $\lambda$ within each atmospheric layer, the doubling-adding algorithm needs to know for each layer and at the given $\lambda$: its extinction optical thickness (the sum of the scattering and absorption optical thicknesses), and the single-scattering albedo (the ratio of the scattering optical thickness to the extinction optical thickness) and the scattering phase of the mixture of particles and gas molecules in the layer."893" Our model atmospheres not only contain the particles, but also gas molecules."," Our model atmospheres not only contain the particles, but also gas molecules."894 The altitude variation of the different atmospheric gases is produced by the code., The altitude variation of the different atmospheric gases is produced by the code.895 The absorption coefficients for H?O and CO were calculated using the HITEMP database (Rothmanetal.2010) assuming Voigt line shapes., The absorption coefficients for $_2$ O and CO were calculated using the HITEMP database \citep{rot10} assuming Voigt line shapes.896" Other molecules that have strong spectral features in the near-infrared, such as CO? and CH4 are predicted by to be present in only very small volume mixing ratios (generally less than 1079 for CO» and several orders of magnitude less for CH4), and should affect the calculated emission spectra only marginally."," Other molecules that have strong spectral features in the near-infrared, such as $_2$ and $_4$ are predicted by to be present in only very small volume mixing ratios (generally less than $^{-6}$ for $_2$ and several orders of magnitude less for $_4$ ), and should affect the calculated emission spectra only marginally."897" Because the focus of this paper is on the scattering effects of clouds, and not so much on identifying gas signatures or comparisons with observations, we ignored the absorption coefficients of these low-concentration gases."," Because the focus of this paper is on the scattering effects of clouds, and not so much on identifying gas signatures or comparisons with observations, we ignored the absorption coefficients of these low-concentration gases."898" To efficiently include the gaseous absorption in our calculations of emission spectra, we used the k method (Lacis&Oinas1991)."," To efficiently include the gaseous absorption in our calculations of emission spectra, we used the $k$ method \citep{lac91}."899" We first calculated the absorption coefficients of the main gases at a high spectral resolution at a grid of 20 temperatures between 500-4000 K and 20 pressures between 107? - 100 bar, which cover the relevant temperature-pressure space for hot exoplanetary atmospheres."," We first calculated the absorption coefficients of the main gases at a high spectral resolution at a grid of 20 temperatures between 500-4000 K and 20 pressures between $^{-9}$ - 100 bar, which cover the relevant temperature-pressure space for hot exoplanetary atmospheres."900" From these high-spectral resolution spectra, we calculated and tabulated correlated k-distribution coefficients thatwe interpolated to the temperature and pressure of each atmospheric layer."," From these high-spectral resolution spectra, we calculated and tabulated correlated $k$ -distribution coefficients thatwe interpolated to the temperature and pressure of each atmospheric layer."901" Also included in our calculations is collision-induced absorption by H2-H», using the absorption coefficients of Borysowetal.(2001);(2002), as well as Rayleigh scattering by Ho-H», for which we use a depolarisation factor of 0.02 (Irwin 2009).."," Also included in our calculations is collision-induced absorption by $_2$ $_2$, using the absorption coefficients of \citet{bor01,bor02}, as well as Rayleigh scattering by $_2$ $_2$, for which we use a depolarisation factor of 0.02 \citep{irw09}. ."902 We calculated the wavelength dependent refractive indices of the various types of dirty particles that occur in our model atmospheres from the refractive indices of their constituents using effective medium theory (Boschetal. 2000).., We calculated the wavelength dependent refractive indices of the various types of dirty particles that occur in our model atmospheres from the refractive indices of their constituents using effective medium theory \citep{bos00}. .903" Then, foreach type of particle, we calculated its extinction"," Then, foreach type of particle, we calculated its extinction"904"episodes in Halo 4 beginning at z= 8, 4.3 and 2.1 are preceded by mergers at z=8.5, 4.7 and 2.4 with haloes of 2x105, 3x105 and 10°Mo, respectively, which bring in fresh gas.","episodes in Halo 4 beginning at $z=8$ , $4.3$ and $2.1$ are preceded by mergers at $z=8.5$, $4.7$ and $2.4$ with haloes of $2\times10^8$, $3\times10^8$ and $10^9\Ms$, respectively, which bring in fresh gas."905" Observations of periodic bursts lasting several hundred million years have been reported for three dwarf galaxies by ?,, while a number of dwarf galaxies (Leo I (?),, Leo A (?),, IC 10 (?),, IC 1613 (?),, DDO 210 (?) and Carina (?))) show extended, quiescent periods between star formation epochs."," Observations of periodic bursts lasting several hundred million years have been reported for three dwarf galaxies by \cite{McQuinn-2009}, while a number of dwarf galaxies (Leo I \citep{Dolphin-2002}, Leo A \citep{Cole-2007}, IC 10 \citep{Cole-2010}, IC 1613 \citep{Skillman-2003}, , DDO 210 \citep{McConnachie-2006} and Carina \citep{Koch-2006}) ) show extended, quiescent periods between star formation epochs."906" ? suggest mergers and gas accretion as triggers for star formation, but note that individual bursts and mergers can no longer be linked observationally after several Gyrs."," \cite{Cole-2010}907 suggest mergers and gas accretion as triggers for star formation, but note that individual bursts and mergers can no longer be linked observationally after several Gyrs."908" 'The star formation history of each individual galaxy in our simulations reflects a combination of internal self-regulation via supernova feedback, and the supply of fresh gas via accretion and mergers."," The star formation history of each individual galaxy in our simulations reflects a combination of internal self-regulation via supernova feedback, and the supply of fresh gas via accretion and mergers."909" These two effects largely determine the variance in stellar mass between the haloes in our simulations; while differences in merger histories increase the variance, self-regulation via feedback decreases it."," These two effects largely determine the variance in stellar mass between the haloes in our simulations; while differences in merger histories increase the variance, self-regulation via feedback decreases it."910" In our sample of six haloes of equal final mass, the galaxy stellar masses vary by about a factor of two."," In our sample of six haloes of equal final mass, the galaxy stellar masses vary by about a factor of two."911 Gas-rich mergers after z—6 imply that the progenitors did not lose all their gas due to the UV background., Gas-rich mergers after $z=6$ imply that the progenitors did not lose all their gas due to the UV background.912" In our simulations, such mergers occur with haloes that would reach masses above ~10°Mo by z=0."," In our simulations, such mergers occur with haloes that would reach masses above $\sim 10^9\Ms$ by $z=0$."913" ? showed that at this mass, a combination of UV and supernova feedback removes gas efficiently, while UV radiation alone is not always sufficient."," \cite{Sawala-2010} showed that at this mass, a combination of UV and supernova feedback removes gas efficiently, while UV radiation alone is not always sufficient."914 Observations of local group dwarf spheroidals (e.g.?) also suggest that reionisation had at most a minor effect on these galaxies., Observations of local group dwarf spheroidals \citep[e.g.][]{Monelli-2010} also suggest that reionisation had at most a minor effect on these galaxies.915 Some major mergers also contribute stars., Some major mergers also contribute stars.916" The fraction of final stellar mass formed outside of the main progenitor ranges from ~5% in Halo 5, accreted at z=5.2, to close to 4096 for Halo 1, resulting from two major mergers at z—3.4 and z=0.8."," The fraction of final stellar mass formed outside of the main progenitor ranges from $\sim5\%$ in Halo 5, accreted at $z=5.2$, to close to $40\%$ for Halo 1, resulting from two major mergers at $z=3.4$ and $z=0.8$."917" Haloes 2 and 6 both accrete ~25% in mergers at z—0.4 and 1, respectively, while haloes 3 and 4 accrete ~7% in mergers at z=0.5 and z=2.4."," Haloes 2 and 6 both accrete $\sim25\%$ in mergers at $z=0.4$ and 1, respectively, while haloes 3 and 4 accrete $\sim7\%$ in mergers at $z=0.5$ and $z=2.4$."918" Since haloes 3, 4 and 5 follow a more typical assembly history, we expect the typical fraction of stars formed outside the main progenitor in dwarf galaxies of M,~10°Mo to be «10%, albeit with possible exceptions."," Since haloes 3, 4 and 5 follow a more typical assembly history, we expect the typical fraction of stars formed outside the main progenitor in dwarf galaxies of $_\star\sim10^8\Ms$ to be $<10\%$, albeit with possible exceptions."919" In general, we find that the mean metallicity evolves with age, indicating the recycling of enriched gas in subsequent generations of stars."," In general, we find that the mean metallicity evolves with age, indicating the recycling of enriched gas in subsequent generations of stars."920" At each stellar age, we also find a spread in metallicities, which indicates the incorporation offresh material."," At each stellar age, we also find a spread in metallicities, which indicates the incorporation offresh material."921" However, we note that due to a lack of diffusive metal mixing, the metallicity spread in our simulated stellar populations can be as high as 3 dex, whichis larger than observed."," However, we note that due to a lack of diffusive metal mixing, the metallicity spread in our simulated stellar populations can be as high as 3 dex, whichis larger than observed."922The analytic continuation of £ to the lower hall-plane can be accomplished by coiplexifviug a aud integrating (1) [rome =1 tor —6) aloug au arbitrary contour iu the upper half-plaue of wr.,The analytic continuation of $F$ to the lower half-plane can be accomplished by complexifying $x$ and integrating (1) from $x=1$ to $x=0$ along an arbitrary contour in the upper half-plane of $x$.923 The shape of the x-coitour determines the shape of the cuts in the lower half-plane of w., The shape of the x-contour determines the shape of the cuts in the lower half-plane of $\omega$.924 We close the semicircle [e—0.5|=0.5., We chose the semicircle $|x-0.5|=0.5$.925 This gives the cuts in the lower hall-plaue of w ruuniug straight down fOl og=ah., This gives the cuts in the lower half-plane of $\omega$ running straight down from $\omega = \pi k$.926 The dispersion function F was calculated utumerically., The dispersion function $F$ was calculated numerically.927 The eleeumoces. both the crustal modes anc the uncdamped Alfven eigenmoces are given in the table.," The eigenmodes, both the Landau-damped crustal modes and the undamped Alfven eigenmodes are given in the table."928 The real entries of the table (what we call Alfven eigenmodes). were coulirmed by a straightforward real-numbers iitegration of (1).," The real entries of the table (what we call Alfven eigenmodes), were confirmed by a straightforward real-numbers integration of (1)."929 Due to the cuts. the late-tiime asyiptotic of the crustal motion will also have algebraically amped modes with [requeucies w=wh.," Due to the cuts, the late-time asymptotic of the crustal motion will also have algebraically damped modes with frequencies $\omega = \pi k$."930 The late time asymptotic is determiued solely by the location of the tips of the cuts aud is not affected by the choice of the x-contour., The late time asymptotic is determined solely by the location of the tips of the cuts and is not affected by the choice of the x-contour.931 The zeros of F are also i|Ttyeudent of the x-coutour., The zeros of $F$ are also independent of the x-contour.932 For generic parameters AL aud cj. uumerical integration seems to be the only way.," For generic parameters $M$ and $c_t$, numerical integration seems to be the only way."933 But there are limiting cases whiἩ cau be treated analytically., But there are limiting cases which can be treated analytically.934 These may serve to confirm that equation (1) actually makes seusible predietious aud also to cheek the nunerical results: L thank Yuri Levin lor showing me the problem aud for useful diseussious., These may serve to confirm that equation (1) actually makes sensible predictions and also to check the numerical results: I thank Yuri Levin for showing me the problem and for useful discussions.935 This work was supported by the David aud Lucile Packard foundation., This work was supported by the David and Lucile Packard foundation.936vector in (he r direction.,vector in the ${\bf r}$ direction.937 If the tensor is isotropic. Η reduces (o a scalar: if the region over which it is determined is representative of the universe as a whole. it is the IIubble constant.," If the tensor is isotropic, ${\bf H}$ reduces to a scalar; if the region over which it is determined is representative of the universe as a whole, it is the Hubble constant."938 It is therefore convenient to call H the Hubbletensor!., It is therefore convenient to call ${\bf H}$ the Hubble.939. The Hubble tensor. quantilving anisotropic motion. is the next more complicated description of cosmic motion after a simple uniform expausion.," The Hubble tensor, quantifying anisotropic motion, is the next more complicated description of cosmic motion after a simple uniform expansion."940 To determine the components of the Hubble tensor from a set of data. a least-squares method is the most straightforward.," To determine the components of the Hubble tensor from a set of data, a least-squares method is the most straightforward."941 We take as à measure of goodness of fit the average square of (he difference between the predicted radial velocity and the observed radiality. Taking (he derivatives of (his with respect to the three components of vy and the six independent components of H and. setting Chem equal to zero eives nine linear equations to be solved for the nine unknowns. a straightforward if tediouscaleulation?.," We take as a measure of goodness of fit the average square of the difference between the predicted radial velocity and the observed radial, Taking the derivatives of this with respect to the three components of ${\bf v}_0$ and the six independent components of ${\bf H}$ and setting them equal to zero gives nine linear equations to be solved for the nine unknowns, a straightforward if tedious."942. An isotropic solution is determined similarly. using four equations in four unknowns.," An isotropic solution is determined similarly, using four equations in four unknowns."943 Distance and radial velocity data for galaxies within 10 Alpe were gathered [rom the ileratiure and are summarized in Table 1.., Distance and radial velocity data for galaxies within 10 Mpc were gathered from the literature and are summarized in Table \ref{table:Data}.944 In gathering the data much use has been made of the NASA/IPAC Extragalactic Database(NED)!., In gathering the data much use has been made of the NASA/IPAC Extragalactic Database.945. The column headings are: (1) Designation: or Chose galaxies which have been catalogued several times. only one was chosen. to maintain readabilitv of thetable’: (2) Apparent B magnitude. from NED: (3) Morphological tvpe. rom NED: (4) Superealactic longitude. in degrees: (5) Superealactic latitude. in degrees: (6) Radial velocity. in kms I: (7) the source for the radial velocitv: (8) Distance. in Mpc:," The column headings are: (1) Designation; for those galaxies which have been catalogued several times, only one was chosen, to maintain readability of the; (2) Apparent $B$ magnitude, from NED; (3) Morphological type, from NED; (4) Supergalactic longitude, in degrees; (5) Supergalactic latitude, in degrees; (6) Radial velocity, in km $^{-1}$; (7) the source for the radial velocity; (8) Distance, in Mpc;"946It is clear from the plot that radius increases as decreases with verv little scatter for the 1.05 models.,It is clear from the plot that radius increases as decreases with very little scatter for the 1.05 models.947 We find that a clegeneracy in predicted radius occurs for models of different mass., We find that a degeneracy in predicted radius occurs for models of different mass.948 Specilicallv. in our analvsis. we see Lad calculated from models lie on a nearly parallel line to that generated by the models having a vertical shift of around HII )ytndeamuchlargerscatter.," Specifically, in our analysis, we see that calculated from models lie on a nearly parallel line to that generated by the models having a vertical shift of around Hz in and a much larger scatter."949Suchashi μα μμ αμ. )yeanleadtothecaleulationofaradiusdif feringbynearly depending on whether the stellar mass is 1.05 or L.10., Such a shift implies that an observed can lead to the calculation of a radius differing by nearly depending on whether the stellar mass is 1.05 or 1.10.950AZAZ.... This degeneracy may be lifted by using solar models with (he assumption of a homologous scaling., This degeneracy may be lifted by using solar models with the assumption of a homologous scaling.951 It is sometimes convenient (o assume homoloev to compare theoretical models bv introducing a corecduced radius (see e.g. Fernandes and Monteiro 2003) such that. We have listed the values of lor each model in Table 3.," It is sometimes convenient to assume homology to compare theoretical models by introducing a “reduced” radius (see e.g. Fernandes and Monteiro 2003) such that, We have listed the values of for each model in Table 3."952" It is easily seen that the values of Che ""reduced spacings are relatively consistent for each mass such that HIE forl.05M models ancl EH forl.10MAL.", It is easily seen that the values of the “reduced” spacings are relatively consistent for each mass such that Hz for 1.05 models and Hz for 1.10.953.. Were our stellar models purely homologous. then the reduced spacing," Were our stellar models purely homologous, then the reduced spacing"954hi addition to the fundameutal theoretical work. futiwe observational programs aimed at detecting the effects of rapid rotation using eground-based optical iuterferometers could be fruitful in the determination O he shapes of ejut stars. where temperature variations οἳ he surface may be probed 2009).,"In addition to the fundamental theoretical work, future observational programs aimed at detecting the effects of rapid rotation using ground-based optical interferometers could be fruitful in the determination of the shapes of giant stars, where temperature variations of the surface may be probed ."955 A program of highlv accurate M1Oolctric studies cau be considered. enabliug one O cletec differences dn luminosity aid colors of rapidly rotating stars m comparison to their sinele-star couiterparts.," A program of highly accurate photometric studies can be considered, enabling one to detect differences in luminosity and colors of rapidly rotating stars in comparison to their single-star counterparts."956" For example. observational evidence exists ha maenetically-active. rapidly rotating. low-mass MS stars din eclipsing biuaries are characterized by effective cluperatures that are lower tiu. radi that are larger hal. ak Iumunosities that are approximately equal to hose predicted frou, corresponding theoretical stellar LOClels of the same mass 2009)."," For example, observational evidence exists that magnetically-active, rapidly rotating, low-mass MS stars in eclipsing binaries are characterized by effective temperatures that are lower than, radii that are larger than, and luminosities that are approximately equal to those predicted from corresponding theoretical stellar models of the same mass ."957 The παλιο stellar models satisfactorily match observations of sinilur-nass stars that are rotating more slowly in wicle binary orbits. (20," The same stellar models satisfactorily match observations of similar-mass stars that are rotating more slowly in wide binary orbits. , ,"95806)... FH). ud others have show that the source of these differences is the magnetic activitv in the rapidly rotating stars., and others have shown that the source of these differences is the magnetic activity in the rapidly rotating stars.959 Whether the racii. effective temperatures aud. Iuninosities im rapidly rotating ooeiut or ΠΟ stars would© snadlulv affected is an interesting aud unresolved question.," Whether the radii, effective temperatures and luminosities in rapidly rotating giant or HB stars would be similarly affected is an interesting and unresolved question."960| Finally. studies on the απναπο1ος n he circuustellar MNam of stars iu the ACD phase with upconiues facilitiesmM. ALMA) will be especially usefi] in providing ou the stellar evolutionary phases where asviunietries develop.," Finally, studies on the asymmetries in the circumstellar envelope of stars in the AGB phase with upcoming facilities, ALMA) will be especially useful in providing constraints on the stellar evolutionary phases where asymmetries develop."961 Sucji studies will be vCry müportant for distinguishiug the contributious of fre inereed population from the ONISine binary population. thereby potentially providing further coustraimts on nucertain population svuthesis input parameters and yossible shaping mechanisms for the origin of the asyiunjetries seen to be prevalent in the post-ACGD and proto-plauetaryv nebula phase.," Such studies will be very important for distinguishing the contributions of the merged population from the existing binary population, thereby potentially providing further constraints on uncertain population synthesis input parameters and possible shaping mechanisms for the origin of the asymmetries seen to be prevalent in the post-AGB and proto-planetary nebula phase."962é1 additional periceuter precession. but also to a recession. of the orbital plane of the star.,"an additional pericenter precession, but also to a precession of the orbital plane of the star."963 These recessions are smaller than the Sebwarzschild effect In qmagnitude because they depend on je dimensionless angular momentum paramctcr \aDJFMT. whichH is- always less than one. and vecause they fall off faster with distance from ie black hole.," These precessions are smaller than the Schwarzschild effect in magnitude because they depend on the dimensionless angular momentum parameter $\chi \equiv J/M^2$, which is always less than one, and because they fall off faster with distance from the black hole."964 However. accumulating evidence sugecsts that MDIT should be rather rapidly rotating. with X larger han 0.5 and possibly as arge as 0.9. so these effects could be significant.," However, accumulating evidence suggests that MBH should be rather rapidly rotating, with $\chi$ larger than 0.5 and possibly as large as 0.9, so these effects could be significant."965 The purpose of this paper is to poiut out that. if a class of stars were to be found with orbital veriods of fractions of a vear. and with sufficieutlv aree orbital ecceutricitics. then the quadrupole-induced precessious could be as large as 10 µας or vear.," The purpose of this paper is to point out that, if a class of stars were to be found with orbital periods of fractions of a year, and with sufficiently large orbital eccentricities, then the quadrupole-induced precessions could be as large as 10 $\mu$ as per year."966 Fieure 1. illustrates this: assunudus a dack hole with 4=0.7. it shows the orbital 1ος required as a function of eccentricity. for he rates of precessious due to Sclavarzsclild (8). rianne-drageie CZ) and quadrupole (25) terms to )o as large as 10. 5. and 1 jras per vear.," Figure \ref{fig1} illustrates this: assuming a black hole with $\chi = 0.7$, it shows the orbital period required as a function of eccentricity, for the rates of precessions due to Schwarzschild (S), frame-dragging $J$ ) and quadrupole $Q_2$ ) terms to be as large as 10, 5, and 1 $\mu$ as per year."967 Figure 2 shows the effect of black hole spiu ou he amplitudes of the relativistic effects., Figure \ref{fig2} shows the effect of black hole spin on the amplitudes of the relativistic effects.968 For orbits with eccentricity 0.9 and periods of one vear and 1 vears. the amplituces of the three effects are slotted i pas per vear.," For orbits with eccentricity 0.9 and periods of one year and 0.1 years, the amplitudes of the three effects are plotted in $\mu$ as per year."969 The precession of the orbital pluie ids the uost important effect here. because it depends oulv on J and Qo: the Sclowarzschild part of the metric affects only the periceuter advance.," The precession of the orbital plane is the most important effect here, because it depends only on $J$ and $Q_2$; the Schwarzschild part of the metric affects only the pericenter advance."970 The orbital plane is determined by its inclination angele ; relative to the plane of the sky aud bv the anele of nodes Q between a reference direction and the intersection of the two planes., The orbital plane is determined by its inclination angle $i$ relative to the plane of the sky and by the angle of nodes $\Omega$ between a reference direction and the intersection of the two planes.971" Staudard astrometric aud Doppler observatious can determine O. ἐν the periceuter angle το, the seniunajor axis « and the orbital ecceutricity ο, and. eiven sufficient observation time. the secular rates of change dO/df. difdt. aud chefet."," Standard astrometric and Doppler observations can determine $\Omega$, $i$, the pericenter angle $\omega$ , the semimajor axis $a$ and the orbital eccentricity $e$, and, given sufficient observation time, the secular rates of change $d\Omega/dt$, $di/dt$, and $d\omega/dt$."972 Ilowever. in order to test the no-hair theorems. 6je nimmst determine five parameters: the mass of the black hole. the magnitude and two angles of its spin. aud the value of the quadrupole momeut.," However, in order to test the no-hair theorems, one must determine five parameters: the mass of the black hole, the magnitude and two angles of its spin, and the value of the quadrupole moment."973" The ""EKepleraueasured ass is determined from the orbital periods of stars. but may require data from a nunuber of stars to fx it separately frou any extended distribution of mass."," The “Kepler-measured” mass is determined from the orbital periods of stars, but may require data from a number of stars to fix it separately from any extended distribution of mass."974 Then. to measure J and Qo. it is necessary and sufficient to measure dO/dt aud difdt for two stars in nou-degeucrate orbits.," Then, to measure $\bf J$ and $Q_2$, it is necessary and sufficient to measure $d\Omega/dt$ and $di/dt$ for two stars in non-degenerate orbits."975 A test of the uo-hairuess of the ceutral object in our galaxy would be compelling evidence that it is truly a black hole of general relativity., A test of the no-hairness of the central object in our galaxy would be compelling evidence that it is truly a black hole of general relativity.976 For the purpose of this rough analysis. itsuffices to work in the post-Newtouian limit.," For the purpose of this rough analysis, itsuffices to work in the post-Newtonian limit."977 The equation of motion of a body of negligible mass in thefield of a body with mass M. aneular momentum J aud," The equation of motion of a body of negligible mass in thefield of a body with mass $M$ , angular momentum $\bf J $ and"978DUAL would like τω thank UK STFC for their financial support and the Roval Society for funding a Sl processor supercomputer wader their Research Grants Scheme.,DHM would like to thank UK STFC for their financial support and the Royal Society for funding a 81 processor supercomputer under their Research Grants Scheme.979 LAG would like to thauk the Roval Society ane Leverhulue Trust for financial support., LMG would like to thank the Royal Society and Leverhulme Trust for financial support.980 We acknowledge the use of data provided by the SoIIO/MDI iustiruiuenut., We acknowledge the use of data provided by the SoHO/MDI instrument.981 The authors would like to thauk the referee for his constructive comments which lave mniproved this paper., The authors would like to thank the referee for his constructive comments which have improved this paper.982cases is there possibly aat velocities that may imdicate imfall.,cases is there possibly at velocities that may indicate infall.983 The oobservatious reveal interstellar aassociated with the LAIC is preseut in large quantities across the whole face of the LMC. with an average column deusity aud patchiness identical to those of the Galactic halo.," The observations reveal interstellar associated with the LMC is present in large quantities across the whole face of the LMC, with an average column density and patchiness identical to those of the Galactic halo."984 Lines of sight projected onto superbubbles aud supergiaut shells have much the same coblunn densities as lines of sight projected onto quiesceut regions., Lines of sight projected onto superbubbles and supergiant shells have much the same column densities as lines of sight projected onto quiescent regions.985" The LMC aabsorptiou is both much broader aud shifted to lower absolute velocities thau the lowerdonization gas (οι, 11))."," The LMC absorption is both much broader and shifted to lower absolute velocities than the lower-ionization gas (e.g., )."986 For reasous discussed in detail by Howk et al. |H]..," For reasons discussed in detail by Howk et al. \cite{howk02},"987 the favored interpretation of these salient aspects of the LMC is that the LMC is surrounded by a hot. hiehlv-ionized halo or corona simular iu may respects to that found in the Milkv Way that gives rise to the observed aabsorptiou.," the favored interpretation of these salient aspects of the LMC is that the LMC is surrounded by a hot, highly-ionized halo or corona – similar in many respects to that found in the Milky Way – that gives rise to the observed absorption."988 Several models eau explain the plivsies of the pproduction within a gaseous halo about the LMC. includiug cooling galactic fountain flows aud interface models (ucl as turbulent musing laver or conductive interface models).," Several models can explain the physics of the production within a gaseous halo about the LMC, including cooling galactic fountain flows and interface models (such as turbulent mixing layer or conductive interface models)."989 The cooling fountain model provides an clegant explanation for the similarity of the average Milkv. Wav and LAIC cool densities., The cooling fountain model provides an elegant explanation for the similarity of the average Milky Way and LMC column densities.990 Though these galaxies differ in oxvecn abundance by a factor of 2.5. the colum density of lighl-ionized iietals iu a cooling flow of hot material is indepeudent of abundance [2]..," Though these galaxies differ in oxygen abundance by a factor of $\sim2.5$, the column density of highly-ionized metals in a cooling flow of hot material is independent of abundance \cite{edgarchevalier86}."991 The column density of in the Edear Chevalier [2] models is a function of the ratio [V/ng. where NV is the cooling rate iu- protons . ad ny is the initial density of the flow.," The column density of in the Edgar Chevalier \cite{edgarchevalier86} models is a function of the ratio $\dot{N}/n_0$, where $\dot{N}$ is the cooling rate (in protons $^{-1}$ ), and $n_0$ is the initial density of the flow."992 The average LMC ccoluun density (Table 1) corresponds to a one-sided mass-fiow rate from the LM disk of The adopted deusity is consistent with estimates of electron cleusitics iu supergiant shells aud diffuse gas using N-ray observations of the LALC [6]., The average LMC column density (Table 1) corresponds to a one-sided mass-flow rate from the LMC disk of The adopted density is consistent with estimates of electron densities in supergiant shells and diffuse gas using X-ray observations of the LMC \cite{points01}.993 It should be noted. however. that the energy input requirements into the ISM αμα mass flow rates from the disk can be siguificautly different if the aarises in turbulent mixing lavers or other interface-type models.," It should be noted, however, that the energy input requirements into the ISM and mass flow rates from the disk can be significantly different if the arises in turbulent mixing layers or other interface-type models."994 Observations of other highly-ionized species (c.g...o 1v)) will be required το distinguish between the cooling flow aud interface models.," Observations of other highly-ionized species (e.g., ) will be required to distinguish between the cooling flow and interface models."995black holes.,black holes.996 I£ nuclear black holes in Sevlert galaxies grew through multiple mergers before the formation of the stellar disks. one mieht expect their spin axes to be uncorrelated with those of the stars and gas.," If nuclear black holes in Seyfert galaxies grew through multiple mergers before the formation of the stellar disks, one might expect their spin axes to be uncorrelated with those of the stars and gas."997 This work was supported by NSF grants AST 96-17088 and 00-71099 and by NASA erants NAG5-GO37 and NAG5-9046., This work was supported by NSF grants AST 96-17088 and 00-71099 and by NASA grants NAG5-6037 and NAG5-9046.998spectra.,spectra.999 This spectrum was obtained using the VESPA correlator svstem and stretelies [rom 218.084 to 218.419 GlIz (the portion which is not displaved contains no obvious features).," This spectrum was obtained using the VESPA correlator system and stretches from $218.084$ to $218.479\,$ GHz (the portion which is not displayed contains no obvious features)."1000 The spectrum has been smoothed to a resolution of 1.25 MIIz per channel to improve our signal {ο noise ratio.," The spectrum has been smoothed to a resolution of $1.25\,$ MHz per channel to improve our signal to noise ratio."1001 This spectrum represents only one LO setting. though we were able to obtain a spectrum of the image band.," This spectrum represents only one LO setting, though we were able to obtain a spectrum of the image band."1002 It confirms Chat the main features in the displaved spectrum are uncontaminated by features from (he image band., It confirms that the main features in the displayed spectrum are uncontaminated by features from the image band.1003 There are 6 lines in this spectrum. only 3 of which can be identified.," There are 6 lines in this spectrum, only 3 of which can be identified."1004 The largest feature. near 213.32 GIIz is the J=24-23 transition of IIC4N. The next line. αἱ around 218.29 GHz is unidentified. and we label i U218a.," The largest feature, near $218.32\,$ GHz is the $J=24-23$ transition of $_3$N. The next line, at around $218.29\,$ GHz is unidentified, and we label it U218a."1005 There does appear to be some non-zero [αν between U218a and (he yN line: however. we are unable to associate it with a carrier or even a rough line fit so it is unlabelled.," There does appear to be some non-zero flux between U218a and the $_3$ N line; however, we are unable to associate it with a carrier or even a rough line fit so it is unlabelled."1006 We identify the line near 218.22 GIlz as the 354—20» transition of formaldehyde.," We identify the line near $218.22\,$ GHz as the $3_{03}-2_{02}$ transition of formaldehyde."1007 The line near 218.16 GlIlIz is the 55;—444 transition of e-C'ylIs.," The line near $218.16\,$ GHz is the $5_{24}-4_{13}$ transition of $_3$ $_2$."1008 The two line blend at the red edee of the spectrum consists of two unidentilied lines. labelled U218b and U218ec.," The two line blend at the red edge of the spectrum consists of two unidentified lines, labelled U218b and U218c."1009 In order to obtain reasonable line fits il was necessary to simultaneously fit U2183b and U218e. aud to constrain the expansion velocity of the fit for U213e.," In order to obtain reasonable line fits it was necessary to simultaneously fit U218b and U218c, and to constrain the expansion velocity of the fit for U218c."1010 The 225.697 GlIz spectrum shows only one line. the 31»—244 line of formaldehyde.," The $225.697\,$ GHz spectrum shows only one line, the $3_{12}-2_{11}$ line of formaldehyde."1011 Given (hat we have carried oul a very deep integration towards IRC+10216. it is worth considering the odds that we have misidentilied the putative II3CO lines due to confusion with previously uncataloged. unidentified lines. or U-lines.," Given that we have carried out a very deep integration towards IRC+10216, it is worth considering the odds that we have misidentified the putative $_2$ CO lines due to confusion with previously uncataloged, unidentified lines, or U-lines."1012 If we take as our null hypothesis that ICO is not responsible for anv of the lines in anv of our spectra. we find that (here is one U-line in our 140.8 Giz spectrum. (wo in our 150.5 GlIz spectrum. one in our 211.2 GlIIz spectrum. four in our 218.2 GIIz spectrum. and one in our 225.7 GIIz spectrum.," If we take as our null hypothesis that $_2$ CO is not responsible for any of the lines in any of our spectra, we find that there is one U-line in our $140.8\,$ GHz spectrum, two in our $150.5\,$ GHz spectrum, one in our $211.2\,$ GHz spectrum, four in our $218.2\,$ GHz spectrum, and one in our $225.7\,$ GHz spectrum."1013 We can then determine the probability (hat five of the nine U-lines should - by random chance - lie at the five HCO frequencies., We can then determine the probability that five of the nine U-lines should - by random chance - lie at the five $_2$ CO frequencies.1014 This is the probability (hat our identification is in error., This is the probability that our identification is in error.1015 Our bandwidth for each of these spectra is 256 MIIz. except for the 218.2 GIIz spectrum where it is 395 MIIz.," Our bandwidth for each of these spectra is $256\,$ MHz, except for the $218.2\,$ GHz spectrum where it is $395\,$ MHz."1016 Our null hypothesis is that (here are no formaldehyde lines in our specira. and that the lines we have been idenüfving as formaldehyde are actually U-lines.," Our null hypothesis is that there are no formaldehyde lines in our spectra, and that the lines we have been identifying as formaldehyde are actually U-lines."1017 The rate of occurence of U-lines in each spectrum is just the munber of U-lines in that spectrum divided by the number of independent resolution elements within (hat band., The rate of occurence of U-lines in each spectrum is just the number of U-lines in that spectrum divided by the number of independent resolution elements within that band.1018 For all spectra except. the. 215.2 GIIz spectrum. (the resolution elements are 1 MlIz wide: [or the 215.2 GIlz spectrum. the resolution elements have been smoothed (o. 1.25 MIIz wide.," For all spectra except the $218.2\,$ GHz spectrum, the resolution elements are $1\,$ MHz wide; for the $218.2\,$ GHz spectrum, the resolution elements have been smoothed to $1.25\,$ MHz wide."1019 since any lime fit which has a central frequency within z0.5 a resolution element of the laboratory formaldehyde Irequency would likely be identified as a transition of formaldehyde. the probability that a single line wouldmeet that criterion is P?=1/256.2/256.4/316. and 1/256. respectively lor the 140.8.150.5.211.2.218.2 and 225.7 GlIz spectra.," Since any line fit which has a central frequency within $\pm0.5$ a resolution element of the laboratory formaldehyde frequency would likely be identified as a transition of formaldehyde, the probability that a single line wouldmeet that criterion is $P=1/256,\>10202/256,\>1/256,\>4/316,$ and $1/256$ , respectively for the $140.8,\>150.5,\>211.2,\>218.2$ and $225.7\,$ GHz spectra."1021 Thus. the odds that we would simultaieously. confuse five independent U-lines with the five observed transitions of formaldehyde is only P?—(1/256)(2/256)(1/256)(4/316)(1/256)~5.9x10. 1”.," Thus, the odds that we would simultaneously confuse five independent U-lines with the five observed transitions of formaldehyde is only $P=(1/256)(2/256)(1/256)(4/316)(1/256)\sim 5.9\times 10^{-12}$ ."1022each with a different value of à.,each with a different value of $\tilde{\alpha}$.1023" In a smooth Frieclmannu-Robertson-Walker (FRW) universe. A=1 in all beams: the metric is given by ds?=di?—e(D)di?kr?)4(0+sin?0do?)]. where a(/) is the cosmic scale factor. and fk is the global curvature parameter (Qj=1—Q4,ὩνκHg)."," In a smooth Friedmann-Robertson-Walker (FRW) universe, $\tilde{\alpha}=1$ in all beams; the metric is given by $ds^2=dt^2-a^2(t)[dr^2/(1-kr^2)+r^2 (d\theta^21024+\sin^2\theta \,d\phi^2)]$, where $a(t)$ is the cosmic scale factor, and $k$ is the global curvature parameter $\Omega_k1025=1-\Omega_m-\Omega_X=-k/H_0^2$ )."1026" The comoving distance ris given by (Weinberg1972) r(z) lasoni) E(z) where ""sinn is defined as sinh if ο,>0. and sin i£ ο<ο."," The comoving distance $r$ is given by \citep{Weinberg72}1027 r(z) _0^z, E(z) , where “sinn” is defined as sinh if $\Omega_k>0$, and sin if $\Omega_k<0$."1028" If O,=0. the sinn and £s disappear from Eq.(1)). leaving only the integral."," If $\Omega_k=0$, the sinn and $\Omega_k$ 's disappear from \ref{eq:r(z)}) ), leaving only the integral."1029 Oyfy(2) is the contribution from dark energy: the dimensionless dark energy density. /(2)=px(z)/px(z 0)., $\Omega_X f_X(z)$ is the contribution from dark energy; the dimensionless dark energy density $f(z)=\rho_X(z)/\rho_X(z=0)$ .1030 For a cosmological constant. Oy=O4. and fy(2)=I.," For a cosmological constant, $\Omega_X=\Omega_\Lambda$, and $f_X(z)=1$."1031 The angular diameter distance is given by da(z)9r(z)(4z). and the Iuminositv distance is given bv dj(2)=(14z)datz).," The angular diameter distance is given by $d_A(z)=r(z)/(1+z)$, and the luminosity distance is given by $d_L(z)=(1+z)^2 d_A(z)$."1032 llowever. our universe is clumpy rather than smooth.," However, our universe is clumpy rather than smooth."1033 According to the focusing theorem in gravitational lens theory. if there is anv shear or matter along a beam connecting a source (o an observer. the angular diameter distance of the source [rom the observer issmaller (han that which would occur if the source were seen through an empty. cone. provided (he affine parameter distance (defined such that its element equals the proper distance element at (he observer) is (hie same ancl the beam has not gone (hrough a caustic.," According to the focusing theorem in gravitational lens theory, if there is any shear or matter along a beam connecting a source to an observer, the angular diameter distance of the source from the observer is than that which would occur if the source were seen through an empty, shear-free cone, provided the affine parameter distance (defined such that its element equals the proper distance element at the observer) is the same and the beam has not gone through a caustic."1034 An increase of shear or matter densitv along the beam decreases the angular diameter distance and. consequently. increases the observable flux for given z., An increase of shear or matter density along the beam decreases the angular diameter distance and consequently increases the observable flux for given $z$.1035 (Schneideretal.1992) For studies of weak lensing magnification (with convergence |r|S0.2(Barber 2000))). we can ienore shear and considerconvergence only. which corresponds to the matter in the beam.," \citep{Sch92} For studies of weak lensing magnification (with convergence $|\kappa| \la 0.2$\citep{Barber00}) ), we can ignore shear and considerconvergence only, which corresponds to the matter in the beam."1036While the range from 115 nm to 310 nm ts covered by the two SOLSTICE instruments. with a resolution of 1 nm. the XPS instrument measures spectra from 0.1 to 34 nm.,"While the range from 115 nm to 310 nm is covered by the two SOLSTICE instruments, with a resolution of 1 nm, the XPS instrument measures spectra from 0.1 to 34 nm."1037 Figure 9. shows a comparison between the observations of the irradiance at 121.5 nm measured by the SOLSTICE instrument and the output of the 24-hour forecast model., Figure \ref{figure_fuv_007_contrib} shows a comparison between the observations of the irradiance at 121.5 nm measured by the SOLSTICE instrument and the output of the 24-hour forecast model.1038 The red and blue lines in the upper panel present the contribution of ephemeral regions. Classes II and IL. respectively.," The red and blue lines in the upper panel present the contribution of ephemeral regions, Classes II and III, respectively."1039 The green line displays the contribution of active regions (Class IV)., The green line displays the contribution of active regions (Class IV).1040 Figure 9bb displays the contribution of umbrae (red line) and penumbrae (blue line)., Figure \ref{figure_fuv_007_contrib}b b displays the contribution of umbrae (red line) and penumbrae (blue line).1041 The contributions are computed by multiplying each element of the input vector by the weights w;., The contributions are computed by multiplying each element of the input vector by the weights $w_i$.1042 The weighted elements of each class are them summed and the total contribution of each class is obtained., The weighted elements of each class are them summed and the total contribution of each class is obtained.1043 Figure 9ccshows the feedback contribution (Le; 4).," Figure \ref{figure_fuv_007_contrib}c cshows the feedback contribution ${ \boldsymbol L} a_{1,i-1}$ )."1044 The large this value is (in absolute term the more the ANN relies on past values to estimate the present one., The large this value is (in absolute term) the more the ANN relies on past values to estimate the present one.1045 That ts. a large feedback implies a reconstruction based on persistence.," That is, a large feedback implies a reconstruction based on persistence."1046 In this particular example (Fig., In this particular example (Fig.1047 9cc). the feedback is negligible.," \ref{figure_fuv_007_contrib}c c), the feedback is negligible."1048 Figure 9dd presents the time series from SOLSTICE (blue line). the neural network output (red line). and the neural network output with a linear transfer function for the first layer (green line).," Figure \ref{figure_fuv_007_contrib}d d presents the time series from SOLSTICE (blue line), the neural network output (red line), and the neural network output with a linear transfer function for the first layer (green line)."1049 The training (80%)) and validation (20%)) sets are indicated in the figure., The training ) and validation ) sets are indicated in the figure.1050 The model reproduces adequately the variability of the training set as well as the validation set. which indicates that the model properly generalizes the relations between the distribution of bipolar magnetic features on the solar disk and the Lyman-e emission.," The model reproduces adequately the variability of the training set as well as the validation set, which indicates that the model properly generalizes the relations between the distribution of bipolar magnetic features on the solar disk and the $\alpha$ emission."1051" Note also that the output of the linear model. in which each neuron has a linear response. in most cases. performs as well as the nonlinear one. except with larger excursions of outliers,"," Note also that the output of the linear model, in which each neuron has a linear response, in most cases, performs as well as the nonlinear one, except with larger excursions of outliers."1052 The coefficients of the model are shown in Figure 10.., The coefficients of the model are shown in Figure \ref{Fig_fuv_007_coeff}.1053 The coefficients of each class considered are indicated as well as the coefficient corresponding to the inner ring., The coefficients of each class considered are indicated as well as the coefficient corresponding to the inner ring.1054 In this example. most of the contribution for the evolution of the irradiance is due to the evolution of the large active regions.," In this example, most of the contribution for the evolution of the irradiance is due to the evolution of the large active regions."1055 As expected. the major contribution to the variability of the Lyman-a emission is due to the evolution of active regions (Class IV). although the feedback also contributes.," As expected, the major contribution to the variability of the $\alpha$ emission is due to the evolution of active regions (Class IV), although the feedback also contributes."1056 Not surprisingly. this contribution mainly comes from active regions that are near the center of the disk.," Not surprisingly, this contribution mainly comes from active regions that are near the center of the disk."1057 This property is. of course. wavelength dependent.," This property is, of course, wavelength dependent."1058 Incidentally. because the model is data driven. we now can use it to infer properties about the radial contribution of specific features for each wavelength.," Incidentally, because the model is data driven, we now can use it to infer properties about the radial contribution of specific features for each wavelength."1059 This opens interesting perspectives that will be investigated in a forthcoming publication., This opens interesting perspectives that will be investigated in a forthcoming publication.1060 The percentual difference between the output of the for 24-hour forecast model and the observations. the model error. is presented in Fig.," The percentual difference between the output of the for 24-hour forecast model and the observations, the model error, is presented in Fig."1061 11. for the training (blue line) and validation (green line) sets from 115 to 310 nm., \ref{figure_mse} for the training (blue line) and validation (green line) sets from 115 to 310 nm.1062 It is noticeable that the model error of the MUV region of the spectra is higher than in the FUV., It is noticeable that the model error of the MUV region of the spectra is higher than in the FUV.1063 The model error for the XPS region of the spectra. which is not shown in the figure. is comparable to the error of the FUV region.," The model error for the XPS region of the spectra, which is not shown in the figure, is comparable to the error of the FUV region."1064 Examples of training sections for the total solar irradiance for forecast periods from 12 hours to 72 hours are displayed in Figures 12--15.., Examples of training sections for the total solar irradiance for forecast periods from 12 hours to 72 hours are displayed in Figures \ref{FigTSI_12}- \ref{FigTSI_72}. .1065 The structure of these figures 1s the same of the Fig., The structure of these figures is the same of the Fig.1066xb Far Ultraviolet Spectroscopic Explorer (FUSE) spectra of tle dwarf nova WW Ceti during ταüescence.,and Far Ultraviolet Spectroscopic Explorer ) spectra of the dwarf nova WW Ceti during quiescence.1067 οuo analysis utilizes newly available accretion disk inodels. photosphere models. aud models combiune white dwarls aud accretion disks aud accretion yelts.," Our analysis utilizes newly available accretion disk models, photosphere models, and models combining white dwarfs and accretion disks and accretion belts."1068 The accretion disk models 'e taken [rou the grid of mocels of Wade&Hubeny(1998).. whicl were recently updated using the lastest versiol of the stellar/accretion disk synthetic spectral codes (see section 3).," The accretion disk models are taken from the grid of models of \citet{wad98}, which were recently updated using the lastest version of the stellar/accretion disk synthetic spectral codes (see section 3)."1069 Our objectiVes 'e to identify the source(s) of the FUV radiation during quiesceice. derive the properties of the WD (if deteced) aud the quiescent. accretion disk. aud characterize the hot components in he systel.," Our objectives are to identify the source(s) of the FUV radiation during quiescence, derive the properties of the WD (if detected) and the quiescent accretion disk, and characterize the hot components in the system."1070 Iu table 1 we list the systei1 parameters we have adopted: (1) CV subtype. (2) orbital period iu days. (3) orbital inclination in ¢legrees. (1) spectral type of the secoudary. (5) mass of the primary in solar masses. (6) mass of tle secoudary in solar masses. (7 apparent magnitude in outburst. auc (8) apparent magnitude iu quiescence.," In table 1 we list the system parameters we have adopted: (1) CV subtype, (2) orbital period in days, (3) orbital inclination in degrees, (4) spectral type of the secondary, (5) mass of the primary in solar masses, (6) mass of the secondary in solar masses, (7) apparent magnitude in outburst, and (8) apparent magnitude in quiescence."1071 The references are |sted below the table., The references are listed below the table.1072 The orbital perio (1.22 |Ours) is well above the period. ga» where lew WD properties are currently known.," The orbital period (4.22 hours) is well above the period gap, where few WD properties are currently known."1073 Systems above the gap terd to have somewla earlier-tvpe secoudaries. higher accretion rates. aud larger ace'etion disks.," Systems above the gap tend to have somewhat earlier-type secondaries, higher accretion rates, and larger accretion disks."1074 Dwarf novae. uulike other CVs. ofer à fairly reliable estimate of their distaCes vla he absolute magnitude at mani1iuu versus orbital period relation for dwarl novae fouud by Warler(1995).," Dwarf novae, unlike other CVs, offer a fairly reliable estimate of their distances via the absolute magnitude at maximum versus orbital period relation for dwarf novae found by \citet{war95}."1075. This relatiouship is «‘Ousistent witl theory 1998)., This relationship is consistent with theory \citep{can98}.1076. For WW Ceti. his relaion vields a «istauce of 186 pe.," For WW Ceti, this relation yields a distance of 186 pc."1077 Tus is midrange of 90—300 pc as derived by Young&Schuekler(1981) σιD>ο near-infrared CCD spectra of tle cool compaulon. slightly higher than the estimae of 130 pe (Patterson19814). aud close to the range of 121—171 pc using Ix inagnitudes (Sproatsetal. 1996)..," This is midrange of $90 - 300$ pc as derived by \citet{you81} using near-infrared CCD spectra of the cool companion, slightly higher than the estimate of 130 pc \citep{pat84} and close to the range of $121 - 171$ pc using K magnitudes \citep{spr96}. ."1078 To remain consistent with the j»arabueters used in Winter&Sion(2003).. we adopted 186 pe as the cistauce to WW Ceti.," To remain consistent with the parameters used in \citet{win03}, we adopted 186 pc as the distance to WW Ceti."1079FUSE is a low-earth orbit satellite. launched iun June 1999.," is a low-earth orbit satellite, launched in June 1999."1080 Its optical system cousists ο ‘fot optical telescopes (mirrors). each separately connected to a dillerent Rowlaud spectrograph.," Its optical system consists of four optical telescopes (mirrors), each separately connected to a different Rowland spectrograph."1081 Τι four diffraction gratiugs of the four Rowland spectrographlis produce four independent. spect CEU two photon counting area detectors., The four diffraction gratings of the four Rowland spectrographs produce four independent spectra on two photon counting area detectors.1082 Two mirrors aud two gratings are coated with SiC to provke waveleneth coverage below 102QA.. while the other two mirrors aud gratiugs are coated wih Al and LiF overcoat.," Two mirrors and two gratings are coated with SiC to provide wavelength coverage below 1020, while the other two mirrors and gratings are coated with Al and LiF overcoat."1083 The Al--LiF coating provides about twice the reflectivity of SiC at waveleietlS 210250A.. and very little reflectivity below 1020 ((hereafter the SiC1. SiC2. LiF] audLiF? channels).," The Al+LiF coating provides about twice the reflectivity of SiC at wavelengths $>$ 1050, and very little reflectivity below 1020 (hereafter the SiC1, SiC2, LiF1 andLiF2 channels)."1084iu the individual meastrements aud coarse sampling do not exclude the possibility that the line flux. tracks the continuum ou timescales as short as hours. as would be expected if most of the line was produced in a putative accretion clisk.,"in the individual measurements and coarse sampling do not exclude the possibility that the line flux tracks the continuum on timescales as short as hours, as would be expected if most of the line was produced in a putative accretion disk."1085 While the spectra fits confirm the preseuce of spectral variability. the origin of the changes in either column deusity and/or photon index variatious is not distinguishable.," While the spectra fits confirm the presence of spectral variability, the origin of the changes in either column density and/or photon index variations is not distinguishable."1086 Therefore. as au additional test. the data were separated iuto two spectra on the basis of the [lux chauge that occurred during the latter part of the monitoring campaign.," Therefore, as an additional test, the data were separated into two spectra on the basis of the flux change that occurred during the latter part of the monitoring campaign."1087" Thus. data from the first six observations were combiued into a ""low state"" spectrum. while data from the last six. spectra comprise a ""high state” spectrum."," Thus, data from the first six observations were combined into a “low state” spectrum, while data from the last six spectra comprise a “high state” spectrum."1088 These two spectra were then fitted to a spectral model tn which the column density aud photou iudex were allowed to vary., These two spectra were then fitted to a spectral model in which the column density and photon index were allowed to vary.1089 The projected confidence regious iu the Εμ plane for this model are shown in Figure 3.., The projected confidence regions in the $\Gamma$ $N_{\rm H}$ plane for this model are shown in Figure \ref{fig3}.1090 Although photon index variations cannot be excluded. a significant change iu the column density is required by the data.," Although photon index variations cannot be excluded, a significant change in the column density is required by the data."1091 Hereafter we take the view that. on the basis of these very simple spectral models. the spectral variability is best assigned largely to variations in the columau deusity.," Hereafter we take the view that, on the basis of these very simple spectral models, the spectral variability is best assigned largely to variations in the column density."1092 Although the above absorbed power-law model provides au excellent flit to the combined datasets. we next cousider what constraints. if any. may be placed on slightly more sophisticated spectral descriptious. such as models inclucing either a Compton reflection compouent or a partially covered source.," Although the above absorbed power-law model provides an excellent fit to the combined datasets, we next consider what constraints, if any, may be placed on slightly more sophisticated spectral descriptions, such as models including either a Compton reflection component or a partially covered source."1093 Specifically we cousidered the possibility that some of the observed spectral variability tay arise due to the presence of au extra compouent with a delayecl temporal respouse relative to the direct. continuum., Specifically we considered the possibility that some of the observed spectral variability may arise due to the presence of an extra component with a delayed temporal response relative to the direct continuum.1094 If the disk-corona moclel cdeseribed iu 81 is correct. then a siguificaut fraction of the hard X-ray flux. should be reprocessed iu the accretion disk.," If the disk-corona model described in 1 is correct, then a significant fraction of the hard X-ray flux should be reprocessed in the accretion disk."1095 The auticipated spectral signatures [rom such reprocessing includes an irou Ίνα [I[noresceuce line aud Compton reflection of the ανα continuuui (George&Fabian1991:Mattetal.1991).," The anticipated spectral signatures from such reprocessing includes an iron $\alpha$ fluorescence line and Compton reflection of the hard continuum \citep{gf91,mat91}."1096. These features have previously been identified in many Sevfert galaxies. aud may also be present iu the spectrum of Mrk 318.," These features have previously been identified in many Seyfert galaxies, and may also be present in the spectrum of Mrk 348."1097 Motivated by this prediction. the data were fitted to a mocel cousistiug of an absorbed. power-law coutinuum withabsorbed Compton reflection from neutral. solar abundant material. as implemented in the moclel (Magdziarz&Zdziarski1995). plus a uz‘row Gaussian liue representiug iron ha emissiou (noel 1).," Motivated by this prediction, the data were fitted to a model consisting of an absorbed power-law continuum with Compton reflection from neutral, solar abundant material, as implemented in the model \citep{mz95} plus a narrow Gaussian line representing iron $\alpha$ emission (model 4)."1098 The inclination (to our line of sight) of the reflecting material was fixed at the default value (i= 607). since the reflection spectrum-— below 20 keV is relatively indepeudent. of the inclination augle.," The inclination (to our line of sight) of the reflecting material was fixed at the default value $i = 60^{\circ}$ ), since the reflection spectrum below 20 keV is relatively independent of the inclination angle."1099 The shape of the incident continuum above 20 keV is important. even when cousicering measurements below this energy because of the effects of Compton downu-scattering: the power-law continuum was therefore exponentially cut-off with au e-foldiug; euergy of 150 keV. similar to tliat observed iu other Seyfert galaxies (Zdziarskietal.1995:Goudek1996).," The shape of the incident continuum above 20 keV is important, even when considering measurements below this energy because of the effects of Compton down-scattering; the power-law continuum was therefore exponentially cut-off with an e-folding energy of 150 keV, similar to that observed in other Seyfert galaxies \citep{zdz95,gon96}."1100. The reflected spectrum should track the contiuuuim on timescales of weeks or less. if it originates iu the putative disk.," The reflected spectrum should track the continuum on timescales of weeks or less, if it originates in the putative disk."1101 Therefore. the relative normalization between the direct aud reflected contiuuuu was initially tied to a single value [or all six spectra (a value of R =1 is expected from a [Tat O/2:=] geometry and isotropic emission).," Therefore, the relative normalization between the direct and reflected continuum was initially tied to a single value for all six spectra (a value of $\cal1102R$ $= 1$ is expected from a flat $\Omega/2\pi = 1$ geometry and isotropic emission)."1103 In this case the besi-fitting parameter values are, In this case the best-fitting parameter values are1104sight-lines. Ostmanetal.(2008) tested both Milky-Way like extinction as well as Small Magellanie Cloud (SAIC) extinction law. both giving comparable goodness of fit.,"sight-lines, \citet{QSO} tested both Milky-Way like extinction as well as Small Magellanic Cloud (SMC) extinction law, both giving comparable goodness of fit."1105 A preference for SAIC dust for extinction of AGNs has been suggested bv Li(2007).., A preference for SMC dust for extinction of AGNs has been suggested by \citet{li}.1106 Recently. the detection of cireumstellar (CS) matter in the local environment surrounding the Type Ia supernova $N2006X in the nearby galaxy MIQO has been reported by (2007).," Recently, the detection of circumstellar (CS) matter in the local environment surrounding the Type Ia supernova SN2006X in the nearby galaxy M100 has been reported by \citet{Patat07}."1107. A shell within a [ον 10/5 cm (~0.01 pe) of the center of the explosion has been suggested (to explain the time-variable Na I D lines in (he SN spectrum., A shell within a few $10^{16}$ cm $\sim 0.01$ pc) of the center of the explosion has been suggested to explain the time-variable Na I D lines in the SN spectrum.1108 Wangetal.(2008a) report. --1.4840.06 and BOB—V)=1.4240.04 mag for SA2006X and a light echo in the lighteurve was found by Wangetal.(2008b) consistent wilh dust illuminated at a distance of 27-170 pe from the site of the explosion.," \citet{Wang08a} report $R_V=1.48 \pm 0.06$ and $E(B-V) = 1.42 \pm11090.04$ mag for SN2006X and a light echo in the lightcurve was found by \citet{Wang08b} consistent with dust illuminated at a distance of 27-170 pc from the site of the explosion."1110 Even if the local environment around this supernova may nol be very common among SNla. similar values for the total to selective extinction ralio have been reported [or several SNIa withgood wavelength coverage.," Even if the local environment around this supernova may not be very common among SNIa, similar values for the total to selective extinction ratio have been reported for several SNIa withgood wavelength coverage."1111 E.g. Ixrisciunasetal.(2007). found. fà=1.5540.08 for SN 1999c]: Elias-Rosaetal.(2006.2008) report Ay=L8040.19 and Ay=1.59+0.07 for $N2003cg and SN 2002cev respectively.," E.g. \citet{Krisciunas07} found $R_V=1.55 \pm 0.08$ for SN 1999cl; \citet{Elias-Rosa06,Elias-Rosa08} report $R_V=1.80 \pm 0.19$ and $R_V=1.59 \pm 0.07$ for SN2003cg and SN 2002cv respectively."1112 Furthermore. a statistical study of optical colors of a sample including 80 near-by SNIa. Nobili&Goobar(2008) found an average value of hy=τὸzx0.2? for SNIa with E(D—V) «0.7. and even lower lor a subsample οἱ low-recldening SNla.," Furthermore, a statistical study of optical colors of a sample including 80 near-by SNIa, \citet{Nobili&Goobar} found an average value of $\bar R_V=1.751113\pm 0.27$ for SNIa with $E(B-V)<$ 0.7, and even lower for a subsample of low-reddening SNIa."1114" Next. we examine (he possibility that low values of Z2, stem from the senmi-diffusive propagation of photons in the neighborhood of the site of the supernova explosion."," Next, we examine the possibility that low values of $R_V$ stem from the semi-diffusive propagation of photons in the neighborhood of the site of the supernova explosion."1115 Photon propagation around a medium of scatterers can be described bv a quasi picture., Photon propagation around a medium of scatterers can be described by a quasi random-walk picture.1116 The reader is referred to (Chandrasekhar1943). [or a beautiful introduction to (his subject., The reader is referred to \citep{chandra} for a beautiful introduction to this subject.1117 Lets consider a localized distribution of dust. particles within a distance Rey trom the explosion site. negligibly small compared to the distance to the observer. d. ie. Haw<Roy«αι where Ryy corresponds to the radius four where the SN radiation emerges.," Lets consider a localized distribution of dust particles within a distance $R_{CS}$ from the explosion site, negligibly small compared to the distance to the observer, $d$, i.e. $R_{SN}< R_{CS} \ll d$, where $R_{SN}$ corresponds to the radius from where the SN radiation emerges."1118 The (trajectory of a photon will be straight until it hits a dust particle at which point the photon can either be scattered or absorbed., The trajectory of a photon will be straight until it hits a dust particle at which point the photon can either be scattered or absorbed.1119" If the photon is scattered in a new direction. it follows a straight path until the next encounter. aud so on until rzHes.The mean Iree path between interactions. A, pr. is thus determined by the number density of scatterers. n. and their ellective cross-section lor scattering and absorption of light. στσ.+ 04:"," If the photon is scattered in a new direction, it follows a straight path until the next encounter, and so on until $r>R_{CS}$.The mean free path between interactions, $\lambda_{eff}$ , is thus determined by the number density of scatterers, $n$ , and their effective cross-section for scattering and absorption of light, $\sigma_{eff}=\sigma_{s}+\sigma_{a}$ :"1120which created them.,which created them.1121 Obaiming the underlying structure from the network is called. cominuuity detection. aud is similar o techuiques for cluster analysis or classification.," Obtaining the underlying structure from the network is called community detection, and is similar to techniques for cluster analysis or classification."1122 Fortunato (2010) reviews these methods. currently the most popular methocl is that of Girvan and Newman (2002) ane the “best” (according to Laucichiuetti aud Fortunato 2009) is that of Rosvall aud. Bergstrom (RB: 2008).," Fortunato (2010) reviews these methods, currently the most popular method is that of Girvan and Newman (2002) and the “best” (according to Lancichinetti and Fortunato 2009) is that of Rosvall and Bergstrom (RB: 2008)."1123 RB have used their algo‘ithin on citation data to show the interrelatiouships betwee1 the major fields of scieuce: their map may very profitably be compared with te similar map of Bolen et al (2009a) who show a similar structure based ou usage data and lield classific:UIOLLS., RB have used their algorithm on citation data to show the interrelationships between the major fields of science; their map may very profitably be compared with the similar map of Bolen et al (2009a) who show a similar structure based on usage data and field classifications.1124 The RB algorithin las been used by Ixurtz. et al (2007) atd Heunekenu et al (2009) to uap the subfields of astronomy. based on both citation data and on 5iared. keywords for journal articles.," The RB algorithm has been used by Kurtz, et al (2007) and Henneken et al (2009) to map the subfields of astronomy, based on both citation data and on shared keywords for journal articles."1125 Attempts to buik a similar map [rom usage cdaa lave not. hus far. been successful. perliaps because of the very broac| reaclership patterus of may astronomers.," Attempts to build a similar map from usage data have not, thus far, been successful, perhaps because of the very broad readership patterns of many astronomers."1126" Another measure obtainable [rom a uetwork graph is the ""importauce"" of the iudividual nodes.", Another measure obtainable from a network graph is the “importance” of the individual nodes.1127 Importance is normally called ceutrality in this οςjnext. auc there are several clifferent centrality ueasures.," Importance is normally called centrality in this context, and there are several different centrality measures."1128 Iu a friendship network. where people are the nodes aud they are linked to other people v [rieudship degree tlie person with the most [rieids would be he person with the highest degree centrality.," In a friendship network, where people are the nodes and they are linked to other people by friendship degree the person with the most friends would be the person with the highest degree centrality."1129 Note that frieudship is directional. I may consider vou my friend. but that does not mean hat you cousider me a frieud: thus the concepts of in-degree aid out-degree.," Note that friendship is directional, I may consider you my friend, but that does not mean that you consider me a friend; thus the concepts of in-degree and out-degree."1130 1 a citatiou uetwork he paper with the highesto iu-degreeo is the most cited j»aper. while review artices would have very ugh out-degree.," In a citation network the paper with the highest in-degree is the most cited paper, while review articles would have very high out-degree."1131" Betweenuess cent‘ality is another ""importauce ueasure.", Betweenness centrality is another “importance” measure.1132 In. a [rieucdship network the most central people are those vvith [rieucs in many different. otherwise autonomous cliques: in a journal to journal citation network the mos cell‘al journals are the interdisciplinary journals (LeycdescdorlE 2007). like Science or Nature. whic1 are between otherwise autououmous fields. such as astronomy and neuroscience.," In a friendship network the most central people are those with friends in many different, otherwise autonomous cliques; in a journal to journal citation network the most central journals are the interdisciplinary journals (Leydesdorff 2007), like Science or Nature, which are between otherwise autonomous fields, such as astronomy and neuroscience."1133 Betweenness centrality is a key measture in au tuformation flow network: the high betweeness centrality nodes facilitae information traisfer between fields., Betweenness centrality is a key measure in an information flow network; the high betweeness centrality nodes facilitate information transfer between fields.1134 The currently most used cent‘ality measure ls (ie expected occupation time for each node when visited by a raudoum walk. wiere the agent. randomly follows links [rom node to node.," The currently most used centrality measure is the expected occupation time for each node when visited by a random walk, where the agent randomly follows links from node to node."1135 This is normally called eigenvector cent‘ality. as the resul is the same as the first eigeuvector of the uode-node counectivity matrix (Boracich 1971).," This is normally called eigenvector centrality, as the result is the same as the first eigenvector of the node-node connectivity matrix (Bonacich 1971)."1136 Google's famous Page-Rauk algorithm (Brin ancl Page 1995) is essentially eigenvector centrality. with ¢ever implementation details.," Google's famous Page-Rank algorithm (Brin and Page 1998) is essentially eigenvector centrality, with clever implementation details."1137 There are several other centrality measures., There are several other centrality measures.1138 Ixurtz aud Bolleu (2010) give a brief introduction: ]xoschüttzki. et al (2005) a cletailec discussion.," Kurtz and Bollen (2010) give a brief introduction; Koschüttzki, et al (2005) a detailed discussion."1139 While measures which: solve for globally optimum ineasures are clearly clesirable aucl useful.," While measures which solve for globally optimum measures are clearly desirable and useful,"1140"Gamma-ray bursts (GRBs) exhibit a remarkable diversity: Fluences range [rom 10.' to 10 ""erg 7. peak energies range from 50kkeV to an MeV. and possibly from the (o the GeV. band (Fishman&Aleeean1995).. and durations extend. from about 2 to","Gamma-ray bursts (GRBs) exhibit a remarkable diversity: Fluences range from $10^{-7}$ to $10^{-3}\,$ erg $^{-2}$, peak energies range from keV to an MeV, and possibly from the X-ray to the GeV band \citep{fm95}, and durations extend from about 2 to"1141(Abazajianetal. 2009)).,\citealt{Abazajian09}) ).1142 We noe that 36 members out of a total of 549 galaxies across all clusers have spectroscopic redshifts from SDSS cM., We note that 36 members out of a total of 549 galaxies across all clusters have spectroscopic redshifts from SDSS ).1143 For sources with spectroscopic redshifts. the mean spectroscopic-to-photometrie redshift offset is -0.0018. with a standard deviation of 0.017.," For sources with spectroscopic redshifts, the mean spectroscopic-to-photometric redshift offset is -0.0018, with a standard deviation of 0.017."1144 Further details can be found in Geachetal. (2011)., Further details can be found in \citet{Geach11}.1145 The clusters span a redshift of 0.07-0.43 of the sample are at 0.15<2<= 0.35). and have a median redshift of (2)=0.25 at which the angular scale is KKpe ! (see Fig. |).," The clusters span a redshift of 0.07–0.43 of the sample are at $0.15\leq z\leq 0.35$ ), and have a median redshift of $\left<z\right>=0.25$ at which the angular scale is kpc $^{-1}$ (see Fig. \ref{fig:histogram}) )."1146 Based on tests performed on mock catalogues. the cluster catalogue is 2904€ complete at a halo mass of 10 MM. (Murphy.Geach&Bower2010).," Based on tests performed on mock catalogues, the cluster catalogue is $>$ complete at a halo mass of $10^{14}$ $_\odot$ \citep{MGB10}."1147. The numberof false positives can be estimated by randomly shuffling the colours of galaxies (while keeping the positions fixed) and re-running the detection algorithm., The number of false positives can be estimated by randomly shuffling the colours of galaxies (while keeping the positions fixed) and re-running the detection algorithm.1148 At the lower membership limit. the number of false detections is expected to be  or «1 of the 66 clusters.," At the lower membership limit, the number of false detections is expected to be $^{-2}$ or $<1$ of the 66 clusters."1149 Further details of the cluster algorithm. selection and completeness can be found in Murphy.Geach&Bower(2010).," Further details of the cluster algorithm, selection and completeness can be found in \citet{MGB10}."1150. We estimate the cluster richness using the commonly used D... statistic. an approximation of the amplitude of the real-space correlation function (Longair&Seldner 1979).," We estimate the cluster richness using the commonly used $B_{\rm gc}$ statistic, an approximation of the amplitude of the real-space correlation function \citep{Longair79}."1151. Yee&Ellingson(2003) show that this statistical measure is reasonably well correlated with the physical properties of the clusters. and we apply these scalings to find the typical cluster scale Root(1.2c04) MMpe and logAdoon/M . c(14.7£0.5). although the errors on individual 5. measurements are large.," \citet{Yee03} show that this statistical measure is reasonably well correlated with the physical properties of the clusters, and we apply these scalings to find the typical cluster scale $R_{200}$ $\simeq(1.2\pm0.4)$ Mpc and $\log M_{200}/$ $_{\odot}$ $\simeq(14.7\pm0.5)$, although the errors on individual $B_{\rm gc}$ measurements are large."1152 The H-ATLAS SDP catalogue consists of 6876 sources detected at >So in either of the 250. 350 or πι bands over a cLtάάοσ- region (Rigbyetal.2011).," The H-ATLAS SDP catalogue consists of 6876 sources detected at $>5\,\sigma$ in either of the 250, 350 or $\mu$ m bands over a $\simeq14.4$ $^{2}$ region \citep{Rigby10}."1153 The 5-σ point source Sensitivity limits (including confusion noise) are 34. 38. and 44mmJy at 250. 350. and sim. respectively.," The $\sigma$ point source sensitivity limits (including confusion noise) are 34, 38, and mJy at 250, 350, and $\mu$ m, respectively."1154 Smithetal.011). have employed a likelihood ratio (LR) method to perform the optical cross-identifications of the 662] j:m-detected sources with the SDSS DR7 catalogue with a limiting r-- magnitude of 22.4 CAbazajianetal.2009)., \citet{Smith10} have employed a likelihood ratio (LR) method to perform the optical cross-identifications of the 6621 $\mu$ m-detected sources with the SDSS DR7 catalogue with a limiting -band magnitude of 22.4 \citep{Abazajian09}.1155. The LR technique assigns a reliability. /?. to each match and indicates the probability that the counterpart is the correct identitication.," The LR technique assigns a reliability, $R$, to each match and indicates the probability that the counterpart is the correct identification."1156 Of the 6876 H-ATLAS sources. 2423 are thus classified as having a reliable G>0.8) optical counterpart. and the remaining 4453 as optically unidentified (/?«0.5 or no optical counterparts).," Of the 6876 H-ATLAS sources, 2423 are thus classified as having a reliable $R\geq0.8$ ) optical counterpart, and the remaining 4453 as optically unidentified $R<0.8$ or no optical counterparts)."1157 The first step of our analysis is to simply measure the surface density of H-ATLAS sources (both optically identitied and unidentified) as a function of projected clusto-centric radius around the 66 clusters (Fig. 2))., The first step of our analysis is to simply measure the surface density of H-ATLAS sources (both optically identified and unidentified) as a function of projected clusto-centric radius around the 66 clusters (Fig. \ref{fig1}) ).1158 As a field control sample. we repeat this exercise 1000 times for a set of 66 random positions across the field.," As a field control sample, we repeat this exercise 1000 times for a set of 66 random positions across the field."1159 As expected. at large radii the surface density around the clusters is indistinguishable from the average Ποιά estimate. however there is a clear positive excess of far-infrared sources within ~2et MMpe for >= 0.25) of the clusters. the significance of which peaks at ~ 23.5'.," As expected, at large radii the surface density around the clusters is indistinguishable from the average `field' estimate, however there is a clear positive excess of far-infrared sources within $\sim5'$ Mpc for $z=0.25$ ) of the clusters, the significance of which peaks at $\sim3.5'$ ."1160 There is an average excess of ~1 source per cluster over the background. although note that by detinition the cluster environments are characterised by an excess surface density of galaxies.," There is an average excess of $\sim1$ source per cluster over the background, although note that by definition the cluster environments are characterised by an excess surface density of galaxies."1161 The total number of H-ATLAS sources detected within 3.5! of the 66 clusters is 401. representing a c3.56 excess of 61x20 sources (the error is Poisson) above the background signal of 332+1 sources on average (the error is the standard error of the mean).," The total number of H-ATLAS sources detected within $3.5'$ of the 66 clusters is 401, representing a $\simeq3.5\,\sigma$ excess of $67\pm20$ sources (the error is Poisson) above the background signal of $332\pm1$ sources on average (the error is the standard error of the mean)."1162 At a radius of 5! from the 66 clusters. we tind 719 sources (a less significant excess of 41+27 sources over our Monte Carlo estimated background signal of 678+1 at the same clustocentric radius).," At a radius of $5'$ from the 66 clusters, we find 719 sources (a less significant excess of $41\pm27$ sources over our Monte Carlo estimated background signal of $678\pm1$ at the same clustocentric radius)."1163 For comparison. we have also repeated the above analysis using the projected radius from the BCG as the cluster centre. and he signal in the r<0.5’ bin clearly increases (see Fig. 2)) —," For comparison, we have also repeated the above analysis using the projected radius from the BCG as the cluster centre, and the signal in the $r<0.5'$ bin clearly increases (see Fig. \ref{fig1}) ) –"1164 with six H-ATLAS sources lying within aaresec of BCGs (note hat the μπι PSF is aaresec)., with six H-ATLAS sources lying within arcsec of BCGs (note that the $\mu$ m PSF is arcsec).1165 This suggests that several H-ATLAS sources are associated with the BCGs. either by lensing a background far-infrared source or that the far-infrared emission is rom the BCG itself. e.g. Edgeetal.(2010).," This suggests that several H-ATLAS sources are associated with the BCGs, either by lensing a background far-infrared source or that the far-infrared emission is from the BCG itself, e.g. \citet{Edge10}."1166.. We have quantified he likelihood of finding this excess signal by chance by using our fonte Carlo simulations and find that for radii 53.5 (where the maximum excess signal occurs) we would expect to see our average detected surface density <0.15€ of the time in randomly sampled apertures of equivalentsize in the field., We have quantified the likelihood of finding this excess signal by chance by using our Monte Carlo simulations and find that for radii $\lesssim3.5'$ (where the maximum excess signal occurs) we would expect to see our average detected surface density $<0.1$ of the time in randomly sampled apertures of equivalentsize in the field.1167 The simulations also reveal that at radii larger than about 5’ the random chance of detecting our measured surface density (or greater) near the clusters above the background becomes 71% , The simulations also reveal that at radii larger than about $5'$ the random chance of detecting our measured surface density (or greater) near the clusters above the background becomes $>1$ 1168In the [ast few. decades. a wealth of cosmological data rom large scale structure (Peacock2005.2d):: the cosmic =microwave background. (Ilxomatsuctal.2009.NALADP 5): supernovae (Asticretal.2006.SNL: Miknaitiset.al. ESSENCE:: lxowalskietal. 2008)): weak lensing Schrabbacketal. 2009))) has revolutionised our vision of the Universe.,"In the last few decades, a wealth of cosmological data (from large scale structure \citep[][2dF]{Peacock:2005}; the cosmic microwave background \citep[][WMAP5]{Komatsu:2009}; ; supernovae \citealt[][SNLS]{Astier:2006}; \citealt[][ESSENCE]{Miknaitis:2007}; \citealt{Kowalski:2008a}) ); weak lensing \citep{Schrabback:2009}) ) has revolutionised our vision of the Universe."1169 In this concordance cosmology. initia quantum [luctuations are. believed. to. have seeded. dark matter perturbations in which the Large Scale Structure we observe today has formed.," In this concordance cosmology, initial quantum fluctuations are believed to have seeded dark matter perturbations in which the Large Scale Structure we observe today has formed."1170 Within this concordance mocde the Universe is composed. only of a small proportion of barvons )). the rest being dark matter(25%... which can be hot or cold) and dark energy.," Within this concordance model the Universe is composed only of a small proportion of baryons ), the rest being dark matter, which can be hot or cold) and dark energy."1171 One of the main challenges today is to unclerstane the nature of the mysterious dark. energy. which causes cosmic acceleration and. constitutes of the Universe's energy clonsity (Albrechtetal.2006:Peacock2006).," One of the main challenges today is to understand the nature of the mysterious dark energy which causes cosmic acceleration and constitutes of the Universe's energy density \citep{DETF, Peacock:2006}."1172. There exists a wealth of potential models for dark energy., There exists a wealth of potential models for dark energy.1173 ‘To distinguish these models the determination of the dark enerey equation of state aw has gained importance since some moclels can result in very dillerent expansion histories., To distinguish these models the determination of the dark energy equation of state $w$ has gained importance since some models can result in very different expansion histories.1174 Current data can constrain the dark. energy. equation of state tw to1054.. with the assumption of Uatness. but a percentage level sensitivity as well as redshift: evolution information are recuired in order to understand the nature of dark energy.," Current data can constrain the dark energy equation of state $w$ to, with the assumption of flatness, but a percentage level sensitivity as well as redshift evolution information are required in order to understand the nature of dark energy."1175 Future cosmic shear surveys showexceptional potential for constraining the dark energy. equation of state ie(z) (Albrechtetal.2006:Peacock2006) and have the advantage of directly tracing the dark matter distribution (sce Lloekstra&Jain2008. for à review).," Future cosmic shear surveys showexceptional potential for constraining the dark energy equation of state $w(z)$ \citep{DETF, Peacock:2006} and have the advantage of directly tracing the dark matter distribution (see \citealt{Hoekstra:2008} for a review)."1176 In fact. cosmic shear survevs have the potential to constrain all sectors of our cosmological model.," In fact, cosmic shear surveys have the potential to constrain all sectors of our cosmological model."1177 As shear measurements depend on the initial seeds of structure. it can be used to probe the slope and running of the initial power spectrum (seee.g.Liuctal.2009) which is central to our understanding of the inflationary model (seee.g.EHamann 2007).," As shear measurements depend on the initial seeds of structure, it can be used to probe the slope and running of the initial power spectrum \citep[see e.g.][]{Liu:2009} which is central to our understanding of the inflationary model \citep[see e.g.][]{Hamann:2007}."1178. Shear measurements have also been used to complement neutrino constraints from. particle. physics (Verenoetal.2009:: Lehiki.Takada.&Takahashi 20093) and ealaxy surveys Clakacda.Ixomatsu.&Futamase2006)... and future weak lensing surveys will provide bounds on the sum of the neutrino masses. the number of massive neutrinos and the hierachy (Llannestacd.Tu.&Wong2006:Ixit 2008b:: DeDernardisetal. 2009)).," Shear measurements have also been used to complement neutrino constraints from particle physics \citealt{Tereno:2008}; \citealt*{Ichiki:2008}) ) and galaxy surveys \citep*{Takada:2006}, and future weak lensing surveys will provide bounds on the sum of the neutrino masses, the number of massive neutrinos and the hierachy \citealt*{Hannestad:2006, Kit2008b}; ; \citealt{debernardisdraft2009}) )."1179 Theparameters that describe each sector are degenerate in the cosmic shear power spectrum. which means fixing," Theparameters that describe each sector are degenerate in the cosmic shear power spectrum, which means fixing"1180The racial profile of the radiation flux. produced bv the magnetic coupling is very different from Chat produced by accretion.,The radial profile of the radiation flux produced by the magnetic coupling is very different from that produced by accretion.1181" For a standard accretion disk. (he radiation flux is zero al r=ry, (the inner boundary. of the disk). gradually rises to a maximum at a radius bevond rj. then decreases slowly. and approaches FxroοE at large (Novikov1973:PageandThorne1974: 1974)."," For a standard accretion disk, the radiation flux is zero at $r=r_{ms}$ (the inner boundary of the disk), gradually rises to a maximum at a radius beyond $r_{ms}$, then decreases slowly, and approaches $F\propto r^{-3}$ at large \citep{nov73,pag74,tho74}."1182". While for a non-accretion disk mmagnelically coupled to a Ixerr black hole. assume (he magnetic field touches the disk at the inner boundary. (hen at Á=75,4; (hie radiation {hax suddenly rises [rom zero (o a sharp peak. then decreases quickly and approaches Fxr7""? at large radii."," While for a non-accretion disk magnetically coupled to a Kerr black hole, assume the magnetic field touches the disk at the inner boundary, then at $r=r_{ms}$ the radiation flux suddenly rises from zero to a sharp peak, then decreases quickly and approaches $F\propto r^{-3.5}$ at large radii."1183 To compare the radiation profile of (he magnetic coupling with the radiation profile of accretion. in Fie.," To compare the radiation profile of the magnetic coupling with the radiation profile of accretion, in Fig."1184 4 we plot both the radiation flux of a non-accretion disk magnetically coupled to a rapidly. rotating black hole and the radiation flux of a standard accretion disk rotating around the same black hole., \ref{fig4} we plot both the radiation flux of a non-accretion disk magnetically coupled to a rapidly rotating black hole and the radiation flux of a standard accretion disk rotating around the same black hole.1185 For the non-accretion disk. the magnetic field is assumed to touch the disk at the inner boundary (the marginally stable orbit).," For the non-accretion disk, the magnetic field is assumed to touch the disk at the inner boundary (the marginally stable orbit)."1186 Obviously. the radiation flux of the non-accretion disk has a much steeper radial profile aud. a sharp peak closer to the center of the clisk. compared to the radiation flux of the standard accretion disk.," Obviously, the radiation flux of the non-accretion disk has a much steeper radial profile and a sharp peak closer to the center of the disk, compared to the radiation flux of the standard accretion disk."1187 For the same models. in Fig.," For the same models, in Fig."1188 we show the emissivity index defined by à=—dInF/dInr. which measures the slope of the racial emissivitv. profile in the disk.," \ref{fig4a} we show the emissivity index defined by $\alpha\equiv - d\ln F/d\ln r$, which measures the slope of the radial emissivity profile in the disk."1189 We see that. throughout the disk the emissivity index for the non-accretion disk wilh magnetic coupling is significantly bigger than (he emissivity index for the standard accretion disk.," We see that, throughout the disk the emissivity index for the non-accretion disk with magnetic coupling is significantly bigger than the emissivity index for the standard accretion disk."1190 At large radii. a approaches 3.5 forthe non-accretion disk. 3 for the stanclard accretion disk.," At large radii, $\alpha$ approaches $3.5$ forthe non-accretion disk, $3$ for the standard accretion disk."1191 Iuser(üng equation (29)) into equation (10)) aud equation (19)). we gel where jj is given bv equation (34)).," Inserting equation \ref{hdel}) ) into equation \ref{flux_ang}) ) and equation \ref{phd}) ), we get where $A_0$ is given by equation \ref{h0}) )."1192 As expected. Pup=Tup.," As expected, $P_{HD} = T_{HD}1193\Omega_0$."1194 Since a disk has two surfaces. the total power of the disk is μυ=AxAO474.," Since a disk has two surfaces, the total power of the disk is ${\cal 1195L}_{HD} = 2 P_{HD} = 4\pi A_0 \Omega_0 r_0\,$."1196 The energy radiated per unit time from the region inside a circle of radius r>ry in the disk is where on the right hand side in the second line we have used equation (8)) (taking Mp— 0) and the boundary. condition gQ=tyne) Q0. in the third line we have used," The energy radiated per unit time from the region inside a circle of radius $r>r_0$ in the disk is where on the right hand side in the second line we have used equation \ref{con_ener}) ) (taking $\dot{M}_D = 0$ ) and the boundary condition $g\Omega (r=r_{ms}) = 0$ , in the third line we have used"1197Temietal.(2005).,\citet{tem05}.1198. The non-axially symmetric. non-stellar component ts visible in the top row (a-c) and quite striking in the bottom row (d-f).," The non-axially symmetric, non-stellar component is visible in the top row (a-c) and quite striking in the bottom row (d-f)."1199 As we discuss in $44 and $55.1. most of this component is due to dust.," As we discuss in 4 and 5.1, most of this component is due to dust."1200" In addition to the nucleus. there is a region approximately 11788 (1.3 kpe) in radius of dust emission 29"" (3.1 kpc) southeast of the nucleus."," In addition to the nucleus, there is a region approximately 8 (1.3 kpc) in radius of dust emission $\arcsec$ (3.1 kpc) southeast of the nucleus."

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