ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 This determines the mean separation of superclusters across voids which is taken as the characteristic length of the model., This determines the mean separation of superclusters across voids which is taken as the characteristic length of the model.3 We generated ten models of box size TOO wwith 431 void centres. in which case the characteristic scale is 115Alpe.. a value observed. in our study of superclusters ancl voids in Paper Land in the study of the cluster correlation function in Paper 11.," We generated ten models of box size 700 with 431 void centres, in which case the characteristic scale is 115, a value observed in our study of superclusters and voids in Paper I, and in the study of the cluster correlation function in Paper II."4 Results for the correlation functions anc power spectra of random models are shown in Figure 2., Results for the correlation functions and power spectra of random models are shown in Figure 2.5 All random moclels have a correlation function with no sign of oscillations., All random models have a correlation function with no sign of oscillations.6 The correlation function of the random supercluster node approaches zero on large scales immediately after the initial maximum., The correlation function of the random supercluster model approaches zero on large scales immediately after the initial maximum.7 The correlation function of the Voronoi model is different., The correlation function of the Voronoi model is different.8 It has a minimum at a separation between 60 and ~100 aand one secondary maximum at ~140Mpc., It has a minimum at a separation between $\sim 60$ and $\sim 100$ and one secondary maximum at $\sim 140$.9 We discuss dillerences between the random supercluster aud Voronoi mioclels later., We discuss differences between the random supercluster and Voronoi models later.10 The analysis of the correlation function of real cluster samples has shown that it depends strongly on the richness of superclusters (see Paper LL)., The analysis of the correlation function of real cluster samples has shown that it depends strongly on the richness of superclusters (see Paper II).11 We have thus made separate analyses of the correlation function for our random mocels for clusters located in rich ancl poor superclusters., We have thus made separate analyses of the correlation function for our random models for clusters located in rich and poor superclusters.12 We shall discuss this problem in more detail below. (Section 7)., We shall discuss this problem in more detail below (Section 7).13 In these models clusters or superclusters are located. with a certain degree of fuzziness. on the corners or on the edges between corners (rods) of a regular rectangular three-dimensional grid.," In these models clusters or superclusters are located, with a certain degree of fuzziness, on the corners or on the edges between corners (rods) of a regular rectangular three-dimensional grid."14 The fuzziness of the model was realized by adding to positions of clusters or superclusters random shifts around the exact position on the corner or the edge of the grid., The fuzziness of the model was realized by adding to positions of clusters or superclusters random shifts around the exact position on the corner or the edge of the grid.15 Depending on thedegree of the fuzziness we, Depending on thedegree of the fuzziness we16"(c= 0.102), which is basically the same as that of Poznanskietal.","$\sigma=0.102$ ), which is basically the same as that of \citet{poznanski}."17"(2010).. Thus, our study fully confirms the results by Poznanskietal.(2010),, but extends the validity of the relation toward later phases."," Thus, our study fully confirms the results by \citet{poznanski}, but extends the validity of the relation toward later phases."18 Improving the accuracy of the velocity measurements has an important aspect in measuring extragalactic distances with SCM or EPM (cf., Improving the accuracy of the velocity measurements has an important aspect in measuring extragalactic distances with SCM or EPM (cf.19 81)., 1).20" Both SCM and EPM need velocities, thus, the results of this paper can be significant for both techniques."," Both SCM and EPM need velocities, thus, the results of this paper can be significant for both techniques."21 SCM was calibrated using ure on day +50., SCM was calibrated using $v_{Fe}$ on day +50.22" However, in many cases getting a spectrum at or around day +50 is not possible."," However, in many cases getting a spectrum at or around day +50 is not possible."23 In these cases Eq.(2)) can be used to estimate Ure(50d)., In these cases \ref{eq2}) ) can be used to estimate $v_{Fe}(50\rmn{d})$.24" We have improved the exponent in Eq.(2)) as —0.546+0.01, based on more data obtained on wider range of phase than previously."," We have improved the exponent in \ref{eq2}) ) as $-0.546 \pm 0.01$, based on more data obtained on wider range of phase than previously."25 The difference between our result and the previous curve (Nugentetal.2006) is the highest around day +20 (Fig.9))., The difference between our result and the previous curve \citep{nugent06} is the highest around day +20 \ref{nug}) ).26 The new curve may result in better constrained vre(50d) when only early-phase spectra obtained around day +20 are available., The new curve may result in better constrained $v_{Fe}(50\rmn{d})$ when only early-phase spectra obtained around day +20 are available.27" However, there are several drawbacks of SCM."," However, there are several drawbacks of SCM."28" For example, the uncertainty in the moment of explosion, i.e. in determining the phase of a particular spectrum can lead to significant error in the distance determination."," For example, the uncertainty in the moment of explosion, i.e. in determining the phase of a particular spectrum can lead to significant error in the distance determination."29" Moreover, as the example of SN 2005cs shows in Fig.9,, some Type II-P SNe can deviate significantly from the average, especially during early phases."," Moreover, as the example of SN 2005cs shows in \ref{nug}, some Type II-P SNe can deviate significantly from the average, especially during early phases."30" Thus, one should be careful when such kind of interpolation or extrapolation is to be applied."," Thus, one should be careful when such kind of interpolation or extrapolation is to be applied."31 The example of SN 2005cs suggests that multi-epoch spectroscopic observations should always be preferred against single-epoch spectra when distance determination is the aim., The example of SN 2005cs suggests that multi-epoch spectroscopic observations should always be preferred against single-epoch spectra when distance determination is the aim.32 The case of EPM is different., The case of EPM is different.33" Since this method does not require calibration, but needs multi-epoch data, deviations in the measured velocities have higher impact."," Since this method does not require calibration, but needs multi-epoch data, deviations in the measured velocities have higher impact."34" To show this, we calculated the EPM-distances of all 5 SNe via the method described in Vinkóetal.(2011).."," To show this, we calculated the EPM–distances of all 5 SNe via the method described in \citet{vinko11dh}."35" We used two sets of velocities for each SNe: i) from the absorption minimum of the Fe 45169 line, ii) Όπιοαει determined in Sec. ??.."," We used two sets of velocities for each SNe: $i)$ from the absorption minimum of the Fe $\lambda$ 5169 line, $ii)$ $v_{model}$ determined in Sec. \ref{sec_synow}."36 'The resulted distances are in Table 3.., The resulted distances are in Table \ref{epm}.37 The correction factors of D05 were applied for all SNe., The correction factors of \citeauthor{dessart2005a} were applied for all SNe.38 Usually the photometric data were interpolated to the epochs of the velocities., Usually the photometric data were interpolated to the epochs of the velocities.39" However, for SN 2004dj Eq."," However, for SN 2004dj Eq."40 2 and Eq., \ref{eq2} and Eq.41" 3 were used to extrapolate the velocity data to the photometric epochs, because of the low number of spectra taken before day 4-50, i.e. during the expansion of the photosphere."," \ref{eq3} were used to extrapolate the velocity data to the photometric epochs, because of the low number of spectra taken before day +50, i.e. during the expansion of the photosphere."42 Data on SN 1999em in NGC 1637 were used for distance determination with EPM several times., Data on SN 1999em in NGC 1637 were used for distance determination with EPM several times.43 Hamuyetal.(2001) used cross-correlation velocities (with the model spectra of E96 as the template set) and the correction factors of E96, \citet{hamuy2001} used cross-correlation velocities (with the model spectra of E96 as the template set) and the correction factors of E9644universe.,universe.45 Since thev become clilficult to observe. from the ground. as their (Mus redshifts oul of (he optical window and the terrestrial skv background grows verv bright. space based measurements are necessary.," Since they become difficult to observe from the ground as their flux redshifts out of the optical window and the terrestrial sky background grows very bright, space based measurements are necessary."46 Wide field instruments are needed to achieve sufficient numbers to study. and stringent. svstematics controlled experiments (o derive accurate results.," Wide field instruments are needed to achieve sufficient numbers to study, and stringent, systematics controlled experiments to derive accurate results."47 For example. ihe Supernova/Acceleration Probe (SNAP: Alderingetal.(2004))) is carefully desiened specifically to achieve high quality (in both statistics and svstematics). well characterized. photometric and spectroscopic observations of thousands of supernovae.," For example, the Supernova/Acceleration Probe (SNAP: \citet{aldering04}) ) is carefully designed specifically to achieve high quality (in both statistics and systematics), well characterized, photometric and spectroscopic observations of thousands of supernovae."48 Space extends the reach of a non-crvogenic telescope to μπα. bevond which thermal noise swamps the astronomical signal.," Space extends the reach of a non-cryogenic telescope to $\mu$ m, beyond which thermal noise swamps the astronomical signal."49 To this wavelength limit the Sill sspectral feature used for classification of Ἔνρο la supernovae (SNe Ia) can be observed to redshift 2=1.7., To this wavelength limit the SiII spectral feature used for classification of Type Ia supernovae (SNe Ia) can be observed to redshift $z=1.7$.50 This redshift limit matches extremely. well the optimum depth for dark energv investigations. bevond which the sensitivitv to the dark energv characteristics [ndes away (Linder&Ihuerer2003).," This redshift limit matches extremely well the optimum depth for dark energy investigations, beyond which the sensitivity to the dark energy characteristics fades away \citep{linhut03}."51. However. a 2-m class space telescope such as SNAP will observe large numbers of supernovae. both SNe Ia ancl other (vpes. at redshilts 2>1.7.," However, a 2-m class space telescope such as SNAP will observe large numbers of supernovae, both SNe Ia and other types, at redshifts $z>1.7$."52 For example. the visible flux could be followed out to zzz4 and the near UV down to (SNe la have almost no emission « 2500A)) out to z6.," For example, the visible flux could be followed out to $z\approx4$ and the near UV down to (SNe Ia have almost no emission $< 2500$ ) out to $z\approx6$."53 In this article we investigate (he usefuluess of space based. wide field observations of SNe bevond 2=1.1 lor cosmology and astrophysics.," In this article we investigate the usefulness of space based, wide field observations of SNe beyond $z=1.7$ for cosmology and astrophysics."54 Section 2. addresses (he cosmological impact of extending precision distance measurements to z>1.7. including gravitational lensing effects: this will be generally applicable to any standardized candle. not just supernovae.," Section \ref{sec:cos} addresses the cosmological impact of extending precision distance measurements to $z>1.7$, including gravitational lensing effects; this will be generally applicable to any standardized candle, not just supernovae."55 The rates ancl vield of supernovae of all tvpes are discussed in relsec:measure.. together with measurement issues such as light eurve fitting. redshift determination. Alalmequist bias. ancl supernova tvping.," The rates and yield of supernovae of all types are discussed in \\ref{sec:measure}, together with measurement issues such as light curve fitting, redshift determination, Malmquist bias, and supernova typing."56 Section 4 investigates what we can learn aboul progenitor age. metallicitv. aud dust properties. aud how (his impacts treatment of svstematic uncertainties of the ϱ1.7 sample.," Section \ref{sec:sys} investigates what we can learn about progenitor age, metallicity, and dust properties, and how this impacts treatment of systematic uncertainties of the $z<1.7$ sample."57 We summarize in relsec:concl (he. prospects for using verv high redshift SNe (obtained for “free”. ancl in conjunction wilh JWST or a TAIT) to advance a variety of astrophivsical fields.," We summarize in \\ref{sec:concl} the prospects for using very high redshift SNe (obtained for “free”, and in conjunction with JWST or a TMT) to advance a variety of astrophysical fields."58 The discovery of the recent acceleration of the cosmic expansion is a breakthrough in the quest to understuxd (he universe., The discovery of the recent acceleration of the cosmic expansion is a breakthrough in the quest to understand the universe.59 To reveal the nature of the dark energy responsible for (he acceleration requires accurate measurements throughout the accelerating epoch and back into the time of deceleration., To reveal the nature of the dark energy responsible for the acceleration requires accurate measurements throughout the accelerating epoch and back into the time of deceleration.60 However. indefinite extension through the matter dominated.," However, indefinite extension through the matter dominated,"61pores of (he same polarity.,pores of the same polarity.62 For example. in Panel (a). the rectangle outlines a region with [lux emergence. where (he negative flix is moving in the upper right direction into the negalive pores and (he positive flux bands are moving in the lower left direction into the positive pores.," For example, in Panel (a), the rectangle outlines a region with flux emergence, where the negative flux is moving in the upper right direction into the negative pores and the positive flux bands are moving in the lower left direction into the positive pores."63 The coalescence of the small-scale fIuxes into the major pores facilitates the accumulation of the magnetic flux on the surface and. therefore. the formation of the large pores shown in Panel (c) and (d).," The coalescence of the small-scale fluxes into the major pores facilitates the accumulation of the magnetic flux on the surface and, therefore, the formation of the large pores shown in Panel (c) and (d)."64 ? simulates the formation of an active region and finds that the counterstreaming motion of opposite polarities is driven bv the Lorentz force., \cite{cheung2010} simulates the formation of an active region and finds that the counterstreaming motion of opposite polarities is driven by the Lorentz force.65 The large pores of negative polarity show a coherent pattern of rotation at the photosphere alter (heir formation in Panel (a) of Figure 11.., The large pores of negative polarity show a coherent pattern of rotation at the photosphere after their formation in Panel (a) of Figure \ref{bzz=0}.66 The rotation of the pores persists during (he emergence aud (he increase of magnetic flux at the photosphere., The rotation of the pores persists during the emergence and the increase of magnetic flux at the photosphere.67 llowever. (he positive polarity on the left does not present a complete rotation pattern during the emerging phase. but the rotation is interrupted by (he horizontal motions of the convective flow.," However, the positive polarity on the left does not present a complete rotation pattern during the emerging phase, but the rotation is interrupted by the horizontal motions of the convective flow."68 The coherent rotation starts to develop on the positive pore alter 5.5 hrs. shown by Panel (e) and (1) in Figure 1H..," The coherent rotation starts to develop on the positive pore after 5.5 hrs, shown by Panel (e) and (f) in Figure \ref{bzz=0}."69 Figure 12. illustrates the evolution of 2. and the horizontal velocity fields at z=—3 Mm. in the convection zone.," Figure \ref{bzz=-3} illustrates the evolution of $B_{z}$ and the horizontal velocity fields at $z = -3$ Mm, in the convection zone."70 Here. we observe a coherent rotation at (his depth on the negative polarity as well.," Here, we observe a coherent rotation at this depth on the negative polarity as well."71 The question is (hen. to what depth does the rotation extend.," The question is then, to what depth does the rotation extend."72" Thus we examine the structure of 4, on the y=0 plane during the rising of the flix rope in the upper panels in Figure 13..", Thus we examine the structure of $u_{y}$ on the $y=0$ plane during the rising of the flux rope in the upper panels in Figure \ref{roty=0}.73" The reversal of the direction of uw, in the right side of the domain corresponds to theprojection of the rotation of the negalive polarity on the y=0 plane.", The reversal of the direction of $u_{y}$ in the right side of the domain corresponds to theprojection of the rotation of the negative polarity on the $y = 0$ plane.74 The coherent rotation starts to extend downward al |—4:00:00 and approaches the depth of -10 Mam in 21 mins. (, The coherent rotation starts to extend downward at $t = 4:00:00$ and approaches the depth of -10 Mm in 21 mins. (75see Panel (a)).,see Panel (a)).76 Panel (c) shows a very coherent. pattern of rotation on the negative polarity al /=5:13:00. while on the positive pore on the left. the rotation is not obvious.," Panel (c) shows a very coherent pattern of rotation on the negative polarity at $t = 5:13:00$, while on the positive pore on the left, the rotation is not obvious."77 Sunspol rotation has long been observed aud studied in detail and has been found in association wilh CMEs (??)..," Sunspot rotation has long been observed and studied in detail and has been found in association with CMEs \citep[]{brown2003,kazachenko2009}. ."78 The rotation mechanism for sunspots found at work, The rotation mechanism for sunspots found at work79From the above results it is clear that diffusive fluxes are much more important in alleviating catastrophic quenching when compared to the Vishniac Cho fluxes (in the form,From the above results it is clear that diffusive fluxes are much more important in alleviating catastrophic quenching when compared to the Vishniac Cho fluxes (in the form80Understanding the details of galaxy. formation remains an important challenge in cosmology.,Understanding the details of galaxy formation remains an important challenge in cosmology.81 As shown by numerical calculations. the first. generation of galaxies should. have formed at very. high redshifts. inside collapsing halos. starting at 265. corresponding to high peaks of the primordial dark matter (DAL) density Ποια (Naozctal. OG).," As shown by numerical calculations, the first generation of galaxies should have formed at very high redshifts inside collapsing halos, starting at $z \sim 65$, corresponding to high peaks of the primordial dark matter (DM) density field \citep{NNB}."82 Cosmic Microwave. Background. (CMD). radiation observations suggest that reionization began at high redshifts., Cosmic Microwave Background (CMB) radiation observations suggest that reionization began at high redshifts.83 This means that a high. abundance of luminous objects must have existed. at that time. since these first Iuminous objects are expected to have heated ancl reionized their surroundings (Barkana&Loeb2001:Wyithe2003:LIaiman&LlolclerCon 2003).," This means that a high abundance of luminous objects must have existed at that time, since these first luminous objects are expected to have heated and reionized their surroundings \citep{rev,WL03,HH03,Cen}."84. The formation of a uminous object inside a halo necessarily requires the existence of barvonie gas there., The formation of a luminous object inside a halo necessarily requires the existence of baryonic gas there.85 Even in halos that are too small for cooling via atomic hyedrogen. the gas content can have substantial. and observable. astrophysical effects.," Even in halos that are too small for cooling via atomic hydrogen, the gas content can have substantial, and observable, astrophysical effects."86 In addition to the possibility of hosting astrophysical sources. such as stars. small halos may produce a 2]-cm signature (Ixuhlenetal.2006:ShapiroNaoz&Barkana2008:FurlanettoOh 2006).. and can block ionizing radiation and. produce an overall delay in the global progress of reionization (Barkana&Loeb2002:etal.2003.2005:MeQOuinn 2007).," In addition to the possibility of hosting astrophysical sources, such as stars, small halos may produce a 21-cm signature \citep{Kuhlen,Shapiro06,NB08, Furlanetto06}, and can block ionizing radiation and produce an overall delay in the global progress of reionization \citep{bl02, iliev2, iss05, mcquinn07}."87. The evolution of the halo gas fraction at various epochs of the Universe is of prime importance. particularly in the carly Universe.," The evolution of the halo gas fraction at various epochs of the Universe is of prime importance, particularly in the early Universe."88 We evaluate here the possible inlluence of a primordial magnetic field on the halo gas fraction., We evaluate here the possible influence of a primordial magnetic field on the halo gas fraction.89 As noted by Cnedin(2000):Cinedin&LIui(1998).. both in the linear and non-linear regimes. the accretion of eas into DM halos is suppressed. below a characteristic mass scale called the filtering mass. Adp.," As noted by \citet{Gnedin2000a, Gnedin1997}, both in the linear and non-linear regimes, the accretion of gas into DM halos is suppressed below a characteristic mass scale called the filtering mass, $M_F$."90 This mass scale coincides with the Jeans mass. M. if the latter does not vary in time.," This mass scale coincides with the Jeans mass, $M_J$, if the latter does not vary in time."91 Otherwise. Mp is a time average of AZ;.," Otherwise, $M_F$ is a time average of $M_J$."92 Thus. an increase in the ambient. pressure in the past. causes an increase in Aly ancl suppresses the aceretion of barvons into DAL halos in a cumulative fashion. producing an increase in Alp.," Thus, an increase in the ambient pressure in the past, causes an increase in $M_J$ and suppresses the accretion of baryons into DM halos in a cumulative fashion, producing an increase in $M_F$."93 Until now. studies focused on the UV. heating of the neutral interstellar gas as the main source of pressure. for determining the filtering mass.," Until now, studies focused on the UV heating of the neutral interstellar gas as the main source of pressure, for determining the filtering mass."94 Phese results are widely used in many semi-analvtic models (e.g. Maccióetal. 2010)). particularly those designed to study the properties of small ealaxies (due to the high redshift. character of the UV. heating).," These results are widely used in many semi-analytic models (e.g. \citealt{Maccio2009}) ), particularly those designed to study the properties of small galaxies (due to the high redshift character of the UV heating)."95specifically we can reject the faint ancl red signature of SNe la al very. high redshifts.,specifically we can reject the faint and red signature of SNe Ia at very high redshifts.96 The discovery images for all four SNe are shown in Figure 3.. and the positional ancl photometric data are listed in Tables 3. ancl 4..," The discovery images for all four SNe are shown in Figure \ref{fig:fig3}, and the positional and photometric data are listed in Tables \ref{tab:tab1} and \ref{tab:tab2}."97 Three SNe were identified in the area of the UDFP field., Three SNe were identified in the area of the UDFP field.98 was discovered in (he GOODS [ollow-up images trom GO 9352. and not detected seven mouths later (to within 50) in the UDFP images.," was discovered in the GOODS follow-up images from GO 9352, and not detected seven months later (to within $\sigma$ ) in the UDFP images."99 The host of IX0302-001 was verv faint. with FGOOGITzz28 mag within a radius. and verv blue. virtually undetectable al F850LP>27.5 in the same aperture.," The host of K0302-001 was very faint, with $F606W\approx 28$ mag within a radius, and very blue, virtually undetectable at $F850LP\ge27.5$ in the same aperture."100 The galaxy could not be sufficiently detected in anv of the deep multi- eround-based data sample assembled for the GOODS (spanning U though A.- ancl was only identified in two ACS bands: F606V and £775.," The galaxy could not be sufficiently detected in any of the deep multi-wavelength ground-based data sample assembled for the GOODS (spanning $U$ though $K_s$ -bands), and was only identified in two ACS bands: $F606W$ and $F775$."101 The lack of photometric measurements of the host galaxy made it difficult to constrain its photometric redshift using the Bavesian Photometrie Redshilt (DPZ) method (Benitez2000).. The, The lack of photometric measurements of the host galaxy made it difficult to constrain its photometric redshift using the Bayesian Photometric Redshift (BPZ) method \citep{2000ApJ...536..571B}.102 phot-z estimate derived of the host of IX0302-001. lacks a significant peak and has a broad confidence interval of 1.03<2 2.22., The $z$ estimate derived of the host of K0302-001 lacks a significant peak and has a broad confidence interval of $1.03<z<2.22$ .103 However. the photometry of the SN is more illuminating.," However, the photometry of the SN is more illuminating."104 The magnitude and colors (specilically the red. FGOGI—F850LP color of 3.33 mag: see 2004a)) match those of the five SNe Ia measured by Riessetal.(20045). at or near maxinun at zδέ1.3., The magnitude and colors (specifically the red $F606W-F850LP$ color of 3.33 mag; see \citeauthor{Riess:2003gz}~ \citeyear{Riess:2003gz}) ) match those of the five SNe Ia measured by \citet{Riess:2004b} at or near maximum at $z\approx1.3$.105 Results from Riessetal.(2004a.b) demonstrate that ~ of SNe with these photometric characteristics are correctly identified as SNe la (with the other being SNe le or Ib).," Results from \citet{Riess:2003gz,Riess:2004b} demonstrate that $\sim$ of SNe with these photometric characteristics are correctly identified as SNe Ia (with the other being SNe Ic or Ib)."106 A firm conclusion we can make is that this SN is too bright and too blue to be a SN Ia (of any previously seen Iuminosity. and color) at 2>1.4., A firm conclusion we can make is that this SN is too bright and too blue to be a SN Ia (of any previously seen luminosity and color) at $z > 1.4$.107 SN 200310 was discovered in the first UDFP stack (mean. date 2003 Ang. 31). and undetected in the GOODS [follow-up comparison images.," SN 2003lt was discovered in the first UDFP stack (mean date 2003 Aug. 31), and undetected in the GOODS follow-up comparison images."108 It was also well detected in the second UDEP stack of mean date 2003 Sep. 12., It was also well detected in the second UDFP stack of mean date 2003 Sep. 12.109 The host galaxy. was well detected in several passbands. and (thus the phot-z lor the host was well constrained al z=1.0 (0.74<21.26 conlidence interval).," The host galaxy was well detected in several passbands, and thus the $z$ for the host was well constrained at $z=1.0$ $0.74<z<1.26$ confidence interval)."110 We find that the photometry and colors of this SN were consistent with those lor a SN Ia discovered ~80 days from maximum light al z=1.0. and inconsistent with tested SN Ia scenarios (varving age. light-curve shape. and extinction) at z>1.4.," We find that the photometry and colors of this SN were consistent with those for a SN Ia discovered $\sim 80$ days from maximum light at $z=1.0$, and inconsistent with tested SN Ia scenarios (varying age, light-curve shape, and extinction) at $z>1.4$."111 SN 2003lu was found in the second UDEP stack. and notdetected in the first UDFP stack.," SN 2003lu was found in the second UDFP stack, and notdetected in the first UDFP stack."112 The single F850£ P-band measurement alone does not allow for a restriction in SN ivpe and redshift space., The single $F850LP$ -band measurement alone does not allow for a restriction in SN type and redshift space.113 However. the phot-z for the bright and. well-detected host. was zo—O.11 (0.0 - 0.25 confidence interval). and therefore we canreject the possibility that this was à SN Ia al z> 1.4.," However, the $z$ for the bright and well-detected host was $z=0.11$ (0.0 - 0.25 confidence interval), and therefore we canreject the possibility that this was a SN Ia at $z>1.4$ ."114 The only SN detected in several epochs of the UDF target. [ield. observations was, The only SN detected in several epochs of the UDF target field observations was115positive flux of the active region is computed by adding the contribution of all the pixels whose flux is larger than -—30GG (before multiplying by the above factor).,positive flux of the active region is computed by adding the contribution of all the pixels whose flux is larger than $-30$ G (before multiplying by the above factor).116 Similarly. the negative flux of the active region is computed by adding all the pixels with fluxes below +30GG. By including pixels with fluxes in the range [-30.430]GG (which represents the peak-to-peak noise) in the computations. we ensure efficient noise cancellation.," Similarly, the negative flux of the active region is computed by adding all the pixels with fluxes below $+30$ G. By including pixels with fluxes in the range G (which represents the peak-to-peak noise) in the computations, we ensure efficient noise cancellation."117 The two polarities nicely coincide in magnitude and show a similar evolution., The two polarities nicely coincide in magnitude and show a similar evolution.118 À linear decay phase is observed during the first three days., A linear decay phase is observed during the first three days.119 The flux decay rate is 9.3xΙΟ MMx day! which is intermediate in the range of values mentioned above., The flux decay rate is $9.3 \times 10^{20}$ Mx $^{-1}$ which is intermediate in the range of values mentioned above.120 We do not persue in this work whether this could have potentially contributed to the formation of the flux rope., We do not persue in this work whether this could have potentially contributed to the formation of the flux rope.121 Magnetic field extrapolations of some form would be necessary to conduct such a study. and this is beyond the scope of this paper.," Magnetic field extrapolations of some form would be necessary to conduct such a study, and this is beyond the scope of this paper."122 After curves show a plateau region. where no more net losses or gains are seen., After curves show a plateau region where no more net losses or gains are seen.123 The fractional decrease is. of course. a lower limit since we do not observe the onset of the decay phase.," The fractional decrease is, of course, a lower limit since we do not observe the onset of the decay phase."124 This plateau region was also encountered by ?:: however. in their study. the amount of flux lost was found to be in the range of 50—70 the initial value.," This plateau region was also encountered by \citet{sainz08}; however, in their study, the amount of flux lost was found to be in the range of $50-70$ the initial value."125 The sliding door phenomenon was seen to occur on July 3rd., The sliding door phenomenon was seen to occur on July 3rd.126 This date sits in the linear decay phase of the AR., This date sits in the linear decay phase of the AR.127 However. this phase was already taking place before and no particular slope change is seen on July 3rd.," However, this phase was already taking place before and no particular slope change is seen on July 3rd."128 The appearance of the orphan penumbrae structures happens on July 4th and 5th. coinciding with the flat section of the flux curve.," The appearance of the orphan penumbrae structures happens on July 4th and 5th, coinciding with the flat section of the flux curve."129 Clearly. these processes (sliding door and orphan-penumbrae generation) cause a minimal impact on the flux curves.," Clearly, these processes (sliding door and orphan-penumbrae generation) cause a minimal impact on the flux curves."130 One way to explain this result would require that the amount of flux change involved in both processes were at. or below. the noise level of the data (20.3x10°! MMx).," One way to explain this result would require that the amount of flux change involved in both processes were at, or below, the noise level of the data $\pm 0.3 \times 10^{21}$ Mx)."131 The first set of spatial scans were taken on 2005 July 3rd. centered on the filament.," The first set of spatial scans were taken on 2005 July 3rd, centered on the filament."132" Two maps with a FOV of 36""x35”. which was unfortunately not large enough to cover the whole active region (see Fig. 3))."," Two maps with a FOV of $36\arcsec \times 35\arcsec$, which was unfortunately not large enough to cover the whole active region (see Fig. \ref{Fig:MDIevol}) ),"133 were acquired with TIP-II between 13:53 and 15:01 UT., were acquired with TIP-II between 13:53 and 15:01 UT.134 The filament is seen all along the vertical direction., The filament is seen all along the vertical direction.135 Slit-reconstructed maps at different wavelengths for one of the two data sets for this day are presented in the first column of Fig. 5.., Slit-reconstructed maps at different wavelengths for one of the two data sets for this day are presented in the first column of Fig. \ref{Fig:TIPmaps}.136 The frames in this figure are located at different positions to approximately represent the alignment of their respective FOVs., The frames in this figure are located at different positions to approximately represent the alignment of their respective FOVs.137 The panel shows a tight filament spine. inferred from the strong absorption. which extends along the vertical direction.," The panel shows a tight filament spine, inferred from the strong absorption, which extends along the vertical direction."138 There are no big pores. but only some small magnetic features (dark patches) seen among the granulation in the continuum image on the panel of the figure.," There are no big pores, but only some small magnetic features (dark patches) seen among the granulation in the continuum image on the panel of the figure."139 The line core image (in the middle row) shows dark areas with larger absorption in regions of weak longitudinal fielc (this line weakens in faculae. as do most photospheric lines).," The line core image (in the middle row) shows dark areas with larger absorption in regions of weak longitudinal field (this line weakens in faculae, as do most photospheric lines)."140 The second set of spectropolarimetric data was taken on July 5th between 7:36 and 14:51 UT. columns 2-4 in Fig. 5..," The second set of spectropolarimetric data was taken on July 5th between 7:36 and 14:51 UT, columns 2–4 in Fig. \ref{Fig:TIPmaps}."141 Each sean took around 20 minutes to complete., Each scan took around 20 minutes to complete.142 The acquired maps were centered at a highly 1teresting area with very tight opposite polarities that correspoded. in continuum image. to pores and orphan penumbrae. all located along the PIL.," The acquired maps were centered at a highly interesting area with very tight opposite polarities that corresponded, in continuum image, to pores and orphan penumbrae, all located along the PIL."143 Note that these maps overlap with the upper half of the former map from July 3rd (see black boxes in Fig., Note that these maps overlap with the upper half of the former map from July 3rd (see black boxes in Fig.144 3. to get a better notion of the FOV)., \ref{Fig:MDIevol} to get a better notion of the FOV).145 The red core intensity Images in the row of Fig., The red core intensity images in the row of Fig.146 5. still show the spine of the filament in the lower part., \ref{Fig:TIPmaps} still show the spine of the filament in the lower part.147 Moreover. the filamet in the upper part appears to be more diffused and extended.," Moreover, the filament in the upper part appears to be more diffused and extended."148 One can easily distinguish dark Helium threads formed on July Sth especially in the panel of Fig. 5.., One can easily distinguish dark Helium threads formed on July 5th especially in the panel of Fig. \ref{Fig:TIPmaps}. .149" Many authors have observed the presence of threads in filaments and prominences before (e.g..2291,"," Many authors have observed the presence of threads in filaments and prominences before \citep[e.g.,][]{menzel60,engvold76,lin05,lin08,okamoto07}."150 It is generally believed that dark thin features in the chromosphere near ARs trace magnetic field lines., It is generally believed that dark thin features in the chromosphere near ARs trace magnetic field lines.151 This idea ts particularly interesting when applied to threads seen in AR filaments. since it could explain the presence of magnetic dips where plasma is trapped.," This idea is particularly interesting when applied to threads seen in AR filaments, since it could explain the presence of magnetic dips where plasma is trapped."152 Nevertheless. care must be taken. since a recent paper by ? proved that chromospheric fibrils mostly. but not always. trace magnetic field lines.," Nevertheless, care must be taken, since a recent paper by \citet{jaime11} proved that chromospheric fibrils mostly, but not always, trace magnetic field lines."153 From our maps we see that the threads observed with TIP-II change only slightly in a time range of 5-6 hours., From our maps we see that the threads observed with TIP-II change only slightly in a time range of 5–6 hours.154This becomes apparent when closely comparing the Helium maps of columns 2 and 4 in Fig. 5..,This becomes apparent when closely comparing the Helium maps of columns 2 and 4 in Fig. \ref{Fig:TIPmaps}.155 The short white arrow in the panel of the last column points at one of these threads. and can be compared with the same position in the core and continuum images.," The short white arrow in the panel of the last column points at one of these threads, and can be compared with the same position in the core and continuum images."156 From these maps we see that the most prominent threads are located above pores or orphan penumbrae., From these maps we see that the most prominent threads are located above pores or orphan penumbrae.157 A more detailed study of the magnetic configuration of these threads is presented below in Sect. ?2.., A more detailed study of the magnetic configuration of these threads is presented below in Sect. \ref{Sect:threads}.158 Strong absorption in the line core is present below the spine of the filament on July Sth (see Fig. 5))., Strong absorption in the line core is present below the spine of the filament on July 5th (see Fig. \ref{Fig:TIPmaps}) ).159 It is remarkable that the axis of the filament seems to lay so low in the atmosphere that even the highest layers of the photospheric Silicon absorption line (at the core of the line) trace it., It is remarkable that the axis of the filament seems to lay so low in the atmosphere that even the highest layers of the photospheric Silicon absorption line (at the core of the line) trace it.160 High resolution (07007I/px) Πα images from the Dutch Open Telescope (DOT:?) for the morning of 2005 July Sth confirm the presence of the filament. which has an inverse S-like shape and a spine in its lower part.," High resolution 071/px) $\alpha$ images from the Dutch Open Telescope \citep[DOT;][]{DOT} for the morning of 2005 July 5th confirm the presence of the filament, which has an inverse S-like shape and a spine in its lower part."161 This is also confirmed by inspection of at 171 limages., This is also confirmed by inspection of at $171$ images.162 Such an inverse S-like shape is likely to be expected in the northern hemisphere (2).., Such an inverse S-like shape is likely to be expected in the northern hemisphere \citep{pevtsov01}.163 The panel of Fig., The panel of Fig.164 6 shows one image of the Ha data set taken by the DOT at 8:44 UT., \ref{Fig:DOT} shows one image of the $\alpha$ data set taken by the DOT at 8:44 UT.165 The filament is surrounded by a bright plage., The filament is surrounded by a bright plage.166 The image reveals small arch-like structures in the upper half of the filament that are almost perpendicular to its axis and. in the spine. then stretch along it towards its center.," The image reveals small arch-like structures in the upper half of the filament that are almost perpendicular to its axis and, in the spine, then stretch along it towards its center."167 These archs can be identified as the H« counterpart of the threads mentioned before., These archs can be identified as the $\alpha$ counterpart of the threads mentioned before.168 A continuumimage (with a, A continuumimage (with a169We uow compare our results for the weak-leusing dspectruni with numerical simulations.,We now compare our results for the weak-lensing bispectrum with numerical simulations.170 Iu addition. we also consider the predictions obtained from the following our simple models. which have been used iu some previous works.," In addition, we also consider the predictions obtained from the following four simple models, which have been used in some previous works."171" We first compute the results obtained from the owest-order (""trec-ordor prediction from standard erturbation theory for the )3D bispectimm (?).. (Aj. 2Pa(hy Prk hop)Pr(he) | eve. where pio»=(sy-ko)/(hyho) and :l25.1 Mas |v"," We first compute the results obtained from the lowest-order (“tree-order”) prediction from standard perturbation theory for the 3D bispectrum \citep{Bernardeau2002}, (k_1,k_2,k_3) = 2 P_L(k_1) P_L(k_2) + 2 where $\mu_{12}= (\vk_1\cdot\vk_2)/(k_1 k_2)$ and = + ) +."172"h Second. we consider a “trec-nonlincar” approximation where in Eq.(28)) we replace the linear 3D power Pp(h) by the nonlinear power ο) frou ?.. oakJu Ευ. Path Pshy) | 2 Third. we cousider the fitting formula frou ?.. Un:ho.ha) = 2 πα. | 2 where the kernel Foxp is an effective kernel that interpolates from the large-scale perturbative result (29)) to a suallseale ansatz where the angular depeudenuce Don, Avudishes."," Second, we consider a “tree-nonlinear” approximation where in \ref{B-treeL-def}) ) we replace the linear 3D power $P_L(k)$ by the nonlinear power $P_S(k)$ from \cite{Smith2003}, (k_1,k_2,k_3) = 2 P_S(k_1) P_S(k_2) + 2 Third, we consider the fitting formula from \cite{Scoccimarro2001a}, (k_1,k_2,k_3) = 2 P_S(k_1) P_S(k_2) + 2 where the kernel $F_{2,\rm NL}$ is an effective kernel that interpolates from the large-scale perturbative result \ref{F2-def}) ) to a small-scale ansatz where the angular dependence on $\mu_{12}$ vanishes."173 Tere we shall use the noulineax power spectitun Ps(h) from ? as well as the nonlinear power spectrin Prane(40) of our model. Eqxs(17))-(18)).," Here we shall use the nonlinear power spectrum $P_S(k)$ from \cite{Smith2003} as well as the nonlinear power spectrum $P_{\rm tang}(k)$ of our model, \ref{P-tang-1}) \ref{P-tang-2}) )."174" Four. we cousider the scale transformation studied Z1 following the spirit of the scale transformation FU,introduced iu ?. for the tvo-poiut correlation function aud next∙ in 7?↻∪↖↖↸↥↴∖↻∩↑⊔∐⊔⋅ for the (29)↴∖⊳⋅ DAbomkey) = lhe. imb ο”. Dy wm, 3e"," Four, we consider the scale transformation studied in \cite{Pan2007}, following the spirit of the scale transformation introduced in \cite{Hamilton1991}175 for the two-point correlation function and next in \cite{Peacock1996} for the power spectrum, (k_1,k_2,k_3) = _1) _2) _3) 2 _1) _2) + 2"176Planetary nebulae (PNe) are the ionised nebulae ejected by Ιow-intermediate[liat mass stars[ that |have undergoneunclere: extensive[ mass loss during the AGB phase.,Planetary nebulae (PNe) are the ionised nebulae ejected by low-intermediate mass stars that have undergone extensive mass loss during the AGB phase.177 The central stars. of planctary nebulae (CSPN) constitute a rich resource to study the [ate stages of binary stellar evolution., The central stars of planetary nebulae (CSPN) constitute a rich resource to study the late stages of binary stellar evolution.178 At least 40 ‘lose binary CSPN are known that have orbital periods less than ~1 day (Aliszalski ct al., At least 40 close binary CSPN are known that have orbital periods less than $\sim$ 1 day (Miszalski et al.179 2011a) and these make up at least 17dE5% of all CSPN (Miszalski et al., 2011a) and these make up at least $17\pm5$ of all CSPN (Miszalski et al.180 20092), 2009a).181 With their short-lived nebulae (~10 ves) close binary CSPN are assured. to have just. recently. passed. through the comumon-envelope (CL) phase (ben Livio. 1993)., With their short-lived nebulae $\sim$ $^4$ yrs) close binary CSPN are assured to have just recently passed through the common-envelope (CE) phase (Iben Livio 1993).182 With significantly. less time to undergo further. angular momentum. loss compared. to other more evolved: post-CI binaries (Schreiber Gannsicke 2003). the orbital periods of close binary CSPN reflect the true post-CL distribution.," With significantly less time to undergo further angular momentum loss compared to other more evolved post-CE binaries (Schreiber Gännsicke 2003), the orbital periods of close binary CSPN reflect the true post-CE distribution."183AX reliable: wav of establishing that the chosen partial coverage model can (or cannot) give rise to a detectable ADR for a given SNR combination is to perform a set of simulations. as explained in the next subsection.,"A reliable way of establishing that the chosen partial coverage model can (or cannot) give rise to a detectable ADR for a given –SNR combination is to perform a set of simulations, as explained in the next subsection."184 Once the detectabilitv. or not. of the ADR has been established. this can be compared. to. the.ασ situation in the observed spectrum.," Once the detectability, or not, of the ADR has been established, this can be compared to the situation in the observed spectrum."185 For each SNR combination there are four possibilities: Cases (ii) and (id) are useful lor estimating absorber sizes: dn case (di)partial coverage ds established and. herefore. the transverse size of the absorber must besmaller han the proper separation of the LOS at the absorbing redshift.," For each –SNR combination there are four possibilities: Cases (ii) and (iii) are useful for estimating absorber sizes: In case (ii) coverage is established and, therefore, the transverse size of the absorber must be than the proper separation of the LOS at the absorbing redshift."186 Conversely. in case (iii)/o/al coverage is established and the transverse size of the absorber must befarger than he proper separation of the LOS.," Conversely, in case (iii) coverage is established and the transverse size of the absorber must be than the proper separation of the LOS."187 Further. a maximum likelihood approach can be used ο estimate most probable absorber sizes from the number ob established. partial and total coverage cases.," Further, a maximum likelihood approach can be used to estimate most probable absorber sizes from the number of established partial and total coverage cases."188 Each of the 100 fitted ppairs mentioned above gives a single r value ai can be used to produce an artificial continuum normalize absorption profile. e..," Each of the 100 fitted pairs mentioned above gives a single $\tau$ value and can be used to produce an artificial continuum normalized absorption profile, $e^{-\tau}$."189 If one adds a term o=1.520 to each data point in this profile. one effectively. introduces excess Hux due to partial coverage from our chosen physical moce 5)).," If one adds a term $\alpha=1.520$ to each data point in this profile, one effectively introduces excess flux due to partial coverage from our chosen physical model )."190 Decause the SNR. varies considerably over the observe: spectrum from ~25 to ~120. for cach region containing a celoublet component an average SNR. value was cetermines by inspection of the spectrum using the task inLRAL.," Because the SNR varies considerably over the observed spectrum from $\sim 25$ to $\sim 120$, for each region containing a doublet component an average SNR value was determined by inspection of the spectrum using the task in."191 For cach Iv)). pair two artificial spectra were produced., For each ) pair two artificial spectra were produced.192 “Phe first spectrum contained 120 dedoublets with a profile e.., The first spectrum contained 120 doublets with a profile $e^{-\tau}$.193 The spacing of the lines was chosen empiricallv so that when subsequently the. lines would be fitted withvrrrr.. blending complications would be absent. ie. even the broadest Lines were well apart from each other.," The spacing of the lines was chosen empirically so that when subsequently the lines would be fitted with, blending complications would be absent, i.e. even the broadest lines were well apart from each other."194 The spectrum was resampled to the resolution of the observed spectrum (0.04 pper pixel) and smoothed to the instrumental resolution of 6.6 , The spectrum was resampled to the resolution of the observed spectrum (0.04 per pixel) and smoothed to the instrumental resolution of 6.6 .195Gaussian noise was added with o=ΒΛl to obtain the desirable final SNR. as measured beforehand for cach region.," Gaussian noise was added with $\sigma=\frac{1}{\rm SNR}$ to obtain the desirable final SNR, as measured beforehand for each region."196 The above process was repeated to produce another set of 120 simulations of the same line aiming to reproduce the ellects of excess Dux., The above process was repeated to produce another set of 120 simulations of the same line aiming to reproduce the effects of excess flux.197 This time gaussian noise with oa=SKHlon =vas added to the unit continuum spectrum and both data and continuum were then inereasecl by a., This time gaussian noise with $\sigma=\frac{1+\alpha}{\rm SNR}$ was added to the unit continuum spectrum and both data and continuum were then increased by $\alpha$.198 This ensured that 1. desired SNR was obtained in this case as well., This ensured that the desired SNR was obtained in this case as well.199 Next. wwas used to fit the artificial spectra.," Next, was used to fit the artificial spectra."200 Each of the 120 artificial doublets in the spectrum was fitted independently. so that 120 separate vvalues were obtained.," Each of the 120 artificial doublets in the spectrum was fitted independently, so that 120 separate values were obtained."201 The starting vyvalues for the iiterations were exactly the same as those used to make the simulated lines. so that one would expect to obtain a good fit. unless the elfects of excess [ux were significant.," The starting values for the iterations were exactly the same as those used to make the simulated lines, so that one would expect to obtain a good fit, unless the effects of excess flux were significant."202 wwas allowed: to fit only a single Voigt profile to each simulated. line., was allowed to fit only a single Voigt profile to each simulated line.203 Phe. option of automatically putting in acditional narrow lines to improve poor fits was not use since such lines were known to be spurious by construction., The option of automatically putting in additional narrow lines to improve poor fits was not used since such lines were known to be spurious by construction.204 The fitting region for each doublet component was centrec on the component aand extended ΣΕ where EWIIM=2Vln2b is the full width at half minimum.," The fitting region for each doublet component was centred on the component and extended over $3\times {\rm FWHM}$, where ${\rm FWHM}=2\sqrt{\ln 2} \ b$ is the full width at half minimum."205 This was done to avoic including too much continuum which can make a poor fi less pronounced., This was done to avoid including too much continuum which can make a poor fit less pronounced.206 If fora given ppair the higher continuum introduced an observable ADI. then. on average. the second set of 120 [its should be markedly poorer than the firstset.," If for a given pair the higher continuum introduced an observable ADR, then, on average, the second set of 120 fits should be markedly poorer than the firstset."207 Otherwise. the two," Otherwise, the two"208The study of magnetic eclueuts at very μπα scales Is One ¢ft the most iuportant topics in solar pliwvsics.,The study of magnetic elements at very small scales is one of the most important topics in solar physics.209 Magnetic Bright Poiuts (AIBPs) are ubiquitous iu the solar photosphere., Magnetic Bright Points (MBPs) are ubiquitous in the solar photosphere.210 They have suall dizuueters. typically less than 300 kni aud are fouid iu the iutererauuar lanes.," They have small diameters, typically less than 300 km, and are found in the intergranular lanes."211 MBPs correspond to areas of kilogauss fieds. are best observed in C-band disk eeitre Huages aud are nuinerous in active reelons Or car suspots.," MBPs correspond to areas of kilogauss fields, are best observed in G-band disk centre images and are numerous in active regions or near sunspots."212 They are formed. weal coniplex process involviug the interaction of he Πα field wih the couvectively wnstable hot rlasuua., They are formed by a complex process involving the interaction of the magnetic field with the convectively unstable hot plasma.213 T physical processes associated with their formalon been outlined iu Scehüssleretal.(2003):5iclvagο(2001):Carlssonetal.(200 1).. usiic forward node of radiative iiagneto-coivection iu he solar photosphere and upper convection zone.," The physical processes associated with their formation have been outlined in \citet{shelyagbp1,shelyagbp2,carlsson}, using forward modelling of radiative magneto-convection in the solar photosphere and upper convection zone."214 Despie the overal SILCCOSS M4 photospheric a sub-phnotosphnerie raciaive 1naegneOQ-convective models to reproduce imany of the observational properties solar radiation. we still «lo LO tly understaud 1ο physical processes invoved in t1ο stronely maguoetised photospheric plasma.," Despite the overall success of photospheric and sub-photospheric radiative magneto-convective models to reproduce many of the observational properties of solar radiation, we still do not fully understand the physical processes involved in the strongly magnetised photospheric plasma."215 I1 particular. it is difficult to use 1ο results of these simlations for studies of acoustic wave propagation through the solar amosphere aud interior.," In particular, it is difficult to use the results of these simulations for studies of acoustic wave propagation through the solar atmosphere and interior."216 Strong convective motions of the photospheric plaslia can hide the signatures of ACOsIc waves. nakius them. a dificult subject in oth παΊσα. aud observatioial investigatious.," Strong convective motions of the photospheric plasma can hide the signatures of acoustic waves, making them a difficult subject in both numerical and observational investigations."217 The developiieu of new inethods for inferring he xoperties of solar plasma using sound waves have becu ollowed. bv the successful modeling of the magioto-acoustic properties iu the solar atmosphere aud iuterior (ITasanetal..2005:ITanasogeal.2007:Παρα&vauSteiner.2009:Vieceshetal.. 2009)..," The development of new methods for inferring the properties of solar plasma using sound waves have been followed by the successful modelling of the magneto-acoustic properties in the solar atmosphere and interior \citep{hasan2, hanasoge, hasan1, fedun, khomenko2, parchevskii, shelyag4, 218steiner1,vigeesh1}."219 ITowever. duc to the 1oni-localitv of radiative processes in the solar atmosphere. a direct comparison of the plasina parameters at a certainyoomctrical depth in the computational box with the solar radiation paraincters at a eivenoptical depth may not be entirely correct.," However, due to the non-locality of radiative processes in the solar atmosphere, a direct comparison of the plasma parameters at a certain depth in the computational box with the solar radiation parameters at a given depth may not be entirely correct."220 The nou-localitv of radiative trausport iust be taken iuto account., The non-locality of radiative transport must be taken into account.221 Iliomoeuko&Collaos(2009) have recently sugeested that the changes in tje height of continuum formation with respect to the equipartition laver (the laver where the Alfvéóun speed is eqal to the sound speed. ey=ος). nav help to explain the appearance of the high-frequency acoustic haloes around suispots.," \citet{khomenkol2009} have recently suggested that the changes in the height of continuum formation with respect to the equipartition layer (the layer where the Alfvénn speed is equal to the sound speed, $v_A=c_s$ ), may help to explain the appearance of the high-frequency acoustic haloes around sunspots."222 παΊσαι siuulations of solu wave phenomena require a static magnetic configuration nioel which Incorporates as many physical properties of the real Sun as »ossible., Numerical simulations of solar wave phenomena require a static magnetic configuration model which incorporates as many physical properties of the real Sun as possible.223 In this paper we provide a recipe to create such a model. based ou the results of ummerical uodelliug of naenueo-convection in the photosphere.," In this paper we provide a recipe to create such a model, based on the results of numerical modelling of magneto-convection in the photosphere."224 We demonstrate hat the spectropoluinetrie properties of t10 Inaegnetic confietration we created successfully reproduces those of MDBPs., We demonstrate that the spectropolarimetric properties of the magnetic configuration we created successfully reproduces those of MBPs.225 Iu Section 2 we describe the tecinique used ο recumstruct the magnetic aud thermal parameters of he MBP model., In Section 2 we describe the technique used to reconstruct the magnetic and thermal parameters of the MBP model.226 The results of the spectro»olarimetric simulaions using the model are preseuted iu Section 3., The results of the spectropolarimetric simulations using the model are presented in Section 3.227 Iu Section Lowe show our preliminary results «n the wave uode couversion in the MDDP and discuss he possible observational signatures., In Section 4 we show our preliminary results on the wave mode conversion in the MBP and discuss the possible observational signatures.228 Our concluding remarks are xeseuted In Section 5., Our concluding remarks are presented in Section 5.229 We use a snapshot from tjo 7age magneto-convection siuulation of the solar photosphere undertaken with the MURAAM code (Voelereta2005) to produce the average MBP uxxdel.," We use a snapshot from the ""plage"" magneto-convection simulation of the solar photosphere undertaken with the MURaM code \citep{voegler1} to produce the average MBP model."230 Since the avecrage naenetic field flux in this sunapslio is relatively hiel (200 CO. a large ΠΠΡΟ of intereranular magnetic ficld coicentrations are generated.," Since the average magnetic field flux in this snapshot is relatively high $200~\mathrm{G}$ ), a large number of intergranular magnetic field concentrations are generated."231 The magnetic feld conceitrationus appear bright iu the cout m(A= 1300À).aIT 11 he € bid.," The magnetic field concentrations appear bright in the continuum $\lambda=4300\mathrm{\AA}$ ), and in the G band."232" This snapshot has been used to demonstrate 16 Inaenetic"" nature of the C-banud bight points (Schiissleretal.203:Shelvagal. 2001)."," This snapshot has been used to demonstrate the magnetic nature of the G-band bright points \citep{shelyagbp1,shelyagbp2}. ."233. To reveal the ]ose structure «ft the vertical component of the magnetic feld Dy. im the AIBPs. we average the depth depeucdices of the verical magnetic field strength over the brigif points. whichn are selected by their culauced C-band lutensity and naenetic field streneth.," To reveal the basic structure of the vertical component of the magnetic field $B_{0z}$ in the MBPs, we average the depth dependences of the vertical magnetic field strength over the bright points, which are selected by their enhanced G-band intensity and magnetic field strength."234 Fig., Fig.235 d shows D. as afunction ¢ot depth., \ref{fig1} shows $B_{0z}$ as afunction of depth.236 Note that 7=0 on the depth scaο COLTCSPOlleIs ο the average, Note that $z=0$ on the depth scale corresponds to the average237The parameter A is eliminated «quite easily.,The parameter $\lambda$ is eliminated quite easily.238" We first multiply each of the A equations by the corresponding 5; ancl then sum them up to eet: Changing the order of summation reduces the first term. after a simple manipulation. {ο simply Using the constraint reduces (he second term to A. and we finally get: and we can simply set A=—V,yy."," We first multiply each of the $K$ equations by the corresponding $b_k$ and then sum them up to get: Changing the order of summation reduces the first term, after a simple manipulation, to simply Using the constraint reduces the second term to $\lambda$, and we finally get: and we can simply set $\lambda = -N_{eff}$."239 The fy equations we are now left with are: We have a set of A non-linear equations in A variables - ὃς. An elegant reduction of the complexity of the problem can be achieved if we set A to AN. by assigning mj=yy lor h=1.....:V.," The $K$ equations we are now left with are: We have a set of $K$ non-linear equations in $K$ variables - $b_k$ 's. An elegant reduction of the complexity of the problem can be achieved if we set $K$ to $N$, by assigning $m_k \equiv y_k$ for $k = 1,\ldots,N$."240 Let us also denote (remember (hat now A= NJ): The NV equations now look like: which is a svstem of .N linear equations in the No variables f;., Let us also denote (remember that now $K=N$ ): The $N$ equations now look like: which is a system of $N$ linear equations in the $N$ variables $h_j$.241 We can easily solve [or them., We can easily solve for them.242 The problem is even more easily solved when we note that the matrix 1j is, The problem is even more easily solved when we note that the matrix $A_{jk}$ is243small but significant re-orientation of the magnetic field is expected. from the wy-plane into the z-direction.,"small but significant re-orientation of the magnetic field is expected, from the $xy$ -plane into the $z$ -direction."244 Plotting the evolution. of the magnetic energies in cach of the three directions however. shows that there is. in fact. no significant erowth in the z-direction (see figure 7)).," Plotting the evolution of the magnetic energies in each of the three directions however, shows that there is, in fact, no significant growth in the $z$ -direction (see figure \ref{hall_ideal_bxyz2}) )."245 This is in distinct opposition with the results (rom Paper L in which significant growth of the magnetic energy in the z-direction was observed for the same level o£ Llall resistivity.," This is in distinct opposition with the results from Paper I, in which significant growth of the magnetic energy in the $z$ -direction was observed for the same level of Hall resistivity."246 Lt is important to recall that the strength of the Hall ellect depends on the current in the svstem., It is important to recall that the strength of the Hall effect depends on the current in the system.247 The current. in urn. depends on the charge densities of the three charged uids.," The current, in turn, depends on the charge densities of the three charged fluids."248 Phe charge density of the dust &rain Duid is 6593τεSOPsatCem 7.," The charge density of the dust grain fluid is $\alpha_3 \rho_3 \approx -8 \times 10^{-18} \,\mbox{statC\,cm}^{-3}$ ."249 However. for the ion and. electron uids. the charge densities are much higher. approximately x5.10“statCem7.," However, for the ion and electron fluids, the charge densities are much higher, approximately $\pm 5 \times 10^{-15} \, \mbox{statC\,cm}^{-3}$."250 Therefore the current in the svsten. J=NM oipivisds primarily due to the velocity dillerence »etween the ion and electron IEuids.," Therefore the current in the system, $\mathbf{J} = \sum_{i} \alpha_i \rho_i \mathbf{v}_i$, is primarily due to the velocity difference between the ion and electron fluids."251 Therefore. while the decoupling of the dust grain [ui rom the magnetic field provides a high Llall resistivity. the strength ofthe Hall effect is in fact also critically dependen on the dvnamies of the ion Iuid relative to the electron [uid.," Therefore, while the decoupling of the dust grain fluid from the magnetic field provides a high Hall resistivity, the strength of the Hall effect is in fact also critically dependent on the dynamics of the ion fluid relative to the electron fluid."252" As the ion fluid. Hall parameter is much greater than 1i will be somewhat decoupled from the neutral Εις, insteac »ing more strongly tied to the magnetic field."," As the ion fluid Hall parameter is much greater than 1 it will be somewhat decoupled from the neutral fluid, instead being more strongly tied to the magnetic field."253 Vhis means hat the relative velocity between the ion and electron Iu will be rather small., This means that the relative velocity between the ion and electron fluid will be rather small.254 As a result. the majority of current in he svstem remains{οἱ to the magnetic field. and the strength ofthe Lall clleet. which is proportional to J.B. is very small.," As a result, the majority of current in the system remains to the magnetic field, and the strength of the Hall effect, which is proportional to $\mathbf{J} \times \mathbf{B}$, is very small."255 Vhis accounts for the growth of the magnetic ield in the z-direction being much less than would naively »f expected., This accounts for the growth of the magnetic field in the $z$ -direction being much less than would naively be expected.256 Put simply. the introduction. of ambipolar resistivity changes which fluids are coupled to which ancl. in doing so. inhibits the Hall elfect.," Put simply, the introduction of ambipolar resistivity changes which fluids are coupled to which and, in doing so, inhibits the Hall effect."257 On a side note. this can also occur in a system with only two charged fuids.," On a side note, this can also occur in a system with only two charged fluids."258 In this case. it is typically the ion luid that is the Larger contributor to both the Lall and aimbipolar conductivity.," In this case, it is typically the ion fluid that is the larger contributor to both the Hall and ambipolar conductivity."259 Phe decoupling of the ion [uid from he magnetic field leads to Llall resistivity. as anv velocity dillerence between the ion and electron Duid can give rise to a current with a component perpendicular to the magnetic ield.," The decoupling of the ion fluid from the magnetic field leads to Hall resistivity, as any velocity difference between the ion and electron fluid can give rise to a current with a component perpendicular to the magnetic field."260 Llowever. the ambipolar resistivity arises due to a low collision rate between the ion IHuid and the neutral uid.," However, the ambipolar resistivity arises due to a low collision rate between the ion fluid and the neutral fluid."261 As a result. the ions do not. in fact. behave in the same way as he neutrals.," As a result, the ions do not, in fact, behave in the same way as the neutrals."262 Their coupling with the magnetic field. though weak. is sullicient to ensure only a minimal relative velocity between the ions and. electrons.," Their coupling with the magnetic field, though weak, is sufficient to ensure only a minimal relative velocity between the ions and electrons."263 In this way. the impact of the Tall effect is similarly. reciucecd.," In this way, the impact of the Hall effect is similarly reduced."264 In a Hall-dominated How. we would expect to see not only a growth in magnetic field strength in the z-direction. but also a resulting growth of kinetic energv in the same irection. as the plasma is influenced to travel out of the gy-plane.," In a Hall-dominated flow, we would expect to see not only a growth in magnetic field strength in the $z$ -direction, but also a resulting growth of kinetic energy in the same direction, as the plasma is influenced to travel out of the $xy$ -plane."265 With even moderate Lall resistivity. this kinetic nergy in the z-direction can become comparable to that in je weclirection (see Paper D.," With even moderate Hall resistivity, this kinetic energy in the $z$ -direction can become comparable to that in the $x$ -direction (see Paper I)."266 However. in this multilluid ase. the magnetic field. experiences. only a minimal re-xientation into the z-direction. ane therefore only the Duids mt are tightly coupled to the magnetic field will experience nv noticeable dynamics in this direction.," However, in this multifluid case, the magnetic field experiences only a minimal re-orientation into the $z$ -direction, and therefore only the fluids that are tightly coupled to the magnetic field will experience any noticeable dynamics in this direction."267 Figure 8. shows jut the bulk [ow demonstrates negligible erowth of kinetic energy in the z-direction (upper panel). while the ion Duid. ing more Closely tied to the magnetic field. demonstrates a verv small. but. non-negligible. growth in this direction (lower panel).," Figure \ref{hall_ideal_kx_perturbB+kz_bz2} shows that the bulk flow demonstrates negligible growth of kinetic energy in the $z$ -direction (upper panel), while the ion fluid, being more closely tied to the magnetic field, demonstrates a very small, but non-negligible, growth in this direction (lower panel)."268 The WI instability is seen to undergo a very cillerent evolution in the presence of multilluid effects., The KH instability is seen to undergo a very different evolution in the presence of multifluid effects.269 La the ideal case. the initial wind-up of the velocity field has the elfect of also winding up the magnetic field. due to strong coupling between the two.," In the ideal case, the initial wind-up of the velocity field has the effect of also winding up the magnetic field, due to strong coupling between the two."270 As the KIL vortex is caused to stretch and expand by the amplified magnetic field. it reaches the periodic y-boundaries of the simulated grid.," As the KH vortex is caused to stretch and expand by the amplified magnetic field, it reaches the periodic $y$ -boundaries of the simulated grid."271 As the neighbouring vortices merge. numerical viscosity allows for magnetic reconnection. which results in the creation of," As the neighbouring vortices merge, numerical viscosity allows for magnetic reconnection, which results in the creation of"272Figure 9. shows the simulation results (relaxation timescales and conversion efficiency of the particle energy into the waves) for the different relative concentrations of the energetic electrons (p/n=107. 107. and 1) while the total plasma density is assumed to be constant (0.=2x10% em? that corresponds to w)/wy= 1077).,"Figure \ref{par_nb} shows the simulation results (relaxation timescales and conversion efficiency of the particle energy into the waves) for the different relative concentrations of the energetic electrons $n_{\mathrm{b}}/n=10^{-4}$, $10^{-2}$, and 1) while the total plasma density is assumed to be constant $n=2\times 10^7$ $\textrm{cm}^{-3}$ that corresponds to $\omega_{\mathrm{p}}/\omega_{\mathrm{B}}=10^{-2}$ )."273 The typical energy of the accelerated electrons £y and the loss-cone boundary a. equal 10 keV and 60°. respectively.," The typical energy of the accelerated electrons $E_{\mathrm{b}}$ and the loss-cone boundary $\alpha_{\mathrm{c}}$ equal 10 keV and $60^{\circ}$, respectively."274 One can see that the relaxation timescales are simply inversely proportional to the concentration of the energetic. particles., One can see that the relaxation timescales are simply inversely proportional to the concentration of the energetic particles.275 The conversion efficiency of the particle energy into the waves increases slightly with increasing 75/72 and varies from to13., The conversion efficiency of the particle energy into the waves increases slightly with increasing $n_{\mathrm{b}}/n$ and varies from to.276"6%.. Figure 10. shows the simulation results for the case when the concentration of the energetic particles is constant (ji=2x10° em?) while the total plasma density varies (which results in different ratios both of n,/n and c/c)."," Figure \ref{par_Y} shows the simulation results for the case when the concentration of the energetic particles is constant $n_{\mathrm{b}}=2\times 10^5$ $\textrm{cm}^{-3}$ ), while the total plasma density varies (which results in different ratios both of $n_{\mathrm{b}}/n$ and $\omega_{\mathrm{p}}/\omega_{\mathrm{B}}$ )."277 With increasing, With increasing278rend for the median velocity. dispersion when considering smaller host-groups distances.,trend for the median velocity dispersion when considering smaller host-groups distances.279 Top panel of figure 1. shows he above mentioned trend. for all svstems in our group sample.," Top panel of figure \ref{masa} shows the above mentioned trend, for all systems in our group sample."280 As we are considering host-group distances starting at 3Alpeh miscaleulation of group velocity. dispersion owing to hosts particles contamination. is not likely to happen.," As we are considering host-group distances starting at $3~Mpc ~h^{-1}$, miscalculation of group velocity dispersion owing to hosts particles contamination, is not likely to happen."281 Assuring that the observed. ellect is not. produced by high velocity host. particles misplaced in nearby groups., Assuring that the observed effect is not produced by high velocity host particles misplaced in nearby groups.282 As stated by Lemson Ixaulfmann (1999). there is a dependence of the halo mass function on the environment. which is skewed towards high mass objects in overdense regions.," As stated by Lemson Kauffmann (1999), there is a dependence of the halo mass function on the environment, which is skewed towards high mass objects in overdense regions."283 Hence. the rising of the velocity dispersion in denser environments. could be the result of a higher abundance of massive haloes.," Hence, the rising of the velocity dispersion in denser environments, could be the result of a higher abundance of massive haloes."284 In order to test this possibility. we compute the mass function in. 1.Mpeἡ thick spherical shells. centered on hosts for several radii (3.5. 9.5. 20.5 ancl 40.5 Alpeh 5).," In order to test this possibility, we compute the mass function in $1~Mpc~h^{-1}$ thick spherical shells, centered on hosts for several radii (3.5, 9.5, 20.5 and 40.5 $Mpc~h^{-1}$ )."285 phis allows us to quantify the dependence. of the mass function on the overdensity (6= 5.89. 1.00. 0.28. 0.05 respectively. for the above radii).," This allows us to quantify the dependence of the mass function on the overdensity $\delta$ = 5.89, 1.09, 0.28, 0.05 respectively, for the above radii)."286 Figure ὸ shows in dashed lines the mass function for the mentioned. racii multiplied by (1|9)t and labelled with the associated os: solid line. represents the total mass function.," Figure \ref{fm} shows in dashed lines the mass function for the mentioned radii multiplied by $(1+\delta)^{-1}$ and labelled with the associated $\delta 's$; solid line, represents the total mass function."287 Due to the overlapping. we shift the curves corresponding to the three highest overdensities by factors LO. 100. ancl 1000 respectively.," Due to the overlapping, we shift the curves corresponding to the three highest overdensities by factors 10, 100 and 1000 respectively."288 As can be seen. the mass function shape does not change for groups with masses 1.4197A.bt«AMx2LOMAL.fot (vertical dashed lines in ligure 2)).," As can be seen, the mass function shape does not change for groups with masses $1.4 \times 10^{12} M_{\odot} ~h^{-1} < M < 2\times 10^{13} M_{\odot} ~h^{-1}$ (vertical dashed lines in figure \ref{fm}) )."289 Llenee. the results obtained (rom this low mass sample will not be allected by the overabundance of massive haloes in high clonsity regions.," Hence, the results obtained from this low mass sample will not be affected by the overabundance of massive haloes in high density regions."290 Based on the previous analysis. we explore the observed velocity dispersion behaviour for groups according to their masses: considering masses greater and lower than 2.01077AL.b. I.," Based on the previous analysis, we explore the observed velocity dispersion behaviour for groups according to their masses; considering masses greater and lower than $2.0 \times 10^{13}~M_{\odot} ~h^{-1}$ ."291 Ns a result of this resampling we Lind that velocity dispersions of low mass groups are strongly alfected w the presence of host clusters (middle panel of figure 1)). whereas high mass groups do not show a significant variation of the median when approaching to their associated: hosts (lower panel of figure 1)).," As a result of this resampling we find that velocity dispersions of low mass groups are strongly affected by the presence of host clusters (middle panel of figure \ref{masa}) ), whereas high mass groups do not show a significant variation of the median when approaching to their associated hosts (lower panel of figure \ref{masa}) )."292 According to this. we focus the ollowing analysis on this low mass group sample.," According to this, we focus the following analysis on this low mass group sample."293 At first sight. the visine of the median velocity dispersion. could be a result of the gravitational influence of he host on its neighbourhood.," At first sight, the rising of the median velocity dispersion, could be a result of the gravitational influence of the host on its neighbourhood."294 This possibility encourages us to analyse the behaviour of the internal energy. ££. in the same way we did for the velocity. dispersion.," This possibility encourages us to analyse the behaviour of the internal energy, $E$, in the same way we did for the velocity dispersion."295" This quantity is estimated by: where the first and second. terms correspond to the kinetic ane potential energies respectively. @ is the 3D velocity dispersion. Agron, the group mass. m the particle mass. N the number of members of à group and ej, the group virial radius."," This quantity is estimated by: where the first and second terms correspond to the kinetic and potential energies respectively, $\sigma$ is the 3D velocity dispersion, $M_{group}$ the group mass, m the particle mass, N the number of members of a group and $R_{vir}$ the group virial radius."296 Top panel of figure 3. shows the, Top panel of figure \ref{sigE2} shows the297The halo model (see Coorav Sheth 2002 for a review) has become the preferred language in which to interpret measurements of galaxy clustering.,The halo model (see Cooray Sheth 2002 for a review) has become the preferred language in which to interpret measurements of galaxy clustering.298 Recently. Zehavi οἱ al. (," Recently, Zehavi et al. ("2992005) have expressed the luminosity dependence: of clustering in the Sloan Digital Sky Survey (SDSS. York et al.,"2005) have expressed the luminosity dependence of clustering in the Sloan Digital Sky Survey (SDSS, York et al."300 2000) Second Data Release (DID. Abazajian et al.," 2000) Second Data Release (DR2, Abazajian et al."301 2004) in terms of the halo mocdel., 2004) in terms of the halo model.302 Skibba et al. (, Skibba et al. (3032006) show that. if Zehavi et al,"2006) show that, if Zehavi et al."304s halo model decomposition is correct. then the luminosity of the central galaxy in a halo depends strongly on halo mass. whereas the luminositics of satellite &alaxies depend only weakly on the masses of their host haloes.,"'s halo model decomposition is correct, then the luminosity of the central galaxy in a halo depends strongly on halo mass, whereas the luminosities of satellite galaxies depend only weakly on the masses of their host haloes."305 The main goal of this paper is to test this prediction., The main goal of this paper is to test this prediction.306 We co this in Section 727. by studying the satellite population in the group catalog provided. by Derlind. ct al. (, We do this in Section \ref{testLsat} by studying the satellite population in the group catalog provided by Berlind et al. (3072006).,2006).308 Ehe abundance of groups decreases and the clustering strength increases with increasing richness. as expected. (Berlind et al.," The abundance of groups decreases and the clustering strength increases with increasing richness, as expected (Berlind et al."309 2007)., 2007).310 This suggests that the test we perform is unlikely to have been biased by incompleteness ellects in the catalog., This suggests that the test we perform is unlikely to have been biased by incompleteness effects in the catalog.311 As an additional check. we show that the satellite population in the group catalogs of Yang et al. (," As an additional check, we show that the satellite population in the group catalogs of Yang et al. ("3122005a) are similar to those from Derlind ct al.,2005a) are similar to those from Berlind et al.313 Dark matter haloes have substructure (e.g. Tormen 1997: Tormen. Diaferio Sver 1998: Gao et al.," Dark matter haloes have substructure (e.g. Tormen 1997; Tormen, Diaferio Syer 1998; Gao et al."314 2004a)., 2004a).315 If we identify subhaloes with satellite galaxies (e.g. Ixravtsov et al., If we identify subhaloes with satellite galaxies (e.g. Kravtsov et al.316 2004: Conroy et al., 2004; Conroy et al.317 2007). then the halo model makes," 2007), then the halo model makes"318left large ambiguity on the mix of emission mechanisms (Stephens&Badhwar1981).,left large ambiguity on the mix of emission mechanisms \citep{SB81}.319. The spatial distribution of (he enerev-integrated eamnima-ravy 1wensily. on the other hand. gave a higher statistical accuracy on which Maver-Ilasselwanderelal.(1982).. Strongetal.(1982). Bloemenetal. (1984).. Bloemenetal. (1985).. and ot1ος sel the path to the Galactic eamnia-ray astronomy.," The spatial distribution of the energy-integrated gamma-ray intensity, on the other hand, gave a higher statistical accuracy on which \citet{Hasselwander82}, , \citet{Strong82}, \citet{Bloemen84}, \citet{Bloemen85}, and others set the path to the Galactic gamma-ray astronomy."320 We refer to Murthy&Wolfendale(1993).. Sehoenlelder(2001). and schlickeiser(2002) [or general references on (he topics ο“(his work.," We refer to \citet{MurthyWolfendale93}, \citet{Schoenfelder01}, and \citet{Schlickeiser02} for general references on the topics of this work."321 When the much improved data obtained with EGRET (Thompsonetal.1993). were studied by Bertschetal.(1993). and IIunteretal.(1997). an excess of about. x(1.52) became apparent in the data in the GeV band relative to the Galactic gamma-ray. emission models cited above.," When the much improved data obtained with EGRET \citep{EGRET} were studied by \citet{Bertsch93} and \citet{Hunter97}, an excess of about $\times (1.5-2)$ became apparent in the data in the GeV band relative to the Galactic gamma-ray emission models cited above."322 This excess is visible along the entire Galactic plane (—10<b«10 deg., This excess is visible along the entire Galactic plane $-10<b<10$ deg.323 and —90«(+90 deg.), and $-90<\ell<+90$ deg.)324 but most pronounced in the central region of the plane (—40«€<440 deg.)., but most pronounced in the central region of the plane $-40<\ell<+40$ deg.).325 Here b and £ are the Galactic latitude aad longitude. respectively.," Here $b$ and $\ell$ are the Galactic latitude and longitude, respectively."326" In literature. the excess is referred (to as the ""GeV Excess”."," In literature, the excess is referred to as the “GeV Excess”."327 Mori(1997) studied the diffuse ΠΠ emission bv using Monte Carlo p-p interaction simulators devloped for accelerator experiments ancl confirmed (hat the EGRET spectrum can not be reproduced with the conventional cosmic proton spectrum., \citet{Mori97} studied the diffuse gamma-ray emission by using Monte Carlo $p$ $p$ interaction simulators devloped for accelerator experiments and confirmed that the EGRET spectrum can not be reproduced with the conventional cosmic proton spectrum.328 Strong and Moskalenko developed a computer program. GALPROP. where the cosmic rav propagation and interaction are numerically calculated in a model Galaxy to obtain the spatial distribution and spectrum. of secondary. particles including gamuna-ravs ancl radio isotopes (Strong&Moskalenko1997.2001)..," Strong and Moskalenko developed a computer program, GALPROP, where the cosmic ray propagation and interaction are numerically calculated in a model Galaxy to obtain the spatial distribution and spectrum of secondary particles including gamma-rays and radio isotopes \citep{Galprop1,Galprop2}."329 The diffuse Galactic σάςΤο spectra have been caleulated. separately for the QUx decay. bremsstralhlung. and inverse-Compton with various parameter settings of GALPROP by Strongetal.(2000).," The diffuse Galactic gamma-ray spectra have been calculated separately for the $\pi^0$ decay, bremsstrahlung, and inverse-Compton with various parameter settings of GALPROP by \citet{SMR00}."330. They noted that: a) the local interstellar spectra of electrons ancl protons (power-law index >2.5 above 10—20 GeV) do not reproduce (he gamma-ray spectrum along the Galactic plane observed by EGRET: b) a very hard electron spectrum (power-law index ~ 1.8) and a modified nucleon spectrum will be needed to minimize the difference between (he prediction and the data in the GeV band: and ο) the GeV excess in (he central Galactic ridge can not be reproduced within the constraint on the proton spectral index imposed by recent cosmic proton measurements and the limit on the electron spectral index (~ 1.9) [rom radio and local cosmic ταν observations., They noted that: a) the local interstellar spectra of electrons and protons (power-law index $\ge 2.5$ above $10-20$ GeV) do not reproduce the gamma-ray spectrum along the Galactic plane observed by EGRET; b) a very hard electron spectrum (power-law index $\sim 1.8$ ) and a modified nucleon spectrum will be needed to minimize the difference between the prediction and the data in the GeV band; and c) the GeV excess in the central Galactic ridge can not be reproduced within the constraint on the proton spectral index imposed by recent cosmic proton measurements and the limit on the electron spectral index $\sim 1.9$ ) from radio and local cosmic ray observations.331 They noted that the excess persists at higher Galactic latitude (|(|>5 deg)., They noted that the excess persists at higher Galactic latitude $|\ell|>5$ deg).332 Dueschingetal.(2001) have also noted that the EGRET spectrum is incompatible with the locally measured cosmic proton spectrum., \citet{Buesching01} have also noted that the EGRET spectrum is incompatible with the locally measured cosmic proton spectrum.333 The GeV Excess has led (o new optimizations of (he Galactic gamma-ray enmission models ancl speculations on possible new eamunma-rayv sources in (he Galaxy., The GeV Excess has led to new optimizations of the Galactic gamma-ray emission models and speculations on possible new gamma-ray sources in the Galaxy.334 One choice is lo assume a harder protonspectrum in the Galactic ridee region as has been noted by, One choice is to assume a harder protonspectrum in the Galactic ridge region as has been noted by335uodel cases shown iu Fie. L.,"model cases shown in Fig. \ref{acorr},"336 the Li abuudance derived roni this line shows very simular scusitivity to the new electron collision data., the Li abundance derived from this line shows very similar sensitivity to the new electron collision data.337 The effects of the new clectron collision data on the abundance measured from the 6101 line are considerable less iu the solar case: onlbv about of the difference shown bv the other two lines., The effects of the new electron collision data on the abundance measured from the 6104 line are considerably less in the solar case: only about of the difference shown by the other two lines.338 In the other cases the influcnee of the electron collision data on he abuudanee measured from the 6101 sxpectral line is again comparable to the ifuence on the 6TÜS and S126 lines., In the other cases the influence of the electron collision data on the abundance measured from the 6104 spectral line is again comparable to the influence on the 6708 and 8126 lines.339" 3 colon problem for calculating non-LTE. abundance Corrections is that they can be subject to enxve vot UWheertautics in the underlying atomic data,", A common problem for calculating non-LTE abundance corrections is that they can be subject to errors from uncertainties in the underlying atomic data.340 We have shown that clectrou collision data from a umber of different. calculations based ou quite different methods are in good or even excellent agrecuucut., We have shown that electron collision data from a number of different calculations based on quite different methods are in good or even excellent agreement.341 Data calculate with advanced close-coupling tecliniques provides data in exccllent agreement. eiving rate cocfhiicicuts for excitation processes Within a factor of 2 for the temperatures of most interest in cool stellar atiuospheres. T—5000 S000 Ik. This. aud the good agreciment with experiuenta results where available (see7).. suggests the data have an uncertainty of simular maeuitucde.," Data calculated with advanced close-coupling techniques provides data in excellent agreement, giving rate coefficients for excitation processes within a factor of 2 for the temperatures of most interest in cool stellar atmospheres, $T \sim 5000$ – 8000 K. This, and the good agreement with experimental results where available \citep[see][]{CCC}, suggests the data have an uncertainty of similar magnitude."342 The seui-enmpirica, The semi-empirical343Iu order to münimuize conuumnication anions processors. we divide potential halos iuto two ists.,"In order to minimize communication among processors, we divide potential halos into two lists."344" For every poteutial laο, we compute the overdensity at the largest possible ou-processor radius."," For every potential halo, we compute the overdensity at the largest possible on-processor radius."345 If the next search radius is larger thaw lis. the halo is added to a list that ums be couinmnuicated.," If the next search radius is larger than this, the halo is added to a list that must be communicated."346 Thus. all ou-processor halos arc| processed. concurrentLy wih no communication.," Thus, all on-processor halos are processed concurrently with no communication."347 Since the volun! of colnnmnicatiou is very suniall. we seud all other ios to every processor.," Since the volume of communication is very small, we send all other halos to every processor."348" Iloπόνο, since this approach is not scalable te, very laree halo catalogs or uunibers of preycessors. We switch to a nnnffered. communication pattern if we cannot alocate a elobal halo catalog."," However, since this approach is not scalable to very large halo catalogs or numbers of processors, we switch to a buffered communication pattern if we cannot allocate a global halo catalog."349 In the butfered approach. halo lists are ouv conuumuicated to the nearest processors «mie at a time.," In the buffered approach, halo lists are only communicated to the nearest processors one at a time."350 The list is conmuumnicated uuib all blocks within the VOtune of the processors halos have been scareied., The list is communicated until all blocks within the volume of the processor's halos have been searched.351 While slower than the all-to-all approacl1. the amount of storage ICL DYOCCSSOL| yequired stavs fixed as the nuuber of processors aud umber of halos grow.," While slower than the all-to-all approach, the amount of storage per processor required stays fixed as the number of processors and number of halos grow."352 In eitLer Case. COMMCation COities unil all halos are fully searched.," In either case, communication continues until all halos are fully searched."353 For lis study. we will use the allto-all approach.," For this study, we will use the all-to-all approach."354 Figure 12(a) shows the strong scaling of the pSO halo finder as a fraction of the total wall clock time in a sing FLΑΡΗ time step., Figure \ref{fig:scaling} shows the strong scaling of the pSO halo finder as a fraction of the total wall clock time in a single FLASH time step.355 We show three ciffercut uuiform: problem sizes: 256°. 512°. and 10212 particles aud zones;," We show three different uniform problem sizes: $256^3$, $512^3$, and $1024^3$ particles and zones."356 We yostarted cach simulation at a represcutative recshift. 50.25. and rau for five time steps.," We restarted each simulation at a representative redshift, $z=0.25$, and ran for five time steps."357 These times do not iuclude optioual portions of the halo finder routine. suc jas writing the halo catalog to disk or tageine particles within halos.," These times do not include optional portions of the halo finder routine, such as writing the halo catalog to disk or tagging particles within halos."358 We performed these calculations on jaguar. a Crav NTS system at Oak Ridec National Laboratory.," We performed these calculations on jaguar, a Cray XT5 system at Oak Ridge National Laboratory."359 Jaguar consists of 16.688 dual six-core AMD Opteron nodes wit1 16 CD of memory per node and has a peak performance of 2.332 etaflops.," Jaguar consists of 16,688 dual six-core AMD Opteron nodes with 16 GB of memory per node and has a peak performance of 2.332 petaflops."360 Our approach offers good strong scaling behavior: we are able to beat or match the scaling performance «t ΕΤΑΡΗ at all problem sizes., Our approach offers good strong scaling behavior: we are able to beat or match the scaling performance of FLASH at all problem sizes.361 At larecr core counts. FLASII has difficulty scaling the Poissou ποvor. whereas the haQ finder maintains good scalability.," At larger core counts, FLASH has difficulty scaling the Poisson solver, whereas the halo finder maintains good scalability."362 However. we ca iiufer that we have poor weak scaling: the halk) fincling steps require ever larger wall clock time as the problem size erows.," However, we can infer that we have poor weak scaling: the halo finding steps require ever larger wall clock time as the problem size grows."363 The oor weak scaling is due to several factorbi., The poor weak scaling is due to several factors.364 First. since these are uniforiii exid. caleulations. at low redshift the varticl| cistribution among processors becomes vehly uubalanced.," First, since these are uniform grid calculations, at low redshift the particle distribution among processors becomes highly unbalanced."365 FLASID is block based and uses a Mortou curve m» lisribute these blocks amoug the processors., FLASH is block based and uses a Morton curve the distribute these blocks among the processors.366 Thus. while cach processor has roughly the same number of blocks. mwe blocks in highly dense regions will couaiu anv more particles than those iu voids.," Thus, while each processor has roughly the same number of blocks, those blocks in highly dense regions will contain many more particles than those in voids."367 Siice our halo fiuder scaus Im'Oug1 particles. there is a lack of concurrency (ue to this inbaliuce.," Since our halo finder scans through particles, there is a lack of concurrency due to this imbalance."368" At small probeni SIZCS, this is not an issue. but with 1tμι 12(b) 5)}."," At small problem sizes, this is not an issue, but with $1024^3$ \ref{fig:adjusted} \ref{fig:massFunc})"369" At small probeni SIZCS, this is not an issue. but with 1tμι 12(b) 5)}.Γ"," At small problem sizes, this is not an issue, but with $1024^3$ \ref{fig:adjusted} \ref{fig:massFunc})"370Au optical telescope cannot transmit spatial frequencies bevoud cj;=x253D/A. where D is the largest dimension of the telescope aperture aud A is the wavelength.,"An optical telescope cannot transmit spatial frequencies beyond $\pm k_{\rm max}=\pm 2\pi371D / \lambda$, where $D$ is the largest dimension of the telescope aperture and $\lambda$ is the wavelength."372 There is no aliasing if For D=2 meters. A=1pu. this samping corresponds to 07005 pixels.," There is no aliasing if For $D=2$ meters, $\lambda = 1\,\mu{\rm m}$, this sampling corresponds to 05 pixels."373 When the data have been sampled at Nyquist or ugher deusity. we cau produce shifted. rotated. or deconvolved versions of the image with no ambieutty (apart from noise).," When the data have been sampled at Nyquist or higher density, we can produce shifted, rotated, or deconvolved versions of the image with no ambiguity (apart from noise)."374 In the9/VAP mission. this will mean that subtraction of the host galaxy Irou supernova images will be essentially perfect. as loug as the template image is Nyquist-sampled.," In the mission, this will mean that subtraction of the host galaxy from supernova images will be essentially perfect, as long as the template image is Nyquist-sampled."375 This holds for other time-doimain signals. such as ticrolenusing. planetary tratsits. aud Ixuiper Bel surveys.," This holds for other time-domain signals, such as microlensing, planetary transits, and Kuiper Belt surveys."376 For weak leusing surveys. Ht means that the systematic ellipticities iiuposed ou galaxies by the PSF can. in theory. be removed nearly perfectly.," For weak lensing surveys, it means that the systematic ellipticities imposed on galaxies by the PSF can, in theory, be removed nearly perfectly."377 Nyquist sampling is thus highly. desirable., Nyquist sampling is thus highly desirable.378 By taking a series of exposures with poiutiugsdithered by a [ractional pixel aniounts. we cau sample the ePSF-couvolved scene imo'e deusely than the pixel eril.," By taking a series of exposures with pointings by a fractional pixel amounts, we can sample the ePSF-convolved scene more densely than the pixel grid."379 ]t is uuportant to realize that te two ellects of pixelization are in [act separable: the ePSF depeucds ou the size of the pixel through the PRE £2Gro): buta.," It is important to realize that the two effects of pixelization are in fact separable: the ePSF depends on the size of the pixel through the PRF $R(x,y)$; but."380 If we choose dither positions ou a grid af. then we elimiuate aliasing as long as μας€Na/a.," If we choose dither positions on a grid $a/N$, then we eliminate aliasing as long as $k_{\rm max} < N\pi / a$."381 We cau therefore obtain Nyquist-sampled data even with large pixels., We can therefore obtain Nyquist-sampled data even with large pixels.382 To first order this comes with uo noise penalty: if. we replace ≺↵⋜↕⊳∖↕∐∑≟↥≺↵≺↵⊸∖↥↽≻∩⊳∖⋯⋅↩∩↥∎⋃∐↩⊺∖∖↽∐∐⋜⊓∐↕∐≺↵↕⋅≺↵≺⇂ . . DO ⋅⋅ ∑⇁⋟⊔≺⇂∩⋀∖−≺↵⊸∖↥↽≻∪⊳∖⋯⋅↩⊳∖≺↵⋜↕∢∙∐∩↕⊔∐≺↵⊺↙∕∕≛∖−⋅↕∐≺↵∐↕∐≺↲↕ otal counts from the source are the same: the ↥∎⋯⋜↕⊔⋯⋜≹∑≟≺↵∐⋜↕⊳∖↕∐≺↵⊳∖⋜⋃∐≺↵⋯⊔↕∣⋈↵↕⋅∩↥∎↜∖ sv. photons per uiuit area (fewer per sample. but more samples per uuit area).," To first order this comes with no noise penalty: if we replace a single exposure of time $T$ with a dithered grid of $N^2$ exposures each of time $T/N^2$, then the total counts from the source are the same; the final image has the same number of sky photons per unit area (fewer per sample, but more samples per unit area)."383 There is. however. au increase in overliead aud read uoise from the extra exposures. aud the data rate must be higher.," There is, however, an increase in overhead and read noise from the extra exposures, and the data rate must be higher."384 What is the optimal ditier pattern?, What is the optimal dither pattern?385 L99a demonstrates that. for image reconstruction. a regularly. interlaced grid ollers the lowest noise.," L99a demonstrates that, for image reconstruction, a regularly interlaced grid offers the lowest noise."386 I lave not encouutered auy reason to execute ally other pattern., I have not encountered any reason to execute any other pattern.387 Iuterlaciug makes the analysis straightforward. and the L99a and tecliuiques can be reudered equivalent in this case.," Interlacing makes the analysis straightforward, and the L99a and techniques can be rendered equivalent in this case."388 Given that interlacing cau recover Nyquist sampling. the remaining drawback to larger pixels is the poorer resolution in the ePSF. which degrades the S/N for background-limited photometry aud [or centroid aud ellipticity ineasurements of mareinally resolved galaxies.," Given that interlacing can recover Nyquist sampling, the remaining drawback to larger pixels is the poorer resolution in the ePSF, which degrades the S/N for background-limited photometry and for centroid and ellipticity measurements of marginally resolved galaxies."389 E will quautify this below., I will quantify this below.390‘Table 6...,Table \ref{tab:summary}.391 Although the results broadly agree with selfsimilar predictions. the residual contamination tends to cause the scalings to appear too flat.," Although the results broadly agree with self--similar predictions, the residual contamination tends to cause the scalings to appear too flat."392 For instance. in the high signal to noise subsample where the effect of sources is clearest. the slope of the jyo/Lx. relation is found to be latter by 0.2 i a fit is attempted before source corrections are mace.," For instance, in the high signal to noise sub–sample where the effect of sources is clearest, the slope of the $y_0/L_\mathrm{X}$ relation is found to be flatter by 0.27 if a fit is attempted before source corrections are made."393 A similar result is found for the yofds scaling relation., A similar result is found for the $y_0/Y_{\mathrm{X}}$ scaling relation.394 We check the consisteney of the set of clusters with the more usual X.rav scaling relations between Lx and Zx. ὃν and Zx. and YS and Lx (e.g. ?)) in the same way as [or the SZ / NXray scaling relations (resultsalso summarised in Table 6)).," We check the consistency of the set of clusters with the more usual X–ray scaling relations between $L_{\mathrm{X}}$ and $T_{\mathrm{X}}$, $Y_{\mathrm{X}}$ and $T_{\mathrm{X}}$, and $Y_{\mathrm{X}}$ and $L_{\mathrm{X}}$ (e.g. \citealp{Morandi2007}) ) in the same way as for the SZ / X–ray scaling relations (resultsalso summarised in Table \ref{tab:summary}) )."395 The slopes that we measure. of 0.49+0.04. 2.19+0.16. and 1.24250.05. are consistent with the similarity expectations of 0.5. 2.5 and 1.25.," The slopes that we measure, of $0.49 \pm 0.04$, $2.19 \pm 0.16$, and $1.24 \pm 0.05$, are consistent with the similarity expectations of 0.5, 2.5 and 1.25."396 As the slight discrepaney for the correlation between Yx and YX is not of hish statistical significance. this study shows our sample to be representative of the population of hot. (£76 kkeV) clusters.," As the slight discrepancy for the correlation between $Y_{\mathrm{X}}$ and $T_{\mathrm{X}}$ is not of high statistical significance, this study shows our sample to be representative of the population of hot $T397\gtrsim 6$ keV) clusters."398 We have observed a complete sample of galaxy clusters using OCRAp. ancl studied the scaling. of the central Compton parameter. yo. with various X.ray quantities.," We have observed a complete sample of galaxy clusters using OCRA–p, and studied the scaling of the central Compton parameter, $y_0$, with various X–ray quantities."399 For each relation. we find. slopes in good. agreement with the predictions from self.similar models.," For each relation, we find slopes in good agreement with the predictions from self–similar models."400 Our study has similarities to that of ?.. and the two samples have 7 clusters in common. although we imposed stricter initial selection criteria.," Our study has similarities to that of \cite{Morandi2007}, and the two samples have 7 clusters in common, although we imposed stricter initial selection criteria."401 ? consider scalings with jo. so we are able to perform a direct comparison.," \citeauthor{Morandi2007} consider scalings with $y_0$ , so we are able to perform a direct comparison."402 Thev find that the go/Zx 7.2)). 2? 1.2)). 7)), They find that the $y_0/T_{\mathrm{X}}$ \ref{sec:scaling}) \cite{Bonamente2008} \ref{sec:scaling}) \citealp{Johansson2010})403 Thev find that the go/Zx 7.2)). 2? 1.2)). 7))., They find that the $y_0/T_{\mathrm{X}}$ \ref{sec:scaling}) \cite{Bonamente2008} \ref{sec:scaling}) \citealp{Johansson2010})404the most promising sources (see. c.e@.. Thorue Bragiusky 1976: Thorne 1995).,"the most promising sources (see, e.g., Thorne Braginsky 1976; Thorne 1995)."405" In particulary, LISA may be able to detect the collapse of a SMS to a SMDII."," In particular, LISA may be able to detect the collapse of a SMS to a SMBH."406 Even more pronisiug is the possible detection of the coalescence of two SMDIIS (LISA Pre-Phase A report 1995)., Even more promising is the possible detection of the coalescence of two SMBHs (LISA Pre-Phase A report 1995).407 The likelihood. of such an event. however. largely depends ou how SMDIIS form aud is therefore still uncertain.," The likelihood of such an event, however, largely depends on how SMBHs form and is therefore still uncertain."408 Tn a seres of papers we revisit the formation of SMBs via the collapse of SAISs. focussing ou the influence of rotation and eecneral relativity.," In a series of papers we revisit the formation of SMBHs via the collapse of SMSs, focussing on the influence of rotation and general relativity."409 We analyze the secular contraction of a uniforlv rotating equilibria configuration via thermal enüsson and mass loss., We analyze the secular contraction of a uniformly rotating equilibrium configuration via thermal emission and mass loss.410 We concentrate on a coufiguration rotating at the niasshedding luit., We concentrate on a configuration rotating at the mass-shedding limit.411 In Bammearte Shapiro (1999. hereafter Paper D. we have shown that the Iuninositv from such a star is considerable reduced below the value of a ronretating spherical star of the sanie mass.," In Baumgarte Shapiro (1999, hereafter Paper I), we have shown that the luminosity from such a star is considerably reduced below the value of a nonrotating spherical star of the same mass."412 Iu this paper. we analyze the structure and stability against collapse of fully relativistic. rotating n=3 xlvtropes in stationary equilibrium.," In this paper, we analyze the structure and stability against collapse of fully relativistic, rotating $n=3$ polytropes in stationary equilibrium."413 SAISs to which these calculations apply are radiation-doninated. iscutropic configurations of sufficient nass that ucither nuclear nurnnug nor electron-positrou pairs are important before he stars reaches the ouset of relativistic eravitational iustabilitv.," SMSs to which these calculations apply are radiation-dominated, isentropic configurations of sufficient mass that neither nuclear burning nor electron-positron pairs are important before the stars reaches the onset of relativistic gravitational instability."414" Stars with AJ>ΟΛΗ, fall in this category (Zeldovich Novvikkov 1971: Fuller. Woosley Weaver 1986)."," Stars with $M \gtrsim 10^6 M_{\odot}$ fall in this category (Zel'dovich kov 1971; Fuller, Woosley Weaver 1986)."415 Moreover. the evolutionary timescale due to cooling has to be longer than the livdrodyvnuauic timescale for the star to evolve iu a quasistationary fashion.," Moreover, the evolutionary timescale due to cooling has to be longer than the hydrodynamic timescale for the star to evolve in a quasistationary fashion."416 According to equations (9) and (10) below. we find that this coustraiut is satisfied for all inasses AL<<LOMAS...," According to equations (9) and (10) below, we find that this constraint is satisfied for all masses $M \lesssim 10^{13} M_{\odot}$."417 We track the quasistationary evolution of such stars to he poit of ouset of radial instability., We track the quasistationary evolution of such stars to the point of onset of radial instability.418 We first identity lis critical configuration analytically by micas of a post-Newtouian cucrey variational method., We first identify this critical configuration analytically by means of a post-Newtonian energy variational method.419 As pointed out by Bisnovatvi-lvogan. Zeldovvich Novvikkov (1967). determining the ousct of relativistic collapse in a rapidly rotating SMS requires asecond-order xost-Newtonian analysis. not a first-order. as in the case of a nonrotatiug star.," As pointed out by Bisnovatyi-Kogan, vich kov (1967), determining the onset of relativistic collapse in a rapidly rotating SMS requires a post-Newtonian analysis, not a first-order, as in the case of a nonrotating star."420 We provide au approximate. post-Newtoman analytic analysis (vigorizing and completing he qualitative argument of Disuovatvi-Ikogau. Zeldovvich Novvikkov (1967) and Zeldovich Novvikkov (1971). who oulv provide a dineusioual estimate of the second post-Newtoniui term).," We provide an approximate, post-Newtonian analytic analysis (rigorizing and completing the qualitative argument of Bisnovatyi-Kogan, vich kov (1967) and Zel'dovich kov (1971), who only provide a dimensional estimate of the second post-Newtonian term)."421 Then. to establish the result rigorously. we use a receut uunerical code (Cook. Shapiro Teukolsky 1992. 1991) to construct rotating equilibrium models in full general relativity.," Then, to establish the result rigorously, we use a recent numerical code (Cook, Shapiro Teukolsky 1992, 1994) to construct rotating equilibrium models in full general relativity."422 We show that the mass of the critical configuration is a unique function of the specific entropy., We show that the mass of the critical configuration is a unique function of the specific entropy.423" The values of R/M. T/[W aud J/AI? at the ousct of collapse are universal πανα, independent| of tle mass or prior evolution."," The values of $R/M$, $T/|W|$ and $J/M^2$ at the onset of collapse are universal numbers, independent of the mass or prior evolution."424 Were AZ is the mass. 7 the (polar) radius. J the angular momentum. £ the rotational and W the exavitatioual potential energy of the star.," Here $M$ is the mass, $R$ the (polar) radius, $J$ the angular momentum, $T$ the rotational and $W$ the gravitational potential energy of the star."425" We also speculate on the likely outcome of collapse for stars which do not disrupt due to thermomuclear explosions durius collapse: it is formed that stars with Af>ΤΟAZ, aud initial mctallicities Z<<0.005 do not explode (Fuller. Woosley Weaver 1986)."," We also speculate on the likely outcome of collapse for stars which do not disrupt due to thermonuclear explosions during collapse; it is found that stars with $M > 10^5 M_{\odot}$ and initial metallicities $Z < 0.005$ do not explode (Fuller, Woosley Weaver 1986)."426 Since these stars start collapsing from a universal critical configuration. the subsequeut. collapse is also uuiquelv. determined and should produce a inique eravitational waveform.," Since these stars start collapsing from a universal critical configuration, the subsequent collapse is also uniquely determined and should produce a unique gravitational waveform."427 We postpone a detailed discussion of this phase for a future paper in which we follow the dynamical collapse mmuerically in general relativity (Banmearte. Shapiro Shibata 1999).," We postpone a detailed discussion of this phase for a future paper in which we follow the dynamical collapse numerically in general relativity (Baumgarte, Shapiro Shibata 1999)."428" The key goals of our study are to decide whether a SMDII. can realle emerge frou, the collapse of a SMS aud to determine the hole parameters if indeed it can be formed this wav.", The key goals of our study are to decide whether a SMBH can really emerge from the collapse of a SMS and to determine the hole parameters if indeed it can be formed this way.429" Alternatively, a rotating supermassive cloud or star could collapse to a weakly relativistic disk (c.g. Wagoucr 1969: Loeb Rasio 1991)."," Alternatively, a rotating supermassive cloud or star could collapse to a weakly relativistic disk (e.g. Wagoner 1969; Loeb Rasio 1994)."430 If the collapsing imucrinost region euters the stroue-field domain. the aneular momentum of this matter must be below the maxiunun value of a Kerr hole (J/A/7=1) for black hole formation to occur eventually.," If the collapsing innermost region enters the strong-field domain, the angular momentum of this matter must be below the maximum value of a Kerr hole $J/M^2 = 1$ ) for black hole formation to occur eventually."431 What happens if the augular momentum exceeds this mit?, What happens if the angular momentum exceeds this limit?432 Does angular momentum dissipation by outflowing gas allow for black hole formation of the core?, Does angular momentum dissipation by outflowing gas allow for black hole formation of the core?433 Or. does gravitational radiation. following the formation of bars or axial currents carry away chough augular momentum to permit collapse?," Or, does gravitational radiation, following the formation of bars or axial currents carry away enough angular momentum to permit collapse?"434 Finally. ifa SAIBI can form by the collapse of a SAIS. what Is its nass and spin given the mass and spin of the SMS at the onset of collapse?," Finally, if a SMBH can form by the collapse of a SMS, what is its mass and spin given the mass and spin of the SMS at the onset of collapse?"435 Tn this paper we deal primarily with the structure. stability and carly secular evolution phases of the SAIS scenario.," In this paper we deal primarily with the structure, stability and early secular evolution phases of the SMS scenario."436 Our calculation. iu effect. sets up the initial data at the onset of collapse.," Our calculation, in effect, sets up the initial data at the onset of collapse."437 Tracking the subsequeut dynamical evolution of these imitial data will resolve the sey questions posed above. aud in this paper we will only speculate briefiv on the outcome of the dvuamical collapse.," Tracking the subsequent dynamical evolution of these initial data will resolve the key questions posed above, and in this paper we will only speculate briefly on the outcome of the dynamical collapse."438 This paper is organized as follows: In Section 2. we xovide a qualitative overview of the problem auc present our basic assunptions., This paper is organized as follows: In Section \ref{Sec2} we provide a qualitative overview of the problem and present our basic assumptions.439 In Section 3/— we diseuss the equilibrimn aud stability of rotating. relativistic SMSs.," In Section \ref{Sec3} we discuss the equilibrium and stability of rotating, relativistic SMSs."440 Iu articular. we determine the critical configuration at which an evolving SMS becomes dynamically uustable to racial serturbations.," In particular, we determine the critical configuration at which an evolving SMS becomes dynamically unstable to radial perturbations."441 We compare results from anu approximate analytical treatment (Section 3.2)) with those from a miuerical. fully relativistic calculation (Section 3.3)).," We compare results from an approximate analytical treatment (Section \ref{anal}) ) with those from a numerical, fully relativistic calculation (Section \ref{numerics}) )."442 ILwius identified the onset of instability. we then solve analytically for the evolution of SMSs during the secular contraction phase up to this critical configuration in Section ," Having identified the onset of instability, we then solve analytically for the evolution of SMSs during the secular contraction phase up to this critical configuration in Section \ref{Sec4}."443Iu Section 5 πο provide some qualitative argunients which sugeest that the direct formation of SMDIIs from the collapse of SMSs indeed may be possible., In Section \ref{coll} we provide some qualitative arguments which suggest that the direct formation of SMBHs from the collapse of SMSs indeed may be possible.444 We stumarize aud discuss our results iu Section 6.., We summarize and discuss our results in Section \ref{Summary}.445 Except where noted otherwise. we adopt gcometrized wits with οσlic throughout this paper.," Except where noted otherwise, we adopt geometrized units with $c \equiv 1 \equiv G$ throughout this paper."446 SAISs may form if collapsing primorcial gas builds up chough eutropy so that the radiation pressure can slow down the collapse (see. Begchuan Rees. 1978. for au alternative scenario).," SMSs may form if collapsing primordial gas builds up enough entropy so that the radiation pressure can slow down the collapse (see Begelman Rees, 1978, for an alternative scenario)."447 Further coutraction will then spin up the uewly formed SAIS to the mass-shedding unit. provided that the eas had some initial augular moment aud that viscosity maiutains uniform rotation.," Further contraction will then spin up the newly formed SMS to the mass-shedding limit, provided that the gas had some initial angular momentum and that viscosity maintains uniform rotation."448 The SAIS will then evolve secularly along the mass-shedding lait. siauultaneouslv enüttius radiation. matter and angular moment (see. e.c. Disuovatvi-kogau. Zeldovich vvikkov 1967: Zeldovich Novvikkov 1971).," The SMS will then evolve secularly along the mass-shedding limit, simultaneously emitting radiation, matter and angular momentum (see, e.g., Bisnovatyi-Kogan, Zel'dovich kov 1967; Zel'dovich kov 1971)."449 Onco it reaches the ouset of radial instability. the star collapses ou a dynauical timescale. auc may ultimately form à SMDIT.," Once it reaches the onset of radial instability, the star collapses on a dynamical timescale, and may ultimately form a SMBH."450 For sufficicutly massive objects (AL>109 A£.). the," For sufficiently massive objects $M \gtrsim 10^6 M_{\odot}$ ), the"451uuiuus the probability of a false For Ay=0. Equation 5. gives the probability of a false detection EEquation 1)) aud cousequeutly (0)x:a.,"minus the probability of a false For $\lamS=0$, Equation \ref{eq:beta} gives the probability of a false detection Equation \ref{eq:alpha}) ) and consequently, $\beta(0) \leq\alpha$."452 This reflecs the trade-off in anv detection algorithia: the colupronuse between nüninizius the nuniber of false detections against maximizing the nunuber of true detections., This reflects the trade-off in any detection algorithm: the compromise between minimizing the number of false detections against maximizing the number of true detections.453 That is. if the detection threshold is set low erough to detect weaker sources. the aleorithiu will also produce a larger nuuber of false positives that are actually backeround fluctuations.," That is, if the detection threshold is set low enough to detect weaker sources, the algorithm will also produce a larger number of false positives that are actually background fluctuations."454 Conversely. the more stringeut the criterion for detection. the smaller t1e probability of detecting a real source (this is illustrated by the location of the threshold S* that defines voth a aud. ο) in Figure 3)).," Conversely, the more stringent the criterion for detection, the smaller the probability of detecting a real source (this is illustrated by the location of the threshold $\thresh$ that defines both $\alpha$ and $\beta$ in Figure \ref{fig:alfabetillus}) )."455 Note that although our notation enpliasizes the dependence of the power ou As. it also depends on Ap. Ts. TR. and rr.," Note that although our notation emphasizes the dependence of the power on $\lamS$ , it also depends on $\lamB$, $\exptime$, $\exptimeB$, and $\rr$ ."456 The power calculation is shown for the simple Poissoji case in Figure L. where HAS) is plotted for different dustances of Ap aud for ciffereat levels of the detecion threshold S*.," The power calculation is shown for the simple Poisson case in Figure \ref{fig:power}, where $\beta(\lamS)$ is plotted for different instances of $\lamB$ and for different levels of the detection threshold $\thresh$."457 As expected. stronger sources are invariably detected.," As expected, stronger sources are invariably detected."458 For a eiven source intensity. an iucrease in the background or a larger detection threshold (ie. lower a) both cause tie detectionprobabilitv to decrease.," For a given source intensity, an increase in the background or a larger detection threshold (i.e., lower $\alpha$ ) both cause the detectionprobability to decrease."459 Iun a typical observation. the," In a typical observation, the"460and angular momentum are transferred. from their orbit to the envelope which is gradually ejected.,and angular momentum are transferred from their orbit to the envelope which is gradually ejected.461 As he cores get closer together their orbital period falls and. this sets up differential rotation within the Cl., As the cores get closer together their orbital period falls and this sets up differential rotation within the CE.462 By its giant nature the CIS is expected to be largely convective., By its giant nature the CE is expected to be largely convective.463 Dillerential rotation and convection are the kev ingredients ofa stellar magnetic dvnamo (Tout&Prinele 1992).., Differential rotation and convection are the key ingredients of a stellar magnetic dynamo \citep{tout1992}. .464 Reeds&Tout(1995). &o so [ar as to sav that this dynamo actually drives the transfer οf οποίον and angular momentum [rom the orbit to the envelope as well as he strong wind that expels the envelope., \citet{regos1995} go so far as to say that this dynamo actually drives the transfer of energy and angular momentum from the orbit to the envelope as well as the strong wind that expels the envelope.465 Irrespective of this. we expect that. at the end of the common envelope evolution. either when he spiralling cores coalcsce or when all the envelope is driven away. there is a very strong magnetic field in the vicinity of the hot degenerate. core.," Irrespective of this, we expect that, at the end of the common envelope evolution, either when the spiralling cores coalesce or when all the envelope is driven away, there is a very strong magnetic field in the vicinity of the hot degenerate core."466 This field can penetrate he nondegenerate surfac “eof the core and become frozen in as it later cools and contracts., This field can penetrate the nondegenerate surface of the core and become frozen in as it later cools and contracts.467 The closer tie cores at the end of CIS evolution the greater the dillerential rotation in the CE and so the stronger he expected frozen in magnetic field., The closer the cores at the end of CE evolution the greater the differential rotation in the CE and so the stronger the expected frozen in magnetic field.468 We then expec the strongest white dwarf magnetic fields to form in the cores of systems that merge curing CI evolution., We then expect the strongest white dwarf magnetic fields to form in the cores of systems that merge during CE evolution.469 A main-sequence companion is likely to cdisolve into the giant envelooc when it has spiralled in deep enough that its density is comparable with its surroundings., A main-sequence companion is likely to disolve into the giant envelope when it has spiralled in deep enough that its density is comparable with its surroundings.470 The spin angular momenunm remaining in the envelope depends on the details of tre CIS. process as well as the initial conditions of the svstem., The spin angular momentum remaining in the envelope depends on the details of the CE process as well as the initial conditions of the system.471 I£ we assume that the remaining envelope has the specilic angular momentum of the original orbit its spin period would have recluced [rom vears to davs., If we assume that the remaining envelope has the specific angular momentum of the original orbit its spin period would have reduced from years to days.472 The degenerate core therefore finds itself at thie' centre. of a rapidly spinning giant to which its spin is [ikelv to be coupled., The degenerate core therefore finds itself at the centre of a rapidly spinning giant to which its spin is likely to be coupled.473 Because of the small size of the core its moment of inertia is negligible compared with that of the Πο envelope., Because of the small size of the core its moment of inertia is negligible compared with that of the remaining envelope.474 Such a giant would itself eenerate a strong dynamo and spin down quite quickly. typically within 1Ho love (Tout&Pringle1992).," Such a giant would itself generate a strong dynamo and spin down quite quickly, typically within $10^4-10^5\,$ yr \citep{tout1992}."475. Thus. except in the rare| case that the envelope is almost completely ejected when the cores merge. we would not expect the HEMW to be rapidly spinning by the time they emerge from t1e Dsgiant envelope.," Thus, except in the rare case that the envelope is almost completely ejected when the cores merge, we would not expect the HFMWDs to be rapidly spinning by the time they emerge from the giant envelope."476 This is consistent with the tencdaney for LIEMVVDs to be extremely. slow rotators. some with spin periods up to 100vr (Wickramasinghe&Ferrario2000).," This is consistent with the tendancy for HFMWDs to be extremely slow rotators, some with spin periods up to $100\,$ yr \citep{wickramasinghe2000}."477. Then. from the COoninioln envelope πλσος that almost Merec. WὉ expect a range of relatively high magnetic field white dwarls in MC which emerge from the CL very close to interictine. the »olars and intermediate polars. with a corresponeing clearth of such fields amongst the single stars (IXoesteretal.2001).," Then, from the common envelope systems that almost merge, we expect a range of relatively high magnetic field white dwarfs in MCVs which emerge from the CE very close to interacting, the polars and intermediate polars, with a corresponding dearth of such fields amongst the single stars \citep{koester2001}."478. Systems which emerge with wider separations s1ould. tend o have much Lower fields., Systems which emerge with wider separations should tend to have much lower fields.479 We note at this point hat. while we do not understand. the precise mechanism «X common envelope evolution. we must expect à range of maenetic icles associated with any given final separation.," We note at this point that, while we do not understand the precise mechanism of common envelope evolution, we must expect a range of magnetic fields associated with any given final separation."480 Vhis is then consistent with the fact that the longest period|»olars tend o have high fields., This is then consistent with the fact that the longest period polars tend to have high fields.481 Indeed they must if the fie cis to be strong cnough to lock the white dwarf spin to t10 orbit atall., Indeed they must if the field is to be strong enough to lock the white dwarf spin to the orbit atall.482feasible.,feasible.483 We therefore developed an approximate procedure based ou the original grid spaciug. calibrated against the few higher resolution SCDNI projections.," We therefore developed an approximate procedure based on the original grid spacing, calibrated against the few higher resolution SCDM projections."484" In grid cells where the self-shieldiug corrected HI column is greater than a threshold value Nyy. we treat as fully neutral all gas particles hat contribute to that grid cell aud meet the following criteria: temperature Z7«30.000 αμα gas density pg>(1000/177)píi(Q5/18,,). where pij, is the virialization overdeusity described in 'e[ssecikdent.."," In grid cells where the self-shielding corrected HI column is greater than a threshold value $N_{{\rm HI},c}$, we treat as fully neutral all gas particles that contribute to that grid cell and meet the following criteria: temperature $T<30,000$ K and gas density $\rho_g > (1000/177) \rho_{vir} (\Omega_b/\Omega_m)$, where $\rho_{vir}$ is the virialization overdensity described in \\ref{ssec:ident}."485 For critical models. the density cut correspouds to 1000Q5.," For critical models, the density cut corresponds to $1000\ \Omega_b$."486" Iu subcritieal models. he deusity cut occurs at the same fraction of the critical deusity as in the ,,=I moclels."," In subcritical models, the density cut occurs at the same fraction of the critical density as in the $\Omega_m=1$ models."487" We ind that for loeSeVue=(20.1.20.7.20.7) at 2=(2.3.1) this procedure reproduces the SCDM high 'esolution values for λος aud 8,55; to within1051."," We find that for $\log N_{{\rm488HI},c} = (20.4, 20.7, 20.7)$ at $z=(2,3,4)$ this procedure reproduces the SCDM high resolution values for $\Omega_{ccg}$ and $\Omega_{obs}$ to within."489. It is possible that some Lyinau limit and/or aabsorption originates from regions other than galactic halos., It is possible that some Lyman limit and/or absorption originates from regions other than galactic halos.490 To investigate this alternative witlin our sitmulatious. we project the entire simulation volume aud compare the area of aand aabsorptiou to the stun of the absorption calculated by projecting each halo individually.," To investigate this alternative within our simulations, we project the entire simulation volume and compare the area of and absorption to the sum of the absorption calculated by projecting each halo individually."491 La the analysis presented here. we use all halos that have at least oue group ideutified by SIXID as described in relssecident at least one concentration of cold gas that is gravitationally bound). whether or uot the halo itself has AL>AM.," In the analysis presented here, we use all halos that have at least one group identified by SKID as described in \\ref{ssec:ident} at least one concentration of cold gas that is gravitationally bound), whether or not the halo itself has $M\geq M_{res}$."492 Above M=Alpes. of the dark matter halos harbor at least ¢ue SIlxID-identilied eroup.," Above $M=M_{res}$, of the dark matter halos harbor at least one SKID-identified group."493" We have removed ΤΟΝ from the analysis in this section due to the extreme paucity of S""ucture in the model.", We have removed TCDM from the analysis in this section due to the extreme paucity of structure in the model.494 For the remaliniug four models. we calculate the total area subteucdec by aabsorption i ie halos with SIXID-identilied groups.," For the remaining four models, we calculate the total area subtended by absorption in the halos with SKID-identified groups."495 Comparing this value to the total area subtended iu au entire volume projection of each simulation at redshifts z=2 aud z=L we fincl agreement within for all the models at both redshifts. aud to better than in five of the eight cases.," Comparing this value to the total area subtended in an entire volume projection of each simulation at redshifts $z=2$ and $z=4$, we find agreement within for all the models at both redshifts, and to better than in five of the eight cases."496 We attribute the remaining differences to having more than one absorber along a eiven line of sight., We attribute the remaining differences to having more than one absorber along a given line of sight.497 Hence. all aabsorptiou iu the simulation occurs within halos with at least oue concentration of cold. gas.," Hence, all absorption in the simulation occurs within halos with at least one concentration of cold, gravitationally-bound gas."498 In aabsorption. five of the eight outputs agree to better than when compared iu this manner.," In absorption, five of the eight outputs agree to better than when compared in this manner."499 However. at 2=lI the results of volume projection and halo projection differed. by and for SCDM. CCDM. and OCDNMI respectively.," However, at $z=4$ the results of volume projection and halo projection differed by, and for SCDM, CCDM, and OCDM respectively."500 We took the worst case. 2=1 CCDM. aud projected all the halos that contaiued at least 32 particles (gas + dark matter). whether or uot they coutained a SIKID-ideutified gas concentration.," We took the worst case, $z=4$ CCDM, and projected all the halos that contained at least 32 particles (gas $+$ dark matter), whether or not they contained a SKID-identified gas concentration."501 When we sium the area subtended by aabsorption in these halos. we find that it now accounts for all but of the," When we sum the area subtended by absorption in these halos, we find that it now accounts for all but of the"502Llurley et al. (,Hurley et al. (503"2004) where one model startec well within r, ane the other started with muss=nm.",2004) where one model started well within $r_{\rm t}$ and the other started with $r_{\rm max} = r_{\rm t}$.504 These are shown in Figure 2bb ancl we clearly distinguish path A ancl path D-like evolution before both clusters end at a similar point., These are shown in Figure \ref{f:fig2}b b and we clearly distinguish path A and path B-like evolution before both clusters end at a similar point.505 In reality we would expect most clusters to evolve between he two extremes of paths A and D as they head. towards 33. particularly curing violent relaxation where clusters will expand and can move along path ο to join D2.," In reality we would expect most clusters to evolve between the two extremes of paths A and B as they head towards B3, particularly during violent relaxation where clusters will expand and can move along path C1 to join B2."506 We see this Oo some extent when we look at the evolution of models d... N2 and N3 in Figure 2ec. Model N3 in particular first evolves across the phase space before starting down path D2.," We see this to some extent when we look at the evolution of models N1, N2 and N3 in Figure \ref{f:fig2}c c. Model N3 in particular first evolves across the phase space before starting down path B2."507" There is also a clear distinction between the evolution of the three models. residing at well separated rjr, values as they start to move down in {οfry."," There is also a clear distinction between the evolution of the three models, residing at well separated $r_{\rm h} / r_{\rm t}$ values as they start to move down in $r_{\rm c} / r_{\rm h}$."508 Of course. owing to the arge half-mass relaxation timescales. the models do not get he opportunity to evolve completely through the parameter space.," Of course, owing to the large half-mass relaxation timescales, the models do not get the opportunity to evolve completely through the parameter space."509 We have now seen that it is possible to reach large ry values for clusters evolving in a weak 6822-like tidal field and that quite distinct rj values can be obtained. by clusters with cülferent initial sizes.," We have now seen that it is possible to reach large $r_{\rm h}$ values for clusters evolving in a weak $\,6822$ -like tidal field and that quite distinct $r_{\rm h}$ values can be obtained by clusters with different initial sizes."510 But can clistinet rj values be obtained by other means?, But can distinct $r_{\rm h}$ values be obtained by other means?511 The first possibility we explore is the inclusion of a primordial binary population (Moclel N2b)., The first possibility we explore is the inclusion of a primordial binary population (Model N2b).512 Figure 3. compares the rj evolution of models N2 and N2b which are identical in setup except for a 5 per cent primordial binary population in the latter., Figure \ref{f:fig3} compares the $r_{\rm h}$ evolution of models N2 and N2b which are identical in setup except for a 5 per cent primordial binary population in the latter.513 We see that the ry evolution is indistinguishable., We see that the $r_{\rm h}$ evolution is indistinguishable.514 This is also true for the evolution of bound. cluster mass (see Table 2)) ancl other general quantities., This is also true for the evolution of bound cluster mass (see Table \ref{t:table2}) ) and other general quantities.515 We note that as an accuracy check models N2 and N2b were both performed twice with dillerent initial random number seeds and the variation between cdilferent realisations of the same model was less than the dillerence between the two model tvpes., We note that as an accuracy check models N2 and N2b were both performed twice with different initial random number seeds and the variation between different realisations of the same model was less than the difference between the two model types.516 For these extended: clusters it is not surprising that the addition of binaries makes little dillerence to the evolution., For these extended clusters it is not surprising that the addition of binaries makes little difference to the evolution.517 The lone relaxation times for Alodels N2 and N2b (see Tables 1. and 2)) mean that the collisional extraction of binding energy [rom the binary orbits will not be ellicient at heating the cluster., The long relaxation times for Models N2 and N2b (see Tables \ref{t:table1} and \ref{t:table2}) ) mean that the collisional extraction of binding energy from the binary orbits will not be efficient at heating the cluster.518" The second: possibility. for internal evolution creating ry, differences between models relates to the formation of tight. BH-BIT binaries which then act as a central energy source to heat the cluster.", The second possibility for internal evolution creating $r_{\rm h}$ differences between models relates to the formation of tight BH-BH binaries which then act as a central energy source to heat the cluster.519 Hurley (2007) showed that the formation of one such lone-lived 111-111 binary could double the rofry ratio compared to a similar model which did not form a DII-DIE binary., Hurley (2007) showed that the formation of one such long-lived BH-BH binary could double the $r_{\rm c} / r_{\rm h}$ ratio compared to a similar model which did not form a BH-BH binary.520" However. we compare the ry, evolution of these models. (IX100-00a. and. WLOO-00b from Llurley 2007) in Figure 3. (and in Tables 2)) and. we sec no clear clistinetion."," However, we compare the $r_{\rm h}$ evolution of these models (K100-00a and K100-00b from Hurley 2007) in Figure \ref{f:fig3} (and in Tables \ref{t:table2}) ) and we see no clear distinction."521 Alackey et al. (, Mackey et al. (5222008) took this further and contrasted. the evolution of clusters with no BII-BII rinaries to that of clusters which retained a [arge number of post-supernovac Bills (~ 200) that subsequently sank to he cluster centre and formed. DII-DIHE binaries (as many as ive such binaries present at any one time).,2008) took this further and contrasted the evolution of clusters with no BH-BH binaries to that of clusters which retained a large number of post-supernovae BHs $\sim 200$ ) that subsequently sank to the cluster centre and formed BH-BH binaries (as many as five such binaries present at any one time).523 The focus was on star clusters in the Large Alagellanic Cloud and as such a tical field the same as For our 6822 case was used (but with Aue= 6kpc rather than. 10κρο ," The focus was on star clusters in the Large Magellanic Cloud and as such a tidal field the same as for our $\,6822$ case was used (but with $R_{\rm gc} = 6\,$ kpc rather than $10\,$ kpc)."524They. found hat the inclusion. of the DII-DBII. binaries could. increase rh by as much as a factor of two bv the time that. the model with no DLII-DII binaries had. reached: core-collapse (compared to a corresponding factor of 20 increase in. re)., They found that the inclusion of the BH-BH binaries could increase $r_{\rm h}$ by as much as a factor of two by the time that the model with no BH-BH binaries had reached core-collapse (compared to a corresponding factor of 20 increase in $r_{\rm c}$ ).525 The rj behaviour first started to diverge after 1 (αντ of evolution. corresponding to roughly one half-mass relaxation ime. with the expansion driven on the shorter relaxation imescale of the centralised. BLL population.," The $r_{\rm h}$ behaviour first started to diverge after $1-2\,$ Gyr of evolution, corresponding to roughly one half-mass relaxation time, with the expansion driven on the shorter relaxation timescale of the centralised BH population."526 However. we note that the most extended. of these models. were in the advanced stages of dissolution at a Hubble time.," However, we note that the most extended of these models were in the advanced stages of dissolution at a Hubble time."527 Another xossibilitv is one that has gathered much attention of late. namely the question of whether or not some star clusters ibour intermecdiate-mass black holes (AAIBLIs).," Another possibility is one that has gathered much attention of late, namely the question of whether or not some star clusters harbour intermediate-mass black holes (IMBHs)."528 Call et al. (, Gill et al. (5292008) compare the rj evolution of models with and withou an IAIBIL and find no significant dillerence until well after core-collapse and even at very [ate times the dilference is still less than a factor of two.,2008) compare the $r_{\rm h}$ evolution of models with and without an IMBH and find no significant difference until well after core-collapse and even at very late times the difference is still less than a factor of two.530 Daumgardt. Makino Llu (2005) looked at the cllect of increasing LAIBIT mass an founcl an increase in 7j of 15 per cent at most.," Baumgardt, Makino Hut (2005) looked at the effect of increasing IMBH mass and found an increase in $r_{\rm h}$ of 15 per cent at most."531 IH should be notedl that the maximum black hole mass included in. the models to date is 1000. and that the heating produce bv significantly more massive LAIBIIs. if indeed they exist. is vet to be documented.," It should be noted that the maximum black hole mass included in the models to date is $1\,000 \, M_\odot$ and that the heating produced by significantly more massive IMBHs, if indeed they exist, is yet to be documented."532 We next look at the evolution of our models. MI ane AP which were evolved in the stronger M31-like tidal field., We next look at the evolution of our models M1 and M2 which were evolved in the stronger M31-like tidal field.533" These models started with dillerent. initial density. profiles so provide an opportunity to look at how the choice of a Plummer or Wing profile alfects the mm, evolution.", These models started with different initial density profiles so provide an opportunity to look at how the choice of a Plummer or King profile affects the $r_{\rm h}$ evolution.534 This is shown in Figure 3. (also in Figure 4)) and we see that at various stages in the evolution the difference can be up to 50 per cent., This is shown in Figure \ref{f:fig3} (also in Figure \ref{f:fig4}) ) and we see that at various stages in the evolution the difference can be up to 50 per cent.535 The radius evolution of models MI ane M2 is studied in more detail in Figure ει., The radius evolution of models M1 and M2 is studied in more detail in Figure \ref{f:fig4}.536 Comparing this to Figure Lo we clearly see that the stronger tidal field drives more rapid evolution for the M31 models relative to their 6822 counterparts.," Comparing this to Figure \ref{f:fig1} we clearly see that the stronger tidal field drives more rapid evolution for the M31 models relative to their $\,6822$ counterparts."537 Indeed. both MI and M2. reach core-collapse prior το 20€vr.," Indeed, both M1 and M2 reach core-collapse prior to $20\,$ Gyr."538 The model with the Wing density profile evolves more rapidly., The model with the King density profile evolves more rapidly.539 This is primarily owing to a greater central density of stars in the initial mioclel which led to a greater rate of dynamical interactions. more mass lost across the tical boundary in the carly stages. and consequently a reduced relaxation timescale.," This is primarily owing to a greater central density of stars in the initial model which led to a greater rate of dynamical interactions, more mass lost across the tidal boundary in the early stages, and consequently a reduced relaxation timescale."540 However. in the," However, in the"541of the so-called. “hot Jupiters”. with a period of 1.09 clays. corresponding to an orbital distance only 3 times the radius ofits host star.,"of the so-called “hot Jupiters”, with a period of 1.09 days, corresponding to an orbital distance only 3 times the radius of its host star."542 Moreover. WASP-I2b has an inflated radius. HcL.SIu. one of the most extreme examples of anomalous racii for hot Jupiters.," Moreover, WASP-12b has an inflated radius, $R\simeq1.8 {\rm \, R_J}$, one of the most extreme examples of anomalous radii for hot Jupiters."543 As a result. the planet fills about half of its Roche lobe (?)..," As a result, the planet fills about half of its Roche lobe \citep{Li2010}."544 With such a short. orbital distance. and large size. a gas giant planet is expected to undergo complete orbital svnchronisation and. circularisation on a short timescale. much. shorter than the age of a typical field main-sequence cool star.," With such a short orbital distance and large size, a gas giant planet is expected to undergo complete orbital synchronisation and circularisation on a short timescale, much shorter than the age of a typical field main-sequence cool star."545 Indeed. most planets. orbiting closer than 0.05 AU are observed to have circular orbits.," Indeed, most planets orbiting closer than 0.05 AU are observed to have circular orbits."546 Llowever. LOO determined. a value of ο=0.049+0.015 for the orbital eccentricity of WASP-12. a significant departure from circularity.," However, H09 determined a value of $e=0.049 \pm 0.015$ for the orbital eccentricity of WASP-12, a significant departure from circularity."547 “Phis would make the planet bv [ar the subject of the strongest. tical dissipation in any known planetary system., This would make the planet by far the subject of the strongest tidal dissipation in any known planetary system.548 The measured. eccentricity is based. on fitting a Ixeplerian orbital motion on the radial velocity measurements collected by 1009 with the SOPLILE spectrometer (7). together with transit photometry., The measured eccentricity is based on fitting a Keplerian orbital motion on the radial velocity measurements collected by H09 with the SOPHIE spectrometer \citep{Perruchot2008} together with transit photometry.549 7.— stuclied the case of WASDP-12 with that value of eccentricitv. ancl found. a large implied. mass loss and dissipation of tidal energy in the planet.," \cite{Li2010} studied the case of WASP-12 with that value of eccentricity, and found a large implied mass loss and dissipation of tidal energy in the planet."550 In a transiting svstem. the time lag between the ransit and the occultation has a strong dependence. on he projected orbital eccentricity (6cosz).," In a transiting system, the time lag between the transit and the occultation has a strong dependence on the projected orbital eccentricity $e \cos \omega$ )."551 Therefore. if the occultation can be detected with sullicient significance. this oovides a stringent test of the eccentricitv.," Therefore, if the occultation can be detected with sufficient significance, this provides a stringent test of the eccentricity."552 2.hereafterLOO have measured the occultation of WASP-12b from he ground with SPICam on the ARC telescope at Apache Point Observatory in the z/ band., \citet[hereafter L09]{Morales2009} have measured the occultation of WASP-12b from the ground with SPICam on the ARC telescope at Apache Point Observatory in the $z'$ band.553 Their best-fit. resul indicated a occultation with a significant time lag compare o the epoch expected. for a circular orbit. with a similar evel of significance to 1109.," Their best-fit result indicated a occultation with a significant time lag compared to the epoch expected for a circular orbit, with a similar level of significance to H09."554 Nevertheless. the presence of residual correlated: noise is apparent in the LOO data. (see Fie. 2)).," Nevertheless, the presence of residual correlated noise is apparent in the L09 data (see Fig. \ref{morales-transit}) ),"555 as expected. for grounc-basecl photometry at such a high accuracy - the depth of the occultation is only abou 0.08.02%., as expected for ground-based photometry at such a high accuracy - the depth of the occultation is only about $\pm$ 0.02.556. As a result. the issue remained inconclusive unti a space-based measurement of the occultation with the Spitzer Space Telescope (?.hereafterC10). unambiguously showed that the timing of the occultation was precisely tha expected for a circular orbit.," As a result, the issue remained inconclusive until a space-based measurement of the occultation with the Spitzer Space Telescope \citep[hereafter C10]{Campo2010} unambiguously showed that the timing of the occultation was precisely that expected for a circular orbit."557 Εις result suggested that the LOO time lag was probably due to instrumental svstematics. and that the orbit of WASP-12 was probably circular. since a fine-tuned alignment would be required to reconcile the Spitzer result with the LO09 value of the eccentricity.," This result suggested that the L09 time lag was probably due to instrumental systematics, and that the orbit of WASP-12 was probably circular, since a fine-tuned alignment would be required to reconcile the Spitzer result with the H09 value of the eccentricity."558 lt is interesting to note that there is an inherent uas in eccentricity measurements. from. radial. velocities. »ecause a [xeplerian orbit cannot get more circular than c—0.," It is interesting to note that there is an inherent bias in eccentricity measurements from radial velocities, because a Keplerian orbit cannot get more circular than $e=0$."559 Any noise applied to a circular orbit. will result. in an eccentric best-fit. orbit., Any noise applied to a circular orbit will result in an eccentric best-fit orbit.560 Uncderestimating the noise will ead to spurious detections of small eccentricities., Underestimating the noise will lead to spurious detections of small eccentricities.561 This was already. recognized in the context of stellar binaries by 2.., This was already recognized in the context of stellar binaries by \cite{Lucy1971}.562 These authors showed that spurious eccentricity. detections ended: to dominate for ο<0.1 for a typical precision at hat time and stellar binary amplitudes., These authors showed that spurious eccentricity detections tended to dominate for $e< 0.1$ for a typical precision at that time and stellar binary amplitudes.563 Four decades later. roth companion masses and RV accuracies having changed ov about three orders of magnitudes. and the same issue resurfaces for exoplanets.," Four decades later, both companion masses and RV accuracies having changed by about three orders of magnitudes, and the same issue resurfaces for exoplanets."564 WASP-14 is. after WASP-12. the known transiting λαοί having a reported. non-circular orbit with the scconc-shortest period (P=2.2 days).," WASP-14 is, after WASP-12, the known transiting planet having a reported non-circular orbit with the second-shortest period (P=2.2 days)."565 This makes it another test-case for tidal evolution of close-in gas elants., This makes it another test-case for tidal evolution of close-in gas giants.566 I£ dts orbital eccentricitv is indeed near 0.1. then his non-zero but. relatively low value — in the context. of he distribution of giant exoplanet eccentricities — makes it likely that this planet has undergone some degree. of orbital evolution. ancl is still subject to strong tidal forces a esent.," If its orbital eccentricity is indeed near 0.1, then this non-zero but relatively low value – in the context of the distribution of giant exoplanet eccentricities – makes it likely that this planet has undergone some degree of orbital evolution, and is still subject to strong tidal forces at present."567 “Therefore its presence may be useful to constrain he tidal svnchronisation timescale., Therefore its presence may be useful to constrain the tidal synchronisation timescale.568" Lt is also an importan object when studying the issue of the anomalous radius of 100 Jupiters because of its inflated size. with A,=1.28tj."," It is also an important object when studying the issue of the anomalous radius of hot Jupiters because of its inflated size, with $R_p=1.28 {\rm \, R_J}$."569 WASP-14 occupies a distinctive. position in the relevan »wanmeter space: irradiation. orbital distance. eccentricity ancl size.," WASP-14 occupies a distinctive position in the relevant parameter space: irradiation, orbital distance, eccentricity and size."570 We obtained 29 racial-velocitv. measurements for WASD-12 (16 during a single night. and. 13 at various values of orbital phase) ancl 11 for WASP-14. using the SOPLILE spectrograph installed on the 1.93-m telescope at OLLP (France).," We obtained 29 radial-velocity measurements for WASP-12 (16 during a single night, and 13 at various values of orbital phase) and 11 for WASP-14, using the SOPHIE spectrograph installed on the 1.93-m telescope at OHP (France)."571 The observations were gathered between 17 January 2009 and 27 March. 9010., The observations were gathered between 17 January 2009 and 27 March 2010.572 The 16. in-transit measurements for WASDP-12 were obtained with the objective of constraining the spin-orbit angle via the ltossiter-MeLaughlin elfect., The 16 in-transit measurements for WASP-12 were obtained with the objective of constraining the spin-orbit angle via the Rossiter-McLaughlin effect.573 SOPLILZ is a spectrograph optimized. for precise radial-velocity measurements and. has. participated. in the detection of numerous transiting exoplanets in the northern hemisphere. notably from the WASP and ColtoT. transit searches.," SOPHIE is a spectrograph optimized for precise radial-velocity measurements and has participated in the detection of numerous transiting exoplanets in the northern hemisphere, notably from the WASP and CoRoT transit searches."574 It reaches a stability of a few flor bright targets., It reaches a stability of a few for bright targets.575 WASP-12 and WASP-14. however. are near the faint end of the capacity of the 1.932m telescope. and were measured in the -clHligh LElliciencv mode of SOPLILE (See77)..," WASP-12 and WASP-14, however, are near the faint end of the capacity of the 1.93-m telescope, and were measured in the “High Efficiency” mode of SOPHIE \citep[See][]{Perruchot2008,Bouchy2009}."576" Ες mode has a higher throughput han the standard mode. the ""High Resolution” mode. thus allowing fainter targets to be measured. but is less optimized or racial velocity."," This mode has a higher throughput than the standard mode, the “High Resolution” mode, thus allowing fainter targets to be measured, but is less optimized for radial velocity."577 When considering the ensemble of data or known transiting planets obtained with SOPLILE. we aave found evidence for large excursions of the velocity point with time (to the level of several dozen lin some cases).," When considering the ensemble of data for known transiting planets obtained with SOPHIE, we have found evidence for large excursions of the velocity zero-point with time (to the level of several dozen in some cases)."578 As part of the constant. improvement of he SOPLILE reduction pipeline. this cllect is monitored. and corrected for as far as possible. but the presence of relatively arge instrumental svstematics in the High Elliciencey data is a possibility. especially with older data collected before we »ecamie aware of the issue.," As part of the constant improvement of the SOPHIE reduction pipeline, this effect is monitored and corrected for as far as possible, but the presence of relatively large instrumental systematics in the High Efficiency data is a possibility, especially with older data collected before we became aware of the issue."579 This must be remembered when »erforming an orbital analysis based on data from the Ligh Efficicney ποσο., This must be remembered when performing an orbital analysis based on data from the High Efficiency mode.580 The orbital parameters of the two transiting planets were calculated from. the racial velocity data. (together. with published. photometry data for the transit and occultation in the case of WASP-12). with a Marko. Chain Monte Carlo (AICAIC) method.," The orbital parameters of the two transiting planets were calculated from the radial velocity data, (together with published photometry data for the transit and occultation in the case of WASP-12), with a Marko Chain Monte Carlo (MCMC) method."581 Phe main advantage of the AICAIC method is that it allows a seamless combination of racial- data with light-curve data both for the transit and occultation. as well as information on the parent star.," The main advantage of the MCMC method is that it allows a seamless combination of radial-velocity data with light-curve data both for the transit and occultation, as well as information on the parent star."582 The, The583result in the lower spatial resolution study by Caselliοἱal.(2002¢).. where cores wilh stars show steep integrated intensity distribution.,"result in the lower spatial resolution study by \citet{cac02}, where cores with stars show steep integrated intensity distribution."584 There is a possibility that the shallow density prolile in cores with stars can be results of the core collapse (Foster&Chevalier1993) and/or core dispersal due to the molecular outflow., There is a possibility that the shallow density profile in cores with stars can be results of the core collapse \citep{fos93} and/or core dispersal due to the molecular outflow.585 The present observations are probably nol enough for disentangling these possibilities. and further observations (high-resolution dust continuum map. near-intrarecl color-excess map. higher resolution Noll imaging. etc) are clesirable.," The present observations are probably not enough for disentangling these possibilities, and further observations (high-resolution dust continuum map, near-infrared color-excess map, higher resolution $_2$ $^+$ imaging, etc) are desirable."586 On the basis of Noll observations toward Taurus. we have studied (he physical properties ol the molecular cloucl core.," On the basis of $_2$ $^+$ observations toward Taurus, we have studied the physical properties of the molecular cloud core."587 The core radius. linewidth. and intensity distribution do not much differ between starless cores and cores with stars.," The core radius, linewidth, and intensity distribution do not much differ between starless cores and cores with stars."588 This result is in contrast with that previously obtained in 0Ο ., This result is in contrast with that previously obtained in $^{13}$ $^+$.589 We suggest that depletion of LLCO causes this difference., We suggest that depletion of $^{13}$ $^+$ causes this difference.590 From the critical pressure analvsis for Taurus cores. there is no svstematic difference between starless cores and cores wilh stars.," From the critical pressure analysis for Taurus cores, there is no systematic difference between starless cores and cores with stars."591 Both are not far from the critical state for equilibrium., Both are not far from the critical state for equilibrium.592 We suggest (hat the starless cores which are almost. thermally. supported. evolve toward star formation bv keeping close to the critical state., We suggest that the starless cores which are almost thermally supported evolve toward star formation by keeping close to the critical state.593 This result is in contrast. wilh that obtained in the intermediate-mass star forming region OMC-2/3. where (he molecular cloud core evolves by dissipating turbulence lurgelv.," This result is in contrast with that obtained in the intermediate-mass star forming region OMC-2/3, where the molecular cloud core evolves by dissipating turbulence largely."594 The density profile is investigated Ilrom the integrated intensity distribution in the cores., The density profile is investigated from the integrated intensity distribution in the cores.595 Cores wilh stus show shallow density profiles. rI.N lo rL lx.," Cores with stars show shallow density profiles, $r^{-1.8}$ to $r^{-1.6}$."596 T. is grateful to Takenori Nakano for comments on the draft and (ο Jeong-Eun Lee for discussion., K. T. is grateful to Takenori Nakano for comments on the draft and to Jeong-Eun Lee for discussion.597we chose spherical regions.,we chose spherical regions.598" We used three levels of zoom, and ended with a spherical region of radius R4=8.56 Mpc, a mass resolution of m3,=3.01x107Mo,, mapw=1.42x105Mo,, and a force resolution &=6.25 kpc (comoving)."," We used three levels of zoom, and ended with a spherical region of radius $R_3 = 8.56$ Mpc, a mass resolution of $m_{3,\text{b}} = 3.01 \times59910^7 $, $m_{3,\text{DM}} = 1.42\times 10^8 $, and a force resolution $\eps = 6.25$ kpc (comoving)."600" These 1287/2 particles of mass mopw and moy at the level 0 give the same mass resolution as a simulation of 128?x10243/2 particles of mass m3pm51.42x105 and mx~3.01x107 Me,, but focused on a smaller volume of radius 8.56 Mpc at level 3."," These $128^3/2$ particles of mass $m_{0\text{DM}}$ and $m_{0\text b}$ at the level 0 give the same mass resolution as a simulation of $128^3\times 6018^3/2 = 1024^3/2$ particles of mass $m_{3\text{DM}} \simeq 1.42\times60210^{8}$ and $m_{3\text b} 603\simeq 3.01\times 10^{7}$ , but focused on a smaller volume of radius 8.56 Mpc at level 3."604" This technique enable us to simulate galaxies with a fairly high resolution starting with a reasonably sized cosmological box, at a smaller CPU cost."," This technique enable us to simulate galaxies with a fairly high resolution starting with a reasonably sized cosmological box, at a smaller CPU cost."605" One of the main characteristics of this technique is that, except at the zeroth level of zoom, the number of particles does not remain constant during the whole simulation."," One of the main characteristics of this technique is that, except at the zeroth level of zoom, the number of particles does not remain constant during the whole simulation."606" At higher levels of zoom, a particle at timestep i inside the level N box, but outside the level N+1 box, can indeed enter the level N+1 box at timestep i+1 and be split into eight high-resolution particles."," At higher levels of zoom, a particle at timestep $i$ inside the level $N$ box, but outside the level $N+1$ box, can indeed enter the level $N+1$ box at timestep $i+1$ and be split into eight high-resolution particles."607" Particles with unrecorded history the enter the box, and a special care must be taken when establishing particle identities."," Particles with unrecorded history the enter the box, and a special care must be taken when establishing particle identities."608" Because of this increasing number of particles, the third level of simulations could not be run further than 9.1 Gyr, or z=0.46, but lower levels of zoom reached z=0."," Because of this increasing number of particles, the third level of simulations could not be run further than $t=9.1$ Gyr, or $z =6090.46$, but lower levels of zoom reached $z= 0$."610" At the third level of zoom, we end up with 90 snapshots, sampled every 100 Myr from t=0.2 Gyr to t=9.1 Gyr, which enables us to build the merger tree of structures, while at the three lower levels of zoom we have 70 snapshots, sampled every 200 Myr from t=0.2 Gyr to t=14 Gyr."," At the third level of zoom, we end up with 90 snapshots, sampled every 100 Myr from $t=0.2$ Gyr to $t=9.1$ Gyr, which enables us to build the merger tree of structures, while at the three lower levels of zoom we have 70 snapshots, sampled every 200 Myr from $t=0.2$ Gyr to $t = 14$ Gyr."611 The latter can be used for a resolution study (see section 7.1))., The latter can be used for a resolution study (see section \ref{sect:resol}) ).612 The properties of each level of zoom are summed up in table 1.., The properties of each level of zoom are summed up in table \ref{tab:sim_zoom}.613" While collisionless particles, namely stars and dark matter, undergo only gravitational forces and are treated by a tree algorithm, gas dynamics is treated by smooth particle hydrodynamics (SPH)."," While collisionless particles, namely stars and dark matter, undergo only gravitational forces and are treated by a tree algorithm, gas dynamics is treated by smooth particle hydrodynamics (SPH)."614 Additional recipes are needed to mimic subgrid physics such as star formation and feedback., Additional recipes are needed to mimic subgrid physics such as star formation and feedback.615" Our physical treatment is described in ?,, The SPH gas is treated with the same equation of state and the same viscosity prescription."," Our physical treatment is described in \citet{2002A&A...388..826S}, The SPH gas is treated with the same equation of state and the same viscosity prescription."616" The range of temperatures is 800—2x10 K. Any dependance of cooling on metallicity is ignored, and only a primordial metallicity (10? Zo) is considered."," The range of temperatures is $800-2\times 10^6$ K. Any dependance of cooling on metallicity is ignored, and only a primordial metallicity $10^{-3}$ $_\odot$ ) is considered."617" A unique timestep per zoom level is adopted, which is respectively 20, 10, 5, and 2.5 Myr for levels 0 to 3."," A unique timestep per zoom level is adopted, which is respectively 20, 10, 5, and 2.5 Myr for levels 0 to 3."618" The softening length for gravity is respectively 50, 25, 12.5, and 6.25 kpc (comoving), and we checked that the SPH smoothing length is not far shorter than the softening length, as shown on the histogram of Fig."," The softening length for gravity is respectively 50, 25, 12.5, and 6.25 kpc (comoving), and we checked that the SPH smoothing length is not far shorter than the softening length, as shown on the histogram of Fig."619 | at t=9 Gyr in the level 3 zoom., \ref{fig:hist_h} at $t = 9$ Gyr in the level 3 zoom.620 The radiative cooling term A is taken from the normalised tables of ? modelling atomic absorption-line cooling from 10 K to 108° K. The background ultraviolet (UV) radiation field is modelled by a constant uniform heating [yy=10724 erg s! term., The radiative cooling term $\Lambda$ is taken from the normalised tables of \citet{1993ApJS...88..253S} modelling atomic absorption-line cooling from $10^4$ K to $10^{8.5}$ K. The background ultraviolet (UV) radiation field is modelled by a constant uniform heating $\Gamma_\text{UV} = 10^{-24}$ erg $^{-1}$ term.621 Star formation is modelled by a Schmidt law with a star formation rate of with n=1., Star formation is modelled by a Schmidt law with a star formation rate of with $n = 1$.622" It is applied to gas particles with densities higher than a density threshold of Gas particles form stars, and have a fraction of stars within them."," It is applied to gas particles with densities higher than a density threshold of Gas particles form stars, and have a fraction of stars within them."623" When this fraction reaches a given threshold (set to 20%)), we search among their neighbours to determine whether there is enough material to form a full star particle, whether the sum of the star fractions among the neighbouring gas"," When this fraction reaches a given threshold (set to ), we search among their neighbours to determine whether there is enough material to form a full star particle, whether the sum of the star fractions among the neighbouring gas"624The PDFs of pure & field. pure noise and & field added by noise are 2?(rr). P(&) and D?(5) respectivelv.,"The PDFs of pure $\kappa$ field, pure noise and $\kappa$ field added by noise are $P^S(\kappa)$, $P^N(\kappa)$ and $P^{S+N}(\kappa)$ respectively."625 The number of maps is V=40. ie. n=1.2..N.," The number of maps is $N=40$, i.e. $n=1,2,\cdots N$."626 Normally. PDFs are normalized to be unit. te. f.{σεραν=1.," Normally, PDFs are normalized to be unit, i.e. $\int^{+\infty}_{-\infty}P(\kappa)d\kappa=1$."627 From here on we ouly consider binned PDFs. choosing AL equally spaced. bins separated by An.," From here on we only consider binned PDFs, choosing $M$ equally spaced bins separated by $\Delta\kappa$."628 Our notation becomes s;=#+LN. mPens. and each PDF ean also carry an appropriate superscript.," Our notation becomes $\kappa_i =\kappa_-+i629\Delta\kappa$, $P_i \equiv P(\kappa_i) \Delta \kappa$, and each PDF can also carry an appropriate superscript."630 The nunber of bins for all PDFs is M= 19. ke. jj=1.2.M.," The number of bins for all PDFs is $M=19$ , i.e. $i,j=1,2, \cdots M$."631 In the form of matrix. C is the signal covariance and C* is a noise covariance.," In the form of matrix, $\mathbf{C}^S$ is the signal covariance and $\mathbf{C}^N$ is a noise covariance."632 The signal covariance is expressed as <> is the average over 40 maps. and I? (&)is the average value of the & field PDF for 40 maps.," The signal covariance is expressed as where $<>$ is the average over 40 maps, and $\bar{P}^S(\kappa)$ is the average value of the $\kappa$ field PDF for 40 maps."633 The noise PDF. which will also serve as (he noise convolution kernel q(&—s). is à Gaussian distribution where o« is the standard deviation of the noise after the wiener filter.," The noise PDF, which will also serve as the noise convolution kernel $g^N(\kappa-\kappa')$, is a Gaussian distribution where $\sigma_N$ is the standard deviation of the noise after the wiener filter."634 We can also think of this kernel as a noise matrix IN For a noisy # field. (he noise deviation of the PDF relative to an invertible convolution can be written as for each map where P (5;)is the PDF of & field with added noise.," We can also think of this kernel as a noise matrix $\mathbf{N}$ For a noisy $\kappa$ field, the noise deviation of the PDF relative to an invertible convolution can be written as for each map where $P^{S+N}(\kappa_i)$ is the PDF of $\kappa$ field with added noise."635 Thus we have thenoise covallance matrix Using the convolution theorem. we have," Thus we have thenoise covariance matrix Using the convolution theorem, we have"636A preliminary look at the distribution of dwarf nova white dwarf temperatures above the period gap. suggests that for orbital periods. P4. between 200 minutes and minutes and ου320 minutes. there may be a clustering of WD temperatures around 30.000Ix. These include U Gem. SS Aur. WW Ceti. BD Pav. RX And. UU Aq! and TU Men.,"A preliminary look at the distribution of dwarf nova white dwarf temperatures above the period gap, suggests that for orbital periods, $_{orb}$, between $\sim 200$ minutes and minutes and $\sim 320$ minutes, there may be a clustering of WD temperatures around 30,000K. These include U Gem, SS Aur, WW Ceti, BD Pav, RX And, UU Aql and TU Men."637 The WD in the long period SU UMa system TU Men has a temperature at the hot extreme of the WDs in the SU UMa systems below the period gap., The WD in the long period SU UMa system TU Men has a temperature at the hot extreme of the WDs in the SU UMa systems below the period gap.638" Above 380 minutes. there appears to be a considerable spread in the WD T,;; with all having T,jj; = 40.000Ix. or greater. typically hotter than the group between 200 minutes and 320 minutes."," Above 380 minutes, there appears to be a considerable spread in the WD $_{eff}$ with all having $_{eff}$ = 40,000K or greater, typically hotter than the group between 200 minutes and 320 minutes."639 This hotter group includes 55 (νο Z Cam. RU Peg. DV Cen and V442 Cen.," This hotter group includes SS Cyg, Z Cam, RU Peg, BV Cen and V442 Cen."640 Possible evidence of a classical nova shell has been advanced [or Z Cam by Shara et al. (, Possible evidence of a classical nova shell has been advanced for Z Cam by Shara et al. (6412007). who constrain the nova outburst to have occurred between 240 and 2400 vears ago.,"2007), who constrain the nova outburst to have occurred between 240 and 2400 years ago."642 If we take our derived temperatures at [ace value aud are mindful of the small nunber of svstems analvzed above the gap. then it is difllicult to convincinglv argue anv plwsical significance to the two groupings.," If we take our derived temperatures at face value and are mindful of the small number of systems analyzed above the gap, then it is difficult to convincingly argue any physical significance to the two groupings."643 However. it is tempting to speculate on several possibilities.," However, it is tempting to speculate on several possibilities."644" If CVs begin their lives at long periods and evolve to shorter periods as expected. then the larger spread of Tip, at the longer periods is possibly manifesting the fact that their long term core-envelope thermal coupling in response lo compressional heating by (üme-averaged accretion ((Sion1995:Towuslev&Bildsten 2003))) has not vel achieved equilibrium."," If CVs begin their lives at long periods and evolve to shorter periods as expected, then the larger spread of $T_{eff}$ at the longer periods is possibly manifesting the fact that their long term core-envelope thermal coupling in response to compressional heating by time-averaged accretion \citep{sio95a, tow03}) ) has not yet achieved equilibrium."645" The ereater spread with £7, mav also be due (ο WDs in CVs having a wider range of core temperatures al (he onset of CV evolution.", The greater spread with $P_{orb}$ may also be due to WDs in CVs having a wider range of core temperatures at the onset of CV evolution.646 That is. it may be possible that some clwarl novae began their mass (ransler while still quite hot.," That is, it may be possible that some dwarf novae began their mass transfer while still quite hot."647 Thev might have become CVs before their cores had cooled to 10*IK. On the other hand. their WDs may be less massive and hence cooler after (he same degree of long term accretion.," They might have become CVs before their cores had cooled to $10^{7}$ K. On the other hand, their WDs may be less massive and hence cooler after the same degree of long term accretion."648 It is also possible that svstems al very long periods wilh evolved secondaries have a different evolutionary history Caan shorter period dwarf novae., It is also possible that systems at very long periods with evolved secondaries have a different evolutionary history than shorter period dwarf novae.649 It is also not unexpected that the long term. time-averaged accretion rales are variable.," It is also not unexpected that the long term, time-averaged accretion rates are variable."650 There may be one important difference apparent between the ditributions of CY WD temperatures above the period gap versus below the period gap., There may be one important difference apparent between the ditributions of CV WD temperatures above the period gap versus below the period gap.651 Namely. the dispersion in CV WD temperatures above (he period eap appear to be substantially greater (han one fines below the period gap where there is a surprisingly narrow dispersion in teniperatures around. 15.000Ix. In order to better illustrate this difference. we have plotted in figure 6 the temperatures of the white dwarls in non-magnetic CVs during nova-like low states and clwarl novae quiescences (filled triangles) and magnetic CVs during polar low states (filled circles).," Namely, the dispersion in CV WD temperatures above the period gap appear to be substantially greater than one finds below the period gap where there is a surprisingly narrow dispersion in temperatures around 15,000K. In order to better illustrate this difference, we have plotted in figure 6 the temperatures of the white dwarfs in non-magnetic CVs during nova-like low states and dwarf novae quiescences (filled triangles) and magnetic CVs during polar low states (filled circles)."652 All of the temperatures except for seven non-magnetic CVs above the period gap are taken from the compilation in Table 7 of Aranjo-Betancor et al. (, All of the temperatures except for seven non-magnetic CVs above the period gap are taken from the compilation in Table 7 of Araujo-Betancor et al. (6532005).,2005).654 The three objects close to the 3 hour upper boundary of the period gap with WD temperatures above 40.000IN. are all VY Sculptoris nova-like variables. TT Ari. MV Lyra and DW UMa.," The three objects close to the 3 hour upper boundary of the period gap with WD temperatures above 40,000K are all VY Sculptoris nova-like variables, TT Ari, MV Lyra and DW UMa."655 While the difference, While the difference656simulations are usually performed with rigid boundary conditions.,simulations are usually performed with rigid boundary conditions.657 On the one hand flows implement rigid boundary conditions., On the one hand Couette-Taylor flows implement rigid boundary conditions.658 Although in real experiments. the vibrations of the boundary play some role in triggering (urbulent motions. there is little doubt that in (hese experiments. turbulence is sell-sustained.," Although in real experiments, the vibrations of the boundary play some role in triggering turbulent motions, there is little doubt that in these experiments, turbulence is self-sustained."659 On (he other haad. from the experiments ol DBidokhtiandTritton(1992) the rotating shear flows with [ree boundary. conditions are turbulent. although by construction no mean steady state can be reached in these svstems.," On the other hand, from the experiments of \citet{Bid92} the rotating shear flows with free boundary conditions are turbulent, although by construction no mean steady state can be reached in these systems."660 Therefore. it seems unlikely that boundary conditions play an important role in (he presence or absence of turbulence in numerical experiments.," Therefore, it seems unlikely that boundary conditions play an important role in the presence or absence of turbulence in numerical experiments."661 In the shearing sheet approximation. the mean shear is imposed by the tidal force term: in rotating Couette simulations. it results from the boundary conditions.," In the shearing sheet approximation, the mean shear is imposed by the tidal force term; in rotating Couette simulations, it results from the boundary conditions."662" In Couette-Tavlor flows. the boundary conditions do not only produce the shear. but also generate a mean radial pressure gradient,"," In Couette-Taylor flows, the boundary conditions do not only produce the shear, but also generate a mean radial pressure gradient."663 Note however that the term —d(DP)/dr/(p)+r(Q)? of Eq. (8))," Note however that the term $-d\langle P \rangle/dr/\langle\rho\rangle664+r\langle\Omega\rangle^2$ of Eq. \ref{NSCT}) )"665 is similar in function to the term 2gQ7r in Eq. (10))., is similar in function to the term $2q\Omega^2 x$ in Eq. \ref{NSSS}) ).666 Furthermore. the mean pressure gradient in Couette-Tavlor experiments is radial. whereas it is longitudinal (streamwise) in the rotating free shear laver experiments of BidokhtianclTritton(1992)..," Furthermore, the mean pressure gradient in Couette-Taylor experiments is radial, whereas it is longitudinal (streamwise) in the rotating free shear layer experiments of \citet{Bid92}."667 This suggests that neither large scale mean pressure gradients. nor tidal terms. make any significant difference on the «question of the onset of turbulence in the various [lows considered here. especially (hat. all eradient terms get out of the way in incompressible flows (they disappear Irom the vorticity equation).," This suggests that neither large scale mean pressure gradients, nor tidal terms, make any significant difference on the question of the onset of turbulence in the various flows considered here, especially that all gradient terms get out of the way in incompressible flows (they disappear from the vorticity equation)."668 Finally. D will show in the next section that the main ellect of the geometry. (which enters through the geometric terms in Couette-Tavlor flows) is to change the conditions of onset of turbulence. but this does not affect the occurrence of turbulence in itself.," Finally, I will show in the next section that the main effect of the geometry (which enters through the geometric terms in Couette-Taylor flows) is to change the conditions of onset of turbulence, but this does not affect the occurrence of turbulence in itself."669 Although such arguments do not exclude more complex possibilities (as. e.g.. that turbulence might be impedecd in shearing sheet [lows by a combination of these [actors instead ol only one of them). this strongly indicates that rotating Couette flows and shearing sheet ones should be turbulent. suggesting that the absence of turbulence in all the published simulations of this kind stems from limitations in (he munerics involved.," Although such arguments do not exclude more complex possibilities (as, e.g., that turbulence might be impeded in shearing sheet flows by a combination of these factors instead of only one of them), this strongly indicates that rotating Couette flows and shearing sheet ones should be turbulent, suggesting that the absence of turbulence in all the published simulations of this kind stems from limitations in the numerics involved."670 This last. point is addressed in the next section., This last point is addressed in the next section.671 The purpose of this section is to point out important features of turbulence in sheared flows. through a phenomenological model developed in section ??..," The purpose of this section is to point out important features of turbulence in sheared flows, through a phenomenological model developed in section \ref{turbord}."672 The consequences of (his model are used in section ?? to identify the potential limitations in the numerics just, The consequences of this model are used in section \ref{cor} to identify the potential limitations in the numerics just673A decade of extrasolar planet discoveries has shown that the process of planet formation is more complex than originally anticipated.,A decade of extrasolar planet discoveries has shown that the process of planet formation is more complex than originally anticipated.674 It leads to a remarkable diversity of planetary configurations. ranging from mierating hot Jupiters to eccentric giant planets. as well as our own “circular” Solar," It leads to a remarkable diversity of planetary configurations, ranging from migrating hot Jupiters to eccentric giant planets, as well as our own “circular” Solar"675followed up in photometry mode 5 sources detected in a shallow 850jm map of the Groth Strip. in an attempt to quantify the amount of Lux boosting present in the map.,"followed up in photometry mode 5 sources detected in a shallow $850\,\mathrm{\mu m}$ map of the Groth Strip, in an attempt to quantify the amount of flux boosting present in the map."676 To interpret the results we have developed a general method to assess the reliability of low SNR. sources., To interpret the results we have developed a general method to assess the reliability of low SNR sources.677 We apply these techniques to a particular SCUBA survey in the “Groth Strip., We apply these techniques to a particular SCUBA survey in the `Groth Strip'.678 The “Groth Strip Survey’ (GSS) is aTelescope (LIST) programme (ΤΟ 5090. PI: Groth) consisting of 28 overlappingLST Wide Field. Planetary. Camera 2 (WEDPC2) medium-deep images. covering an area of 1132aremin?. forming a long strip centred on16388... (12000). at a Galactic latitude of b=607.," The `Groth Strip Survey' (GSS) is a ) programme (GTO 5090, PI: Groth) consisting of 28 overlapping Wide Field Planetary Camera 2 (WFPC2) medium-deep images, covering an area of $113\,\mathrm{arcmin^{2}}$, forming a long strip centred on, (J2000), at a Galactic latitude of $b\simeq60^{\circ}$."679 The GSS was the deepestUST cosmological integration before the LDF. reaching a imiting Vega magnitude of ~27.5 28 in both the and bands (Grothetal.1994).," The GSS was the deepest cosmological integration before the HDF, reaching a limiting Vega magnitude of $\sim27.5$ –28 in both the and bands \citep{Groth}."680. The GSS has an enormous egacy value. since extensive multi-wavelength observations centred. on this region. have been conducted or are xanned.," The GSS has an enormous legacy value, since extensive multi-wavelength observations centred on this region have been conducted or are planned."681. Morphological ancl photometric information from. he WEPC2 images are provided. by the Medium: Deep Survey (AIDS) database (Ratnatunga.Criliths&Ostran-der1999). and the Deep Extragalactic Evolutionary Probe (DEEP) survey (Simardctal.2002)., Morphological and photometric information from the WFPC2 images are provided by the Medium Deep Survey (MDS) database \citep{Ratnatunga} and the Deep Extragalactic Evolutionary Probe ) survey \citep{Simard}.682. X-ray sources have also been identified in an SOksNALALNewtou observation of the GSS (Mivajictal.2004)...," X-ray sources have also been identified in an $80\,\mathrm{ks}$ observation of the GSS \citep{Miyaji}."683 The GSS is currently. part of the on-going survey anc is also targetted to be a major component of upcoming large surveys in the UV (using the Galaxy Evolution Explorer. GALEN?)). in the optical (as part of the Canaca-brance-Llawaii ‘Telescope Legacy Survey. CELETLS1). and in the LR (the Spitzer GLO IRAC Deep Survey).," The GSS is currently part of the on-going survey and is also targetted to be a major component of upcoming large surveys in the UV (using the Galaxy Evolution Explorer, ), in the optical (as part of the Canada-France-Hawaii Telescope Legacy Survey, ), and in the IR (the GTO IRAC Deep Survey)."684 In this paper. we present 850sam SCUBA observations of about 60 per cent of the original ΝΕΡΟ coverage of the GSS.," In this paper, we present $850\,\mathrm{\mu m}$ SCUBA observations of about 60 per cent of the original WFPC2 coverage of the GSS."685 We have also performed confirmation photometry on some of the sources., We have also performed confirmation photometry on some of the sources.686 Our goal is to make the S501 map ancl source list available to the community so that it may be correlated against existing and future data sets at other wavelengths.," Our goal is to make the $850\,\mathrm{\mu m}$ map and source list available to the community so that it may be correlated against existing and future data sets at other wavelengths."687 No claim is mace that this survey is cither the deepest or the most extensive performed. using SCUBA., No claim is made that this survey is either the deepest or the most extensive performed using SCUBA.688 Llowever. the observations cover enough integration time that we expect a handful of real sources to be detected. and our survey represents the best submillimetre data likely to be available in this field until the advent of SCUBA-2.," However, the observations cover enough integration time that we expect a handful of real sources to be detected, and our survey represents the best submillimetre data likely to be available in this field until the advent of SCUBA-2."689 A roughly TOzarcmin? portion of the Groth Strip (GSS) was observed. with a resolution of 14.7 arcsec and 7.5 aresec at S50 and 4504n. respectively. with the 152m. JCAL atop Alauna Wea in Hawaii in January 1999 ancl January 2000.," A roughly $70\,\mathrm{arcmin}^{2}$ portion of the Groth Strip (GSS) was observed with a resolution of 14.7 arcsec and 7.5 arcsec at 850 and $450\,\mathrm{\mu m}$, respectively, with the 15-m JCMT atop Mauna Kea in Hawaii in January 1999 and January 2000."690" The GSS SCUBA map is centred on RA=1216400"". Dee=52""L000"" (J2000)."," The GSS SCUBA map is centred on $\,{=}\,14^{\mathrm{h}}16^{\mathrm{m}}00^{\mathrm{s}}$, $\,{=}\,52^{\circ}10^\prime00^{\prime\prime}$ (J2000)."691 52 overlapping 64-point jiggle maps of the GSS were obtained. providing measurements of the continuum at both wavelengths simultaneously. with SCUBA (Holland.1999).. which has a field of view of 2.3 aremin.," 52 overlapping 64-point jiggle maps of the GSS were obtained, providing measurements of the continuum at both wavelengths simultaneously with SCUBA \citep{Holland}, which has a field of view of 2.3 arcmin."692 The atmospheric zenith opacity. at 225Cllz was monitored with the Caltech Submillimetre Observatory (CSO) tau (toso) monitor.," The atmospheric zenith opacity at $225\,\mathrm{GHz}$ was monitored with the Caltech Submillimetre Observatory (CSO) tau $\tau_{\mathrm{CSO}}$ ) monitor."693 The roso ranged from 0.08 to 0.09 in January 1999 and from 0.05 to 0.08 in January 2000., The $\tau_{\mathrm{CSO}}$ ranged from 0.03 to 0.09 in January 1999 and from 0.05 to 0.08 in January 2000.694 The weather was generally more stable for the latter set of data., The weather was generally more stable for the latter set of data.695 The secondary mirror was chopped. at ai stanclarc frequeney of 2SHz in azimuth to reduce the effect of rapic sky variations.," The secondary mirror was chopped at a standard frequency of $\simeq6968\,\mathrm{Hz}$ in azimuth to reduce the effect of rapid sky variations."697 Phe telescope was also ‘nodded’ on ancl off the source., The telescope was also `nodded' on and off the source.698 A 40 aresee chopthrow was used at à position angle of 54. almost parallel to the lengthwise orientation of the strip.," A 40 arcsec chop–throw was used at a position angle of $54^{\circ}$, almost parallel to the lengthwise orientation of the strip."699 Pointing checks were performed hourly on blazars ancl planets and varied by less than 3 aresec in azimuth anc by less than 2 aresec in elevation., Pointing checks were performed hourly on blazars and planets and varied by less than 3 arcsec in azimuth and by less than 2 arcsec in elevation.700 The overlapping jigele maps were co-added to produce a final map with a tota integration time of 18 hours and 50 minutes., The overlapping jiggle maps were co-added to produce a final map with a total integration time of 18 hours and 50 minutes.701 We used SURE (SCUBA User Recuetion Facility: Jenness&Lightfoot 1998)) scripts together with locally developed code (Borys2002) to reduce the data., We used SURF (SCUBA User Reduction Facility; \citealt{Jenness}) ) scripts together with locally developed code \citep{Borysthesis} to reduce the data.702 The SURE map and our map look similar., The SURF map and our map look similar.703 The benefit of using our own code to analyse the data is that it makes a map with minimally: correlated pixels ancl provides an estimate of the noise in each. pixel., The benefit of using our own code to analyse the data is that it makes a map with minimally correlated pixels and provides an estimate of the noise in each pixel.704 We chose 3 aresec pixels oriented. along ltA.Dec coordinates.," We chose 3 arcsec pixels oriented along RA,Dec coordinates."705 This pixel size is slightly too large for 450pim studies. but has proven to be adequate at. S50jum (sce Borysctal. 2003)).," This pixel size is slightly too large for $450\,\mathrm{\mu m}$ studies, but has proven to be adequate at $850\,\mathrm{\mu m}$ (see \citealt{Borys2003}) )."706 Calibration data were reduced in the same wav as the CSS ata., Calibration data were reduced in the same way as the GSS data.707 The Εις conversion factors (FCEs) over 3 of the 4 nights in January 1999 and all 3 nights in January 2000 agree with the monthly averages to within 10 per cent (see the ΑΟΛΕΤΕ calibration web-page)., The flux conversion factors (FCFs) over 3 of the 4 nights in January 1999 and all 3 nights in January 2000 agree with the monthly averages to within 10 per cent (see the JCMT calibration web-page).708 The PCE value for one night in January was 30 per cent higher than the monthly average and this could indicate that the sky was so variable that the zco was not accurately rellecting the opacity along 1e line of sight to the object., The FCF value for one night in January was 30 per cent higher than the monthly average and this could indicate that the sky was so variable that the $\tau_{\rm CSO}$ was not accurately reflecting the opacity along the line of sight to the object.709 The calibration uncertainty is omitted from our quoted error values since it is not a major contributor to the global uncertainty of our low SNR data and has no effect on our source detection method., The calibration uncertainty is omitted from our quoted error values since it is not a major contributor to the global uncertainty of our low SNR data and has no effect on our source detection method.710 The 8504n map has a mean consistent with zero. as expected. from dillerential measurements. and an rms of 3.5mJv.," The $850\,\mathrm{\mu m}$ map has a mean consistent with zero, as expected from differential measurements, and an rms of $3.5\,\mathrm{mJy}$."711 The final map is shown in Fig. L.., The final map is shown in Fig. \ref{fig:850map}.712 Phe 450ji map also has à mean consistent with zero and an rms of 50mv.," The $450\,\mathrm{\mu m}$ map also has a mean consistent with zero and an rms of $50\,\mathrm{mJy}$."713 Given the 14.7 aresee beam. a high-redshift galaxy wil be unresolved ancl will appear as a positive source Hanke bv 2 negative sources.," Given the 14.7 arcsec beam, a high-redshift galaxy will be unresolved and will appear as a positive source flanked by 2 negative sources."714 The source density at S50/m (see e.g. Scottetal.2002.. Borysοἱal. 2003.. Webbetal. 2003)) suggests that only a handful of sources will be recoverec in our map.," The source density at $850\,\mathrm{\mu m}$ (see e.g. \citealt{Scott}, \citealt{Borys2003}, \citealt{Webb}) ) suggests that only a handful of sources will be recovered in our map."715 Llenee we do not expect many overlapping sources. and therefore sources were extracted by fitting theraw rebinned map with a three-Iobed. PSE of an. isolate point-source with the same chop throw and position angle as the map data.," Hence we do not expect many overlapping sources, and therefore sources were extracted by fitting theraw rebinned map with a three-lobed PSF of an isolated point-source with the same chop throw and position angle as the map data."716 A fit to the PSE model centred on each, A fit to the PSF model centred on each717To reproduce algorithm & in ?.. let the initial guess for q' be Then iterate equation once. producing qo and po ave then given bv equations and(16c).. with this choice for q'.,"To reproduce algorithm 8 in \citet{Omelyan2006}, let the initial guess for $q'$ be Then iterate equation once, producing $q_2$ and $p_2$ are then given by equations and, with this choice for $q'$."718 This choice of initial guess and single iteration allows the algorithm to be written compositionally as This is exactly the sequence of operations in ?.. algorithun. 8: equation is the approximation derived in ? to the loree gradient recuired in the corresponding algoritlim of ?..," This choice of initial guess and single iteration allows the algorithm to be written compositionally as This is exactly the sequence of operations in \citet{Omelyan2006}, algorithm 8; equation is the approximation derived in \citet{Omelyan2006} to the force gradient required in the corresponding algorithm of \citet{Chin2003}."719 The algorithm needs four force evaluations lor a single step. but only tree in a simulation because the first force evaluation of a step occurs at the same position as the last force evaluation of the previous step.," The algorithm needs four force evaluations for a single step, but only three in a long-running simulation because the first force evaluation of a step occurs at the same position as the last force evaluation of the previous step."720 The algorithm exactly conserves pliase-space volume and momentum. but is only fourth-order svuiplectic (in 2»-dimensional pliase-spaces with nz» 1).," The algorithm exactly conserves phase-space volume and momentum, but is only fourth-order symplectic (in $2n$ -dimensional phase-spaces with $n721> 1$ )."722 As stated above. in practice we find that the energy. error [rom this algorithm in N-body simulations is significantly worse than that from the following algorithm.," As stated above, in practice we find that the energy error from this algorithm in $N$ -body simulations is significantly worse than that from the following algorithm."723 We compare (he energv error behavior of the aleorithms in Figure I.., We compare the energy error behavior of the algorithms in Figure \ref{OmelyanVsUs}.724 As we shall see in Section 5.. it is not. in general. possible to iterate equation in the presence of individual timesteps.," As we shall see in Section \ref{IndividualTimeSteps}, it is not, in general, possible to iterate equation in the presence of individual timesteps."725 Iterating equation for a particle corresponds (o, Iterating equation for a particle corresponds to726 Ina flat. matter-dominated universe. we would not expect to see an ISW effect as the large-scale gravitational potentials do not changetime.,"In a flat, matter-dominated universe, we would not expect to see an ISW effect as the large-scale gravitational potentials do not change."727 However. in a universe dominated by DE or curvature. we should detect a so called ISW elect. which provides a direct measure of these quantities at the redshift of the changing potentials. i.c.. the effect does not depend on the previous history of the erowth of structure.," However, in a universe dominated by DE or curvature, we should detect a so called ISW effect, which provides a direct measure of these quantities at the redshift of the changing potentials, i.e., the effect does not depend on the previous history of the growth of structure."728 The late-time ISW elfect introduces additional secondary anisotropies on top —of the primary— CALB Óluctuations and is therefore hard to detect directly., The late-time ISW effect introduces additional secondary anisotropies on top of the primary CMB fluctuations and is therefore hard to detect directly.729 However. the ISW ellect can be seen via the eross-correlation of the €MD with tracers in the large-scale structure of the universe as outlined by Crittenden&Turok(1996)...," However, the ISW effect can be seen via the cross-correlation of the CMB with tracers in the large-scale structure of the universe as outlined by \citet{1996PhRvL..76..575C}."730 This has now been achieved by a number of authors using a host of dillerent. galaxy datasets (Fosalba.Gaztanaga.&Cas-al.2008:Ciranett.Nevrinck.&Szapucdi 2008)..," This has now been achieved by a number of authors using a host of different galaxy datasets \citep{2003ApJ...597L..89F,7312003astro.ph..7335S,7322004Natur.427...45B,7332004ApJ...608...10N,7342004PhRvD..69h3524A, 7352004MNRAS.350L..37F,7362005PhRvD..72d3525P,7372006MNRAS.372L..23C, 7382006PhRvD..74f3520G,7392007MNRAS.377.1085R, 7402008PhRvD..78d3519H,7412008ApJ...683L..99G}."742 In this paper. we exploit the recent analysis of Ciannantonioetal.(2008) and focus on the subset of intermecdiate-redshift (2< 0.4) SDSS data they used.," In this paper, we exploit the recent analysis of \citet{2008PhRvD..77l3520G} and focus on the subset of intermediate-redshift $z<0.4$ ) SDSS data they used."743 Even this subset of cata shows a detection of the ISW elfect a the 36. level (Ciannantonio2008a).., Even this subset of data shows a detection of the ISW effect at the $3\sigma$ level \citep{giannantonio_private}.744 The contours for this new determination of the ISW οσο are plotted in. Figs. 4.. 5..," The contours for this new determination of the ISW effect are plotted in Figs. \ref{fig_sn_bao_qs_isw}, \ref{fig_sn_gs_isw_curvature},"745 and 6.., and \ref{fig_sdss_plus_gs_and_isw}.746 In Table 1.. we present the combination of this new ISW cllect measurement with our SDSS-II SN ane BAO data. using the same procedure as discussed in Section -5.1.1..," In Table \ref{table_w}, we present the combination of this new ISW effect measurement with our SDSS-II SN and BAO data, using the same procedure as discussed in Section \ref{section_gs_structure}."747 We provide in Table 1 measurements of w anc Quy [rom various combinations of the four data-sets considered herein (SN. BAO. RS. IS8W).," We provide in Table \ref{table_w} measurements of $w$ and $\Omega_M$ from various combinations of the four data-sets considered herein (SN, BAO, RS, ISW)."748" The most stringent constraint comes from the combination of all the probes giving w=OSL(15 and Oy,=0.22Qu which is competitive eiven the restricted. redshift range considered in this analvsis."," The most stringent constraint comes from the combination of all the probes giving $w=-0.81^{+0.16}_{-0.18}$ and $\Omega_M=0.22^{+0.09}_{-0.08}$, which is competitive given the restricted redshift range considered in this analysis."749 However. much of this constraint comes from the combination of just. the SDSS-LL SNe anc LSW measurements (See Table 1)).," However, much of this constraint comes from the combination of just the SDSS-II SNe and ISW measurements (See Table \ref{table_w}) )."750 Phe ISW contours already include correlations between different angular and recishift bins and cosmic variance. ancl could therefore be considered stable (see e.g. Giannantonioetal. 2008)).," The ISW contours already include correlations between different angular and redshift bins and cosmic variance, and could therefore be considered stable (see e.g. \citealt{2008PhRvD..77l3520G}) )."751 Similarly the contours we use for recdshift-space distortions include the cominant uncertainty coming from the galaxy bias (see the procedure laid. out. in Section 5.1.1))., Similarly the contours we use for redshift-space distortions include the dominant uncertainty coming from the galaxy bias (see the procedure laid out in Section \ref{section_gs_structure}) ).752 Percivalctal.(2009) has done several checks and found that their result is robust against variations in sample selection. number of redshift slices. calibration ancl other potential influences.," \cite{2009arXiv0907.1660P} has done several checks and found that their result is robust against variations in sample selection, number of redshift slices, calibration and other potential influences."753 Therefore. the results presented in. Table. 1 includes major uncertainties allecting the other probes but only the statistical uncertainties [from the SDSS-SN data on the measured. cosmological parameters.," Therefore, the results presented in Table 1 includes major uncertainties affecting the other probes but only the statistical uncertainties from the SDSS-SN data on the measured cosmological parameters."754 As discussed in IWwessleretal.(2009).. the SDSS-LL SN distances also depend on the detailed. choices and assumptions within the AILCS2k2 supernova light-curve fitting procedure. including dillerent training vectors. priors on ly and Ay. uncertainties in zero points and the filter systems. anc selection biases.," As discussed in \citet{kessler}, the SDSS-II SN distances also depend on the detailed choices and assumptions within the MLCS2k2 supernova light-curve fitting procedure, including different training vectors, priors on $A_V$ and $R_V$, uncertainties in zero points and the filter systems, and selection biases."755" To quantify, the systematic uncertainties associated with these parameter. choices. we repeat our analysis above for these cillerent choices and. following the procedure laid out in [xessleretal.(2009)... we calculate a variation of Aw=£0.15 with respect to the fiducial AILOS2k2 reduction presented in Table 1 in the case of combining all four constraints and slightly. larger. values for the other cases."," To quantify the systematic uncertainties associated with these parameter choices, we repeat our analysis above for these different choices and, following the procedure laid out in \citet{kessler}, we calculate a variation of $\Delta w=\pm 0.15$ with respect to the fiducial MLCS2k2 reduction presented in Table \ref{table_w} in the case of combining all four constraints and slightly larger values for the other cases."756 Our estimates of the systematic uncertainty for ALCS2k2 are [larger than the values caleulated in Kessleretal.(2009) because they use the BAO cl-parameter from Eisensteinetal.(2005)... ancl the added constraints on 1 ancl i derived from using the CAIB R-parameter (Ixomatsuetal.2008)...," Our estimates of the systematic uncertainty for MLCS2k2 are larger than the values calculated in \citet{kessler} because they use the BAO $A$ -parameter from \citet{2005ApJ...633..560E}, and the added constraints on $\Omega_M$ and $w$ derived from using the CMB $R$ -parameter \citep{2008arXiv0803.0547K}."757 We reproduce their values for the svstematic uncertainties on AILCS2k2 (Awzz0.1). if we include these constraints in our analvsis.," We reproduce their values for the systematic uncertainties on MLCS2k2 $\Delta w \approx 0.1$ ), if we include these constraints in our analysis."758 Llowever. in this paper. we restrict our analysis to intermediate-redshift probes and therefore do not include the CMD constraints. which results in larger uncertainties.," However, in this paper, we restrict our analysis to intermediate-redshift probes and therefore do not include the CMB constraints, which results in larger uncertainties."759 Our analvsis of the MLCS2k2 svstematic uncertainties discussed. above does not include the large shift in w discussed in Ixesslerctal.(2009) when the rest-frame C- band template is removed in the light-curve fitting., Our analysis of the MLCS2k2 systematic uncertainties discussed above does not include the large shift in $w$ discussed in \citet{kessler} when the rest-frame $U$ -band template is removed in the light-curve fitting.760 As seen in Fable 6 of Ixessleretal.(2009).. removing the rest.[rame Uband results ina 0.31 shift in e. while we find a shift of 0.48 if we remove this data.," As seen in Table 6 of \citet{kessler}, removing the rest–frame U–band results in a $-0.31$ shift in $w$, while we find a shift of $-0.43$ if we remove this data."761 This particular uncertainty would therefore give rise to a bimodal result either centered around dw2OS (with Uband included) or αν--12 (without. U-band). vet both consistent with w=1 within he errors.," This particular uncertainty would therefore give rise to a bimodal result either centered around $w\simeq-0.8$ (with U–band included) or $w=-1.2$ (without U-band), yet both consistent with $w=-1$ within the errors."762 We do not add the uncertainty due to excluding the rest[rame Uband to our svstematic errors. because we relieve it is incorrect to exclude this data from the lightcurve fitting., We do not add the uncertainty due to excluding the rest–frame U–band to our systematic errors because we believe it is incorrect to exclude this data from the light--curve fitting.763 Even though there is evidence for diversity in he UV spectra of SNe Ia (see. Ellis et al., Even though there is evidence for diversity in the UV spectra of SNe Ia (see Ellis et al.764 2008: Foley. et al., 2008; Foley et al.765 2008). the removal of the rest-frame Woband data from he SDSSonly analysis results in the light curve litter using only two filters at z«0.2 to constrain the colors of the SNe.," 2008), the removal of the rest-frame U–band data from the SDSS–only analysis results in the light curve fitter using only two filters at $z<0.2$ to constrain the colors of the SNe."766 This provides significant freedom to the MLECS2E?2 fitter and hen the priors on the fitted parameters become important., This provides significant freedom to the MLCS2k2 fitter and then the priors on the fitted parameters become important.767 We note that wis only shifted by 0.1 when using the SALT ight curve Litter (seeTableSinIxessleretal.2000). on the SDSSonly sample with the rest-frame Uband. excluded., We note that $w$ is only shifted by $-0.1$ when using the SALT light curve fitter \citep[see Table 8 in][]{kessler} on the SDSS–only sample with the rest-frame U–band excluded.768 ‘This is the only noticeable dillercnee between these two light curve fitting methodologies when considering the SDSSonly sample: namely the error on aw when the rest-frame Uoband is excluded., This is the only noticeable difference between these two light curve fitting methodologies when considering the SDSS–only sample; namely the error on $w$ when the rest-frame U–band is excluded.769 Finally. Ixessleretal.(2009). also sees a clear jump in the SDSS Llubble diagram at z20.2 when the rest-frame Woband is excluded from the AILCS2k2 analysis (see their Section 10.1.3 and Fig.," Finally, \citet{kessler} also sees a clear jump in the SDSS Hubble diagram at $z\simeq0.2$ when the rest-frame U–band is excluded from the MLCS2k2 analysis (see their Section 10.1.3 and Fig."770 30). indicating that a constant w model is not à good fit in this case.," 30), indicating that a constant $w$ model is not a good fit in this case."771" Me present an. analysis of the luminosity distances of Type la Supernovae from the Sloan Digital Sky Survey- (SDSS-1I) Supernova Survey in conjunction with other intermediate redshift ἐς< 0.4) cosmological measurements including redshift-space distortions from the 2dECIUS. the TSW. οσο, and the BAO. distance. scale from both the SDSS and δα."," We present an analysis of the luminosity distances of Type Ia Supernovae from the Sloan Digital Sky Survey-II (SDSS-II) Supernova Survey in conjunction with other intermediate redshift $z<0.4$ ) cosmological measurements including redshift-space distortions from the 2dFGRS, the ISW effect, and the BAO distance scale from both the SDSS and 2dFGRS."772 We have analyzed the SDSS-LL SN luminosity distances using several, We have analyzed the SDSS-II SN luminosity distances using several773the accretion rate. the midplane pressure (and therefore jet Iuminositv) declines xin.,"the accretion rate, the midplane pressure (and therefore jet luminosity) declines $\propto \dot m^{4/5}$."774 This break (ime is «quite late in the development of the flare for low-mass events. but when the black hole mass is relatively large. it could take place as early as c30/0.," This break time is quite late in the development of the flare for low-mass events, but when the black hole mass is relatively large, it could take place as early as $\simeq 30 t_0$."775 Although the theory of jet and clisk emission from tidal disruptions as we have presented it contains a large number of free parameters. in anv given event (here are also potentially a sizable number of observable properties (hat may be used (o constrain these parameters.," Although the theory of jet and disk emission from tidal disruptions as we have presented it contains a large number of free parameters, in any given event there are also potentially a sizable number of observable properties that may be used to constrain these parameters."776 In nearly every. event. il is possible to measure (he characteristic time /p.," In nearly every event, it is possible to measure the characteristic time $t_0$."777" Optical and/or ultraviolet observations often give an indicator of the peak thermal disk luminosity. Lug: we describe this as only an ""indicator"" because. as we discuss below. (here is likelv to be a sizableand uncertainbolometric correction."," Optical and/or ultraviolet observations often give an indicator of the peak thermal disk luminosity, $L_{d0}$; we describe this as only an “indicator"" because, as we discuss below, there is likely to be a sizable—and uncertain—bolometric correction."778" When there is hard X-ray enission. the peak jet luminosity Ljj can also be obtained: if an event can be followed long enough. it mav also be possible to measure (wo (mes related to (he transition from super- to sub-Eddington accretion: the (nme fj, al which the jet Iuninosity flattens. and the time lai 04 Which the disk luninositv begins (o diminish."," When there is hard X-ray emission, the peak jet luminosity $L_{j0}$ can also be obtained; if an event can be followed long enough, it may also be possible to measure two times related to the transition from super- to sub-Eddington accretion: the time $t_{\rm jet}$ at which the jet luminosity flattens, and the time $t_{\rm disk}$ at which the disk luminosity begins to diminish."779 In this section. we will lav out a eeneral formalism for using these observables as parameter constraints and then apply Chat method to a specilic example. Swill J2058.44-0516.," In this section, we will lay out a general formalism for using these observables as parameter constraints and then apply that method to a specific example, Swift J2058.4+0516."780 As shown by Lodatoetal. (2009).. the accretion rale peaks at a time Peg) past pericenter passage (see equ. 3)).," As shown by \cite{lkp09}, , the accretion rate peaks at a time $P_{\rm orb}(a_{\rm min})$ past pericenter passage (see eqn. \ref{eq:porb_min}) ),"781 and diminishes thereafter as a power-law in time., and diminishes thereafter as a power-law in time.782" If we identilv the time of peak flare Iuminosity. /j with that orbital period. we obtain the constraint where /,is measured in davs."," If we identify the time of peak flare luminosity $t_0$ with that orbital period, we obtain the constraint where $t_0$is measured in days."783magnifications is weaker at j/1. showing considerable scatter for all of the models.,"magnifications is weaker at $\mu > 1$, showing considerable scatter for all of the models."784 This can be understood in terms of the clustering of the caustie network in regions of high magnification which exhibits structure on quite small scales., This can be understood in terms of the clustering of the caustic network in regions of high magnification which exhibits structure on quite small scales.785 With this. the magnification of the continuum mirrors this small scale caustic structure. whereas the BLR is magnified by a weighted average of the larger scale caustic structure.," With this, the magnification of the continuum mirrors this small scale caustic structure, whereas the BLR is magnified by a weighted average of the larger scale caustic structure."786 Interestingly. for all the models. there is also a non-zero probability that while the continuum source is being strongly magnitied. the over all BLR region is undergoing demagnification.," Interestingly, for all the models, there is also a non-zero probability that while the continuum source is being strongly magnified, the over all BLR region is undergoing demagnification."787 The reverse of this. however. appears to be significantly rarer in most models.," The reverse of this, however, appears to be significantly rarer in most models."788 The situation is very similar for the larger BLR models (Figure 6)., The situation is very similar for the larger BLR models (Figure \ref{fig5}) ).789 As expected from Figure 3. the distributions of BLR magnification are somewhat narrower than the smaller BLR model.," As expected from Figure \ref{fig2}, the distributions of BLR magnification are somewhat narrower than the smaller BLR model."790 Again. no clear correlation of the continuum and BLR magnification is apparent with the continuum source undergoing significant magnitication while the BLR is relatively unmagnitied.," Again, no clear correlation of the continuum and BLR magnification is apparent with the continuum source undergoing significant magnification while the BLR is relatively unmagnified."791 It is also apparent that while there is the general correlation between the magnification of the two regions. there is still a significant range over which the continuum source can be substantially magnified while the BLR undergoes a magnification of ~1.," It is also apparent that while there is the general correlation between the magnification of the two regions, there is still a significant range over which the continuum source can be substantially magnified while the BLR undergoes a magnification of $\sim1$."792 Hence. a microlensing fluctuation observed in broadband photometric monitoring will not necessarily be an indicator of strong microlensing of the BLR.," Hence, a microlensing fluctuation observed in broadband photometric monitoring will not necessarily be an indicator of strong microlensing of the BLR."793 Rather than spectroscopic monitoring. however. broadband. monitoring. could be combined with observations obtained through a narrow band filter which covers a broad line in the quasar spectrum.," Rather than spectroscopic monitoring, however, broadband monitoring could be combined with observations obtained through a narrow band filter which covers a broad line in the quasar spectrum."794 With this. a plot similar to those presented in Figures 5. and 6. could be constructed and compared to simulations.," With this, a plot similar to those presented in Figures \ref{fig4} and \ref{fig5} could be constructed and compared to simulations."795 As well as the total magnification of the emission lines. it is important to characterize the moditication of the emission line orofile due to differential magnification effects.," As well as the total magnification of the emission lines, it is important to characterize the modification of the emission line profile due to differential magnification effects."796 This can be seen as a shift in the velocity centroid of the emission line., This can be seen as a shift in the velocity centroid of the emission line.797 In undertaking his. however. it is important to note the S'S and 1 models display surface brightness structure which is symmetrical in velocity. and any gravitational lensing magnification results in identical line oofile modification at positive and negative velocities. leading to a centroid shift of zero.," In undertaking this, however, it is important to note the $SS$ and $BS$ models display surface brightness structure which is symmetrical in velocity, and any gravitational lensing magnification results in identical line profile modification at positive and negative velocities, leading to a centroid shift of zero."798 Therefore. in the following study only the »ositive velocity component of the emission lines are considered or the SS’ and £5 models. whereas the positive velocity and the otal emission line profile are considered for the A21 and AA1 models.," Therefore, in the following study only the positive velocity component of the emission lines are considered for the $SS$ and $BS$ models, whereas the positive velocity and the total emission line profile are considered for the $KD1$ and $KM1$ models."799 Figure 7 presents the distribution of the measured centroid of he positive velocity component of the BLR emission line for euch of the models presented in this paper., Figure \ref{fig6} presents the distribution of the measured centroid of the positive velocity component of the BLR emission line for each of the models presented in this paper.800 The black line presents the distributions for the smaller BLR models for each lensed image. whereas the thicker. grey line represents the larger BLR models.," The black line presents the distributions for the smaller BLR models for each lensed image, whereas the thicker, grey line represents the larger BLR models."801 The vertical dot-dashed line running vertically through the panels, The vertical dot-dashed line running vertically through the panels802This is achieved withpreconditionzng.,This is achieved with.803 Instead of solving Eq., Instead of solving Eq.804 directly. one solves with the preconditioniug matrix B.," directly, one solves with the preconditioning matrix ${\cal B}$."805 Now the iterative solver deals with the matrix BY., Now the iterative solver deals with the matrix ${\cal B}\cal J$ .806 IE B is a good approximation to F+. then BF will be close to the identity matrix. the condition πο will be close to unity; aud the linear solver will converge quickly.," If ${\cal B}$ is a good approximation to ${\cal J}^{-1}$, then ${\cal B}{\cal J}$ will be close to the identity matrix, the condition number will be close to unity, and the linear solver will converge quickly."807 Ποιος the problem reduces to finding a matrix B that approximates JF+ sufficiently well and that cau be computed eficieutly., Hence the problem reduces to finding a matrix $\cal B$ that approximates ${\cal J}^{-1}$ sufficiently well and that can be computed efficiently.808 There exist may different approaches. most notably finite differcuce precouditioniug|?] aud finite clement preconditioniug|?|:: we will follow a two-stage process proposed by Orszag|?|..," There exist many different approaches, most notably finite difference \cite{Orszag:1980} and finite element \cite{Deville-Mund:1985}; ; we will follow a two-stage process proposed by \cite{Orszag:1980}."809 First. initialize a matrix Arp witha finite differcuce approximation of the Jacobian 7.," First, initialize a matrix ${\cal A}_{FD}$ with a finite difference approximation of the Jacobian $\cal J$."810 Second. approximately invert Arp to construct B. Iu one spatial dimension Arp is tridiagonal and direct inversion 5=App ls feasible.," Second, approximately invert ${\cal A}_{FD}$ to construct ${\cal B}$, In one spatial dimension ${\cal A}_{FD}$ is tridiagonal and direct inversion ${\cal B}\equiv{\cal A}_{FD}^{-1}$ is feasible."811 In two or more dimensions. direct inversion of Arp is too expensive: for problems iu one two-dimensional subdomain. hardcoded incomplete LU-factorizatious have been developed?|..," In two or more dimensions, direct inversion of ${\cal A}_{FD}$ is too expensive; for problems in one two-dimensional subdomain, hardcoded incomplete LU-factorizations have been \cite{Canuto-Hussaini}."812 Tn our case we lave to deal with the additional complexity that the Jacobian aud therefore Arp contains matching conditions., In our case we have to deal with the additional complexity that the Jacobian and therefore ${\cal A}_{FD}$ contains matching conditions.813 Since we choose the domain decomposition at xuutinc. nothing is known about the particular structure of the subdomains.," Since we choose the domain decomposition at runtime, nothing is known about the particular structure of the subdomains."814 We proceed as follows: We initialize App with the finite differeuce approximation of J., We proceed as follows: We initialize ${\cal A}_{FD}$ with the finite difference approximation of ${\cal J}$.815 It is sufficient to include those terms of the Jacobian in App that cause the condition number to Increase with the expansion order., It is sufficient to include those terms of the Jacobian in ${\cal A}_{FD}$ that cause the condition number to increase with the expansion order.816 These are the secoud spatial derivatives aud the first derivatives from matching conditions aud boundary conditions. Eqs.," These are the second spatial derivatives and the first derivatives from matching conditions and boundary conditions, Eqs."817 and(386)., and.818. Iucludiug the value matching conditions(38cd)..OSf).. in Arp inproves the ability of the precouditioncr to represent modes extending over several subdomains aud thus decreases the wuuber of iterations. too.," Including the value matching conditions, in ${\cal819 A}_{FD}$ improves the ability of the preconditioner to represent modes extending over several subdomains and thus decreases the number of iterations, too."820 In the first example iu section [1 we demonstrate that precoucditiouing is iudeed necessary. aud that one should precondition not only the ποσο order derivatives. but also the matching conditions.," In the first example in section \ref{sec:Example1} we demonstrate that preconditioning is indeed necessary, and that one should precondition not only the second order derivatives, but also the matching conditions."821 Some details about the finite difference approximations are eiven in appendix A.., Some details about the finite difference approximations are given in appendix \ref{sec:FD-details}.822 Taving set up Arp we theu use the software package ¢|?| for the approximate inversion of Eq., Having set up ${\cal A}_{FD}$ we then use the software package \cite{petsc-home-page} for the approximate inversion of Eq.823(17)... PETSc provides niuiv general purpose precouditiouers that pertorm the step either explicitly or müiplicitlv. most notable ILU aud the overlapping Sclavarz method.," PETSc provides many general purpose preconditioners that perform the step either explicitly or implicitly, most notably ILU and the overlapping Schwarz method."824 With PETSc we can explore these to find the most cficient onc., With PETSc we can explore these to find the most efficient one.825 We will describe our particular choices for preconditioning below for cach example., We will describe our particular choices for preconditioning below for each example.826 Ceneralizing S to multiple dimensions is conceptually straightforward. since Eqs.," Generalizing $\cal S$ to multiple dimensions is conceptually straightforward, since Eqs."827 generalize nicely to higher dimensions., generalize nicely to higher dimensions.828 In order to simplify the matching between touching subdomains. we require that ou a surface shared by touching subdomains. the collocation points are identical.," In order to simplify the matching between touching subdomains, we require that on a surface shared by touching subdomains, the collocation points are ."829 If for example. two three-cdimensioual rectangular blocks touch along the .c-axis. then both blocks must have ideutical lower and upper boundsof the blocks along the y and z axis aud both blocks unst use the same mappines and the same munberof collocation poiuts along the y- aud," If, for example, two three-dimensional rectangular blocks touch along the $x$ -axis, then both blocks must have identical lower and upper boundsof the blocks along the $y$ and $z$ axis and both blocks must use the same mappings and the same numberof collocation points along the $y$- and"830"birth is between 5 and 185 km s!, while the progenitor mass Mp; is between 1.25and 2.65 Mo, both with confidence.","birth is between 5 and 185 km $^{-1}$, while the progenitor mass $M_{2i}$ is between 1.25and 2.65 $_\sun$, both with confidence."831" Both polar and planar kicks are allowed, but planar kicks are more favorable than polar ones."," Both polar and planar kicks are allowed, but planar kicks are more favorable than polar ones."832 The spin tilt angle of NSI is smaller than 16.4? with confidence., The spin tilt angle of NS1 is smaller than $^\circ$ with confidence.833" At the current time and at the measured distance, PSR J1756-2251 has a total transverse velocity between 6.0 and 64.5 km s!, and a radial velocity between —110 and 98 km s, both with confidence."," At the current time and at the measured distance, PSR J1756-2251 has a total transverse velocity between 6.0 and 64.5 km $^{-1}$, and a radial velocity between $-110$ and 98 km $^{-1}$, both with confidence."834" Furthermore, this binary is equally likely to be moving towards us as away from us."," Furthermore, this binary is equally likely to be moving towards us as away from us."835 When comparing with Wang et al. (, When comparing with Wang et al. (836"2006), we have tighter constrained limits on V; and M);, due to the fact that we have the additional constraint on the proper motion JigA..","2006), we have tighter constrained limits on $V_k$ and $M_{2i}$, due to the fact that we have the additional constraint on the proper motion $\mu_{R.A.}$."837" The two neutron stars have masses of 1.62 and 1.11 Mo, where the more massive one is NS1."," The two neutron stars have masses of 1.62 and 1.11 $_\sun$, where the more massive one is NS1."838" However, each mass measurement has an uncertainty of ~0.5 Mo."," However, each mass measurement has an uncertainty of $\sim$ 0.5 $_\sun$."839 PSR J1811 has a characteristic age of 1830 Myr., PSR J1811 has a characteristic age of 1830 Myr.840" The neutron stars are in an orbit with a period of 18.8 days, and an eccentricity of 0.828."," The neutron stars are in an orbit with a period of 18.8 days, and an eccentricity of 0.828."841" At the current time, this binary is close to the galactic plane, at |=12.8? and b=0.44°, and at a distance of 6.0 kpc away from us."," At the current time, this binary is close to the galactic plane, at $l = 12.8^\circ$ and $b = 0.44^\circ$, and at a distance of 6.0 kpc away from us."842" Like PSR J1756-2251, there are currently no spin tilt nor proper motion measurements available."," Like PSR J1756-2251, there are currently no spin tilt nor proper motion measurements available."843 The results are displayed in Figures 13 and 14., The results are displayed in Figures 13 and 14.844" The 2D V;- Mp; joint distribution shows that the kick given to NS2 at birthprobability is less than 310 km s!, while the progenitor mass Mp; is between 1.11 and 8.0 Mo, both with confidence."," The 2D $V_k$ $M_{2i}$ joint probability distribution shows that the kick given to NS2 at birth is less than 310 km $^{-1}$, while the progenitor mass $M_{2i}$ is between 1.11 and 8.0 $_\sun$, both with confidence."845" Both polar and planar kicks are allowed, but the planar kicks are more favorable than the polar ones."," Both polar and planar kicks are allowed, but the planar kicks are more favorable than the polar ones."846" The spin tilt angle 0, is smaller than 57.6? with confidence.", The spin tilt angle $\theta_t$ is smaller than $^\circ$ with confidence.847" At the measured distance, the total transverse velocity of PSR J1811-1736 at the current epoch is between 4 and 202 km s, and the radial velocity between -90 and 210 km s! with confidence, which means this binary is likely moving away from us."," At the measured distance, the total transverse velocity of PSR J1811-1736 at the current epoch is between 4 and 202 km $^{-1}$, and the radial velocity between -90 and 210 km $^{-1}$ with confidence, which means this binary is likely moving away from us."848 Although our upper boundary of the confidence intervals of M»; is the same as the upper limit found by Wang et al. (, Although our upper boundary of the confidence intervals of $M_{2i}$ is the same as the upper limit found by Wang et al. (849"2006), the value of our lower boundary is less than their lower limit.","2006), the value of our lower boundary is less than their lower limit."850 This is because Wang et al. (, This is because Wang et al. (851"2006) put a conservative lower limit of 2.1 Mo on the progenitor mass of a neutron star, which we did not.","2006) put a conservative lower limit of 2.1 $_\sun$ on the progenitor mass of a neutron star, which we did not."852" On the other hand, our limits on V; are more constrained than those of Wang et al. ("," On the other hand, our limits on $V_k$ are more constrained than those of Wang et al. ("853"2006), as we compute confidence levels instead of allowed ranges of solution as Wang et al. (","2006), as we compute confidence levels instead of allowed ranges of solution as Wang et al. ("8542006).,2006).855" The two neutron stars of this binary have masses of 1.14 and 1.36 Mo, where the less massive one is NS1."," The two neutron stars of this binary have masses of 1.14 and 1.36 $_\sun$, where the less massive one is NS1."856" However, there is an uncertainty of ~0.5 Mo in the mass measurements."," However, there is an uncertainty of $\sim$ 0.5 $_\sun$ in the mass measurements."857 The characteristic age is 12.4 , The characteristic age is 12.4 Gyr.858"For the same reason as PSR J1518+4904, we set an the upper Gyr.limit of 10 Gyr on the age of this binary in our analysis."," For the same reason as PSR J1518+4904, we set an the upper limit of 10 Gyr on the age of this binary in our analysis."859" The neutron stars are orbiting each other with a period of 1.18 days, and an orbital eccentricity of 0.139."," The neutron stars are orbiting each other with a period of 1.18 days, and an orbital eccentricity of 0.139."860" At current time, this binary is out of the galactic plane, at |=53.3? and b=15.6°, and it is 1.2 kpc away from us."," At current time, this binary is out of the galactic plane, at $l = 53.3^\circ$ and $b = 15.6^\circ$, and it is 1.2 kpc away from us."861" Although there is no spin tilt nor proper motion measurements available at current time, Lorimer et al. ("," Although there is no spin tilt nor proper motion measurements available at current time, Lorimer et al. ("8622005) derived that the transverse velocity is smaller than 118 km κ”.,2005) derived that the transverse velocity is smaller than 118 km $^{-1}$.863 The results are shown in Figure 15., The results are shown in Figure 15.864" The Υι-Μοι joint probability distribution shows that the kick given to NS2 at birth is between 5 and 225 km s, while the progenitor mass Mp; is between 1.4 and 6.1 Mo with confidence."," The $V_k$ $M_{2i}$ joint probability distribution shows that the kick given to NS2 at birth is between 5 and 225 km $^{-1}$ , while the progenitor mass $M_{2i}$ is between 1.4 and 6.1 $_\sun$ with confidence."865" The PDFs of 6, and 6’ are similar to those of PSR J1756-2251.", The PDFs of $\theta_t$ and $\theta'$ are similar to those of PSR J1756-2251.866" Both polar and planar kicks are allowed, but planar kicks are"," Both polar and planar kicks are allowed, but planar kicks are"867(e.g. Shapley et al.,(e.g. Shapley et al.868 2003. Nagao et al.," 2003, Nagao et al."869 2008. di Serego Alighieri et al.," 2008, di Serego Alighieri et al."870 2008)., 2008).871 However. near-infrared spectroscopy of the sensitivity required to detect this line at 2>7 will certainly not be available until the (WSTY. and even then some theoretical predictions indicate that it is unlikely to be found in detectable objects (Salvaterra. Ferrara Dayal 2011. but see also Pawlik. Milosavljevie Bromm 2011).," However, near-infrared spectroscopy of the sensitivity required to detect this line at $z > 7$ will certainly not be available until the ), and even then some theoretical predictions indicate that it is unlikely to be found in detectable objects (Salvaterra, Ferrara Dayal 2011, but see also Pawlik, Milosavljevic Bromm 2011)."872 By necessity. therefore. recent attention has focussed on whether the broad-band near-infrared photometry which has now been successfully used to discover galaxies at. 20.58.5 (eg. Ίοιο et al.," By necessity, therefore, recent attention has focussed on whether the broad-band near-infrared photometry which has now been successfully used to discover galaxies at $z \simeq 6.5 - 8.5$ (e.g. McLure et al."873 2010: Oesch et al., 2010; Oesch et al.874 2010: Bouwens et al., 2010; Bouwens et al.875 2010a: Bunker et al., 2010a; Bunker et al.876 2010: Finkelstein et al., 2010; Finkelstein et al.877 2010: Vanzella et al., 2010; Vanzella et al.878 2011) can actually be used to establish the rest-frame continuum slopes of he highest redshift galaxies., 2011) can actually be used to establish the rest-frame continuum slopes of the highest redshift galaxies.879" Specifically. very young. metal-poor stellar populations are arguably expected to result in substantially pluer continuumslopes around À,,.;&1500À than have been detected to date in galaxies discovered at any lower redshift 2.«6.5 (e.g. Steidel et al."," Specifically, very young, metal-poor stellar populations are arguably expected to result in substantially bluer continuumslopes around $\lambda_{rest} \simeq 1500$ than have been detected to date in galaxies discovered at any lower redshift $z < 6.5$ (e.g. Steidel et al."880 1999: Meurer et al., 1999; Meurer et al.881 1999: Adelberger Steidel 2000: Ouchi et al., 1999; Adelberger Steidel 2000; Ouchi et al.882 2004: Stanway et al., 2004; Stanway et al.883 2005: Bouwens et al., 2005; Bouwens et al.884 2006: Hathi et al., 2006; Hathi et al.885 2008: Bouwens et al., 2008; Bouwens et al.886 2009: Erb et al., 2009; Erb et al.887 2010)., 2010).888 It has become the normal convention to parameterise the ultra-violet continuum slopes of galaxies in terms of a power-law index. 71. where fyxA (teg. Meurer et al.," It has become the normal convention to parameterise the ultra-violet continuum slopes of galaxies in terms of a power-law index, $\beta$, where $f_{\lambda} \propto889\lambda^{\beta}$ (e.g. Meurer et al."890 1999: thus. 7=2 corresponds to a source which has a flat spectrum in terms of fv. and hence has zero colour in the AB magnitude system).," 1999; thus, $\beta = -2$ corresponds to a source which has a flat spectrum in terms of $f_{\nu}$, and hence has zero colour in the AB magnitude system)."891 As discussed by several authors. while the bluest galaxies observed at 22:3 dthave 22 values as low (i.e. blue) as;=3 can in principle be produced by a young. low-metallicity stellar population (e.g. Bouwens et al.," As discussed by several authors, while the bluest galaxies observed at $z \simeq 3 - 4$ have $\beta \simeq -2$, values as low (i.e. blue) as $\beta = -3$ can in principle be produced by a young, low-metallicity stellar population (e.g. Bouwens et al."892 2010b: Schaerer 2002)., 2010b; Schaerer 2002).893 However. for this idealized prediction to actually be realized in practice. several conditions have to besatisfied simultaneously. namely i) the stellar population has to be very young (e.g. /.< 30MMyr for Zc10Z.. or!« 3MMvr for Z~10 7Z.). ii the starlight must obviously be completely free from any signiticant dust extinction. and iii) the starlight must also be significantly contaminated by (redder) nebular continuum (a condition which has important implications for UV photon escape fraction. and hence reionization — see. for example. Robertson et al.," However, for this idealized prediction to actually be realized in practice, several conditions have to besatisfied simultaneously, namely i) the stellar population has to be very young (e.g. $t < 30$ Myr for $Z \simeq 10^{-3}\,{\rm Z_{\odot}}$, or $t < 3$ Myr for $Z \simeq 10^{-2}\,{\rm Z_{\odot}}$ ), ii) the starlight must obviously be completely free from any significant dust extinction, and iii) the starlight must also be significantly contaminated by (redder) nebular continuum (a condition which has important implications for UV photon escape fraction, and hence reionization – see, for example, Robertson et al."894 2010)., 2010).895 For this reason. the recent report by Bouwens et al. (," For this reason, the recent report by Bouwens et al. ("8962010b) (supported to some extent by Finkelstein et al.,2010b) (supported to some extent by Finkelstein et al.897 2010) that the faintest galaxies detected at 2>>6.5 do indeed display an average value of 7)=3.00.2 is both exciting and arguably surprising enough to merit further detailed and independent investigation., 2010) that the faintest galaxies detected at $z > 6.5$ do indeed display an average value of $\langle \beta \rangle = -3.0 \pm 0.2$ is both exciting and arguably surprising enough to merit further detailed and independent investigation.898 This is especially the case because some authors are already beginning to assume that the existence of such extreme blue slopes is a robust result. already ripe for detailed theoretical interpretation (e.g. Taniguchi et al.," This is especially the case because some authors are already beginning to assume that the existence of such extreme blue slopes is a robust result, already ripe for detailed theoretical interpretation (e.g. Taniguchi et al."899 2010)., 2010).900 The aim of this paper is to carefully assess whether the currentHST WFC3 data do indeed provide clear evidence for such extremely blue slopes in faint galaxies at 2—7., The aim of this paper is to carefully assess whether the current WFC3 data do indeed provide clear evidence for such extremely blue slopes in faint galaxies at $z \simeq 7$.901 There are a number of potentially subtle biases which can affect the determination of UV continuum slopes from the WFC3/IR data. especially when. as is inevitably the case for the faintest objects. the results have to be based on the colours of galaxies whose individual 2 values have associated errors which can be as large as A—c1.5.," There are a number of potentially subtle biases which can affect the determination of UV continuum slopes from the WFC3/IR data, especially when, as is inevitably the case for the faintest objects, the results have to be based on the colours of galaxies whose individual $\beta$ values have associated errors which can be as large as $\Delta \beta \simeq \pm 1.5$."902 To check for. and attempt to quantify. the extent of any such biases we undertake two different approaches in this paper.," To check for, and attempt to quantify, the extent of any such biases we undertake two different approaches in this paper."903 First. we take advantage of the dynamic range offered by the available public WFC3/IR imaging to explore how derived values of 2 Gund average values (2322) depend on galaxy candidate robustness and signal:noise ratio as we approach the flux limit of a given survey.," First, we take advantage of the dynamic range offered by the available public WFC3/IR imaging to explore how derived values of $\beta$ (and average values $\langle \beta \rangle$ ) depend on galaxy candidate robustness and signal:noise ratio as we approach the flux limit of a given survey."904 Second. we undertake and analyse a set of fairly simple (but complete end-to-end) simulations to explore what apparent values of (and trends in) (2? would be deduced from the existing WFC3/IR data for different assumed input values of «7=—2.2.5.53 combined with realistic estimates of the faint-end slope of the 2=7 galaxy luminosity function.," Second, we undertake and analyse a set of fairly simple (but complete end-to-end) simulations to explore what apparent values of (and trends in) $\langle \beta \rangle$ would be deduced from the existing WFC3/IR data for different assumed input values of $\beta = -2, -2.5, -3$ combined with realistic estimates of the faint-end slope of the $z \simeq 7$ galaxy luminosity function."905 The layout of this paper is as follows., The layout of this paper is as follows.906 First. in Section 2 we briefly review how we have selected three new. high-redshift galaxy samples from the WFC3/IR+ACS+IRAC imaging of the Hubble Ultra Deep Field (HUDF). the HUDF Parallel Field 2 (HUDFO9-2j. and the Early Release Science imaging (ERS) of the northern portion of GOODS-South.," First, in Section 2 we briefly review how we have selected three new, high-redshift galaxy samples from the WFC3/IR+ACS+IRAC imaging of the Hubble Ultra Deep Field (HUDF), the HUDF Parallel Field 2 (HUDF09-2), and the Early Release Science imaging (ERS) of the northern portion of GOODS-South."907 The reduction of theAST data. the deconfusion of theSpizer TRAC data. and the extraction. analysis. classification and redshift estimation of the galaxies uncovered from this imaging are described in detail in MeLure et al. ," The reduction of the data, the deconfusion of the IRAC data, and the extraction, analysis, classification and redshift estimation of the galaxies uncovered from this imaging are described in detail in McLure et al. ("9082011). as this underpins the extraction of a new robust galaxy sample at 6<2«S87 which is the focus of the MeLure et al. (,"2011), as this underpins the extraction of a new robust galaxy sample at $6 < z < 8.7$ which is the focus of the McLure et al. ("9092011) study.,2011) study.910 In this study we retain not only the robust 2-6 sources detailed in MeLure et al. (, In this study we retain not only the robust $z > 6$ sources detailed in McLure et al. (9112011). but all galaxies from the larger parent sample with acceptable redshift solutions at 24.5. which are classified as either ROBUST or UNCLEAR.,"2011), but all galaxies from the larger parent sample with acceptable redshift solutions at $z > 4.5$, which are classified as either ROBUST or UNCLEAR."912 This allows us to explore trends in «ή over a reasonably wide range in redshift (5«z«tN and UVluminosity(. 22<Misig«LS) and also to explore potential biases introduced by the exclusion or inclusion of galaxies with less robust photometric redshifts.," This allows us to explore trends in $\beta$ over a reasonably wide range in redshift $5 < z < 8$ ) and UV luminosity $-22 < M_{UV,AB} < 18$ ), and also to explore potential biases introduced by the exclusion or inclusion of galaxies with less robust photometric redshifts."913 In Section 3 we explain how we determined the rest-frame UV continuum slope. «2. for the galaxies extracted from the different imaging datasets at different redshifts.," In Section 3 we explain how we determined the rest-frame UV continuum slope, $\beta$, for the galaxies extracted from the different imaging datasets at different redshifts."914 Then. in Section + we present and analyse our results. and demonstrate what level of data quality is actuallyrequired to achieve internally consistent results between the different galaxy samples uncovered from surveys of varying depths.," Then, in Section 4 we present and analyse our results, and demonstrate what level of data quality is actually to achieve internally consistent results between the different galaxy samples uncovered from surveys of varying depths."915 We move on to describe and analyse our simulations in Section 5 before discussing the implications of our findings in Section 6., We move on to describe and analyse our simulations in Section 5 before discussing the implications of our findings in Section 6.916 A summary of our conclusions is then presented in Section 7., A summary of our conclusions is then presented in Section 7.917" All magnitudes are quoted in the AB system (Oke Gunn 1983) and any cosmological calculations assume (3;=0.3. Oy—0.7. and ff,=τὸkms*\Ipei."," All magnitudes are quoted in the AB system (Oke Gunn 1983) and any cosmological calculations assume $\Omega_M = 0.3$, $\Omega_{\Lambda} = 0.7$, and $H_0 = 70\,{\rm kms^{-1}Mpc^{-1}}$."918 The candidate galaxies were all selected from our own reductions of the pubicly available near-infrared WFC3/IR imaging of the HUDF. ERS and HUDFO9-2? fields. as described in McLure et al. ," The candidate galaxies were all selected from our own reductions of the pubicly available near-infrared WFC3/IR imaging of the HUDF, ERS and HUDF09-2 fields, as described in McLure et al. ("919@OlL) Ove note that the HUDF WFC3/IR imaging is the same vear-l. 2009. imaging as utilised in MeLure et al.,"2011) (we note that the HUDF WFC3/IR imaging is the same year-1, 2009, imaging as utilised in McLure et al."920 2010)., 2010).921 In brief. candidate selection in all three fields was undertaken by first selecting sources with (Bertin Arnouts 1996) down to a deep signal:noise limit in each of the WFC3/IR YiosYoox. Jies and {του images. and then forming the superset of near-infrared selected sources by merging these catalogues.," In brief, candidate selection in all three fields was undertaken by first selecting sources with (Bertin Arnouts 1996) down to a deep signal:noise limit in each of the WFC3/IR $Y_{105}/Y_{098}$, $J_{125}$ and $H_{160}$ images, and then forming the superset of near-infrared selected sources by merging these catalogues."922 Then. as again detailed in MeLure et al. (," Then, as again detailed in McLure et al. ("9232011). photometric redshifts (with associated. probability distributions) were derived for all potential sources based on 0.6-aresee diameter flux-density measurements made on the available HS7 ACS optical imaging. the WFC3/IR imaging. and the Spifcer TRAC imaging (after deconfusion of the TRAC images based on the WFC3/IR {τω or {τος data).,"2011), photometric redshifts (with associated probability distributions) were derived for all potential sources based on 0.6-arcsec diameter flux-density measurements made on the available ACS optical imaging, the WFC3/IR imaging, and the IRAC imaging (after deconfusion of the IRAC images based on the WFC3/IR $H_{160}$ or $J_{125}$ data)."924 The samples were then culled to retain only sources with an acceptable solution at redshift 54.5 (ie. redshift solutions, The samples were then culled to retain only sources with an acceptable solution at redshift $z > 4.5$ (i.e. redshift solutions925Establishing a firm link between a galaxy’s morphology and its spectrum is advantageous for several reasons.,Establishing a firm link between a galaxy's morphology and its spectrum is advantageous for several reasons.926 For instance. galaxy spectra can be accurately determined to much greater redshifts and for fainter objects than morphologies.," For instance, galaxy spectra can be accurately determined to much greater redshifts and for fainter objects than morphologies."927 Also. most large redshift surveys currently taking place will contain many thousands of galaxy spectra but little information relating to the optical morphologies of those galaxies.," Also, most large redshift surveys currently taking place will contain many thousands of galaxy spectra but little information relating to the optical morphologies of those galaxies."928" In particular the separation of different morphological types of galaxies in these redshift surveys will be very useful as a means of separating objects for follow- observations to determine independent distance measurements using either D,—c or the Tully-Fisher relation.", In particular the separation of different morphological types of galaxies in these redshift surveys will be very useful as a means of separating objects for follow-up observations to determine independent distance measurements using either $D_n-\sigma$ or the Tully-Fisher relation.929 In this paper I have tried to quantify the link between galaxy spectra and morphology using several advanced statistical methods: namely. Fisher's linear discriminant and Artificial Neural Networks.," In this paper I have tried to quantify the link between galaxy spectra and morphology using several advanced statistical methods; namely, Fisher's linear discriminant and Artificial Neural Networks."930 The best results produced suggest that it is possible to use optical galaxy spectra to create galaxy samples containing of the Early type galaxies present and of the Late types respectively., The best results produced suggest that it is possible to use optical galaxy spectra to create galaxy samples containing of the Early type galaxies present and of the Late types respectively.931 The contamination between these samples depends on the morphological mix of the survey under consideration., The contamination between these samples depends on the morphological mix of the survey under consideration.932 In the case of the bj-selected 2?4FGRS the most significant contamination will be of mis-classified Late types in the Early type sample (~ contamination). in the case of a near-infrared selected sample this situation will be reversed.," In the case of the $\bj$ -selected 2dFGRS the most significant contamination will be of mis-classified Late types in the Early type sample $\sim40\%$ contamination), in the case of a near-infrared selected sample this situation will be reversed."933 Essentially the results obtained using more advanced statistical techniques (Sections 4 and 5) are comparable to those that could be obtained simply using the default 3HFGRS spectral classification η) (Madgwick 22002) which can be accessed from the 2UFGRSdatabase?., Essentially the results obtained using more advanced statistical techniques (Sections 4 and 5) are comparable to those that could be obtained simply using the default 2dFGRS spectral classification $\eta$ (Madgwick 2002) which can be accessed from the 2dFGRS.934. This is an interesting result and certainly adds significantly to the physical interpretation of this parameter., This is an interesting result and certainly adds significantly to the physical interpretation of this parameter.935 Another interesting aspect of this analysis is that the Fisher discriminant (Section 4) identified the bbreak to be the most essential element of a galaxy's spectrum for the purposes of estimating its morphology., Another interesting aspect of this analysis is that the Fisher discriminant (Section 4) identified the break to be the most essential element of a galaxy's spectrum for the purposes of estimating its morphology.936 This result is somewhat expected since the general correlation between galaxy morphology and colour is already well established., This result is somewhat expected since the general correlation between galaxy morphology and colour is already well established.937 However. it is intriguing to see this result derived in a quantitative manner from the observed spectra themselves.," However, it is intriguing to see this result derived in a quantitative manner from the observed spectra themselves."938 The results presented in this paper are essentially limited by the coarseness of the morphological classification adopted. which for practical reasons can only be divided into two separate types (rather than a more realistic sequence of types).," The results presented in this paper are essentially limited by the coarseness of the morphological classification adopted, which for practical reasons can only be divided into two separate types (rather than a more realistic sequence of types)."939 As larger samples of more accurately morphologically classitied galaxies become available it will be interesting to repeat the analysis presented here. in order to determine whether even more information can be recovered to link a galaxys morphology and spectrum.," As larger samples of more accurately morphologically classified galaxies become available it will be interesting to repeat the analysis presented here, in order to determine whether even more information can be recovered to link a galaxy's morphology and spectrum."940 I wish to thank Ofer Lahav for suggesting this project and providing plenty of invaluable advice and suggestions., I wish to thank Ofer Lahav for suggesting this project and providing plenty of invaluable advice and suggestions.941 Raven Kaldare and Andrew Firth were very helpful in explaining the intricacies of Artificial Neural Networks to me., Raven Kaldare and Andrew Firth were very helpful in explaining the intricacies of Artificial Neural Networks to me.942 I would also like to thank the anonymous referee for their helpful comments on the draft of this paper., I would also like to thank the anonymous referee for their helpful comments on the draft of this paper.943 The efforts of the 2dFGRS collaboration. in preparing and compiling the data used in this analysis. are greatly appreciated.," The efforts of the 2dFGRS collaboration, in preparing and compiling the data used in this analysis, are greatly appreciated."944 This work was supported by an Isaac Newton studentship from the Institute of Astronomy and Trinity College. Cambridge.," This work was supported by an Isaac Newton studentship from the Institute of Astronomy and Trinity College, Cambridge."945low-level of 5-rav. emission for this object which is stable over several vears and strongly constrains the blazar's VILE quicscent state (Aharonianetal.2010).. but whose origin is still unknown.,"low-level of $\gamma$ -ray emission for this object which is stable over several years and strongly constrains the blazar's VHE quiescent state \citep{prep}, but whose origin is still unknown."946 The low state of PINS 2155-304 (2= 0.116) has been studied recently in a multiwavelength campaign by HLIZS.S. and the LAT instrument. onboard Fermi (Abaronianοἱal. 2009).. with which the observations presented. here are simultaneous.," The low state of PKS 2155-304 $z = 0.116$ ) has been studied recently in a multiwavelength campaign by H.E.S.S. and the LAT instrument onboard Fermi \citep{b1c}, with which the observations presented here are simultaneous."947 The time-averaged SED of the source was moceled. as a single-zone svncehrotron-selt. Compton. (88C€) »ocess which fitted the entire profile., The time-averaged SED of the source was modeled as a single-zone synchrotron-self Compton (SSC) process which fitted the entire profile.948 Phe derived relations oetween the optical and VILE fluxes. suggest. that. the ormer provides the target photons for the inverse-C'ompton (1C) emission. but a detailed study of the energeties. of he model shows that a single-zone description cannot accommodate the entire multibanc temporal behaviour of he light-curve.," The derived relations between the optical and VHE fluxes suggest that the former provides the target photons for the inverse-Compton (IC) emission, but a detailed study of the energetics of the model shows that a single-zone description cannot accommodate the entire multiband temporal behaviour of the light-curve."949 Part of the aim of this paper is to exploit he contemporancity of our data to propose an explanation or the lack of temporal correlation observed between the optical and the high-encrey components of the SED. and o give further support to the proposal by Aharonianctal.(2009) that a multi-zone mocel is necessary to describe the cquiescent state emission of this DL Lac.," Part of the aim of this paper is to exploit the contemporaneity of our data to propose an explanation for the lack of temporal correlation observed between the optical and the high-energy components of the SED, and to give further support to the proposal by \cite{b1c} that a multi-zone model is necessary to describe the quiescent state emission of this BL Lac."950 PIS 2155-304 has been the target of several optical »obuimetrie campaigns which have probed its long aud short term behaviour., PKS 2155-304 has been the target of several optical polarimetric campaigns which have probed its long and short term behaviour.951 The polarisation degree is observed ο assume typical values between ~3-74.. with significant variability. registered. down to. sub-hour timescales (e.g. Aneruchowctal. 2005)).," The polarisation degree is observed to assume typical values between $\sim$, with significant variability registered down to sub-hour timescales (e.g. \citealt{micro}) )."952 The polarisation vector. shows evidence of preferential cürection within the range 100-140 (Tommasietaal.(2001). and references therein)., The polarisation vector shows evidence of a preferential direction within the range $^\circ$ \cite{tommasi} and references therein).953 Frequeney dependent polarisation (FDP) has also been detected. on several occasions (Smith&Sitko1991:Smithetal.1992:Allenetal.1993). ancl determined. to be intrinsic to the svnchrotron source.," Frequency dependent polarisation (FDP) has also been detected on several occasions \citep{b22a, b22c, allen} and determined to be intrinsic to the synchrotron source."954 In radio. the parsec-scale. jet. of. PINS 2155-304 was imaged twice at 15 €illz bv Piner&IEcwards(2004) and Pineretal.(2008).," In radio, the parsec-scale jet of PKS 2155-304 was imaged twice at 15 GHz by \cite{b20} and \cite{b21}."955. A single jet component is resolved downstream from the radio core. moving with a derived bulk Lorentz factor E 3.," A single jet component is resolved downstream from the radio core, moving with a derived bulk Lorentz factor $\Gamma \sim$ 3."956 Polarised radio Lux was detected in those images coming from the core component alone. and the polarisation vector (1317) was seen to be closely aligned with the jet-projectecl position angle (PLA.  10-1607).," Polarised radio flux was detected in those images coming from the core component alone, and the polarisation vector $131^\circ$ ) was seen to be closely aligned with the jet-projected position angle (P.A. $\sim$ $^\circ$ )."957 In the optically thin regime this is evidence [or the presence of a dominant. magnetic field. component transverse to the Dow., In the optically thin regime this is evidence for the presence of a dominant magnetic field component transverse to the flow.958 The polarisation degree of the core exhibited a spatial gracient. between that increased in the upstream direction., The polarisation degree of the core exhibited a spatial gradient between that increased in the upstream direction.959 The existence of a preferred. position angle in optical similar to that of the mme-wave core favours the presence of a dominant or large scale component with a regular magnetic ield which is associated with both emissions., The existence of a preferred position angle in optical similar to that of the mm-wave core favours the presence of a dominant or large scale component with a regular magnetic field which is associated with both emissions.960 Furthermore. similar values of the polarisation degree seen in both bands and. the lack of polarised emission [rom other parts of the jet in the VLBI images suggests the unresolved: polarised! optical emission originates in the pe-seale radio core.," Furthermore, similar values of the polarisation degree seen in both bands and the lack of polarised emission from other parts of the jet in the VLBI images suggests the unresolved polarised optical emission originates in the pc-scale radio core."961 “Phis ivpothesis will be adopted here. motivated as well by recent studies which usec VLBI maps to compare the optical »ó»Llarisation properties of the jet with the radio images. ancl associated the variable emission with the position of the 43 Gllz core (Lister 2006)..," This hypothesis will be adopted here, motivated as well by recent studies which used VLBI maps to compare the optical polarisation properties of the jet with the radio images, and associated the variable emission with the position of the 43 GHz core \citep{b15,962jorstad07, gabuzda}. ."963bv lower hybrid waves survive (bx equating the collisional equilibration rate with the wind expansion rale).,by lower hybrid waves survive (by equating the collisional equilibration rate with the wind expansion rate).964 Such densiües are only [ound at or bevond the radial position where ion charge states [reeze in. and so nonthermal electrons appear unlikely to produce a significant change (ο our charge state results. given the other current observational constraints.," Such densities are only found at or beyond the radial position where ion charge states freeze in, and so nonthermal electrons appear unlikely to produce a significant change to our charge state results, given the other current observational constraints."965 However lower hvbrid waves do appear to be a viable means for producing the electron distributions observed in the [ast solar wind., However lower hybrid waves do appear to be a viable means for producing the electron distributions observed in the fast solar wind.966 The determination that 5!=5;M;/wfq?(wfhv;yc0.5—1 is necessary to produce the observed charge states requires the existence of density gradients in the fast wind with scale lengths on the order of the a-particle gvroradius. which is about 0.1 km at 1.5 HR...," The determination that $\gamma ^{\prime}=967\gamma _iM_i/\omega Afq^2\left(\omega /kv_{iy}\right)^2\simeq 0.5-1$ is necessary to produce the observed charge states requires the existence of density gradients in the fast wind with scale lengths on the order of the $\alpha$ -particle gyroradius, which is about 0.1 km at 1.5 $R_{\sun}$."968 Badio scintillation observations demonstrating the existence of such size scales in the solar wind in the ecliptic plane have rather a long history (e.g.Coles&Harmon1939:Armstrong1990:Colesetal. 1991).," Radio scintillation observations demonstrating the existence of such size scales in the solar wind in the ecliptic plane have rather a long history \citep[e.g.][]{coles89,armstrong90,coles91}."969. These are found perpendicular to the magnetic field. with larger size scales (Uvpicallv a factor of LO within 6 A... becoming more isotropic al larger distances) inferred along the radial direction.," These are found perpendicular to the magnetic field, with larger size scales (typically a factor of 10 within 6 $R_{\sun}$, becoming more isotropic at larger distances) inferred along the radial direction."970 Colesοἱal.(1995) inferred. values of dn? in polar regions al solar mininmmn to be around 1/10 to 1/15 of that observed in equatorial regions. but due to a lack of knowledge of n. in polar regions. were unable to sav anvthing about the variation ol ón./n..," \citet{coles95}971 inferred values of $\delta n_e^2$ in polar regions at solar minimum to be around 1/10 to 1/15 of that observed in equatorial regions, but due to a lack of knowledge of $n_e$ in polar regions, were unable to say anything about the variation of $\delta n_e/n_e$."972" The density measurements reviewed in this paper indicate electron clensilies in polar regions a [actor of 1/2 to 1/3 of those in equatorial regions. making ο, in polar regions of similar order to. but still slightly smaller than that in equatorial regions."," The density measurements reviewed in this paper indicate electron densities in polar regions a factor of 1/2 to 1/3 of those in equatorial regions, making $\delta n_e/n_e$ in polar regions of similar order to, but still slightly smaller than that in equatorial regions."973" Absolute values of ón,./n. in coronal hole regions of interest here have been determined observalionally by Ofmanetal.(1997) to be from 0.1 (o a few times 0.1.", Absolute values of $\delta n_e/n_e$ in coronal hole regions of interest here have been determined observationally by \citet{ofman97} to be from 0.1 to a few times 0.1.974 This is smaller than the value ~1 tacitly assumed here. (he consequence of which is discussed further below.," This is smaller than the value $\sim 1$ tacitly assumed here, the consequence of which is discussed further below."975 Gralletal.(1997) present more data on the transition from anisotropy. inside 5-6 H. on scales of order 10 km to isotropy further out. concluding that à real change in the microstructure rather than in Alfvénn wave turbulence takes place. again with reference to (he eclipüe plane.," \citet{grall97} present more data on the transition from anisotropy inside 5-6 $R_{\sun}$ on scales of order 10 km to isotropy further out, concluding that a real change in the microstructure rather than in Alfvénn wave turbulence takes place, again with reference to the ecliptic plane."976" Feldmanetal.(1996) review these interplanetary scintillation observations together wilh Ulysses observations to constrain the high speed wind structure near ils coronal base. and argue that the plasma is ""sufficiently structured to relax through generation of a οκανε instability (hat results in electrostatic waves having A-vectors oriented perpendicular to BY. which is precisely the motivation for the current work."," \citet{feldman96} review these interplanetary scintillation observations together with Ulysses observations to constrain the high speed wind structure near its coronal base, and argue that the plasma is “sufficiently structured to relax through generation of a drift-wave instability that results in electrostatic waves having $k$ -vectors oriented perpendicular to B”, which is precisely the motivation for the current work."977" Grallοἱal.(1997). go further and show that within 6 A24. large scale turbulence is isotropic with a Ixolmogorov spectrum (structure function x scale""). while smaller scale turbulence shows anisotropy with higher structure functions (x scale) than Ixolmogorov turbulence would predict."," \citet{grall97}978 go further and show that within 6 $R_{\sun}$ large scale turbulence is isotropic with a Kolmogorov spectrum (structure function $\propto {\rm scale}^{5/3}$ ), while smaller scale turbulence shows anisotropy with higher structure functions $\propto $ scale) than Kolmogorov turbulence would predict."979 The scale at which, The scale at which980As far as infrared. data is available. 10/11 variable sources show evidence for the presence of a cireumstellar disk.,"As far as infrared data is available, 10/11 variable sources show evidence for the presence of a circumstellar disk."981 Since the disk fractions in the samples are high. this does not imply a statistically significant connection between variability and disk. but it gives several options to explain the nature of the variabilitv.," Since the disk fractions in the samples are high, this does not imply a statistically significant connection between variability and disk, but it gives several options to explain the nature of the variability."982 Without. disks. only two options remain. eclipses by a companion and chromospheric Πάνος.," Without disks, only two options remain, eclipses by a companion and chromospheric flares."983 Both are relatively short events on timescales of hours ancl thus unlikely to be detected: with only two epochs., Both are relatively short events on timescales of hours and thus unlikely to be detected with only two epochs.984 With an accretion disk. additional. explanations become viable: a) variations in the hot spots generated by an accretion shock. b) variable circumstellar extinction. c) variable emission [rom a cust disk. d) eclipses bv optically thick cireumstellar material (2)..," With an accretion disk, additional explanations become viable: a) variations in the hot spots generated by an accretion shock, b) variable circumstellar extinction, c) variable emission from a dusty disk, d) eclipses by optically thick circumstellar material \citep{2001AJ....121.3160C}."985 With two epochs it is not possible to unambiguously decide between these options. however. the colour of the variabilitv gives ao first hint.," With two epochs it is not possible to unambiguously decide between these options, however, the colour of the variability gives a first hint."986 Lot spots ancl extinction cause decreasing amplitudes: towards longer wavelengths. ie. αν<dJ or αν«dif.," Hot spots and extinction cause decreasing amplitudes towards longer wavelengths, i.e. $dK < dJ$ or $dK< dH$."987 The reverse is the case for variable clisk emission., The reverse is the case for variable disk emission.988 Eclipses would cause grey absorption. i.c. similar amplitudes in dilferent. bands.," Eclipses would cause grey absorption, i.e. similar amplitudes in different bands."989 As seen in Table 1.. 5/13 clearly fall in the first category. 2/13 in the second. and 6/13 in the third.," As seen in Table \ref{var}, 5/13 clearly fall in the first category, 2/13 in the second, and 6/13 in the third."990 With reddening laws for standard. dust properties. variable extinction. causes J-band. amplitudes that are 1.5 times larger than in H-band and 2.5 times larger than in the Ix-band (2)... ," With reddening laws for standard dust properties, variable extinction causes J-band amplitudes that are 1.5 times larger than in H-band and 2.5 times larger than in the K-band \citep{2009MNRAS.398..873S}. ."9913 objects from Table 1. fit these requirements (ISO-Oph-21. I5O-Oph-65. NMDBOJ6).," 3 objects from Table \ref{var} fit these requirements (ISO-Oph-21, ISO-Oph-65, MBO46)."992 The other two with decreasing amplitude towards longer wavelength are better explained. by variable hot spots. which causes less colour variations than extinction.," The other two with decreasing amplitude towards longer wavelength are better explained by variable hot spots, which causes less colour variations than extinction."993 For a delinite decision about the nature of. the variability. follow-up spectroscopy and further multi-baand monitoring is required.," For a definite decision about the nature of the variability, follow-up spectroscopy and further multi-band monitoring is required."994 As noted in Sect. 3..," As noted in Sect. \ref{s2},"995 the current sample might still be allectecd by erowcding. companions or other problems with the photometry.," the current sample might still be affected by crowding, companions or other problems with the photometry."996 Particularly the 6 objects with almost equal amplitudes in several bands seem highly interesting for follow-up. as they might contain equivalents to INKII5D (7). which could give detailed insights into the structure of the disk.," Particularly the 6 objects with almost equal amplitudes in several bands seem highly interesting for follow-up, as they might contain equivalents to KH15D \citep{2002PASP..114.1167H} which could give detailed insights into the structure of the disk."997 One other possible application for the results presented. in this paper is to derive constraints for scenarios of “cpisoclic accretion. Le. the hypothesis that a laree fraction of the stellar mass is accreted in short episodic bursts of accretion.," One other possible application for the results presented in this paper is to derive constraints for scenarios of 'episodic accretion', i.e. the hypothesis that a large fraction of the stellar mass is accreted in short episodic bursts of accretion."998 Episodic aceretion might be the explanation for the dramatic outbursts in FU Ori-type objects. and it could. also resolve the problem of the underluminosity of protostars (e.g.2)..," Episodic accretion might be the explanation for the dramatic outbursts in FU Ori-type objects, and it could also resolve the problem of the underluminosity of protostars \citep[e.g.][]{1996ARA&A..34..207H}."999 Based on Spitzer photometry. ? find that half the mass of LT ‘Tauri stars is accreted in only of the Class L lifetime. which is 0.5 MMvr.," Based on Spitzer photometry, \citet{2009ApJS..181..321E} find that half the mass of T Tauri stars is accreted in only of the Class I lifetime, which is $\sim 0.5$ Myr."1000" Fhis implies that episodes with strong accretion of >10.7AZ. vr.to which last in total a few 107 vs are interspersed. with significantly longer quiescent phases with much lower accretion rates (<10""AZ. vr.+)."," This implies that episodes with strong accretion of $>10^{-5}\,M_{\odot}$ $^{-1}$ which last in total a few $10^5$ ys are interspersed with significantly longer quiescent phases with much lower accretion rates $<10^{-6}\,M_{\odot}$ $^{-1}$ )."1001 ‘These numbers are supported bv the available submim data from embedded: protostars (7)., These numbers are supported by the available submm data from embedded protostars \citep{2009ApJ...692..973E}.1002 There is strong interest in episodic accretion [roni jeoretical work on star and planet formation., There is strong interest in episodic accretion from theoretical work on star and planet formation.1003 Numerical simulations of the gravitational cloud collapse (22). actually owediet/ episodic accretion to occur. with duty evcles ii are consistent with the current constraints by the bservations (e.g.. of protostars with accretion rates > ve1 ).," Numerical simulations of the gravitational cloud collapse \citep{2006ApJ...650..956V,2009ApJ...704..715V} actually predict episodic accretion to occur, with duty cycles that are consistent with the current constraints by the observations (e.g., of protostars with accretion rates $>10^{-5}\,M_{\odot}$ $^{-1}$ )."1004 Models of ⋅⋠⋠episodic accretion. can reproduce 16 observed. luminosity spread. in LR diagrams. with uiescent phases of 107 to 10? ver (?)..," Models of episodic accretion can reproduce the observed luminosity spread in HR diagrams, with quiescent phases of $10^3$ to $10^4$ yr \citep{2009ApJ...702L..27B}."1005 Phese Tull? allow for 1¢ formation of low-mass stars. brown cdwarls. and planets via disk fragmentation. and their curation may be critical or the frequency of these objects (?)..," These 'lulls' allow for the formation of low-mass stars, brown dwarfs, and planets via disk fragmentation, and their duration may be critical for the frequency of these objects \citep{2011ApJ...730...32S}."1006 Episodic aceretion causes variability on very. long imescales of hundreds. of vears or more., Episodic accretion causes variability on very long timescales of hundreds of years or more.1007 One wav of improving the constraint on the aforementioned. models is hus to monitor the brightness of large samples of accreting YSOs over long time windows. to identify possible outbursts and derive their frequency.," One way of improving the constraint on the aforementioned models is thus to monitor the brightness of large samples of accreting YSOs over long time windows, to identify possible outbursts and derive their frequency."1008 Ehe increase in accretion rate should. be approximately proportional to the increase in bolometric luminosity. if the gravitational energv. of the accreted material is fully converted to radiation.," The increase in accretion rate should be approximately proportional to the increase in bolometric luminosity, if the gravitational energy of the accreted material is fully converted to radiation."1009 Lt is dillicult to assess the effect of an accretion burst on the near-infrared) magnitudes ancl colours. without knowing the spectral energy. clistribution of theaccretion shockfront and the effects of increased. aceretion on the heating aud," It is difficult to assess the effect of an accretion burst on the near-infrared magnitudes and colours, without knowing the spectral energy distribution of theaccretion shockfront and the effects of increased accretion on the heating and"1010"Then the force-free condition (43)) reads From this we find that and One can see that the spacial part of 7. which we will denote as J!=JT|UD. has the following components parallel and perpendicularto 2! The coellicient 77D, in Eq.760 can be expressed in terms of the electric and magnetic fields ancl their derivatives. making this equation an explicit) expression for ","Then the force-free condition \ref{FFC}) ) reads From this we find that and One can see that the spacial part of $I^\mu$, which we will denote as ${\cal J}^\mu={\cal J}^\mu_\parallel+ {\cal J}^\mu_\perp $, has the following components parallel and perpendicularto $B^\mu$ The coefficient $I^\nu B_\nu$ in \ref{Jpa} can be expressed in terms of the electric and magnetic fields and their derivatives, making this equation an explicit expression for ${\cal J}^\mu_\parallel$."1011"Following Mcelxinney(2006) we first contract the Alaxwell-AmpeérreJy. law (8)) with D"" to find that where the comma indicates partial derivative.", Following \citet{M06} we first contract the Maxwell-Ampérre law \ref{Maxw2}) ) with $B^\mu$ to find that where the comma indicates partial derivative.1012" Phen we contract the Maxwell-Faraday equation (7)) with D, to find that ‘Thus. where the semi-colon stands for covariant dillerentiation."," Then we contract the Maxwell-Faraday equation \ref{Maxw1}) ) with $D_\nu$ to find that Thus, where the semi-colon stands for covariant differentiation."1013" The corresponding expression in Mcelxinney(2006) is a little bit cüllerent because it includes the term 2°D(nas,|nui). which equals to zero."," The corresponding expression in \citet{M06} is a little bit different because it includes the term $ B^\alpha D^\beta(n_{\beta;\alpha}+n_{\alpha;\beta})$, which equals to zero."1014 Collecting all the results. we obtain lt is easy to verify that in the 311 notation I2q.NI is identical to τος. which does not include neither the lapse function nor the shift vector. nor the time derivatives of B and D.," Collecting all the results, we obtain It is easy to verify that in the 3+1 notation \ref{J} is identical to \ref{j}, which does not include neither the lapse function nor the shift vector, nor the time derivatives of $\bB$ and $\bD$ ."1015 lt is a pleasure to thank Maximi Lyutikoy and. Jonathan Alclxinney for stimulating discussions., It is a pleasure to thank Maxim Lyutikov and Jonathan McKinney for stimulating discussions.1016spatial extent. (~630 kpc) the LS diameter feld for the more distant. NGC 1399 is spatially equivalent to the 27-ciameter AIST field.,spatial extent $\sim\!630 \; \mbox{kpc}$ ) – the $1.8^\circ$ -diameter field for the more distant NGC 1399 is spatially equivalent to the $2^\circ$ -diameter M87 field.1017" Within the magnitude range Mp,<10.5 we estimate. by adjusting for completeness ancl using Poisson statistics for uncertainty estimation. that AIST has 25+48 luminous CSSs. or half the number (47+ 12) estimated. for NGC 1399."," Within the magnitude range $M_{b_J}<-10.5$ we estimate, by adjusting for completeness and using Poisson statistics for uncertainty estimation, that M87 has $25\pm8$ luminous CSSs, or half the number $47\pm12$ ) estimated for NGC 1399."1018" ""his finding contrasts sharply with the relative size of the innermost GC populations. usually expressed. as the Iuminositv-scaled specific [requencey Sx? (seereviewby ?).. "," This finding contrasts sharply with the relative size of the innermost GC populations, usually expressed as the luminosity-scaled specific frequency $S_N$ \citep[see review by][]{Elmegreen..1999}. ."1019Dased on observations within 7aremin of AIST and NCC 1399. 7? caleulated Sy of G41 and 3.7+0.8. galaxy luminosities of V=8.54+0.01 and V=9.02+0.06. ancl total GC populations of 4700=400 and 2300300 respectively.," Based on observations within $7 \; \mbox{arcmin}$ of M87 and NGC 1399, \citet{Forte..2002} calculated $S_N$ of $6\pm1$ and $3.7\pm0.8$, galaxy luminosities of $V=8.54\pm0.01$ and $V=9.02\pm0.06$, and total GC populations of $4700\pm400$ and $2300\pm300$ respectively."1020 LU luminous CSSs are simply an extension of the central giant clliptical galaxy GC population. we would expect the Virgo cluster core to have a luminous CSS population 4 times ereater than we have estimated. from. our redshift surveys.," If luminous CSSs are simply an extension of the central giant elliptical galaxy GC population, we would expect the Virgo cluster core to have a luminous CSS population $\sim4$ times greater than we have estimated from our redshift surveys."1021 Even though the Sv estimates are not redshift confirmed we consider they are likely to be accurate within a factor of ~2. so our contrary estimates for the luminous CSS populations may be due either to a real dillerence with the GC populations or to uncertainties inpopulation estimates," Even though the $S_N$ estimates are not redshift confirmed we consider they are likely to be accurate within a factor of $\sim\!2$, so our contrary estimates for the luminous CSS populations may be due either to a real difference with the GC populations or to uncertainties inpopulation estimates"10221981).,.1023 lt was known onlv as a y-ray source unül a promising candidate was detected in N-ravs by the Einstein Observatory (Dignami.Caraveo.&Lamb1933).. and associated with an optical counterpart (Dignamietal.1987:Halpern&Tytler1938:1983).," It was known only as a $\gamma$ -ray source until a promising candidate was detected in X-rays by the Einstein Observatory \citep{bi83}, and associated with an optical counterpart \citep{bi87,ht88,bi88}."1024. Subsequently. Geminga was found to be a rotation-powered pulsar will a period of 237 ms in N-ravs by citephh92.. and in s-ravs by the Energetic Ganuna hay Experiment Telescope (EGRET) on theObservatory (Bertchetal.1992).," Subsequently, Geminga was found to be a rotation-powered pulsar with a period of 237 ms in X-rays by \\citep{hh92}, and in $\gamma$ -rays by the Energetic Gamma Ray Experiment Telescope (EGRET) on the \citep{be92}."1025. Prior to the discovery of the 237 ms spin period of Genminga. claims had been made lor various periods in (he range 5960 s in 5-ravs and in N-ravs (Thompsonetal.1977:MasnouLOTT:Zvskin&Abukanov1983;Bienami.Caraveo.&Paul1984:Zvskin1988:lxaulοἱal. 1985)... but no such detections have been mace in hieh quality A-rayv and οταν observations during the past decade.," Prior to the discovery of the 237 ms spin period of Geminga, claims had been made for various periods in the range 59–60 s in $\gamma$ -rays and in X-rays \citep{th77,ma77,zm83,bi84,zy88,ka85}, but no such detections have been made in high quality X-ray and $\gamma$ -ray observations during the past decade."1026 The optical spectrum of Genmünga is predominantly non-thermal. with possible ion ev¢lotvon features (Martin.Halpern.&Sehimninovich1998:Mignanm.Caraveo.Dienami 1993).," The optical spectrum of Geminga is predominantly non-thermal, with possible ion cyclotron features \citep{mhs98,mcb98}."1027. Sheareretal.(1998) reported optical modulation from Genminga that resembles ils 5-rav light curve.," \cite{sh98}1028 reported optical modulation from Geminga that resembles its $\gamma$ -ray light curve."1029 Geminga is unusual as a rotation-powered pulsar because il is not a strong radio source., Geminga is unusual as a rotation-powered pulsar because it is not a strong radio source.1030 In 1997. three groups (Malofeev&Malov1997;IxuzminLosovskii1997:Shitov&Pugachev1997) claimed detection of pulsed radio emission at 102 MIIz. but observations at other radio [requencies have so [ar been negative (Ramachandran.Lazio 1999)..," In 1997, three groups \citep{mm97,kl97,sp97} claimed detection of pulsed radio emission at 102 MHz, but observations at other radio frequencies have so far been negative \citep{rdi98,mcl99,bfb99,kl99}."1031 A phase-connected ephemeris covering the first 27 vears of 5-ray observations of Geminga was presented and updated by Mattox. Halpern. Caraveo (1998. 2000).," A phase-connected ephemeris covering the first 27 years of $\gamma$ -ray observations of Geminga was presented and updated by Mattox, Halpern, Caraveo (1998, 2000)."1032 In this paper we present the results of a long observation with the CASCA). which allows us to better constrain the hard X-ray spectrum of Geminga and perform pulse-phase spectroscopy.," In this paper we present the results of a long observation with the ), which allows us to better constrain the hard X-ray spectrum of Geminga and perform pulse-phase spectroscopy."1033 X-ray. pulse (mes of arrival are compared with the latest ephemeris from EGRET., X-ray pulse times of arrival are compared with the latest ephemeris from EGRET.1034" Additional constraints on the hard X-ray enussion are derived from an observation by (theExplorer Proportional Counter Arrav PCA),", Additional constraints on the hard X-ray emission are derived from an observation by the Proportional Counter Array PCA).1035 A log of the observations used in this paper is given in Table 1.., A log of the observations used in this paper is given in Table \ref{tbl-1}.1036 A six-day observation ol Geminga was obtained by iin 1999 October 511., A six-day observation of Geminga was obtained by in 1999 October 5–11.1037 Observations by were made in 1996 April and May., Observations by were made in 1996 April and May.1038 EGRET made many 5-rayv. observations of Geminga since 1991. until CGRO was de-orbited in 2000.," EGRET made many $\gamma$ -ray observations of Geminga since 1991, until was de-orbited in 2000."1039(see.e.g..Milosavljevié&Nakar2006:Katzetal.2007).. in which case our analysis should be interpreted as applying to the highest energy accelerated particles. and to the magnetic field component. with its own characteristic correlation length Ager. that has the greatest influence on the dynamics of these particles.,"\citep[see, e.g.,][]{Milosavljevic:06,Katz:07}, in which case our analysis should be interpreted as applying to the highest energy accelerated particles, and to the magnetic field component, with its own characteristic correlation length $\lambda_{\rm def}$, that has the greatest influence on the dynamics of these particles."1040 We also assume that the blastwave propagates into à quasi-homogeneous medium with average density p—yn., We also assume that the blastwave propagates into a quasi-homogeneous medium with average density $\bar \rho\sim m_{\rm p} n$.1041 The highest energy protons can reach the farthest from the shock to a distance Asa)~RSI. where R is the radius of the blastwave. and the factor of one eighth is peculiar to adiabatie spherical ultrarelativistic blastwaves propagating into uniform density media (Blandford&McKee1976).," The highest energy protons can reach the farthest from the shock to a distance $\Delta_p(\gamma_{p,{\rm max}})\sim R/8\Gamma^2$, where $R$ is the radius of the blastwave, and the factor of one eighth is peculiar to adiabatic spherical ultrarelativistic blastwaves propagating into uniform density media \citep{Blandford:76}."1042". Let LU’), denote the energy density in radiation at radius AR in the shock frame which is a fraction equ(απ)/Ew of the total isotropic equivalent energy of the blastwave £j.", Let $U_{\rm sh}$ denote the energy density in radiation at radius $R$ in the shock frame which is a fraction $\epsilon_{\rm rad}=(4\pi/3) R^3 U_{\rm sh}/E_{\rm tot}$ of the total isotropic equivalent energy of the blastwave $E_{\rm tot}$.1043" Equating the inverse Compton power io,ecUn. where sesh~efT Is the electron Lorentz factor in the shock frame. σι is the Thompson cross section. and we neglected the Klein-Nishina effects (e.g..Li&Waxman2006).. to the energy gain ~Μος per DSA cycle of duration ~Ac/eDA,/c. we obtain the maximum Lorentz factor to which electrons can be accelerated. in spite of the cooling. as a function of the Lorentz factor to which the non-cooling protons can be accelerated . LIC.(1) which. as usual. is expressed in the rest frame of the shock upstream."," Equating the inverse Compton power $\frac{4}{3} \sigma_{\rm T} c \gamma_{e,{\rm sh}}^2 U_{\rm sh}$, where $\gamma_{e,{\rm sh}}\sim \gamma_e/\Gamma$ is the electron Lorentz factor in the shock frame, $\sigma_{\rm T}$ is the Thompson cross section, and we neglected the Klein-Nishina effects \citep[e.g.,][]{Li:06}, to the energy gain $\sim \gamma_{e,{\rm sh}} m_e c^2$ per DSA cycle of duration $\sim \Delta_{e,{\rm sh}}/c \sim \Gamma\Delta_e/c$, we obtain the maximum Lorentz factor to which electrons can be accelerated, in spite of the cooling, as a function of the Lorentz factor to which the non-cooling protons can be accelerated , , which, as usual, is expressed in the rest frame of the shock upstream."1044 Here. we have eliminated the blastwave radius R via the relation R2CITE /88T7pc)? applicable to an adiabatic spherical blastwaves propagating into uniform density media (Blandford&McKee1976).," Here, we have eliminated the blastwave radius $R$ via the relation $R=(17 E_{\rm tot}/8\pi\Gamma^2 \bar\rho c^2)^{1/3}$ applicable to an adiabatic spherical blastwaves propagating into uniform density media \citep{Blandford:76}."1045. The magnetic field length scale Ager (in the case of a tangled field) and strength squared do not appear in equation (1)) because they have been Biaexpressed in terms of the maximum proton Lorentz factor that can be accelerated by deflection in a field with these properties via By=[έςπρο”e)/T?|/CR/8T*) (coherent field) and Naotπμο87) (tangled field).," The magnetic field length scale $\lambda_{\rm def}$ (in the case of a tangled field) and strength squared $B_{\rm def}^2$ do not appear in equation \ref{eq:gamma_e_max}) ) because they have been expressed in terms of the maximum proton Lorentz factor that can be accelerated by deflection in a field with these properties via $B_{\rm def} =[(\gamma_{p,{\rm max}} m_p c^2 /e)/\Gamma^3]/(R/8\Gamma^2)$ (coherent field) and $\lambda_{\rm def} B_{\rm def}^2 =[(\gamma_{p,{\rm max}} m_p c^2 /e)^2/\Gamma^4]/(R/8\Gamma^2)$ (tangled field)."1046 The nondimensional distance from the shock that the most energetic electrons can reach. relative to the distance that the protons can reach. can be expressed as (," The nondimensional distance from the shock that the most energetic electrons can reach, relative to the distance that the protons can reach, can be expressed as ."1047"3) For typicalc values of ej4. Tmaxag£i. D. PEtand ‘iyη. thisoy becomes μα... which shows that for ~p.nax»109. regardless of the magnetic field geometry. the electrons are unable to travel as far from the shock as the protons and xo,«I in either case."," For typical values of $\epsilon_{\rm rad}$, $E_{\rm tot}$, $\Gamma$, and $n$, this becomes which shows that for $\gamma_{p,{\rm max}}\gg 10^3$, regardless of the magnetic field geometry, the electrons are unable to travel as far from the shock as the protons and $x_{\rm cool}\ll 1$ in either case."1048 Note that for a coherent confining field STA 40 IT Πεἰά).. implying(GE? that(Gee if the confinement is dominated(7) by a pre- Microgauss upstream magnetic field we expect that v10°—105. while a larger value is expected if the shockpanas precursor generates a magnetic field in which the tangled component dominates particle deflection.," Note that for a coherent confining field 7 10^5 ) , implying that if the confinement is dominated by a pre-existing microgauss upstream magnetic field we expect that $\gamma_{p,{\rm max}} \sim 10^5-10^6$ , while a larger value is expected if the shock precursor generates a magnetic field in which the tangled component dominates particle deflection."1049 Therefore we always expect that xo;«I., Therefore we always expect that $x_{\rm cool}\ll 1$.1050 In what follows. we ignore the interior region A«A.Ceanay) populated by nonthermal particles of either sign and assume that the exterior region A>Ao contains only nonthermal ions. which we have assumed to be protons.," In what follows, we ignore the interior region $\Delta < \Delta_e(\gamma_{e,{\rm max}})$ populated by nonthermal particles of either sign and assume that the exterior region $\Delta > \Delta_e(\gamma_{e,{\rm max}})$ contains only nonthermal ions, which we have assumed to be protons."1051 The nonthermal particle concentration at a given distance ahead of the shock will be dominated by the lowest energy particles that reach that distance., The nonthermal particle concentration at a given distance ahead of the shock will be dominated by the lowest energy particles that reach that distance.1052" Thus. we can relate the nonthermal proton density 7, in the shock upstream to their energy distribution Nap)8) where Δημtup(5) 1s: the total number ofc nonthermal protons inη the shock upstream with Lorentz factors less than >."," Thus, we can relate the nonthermal proton density $n_{\rm ntp}$ in the shock upstream to their energy distribution ), where $N^{({\rm up})}_{\rm ntp}(\gamma)$ is the total number of nonthermal protons in the shock upstream with Lorentz factors less than $\gamma$ ."1053 We assume that the accelerated particle spectrum in the shock downstream resulting from DSA contains equal energy on all energy scales. dNaariel)/dx57= (Lemoine:&Pel-letier2003:Ellison&Double2002.2004.cf. e.g.) this assumption is not critical as somewhat steeper spectra. expected when particle scattering in the shock downstream is not isotropic (e.g..Keshet&Waxman2005:Lemoine&Revenu 2006).. lead to similar conclusions.," We assume that the accelerated particle spectrum in the shock downstream resulting from DSA contains equal energy on all energy scales, $dN_{\rm ntp}^{({\rm down})}/d\gamma \propto \gamma^{-2}$ \citep[cf. e.g.,]{Lemoine:03,Ellison:02,Ellison:04}; this assumption is not critical as somewhat steeper spectra, expected when particle scattering in the shock downstream is not isotropic \citep[e.g.,][]{Keshet:05,Lemoine:06a}, lead to similar conclusions."1054" Ignoring the energy in nonthermal protons located in the upstream. we may normalize the spectrum by requiring that ↷↴⋯∕↗∠⋅−↙⊽∕⊓⋯∠∣↷↴⋮←↽⋯∊⇂↭⇂∙≺⊖⋟ where ey, i5 the fraction of the total energy in the accelerated protons."," Ignoring the energy in nonthermal protons located in the upstream, we may normalize the spectrum by requiring that m_p c^2 =, where $\epsilon_{\rm nt}$ is the fraction of the total energy in the accelerated protons."1055 The minimum Lorentz factor of the nonthermal particles. resulting from a single scattering across the shock is paninvI? (Gallant&Achterberg1999).. but the dependence ON >panin IS only logarithmic.," The minimum Lorentz factor of the nonthermal particles, resulting from a single scattering across the shock is $\gamma_{p,{\rm min}} \sim \Gamma^2$ \citep{Gallant:99}, but the dependence on $\gamma_{p,\rm min}$ is only logarithmic."1056 To relate Nd to Nae”. let P~1 denote the probability that a particle in the shock upstream. upon returning to the shock. is scattered again into the shock upstream.," To relate $N^{({\rm up})}_{\rm ntp}$ to $N^{({\rm down})}_{\rm ntp}$, let $P\sim \frac{1}{2}$ denote the probability that a particle in the shock upstream, upon returning to the shock, is scattered again into the shock upstream."1057 The downstreamthen contains theparticles that are not re- into the upstream. but areentrapped within and are advecting with the downstream.," The downstreamthen contains theparticles that are not re-scattered into the upstream, but areentrapped within and are advecting with the downstream."1058 Conservation of nonthermal proton flux at the shock transitionthen, Conservation of nonthermal proton flux at the shock transitionthen1059for the residuals and the whole procedure was repeated until no feature exceeding ANOVA value of 15 appeared.,for the residuals and the whole procedure was repeated until no feature exceeding ANOVA value of 15 appeared.1060 Both methods yielded the same results within. statistical errors., Both methods yielded the same results within statistical errors.1061 The only discrepancies appeared when a true frequency and its alias had similar amplitudes and the first method preferred one peak while the second method preferred the other., The only discrepancies appeared when a true frequency and its alias had similar amplitudes and the first method preferred one peak while the second method preferred the other.1062 In such a cases we chose the frequency. which vielded a fit with lower c.," In such a cases we chose the frequency, which yielded a fit with lower $\sigma$."1063 In the course of our analysis we identified many RR Lyr variables with secondary periodicities close to the primary (radial) pulsation frequency., In the course of our analysis we identified many RR Lyr variables with secondary periodicities close to the primary (radial) pulsation frequency.1064 These objects. commonly referred to as Blazhko RR Lyr stars. are discussed elsewhere (Moskalik Olech 2008: 2009).," These objects, commonly referred to as Blazhko RR Lyr stars, are discussed elsewhere (Moskalik Olech 2008; 2009)."1065 In six of the RRe variables we detected multiperiodicity of a different kind — a secondary mode appeared at a frequency much higher than the primary one., In six of the $c$ variables we detected multiperiodicity of a different kind – a secondary mode appeared at a frequency much higher than the primary one.1066 These stars are listed in Table I., These stars are listed in Table 1.1067 The most interesting case is variable VIO., The most interesting case is variable V10.1068 Its primary period of δι=0.3749759 day and its light curve are typical for RRe pulsator., Its primary period of $P_1=0.3749759$ day and its light curve are typical for $c$ pulsator.1069 Prewhitening led to discovery of the second frequency. corresponding to the period of P»=0.299176 day.," Prewhitening led to discovery of the second frequency, corresponding to the period of $P_2=0.299176$ day."1070 The resulting period ratio of P2/P)=0.79785 is characteristic for simultaneous pulsation in the first and second overtone (FO/SO double mode variable)., The resulting period ratio of $P_2/P_1=0.79785$ is characteristic for simultaneous pulsation in the first and second overtone (FO/SO double mode variable).1071 The light curve of VIO. its Fourier power spectrum and power spectrum of the prewitened light curve are shown in 1.," The light curve of V10, its Fourier power spectrum and power spectrum of the prewitened light curve are shown in 1."1072 Both £ and the combination peak fj+f» ale clearly visible., Both $f_2$ and the combination peak $f_1+f_2$ ale clearly visible.1073 We note. that the spectral window is not very good and it is possible that the true secondary frequency is at the 1-day alias of the highest peak.," We note, that the spectral window is not very good and it is possible that the true secondary frequency is at the 1-day alias of the highest peak."1074" If this is the case. then P»= day. giving period ratio of P2/P,=0.61371."," If this is the case, then $P_2 =10750.230126$ day, giving period ratio of $P_2/P_1=0.61371$."1076 This solutionis listed in the second line of Table 1., This solution is listed in the second line of Table 1.1077 It yields higher dispersion of the least-square fit. but it cannot be definitely excluded.," It yields higher dispersion of the least-square fit, but it cannot be definitely excluded."1078 Nevertheless. the most likely period ratio in VIO is ~0.80. which makes this star a strong candidate to be the first FO/SO double mode pulsator among RR Lyr variables.," Nevertheless, the most likely period ratio in V10 is $\sim\! 0.80$, which makes this star a strong candidate to be the first FO/SO double mode pulsator among RR Lyr variables."1079 We found five more double mode pulsators with high frequency secondary modes., We found five more double mode pulsators with high frequency secondary modes.1080 Their properties are summarized also in Table |., Their properties are summarized also in Table 1.1081 In 2 we display light curves. original power spectra and power spectra of prewitened light curves of these stars.," In 2 we display light curves, original power spectra and power spectra of prewitened light curves of these stars."1082 Judging from shapes of their light curves. there 1s no doubt that in all five stars the primary frequency corresponds to the first overtone.," Judging from shapes of their light curves, there is no doubt that in all five stars the primary frequency corresponds to the first overtone."1083 There is also no doubt that secondary frequencies are real., There is also no doubt that secondary frequencies are real.1084 The first three star. V350. V8] and V87. are similar to VIO: they display the period ratios of either ~0.80 or ~0.61. depending on the choice of an alias.," The first three star, V350, V81 and V87, are similar to V10: they display the period ratios of either $\sim\! 0.80$ or $\sim\! 0.61$, depending on the choice of an alias."1085 This time. selecting the true alias is not possible. however. because both choices lead to least-square fits of the same quality.," This time, selecting the true alias is not possible, however, because both choices lead to least-square fits of the same quality."1086 We were initially tempted to reject the period ratio of ~0.61 as unphysical., We were initially tempted to reject the period ratio of $\sim\! 0.61$ as unphysical.1087 As it turned out. this would be unjustified.," As it turned out, this would be unjustified."1088 The most surprising result was found for the other two double mode pulsators. V105 and V19.," The most surprising result was found for the other two double mode pulsators, V105 and V19."1089 For these two variables, For these two variables109011998).,1998).1091 These color features will be explored in a later paper., These color features will be explored in a later paper.1092 This dataset is also sufficiently high in S/N to allow us to compare the color of individual pixels with the pixel's surface brightness., This dataset is also sufficiently high in S/N to allow us to compare the color of individual pixels with the pixel's surface brightness.1093" This is accomplished by assigning to each pixel a mean B—V color and a surface brightness, based on its calibrated V flux divided by pixel area."," This is accomplished by assigning to each pixel a mean $B-V$ color and a surface brightness, based on its calibrated $V$ flux divided by pixel area."1094" This plot, using 280,000 pixels above 25 V mag arcsecs? is shown in top panel of Figure 16."," This plot, using 280,000 pixels above 25 $V$ mag $^{-2}$, is shown in top panel of Figure 16."1095 Each color-j/ data point is treated as a 2D gaussian with a standard deviation tied to the color and surface brightness error of the pixel., Each $\mu$ data point is treated as a 2D gaussian with a standard deviation tied to the color and surface brightness error of the pixel.1096 All the pixels are summed and binned to produce the density diagrams in Figure 16., All the pixels are summed and binned to produce the density diagrams in Figure 16.1097A full tutorial is available to new volunteers of the website to illustrate the different questions using real PTF data.,A full tutorial is available to new volunteers of the website to illustrate the different questions using real PTF data.1098" Once a volunteer has examined a candidate, their response is converted into a score, S, as follows."," Once a volunteer has examined a candidate, their response is converted into a score, $S$, as follows."1099constant.,constant.1100 Accordingly. masses based on shear measurements are subject to a possible upward. correction arising from a ‘mass sheet degeneracy," Accordingly, masses based on shear measurements are subject to a possible upward correction arising from a `mass sheet degeneracy'."1101 With sullicienthy wide-field data it is possible to make the assumption that the surface mass density will approach zero at large distances [rom the cluster., With sufficiently wide-field data it is possible to make the assumption that the surface mass density will approach zero at large distances from the cluster.1102 However. with independent knowledge of the magnification of the lens. the mass-sheet degeneracy can be broken regardless of the field of view of the data.," However, with independent knowledge of the magnification of the lens, the mass-sheet degeneracy can be broken regardless of the field of view of the data."1103 Pwo methods have been proposed. to make use of this magnification information and calibrate the absolute scale of the mass distribution. cither through the change of image size at fixed surface brightness (Bartelmann Naravan 1995) or source counts (Broadhurst. Taylor Peacock 1995).," Two methods have been proposed to make use of this magnification information and calibrate the absolute scale of the mass distribution, either through the change of image size at fixed surface brightness (Bartelmann Narayan 1995) or source counts (Broadhurst, Taylor Peacock 1995)."1104" This paper is concerned with exploring the role that infrared imaging ollers in the gravitational depletion (or ""convergence) method for estimating the total masses of clusters.", This paper is concerned with exploring the role that infrared imaging offers in the gravitational depletion (or `convergence') method for estimating the total masses of clusters.1105 The depletion method. was first. suggested: by Aroadhurst. “Taylor Peacock (1995) who predicted. the diminution in background galaxy. surface number density as a function of radius expected behind a lensing cluster.," The depletion method was first suggested by Broadhurst, Taylor Peacock (1995) who predicted the diminution in background galaxy surface number density as a function of radius expected behind a lensing cluster."1106 Here we are concerned with extending the original test to near-infrared wavelengths where. in principle. there are significant advantages. namely the flatter number-count. slope and a more accurate colour discrimination between foreground and background. populations.," Here we are concerned with extending the original test to near-infrared wavelengths where, in principle, there are significant advantages, namely the flatter number-count slope and a more accurate colour discrimination between foreground and background populations."1107 The unique wide-field capabilities of the panoramic near-infrared. Cambridge Infrared Survey lnstrument (CIRSL Beckett 1998) allow us to test the method on the rich cluster Abell 2219 2—0.22).," The unique wide-field capabilities of the panoramic near-infrared Cambridge Infrared Survey Instrument (CIRSI, Beckett 1998) allow us to test the method on the rich cluster Abell 2219 $z$ =0.22)."1108 A plan of the paper follows., A plan of the paper follows.1109 In 62 we review the eravitational depletion method. illustrating the cilliculties associated with its implementation at optical wavelengths and the potential gains of repeating the experiment at near-infrared wavelengths., In $\S$ 2 we review the gravitational depletion method illustrating the difficulties associated with its implementation at optical wavelengths and the potential gains of repeating the experiment at near-infrared wavelengths.1110 In. §32 we present new observations of Abell 2219 made at the prime focus of the 4.2m. William Lerschel telescope and discuss the techniques used to reduce the data as well as the methods used to create a sample of background. galaxies., In $\S$ 3 we present new observations of Abell 2219 made at the prime focus of the 4.2m William Herschel telescope and discuss the techniques used to reduce the data as well as the methods used to create a sample of background galaxies.1111 5&4 discusses the depletion signal observed in the context of various mass models and reviews the uncertainties involved., $\S$ 4 discusses the depletion signal observed in the context of various mass models and reviews the uncertainties involved.1112 In §5 we discuss the prospects of routinely estimating cluster masses using this method both with CIRSL and with the upcoming suite of wide field infrared survey telescopes., In $\S$ 5 we discuss the prospects of routinely estimating cluster masses using this method both with CIRSI and with the upcoming suite of wide field infrared survey telescopes.1113" The gravitational depletion or the ""convergence method of breaking the mass-sheet degeneracy (Broachurst. Taylor. Peacock 1995) relies on the change in the surface number density of background galaxies induced by the magnification elect. of à. gravitational lens."," The gravitational depletion or the `convergence' method of breaking the mass-sheet degeneracy (Broadhurst, Taylor, Peacock 1995) relies on the change in the surface number density of background galaxies induced by the magnification effect of a gravitational lens."1114 Since only source counts are involved. exquisite image quality (essential for. shear measurements) is not. necessary.," Since only source counts are involved, exquisite image quality (essential for shear measurements) is not necessary."1115 Furthermore. as the elect depends on the magnification (i. absolute mass estimates are possible if the redshift’ distribution of the background sources is reasonably well-understood.," Furthermore, as the effect depends on the magnification $\mu$, absolute mass estimates are possible if the redshift distribution of the background sources is reasonably well-understood."1116 Theintrinsic (unlensed) counts my of galaxies brighter than some limiting magnitude m. are transformed. to the observed (lensed) counts 9 by where à is the logarithmic slope of the number counts. Two competing elfects serve to. change the. lensed surface number density of the background galaxies.," Theintrinsic (unlensed) counts $n_{0}$ of galaxies brighter than some limiting magnitude $m$ are transformed to the observed (lensed) counts $n$ by where $\alpha$ is the logarithmic slope of the number counts, Two competing effects serve to change the lensed surface number density of the background galaxies."1117 Source magnification clearly increases the surface number density by magnifving galaxies that would otherwise be lainter than the limiting magnitude., Source magnification clearly increases the surface number density by magnifying galaxies that would otherwise be fainter than the limiting magnitude.1118 Llowever. focusing within the beam. clilutes the overall surface number density.," However, focusing within the beam dilutes the overall surface number density."1119 The net. effect depends on the value of a: for a0.4 there will be an overall increase in observed surface number density. while [or a«O04 a depletion is measured.," The net effect depends on the value of $\alpha$ : for $\alpha>0.4$ there will be an overall increase in observed surface number density, while for $\alpha<0.4$ a depletion is measured."1120 Unfortunately. at the limits where a sizeable [raction of field. galaxies are expected to be behind an intermediate redshift’ cluster. the slope of the optical field. counts.OAL. produces only a weak effect.," Unfortunately, at the limits where a sizeable fraction of field galaxies are expected to be behind an intermediate redshift cluster, the slope of the optical field counts, produces only a weak effect."1121 In. order. to demonstrate the elfect in one of the most massive clusters known. Abell 1689 (2—0.18). Tavlor (1998) restrict their analysis to à red subsample known from blank field studies to have a flatter slope (o« Q4).," In order to demonstrate the effect in one of the most massive clusters known, Abell 1689 $z$ =0.18), Taylor (1998) restrict their analysis to a red subsample known from blank field studies to have a flatter slope $\alpha<0.4$ )."1122 ὃν colour-selecting sources redder than the sequence of cluster spheroidals. Tavlor simultaneously secure a background. population whose à. is sulliciently low or the depletion method. to work. and. with an unlensed surface number densitv of 12 7.," By colour-selecting sources redder than the sequence of cluster spheroidals, Taylor simultaneously secure a background population whose $\alpha$ is sufficiently low for the depletion method to work, and with an unlensed surface number density of 12 $^{-2}$."1123 Fort. Mellier Dantel-Fort. (1997). also search for an optical depletion ellect behind the cluster CL0024|1654. by restricting their search to the magnitude ranges 26«D28 and I1κ26.5 where the slopes are found. to be and0.," Fort, Mellier Dantel-Fort (1997) also search for an optical depletion effect behind the cluster CL0024+1654, by restricting their search to the magnitude ranges $26<B<28$ and $24<I<26.5$ where the slopes are found to be and."112425... However. they apply no colour selection to remove faint cluster members in this magnitude range. and furthermore are left. with an extremely low number density of only a few galaxies per square arcmin.," However, they apply no colour selection to remove faint cluster members in this magnitude range, and furthermore are left with an extremely low number density of only a few galaxies per square arcmin."1125 Similarly. Athreva (in. preparation) use photometric redshifts ο isolate a background. population for their weak lensing analysis of MS. 1005-1934. but ave hamperecl by a small iclel of view and background. clustering.," Similarly, Athreya (in preparation) use photometric redshifts to isolate a background population for their weak lensing analysis of MS 1008-1224, but are hampered by a small field of view and background clustering."1126 Clearly. balancing accurate discrimination of the lensing foreground from the xickeround. population while maintaining both a Ilat slope and sullicicnt numbers of background. galaxies is of crucial importance. and it is for this reason that we turn to wicde- infrared observations.," Clearly, balancing accurate discrimination of the lensing foreground from the background population while maintaining both a flat slope and sufficient numbers of background galaxies is of crucial importance, and it is for this reason that we turn to wide-field infrared observations."1127 llere we are concerned with extending the depletion method to near-infrared wavelengths. and we illustrate the ;xossible advantages via an initial application to the rich cluster Abell 2219.," Here we are concerned with extending the depletion method to near-infrared wavelengths, and we illustrate the possible advantages via an initial application to the rich cluster Abell 2219."1128 The slope of the number counts IHattens at longer wavelengths. because of a reduced: sensitivity o intermecdiate-redshift star forming galaxies (Ellis. 19, The slope of the number counts flattens at longer wavelengths because of a reduced sensitivity to intermediate-redshift star forming galaxies (Ellis 1997).1129 Aloreover. this Hlattening occurs at. progressively brighter apparent magnitudes. s," Moreover, this flattening occurs at progressively brighter apparent magnitudes. ,"1130election. the slope of the countsat infrared. wavelengths is sub-critical with a~0.25 at a relatively bright magnitude of A7 I8.," the slope of the countsat infrared wavelengths is sub-critical with $\alpha1131\sim 0.25$ at a relatively bright magnitude of $K\simeq 18$ ."1132We used the ISIS package to combine [οw of the best-seeiug iunages in each band into a template image. and then subtracted the template from each individual image. alter convolving the template to the seeing iu each iuage.,"We used the ISIS package to combine four of the best-seeing images in each band into a template image, and then subtracted the template from each individual image, after convolving the template to the seeing in each image."1133 The resiπιο subtracted images allowed us to measure all variable sources in tle observed field. including IRS165W.," The resulting subtracted images allowed us to measure all variable sources in the observed field, including IRS16SW."1134 We photometrically calibraed the light οιrves by comparing the brightuess of IRSIGSW in the template image to the brighless 0[isolated stars in the frame., We photometrically calibrated the light curves by comparing the brightness of IRS16SW in the template image to the brightness of isolated stars in the frame.1135 These stars varied by <0.5% over the course of tIe 2001 obse‘ving season: 11e brightuess of these stars were assumed to be the salue as reported by Blum.Sellgren.&DePoy(1996)., These stars varied by $\la 0.5\%$ over the course of the 2001 observing season; the brightness of these stars were assumed to be the same as reported by \citet{bsdp96}.1136. Ilutercoimparisou of 10 of these stars suggests that the absolute caibration of the pleMometry is accurate to ~1056;, Intercomparison of 10 of these stars suggests that the absolute calibration of the photometry is accurate to $\sim10\%$.1137 We note that find the mean Ix brightuess Gay) of IRSIGSW to be ~9.61 mag: we fiidly = 9.50.1 mag., We note that \citet{ott99} find the mean K brightness $m_{K}$ ) of IRS16SW to be $\sim$ 9.61 mag; we find $m_{K}$ $=$ $\pm$ 0.1 mag.1138 The reatively Insignificait differeuce could be due to slight clilferences in the ellective waveleneth of the filers used in the tw«) data sets. since IRSIOSW is very red.," The relatively insignificant difference could be due to slight differences in the effective wavelength of the filters used in the two data sets, since IRS16SW is very red."1139 Our ineastremenut is also cousistent with srevious high auglar resolution measurements of Ην (e.g. Simon e al., Our measurement is also consistent with previous high angular resolution measurements of $m_{K}$ (e.g. Simon et al.1140 1990. Sunons. Hodapp. Becklin 1990. DePoy Sharp 1991. aud Blum. Selleren. DePoy 1996).," 1990, Simons, Hodapp, Becklin 1990, DePoy Sharp 1991, and Blum, Sellgren, DePoy 1996)."1141 We find that the mean H—k color oL IRS168W is 2.620.125 imag., We find that the mean $-$ K color of IRS16SW is $\pm$ 0.15 mag.1142 Previous determinations of the H-Jx color of IRSIGSW inclule QU-EO.0T mae (Blum.Sellgreu.&DePoy1996).. 2.05 mae (Rieke. Rieke. Paul 1989). 2.1-£0.3 1jag (Simous. Hodapp. aud Becklin 1990). 2.£ mae (Ixrabbe el al.," Previous determinations of the $-$ K color of IRS16SW include $\pm$ 0.07 mag \citep{bsdp96}, 2.05 mag (Rieke, Rieke, Paul 1989), $\pm$ 0.3 mag (Simons, Hodapp, and Becklin 1990), 2.4 mag (Krabbe et al."1143 1995). and. 2.8+0.2 (DePoy 5iurp 1991).," 1995), and $\pm$ 0.2 (DePoy Sharp 1991)."1144 Our measurement is generalv consistent. with these previous determiuations. althoug Lit ds somewhat redder than the most precise (e.g. Blum. Selleren. DePoy 1996).," Our measurement is generaly consistent with these previous determinations, although it is somewhat redder than the most precise (e.g. Blum, Sellgren, DePoy 1996)."1145 The mareinaly significant (o) difference between our determination of the H—kx color of IRSIOSW aud tha oL Blum.Selleren.&DePoy(1996) suggests that our H- inaguitudes uay contaiu systematic uncertainties., The marginally significant $\sim$ $\sigma$ ) difference between our determination of the $-$ K color of IRS16SW and that of \citet{bsdp96} suggests that our H-band magnitudes may contain systematic uncertainties.1146 Note that Blum.Selleren.&DePoy(1996) ujeasured the H—kx «‘olor ou a single nigit (13 July 1993). πο the variability of the color of IRSIGSW (see below) does not account for the cdiTerence.," Note that \citet{bsdp96} measured the $-$ K color on a single night (13 July 1993), so the variability of the color of IRS16SW (see below) does not account for the difference."1147 We searched [or the periodic sigial in the H and Ek light. curves of IRSIGSW using the Multibarmonic Aialysis of Variances (ANOVA) period-search algoritlun desc‘ibecl by Cerny (1996)., We searched for the periodic signal in the H and K light curves of IRS16SW using the Multiharmonic Analysis of Variances (ANOVA) period-search algorithm described by \citet{sc96}.1148.. We used a C-Iaunguage implementation based ou a program provided by Christophe Alarc for this anaysis., We used a C-language implementation based on a program provided by Christophe Alard for this analysis.1149 Two harmonies were required to get a good periodogam fit. giving a period . variability of 9.7254 0.005 days. consistent with that reported by Ott.Eckwart.&Cenzel(1999).," Two harmonics were required to get a good periodogram fit, giving a period of variability of $\pm$ 0.005 days, consistent with that reported by \citet{ott99}."1150. The period found or each of the Haud Ex lighteurves was consistent to within tlie stated Πο alid we see LO evicence for higher lrequency overtones., The period found for each of the H and K lightcurves was consistent to within the stated uncertainty and we see no evidence for higher frequency overtones.1151 Figure 3 shows tlie pase-folded light curves a H and Is for IRSIGSW., Figure \ref{fig:f1} shows the phase-folded light curves at H and K for IRS16SW.1152 We note tha the shape of the light curve is similar to that [otud by (1999)., We note that the shape of the light curve is similar to that found by \citet{ott99}.1153. There are some cillerences. however.," There are some differences, however."1154 La particular. our light curve shows more CoutintOUS Chanee in brightsess than that of Ott.Eckhart.&Cenzel(1999):: we see uo evidence of ay part X tlie light curve that remains constant for a substaital fraction of the phase.," In particular, our light curve shows more continuous change in brightness than that of \citet{ott99}; we see no evidence of any part of the light curve that remains constant for a substantial fraction of the phase."1155 Also shown in Figure 3) is the color chauge iu IRSI68W over the period of variation., Also shown in Figure \ref{fig:f1} is the color change in IRS16SW over the period of variation.1156 The H—N color of the source Changes by a total of 0.16250.02 mae (excusive of systematic calibration, The $H-K$ color of the source changes by a total of $\pm$ 0.03 mag (exclusive of systematic calibration1157«mall. about 0.5 (vanPutten2004) up to ~2.5% (Guetta&DellaValle2007).,"small, about 0.5 \citep{van04} up to $\sim 2.5\%$ \citep{gue07}."1158. It suggests the existence of many failed GRD-supernovae. notably supernovae with relativistic ejecta. supernovae with pronounced aspherical explosions and radio- loud supernovae (e.g. Valle(2010) ancl references therein).," It suggests the existence of many failed GRB-supernovae, notably supernovae with relativistic ejecta, supernovae with pronounced aspherical explosions and radio- loud supernovae (e.g. \cite{del10} and references therein)."1159 Therefore. (he rate of events of interest to potential bursts in gravitational waves appears lo be 1-2 orders of magnitude larger than the event rate of successful GRB-supernovae.," Therefore, the rate of events of interest to potential bursts in gravitational waves appears to be 1-2 orders of magnitude larger than the event rate of successful GRB-supernovae."1160 In. addition. also (wpe I1 SNe. whose event rate is 3-4 (times larger (han that of twpe Ib/c (Cappellaro.Evans&Turatto1999:Mannucciοἱal.2005 ).. mav explode and expand asvinmetrically (Ilóflich.Wheeler&Wane1999:Ishikawaοἱal. 1992).. suggesting a sienilicant additional potential for gravitational-waves burst production.," In addition, also type II SNe, whose event rate is 3-4 times larger than that of type Ib/c \citep{cap99,man05}, , may explode and expand asymmetrically \citep{hoe99,ish92}, suggesting a significant additional potential for gravitational-waves burst production."1161 A blind rather than a triggered search for bursts events in the local Universe seems to be appropriate by taking advantage of the all-sky monitoring capability of (he detectors in view of a beaming [actor of gamma-ray bursts of /;«10 (0>25 deg) up to a lew hundred (8~4 deg. Frailetal.(2001):vanPutten&RegimbauDellaValle (2007))).," A blind rather than a triggered search for bursts events in the local Universe seems to be appropriate by taking advantage of the all-sky monitoring capability of the gravitational-wave detectors in view of a beaming factor of gamma-ray bursts of $f_b<10$ $(\theta>25$ deg) up to a few hundred $\theta\sim 4$ deg, \cite{fra01,van03,gue07}) )."1162 A blind search is also expected to be competitive with current X/optical survevs for detecting the shock break-out associated with an emerging CC-SNe. as it lasts onlv a lew dozens or minutes up (o a few hours. and it naturally includes the possibilitv of long GRBs coming from merger events with no supernova. which may be exemplified by the long event GRDO60614 of duraton 102 s discovered by While (he energy output in long gravitational wave bursts (GWDs) produced by rapidly rotating black holes should be large. searching for these bursts by matched. filtering is challenging in view of anticipated phase-incoherence due to turbulent magnetohyvdrodsynamical motions in the inner disk or torus.," A blind search is also expected to be competitive with current X/optical surveys for detecting the shock break-out associated with an emerging CC-SNe, as it lasts only a few dozens or minutes up to a few hours, and it naturally includes the possibility of long GRBs coming from merger events with no supernova, which may be exemplified by the long event GRB060614 of duraton 102 s discovered by While the energy output in long gravitational wave bursts (GWBs) produced by rapidly rotating black holes should be large, searching for these bursts by matched filtering is challenging in view of anticipated phase-incoherence due to turbulent magnetohydrodynamical motions in the inner disk or torus."1163 llere. we focus on the detection of a trajectory in (he time frequency. domain produced bv long GWDs. satisfving phDase-coherence on short up to intermediate timescales.," Here, we focus on the detection of a trajectory in the time frequency domain produced by long GWBs, satisfying phase-coherence on short up to intermediate timescales."1164 This objective goes further (han the detection of a burst signal. with the aim to extract reasonably accurate information on the burst evolution.," This objective goes further than the detection of a burst signal, with the aim to extract reasonably accurate information on the burst evolution."1165 Inevitably. the sensitivity distance lor extracting trajectories is considerably more conservative than the sensitivity clistance [or a detection per se.," Inevitably, the sensitivity distance for extracting trajectories is considerably more conservative than the sensitivity distance for a detection per se."1166 We shall discuss a new matched filtering detection algorithm to detect. trajectories in the lime frequency domain for long GWDs with slowly varving frequencies lasting tens of seconds with intermittent phase coherence., We shall discuss a new matched filtering detection algorithm to detect trajectories in the time frequency domain for long GWBs with slowly varying frequencies lasting tens of seconds with intermittent phase coherence.1167 For a burst lasting 50 s. for example. the algoritlàn searches by matched filtering using segmented templates on a time scale ol. e.g.. 1s. This procedure gives a compromise between optimal matched lillerine. applicable to phase-coherence extending over the entire burst duration as in binary coalescence of two black holes. and second order methods by correlation of independent detector signals in the time-domain.," For a burst lasting 50 s, for example, the algorithm searches by matched filtering using segmented templates on a time scale of, e.g., 1 s. This procedure gives a compromise between optimal matched filtering, applicable to phase-coherence extending over the entire burst duration as in binary coalescence of two black holes, and second order methods by correlation of independent detector signals in the time-domain."1168 For our example. the compromise results in a sensitivity.distance below that," For our example, the compromise results in a sensitivitydistance below that"1169reproduce multiplicity aud pseudo-rapidity distribution of particles. but simulations were done for differen values of menn transverse momenutun of particles in order to estimate the systematic uncertainties of ΠοΠΠ [2]..,"reproduce multiplicity and pseudo-rapidity distribution of particles, but simulations were done for different values of mean transverse momentum of particles in order to estimate the systematic uncertainties of measurements \cite{UA5diff}."1170" Tu UCAS MC generator 0) the cross-section of sinele-diffraction dissociation as a functiou of diffracte «ποια niass Was parauetrized as follows: and masses were generated in the interval from 1.08 GeV (Sin, pony) to vO.05s (see [2]. and [3]. for more At fragmentation of a diffracted. system in siugle-diffractive interaction the distribution of particles is centered around yyclus/M) and covers he rapiditv region from ποAPP) ο ραmlutsfn).", In UA5 MC generator \cite{UA5gener} the cross-section of single-diffraction dissociation as a function of diffracted system mass was parametrized as follows: and masses were generated in the interval from 1.08 GeV $m_{\pi} + m_p$ ) to $\sqrt{0.05s}$ (see \cite{UA5diff} and \cite{UA5gener} for more At fragmentation of a diffracted system in single-diffractive interaction the distribution of particles is centered around $y_0\simeq\ln(\sqrt{s}/M)$ and covers the rapidity region from $y_{min} \simeq \ln(\sqrt{s}m_p/M^2)$ to $y_{max} \simeq \ln(\sqrt{s}/m_p)$.1171 When the lass of the diffracted systel ds αιμα. then the particles are nally concentrated a the forward region., When the mass of the diffracted system is small then the particles are mainly concentrated at the forward region.1172 Iucreasiug he amass of the diffracted system the distribution OVOY o»eudo)rapidities moves to nüd-rapidities and he spread of the distribution becomes wider., Increasing the mass of the diffracted system the distribution over (pseudo)rapidities moves to mid-rapidities and the spread of the distribution becomes wider.1173 Thus acceptances of different trigecrs are sensitive to different imass regious of diffracted svsteni (at given center of mass energv)., Thus acceptances of different triggers are sensitive to different mass regions of diffracted system (at given center of mass energy).1174 Iu particular. if the triggers are uot placed in very forward region then the particles produced frou low-mass diffracted system will not Lit the Tu Ref.," In particular, if the triggers are not placed in very forward region then the particles produced from low-mass diffracted system will not hit the In Ref."1175 |2] UAS claims that masses below 2.5 fe? were alinost never scen by the detector., \cite{UA5diff} UA5 claims that masses below 2.5 $c^2$ were almost never seen by the detector.1176 For this purpose they investigated Ώρος. «ποσολος chhaucing this low-mass region by 50% and studvius the consequences of this eliauge in their Iu Table 1. we present trieeer efficicucics for sinele-diffractive events as reporte by UA5 in Ref [2]., For this purpose they investigated trigger efficiencies enhancing this low-mass region by $\%$ and studying the consequences of this change in their In Table \ref{Tb:TriggEff} we present trigger efficiencies for single-diffractive events as reported by UA5 in Ref \cite{UA5diff}.1177" Those marked with an asterisk were used for the cross-section calculations. while the others were used o calculate the systematic If the triegers of UAS detector were not sensitive o the masses bellow 2.5 οἱ then the triggering efficiency for the case wheu this mass region is enliauced wy HOM must be related with the trigecringOO efficiency uarked with an asterisk with the following relation: UsimgESI the"" oparanieterizatiowaleterization 5 (5)) ομοonc οἱui casils""asilv evaluate the factor in the denominator: Thus the “re-normalized” efficiencies will be: Comparing these uuubers with the corresponding iuubers in Table 1. we conclude that at Vs = 200 CoV the triggers saw some low-ass (AM< 2.5 /e3j sinele-difftactive eveuts but at Vs = 900 GeV hey did not."," Those marked with an asterisk were used for the cross-section calculations, while the others were used to calculate the systematic If the triggers of UA5 detector were not sensitive to the masses bellow 2.5 $c^2$ then the triggering efficiency for the case when this mass region is enhanced by $\%$ must be related with the triggering efficiency marked with an asterisk with the following relation: Using the parameterization \ref{Eq:SDvsM2}) ) one can easily evaluate the factor in the denominator: Thus the ""re-normalized"" efficiencies will be: Comparing these numbers with the corresponding numbers in Table \ref{Tb:TriggEff} we conclude that at $\sqrt{s}$ = 200 GeV the triggers saw some low-mass $M <$ 2.5 $c^2$ ) single-diffractive events but at $\sqrt{s}$ = 900 GeV they did not."1178" This allows us to claim that at 900 GeV UAS performed modcldependent extrapolation o the low-anass region and the seen cross-section of sinele-diffraction dissociation. cll, has αμράσα, by .actor PED1.19 (=Iu(0.055/1.082)EwD/η2 I1n(0.055/2.57)) in: order o obtain the ""total sinele-diffraction cross-section."," This allows us to claim that at 900 GeV UA5 performed model-dependent extrapolation to the low-mass region and the seen cross-section of single-diffraction dissociation, $\sigma_{SD}^{HM}$, has multiplied by factor 1.19 $=\ln(0.05s/1.08^2)/\ln(0.05s/2.5^2)$ ) in order to obtain the ""total"" single-diffraction cross-section."1179 Thus in Eq. CI) , Thus in Eq. \ref{Eq:RSdNsd}) )1180as cross-section of sinele-diffraction dissociation must be understood the following quantity: Iu Ref., as cross-section of single-diffraction dissociation must be understood the following quantity: In Ref.1181 |l] UAS reported the result of measurement of the ratio of the inelastic cross-sections at Vs= 200 aud 900 GeV: The first error is statistical aud the second error systematic which includes contributions of background corrections for lun aud 2-arià trigecrs. trieecr cticiencics ων sinele-diffractive and lon-sinele diffractive processes aud Iwnuinositv," \cite{UA5inelXS} UA5 reported the result of measurement of the ratio of the inelastic cross-sections at $\sqrt{s} =$ 200 and 900 GeV: The first error is statistical and the second error systematic which includes contributions of background corrections for 1-arm and 2-arm triggers, trigger efficiencies for single-diffractive and non-single diffractive processes and luminosity"1182the svstem will be excited strongly by the lorcing compared to the case where the forcing frequency is not close to a natural one.,the system will be excited strongly by the forcing compared to the case where the forcing frequency is not close to a natural one.1183 The purpose of this paper is to explore (he possibility of resonance in [Iux-transport dvnamos relevant to the solar cycle., The purpose of this paper is to explore the possibility of resonance in flux-transport dynamos relevant to the solar cycle.1184 In flux transport dvnamos. (here are several physical properties that help determine the unforced [requencies of (he svstem.," In flux transport dynamos, there are several physical properties that help determine the unforced frequencies of the system."1185 These include differential rotation. meridional circulation. the so-called a-effect. or kinetic helicity. ancl (urbulent magnetic diffusion.," These include differential rotation, meridional circulation, the so-called $\alpha$ -effect, or kinetic helicity, and turbulent magnetic diffusion."1186" It is now well established (Dikpati and Charbonnean. 1999) that. unless the magnetic diffusivitv is very large. meridional flow at the bottom of the dynamo laver is primarily responsible for the real part of (he natural frequency of (he dynamo, which determines (he speed with which induced toroidal ancl poloidal fields near (he bottom migrate toward (he equator."," It is now well established (Dikpati and Charbonneau, 1999) that unless the magnetic diffusivity is very large, meridional flow at the bottom of the dynamo layer is primarily responsible for the real part of the natural frequency of the dynamo, which determines the speed with which induced toroidal and poloidal fields near the bottom migrate toward the equator."1187 Therefore the closeness of the frequency of forcing at the top to the speed of the flow at the bottom could help determine how much cvuamo response there is., Therefore the closeness of the frequency of forcing at the top to the speed of the flow at the bottom could help determine how much dynamo response there is.1188 since (he forcing al the top is created by emergence of concentrated magnetic Πας from ihe bottom. in the form of active regions. and the rate of movement of the zone where aclive regions are found moves toward the equator (not coincidentally) al a rate close to (he meridional flow speed near the bottom. we mieht expect the conditions for resonance to occur in the bottom laver to be favorable.," Since the forcing at the top is created by emergence of concentrated magnetic flux from the bottom, in the form of active regions, and the rate of movement of the zone where active regions are found moves toward the equator (not coincidentally) at a rate close to the meridional flow speed near the bottom, we might expect the conditions for resonance to occur in the bottom layer to be favorable."1189 On the other hand. we know from observations (Ulrich. 2010 ancl references therein) that the meridional flow at the top of the convection zone is loward the poles. opposite to the propagation of the surface forcing as well as 5-10 times faster.," On the other hand, we know from observations (Ulrich, 2010 and references therein) that the meridional flow at the top of the convection zone is toward the poles, opposite to the propagation of the surface forcing as well as 5-10 times faster."1190 Thus we should not expect resonance {ο occur near (he surface., Thus we should not expect resonance to occur near the surface.1191 It is also well known (Ulrich 2010 and references therein) that the meridional circulation varies with (ime., It is also well known (Ulrich 2010 and references therein) that the meridional circulation varies with time.1192 This time variation is now being incorporated into a f[Iux-irausport dvnamo used for prediction by Dikpati aud colleagues., This time variation is now being incorporated into a flux-transport dynamo used for prediction by Dikpati and colleagues.1193 In the 2006 prediction. meridional circulation eenerallv was kept fixed in time.," In the 2006 prediction, meridional circulation generally was kept fixed in time."1194 Dikpati et al (2006). Dikpati and Gilman (2006) recognized that such time variations could be important. but felt they Iacked sullicient knowledge of its variations to include them.," Dikpati et al (2006), Dikpati and Gilman (2006) recognized that such time variations could be important, but felt they lacked sufficient knowledge of its variations to include them."1195 Thev adjusted the time-independent meridional flow aniplitucde lo give the average period of (he past solar evcles. ancl stretched or compressed all the surface forcing data to the same period. to avoid any artificial or non-phyvsical mismatches between the natural diamo period and (he period of the forcing.," They adjusted the time-independent meridional flow amplitude to give the average period of the past solar cycles, and stretched or compressed all the surface forcing data to the same period, to avoid any artificial or non-physical mismatches between the natural dynamo period and the period of the forcing."1196 Bul there can also in principle in the Sun be real dillerences between (he period οἱ the top forcing that was created by the previous cvele. and the Ireqency of equatorwarel propagation associated with the meridional Low speed at the bottom.," But there can also in principle in the Sun be real differences between the period of the top forcing that was created by the previous cycle, and the freqency of equatorward propagation associated with the meridional flow speed at the bottom."1197 In dvnamos forced al the top with a specilied period. (he amplitude of the induced fields within the dvnamo domain will be affected by (his frequency difference.," In dynamos forced at the top with a specified period, the amplitude of the induced fields within the dynamo domain will be affected by this frequency difference."1198 The model we present here in ellect studies how this amplitude is affected. by treating the meridional flow at the bottom as a free parameter while keeping the Ireequency of the top forcing fixed.," The model we present here in effect studies how this amplitude is affected, by treating the meridional flow at the bottom as a free parameter while keeping the frequency of the top forcing fixed."1199First. when the kinetic helicity increases. the number of bound magnetic eigenmocles increases significantly.,"First, when the kinetic helicity increases, the number of bound magnetic eigenmodes increases significantly."1200 Their growth rates. À;. become strongly concentrated near the growth rate of the [astest unbouncl eigenmode. Ay. (," Their growth rates, $\lambda_n$, become strongly concentrated near the growth rate of the fastest unbound eigenmode, $\lambda_0$. ("

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