ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 The results for these cases (not shown) indicate that the VLA can detect them out to z8 and bevond =—30. respectively. while the SIVA caneasily detect ihem bevond z—30.," The results for these cases (not shown) indicate that the VLA can detect them out to $z \sim 8$ and beyond $z \sim 30$, respectively, while the SKA caneasily detect them beyond $z \sim 30$."3 Figure 13. shows the light curves of the energetic Ην afterglows at 2:=6 and v~200 MIIz and at z19 and ν~100 MlIz. as well as the 5o sensitivities of the VLA. LOFAR and SIVA.," Figure \ref{fig:HN} shows the light curves of the energetic HN afterglows at $z=6$ and $\nu \sim 200$ MHz and at $z=13$ and $\nu \sim 100$ MHz, as well as the $5 \sigma$ sensitivities of the VLA, LOFAR and SKA."4 This shows that the VLA. LOFAR and SIXÀ can detect such HN alterglows at low frequencies e100 MlIZ and high redshifts 2~10.," This shows that the VLA, LOFAR and SKA can detect such HN afterglows at low frequencies $\sim 100$ MHz and high redshifts $z \sim 10$."5" The peak flux indicated is about ~107-10"" jeJv at the redshifted 21 cm frequenev. p=1420/(1+2) MIIz. for 2=6."," The peak flux indicated is about $\sim 10^{2}$ $10^{3}$ $\mu$ Jy at the redshifted 21 cm frequency, $\nu=1420/(1+z)$ MHz, for $z \simg 6$."6 The reverse shock enission is comparable to the forward shock emission. aud the redshilt dependence is weak.," The reverse shock emission is comparable to the forward shock emission, and the redshift dependence is weak."7 We also calculated the moderate energy LIN case E~1077 erg and the high density HEN case ncLO? Ὁ to find that the peak flux at ~100 MIIz in both cases is about an order of magnitude below the flix in Figure 13.., We also calculated the moderate energy HN case $E \sim 10^{53}$ erg and the high density HN case $n \sim 10^{2}$ $^{-3}$ to find that the peak flux at $\sim 100$ MHz in both cases is about an order of magnitude below the flux in Figure \ref{fig:HN}.8 One caveat about the ΗΝ emission is (hat one may. have no prior information about the sky position because of the preponderant lack of detected gamma-ray emission., One caveat about the HN emission is that one may have no prior information about the sky position because of the preponderant lack of detected gamma-ray emission.9 However the number of ΗΝ alterglows at 26 on the skv is estimated as ~10 events 107. where brea~101 days is the peak time of the IINe. and we assume a fraction f.~50% of all GRBs on the sky originating at 26 (Bromm&Loeb2002) and. a ratio of the ΗΝ rate to the GRB one fus;conp~ 1.," However the number of HN afterglows at $z \simg 6$ on the sky is estimated as $\sim 10^{3}$ events $^{-1} \times t_{\rm peak} 10f_{z} f_{\rm HN/GRB} \sim 10^{3}$ , where $t_{\rm peak} \sim 10^{3}$ days is the peak time of the HNe, and we assume a fraction $f_{z} \sim 50$ of all GRBs on the sky originating at $z \simg 6$ \citep{bromm02a}11 and a ratio of the HN rate to the GRB one $f_{\rm HN/GRB}\sim 1$ ."12 Thus the imaging of ~40 deg? of sky would lead to one IIN afterglow at zZ 6. while the field of view of the SIVA may be larger than this.," Thus the imaging of $\sim 40$ $^{2}$ of sky would lead to one HN afterglow at $z \simg 6$ , while the field of view of the SKA may be larger than this."13 Thus. LIN alterelows could be detected as a by-product of other related or unrelated observing prograis.," Thus, HN afterglows could be detected as a by-product of other related or unrelated observing programs."14llowever. the sensitivity of the M67 TO morpholoey iuplies that also other effects may influence dt. apart from the metallicity.,"However, the sensitivity of the M67 TO morphology implies that also other effects may influence it, apart from the metallicity."15 The nuclear reaction rates were already ineutioued., The nuclear reaction rates were already mentioned.16 Other possible aspects could be the amount of overshooting. atomic diffusion. aud the pre-nian sequence historv.," Other possible aspects could be the amount of overshooting, atomic diffusion, and the pre-main sequence history."17 Last. but not least. technical details of the stellar evolution codes may play a role.," Last, but not least, technical details of the stellar evolution codes may play a role."18 It is therefore necessary to show that our results do not depend ou the particular numerical code., It is therefore necessary to show that our results do not depend on the particular numerical code.19" As a first. aud crucial step. we have successfully attempted to reproduce the key result by ο,"," As a first, and crucial step, we have successfully attempted to reproduce the key result by VG07."20 This will also show where changes to their procedure are indicated., This will also show where changes to their procedure are indicated.21 The first step concerns the solar model calibration., The first step concerns the solar model calibration.22 Tere. as for the M67 models. VGOT used NACRE unclear reaction rates. the OPAL (Telesias&Rogers1996) and Fergusonctal.(2005) opacities (as is done iu our code). but ignored diffusion.," Here, as for the M67 models, VG07 used NACRE nuclear reaction rates, the OPAL \citep{ri:96} and \citet{af:05} opacities (as is done in our code), but ignored diffusion."23 This point is crucial. as we will show later on.," This point is crucial, as we will show later on."24 Some amount of convective overshooting (see L.1)) was included for the M67 models. but is uot relevant— for the solar calibration.," Some amount of convective overshooting (see \ref{s:over}) ) was included for the M67 models, but is not relevant for the solar calibration."25 For the atimospheres they used the MARCS iodcel (Gustafsson20033., For the atmospheres they used the MARCS model \citep{marcs:2003}.26.. In this respect we differ. since we use standard Eddington grey atinospheres.," In this respect we differ, since we use standard Eddington grey atmospheres."27 However. as shown by VaudeuBerectal.(2008).. this has in our resent case no significant ifiueuce on the tracks ou the nain-sequeuce and subeiaut brauch.," However, as shown by \citet{veeg:2008}, this has in our present case no significant influence on the tracks on the main-sequence and subgiant branch."28 Table contains in the first two rows the resulting solar model parameters by VOOT and in rows 3 aud | he equivalent ones obtained with our code., Table \ref{t:ssm} contains in the first two rows the resulting solar model parameters by VG07 and in rows 3 and 4 the equivalent ones obtained with our code.29 Additionally. we also show the results when using the Dartinouth and LPCODE codes L3)).," Additionally, we also show the results when using the Dartmouth and LPCODE codes \ref{s:codecomp}) )."30 Note that the iuixiug cheth paramecters can never be compared idu their absolute values due to the different formulations of MILT., Note that the mixing length parameters can never be compared in their absolute values due to the different formulations of MLT.31 Overall. the agreement with VGOT for the initial abundances is within with our codes returning systematically lower iuitial metallicities (by 35€)) for the ACSU5 mixture.," Overall, the agreement with VG07 for the initial abundances is within, with our codes returning systematically lower initial metallicities (by ) for the AGS05 mixture."32 Although a small effect. it additionally disfavors the appearance of a convective core in the M67 TO.," Although a small effect, it additionally disfavors the appearance of a convective core in the M67 TO."33 Usine these initial composition values we calculated stellar tracks and isochrones for M67. which we show in Fieure 1.," Using these initial composition values we calculated stellar tracks and isochrones for M67, which we show in Figure \ref{f:vgrep}."34 The πιο values for distance aud reddening are ddeutieal Ίσα].to WOOT., The numerical values for distance and reddening are identical to VG07.35 The boest-fitting isochrones have somewhat higher ages (by 0.3 Car)., The best-fitting isochrones have somewhat higher ages (by 0.3 Gyr).36 The TO aatss is 1.229 respectively 1.200Αν for the old aud Lew conipositiou.," The TO mass is $1.229$ respectively $1.200\,\msun$ for the old and new composition."37 One recognizes the same basic result as in VCO: for the ACGSO05 mixture. the isochrone does rot show the characteristic hook.," One recognizes the same basic result as in VG07: for the AGS05 mixture, the isochrone does not show the characteristic hook."38 However. it cisplavs a slight iuclination indicating the presence of a very small convective core at the TO amass.," However, it displays a slight inclination indicating the presence of a very small convective core at the TO mass."39" Consistent with this norphological sigu. the TO mass is mareinally higher han Mo; which is L175AL... while in the case of the CSOS nüxture it is clearly above A44,=1.139AL..."," Consistent with this morphological sign, the TO mass is marginally higher than $M_\mathrm{ccc}$, which is $1.175\,\msun$, while in the case of the GS98 mixture it is clearly above $M_\mathrm{ccc}=1.139\,\msun$."40 These values appear to be very similar to those found w (ιο (see their Table 1)., These values appear to be very similar to those found by VG07 (see their Table 1).41" This exercise deimoustrates hat we are able to reproduce correctly VGOT and that heir result is independent of the stellar evolution code used,", This exercise demonstrates that we are able to reproduce correctly VG07 and that their result is independent of the stellar evolution code used.42 VQGOT already emphasized. that atomic diffusion (effectively sedimentation) could modify this result as it leads to an increase of metallicity iu the core over time., VG07 already emphasized that atomic diffusion (effectively sedimentation) could modify this result as it leads to an increase of metallicity in the core over time.43 As explained in the previous subsection. this will favor the occurrence of a convective core and reduce Aloe.," As explained in the previous subsection, this will favor the occurrence of a convective core and reduce $M_\mathrm{ccc}$."44 However. the solar model calibration should also iuclude diffusion. as it was shown that onlv with this plivsical effect the best agreement with the seismic Sun can be achieved.," However, the solar model calibration should also include diffusion, as it was shown that only with this physical effect the best agreement with the seismic Sun can be achieved."45 Ouly in this case the solar parameters. in particular the initial composition is determined as accurately as possible.," Only in this case the solar parameters, in particular the initial composition is determined as accurately as possible."46 The corresponding results are listed in Table 1 as, The corresponding results are listed in Table \ref{t:ssm} as47quautum uumber of magnetic [lux tubes Np = eo (ch))—2zLE S) =—,quantum number of magnetic flux tubes N_B = e /( c ) = ) =.48"uec This quautuim uumber is tlie ""hair: an observer at infinity cau measure the correspoucding Poyutiug flux aud infer the nunuber Ny.", This quantum number is the “hair”: an observer at infinity can measure the corresponding Poynting flux and infer the number $N_B$.49 The conserved poloidal magnetice flux (2.3)) implies a oon the horizon of the =aT(GADPPOBySR —— Sp6πῶςPN (T, The conserved poloidal magnetic flux \ref{NB}) ) implies a on the horizon of the = = 6 (.50hepJ) We cau then verify that the resulting wwill have no problem in breaking the vacuum: the rotation of the leads to the appearance of the iuductive wwith a total potential drop within the ool the order sae = GPRSDUE (i, We can then verify that the resulting will have no problem in breaking the vacuum: the rotation of the leads to the appearance of the inductive with a total potential drop within the of the order a e = = (.51SEU This is sufficiently high. to break the vacutun via radiative effects aud produce a highly conducting plasma., This is sufficiently high to break the vacuum via radiative effects and produce a highly conducting plasma.52 Iu additiou. even iu the relatively weak [n]eravitatioual field of astar. the eeneral relativistic effects of the rotatiou of space-time (the Lense-Thirring precessiou) domiuate the accelerating," In addition, even in the relatively weak gravitational field of a, the general relativistic effects of the rotation of space-time (the Lense-Thirring precession) dominate the accelerating"53Opportunity observations carried out with the Swift N-ray Telescope (XRT) aud Ultraviolet and Optical Telescope (UVOT). as well as with 0.1300 GeV fluxes iude public by the Fermi Science Support Center.,"Opportunity observations carried out with the Swift X-ray Telescope (XRT) and Ultraviolet and Optical Telescope (UVOT), as well as with 0.1–300 GeV fluxes made public by the Fermi Science Support Center."54 The observations are described in Section 2.., The observations are described in Section \ref{sec:obs}.55 The light curves. correlation functious. aud SED are discussed iu Section 3..," The light curves, correlation functions, and SED are discussed in Section \ref{sec:results}."56 Photometric monitoring of wwas carried out on the 1 telescope located at Cerro Tololo Tateramerican Observatory (CTIO) with the ANDIC'ANT instiuueut., Photometric monitoring of was carried out on the 1.3m telescope located at Cerro Tololo Interamerican Observatory (CTIO) with the ANDICAM instrument.57" ANDICAAT is a dual-channel nuager with a dichroic that feeds au optical CCD aud an IR imager. which can obtain simultancous data from 0.1 to 2.2 ji,"," ANDICAM is a dual-channel imager with a dichroic that feeds an optical CCD and an IR imager, which can obtain simultaneous data from 0.4 to 2.2 $\mu$."58 Our campaign began with observations in D. VOR aud Jebauds with a cadeuce of oue observation every 2 nights.," Our campaign began with observations in B, V, R and J-bands with a cadence of one observation every 2 nights."59 After it became clear that 3€ 1513 was exhibiting interesting and varied behavior. we added Is-band observations and increased the cadence to one observation every night.," After it became clear that 3C 454.3 was exhibiting interesting and varied behavior, we added K-band observations and increased the cadence to one observation every night."60 The SATARTS photometric data and light curves for aas well as all other Fermi/LAT monitored blazars visible from CTIO are made publicly available on a 1-2 dav timescale ou tle web., The SMARTS photometric data and light curves for as well as all other Fermi/LAT monitored blazars visible from CTIO are made publicly available on a 1-2 day timescale on the web.61 Optical data were bias-subtracted. oversean-subtracted. and flat— fielded— usine —in IRAF.," Optical data were bias-subtracted, overscan-subtracted, and flat fielded using in IRAF."62 The optical photometry was calibrated using published juaenitudes of a secondary standard in the field of 3€ 1513 (Craine1977:Auegioue1971:Fioruccietal. 1998).," The optical photometry was calibrated using published magnitudes of a secondary standard in the field of 3C 454.3 \citep{craine71, angione71, fiorucci98}."63. Infrared data were skv-subtracted. flat fielded. aud dithered images combined using in-house IRAF scripts," Infrared data were sky-subtracted, flat fielded, and dithered images combined using in-house IRAF scripts."64 The infrared. photometry was calibrated using 2\TASS inagnuitudes of a secondary. standard star (the same star used in optical photometry calibration) im the field of 3€ 151.3., The infrared photometry was calibrated using 2MASS magnitudes of a secondary standard star (the same star used in optical photometry calibration) in the field of 3C 454.3.65 We estimated photometric errors by calculating the 1-0 variation in magnitude of comparison stars with comparable magnitude to 3€ 151.3., We estimated photometric errors by calculating the $\sigma$ variation in magnitude of comparison stars with comparable magnitude to 3C 454.3.66" These are as follows: By, = 0.02 mae. Vay = 0.02 mae. R44 = 0.02. Jor — 0.01 mae. and Kay = 0.0L mae."," These are as follows: $_{\rm err}$ = 0.02 mag, $_{\rm67err}$ = 0.02 mag, $_{\rm err}$ = 0.02, $_{\rm err}$ = 0.04 mag, and $_{\rm err}$ = 0.04 mag."68 Figue 3. shows the D-baud lieht curve normalized ο its flux at JD 2151700., Figure \ref{fig:lc} shows the B-band light curve normalized to its flux at JD 2454700.69 Figure 3. shows two SEDs orISLS: one averaged over the actively faring xxiod up to JD 2151750. aud a second averaged over the relatively quiesceut period after that dav.," Figure \ref{fig:sed} shows two SEDs for: one averaged over the actively flaring period up to JD 2454750, and a second averaged over the relatively quiescent period after that day."70 To compute the Huxes. mmeuitiudes were dereddened using the extinction relations in Cardellietal.(1989) together with the value or Ap eiven by Schlegeletal.(1998). aud converted into Hux deusitics using the zero-poiut fluxes even by Desselletal.(1998). and Beckwithetal.(1976) The Fermi Space Telescope (formerly GLAST) was launched ou 11. June 2008.," To compute the fluxes, magnitudes were dereddened using the extinction relations in \citet{cardelli89} together with the value for $_{\rm B}$ given by \citet{schlegel98} and converted into flux densities using the zero-point fluxes given by \citet{bessell98} and \citet{beckwith76}71 The Fermi Space Telescope (formerly GLAST) was launched on 11 June 2008."72" The Fermi observatory Large Area Telescope (LAT) is designed to measure tle cosmic eanuna-rav flux up to ~ 300 (ιο, The LAT is au nuage. wide feld-ofview high-enerew pair conversiou telescope with οπσον range frou ~ 20 MeV to z 300 GeV. and survevs the sky every three hours2007)."," The Fermi observatory Large Area Telescope (LAT) is designed to measure the cosmic gamma-ray flux up to $\sim$ 300 GeV. The LAT is an imaging, wide field-of-view high-energy pair conversion telescope with energy range from $\sim$ 20 MeV to $\gsim$ 300 GeV, and surveys the sky every three hours."73. As a service to the commuuity and im order to support correlated wunltiwaveleneth observations. the LAT Instrument Science Operations Center provides daily aud weekly averaged fluxes for a uuuber of blazars. of which iis onc.," As a service to the community and in order to support correlated multiwavelength observations, the LAT Instrument Science Operations Center provides daily and weekly averaged fluxes for a number of blazars, of which is one."74 Fluxes aud lo uncertainties for three bands. 0.1300 GeV. 0.3.1 GeV. and 1300 GeV. using preliminary iustruinent response functions and calibrations. are made available online roughly once per week. with the caveat that the carly flux estimates are not absolutely calibrated. aud. aay have variatious of up to due to uncorrected systematic effects.," Fluxes and $\sigma$ uncertainties for three bands, 0.1--300 GeV, 0.3–1 GeV, and 1–300 GeV, using preliminary instrument response functions and calibrations, are made available online roughly once per week, with the caveat that the early flux estimates are not absolutely calibrated, and may have variations of up to due to uncorrected systematic effects."75 Because the observed variations are well correlated witli independently iieasured IB. optical. aud UV variations. we conclude the ezuuinia-ray variations will not chauge senificautlv even if they are eventually recalibrated. and in any case. our key results are robust against fluctuations im gauunia-rav intensity.," Because the observed variations are well correlated with independently measured IR, optical, and UV variations, we conclude the gamma-ray variations will not change significantly even if they are eventually recalibrated, and in any case, our key results are robust against fluctuations in gamma-ray intensity."76 We show the ]lieht curve in the 0.1300 GeV band in Figure 3 normalized to its photon fux at JD 2151700., We show the light curve in the 0.1–300 GeV band in Figure \ref{fig:lc} normalized to its photon flux at JD 2454700.77 Fluxes shown in Fieure 3. are computed from the publicly released data in the 0.81 GeV and 1300 Ce bands by assundue a power-law spectru of photon iudex [=2., Fluxes shown in Figure \ref{fig:sed} are computed from the publicly released data in the 0.3–1 GeV and 1–300 GeV bands by assuming a power-law spectrum of photon index $\Gamma$ =2.78 Since being identified in June 2008 as an extraordinarily bright eamuna-rav source (Vittorinietal.2008:Crasparriui 2008).. hhas been the subject of umimerous Swift target of opportunity observations. mceludiug one by PI Douniug covering 22 September - 02 October. 2008.," Since being identified in June 2008 as an extraordinarily bright gamma-ray source \citep{vittorini08, gasparrini08}, has been the subject of numerous Swift target of opportunity observations, including one by PI Bonning covering 22 September - 02 October, 2008."79 The Swift satellite (Coliyelsetal.2001). has three. instruments: a codedanask Burst Alert Telescope (BAT.Dartheluival. 2005).. an N-rav Telescope covering the euergv range 0.220 keV (XRT.Durrowsctal.2005j.. aud an Ultraviolet/Optical Telescope covering 170600 uu (UVOT.Romingetal.2005).," The Swift satellite \citep{gehrels04} has three instruments: a coded-mask Burst Alert Telescope \citep[BAT,][]{barthelmy05}, an X-ray Telescope covering the energy range 0.2–20 keV \citep[XRT,][]{burrows05}, and an Ultraviolet/Optical Telescope covering 170–600 nm \citep[UVOT,][]{roming05}."80 Swift data are made public to the community within a few davs of the observations: therefore we were able to collect all available data within the period of our SMARTS observations., Swift data are made public to the community within a few days of the observations; therefore we were able to collect all available data within the period of our SMARTS observations.81 We reduced the data from the ταν telescope (XRT) aud the Ultraviolet Optical Telescope (CVOT) according to the standard recipes given by the Swift data analysis maunals., We reduced the data from the X-ray telescope (XRT) and the Ultraviolet Optical Telescope (UVOT) according to the standard recipes given by the Swift data analysis manuals.82 For each obsid. the UVOT data for each exposure were co-added with the taskΙ," For each obsid, the UVOT data for each exposure were co-added with the task."83"Ο, The source magnitudes were then computed from a source region of 5.5 arcsec using the taskveotsorrce, which performs aperture photometry on the source aud returns the count rate. fux density. and magnitude in the Swift/UVOT photometric svstem (Pooleetal.2008)."," The source magnitudes were then computed from a source region of 5.5 arcsec using the task, which performs aperture photometry on the source and returns the count rate, flux density, and magnitude in the Swift/UVOT photometric system \citep{poole08}."84. We correct these for interstellar extinction as described iu Section 2.1.., We correct these for interstellar extinction as described in Section \ref{sec:smarts}.85 Lieht curves from the UVOT D and WI bands are shown in Figure 3. and average fluxes before aud after JD 2151750 in Figure 3..," Light curves from the UVOT B and W1 bands are shown in Figure \ref{fig:lc}, and average fluxes before and after JD 2454750 in Figure \ref{fig:sed}."86 For each obsid. the NRT level2 event list was eenerated via0.41.5. with the default filtering and screening criteria. sclecting photon counting (PC) data with NRT event evades 0-12.," For each obsid, the XRT level-2 event list was generated via with the default filtering and screening criteria, selecting photon counting (PC) data with XRT event grades 0-12."87 We extracted the source spectrum from a region centered at the source with a radius of 60 arcsec aud subtracted the backerouud ποια a nearby source-free region., We extracted the source spectrum from a region centered at the source with a radius of 60 arcsec and subtracted the background from a nearby source-free region.88 Spectra were rebiuned to 25 cts/bin. fit with an absorbed power hav. aud the," Spectra were rebinned to 25 cts/bin, fit with an absorbed power law, and the"89The discovery of “eaps” along the blue horizoutal brauch (IB) in globular clusters as well as of loug extensions towards higher temperatures has trieeered several spectroscopic investigations (Moohler 1999 and referencest therein) vieldineo the followineoO results:tCt Two scenarios. have been sugeested to account for. the DIID stars: by a combinatio,The discovery of “gaps” along the blue horizontal branch (HB) in globular clusters as well as of long extensions towards higher temperatures has triggered several spectroscopic investigations (Moehler \cite{moeh99} and references therein) yielding the following results: Two scenarios have been suggested to account for the low gravities of BHB stars:90The discovery of “eaps” along the blue horizoutal brauch (IB) in globular clusters as well as of loug extensions towards higher temperatures has trieeered several spectroscopic investigations (Moohler 1999 and referencest therein) vieldineo the followineoO results:tCt Two scenarios. have been sugeested to account for. the DIID stars: by a combination,The discovery of “gaps” along the blue horizontal branch (HB) in globular clusters as well as of long extensions towards higher temperatures has triggered several spectroscopic investigations (Moehler \cite{moeh99} and references therein) yielding the following results: Two scenarios have been suggested to account for the low gravities of BHB stars:91where 7=0 and £1 (sec YLUS: YLPOs).,where $n=0$ and $\pm 1$ (see YL08; YLP08).92 Using Equatious(C.1)) for (C1)) combined with (09)). we obtain Πο for the evro-resonaut acceleration à2+1. aud d?k=2z42dkdi has been used for fast modes.," Using Equations\ref{fast}) ) for \ref{eq:gyroapp}) ) combined with \ref{eq:Rn}) ), we obtain (w)] for the gyro-resonant acceleration $n=\pm 1$, and $d^{3}k=2\pi k^{2}dk d\eta$ has been used for fast modes."93" Iu the above equation. £ is the injection scale of turbulence. w=kpey(Qo=μμKL.HRchusο,dV?Vi. y=cos. his the cut-off of turbulence cascade due to damping. and J, is second order Bessel function."," In the above equation, $L$ is the injection scale of turbulence, $w={k_{\perp}94 v_{\perp}}/{\Omega}, x=k/k_{\min}=kL, R=vk_{\min}/\Omega, M_{\A}^{2}=95 \delta V^{2}/V_{\A}^{2}$, $\eta=\cos\theta$, $k_{c}$ is the cut-off of turbulence cascade due to damping, and $J_{n}$ is second order Bessel function."96MÀ For the trausit time acceleration (TTD). 7=0. we obtain where £ isthe injection scale of turbulence. «=Ape/O0c=khuRELRchu.AR—óp?Vi.," For the transit time acceleration (TTD), $n=0$, we obtain where $L$ isthe injection scale of turbulence, $w={k_{\perp}97v_{\perp}}/{\Omega}, x=k/k_{\min}=kL, R=vk_{\min}/\Omega, M_{\A}^{2}=98\delta V^{2}/V_{\A}^{2}$."99" Iu the QLT. HR, is replaced by 6 fiction. Equations (C10)) aud (C'L1)) become aud fe"," In the QLT, $R_{n}$ is replaced by $\delta$ function, Equations \ref{eq:appdpg}) ) and \ref{eq:appdpt})) become and )."100" Iu the QLT. HR, is replaced by 6 fiction. Equations (C10)) aud (C'L1)) become aud fee"," In the QLT, $R_{n}$ is replaced by $\delta$ function, Equations \ref{eq:appdpg}) ) and \ref{eq:appdpt})) become and )."101" Iu the QLT. HR, is replaced by 6 fiction. Equations (C10)) aud (C'L1)) become aud fee "," In the QLT, $R_{n}$ is replaced by $\delta$ function, Equations \ref{eq:appdpg}) ) and \ref{eq:appdpt})) become and )."102" Iu the QLT. HR, is replaced by 6 fiction. Equations (C10)) aud (C'L1)) become aud fee 1"," In the QLT, $R_{n}$ is replaced by $\delta$ function, Equations \ref{eq:appdpg}) ) and \ref{eq:appdpt})) become and )."103" Iu the QLT. HR, is replaced by 6 fiction. Equations (C10)) aud (C'L1)) become aud fee 15"," In the QLT, $R_{n}$ is replaced by $\delta$ function, Equations \ref{eq:appdpg}) ) and \ref{eq:appdpt})) become and )."104" Iu the QLT. HR, is replaced by 6 fiction. Equations (C10)) aud (C'L1)) become aud fee 15)"," In the QLT, $R_{n}$ is replaced by $\delta$ function, Equations \ref{eq:appdpg}) ) and \ref{eq:appdpt})) become and )."105We caleulate the mass of A1644 in two wavs.,We calculate the mass of A1644 in two ways.106" Our first mass estimate depends on the ""eaustic technique of Diaferio&Geller(1997).", Our first mass estimate depends on the “caustic” technique of \citet{dia97}.107. A hierarchical clustering model predicts (he existence of two caustic curves with amplitude C2) approximately equal to the escape velocity from the cluster at racius A., A hierarchical clustering model predicts the existence of two caustic curves with amplitude $A(R)$ approximately equal to the escape velocity from the cluster at radius $R$ .108 Dialerio(1999). shows that ACH) is related to the mass of the cluster interior to 2: We use the techniques of Dialerio(1999) wilh smoothing parameter q=25 lo calculate the caustics of A1644 (Figure 8))., \citet{dia99} shows that $A(R)$ is related to the mass of the cluster interior to $R$ : We use the techniques of \citet{dia99} with smoothing parameter $q=25$ to calculate the caustics of A1644 (Figure \ref{fig-caust}) ).109 Of the 141 presumed cluster members. 127 lie within the causties; the lourteen remaining galaxies may in fact be outliers.," Of the 141 presumed cluster members, 127 lie within the caustics; the fourteen remaining galaxies may in fact be outliers."110 Equation 2 automatically excludes these outliers from the caustic mass determination.," Equation \ref{eqn-caustic}111 automatically excludes these outliers from the caustic mass determination."112 Our second mass estimate uses a virial estimator (Dinnev&Tremaine1987): where cj; is the radial velocity of each galaxy. with respect to the cluster mean and H;is the galaxys position relative to the ¢D. This estimator assumes that (he galaxies are embedded in a dilfuse dark matter distribution. and that the spatial arrangement of galaxies traces the dark matter.," Our second mass estimate uses a virial estimator \citep{bin87}: where $v_{p,i}$ is the radial velocity of each galaxy with respect to the cluster mean and is the galaxy's position relative to the cD. This estimator assumes that the galaxies are embedded in a diffuse dark matter distribution, and that the spatial arrangement of galaxies traces the dark matter."113 The virial mass is verv sensitive to outliers., The virial mass is very sensitive to outliers.114" In Figure 9. we first plot M,j,;,; using the 141 galaxies with 10.000 km |«ez<20.000 knis !."," In Figure \ref{fig-massdiff} we first plot $M_{virial}$ using the 141 galaxies with 10,000 km $^{-1}<cz<20,000$ km $^{-1}$."115 The virial mass decreases by a [actor ol two or more. even al large radius. when we include only those galaxies which lie inside the causties.," The virial mass decreases by a factor of two or more, even at large radius, when we include only those galaxies which lie inside the caustics."116 For comparison. we plot. ως for three different values of the smoothing parameter; (he caustic mass is much more robust.," For comparison, we plot $M_{caustic}$ for three different values of the smoothing parameter; the caustic mass is much more robust."117 Equation 3. overestimates (he true value of M because we have not subüiracted the virial surface term (The&White1986)., Equation \ref{virial-eqn} overestimates the true value of $M$ because we have not subtracted the virial surface term \citep{the86}.118". When the surface term C'(r) is included. the corrected virial mass is where p(r) is the radial density distribution.o, is the radial component of the velocity dispersion. aud o(<5) is theintegrated. velocity dispersion within the limiting radius5 (Girardietal.1998 ).."," When the surface term $C(r)$ is included, the corrected virial mass is where $\rho(r)$ is the radial density distribution,$\sigma_r$ is the radial component of the velocity dispersion, and $\sigma(<b)$ is theintegrated velocity dispersion within the limiting radius$b$ \citep{gir98}. ."119however. since (he time for particles to accelerate to their terminal [all speed «S01) is small (Woitke IlLelling 2003).,"however, since the time for particles to accelerate to their terminal fall speed ${\rm v}^{\rm sed}(a)$ is small (Woitke Helling 2003)."120" Even if grains are stopped by a collision. the grains will continue falling under the influence of gravity and they will achieve their terminal drift. velocity again quickly,"," Even if grains are stopped by a collision, the grains will continue falling under the influence of gravity and they will achieve their terminal drift velocity again quickly."121 This does not take turbulent mixing into account which would increase the sedimentation time., This does not take turbulent mixing into account which would increase the sedimentation time.122 Laree-scale convective replenishment is taken into account as part of (he atmosphere simulation where it impacts the dust lormation process and by that the gravitational settling., Large-scale convective replenishment is taken into account as part of the atmosphere simulation where it impacts the dust formation process and by that the gravitational settling.123" We assume that the dust. and the gas (including thermal electrons) have the sametemperature. Z4,=Lina."," We assume that the dust and the gas (including thermal electrons) have the sametemperature, $T_{\rm gas}=T_{\rm dust}$."124 Woitke IPelling (2003) showed that the liberation of latent heat of condensation and the heating bv friction is well balanced by radiative cooling aud inelastic collisions with the gas particles for grain sizes to be expected in clouds of substellar ab(mospheres., Woitke Helling (2003) showed that the liberation of latent heat of condensation and the heating by friction is well balanced by radiative cooling and inelastic collisions with the gas particles for grain sizes to be expected in clouds of substellar atmospheres.125 We further assume that the electrons thermalise with the gas or dust. hence T.=Ta.," We further assume that the electrons thermalise with the gas or dust, hence $T_{\rm e}=T_{\rm126gas}$."127" Ilowever. T.=Ly, may lead to an underestimation of the electron pressure py. as electrons tend to have higher kinetic energies than Ty. in particular when originating from non-equilibrium processes like in streamers."," However, $T_{\rm e}=T_{\rm gas}$ may lead to an underestimation of the electron pressure $p_{\rm e}$ as electrons tend to have higher kinetic energies than $T_{\rm gas}$ in particular when originating from non-equilibrium processes like in streamers."128 For a first approximation. we retain (his assumption and calculate an electron pressure equivalent. We have shown in Sect.," For a first approximation, we retain this assumption and calculate an electron pressure equivalent, We have shown in Sect."129 2? that only turbulence-enhancecl dust-dust collisions are capable of achieving appropriate relative erain-grain velocities to Iree electrons [rom the outer grain lattice (Fig. 12))., \ref{sss:en} that only turbulence-enhanced dust-dust collisions are capable of achieving appropriate relative grain-grain velocities to free electrons from the outer grain lattice (Fig. \ref{fig:col_energy}) ).130 These grains have sizes between z 0.01;an and z 0.5/0 (Fig. 10)).," These grains have sizes between $\approx1310.01\mu$ m and $\approx 0.5\mu$ m (Fig. \ref{fig:grain_size}) )."132 They are made of a mix of silicates (MgoSiO[s]. MgSiOs[s]. S10»|s]) which takes up 280% of the erain volume with 21554 iron inclusions (Figs. 8.. 9)).," They are made of a mix of silicates $_2$ $_4$ [s], $_3$ [s], $_2$ [s]) which takes up $\approx$ of the grain volume with $\approx$ iron inclusions (Figs. \ref{fig:Vd5}, \ref{fig:Vd3}) )."133 Figure 13. compares the atmospheric. (hermal electron. pressure p. as result of the atmosphere simulation (solid black line) with the electron pressure pc resulting from turbulence-enhanced dust-dust collisions producing N23 charges (guided bv," Figure \ref{fig:p_e} compares the atmospheric, thermal electron pressure $p_{\rm e}$ as result of the atmosphere simulation (solid black line) with the electron pressure $p_{\rm134e,col}$ resulting from turbulence-enhanced dust-dust collisions producing N=8 charges (guided by"135For all our LAS sources. apart from Mira aud WA Pc. the Galactic vackeround FIR enüssou was strong. aud offsource spectra were taken to enable the backerouncd to be subtracted from the ou-source spectrum.,"For all our LWS sources, apart from Mira and WX Psc, the Galactic background FIR emission was strong, and off-source spectra were taken to enable the background to be subtracted from the on-source spectrum."136 Galactic backeround flux levels were oulv significant for À>100 yan. The Galactic background emissiou is extended compared to the LAWS beam. and therefore gives rise to strong frineineC»o in both the on- and off-source spectra.," Galactic background flux levels were only significant for $\lambda \ge 100$ $\mu$ m. The Galactic background emission is extended compared to the LWS beam, and therefore gives rise to strong fringing in both the on- and off-source spectra."137 The 1ckeround-subtracted spectra do not show friugiug. oexdicatiug tha the ΟΠΤΗ stars are point-like to the LAWS. as expected.," The background-subtracted spectra do not show fringing, indicating that the OH/IR stars are point-like to the LWS, as expected."138 After averaging and backerouud subtraction (1f llOCCSSIaYV). each observation consisted of ten subspectra (one per detector). which were rescaled by sinall factors to eive the cousisteut fluxes in regions of overlap. auc merged to eive a final spectrum.," After averaging and background subtraction (if necessary), each observation consisted of ten subspectra (one per detector), which were rescaled by small factors to give the consistent fluxes in regions of overlap, and merged to give a final spectrum."139" One of the main eoals of this ar is to study the overall ISO spectra of the selectedi""objects.", One of the main goals of this article is to study the overall ISO spectra of the selected objects.140 Therefore. it Is necessary to jolu he SWS ancl S spectra m such a way that the flux levels and slopes o the spectra agree for xti LWS and SWS.," Therefore, it is necessary to join the SWS and LWS spectra in such a way that the flux levels and slopes of the spectra agree for both LWS and SWS."141" Differences in the fux levels of the IWS and SWS προςra are mostly due to flux calibration Tucerantis,", Differences in the flux levels of the LWS and SWS spectra are mostly due to flux calibration uncertainties.142 Although the spectral shape is very reliable. 1e absolute flux calibration wucertainty is for the SWS at ja (Schaeidt et al. 1996)).," Although the spectral shape is very reliable, the absolute flux calibration uncertainty is for the SWS at 45 $\mu$ m (Schaeidt et al. \cite{schaeidt}) ),"143 and for 1ο TAS at the sue waveleneth (Swinvard et al. 1998) , and for the LWS at the same wavelength (Swinyard et al. \cite{swin98}) ).144Therefore. differences between the flux levels of LAWS aud SWS which are smaller than are acceptable within ie linuts of the combined error bars.," Therefore, differences between the flux levels of LWS and SWS which are smaller than are acceptable within the limits of the combined error bars."145 The SWS and IWS spectra were scaled according to 111 fluxcs in the overlap region., The SWS and LWS spectra were scaled according to their fluxes in the overlap region.146 Generally this resulted iu a shift of less than (see Table 1})., Generally this resulted in a shift of less than (see Table \ref{obs}) ).147 In the case of Mira and WX Psc. a iimch larger shift was required. prestmably due to the laree time interval between the SWS aud LAWS observations of these variable stars.," In the case of Mira and WX Psc, a much larger shift was required, presumably due to the large time interval between the SWS and LWS observations of these variable stars."148 The combined spectra are presented in Fig. l.," The combined spectra are presented in Fig. \ref{fig1},"149 iu AFA units., in $\lambda F_\lambda$ units.150 The spectra are ordered by increasing optical depth in the observed 10-42 silicate absorption. z. aud hence are in approximate order of increasing mass-loss rate. assundue roughlv simular hwunuinosities.," The spectra are ordered by increasing optical depth in the observed $\mu$ m silicate absorption, $\tau_{\rm s}$, and hence are in approximate order of increasing mass-loss rate, assuming roughly similar luminosities."151 By anocdelling the oeifrared excess cluission of O-rich AGB stars. Schutte Ticlens (1989)) aud Justtanout Ticlens (1992)) have determined the dust nass loss rates for several oexdividual O-rich ACB stars.," By modelling the infrared excess emission of O-rich AGB stars, Schutte Tielens \cite{schutte}) ) and Justtanont Tielens \cite{justtiel}) ) have determined the dust mass loss rates for several individual O-rich AGB stars."152 Their results are sumunarizec in Table 2.. where our sources are listed in the same order as in Fig. 1," Their results are summarized in Table \ref{massloss}, where our sources are listed in the same order as in Fig. \ref{fig1}."153 According to Table 2.. our saniple is indeed ordered with increasiug mass loss rate. excludiug WX Psc.," According to Table \ref{massloss}, our sample is indeed ordered with increasing mass loss rate, excluding WX Psc."154" The values of z, measured frou the spectra are the apparent optical depth compared to our continua fit to the overall SED. or to an assiuned silicate emission profile for CRE 2199 and WX Psc."," The values of $\tau_{\rm s}$ measured from the spectra are the apparent optical depth compared to our continuum fit to the overall SED, or to an assumed silicate emission profile for CRL 2199 and WX Psc."155" ""They therefore represent only a part of the total L0-jau silicate optical depth owardls the sources.", They therefore represent only a part of the total $\mu$ m silicate optical depth towards the sources.156 This is evident from Table 2.. where the measured Τ. are quoted. along with he optical depths derived for some of our sources by DmJusttanont Tieleus (1992)). using radiative transter modelling.," This is evident from Table \ref{massloss}, where the measured $\tau_{\rm s}$ are quoted, along with the $\mu$ m optical depths derived for some of our sources by Justtanont Tielens \cite{justtiel}) ), using radiative transfer modelling."157 A, A158A ανασα]. classification scheme for miuor bodies in the outer solar svstem is preseuted by Claciuaetal.(2008) (hereafter GMIV).,A dynamical classification scheme for minor bodies in the outer solar system is presented by \citet{GlaMarVan08} (hereafter GMV).159" Thev define inner classical belt objects as those that have semünajor axes ως than 39.1 AU. are not Centaurs, are not scattered disk objects. and are not in resonant orbits."," They define inner classical belt objects as those that have semimajor axes less than 39.4 AU, are not Centaurs, are not scattered disk objects, and are not in resonant orbits."160" As explained in (ΛΙ, he stable tuner classical belt is not disconuecte from the main classical belt. which contains objects on stable. uon-resonanut orbits with @= I8 AU."," As explained in GMV, the stable inner classical belt is not disconnected from the main classical belt, which contains objects on stable, non-resonant orbits with = $-$ 48 AU."161 GAIV only classify objects that moet certain criteria for having sufficient astrometrv a9 of May 2006., GMV only classify objects that met certain criteria for having sufficient astrometry as of May 2006.162 Thev list 17 as inner classical Iuiper belt objects (hereafter ICKBO) objects. and over 250 main classical Kuiper belt objects (hereafter MCTISBOs)., They list 17 as inner classical Kuiper belt objects (hereafter ICKBO) objects and over 250 main classical Kuiper belt objects (hereafter MCKBOs).163 As more recent astromietry is available. we searched the continuously updated listing ofthe Deep Ecliptic Survey (DES) team (Elliotal.2005) for possible ICKDOs in additioa to those identified i CADW.," As more recent astrometry is available, we searched the continuously updated listing of the Deep Ecliptic Survey (DES) team \citep{Elliot05} for possible ICKBOs in addition to those identified in GMV."164 We searched for objects with < 39.1 AU which the DES team defiuitivelv classifies as “classical” objects based on their detailed orbital integrations.," We searched for objects with $<$ 39.4 AU which the DES team definitively classifies as “classical"" objects based on their detailed orbital integrations."165 Two adcditioua ΠΟΡΟΣ of the iuner classical belt (111897. anc Ww103 QAÀ92) were found in this wav., Two additional members of the inner classical belt (144897 and 2003 QA92) were found in this way.166 Neither of jese objects are classified in (ΛΑΟ, Neither of these objects are classified in GMV.167", Of the 17 ICKBOs identified in CATV. five are classified by the DES teal as “scatteres jer"" objects. rather than classical objects."," Of the 17 ICKBOs identified in GMV, five are classified by the DES team as “scattered near"" objects, rather than classical objects."168 Al five of these objects have orbital inclinations over1, All five of these objects have orbital inclinations over.169"05, Thus. there is some disagreenieut over the classification of some objects in the < 39.1 AU region."," Thus, there is some disagreement over the classification of some objects in the $<$ 39.4 AU region."170" However. all but one of the objects for which colors are available have orbital inclinatious less than103, and so are probably members of the iuner classical belt."," However, all but one of the objects for which colors are available have orbital inclinations less than, and so are probably members of the inner classical belt."171 If we use he CATV classification. augmented by the 2 additional objects. the iuner classical velt has 19 known objects.," If we use the GMV classification, augmented by the 2 additional objects, the inner classical belt has 19 known objects."172 INavelaarsetal.(2009) estimates that the inner disk KDBOs max have a population 10 to 20 times zinaller than the main belt., \citet{CFEPS09} estimates that the inner disk KBOs may have a population 10 to 20 times smaller than the main belt.173" Evidence that the main classical Kuiper Belt is composed of a ""coll aud “lot” population has been presented bv Brown(2001)."," Evidence that the main classical Kuiper Belt is composed of a “cold"" and “hot"" population has been presented by \citet{Brown01}."174.. There is sole evidence of differences in the physical properties between the cold auc hot populations (see. Peisinho.LacerdaaudJewitt(2008) andl references therein)., There is some evidence of differences in the physical properties between the cold and hot populations (see \citet{Pei08} and references therein).175 However the dividing liue iu inclination between the cold aud hot populations is not sharp. and indeed a simple dividing liue may uot be useful. as the two populations may overlap.," However the dividing line in inclination between the cold and hot populations is not sharp, and indeed a simple dividing line may not be useful, as the two populations may overlap."176 Drown(2001) models the two populatious as separate Gaussians in inclination. with the cold population having == aaud the hot having aaround177.," \citet{Brown01} models the two populations as separate Gaussians in inclination, with the cold population having = and the hot having around."177. Culbis.ElliotaudKane(2006) use a inclination of about tto separate cold (core) and hot (halo) classical objects., \citet{Gulbis06} use a inclination of about to separate cold (core) and hot (halo) classical objects.178 Towever. Poeixiulho.LacerdaaudJewitt(2008) fud that tli colors of classical main belt objects are uniforiuly red up to an inclination of 12°-- that is. they do not see a break iu colors at57.," However, \citet{Pei08} find that the colors of classical main belt objects are uniformly red up to an inclination of - that is, they do not see a break in colors at."179. Our initial eoa was fo measure the color of ICKDOs with he lowest values of aud as these could ο an extension of the main cold classical belt awards the Sun.," Our initial goal was to measure the color of ICKBOs with the lowest values of and, as these could be an extension of the main cold classical belt towards the Sun."180 If this were the case. the inner objects would exteud the seniunajor axis range of the classical belt aud provide a larger range of sciunmajor axis in which to look for correlations between seniuajor axis and plivsical properties than the «range provided bv the main cold classical belt KBOs alone.," If this were the case, the inner objects would extend the semimajor axis range of the classical belt and provide a larger range of semimajor axis in which to look for correlations between semimajor axis and physical properties than the range provided by the main cold classical belt KBOs alone."181 However. new results on the structure of the Ixuiper Belt obtained from surveys analyzed with observational biases taken iuto account (Navelaarsetal.2009) indicate the possibility that the iucr t objects are not analogous to the cold main belt but are perhaps more analogous to the hot classical volt objects;," However, new results on the structure of the Kuiper Belt obtained from surveys analyzed with observational biases taken into account \citep{CFEPS09}182 indicate the possibility that the inner belt objects are not analogous to the cold main belt but are perhaps more analogous to the hot classical belt objects."183 Such ho objects originate αἲ siguificantlv different heliocentrie distances upared to thei prescut locations., Such hot objects originated at significantly different heliocentric distances compared to their present locations.184 Iavelaarsetal.(2009) argue. from the uuuber of expectec and observed Πιο disk objects at low.. that the ιο disk is most likely devoid of a col coniponcnt. bu this conclusion is uncertain due to the small uuuber of Πο disk objects fou so far in their survey.," \citet{CFEPS09} argue, from the number of expected and observed inner disk objects at low, that the inner disk is most likely devoid of a cold component, but this conclusion is uncertain due to the small number of inner disk objects found so far in their survey."185 Tn contradiction to the I&aveliuusetal.(2009) results. LykawkaaudMui(2007) specifically posit a cold πιο disk.," In contradiction to the \citet{CFEPS09} results, \citet{LykMuk07} specifically posit a inner disk."186 These authors state that cold classical KBOs ave located in the inucr disk reeion- 37 AU <a < LAU (q < 37 AU) as well as. ofcourse. in the main belt region (12 AU <a < 17.5 AU).," These authors state that cold classical KBOs are located in the inner disk region- 37 AU $<$ a $<$ 40AU (q $<$ 37 AU)- as well as, ofcourse, in the main belt region (42 AU $<$ a $<$ 47.5 AU)."187 Thus. to sumunarize. the iuner classical disk," Thus, to summarize, the inner classical disk"188IRAS 07140-2321 (also known as S.XO 173329) is a PAGB star belonging to a spectroscopic binary with a cust. circumbinarvy disc (Van Winckel et al.,IRAS 07140-2321 (also known as SAO 173329) is a PAGB star belonging to a spectroscopic binary with a dusty circumbinary disc (Van Winckel et al.189 2000. De Ruyter ct al.," 2000, De Ruyter et al."190 2006: Giclen et al., 2006; Gielen et al.191 2008)., 2008).192 Ehe orbital period is 116 days (De Ruyter et al., The orbital period is 116 days (De Ruyter et al.193 2006)., 2006).194 Photometricallv. the star is an irregular small amplituce variable for which Wiss et al. (," Photometrically, the star is an irregular small amplitude variable for which Kiss et al. ("1952007) suggests variations with periods of about 24 and 60 clays.,2007) suggests variations with periods of about 24 and 60 days.196 Here. we are responding to a call by Van Winckel (1997) who published the only previously reported abundance anavsis and wrote “SAO 173329 is à metal-deficient object for which more data are needed.," Here, we are responding to a call by Van Winckel (1997) who published the only previously reported abundance analysis and wrote `SAO 173329 is a metal-deficient object for which more data are needed'."197" Specificallv. Van Winckel notec the lack of an oxvgen abundance determination and the need for ""more &ood lines."," Specifically, Van Winckel noted the lack of an oxygen abundance determination and the need for `more good lines'."198 Phe lack of abundance data for heavy or s-process elements was also a notable omission., The lack of abundance data for heavy or $s$ -process elements was also a notable omission.199 Results from our analysis summarized in Table 6 are based on the model atmosphere summarized. in Table. 2., Results from our analysis summarized in Table 6 are based on the model atmosphere summarized in Table 2.200 The star is metal-poor: Fe/ll] =0.9., The star is metal-poor: [Fe/H] $= -0.9$.201 The C/O ratio of 0.4 and the limited data on heavy element abundances show that this star did not evolve from a thermally pulsing ACD star., The C/O ratio of 0.4 and the limited data on heavy element abundances show that this star did not evolve from a thermally pulsing AGB star.202 The N abundance shows evidence of Ν enrichment bv the First Dredge-Up (FDU)., The N abundance shows evidence of N enrichment by the First Dredge-Up (FDU).203 The observed. N/Fe] after Non-L'TE correction of 0.4 dex (Lyubimkoy et al., The observed [N/Fe] after Non-LTE correction of $-0.4$ dex (Lyubimkov et al.204 2011) is |0.3 dex which is similar to FDU prediction of | 0.5 dex as eiven in Schaller (1092)., 2011) is $+0.3$ dex which is similar to FDU prediction of $+$ 0.5 dex as given in Schaller (1992).205 Heavy elements Y. Zr and Ba are not enriched. relative to Fe.," Heavy elements – Y, Zr and Ba are not enriched relative to Fe."206 For elements in common. our abundances are in fair agreement with those reported. by Van Winckel (1997) who used solar gf-values and a dilferent evicl of model atmospheres.," For elements in common, our abundances are in fair agreement with those reported by Van Winckel (1997) who used solar -values and a different grid of model atmospheres."207 Abundance dillerences between those in Table 6 and those reported. by Van Winckel for a 7000 Ix. model atmosphere are small (except. for and Cr1)): 8. N/Ee] (present. work ΑΛΛΟ) is 0.20 dex forCr. [0.11 dex forNr. 10.43 dex for St. 0.22 forCat. 0.22 forVit. | 0.37 forCri. [0.14 forMn... | 0.13 for Nirand 0.03 for Zn.," Abundance differences between those in Table 6 and those reported by Van Winckel for a 7000 K model atmosphere are small (except for and ): $\delta$ [X/Fe] (present work $-$ VW97) is $-$ 0.20 dex for, $+$ 0.11 dex for, $+$ 0.43 dex for $-$ 0.22 for, $-$ 0.22 for, $-$ 0.37 for, $+$ 0.14 for, $+$ 0.13 for and $-$ 0.03 for ."208 The inspection of the estimated abundances shows that the observed S/Ee] is. 10.6: the possible a enrichment. of [0.3 dex expected at Fe/l of 0.9 may. indicate actual S/Fe] of 10.3 dex., The inspection of the estimated abundances shows that the observed [S/Fe] is $+$ 0.6; the possible $\alpha$ enrichment of $+$ 0.3 dex expected at [Fe/H] of $-$ 0.9 may indicate actual [S/Fe] of $+$ 0.3 dex.209 But nearly zero. Zn/Ec] and. lack of depletion for high Te: elements Ca and Se shows that the star is not alfected. by dust-gas winnowing., But nearly zero [Zn/Fe] and lack of depletion for high $_{C}$ elements Ca and Sc shows that the star is not affected by dust-gas winnowing.210 Lt is surprising eiven the fact that the star is a spectroscopic binary with an orbital period of only 115.9 days (Van Winckel & Revniers 2000) and has detected. circumstellar material., It is surprising given the fact that the star is a spectroscopic binary with an orbital period of only 115.9 days (Van Winckel $\&$ Reyniers 2000) and has detected circumstellar material.211 I0 appears that conditions or effective dust-gas winnowing are far from unclerstooct., It appears that conditions for effective dust-gas winnowing are far from understood.212 This cool variable exhibits TiO. bands in its spectrum ab dts Coolest. phases (IxIochkoya Panchuk 1996) which necessarily impair a full abundance analysis at such phases., This cool variable exhibits TiO bands in its spectrum at its coolest phases (Klochkova Panchuk 1996) which necessarily impair a full abundance analysis at such phases.213 Luck Bond (1989) undertook an analysis of an image-tube spectrum. obtained in 1981 and found the star was metal-»or Fe/1]— 1.0) with a larger under-abundance of s-oocess elements., Luck Bond (1989) undertook an analysis of an image-tube spectrum obtained in 1981 and found the star was metal-poor $=-1.0$ ) with a larger under-abundance of $s$ -process elements.214 Noting that all of the elements deficient with respect to iron. had. second. ionization. potentials less han the ionization potential of hydrogen. they speculated hat Lyman continuum emission [roni shock waves in he atmosphere over-ionized. these elements and. therefore hey appear under-abundant when a standard analysis with a classical atmosphere is. performed.," Noting that all of the elements deficient with respect to iron had second ionization potentials less than the ionization potential of hydrogen, they speculated that Lyman continuum emission from shock waves in the atmosphere over-ionized these elements and therefore they appear under-abundant when a standard analysis with a classical atmosphere is performed."215" Wlochkova ""anchuük (1996...1998) reported abundance analysesfrom CCD spectra of AL CAL taken at three different: epochs."," Klochkova Panchuk (1996,1998) reported abundance analysesfrom CCD spectra of AI CMi taken at three different epochs."216"rrates, less than a factor of 2 in the temperature range logT=7.8—7.9.","rates, less than a factor of 2 in the temperature range $\log T = 7.8 - 7.9$."217 The evolutionary characteristics of the core helium flash and the hydrogen mixing event are summarized in Table 2.., The evolutionary characteristics of the core helium flash and the hydrogen mixing event are summarized in Table \ref{tab:he-flash}.218" Each column gives the model identifier defined in Table 1,, the helium core mass Mi@X and the helium burning rate pEMax when the helium burning rate reaches maximum, the mass coordinate Mp(g and the maximum temperature TEB!3X at the base of the convective shell, driven by the core helium flash, the helium burning rate LIM* at the onset of hydrogen mixing at the RGB, and the time intervals, At’) and Af, to it from the appearance of helium flash-driven convection and from the stage of maximum helium burning, respectively."," Each column gives the model identifier defined in Table \ref{tab:model}, the helium core mass $M_{1}\ups{max}$ and the helium burning rate $L\lows{He}\ups{max}$ when the helium burning rate reaches maximum, the mass coordinate $M\lows{BCS}$ and the maximum temperature $T\lows{BCS}\ups{max}$ at the base of the convective shell, driven by the core helium flash, the helium burning rate $L\lows{He}\ups{mix}$ at the onset of hydrogen mixing at the RGB, and the time intervals, $\Delta t^\prime$ and $\Delta t\lows{mix}$, to it from the appearance of helium flash-driven convection and from the stage of maximum helium burning, respectively."219 The mass M; of helium core is defined as the mass coordinate where the abundance of hydrogen is half of the surface abundance of hydrogen., The mass $M_1$ of helium core is defined as the mass coordinate where the abundance of hydrogen is half of the surface abundance of hydrogen.220" In this section, we discuss in detail the evolutionary behavior of mmodels with respect to the differences in initial mass and input physics."," In this section, we discuss in detail the evolutionary behavior of models with respect to the differences in initial mass and input physics."221 Variations in several quantities characterizing model stars are summarized in Figure 4 as a function of the hydrogen abundance at the center., Variations in several quantities characterizing model stars are summarized in Figure \ref{fig:phys} as a function of the hydrogen abundance at the center.222" In a mmodel, due to the absence of CNO catalysts, p-p chain reactions are initially the only mode of energy generation by hydrogen burning."," In a model, due to the absence of CNO catalysts, p-p chain reactions are initially the only mode of energy generation by hydrogen burning."223" Because of the weak temperature dependence of the energy-generation rate, the central temperature keeps rising as the hydrogen abundance decreases (top panel of Fig. 4))."," Because of the weak temperature dependence of the energy-generation rate, the central temperature keeps rising as the hydrogen abundance decreases (top panel of Fig. \ref{fig:phys}) )."224" As the central temperature increases, the ggradually becomes active and CNO-cycle reactions begin to occur."," As the central temperature increases, the gradually becomes active and CNO-cycle reactions begin to occur."225" Eventually, CNO-cycle reactions dominate the p-p chains with regard to total energy production."," Eventually, CNO-cycle reactions dominate the p-p chains with regard to total energy production."226" When this first occurs, the central abundance by mass of catalysts is 107—107? at logT,cXqno7.8—7.9 (top and middle panels of Fig. 4))."," When this first occurs, the central abundance by mass $X \lows{CNO}$ of catalysts is $10^{-11} - 10^{-9}$ at $\log T_{c} \simeq 7.8 - 7.9$ (top and middle panels of Fig. \ref{fig:phys}) )."227" Because of lower central temperatures, the less massive the star, the later is the evolutionary stage (and the smaller is the central hydrogen abundance) at which the transition from burning dominated by the p-p chains to burning dominated by the CNO-cycle reactions takes place."," Because of lower central temperatures, the less massive the star, the later is the evolutionary stage (and the smaller is the central hydrogen abundance) at which the transition from burning dominated by the p-p chains to burning dominated by the CNO-cycle reactions takes place."228" For M<0.8Mo, hydrogen is depleted in the center before a transition can take place."," For $M \leq 0.8 \msun$, hydrogen is depleted in the center before a transition can take place."229" After the CNO cycle takes over as the main source of energy generation, because of the strong temperature dependence of CNO-cycle reactions, the central temperature remains nearly constant."," After the CNO cycle takes over as the main source of energy generation, because of the strong temperature dependence of CNO-cycle reactions, the central temperature remains nearly constant."230" At the same time, the core expands because of the central concentration of energy generation and the rate of production of catalysts slows down; the abundances of catalysts saturate at Xango~1071?—1075."," At the same time, the core expands because of the central concentration of energy generation and the rate of production of catalysts slows down; the abundances of catalysts saturate at $X \lows{CNO} \simeq 10^{-10} - 10^{-8}$."231 The transition to the CNO-cycle dominated phase is accompanied by the formation of a convective zone which develops outward from the center as described in the lower panel of Fig. 4.., The transition to the CNO-cycle dominated phase is accompanied by the formation of a convective zone which develops outward from the center as described in the lower panel of Fig. \ref{fig:phys}.232" The growth of the convective core is also evident in the middle panel of Fig. 4,,"," The growth of the convective core is also evident in the middle panel of Fig. \ref{fig:phys},"233" which shows that the hydrogen abundance at the center, X,, stops decreasing monotonically and increases for a time as evolution progresses."," which shows that the hydrogen abundance at the center, $X_{c}$, stops decreasing monotonically and increases for a time as evolution progresses."234" Central convection is caused by a thermonuclear runaway and persists after the transition; due to the larger temperature dependence of the CNO-cycle energy-generation rate, energy generation is highly concentrated toward the center."," Central convection is caused by a thermonuclear runaway and persists after the transition; due to the larger temperature dependence of the CNO-cycle energy-generation rate, energy generation is highly concentrated toward the center."235 Both the inward mixing of hydrogen from outer hydrogen-rich layers and the outward mixing of CNO elements generated near the center during the thermonuclear runaway amplify the average hydrogen-burning rate over the region encompassed by convection relative to the average rate in the absence of convection., Both the inward mixing of hydrogen from outer hydrogen-rich layers and the outward mixing of CNO elements generated near the center during the thermonuclear runaway amplify the average hydrogen-burning rate over the region encompassed by convection relative to the average rate in the absence of convection.236" For stars of mass 0.9€M/Mg<1.2, the transition from the p-p chain dominated phase to the CNO-cycle dominated phase is delayed until the core has already begun to contract rapidly and electrons have begun to become degenerate at the center; the maximum energy generation has already shifted away from the center and core contraction has initiated the expansion of the envelope."," For stars of mass $0.9 \leq M / \msun \leq 1.2$, the transition from the p-p chain dominated phase to the CNO-cycle dominated phase is delayed until the core has already begun to contract rapidly and electrons have begun to become degenerate at the center; the maximum energy generation has already shifted away from the center and core contraction has initiated the expansion of the envelope."237 A thermonuclear runaway called the core helium-hydrogen (He-H) flash takes place (Fujimotoetal.1990)., A thermonuclear runaway called the core helium-hydrogen (He-H) flash takes place \citep{fuj90}.238". In Fig. 3,,"," In Fig. \ref{fig:rhot},"239" a first increase in the central temperature with decreasing central density indicates that the electron degeneracy is lifted; then, the temperature turns to decrease with the density so as to settle in the thermal equilibrium state where the nuclear energy generation balances the energy loss from the core."," a first increase in the central temperature with decreasing central density indicates that the electron degeneracy is lifted; then, the temperature turns to decrease with the density so as to settle in the thermal equilibrium state where the nuclear energy generation balances the energy loss from the core."240 In this, In this241spectra with about 2000 source counts each to put reasonable constraints on the plasma temperature profile up to 1110kpe.,"spectra with about $2\,000$ source counts each to put reasonable constraints on the plasma temperature profile up to $1140242\mbox{ kpc}$."243 The contribution from the source to the total count rate decreases from more 054 in the innermost spectrum to about 30% in the outermost one., The contribution from the source to the total count rate decreases from more $95\%$ in the innermost spectrum to about $30\%$ in the outermost one.244 We also evaluated the distribution of the plasma temperature values 1n sectors according to the asymmetrical surface brightness shown in Fig. 2.., We also evaluated the distribution of the plasma temperature values in sectors according to the asymmetrical surface brightness shown in Fig. \ref{xray_asi}.245 These best-fit values for a two-dimensional map and for an azimuthally averaged profile are represented in Figs., These best-fit values for a two-dimensional map and for an azimuthally averaged profile are represented in Figs.246 3. and 4.., \ref{fig:mapt} and \ref{fig:temp}.247 We obtained the Redistribution Matrix Files (RMFs) and Auxiliary Response Files (ARFs) by using the routines and with the QEU files included in the package., We obtained the Redistribution Matrix Files (RMFs) and Auxiliary Response Files (ARFs) by using the routines and with the QEU files included in the package.248 An emission from an optically-thin plasma — Kaastra 1992. Liedhal et 11995. in v. Εν1ο — Amaud 1996) with the metal abundance fixed to 0.3 times the solar value (Anders Grevesse 1989) and absorbed from the interstellar medium parametrized using the Tübbingen-Boulder model inXSPEC:: Wilms. Allen MeCray 2000) was adoptec to reproduce the observed spectra.," An emission from an optically-thin plasma – Kaastra 1992, Liedhal et 1995, in v. 11.1.0 – Arnaud 1996) with the metal abundance fixed to 0.3 times the solar value (Anders Grevesse 1989) and absorbed from the interstellar medium parametrized using the Tübbingen-Boulder model in; Wilms, Allen McCray 2000) was adopted to reproduce the observed spectra."249 A galactic column density fixed to 7.0.«10?em? (from radio HI maps in Dickey Lockman 1990) was assumed., A galactic column density fixed to $7.0 \times 10^{20} \mbox{ cm}^{-2}$ (from radio HI maps in Dickey Lockman 1990) was assumed.250 A local background was adopted also considering the relatively high column density of this field with respect to the blank field available for the same CCD and the proper observational period., A local background was adopted also considering the relatively high column density of this field with respect to the blank field available for the same CCD and the proper observational period.251 The overall spectral fit of the counts collected within 1100kpe from the adopted centerprovides an emission weighted temperature of τὸ|Gs1.0keV and a bolometric luminosity of 1.6«107ergs1l (0.9«107 in the 2-10keV band).," The overall spectral fit of the counts collected within $1100 \mbox{252kpc}$ from the adopted centerprovides an emission weighted temperature of $7.2^{+1.0}_{-0.8} \mbox{ keV}$ and a bolometric luminosity of $1.6 \times 10^{45} \mbox{ erg s}^{-1}$ $0.9 \times25310^{45}$ in the $2$ $10 \mbox{ keV}$ band)."254 In accordance with the weak lensing analysis described in the following section. we assume a spherical geometry for both the dark matter halo and the X-ray emitting plasma (note that negligible effects. when compared with our statistical uncertainties. can be introduced on the mass estimate due to the aspherical X-ray emission. see. e.g.. Piffaretti et al.," In accordance with the weak lensing analysis described in the following section, we assume a spherical geometry for both the dark matter halo and the X-ray emitting plasma (note that negligible effects, when compared with our statistical uncertainties, can be introduced on the mass estimate due to the aspherical X-ray emission, see, e.g., Piffaretti et al."255 2002)., 2002).256 The values of gas density and temperature in volume shells are recovered from the projected spectral results as described in Ettori et ((2002)., The values of gas density and temperature in volume shells are recovered from the projected spectral results as described in Ettori et (2002).257 To measure the total gravitating mass As. we then constrained the parameters of an assumed mass model by fitting the deprojected gas temperature (shown in Fig. 4))," To measure the total gravitating mass $M_\mathrm{tot}$, we then constrained the parameters of an assumed mass model by fitting the deprojected gas temperature (shown in Fig. \ref{fig:temp}) )"258 with the temperature profile obtained by inversion of the equation of the hydrostatic equilibrium between the dark matter potential and the intracluster plasma. In this equation. gf=0.6 is the mean molecular weight in am.u..," with the temperature profile obtained by inversion of the equation of the hydrostatic equilibrium between the dark matter potential and the intracluster plasma, In this equation, $\mu=0.6$ is the mean molecular weight in a.m.u.,"259" G is the gravitational constant. (7, is the proton mass. and #,. is the deprojected electron density."," $G$ is the gravitational constant, $m_{\rm p}$ is the proton mass, and $n_{\rm e}$ is the deprojected electron density."260 We considered both the King approximation to the isothermal sphere (King 1962) and a avarro. Frenk White (1997) dark matter density profile as mass models (see details in Ettort et 22002).," We considered both the King approximation to the isothermal sphere (King 1962) and a Navarro, Frenk White (1997) dark matter density profile as mass models (see details in Ettori et 2002)."261 By fitting the temperature profile in Fig. 4.. ," By fitting the temperature profile in Fig. \ref{fig:temp}, ,"262we measured the best fit parameters (ήο)=(616£390.1.2+0.9) for a King and (1122+287.2.5d:0.8) for a NEW mass model.," we measured the best fit parameters $(r_{\rm s}, c) = (646 \pm 390, 4.2 \pm 0.9)$ for a King and $(1122 \pm 287, 2.3 \pm 0.8)$ for a NFW mass model."263the rms number density for the parallel mocel is zz40 5 while it is only 10 emi. for the perpendicular modoel.,"the rms number density for the parallel model is $\approx26440$ $^{-3}$, while it is only 10 $^{-3}$ for the perpendicular model."265 This large variation is due to the large dillerence in the density of the boundary laver between the models (see Sect. 22)), This large variation is due to the large difference in the density of the boundary layer between the models (see Sect. \ref{sect:results}) ).266 Only models with small angles between the shock normal and the magnetic field have mean densities similar to those of observed: GAICs., Only models with small angles between the shock normal and the magnetic field have mean densities similar to those of observed GMCs.267 Large angle models only reach mean densities similar to cilfuse LEE clouds., Large angle models only reach mean densities similar to diffuse HI clouds.268 Such a dependence of the density structure on the magnetic field orientation is also observed by Leitsch.Stone.&Hartmann(2009)., Such a dependence of the density structure on the magnetic field orientation is also observed by \citet{HSH09}.269. Observations show that molecular clouds are magnetically dominated with plasma <7 of the order 0.04 - 0.6 (Crutcher.lleiles., Observations show that molecular clouds are magnetically dominated with plasma $\beta$ of the order 0.04 - 0.6 \citep{CHT03}.270& Troland|2003 ).. Figure 9 shows the mass- mean of Z.," Figure \ref{fig:betaav}271 shows the mass-weighed mean of $\beta$."272 This weighted. mean value of 33 for the parallel shock mocdel does not lie within the observed range., This weighted mean value of $\beta$ for the parallel shock model does not lie within the observed range.273 During the carly stages of the evolution the gas behind the slow-mode shock has a large thermal pressure. while the magnetic pressure is small.," During the early stages of the evolution the gas behind the slow-mode shock has a large thermal pressure, while the magnetic pressure is small."274 Hence. the plasma <7 is large for the high-density eas in the boundary laver (which dominates the mean value of 3). be. 3225.," Hence, the plasma $\beta$ is large for the high-density gas in the boundary layer (which dominates the mean value of $\beta$ ), i.e. $\beta \approx 5$."275 After about 2.5 Myr. the weighted mean value of «3 decreases as the thermally unstable gas behind the fast-moce shock becomes maenctically dominated.," After about 2.5 Myr, the weighted mean value of $\beta$ decreases as the thermally unstable gas behind the fast-mode shock becomes magnetically dominated."276 Although the weighted mean value of 3 is now around unity. Fig.," Although the weighted mean value of $\beta$ is now around unity, Fig."277 10. shows that a significant mass fraction of the cloud has 3<0.1., \ref{fig:massbelow} shows that a significant mass fraction of the cloud has $\beta < 0.1$.278 Xt Lu. about of the eas is significantly magnetically dominated.," At $t_{cc}$, about of the gas is significantly magnetically dominated."279 The other models do produce a cloud with a weighted mean J of the order of 0.4 (see Fig. 9))., The other models do produce a cloud with a weighted mean $\beta$ of the order of 0.4 (see Fig. \ref{fig:betaav}) ).280 The main reason for this has to do with the role. plaved. by. the transverse component of the magnetic field., The main reason for this has to do with the role played by the transverse component of the magnetic field.281 While the thermal pressures behind the fast-nmioce and. slow-niocle shock are not as high as in the parallel shock maioclel (i.e. the transition from the warm phase to the cold. phase is smoother). the magnetic field. is significantly. compressed behind the fast-mode shock.," While the thermal pressures behind the fast-mode and slow-mode shock are not as high as in the parallel shock model (i.e. the transition from the warm phase to the cold phase is smoother), the magnetic field is significantly compressed behind the fast-mode shock."282 The combined result of these ellects produces a lower 7 in both the boundary [ayer and within the cloud., The combined result of these effects produces a lower $\beta$ in both the boundary layer and within the cloud.283 Figure LO indeed shows that magneticallv-dominated. gas appears much earlier for shock models with a transverse component to the magnetic field., Figure \ref{fig:massbelow} indeed shows that magnetically-dominated gas appears much earlier for shock models with a transverse component to the magnetic field.284 After only 53 Myr. already of the total mass in these models. is maenctically dominated.," After only 3 Myr, already of the total mass in these models is magnetically dominated."285 Our simulations show that. to. produce clouds with magneticallv-dominated high-density gas. the angle between the shock normal and the magnetic field must be small.," Our simulations show that, to produce clouds with magnetically-dominated high-density gas, the angle between the shock normal and the magnetic field must be small."286 While perpendicular shocks produce magnetically-dominated gas at. low densities. high-density clumps with 139»1 arise in the parallel shock moclels.," While perpendicular shocks produce magnetically-dominated gas at low densities, high-density clumps with $\beta \gg 1$ arise in the parallel shock models."287 Our models show that large fractions of the cloud are magnetically dominated., Our models show that large fractions of the cloud are magnetically dominated.288 Vhis provides the ideal conditions for MIID waves to generate high-density clumps ancl cores within the cloud (Falle&Lartquist2002:VanLoo.Falle.]larteuist2006:VanLooetal. 2008).," This provides the ideal conditions for MHD waves to generate high-density clumps and cores within the cloud \citep{FH02,VFH06,VFH08}."289. For shock mocdels with a transverse Component of the magnetic field. this process initiates earlier suggesting a higher degree of fragmentation.," For shock models with a transverse component of the magnetic field, this process initiates earlier suggesting a higher degree of fragmentation."290 On top of that. another process is effective in these mocels.," On top of that, another process is effective in these models."291 As the transition from the thermallv-stable warm phase to the cold one follows the unstable part of the equilibrium curve. small. perturbations can initiate the formation of dense. cold clumps embedded in warm. cilfuse eas (Enutsulka&Ixovama 2007).," As the transition from the thermally-stable warm phase to the cold one follows the unstable part of the equilibrium curve, small perturbations can initiate the formation of dense, cold clumps embedded in warm, diffuse gas \citep{KI06}."292. Unfortunately. we cannot. Follow. these clump and core formation processes as our resolution is insullicient.," Unfortunately, we cannot follow these clump and core formation processes as our resolution is insufficient."293 While a low resolution is partly to blame for the low amount of fragmentation. the uniform initial conditions of the cloud also play an important role.," While a low resolution is partly to blame for the low amount of fragmentation, the uniform initial conditions of the cloud also play an important role."294 In the colliding driven models of Hennebellectal.(2008) and. Hoeitsch.Stone.&Hartmann (2009).. the generation of cold. dense cores and clumps relies on seeded perturbations in either the incoming Low or at the collision [ront.," In the colliding flow-driven models of \citet{Hetal08} and \citet{HSH09}, the generation of cold dense cores and clumps relies on seeded perturbations in either the incoming flow or at the collision front."295. Without these perturbations. the collision region remains roughly uniform and fragmentation occurs on very long timescales.," Without these perturbations, the collision region remains roughly uniform and fragmentation occurs on very long timescales."296 Therefore. it can be expected that. the. introduction. of perturbations within the cloud and at the edge of the cloud would produce much more fragmentation.," Therefore, it can be expected that the introduction of perturbations within the cloud and at the edge of the cloud would produce much more fragmentation."297 Furthermore. our simulations cdo not include the οσοι οἱ sell-eravity.," Furthermore, our simulations do not include the effect of self-gravity."298 While self-gravitv is dynamically unimportant for the elobal evolution of the cloud. i.e. the," While self-gravity is dynamically unimportant for the global evolution of the cloud, i.e. the"299Classical novae are binary systems in which mass is ransferred. from a main-sequence star on to a white dwarf ov Roche-lobe overllow.,Classical novae are binary systems in which mass is transferred from a main-sequence star on to a white dwarf by Roche-lobe overflow.300 The critical amount of mass that can be accreted on to the surface of the white dwarf prior oan outburst is a stronglv decreasing function ofthe white clwarl mass Clruran&Livio1986)., The critical amount of mass that can be accreted on to the surface of the white dwarf prior to an outburst is a strongly decreasing function of the white dwarf mass \citep{truran86}.301. At this mass limit. the emperature and. density at the base of the accreted laver are high. enough for hydrogen to ignite.," At this mass limit, the temperature and density at the base of the accreted layer are high enough for hydrogen to ignite."302 Phe temperature hen rises rapidly in a thermonuclear runaway (Starrfield.Sparks&Shaviv1988) and the pressure at the base of the accreted [aver becomes high enough that the accreted. mass (and sometimes a little more) is ejected (e.g.Ixovetz&Pri-alnik 1985)., The temperature then rises rapidly in a thermonuclear runaway \citep{starrfield88} and the pressure at the base of the accreted layer becomes high enough that the accreted mass (and sometimes a little more) is ejected \citep[e.g.][]{kovetz85}.303. Recurrent novae show outbursts at intervals of 10.SOvr (Warner1995:Webbinketal.1987).," Recurrent novae show outbursts at intervals of $10-80\,\rm yr$ \citep{warner95, webbink87}."304. To account. for the short timescale between the outbursts. the white cwarf in a recurrent nova svsteni must have a mass. Mj. close to he Chancdrasekhar limit (e.g.Kato&Lachisu1988.1989).," To account for the short timescale between the outbursts, the white dwarf in a recurrent nova system must have a mass, $M_1$, close to the Chandrasekhar limit \citep[e.g.][]{kato88,kato89}."305. We consider in more detail the recurrent nova U Sco that most recently erupted in 2010., We consider in more detail the recurrent nova U Sco that most recently erupted in 2010.306" The evolved. companion in U Sco has a mass of Alo=(SSM. so the mass ratio. AlofAl,= 0.64. is relatively large."," The evolved companion in U Sco has a mass of $M_2=0.88\,\rm M_\odot$ so the mass ratio, $q=M_2/M_1=0.64$ , is relatively large."307 In Section 2 we begin by re-examining all the previously proposed: sources of orbital period change during a nova outburst., In Section \ref{old} we begin by re-examining all the previously proposed sources of orbital period change during a nova outburst.308 We first describe a simple. model where the material carries away its specific angular momentum. then we include mass acerction on to the companion and frictional angular momentum losses as the binary moves through the common envelope.," We first describe a simple model where the material carries away its specific angular momentum, then we include mass accretion on to the companion and frictional angular momentum losses as the binary moves through the common envelope."309 In Section 30 we propose a new mechanism for orbital period change involving the magnetic Ποια on the secondary star., In Section \ref{new} we propose a new mechanism for orbital period change involving the magnetic field on the secondary star.310 In Section 4 we apply our mocel to the outbursts in the recurrent nova U Sco., In Section \ref{usco} we apply our model to the outbursts in the recurrent nova U Sco.311 We consider first a simple model of the outburst where the ejected material carries away the specific angular momentum. of the white chwarl, We consider first a simple model of the outburst where the ejected material carries away the specific angular momentum of the white dwarf.312 Phe non-degenerate mass accumulated on to the surface of the white cwarf is very thin., The non-degenerate mass accumulated on to the surface of the white dwarf is very thin.313 The envelope is ejected when the pressure at. the surface. of the white cwarl reaches a critical value of the order of Pay=1dynem7 (eg.FujimotoI982z.b:MacDonald 1983).," The envelope is ejected when the pressure at the surface of the white dwarf reaches a critical value of the order of $P_{\rm crit}=10^{20}\,\rm dyn\,cm^{-2}$ \citep[e.g.][]{fujimoto82a,fujimoto82b,macdonald83}."314". The critical amount of mass that accumulates before a nova outburst is of order for a white dwarf of mass M, and radius Z2.", The critical amount of mass that accumulates before a nova outburst is of order for a white dwarf of mass $M_1$ and radius $R_1$.315 Both theory and. observations suggest that all the the material that has been accreted since the last outburst is ejected in the outburst The angular momentum of the binary star svsteni is, Both theory and observations suggest that all the the material that has been accreted since the last outburst is ejected in the outburst The angular momentum of the binary star system is316Alost modern theories of structure formation. including hose based. on inflation or topological defects in the early Universe. predict a near scale-invariant spectrum of density »erturbations on large spatial scales.,"Most modern theories of structure formation, including those based on inflation or topological defects in the early Universe, predict a near scale-invariant spectrum of density perturbations on large spatial scales."317 On small spatial scales. A&10h!Mpe. the observed. Uuctuations in the galaxy distribution differ very substantially from a scale-invariant orm.," On small spatial scales, $\lambda \simlt 10 \hmpc$, the observed fluctuations in the galaxy distribution differ very substantially from a scale-invariant form."318 For example. the power spectra estimated from infra-red and. optically selected: redshift surveys are. reasonably well approximated by ΟΓΑ}x&D oat wavenumbers &oX1 . -- ⊔⇂↥↳∖↓↓≻≼∙⋜⋯∠⇂↕⇂⊔⊾↓⋅≺⋅↓⊳∖⊔∪≼∙∪⊔∖⇁↓⊔≼∙↓⊔⋏∙≟≺⊾∖⇁↓⊔⊾⊔⊓⋅⇂∪↓⋅⋜↧. ⋅ ⊔↓⋅⊔−∪∖⇁⋖⋅↓⋅↿∪⋜↧≻≼∼⋜↧↓⋖⋅−↕↓↕∖⇁⋜↧↓⋅↕⋜↧↓↕↿⇂⋅∪↓⋅⊔↓⊳∫↗↿∖∕⋅⋅⊐∖∕⋅⋅⊳⋜∐⊳∖⊔↓⋜↧∐⋖⋅↓⋅ ∖∖⋎⋜↧∖⇁⋖⋅↓⋯⊔↓∣⋊⋅↓⋅⊳∖⊳∐∪∖∖⊽≺," For example, the power spectra estimated from infra-red and optically selected redshift surveys are reasonably well approximated by $P(k) \propto k^{-1.5}$ at wavenumbers $k \simgt 0.1319\hmpcrev$ and there is no convincing evidence for a turn-over to a scale-invariant form, $P(k) \propto k$, at smaller wavenumbers."320⋅∖⇁≺⋅↓⋅⊳⊳∖⋯∙⇂↥⋜↧⋯↓⋅⊔−∪∖⇁≺⊾↓⋅⊔⋯⊳∖↥≺⋅⇀∖⊲↓⊳∖∣⊳∖⊲↓⊔⊓⋅ ⊔↓⋖⋅⋜↧⊳∖⊔↓⋅⋖⊾⊔↓∢⋅↓∐⊳∖∪⇂⋅↿⇂↥⋖⊾↓↕↓↕≼∙↓⋅⋖⋟∖∖⊽⋜↧∖⇁∢⋅∣⋡⋯⇍↳⋏∙≟↓⋅∪⊔⊔∠⇂∐⋯∼⊔⋜⊔⊲↓∪⊔⊳∖∪⊔ ⋜⋯⋏∙≟⊔↓⋜⊔⋅⊳∖≼∼⋜↧↓∢⋅⊳∖∕∿⊽↓↾⊳∖⊔⋏∙≟⋏∙≟⋖⋅⊳∖↿⋜↧⊔⋖⋅⋜⊔⋅≻≼⇍⋜↧↓⋖⊾−↕↓↕∖⇁⋜↧↓⋅↕⋜↧↓↕↿⊳∖↓≻∢⊾≼⇍⇂↓⋅⊔⊔↓ o ∪⇂∎↓≻∢⊾↓⋅∣⊔↓⋅∣⋡⋜∐⊲↓∪⊔⋡∖∪⊔≱∖↓≻⋜∐⊲↓⋜↧↓⊳∖≼⇍⋜↧↓∢⊾⊳∖∕⊽↓∪∪∣∣⊥↳∖↓≻≼∙↿∖≱∖⋖⋅∢⋅↥⇂↥∢⋅ reviews by Scott.Silk&White1995. and Bond 1996)).," However, such a turn-over must exist since measurements of the microwave background fluctuations on angular scales $\simgt 1^{\circ}$ suggest a near scale-invariant spectrum of perturbations on spatial scales $\simgt 100 \hmpc$ (see the reviews by \pcite{SSW95} and \pcite{Bond96}) )."321 A convincing detection of à turn-over in the power spectrum. of density irregularities. is therefore of uncamental significance ancl would establish a direct link xtween Lluctuations observed in the microwave background radiation and those observed in the clensity clistribution., A convincing detection of a turn-over in the power spectrum of density irregularities is therefore of fundamental significance and would establish a direct link between fluctuations observed in the microwave background radiation and those observed in the density distribution.322 Furthermore. in theories such as the Cold. Dark Matter (CDM) model. a peak in the power spectrum is predicted on the scale of the Hubble radius at the time that matter and radiation have equal density. A4.710(057)‘Alpe (sce e.g. Efstathiou 1990)).," Furthermore, in theories such as the Cold Dark Matter (CDM) model, a peak in the power spectrum is predicted on the scale of the Hubble radius at the time that matter and radiation have equal density, $\lambda_{equ} \sim 10 (\Omega h^{2})^{-1} {\rm Mpc}$ (see e.g. \pcite{Efst90}) )."323 An observation of a peak in the power spectrum of galaxy. clustering can therefore be used o constrain the parameter P=Of that is fundamental to CDAL mocels., An observation of a peak in the power spectrum of galaxy clustering can therefore be used to constrain the parameter $\Gamma = \Omega h$ that is fundamental to CDM models.324 There is some tentative evidence for a turn-over at a wavenumber &~0.025 in the three-dimensional power spectrum. inferred from the two-dimensional clustering of ealaxies measured from the APM galaxy. survey (Baugh&Efstathiou 1993.. Baugh&Efstathiou 1994.. see for example Figure 11 of Baugh&Efstathiou 1994)).," There is some tentative evidence for a turn-over at a wavenumber $k325\sim 0.025$ in the three-dimensional power spectrum inferred from the two-dimensional clustering of galaxies measured from the APM galaxy survey \pcite{BEI}, \pcite{BEII}, see for example Figure 11 of \pcite{BEII}) )."326 Gaztanaga&Baugh(1997) have carefully investigated the significance of this observed. turn-over by repeating. using simulations of the APAL galaxy survey. the procedure of inverting the," \scite{GB97} have carefully investigated the significance of this observed turn-over by repeating, using simulations of the APM galaxy survey, the procedure of inverting the"327of the small number of SED templates used here not being sufficient.,of the small number of SED templates used here not being sufficient.328" SXDF850.69 is designated as a less secure association by C08 as the position of the associated radio source is 13"" away from the SCUBA position.", SXDF850.69 is designated as a less secure association by C08 as the position of the associated radio source is 13” away from the SCUBA position.329 We find a weak (In Bio=5.3) alternative association here., We find a weak $\ln$ $_{tot}=5.3$ ) alternative association here.330 SXDFS850.74 is also designated as less secure by C08., SXDF850.74 is also designated as less secure by C08.331 This is another relatively nearby (Zpnot= 0.7) optical galaxy with a very faint associated SWIRE source., This is another relatively nearby $z_{phot}=0.7$ ) optical galaxy with a very faint associated SWIRE source.332 Again we find a weak (In Biot= 6.1) alternative association., Again we find a weak $\ln$ $_{tot}=6.1$ ) alternative association.333 SXDF850.88 is another less secure association from C08., SXDF850.88 is another less secure association from C08.334" Here we make an association with a closer, higher z object, but again with weak evidence (In Brot= 6.1)."," Here we make an association with a closer, higher $z$ object, but again with weak evidence $\ln$ $_{tot}=6.1$ )."335" A good example of a difficult, but correctly made, association is SXDF850.6."," A good example of a difficult, but correctly made, association is SXDF850.6."336 This source is one of the most confused scenarios and the only one in our sample to have a definitive sub-mm position from interferometric sub-mm observations with the SMA (Iono et al., This source is one of the most confused scenarios and the only one in our sample to have a definitive sub-mm position from interferometric sub-mm observations with the SMA (Iono et al.337 in prep)., in prep).338 Figure 3 shows the postage stamp image for SXDF850.6 and the first 6 best fit SEDs for each possible optical+SWIRE source., Figure \ref{fig:sxdf850.6} shows the postage stamp image for SXDF850.6 and the first 6 best fit SEDs for each possible optical+SWIRE source.339 Clearly SXDF850.6 is one of the most difficult cases in the sample for cross-identification., Clearly SXDF850.6 is one of the most difficult cases in the sample for cross-identification.340" The true sub-mm source is also one of the most distant, with several other sources closer to the sub-mm position."," The true sub-mm source is also one of the most distant, with several other sources closer to the sub-mm position."341" From the values in Figure 3 it is clear that simply using the X? statistic would not be sufficient in this case; the lowest x? is given by the fourth closest which has In Bseq= —3.43, while the true ID (#66) has worse x”, but significantly greater In Bsea."," From the values in Figure \ref{fig:sxdf850.6} it is clear that simply using the $\chi^2$ statistic would not be sufficient in this case; the lowest $\chi^2$ is given by the fourth closest which has ln $_{sed}=-3.43$ , while the true ID 6) has worse $\chi^2$, but significantly greater ln $_{sed}$."342" This demonstrates the power of using the Bayesian evidence, which takes into account both the likelihood of an association being the correct match, with the observed sub-mm fluxand the likelihood of an association being the incorrect match, with undetected sub-mm flux."," This demonstrates the power of using the Bayesian evidence, which takes into account both the likelihood of an association being the correct match, with the observed sub-mm flux the likelihood of an association being the incorrect match, with undetected sub-mm flux."343" While the results of our approach on individual sources are informative, it is worth considering the completeness and reliability statistics as presented in Section ??.."," While the results of our approach on individual sources are informative, it is worth considering the completeness and reliability statistics as presented in Section \ref{sec:scubsims}."344 For no cut on evidence we recover 24 of the 33 associations presented in 107/C08., For no cut on evidence we recover 24 of the 33 associations presented in I07/C08.345" For a reasonable evidence threshold, i.e. In Bi;>8 we recover 20 I07/C08 associations with one discrepant (SXDF850.10), translating to a completeness rate, with reliability."," For a reasonable evidence threshold, i.e. ln $B_{tot}>8$ we recover 20 I07/C08 associations with one discrepant (SXDF850.10), translating to a completeness rate, with reliability."346" However it is possible, if not likely, that some of the associations presented in 107/C08 are not correct."," However it is possible, if not likely, that some of the associations presented in I07/C08 are not correct."347" In fact C08 go so far as to indicate which associations they are not confident in; SXDF850.14, SXDF850.24, SXDF850.69, SXDF850.74 SXDF850.88."," In fact C08 go so far as to indicate which associations they are not confident in; SXDF850.14, SXDF850.24, SXDF850.69, SXDF850.74 SXDF850.88."348 Of these we only recover one with reasonable evidence (SXDF850.14)., Of these we only recover one with reasonable evidence (SXDF850.14).349 If we exclude these associations from our 107/C08 “truth” list then our completeness improves to72%., If we exclude these associations from our I07/C08 “truth” list then our completeness improves to.350. Encouragingly these completeness and reliability rates are very close to those predicted from simulations in the previous section., Encouragingly these completeness and reliability rates are very close to those predicted from simulations in the previous section.351 A comparison of the photo-z estimates between C08 and here is given in Table 3.., A comparison of the $z$ estimates between C08 and here is given in Table \ref{tab:scubaresults}.352" There is some level of agreement with the C08 photo-z measurements, although in a few cases the redshifts are clearly discrepant."," There is some level of agreement with the C08 photo-z measurements, although in a few cases the redshifts are clearly discrepant."353" This is more clearly seen in Figure 4,, where the distribution of both sets of photo-z estimates is shown."," This is more clearly seen in Figure \ref{fig:zhist}, where the distribution of both sets of $z$ estimates is shown."354 Also shown is the redshift distribution for spectroscopically confirmed SCUBA galaxies from Chapman (2005)., Also shown is the redshift distribution for spectroscopically confirmed SCUBA galaxies from \nocite{Chapman2005}{ (2005).355" The median redshift for associations presented here is z—1.73, slightly higher than the C08 measure of the same sample (z— 1.44) and significantly lowerthan the Chapman et al."," The median redshift for associations presented here is $z=1.73$, slightly higher than the C08 measure of the same sample $z=1.44$ ) and significantly lowerthan the Chapman et al."356 sample which has a median of z— 2.5., sample which has a median of $z=2.5$ .357frequencies (IF. or equivalently. baseband converters) were recorded in each polarization. with 8 Ally per IF. and a total aggregate bit rate of 128 Mbits/s. The data were correlated bv the VLBA correlator in Soccoro.,"frequencies (IF, or equivalently, baseband converters) were recorded in each polarization, with 8 MHz per IF, and a total aggregate bit rate of 128 Mbits/s. The data were correlated by the VLBA correlator in Soccoro."358 The preliminary calibration. [ringe fitting. polarization calibration and imaging were done using the Astronomical Image Processing Svstem (AIPS) following standard methods.," The preliminary calibration, fringe fitting, polarization calibration and imaging were done using the Astronomical Image Processing System (AIPS) following standard methods."359 The global VLBI array used for the February 23. 1993 observations included the Effelsberg (EB). Green Bank (GB). and Medicina (AIC) telescopes. the phased Very Large Array (Y¥27). and the Hancock (LIN). North Liberty (NL). Brewster (BR) and Owens Valley (OV) VLBA antennas.," The global VLBI array used for the February 23, 1993 observations included the Effelsberg (EB), Green Bank (GB), and Medicina (MC) telescopes, the phased Very Large Array (Y27), and the Hancock (HN), North Liberty (NL), Brewster (BR) and Owens Valley (OV) VLBA antennas."360 Ellelshere was used as the reference antenna al all stages of the calibration., Effelsberg was used as the reference antenna at all stages of the calibration.361 The unpolarized source OQ 208 was used as the instrumental polarization (D-term) calibrator in the AIPS taskLPC'AL., The unpolarized source OQ 208 was used as the instrumental polarization $D$ -term) calibrator in the AIPS task.362 The absolute electric-vector polarization angle (EVPA or Y) calibration was performed by comparing the total VLBI-scale and (simultaneously measured) VLA core polarizations for the compact polarized source OJ 287., The absolute electric-vector polarization angle (EVPA or $\chi$ ) calibration was performed by comparing the total VLBI-scale and (simultaneously measured) VLA core polarizations for the compact polarized source OJ 287.363 The July 13. 1995 and June 23. 1993 observations were obtained using the ten telescopes ol the American VLBA.," The July 13, 1995 and June 28, 1998 observations were obtained using the ten telescopes of the American VLBA."364 Los Alamos was used as the reference antenna at all stages of the calibration., Los Alamos was used as the reference antenna at all stages of the calibration.365" The unpolarized source 3C84 and the nearly unresolved polarized. source O749+540 were used for the D-term calibration for the July 1995 and June 1998 observations. respectively,"," The unpolarized source 3C84 and the nearly unresolved polarized source 0749+540 were used for the $D$ -term calibration for the July 1995 and June 1998 observations, respectively."366 Short 53-minute VLA snapshots of LO HEDLs. including five of the four lIBLs for which 1995.53 images are presented here. were made al 4.9. 8.4. and 15.0 GIIz on July 18. 1995. onlv a few davs after the July 1995 VLBA observations.," Short 2–3-minute VLA snapshots of 10 HBLs, including five of the four HBLs for which 1995.53 images are presented here, were made at 4.9, 8.4, and 15.0 GHz on July 18, 1995, only a few days after the July 1995 VLBA observations."367 We used the results of these 4.9 GlIIz observations lor OJ287 for the EVPA calibration of the VLBA data. assuming (hat the polarization position angle of OJ287 did not vary between the VLA and VLBI observations.," We used the results of these 4.9 GHz observations for OJ287 for the EVPA calibration of the VLBA data, assuming that the polarization position angle of OJ287 did not vary between the VLA and VLBI observations."368 Unfortunatelv. we did not have integrated. polarization measurements of any compact polarized sources observed during our June 1993 VLBA run nearby in time to those VLBA observations.," Unfortunately, we did not have integrated polarization measurements of any compact polarized sources observed during our June 1998 VLBA run nearby in time to those VLBA observations."369 Instead. we applied the EVPA calibration determined for VLBA observations in March. and April 1005. based on integrated polarization measurements within a lew davs of those experiments and using the same reference antenna (Los Alamos).," Instead, we applied the EVPA calibration determined for VLBA observations in March and April 1998, based on integrated polarization measurements within a few days of those experiments and using the same reference antenna (Los Alamos)."370 The EVPA, The EVPA371surface of cach excised sphere: ὃν ia Eq.,surface of each excised sphere: $\partial/\partial r$ in Eq.372 denotes the radial derivative in a coordinate svstem centered. at the center of sphere 7., denotes the radial derivative in a coordinate system centered at the center of sphere $i$ .373 Figure | sketches the domain decomposition used for the computational domain D., Figure \ref{fig:Domains-BBH} sketches the domain decomposition used for the computational domain $\cal D$.374 We surround each excised sphere with a spherical shell., We surround each excised sphere with a spherical shell.375 These two splerical shells are matched together with 5«3 rectangular blocks. where the two blocks that contain the excised splieres Sy. are removed.," These two spherical shells are matched together with $5\times 3\times 3$ rectangular blocks, where the two blocks that contain the excised spheres $S_{1,2}$ are removed."376 Finally. we surround this structure with a third spherical shell extending to very large outer radius.," Finally, we surround this structure with a third spherical shell extending to very large outer radius."377 This gives a total of 16 subdomains. namely 3 shells aud. 13 rectangular blocks.," This gives a total of 46 subdomains, namely 3 shells and 43 rectangular blocks."378 Iu the iuner spheres we use a log mapping for the radial coordinate., In the inner spheres we use a log mapping for the radial coordinate.379 In the rectangular blocks. a combination of linear aud οσααπο mappings 1s used similar to the 2D example iu figure 2..," In the rectangular blocks, a combination of linear and logarithmic mappings is used similar to the 2D example in figure \ref{fig:SketchRectangles}."380 In the outer sphere an inverse mapping is used which is well adapted to the fall-off behavior c~1|ar++++ for laree radii +.," In the outer sphere an inverse mapping is used which is well adapted to the fall-off behavior $\psi\sim3811+a\,r^{-1}+\cdots$ for large radii $r$."382 The outer radius of the outer spherical shell is chosen to be 10? or 1019 and a Dirichlet boundary condition c= Lis used to approximate Eq., The outer radius of the outer spherical shell is chosen to be $10^9$ or $10^{10}$ and a Dirichlet boundary condition $\psi=1$ is used to approximate Eq.383(55).. We now present two solutionswith different sizes aud locatious of the excised spheres., We now present two solutionswith different sizes and locations of the excised spheres.384 Iu sections 1.2.3 to 1.2.6. we then discuss several topics including preconcditioniug and parallelization.," In sections \ref{sec:Example2-Preconditioning} to \ref{sec:Example2-ParallelExecution}, we then discuss several topics including preconditioning and parallelization."385 First we choose two equal sized spheres with radi ry=ro1., First we choose two equal sized spheres with radii $r_1=r_2=1$.386" The separation between the centers of the spheres is chosen to be 10. the outer radius of the outer sphereis 10°,"," The separation between the centers of the spheres is chosen to be 10, the outer radius of the outer sphereis $10^9$ ."387(2001).,.388".. The advantage of this imiechauisni is that the oscillatory state is expected to be active only in a very narrow range of radi from r,,2rs tor, =les and hence a siunall rauge of accretion rates. as we observed for the 1 Tz QPO (see 3.2))."," The advantage of this mechanism is that the oscillatory state is expected to be active only in a very narrow range of radii from $r_{m}\simeq r_{c}$ to $r_{m}=1.5r_{c}$ and hence a small range of accretion rates, as we observed for the 1 Hz QPO (see \ref{fastdecayjump}) )."389 The Spruit-Taai instability could modulate the accretion flow at high amplitude. which would fit the observations of very high fractional rius amplitudes for the QPO.," The Spruit-Taam instability could modulate the accretion flow at high amplitude, which would fit the observations of very high fractional rms amplitudes for the QPO."390 The instability would also be compatible with the continued presence of accretion-powered pulsations. since accretion could still be fimneled even if the ier edee of the disk were oscillating.," The instability would also be compatible with the continued presence of accretion-powered pulsations, since accretion could still be funneled even if the inner edge of the disk were oscillating."391 Finally. the frequency of the iustabilitv has a weak depeudeuce on the mass accretion rate (see Fie.," Finally, the frequency of the instability has a weak dependence on the mass accretion rate (see Fig."392" Lin Spruit&Taam 1993)). rising or falling whether r,, is greater or less than +..."," 4 in \citealt{spr93}) ), rising or falling whether $r_{m}$ is greater or less than $r_{c}$."393 This weak dependence las been observed in JLs0s (Fig. 7)), This weak dependence has been observed in J1808 (Fig. \ref{rms-flux-freq}) )394 with thefrequency rising with X-ray fux. thus sugeestiug Fuzd," with thefrequency rising with X-ray flux, thus suggesting $r_{m}>r_{c}$."395 Tu sunu. most of the miecliauisiis examined eauuot. based on our current understanding of how thev work. explain key features of the 1 Wz OPO (see Table 2).," In summary, most of the mechanisms examined cannot, based on our current understanding of how they work, explain key features of the 1 Hz QPO (see Table 2)."396 The mechanisius that remain plausible are all associated with. or fine-tuned by. the onset of the propeller regime.," The mechanisms that remain plausible are all associated with, or fine-tuned by, the onset of the propeller regime."397 There are a nunibber of other pieces of evidence (ch 77)), There are a number of other pieces of evidence (cf. \ref{1Hz:intro}) )398 that also point to major chanees in the accretion enviroment at the huuinositv where the 1 Uz QPO sets iu (Wijnandsctal.2001.. Wijuands 2003.. Campanactal. 2008)) - changes which might be explained by the onset of the propeller.," that also point to major changes in the accretion environment at the luminosity where the 1 Hz QPO sets in \citealt{wij01}, \citealt{wij03}, \citealt{cam08}) ) - changes which might be explained by the onset of the propeller."399 Ina addition there are timime results sugeesting a major clhauee iu disk structure around this time. such as the ~0.2 phase dift in the fundamental (arguiug for a major chauge iu the disk cnviromment around this time). the change iu the soft lag behavior (artimanetal.20095).. ancl the (debated) detection of an accretion torque (Burderiotal.2006:Tartinanet 2008).," In addition there are timing results suggesting a major change in disk structure around this time, such as the $\sim0.2$ phase drift in the fundamental (arguing for a major change in the disk environment around this time), the change in the soft lag behavior \citep{har09b}, and the (debated) detection of an accretion torque \citep{bur06, har08}."400. The mechanism proposed by Spruit&Taam(1993) seclus to be the most promusing candidate to explain the Lz QPO. although the precise details of the time scales for this iustabilitv in the situation when funnel flows are relevant remain to be worked out.," The mechanism proposed by \citet{spr93} seems to be the most promising candidate to explain the 1 Hz QPO, although the precise details of the time scales for this instability in the situation when funnel flows are relevant remain to be worked out."401 It has a precise ouset point associated with the carly propeller regiae. should remain relatively stable iu frequency as accretion rate varies slightly aud is only expected in a narrow rauge of accretion rates.," It has a precise onset point associated with the early propeller regime, should remain relatively stable in frequency as accretion rate varies slightly and is only expected in a narrow range of accretion rates."402 Other mechanisius may also plav a role. perhaps in concert with the Spruit-Taam mstabilitv.," Other mechanisms may also play a role, perhaps in concert with the Spruit-Taam instability."403 In 1.2.0 we ueutioned that new classes of interchange iustabilities uieht operate near the propeller transition. perhaps cading to sporadic accretion.," In \ref{interchange} we mentioned that new classes of interchange instabilities might operate near the propeller transition, perhaps leading to sporadic accretion."404 In 1.2.0 we discussed he possibility of the ionization instability trigecring on short leugthseales in the inner regions of the disk once he source cuters the[um propeller regime., In \ref{thermalvisc} we discussed the possibility of the ionization instability triggering on short lengthscales in the inner regions of the disk once the source enters the propeller regime.405 This possibility is xuwtieularlv plausible if the disk is already close to the ransition frou outburst to quiescence., This possibility is particularly plausible if the disk is already close to the transition from outburst to quiescence.406 The ionization instability imuüsht reiutorce the Spruit-Taam instability uechanisia. and could also fine-tune the onset coucditious or the 1 Tz OPO (see ?27)).," The ionization instability might reinforce the Spruit-Taam instability mechanism, and could also fine-tune the onset conditions for the 1 Hz QPO (see \ref{1808etal}) )."407 The number of empty ficlds in Table 2 refiects the scale of the modeling work required to resolve these questions., The number of empty fields in Table 2 reflects the scale of the modeling work required to resolve these questions.408 Tt is hard to uuderstaud why the 1 Wz QPO does not appear diving the faint re-flares m the 2008 outburst., It is hard to understand why the 1 Hz QPO does not appear during the faint re-flares in the 2008 outburst.409 8 out of 5? observations were in the 2-15 mCrab rauge diving the re-flaring state., 8 out of 57 observations were in the 2-15 mCrab range during the re-flaring state.410 The reason why the 1 IIz ΟΡΟ is uot observed in these 8 observations is aa open problem., The reason why the 1 Hz QPO is not observed in these 8 observations is an open problem.411 Although poorly coustrained. the 1998 outburst exhibited a similar behavior. aud on several occasions diving the 2000. 2002 aud 2005 outbursts the 1 Πε QPO also remained undetected even for fluxes iu the 2-15 mCrab ranec. with fractional ruis amplitude upper Μιάτς of ~105€.," Although poorly constrained, the 1998 outburst exhibited a similar behavior, and on several occasions during the 2000, 2002 and 2005 outbursts the 1 Hz QPO also remained undetected even for fluxes in the 2-15 mCrab range, with fractional rms amplitude upper limits of $\sim 10\%$."412 Clearly the 1 ITz QPO inechanisin is not always triggeredoo even in the 215 mCrab range in 1505., Clearly the 1 Hz QPO mechanism is not always triggered even in the 2–15 mCrab range in J1808.413" Iu order to cuter the propeller regime. JlsO0S needs ο be at the point where r,,r.."," In order to enter the propeller regime, J1808 needs to be at the point where $r_m \sim r_c$ ."414 Equatiug the crude expressious elven in eq.(3)) aud CL). we obtain a relation οποσα accretion rate. magnetic field and spin rate.," Equating the crude expressions given in \ref{rc}) ) and \ref{rm}) ), we obtain a relation between accretion rate, magnetic field and spin rate."415 Figure 1) shows the conditions for propeller onset for articular combination of these parameters., Figure \ref{propeller} shows the conditions for propeller onset for particular combination of these parameters.416" Clearly this Is Very approxinate. siuce it is based on the simplest estimates of r,, and 57. and ignores cependeucies on nass and radius. but suffücieut to uuderstaud whether he propeller scenario is a realistic possibility."," Clearly this is very approximate, since it is based on the simplest estimates of $r_m$ and $r_c$, and ignores dependencies on mass and radius, but sufficient to understand whether the propeller scenario is a realistic possibility."417 We plot the mass accretion rate values of three well shown AMNDPs: NTE J18507-291 (spin frequency 190 Tz). Jls0s (101 Wz) aud Τι J00291|291 (599 Iz).," We plot the mass accretion rate values of three well known AMXPs: XTE J1807-294 (spin frequency 190 Hz), J1808 (401 Hz) and IGR J00291+294 (599 Hz)."418 The first object was chosen because its spin frequency is one of the owest known annone AMINPs aud its outburst spans a wide range of Iuuünosities., The first object was chosen because its spin frequency is one of the lowest known among AMXPs and its outburst spans a wide range of luminosities.419 ICR 00291|29£ vas chose )ecause its neutron star has the hiehest spin frequency shown anone AMINPs., IGR J00291+294 was chosen because its neutron star has the highest spin frequency known among AMXPs.420 The mass accretion rates uxed in Fig., The mass accretion rates used in Fig.421 10. are calculated Or N-rav fluxes in the 210 keV enerey baud. bx assuniue a neutron star imass of l. 1A. and an efficiency of for the conversion of rest mass enerev of the accreted imuaterial into N-rawv flux.," \ref{propeller} are calculated for X-ray fluxes in the 2–10 keV energy band, by assuming a neutron star mass of 1.4 $M_{\odot}$ and an efficiency of for the conversion of rest mass energy of the accreted material into X-ray flux."422 Since these lass accretion rates do not refer to bolometric fluxes. they have to be considered lower limits.," Since these mass accretion rates do not refer to bolometric fluxes, they have to be considered lower limits."423 We also marked the bolometric bpuuinositv of cach source (as reported in Cderlinskietal.2002.. Falaugaetal. 2005a.b)) for assunied distances of 8.5 kpe (IGR and NTE J1807-291) and 3.5 kpe (11505).," We also marked the bolometric luminosity of each source (as reported in \citealt{gie02}, \citealt{fal05a, fal05b}) ) for assumed distances of 8.5 kpc (IGR and XTE J1807-294) and 3.5 kpc (J1808)."424 The very broad range of luuinositics of JISOS are observed thanks to the deeper observations of 31. Campanactal. 2008)) and (AVijuaucls 2003).," The very broad range of luminosities of J1808 are observed thanks to the deeper observations of \ref{re-flarings}, \citealt{cam08}) ) and \citep{wij03}."425. For all three sources. the couditious for propeller ouset should be encountered if the field streneth is ~105 Ci For JisOS. with a spin of LOL IIz aud an accretion rate that runs from a few percent of Eddington at peak. down to less than 0.001 iu the dips between the re-flares. the svsteni must always cuter the propeller regnuue at sane accretion rate. while for B«109 C the system will not cuter the propeller regiae in the observed rauge of mass accretion rates.," For all three sources, the conditions for propeller onset should be encountered if the field strength is $\sim 10^{8}$ G. For J1808, with a spin of 401 Hz and an accretion rate that runs from a few percent of Eddington at peak, down to less than 0.001 in the dips between the re-flares, the system must always enter the propeller regime at same accretion rate, while for $B<10^{6}$ G the system will not enter the propeller regime in the observed range of mass accretion rates."426 The range of magnetic fields is (B~OL 1.5« 105€) as reported by Hartinanetal. 2009a)..," The range of magnetic fields is $B\sim 0.4$ $1.5\times 10^{8}$ G) as reported by \citet{har08, har09}. ."427 The rauge of accretion rates for which the 1IIz QPO appears (iuferred from the 2-15 ιατα Nara flux. 3.2)) lies just below this range.," The range of accretion rates for which the 1 Hz QPO appears (inferred from the 2-15 mCrab X-ray flux,\ref{fastdecayjump}) ) lies just below this range."428 This coiucideuce is quite impressive since the accretion rates are lower limits., This coincidence is quite impressive since the accretion rates are lower limits.429feature is blended with an line that strengthens toward the later (vpes (as do the other lines from (he latter ion). interfering with the visual trend: this blend is elucidated at a larger scale in Figure 5.,"feature is blended with an line that strengthens toward the later types (as do the other lines from the latter ion), interfering with the visual trend; this blend is elucidated at a larger scale in Figure 5."430 Finally. the trend is relatively weak throughout this range. although the ratio reverses between (he extreme cases of WD 150136 ad ;2 Cru (the spectrogram of ILD 93250 has lower S/N and is unreliable al the longer wavelengths).," Finally, the trend is relatively weak throughout this range, although the ratio reverses between the extreme cases of HD 150136 and $\beta$ Cru (the spectrogram of HD 93250 has lower S/N and is unreliable at the longer wavelengths)."431 The large N/O ratios in ¢ Pup and € Per are most likely abundance effects in processed material. as previously derived in the former spectrum by Kahn et ((2001) in agreement with prior photospheric/wind analyses: see also Oskinova. et ((2006).," The large N/O ratios in $\zeta$ Pup and $\xi$ Per are most likely abundance effects in processed material, as previously derived in the former spectrum by Kahn et (2001) in agreement with prior photospheric/wind analyses; see also Oskinova et (2006)."432 Note that the behaviors of the ionization ratios are themselves an ionization effect. with the intermediate Ne lines providing the best response to the relevant parameter range.," Note that the behaviors of the ionization ratios are themselves an ionization effect, with the intermediate Ne lines providing the best response to the relevant parameter range."433 Quantitative measurements (and corresponding uncertainties) of these line ratios. as well as the implied temperatures. are given by Waldron Cassinelli (2007).," Quantitative measurements (and corresponding uncertainties) of these line ratios, as well as the implied temperatures, are given by Waldron Cassinelli (2007)."434 We present measurements of the Ne ratios below., We present measurements of the Ne ratios below.435 It is noteworthy that the binary nature of several objects. which may have colliding winds. does not interfere with these observed trends. although it may contribute to some ol the scatter in them.," It is noteworthy that the binary nature of several objects, which may have colliding winds, does not interfere with these observed trends, although it may contribute to some of the scatter in them."436 Neither does the light to moderate range of interstellar extinctions among them (Table 1). for whieh no correction has been made here.," Neither does the light to moderate range of interstellar extinctions among them (Table 1), for which no correction has been made here."437 The seven stars with E(B-V) between 0.3 and 0.5 are expected to have emission features longward of 15 eexlincted by [actors up to 23., The seven stars with E(B-V) between 0.3 and 0.5 are expected to have emission features longward of 18 extincted by factors up to 2–3.438 One might be concerned that the earlier (wpe normal stars tend to have the higher interstellar extinctions. but ¢ Pup provides the counterexample with an early (vpe and low extinction that fits the X-ray line sequence well.," One might be concerned that the earlier type normal stars tend to have the higher interstellar extinctions, but $\zeta$ Pup provides the counterexample with an early type and low extinction that fits the X-ray line sequence well."439 OF course. wind or interstellar extinction always affects the longer wavelengths more. so it cannot cause the relatively weaker high ionization leatures at the later (vpes.," Of course, wind or interstellar extinction always affects the longer wavelengths more, so it cannot cause the relatively weaker high ionization features at the later types."440 Neither would it affect the ratios of the close pairs of IH-like to IHe-like lines significantly., Neither would it affect the ratios of the close pairs of H-like to He-like lines significantly.441 The present sample is not adequate to investigate Iuminosity effects in detail. but there are a [ew suggestive indications of an ionization correlation with that dimension as well.," The present sample is not adequate to investigate luminosity effects in detail, but there are a few suggestive indications of an ionization correlation with that dimension as well."442 As noted above. the line persists to a slighilv later (wpe in (he supergiants.," As noted above, the line persists to a slightly later type in the supergiants."443 More svstematically. it can be seen that the and lines remain stronger al later (vpes in the supergiants than on (he main sequence (see also Waldron Cassinelli 2007).," More systematically, it can be seen that the and lines remain stronger at later types in the supergiants than on the main sequence (see also Waldron Cassinelli 2007)."444 Indeed. + Ori rather breaks these trends in Figure 3. which may well be due to its giant nature.," Indeed, $\iota$ Ori rather breaks these trends in Figure 3, which may well be due to its giant nature."445 More extensive coverage of intermediate luminosity Classes wilh N-rav data of this equality is required to determine whether (hese effects correlate in detail with that dimension., More extensive coverage of intermediate luminosity classes with X-ray data of this quality is required to determine whether these effects correlate in detail with that dimension.446burst. then the source decreased. by nearly four orders of magnitude in lux in one dav!,"burst, then the source decreased by nearly four orders of magnitude in flux in one day!"447 However. with the current data it cannot be assessed whether or not the source had a similar ecay rate in the time between the tvpe-I X-ray burst and vw start of the NRL observations.," However, with the current data it cannot be assessed whether or not the source had a similar decay rate in the time between the type-I X-ray burst and the start of the XRT observations."448 Furthermore. it is also unclear if the occurrence of the burst in some way triggered the decay. of the source or if the two are unrelated.," Furthermore, it is also unclear if the occurrence of the burst in some way triggered the decay of the source or if the two are unrelated."449 The observed tentative change in spectral shape has been seen for many neutron-star X-ray transients., The observed tentative change in spectral shape has been seen for many neutron-star X-ray transients.450 Phose systems typically change their spectral shape from thermally dominated. to non-thermal dominated: around a few times LO’? erg s (seec.g.Maccarone&Coppi2003:Gladstonectal.2007).. which is close to the X-ray. luminosity at which we observe the spectral shape of Swift J1749.4.2807 to change.," Those systems typically change their spectral shape from thermally dominated to non-thermal dominated around a few times $10^{36}$ erg $^{-1}$ \citep[see e.g.][]{2003MNRAS.338..189M,2007MNRAS.378...13G}, which is close to the X-ray luminosity at which we observe the spectral shape of Swift J1749.4–2807 to change."451 The exact duration of the outburst is also unclear., The exact duration of the outburst is also unclear.452 Lt is possible that the source was active for a considerable amount of time (clavs to even weeks) before the BAT burst occurred., It is possible that the source was active for a considerable amount of time (days to even weeks) before the BAT burst occurred.453 LW true. the 210 keV. tux of the source before the burst should not have been much above approximately 5.10 ος (corresponding to a few times 107 erg +) otherwise we would have detected the source with the ΑΗΑΡΑ," If true, the 2–10 keV flux of the source before the burst should not have been much above approximately $5 \times 10^{-10}$ erg $^{-1}$ (corresponding to a few times $10^{36}$ erg $^{-1}$ ) otherwise we would have detected the source with the /ASM."454 Lt is also possible that the rise and the peak were as fast as the decay observed in this source., It is also possible that the rise and the peak were as fast as the decay observed in this source.455 For a type- X-ray burst to occur. a certain amount of matter must be accreted.," For a type-I X-ray burst to occur, a certain amount of matter must be accreted."456 However. for ordinary neutron star LAINBs the bursts can recur within hours to a clay when they have luminosities similar to those observed for our source when the burst occurred (Gallowayetal.2006)...," However, for ordinary neutron star LMXBs the bursts can recur within hours to a day when they have luminosities similar to those observed for our source when the burst occurred \citep{2006astro.ph..8259G}."457 Pherefore. it is possible that the source was active for only a day or so and still accumulated enough matter to exhibit the burst. and then disappeared. again.," Therefore, it is possible that the source was active for only a day or so and still accumulated enough matter to exhibit the burst and then disappeared again."458 Sources which exhibit such short outbursts are easily missed by monitoring instruments., Sources which exhibit such short outbursts are easily missed by monitoring instruments.459 This could then indicate that a significant number of similar systems may be present in our Galaxy but which are usually missed when they are in outburst., This could then indicate that a significant number of similar systems may be present in our Galaxy but which are usually missed when they are in outburst.460 Their faint accretion luminosity and their short outbursts might make them very clillicult to detect with monitoring instruments: their bright tvpe X-ray bursts might also easily be Interestingly. there is one class of neutron-star X-ray binaries which might be such a class of sources and. which might be related to Swift J1749.4.2807: ve so-called: burst-only sources (seeCornelisseetal.2004.foranoverviewofthese sources).," Their faint accretion luminosity and their short outbursts might make them very difficult to detect with monitoring instruments; their bright type-I X-ray bursts might also easily be Interestingly, there is one class of neutron-star X-ray binaries which might be such a class of sources and which might be related to Swift J1749.4–2807: the so-called burst-only sources \cite[see][for an461overview of these sources]{2004NuPhS.132..518C}."462 These svstenis are accreting neutron star sources which were discovered (mostly withBeppoSAX but also with INTEGRAL) because à type-L X-ray burst was detected. from them but which could not be detected outside the bursts with any of the monitoring instruments in orbit., These systems are accreting neutron star sources which were discovered (mostly with but also with ) because a type-I X-ray burst was detected from them but which could not be detected outside the bursts with any of the monitoring instruments in orbit.463 The accretion luminosities of these sources at the time of the tvpe-bE: X-ray bursts. should. be below ~107 erg s+ for them to remain uneetectable., The accretion luminosities of these sources at the time of the type-I X-ray bursts should be below $\sim$$10^{36}$ erg $^{-1}$ for them to remain undetectable.464 More. sensitive follow-up observations with for example or found that although some are. persistent sources with very low luminosities. most of them were likely neutron-star transients which most of the time were in a very dim cquiescent state (with X-ray luminosities of the order of 107 erg 5 or less: see Cornelisseetal.2002b.2004)).," More sensitive follow-up observations with for example or found that although some are persistent sources with very low luminosities, most of them were likely neutron-star transients which most of the time were in a very dim quiescent state (with X-ray luminosities of the order of $10^{32}$ erg $^{-1}$ or less; see \citealt{2002A&A...392..931C,2004NuPhS.132..518C}) )."465 In such systems. the tvpe-I bursts were seen during one of their very-faint X-ray outbursts.," In such systems, the type-I bursts were seen during one of their very-faint X-ray outbursts."466" One of these burst-only sources (called SAX J2224.915421: Cornelissectal.2002a)) was of particular interest because within S hours after the Wide Field Camera ofBeppoS discovered. it through its burst""... AX pointed. at the sourceusing the Narrow Field. Instrument (NEL) and could detect the source only at a2 10 keV flux of ~13510Pores Lom 7 (Antonellietal.1999) resulting in a luminosity of Ss.1077 erg s (assumingadistanceof7.1kpe:Cornelisseetal. 2002a).."," One of these burst-only sources (called SAX J2224.9+5421; \citealt{2002A&A...392..885C}) ) was of particular interest because within 8 hours after the Wide Field Camera of discovered it through its , pointed at the sourceusing the Narrow Field Instrument (NFI) and could detect the source only at a 2–10 keV flux of $\sim4671.3\times 10^{-13}$ erg $^{-1}$ $^{-2}$ \citep{1999GCN...445....1A} resulting in a luminosity of $\sim 8468\times 10^{32}$ erg $^{-1}$ \citep[assuming a distance of 7.1 kpc;][]{2002A&A...392..885C}. ."469 This detection of the source at à very faint level only 8 hours after the occurrence of the burst is very reminiscent of what we have observed for Swift JI749.-42807., This detection of the source at a very faint level only 8 hours after the occurrence of the burst is very reminiscent of what we have observed for Swift J1749.4–2807.470 Only ~S hours after the burst. the ARP 210 keV Dux of Swift τι2807 had. decreased already to around 510 eres tem 7. which is of the same order of magnitude as the [lux observed. for SAN J22?P4.9|5421 outside its burst.," Only $\sim$ 8 hours after the burst, the XRT 2–10 keV flux of Swift J1749.4–2807 had decreased already to around $5\times 10^{-13}$ erg $^{-1}$ $^{-2}$, which is of the same order of magnitude as the flux observed for SAX J2224.9+5421 outside its burst."471 Cornelisseetal.(20025) suggested. that SAX 2224.9|5421 could be bursting at very low (near quiescent) X-ray luminosities. but our results on Swilt 1749.4.2807 also suggest that both sources could be very similar sources which exhibit a relatively faint (but not very faint) outburst but they decay. very. rapidly after the occurrence of their tvpe-E X-ray bursts.," \citet{2002A&A...392..931C} suggested that SAX J2224.9+5421 could be bursting at very low (near quiescent) X-ray luminosities, but our results on Swift J1749.4–2807 also suggest that both sources could be very similar sources which exhibit a relatively faint (but not very faint) outburst but they decay very rapidly after the occurrence of their type-I X-ray bursts."472 Determining the exact accretion. luminosity at which the bursts occur is important in understanding the burst physics since the burst. properties depend: strongly on the accretion rate at the time the burst occurs., Determining the exact accretion luminosity at which the bursts occur is important in understanding the burst physics since the burst properties depend strongly on the accretion rate at the time the burst occurs.473 Although the accretion situation is evident for Swift 1749.42807. it remains unclear lor SAN 2224.9|5421.," Although the accretion situation is evident for Swift J1749.4–2807, it remains unclear for SAX J2224.9+5421."474 Clearly. for these svstems and others similar to them. the very short slew time available with is necessary to distinguish between the cillerent scenarios.," Clearly, for these systems and others similar to them, the very short slew time available with is necessary to distinguish between the different scenarios."475 Swift J1749.4.2807 decaved rapidly to a constant level which was verv similar to what saw [rom he source six vears before the occurrence of the burst and our months after it., Swift J1749.4–2807 decayed rapidly to a constant level which was very similar to what saw from the source six years before the occurrence of the burst and four months after it.476 Therefore. this constant [Dux level very ikelv represents the quiescent [ux of the source which. for a distance of 6.7 προ results in à 210 keV luminosityof A5LO «1075 erg * (seealsoHalpern2006)..," Therefore, this constant flux level very likely represents the quiescent flux of the source which, for a distance of 6.7 kpc, results in a 2–10 keV luminosityof 0.5–1.0 $\times 10^{33}$ erg $^{-1}$ \citep[see also][]{2006GCN..5210....1H}."477" ""Phis is very similar to the quiescent Luminosity seen for other neutron-star N-rav. transients in their quiescent state.", This is very similar to the quiescent luminosity seen for other neutron-star X-ray transients in their quiescent state.478 Sadly. due to he faintness of the source no spectral information could x obtained but the high Ny (as measured. in outburst with the NICE) in-front. of the source makes it cüllicult to detect any soft. thermal component and it is very likely that he emission we observe is (mostlv) due to a non-thermal component.," Sadly, due to the faintness of the source no spectral information could be obtained but the high $N_{\rm H}$ (as measured in outburst with the XRT) in-front of the source makes it difficult to detect any soft, thermal component and it is very likely that the emission we observe is (mostly) due to a non-thermal component."479 With the current data no sensible upper limits can be obtained on any thermal component with which we could test cooling mocels for acerction-heatec neutron stars., With the current data no sensible upper limits can be obtained on any thermal component with which we could test cooling models for accretion-heated neutron stars.480 A longer exposureobservation with (with thesource on-axis) or a deep observation (with its much lowerbackground) is needed to study the quiescent emission of this source with the detall necessary to allow, A longer exposureobservation with (with thesource on-axis) or a deep observation (with its much lowerbackground) is needed to study the quiescent emission of this source with the detail necessary to allow481been observed with the IRS: 19 are in our program 40038. 4 in archival program 20125 (G. Lagache. PI.) one in archival program 20083. (M. Lacy. P.I.) and one in archival program 40539 (G. Helou. P.I.).,"been observed with the IRS: 19 are in our program 40038, 4 in archival program 20128 (G. Lagache, P.I.) one in archival program 20083 (M. Lacy, P.I.) and one in archival program 40539 (G. Helou, P.I.)."482 Characteristics and observational details of these 25 sources are 5given in Table I., Characteristics and observational details of these 25 sources are given in Table 1.483 Spilzer spectroscopic observations were made with the Short Low module in orders Land 2 (SLI and οἱ) and with the Long Low module in orders 1: and 2 (LL1 and LL2). described in Ποιοetal.(2004).," $Spitzer$ spectroscopic observations were made with the Short Low module in orders 1 and 2 (SL1 and SL2) and with the Long Low module in orders 1 and 2 (LL1 and LL2), described in \citet{hou04}."484.. These give low resolution spectral coverage [rom 5 to 35πμ]., These give low resolution spectral coverage from $\sim$ to $\sim$.485 For our new observations. sources were placed on the slit by using the IRS peakup mocle with the blue camera < A « 18.7jmm)).," For our new observations, sources were placed on the slit by using the IRS peakup mode with the blue camera $<$ $\lambda$ $<$ )."486 All images when the source was in one of the two nod positions on each slit were coadded (o obtain the image of the source spectrum., All images when the source was in one of the two nod positions on each slit were coadded to obtain the image of the source spectrum.487 The background. whieh was subtracted was determined. from coacldecl background. images that added both nod positions having the source in the other slit (i.e.. both nods on the LL1 slit when the source is in the LL? slit produce LL1 images of background only).," The background which was subtracted was determined from coadded background images that added both nod positions having the source in the other slit (i.e., both nods on the LL1 slit when the source is in the LL2 slit produce LL1 images of background only)."488 The difference between coadded source images minus coadded background images was used [or the spectral extraction. eiving (wo independent extractions of the spectrum for each order.," The difference between coadded source images minus coadded background images was used for the spectral extraction, giving two independent extractions of the spectrum for each order."489 These independent spectra were compared to reject anv hiehlv outlving pixels in either spectrum. and a final mean spectrum was produced.," These independent spectra were compared to reject any highly outlying pixels in either spectrum, and a final mean spectrum was produced."490 The extraction of one dimensional spectra Irom the two dimensional images was done with the SMART analvsis package (Iigdonetal.2004).. beginning with the Basie Calibrated Data products. version 15. of the Spitzer [ux calibration pipeline.," The extraction of one dimensional spectra from the two dimensional images was done with the SMART analysis package \citep{hig04}, beginning with the Basic Calibrated Data products, version 15, of the $Spitzer$ flux calibration pipeline."491 Final spectra were to the approximate resolution of the different URS modules for SLI and SL2. for LL2. and [or LL1).," Final spectra were boxcar-smoothed to the approximate resolution of the different IRS modules for SL1 and SL2, for LL2, and for LL1)."492 Spectra for all FLS sources in Table 1 are illustrated among the spectra in Figures 1-4., Spectra for all FLS sources in Table 1 are illustrated among the spectra in Figures 1-4.493 Spectra for FLS starbursts are in Figure 1 and are truncated al in the rest [rame because of the absence of any significant features in the low resolution spectra bevond that wavelength: most Bootes starburst spectra were illustrated in (2007)., Spectra for FLS starbursts are in Figure 1 and are truncated at in the rest frame because of the absence of any significant features in the low resolution spectra beyond that wavelength; most Bootes starburst spectra were illustrated in \citet{hou07}.494. Spectra for Bootes and FLS AGN in Table 3 are illustrated in Figures 2-4., Spectra for Bootes and FLS AGN in Table 3 are illustrated in Figures 2-4.495 Measured spectral parameters for all starbursts with URS spectra Irom FLS and Bootes, Measured spectral parameters for all starbursts with IRS spectra from FLS and Bootes496for the seunple of Murphy: Webb et al.,"for the sample of Murphy, Webb et al."497"tt. ""This result implies that B>>££). ancl therefore. it also means that the NLED contribution is quite negligible for this sample given the present estimate D,=(0.008+=0.002) μα CMbelek οἱ al."," This result implies that $B \gg B_1$, and therefore, it also means that the NLED contribution is quite negligible for this sample given the present estimate $B_1 = \left(0.008 \pm 0.002 \right)~\mu$ G (Mbelek et al."498 2006)., 2006).499 Thus. we conclude from the measurements of Webb et al.," Thus, we conclude from the measurements of Webb et al."500 and Murphy et al., and Murphy et al.501 that over the redshift range 0.2<z3.7 (Murphy. οἱ al., that = (- 0.543 0.116 ) < 0 over the redshift range $0.2 < z < 3.7$ (Murphy et al.502 2003)., 2003).503" Therefore. relation (24)) can be rewritten as 1. we have whereset D,=13)(Aeccn)+4(0.1654 μα. Thus. comparing the magnitude £D of the mean magnetic field within an intergalactic gas cloud absorber to D.. one of the three following conclusions may be reached: 0.5 trucem 1) no variation of ay. should. be observed from. any sample of absorbing intcrealactic eas cloud such that D.."," Therefore, relation \ref{eq.10}) ) can be rewritten as = -, where we have set $B_{\rm c} = B_1 (\;- \langle \frac{\Delta\alpha_{\rm504GGR}}{\alpha} \rangle )^{-1/4} = (0.165 \pm 0.033)~\mu$ G. Thus, comparing the magnitude $B$ of the mean magnetic field within an intergalactic gas cloud absorber to $B_{\rm c}$, one of the three following conclusions may be reached: 0.5 truecm 1) no variation of $\alpha_{\rm obs}$ should be observed from any sample of absorbing intergalactic gas cloud such that $B \simeq B_{\rm c}$ ."505 This could be the case of Chand et al. (, This could be the case of Chand et al. (5062004). Srianand et al. (,"2004), Srianand et al. ("5072004) samples. but see Murphy et al. (,"2004) samples, but see Murphy et al. ("50820076) quoted above and the answer of Sriananel ct al. (,2007e) quoted above and the answer of Srianand et al. (5092007). 0.5 trucem 2) a negative variation of a... should be observed from any sample of absorbing intergalactic gas cloud such that 2D. (ease of Murphy. Webb ct al.,"2007), 0.5 truecm 2) a negative variation of $\alpha_{\rm obs}$ should be observed from any sample of absorbing intergalactic gas cloud such that $B > B_{c}$ (case of Murphy, Webb et al."510 samples). 0.5 trucem 3) a positive variation of eon. should be observed from any sample of absorbing intergalactic gas cloud such that D«D. (case of Levshakov ct al.," samples), 0.5 truecm 3) a positive variation of $\alpha_{\rm obs}$ should be observed from any sample of absorbing intergalactic gas cloud such that $B < B_{c}$ (case of Levshakov et al."511 sample)., sample).512 Aleanwhile. notice that the LL column densities are provided. neither by Srianand ct al.," Meanwhile, notice that the HI column densities are provided neither by Srianand et al.,"513 Chand et. al., Chand et al.514 nor bv Levshakov et al., nor by Levshakov et al.515 for their studies on the cosmological variation of the fine structure constant., for their studies on the cosmological variation of the fine structure constant.516 However. Srianand et al.," However, Srianand et al."517 pointed. out. that. they have avoided. sub-Damped Lyman Alpha systems. ie. NCL)z10277 7 (Srianand et al.," pointed out that they have avoided sub-Damped Lyman Alpha systems, i. e., $N(HI)518\geq 10^{19}$ $^{-2}$ (Srianand et al."519 2004)., 2004).520" Nevertheless. Boksenberg and Snijders (1981) derived limits to the neutral hvdrogen column density of 510! « Vf) 2en. from their observations of the 2.5,=15251 richest absorpsion system. identified: in the optical region towarels OQ 1101-264."," Nevertheless, Boksenberg and Snijders (1981) derived limits to the neutral hydrogen column density of 5 < N(H) 2, from their observations of the $z_{abs} = 1.8387$ richest absorpsion system identified in the optical region towards Q 1101-264."521 llence. on account that /N(£44)~INCIE)/1000. « AGIT): which implies 0.060 ; DLIUE recen in accordance with the magnitude of the magnetic field RETO rtereel ο. 1.1 « « −⋅2.6m derived from relation SSS(27)) and the new measurement of <<Aenea bv Levshakov et al. (," Hence, on account that $N(H{I}) \sim N(H)/1000$, < N(HI), which implies 0.069 < < 0.144 0.2truecm in accordance with the magnitude of the magnetic field 0.075 < < 0.227 0.2truecm 0.2truecm 1.1 < < 2.6 derived from relation \ref{eq.11}) ) and the new measurement of $<\; \Delta\alpha_{\rm522obs}/\alpha \;>$ by Levshakov et al. ("5232007).,2007).524 We have estimated the distances of the gas. cloud absorbers from the Llubble law by using Jf=68 km s Alpe+., We have estimated the distances of the gas cloud absorbers from the Hubble law by using $H_{0} = 68$ km $^{-1}$ $^{-1}$.525 We emphasize that the estimates of D. in relations (25)) and (30)) are consistent with the avalaible astrophysical data on the magnetic field strength within intergalactic gas clouds., We emphasize that the estimates of $B$ in relations \ref{le-champ-intensite}) ) and \ref{b-field-limit}) ) are consistent with the avalaible astrophysical data on the magnetic field strength within intergalactic gas clouds.526 By using a nonlinear eletrodvnamiücs theory in. which the ellective Lagrangian is the first. order. approximation (after. Alaxwell’s term) of a polynomial series of inverse powers of the electromagnetic invariant quantity δν we have presented a consistent explanation of the controversial results regarding a hypotctical variation of the fine structure constant à since the recombination era.," By using a nonlinear eletrodynamics theory in which the effective Lagrangian is the first order approximation (after Maxwell's term) of a polynomial series of inverse powers of the electromagnetic invariant quantity $F$, we have presented a consistent explanation of the controversial results regarding a hypotetical variation of the fine structure constant $\alpha527$ since the recombination era."528 In these lines. one can state that the large set of observations of quasar absorption svstems are mapping the structure of the intergalactic magnetic field in several directions between the Earth ane absorbers in the sky. in addition to the expansion of the universe as a whole.," In these lines, one can state that the large set of observations of quasar absorption systems are mapping the structure of the intergalactic magnetic field in several directions between the Earth and absorbers in the sky, in addition to the expansion of the universe as a whole."529 In other words. the fact that the ballpark of the observations seem to be controversial could. be interpreted. as an indication that the strength of the local magnetic field in cach of the observed. systems is most likely different from each other.," In other words, the fact that the ballpark of the observations seem to be controversial could be interpreted as an indication that the strength of the local magnetic field in each of the observed systems is most likely different from each other."530 Lenee. any conclusive statement on the actual cosmological evolution of the fine structure constant à rests on a better understanding of the interealactic magnetic field. strength and structure over the whole sky. ancl also on more accurate measurements of the relative magnitude of the fine splitting between resonance absorption lines from far away (quasars.," Hence, any conclusive statement on the actual cosmological evolution of the fine structure constant $\alpha$ rests on a better understanding of the intergalactic magnetic field strength and structure over the whole sky, and also on more accurate measurements of the relative magnitude of the fine splitting between resonance absorption lines from far away quasars."531he Av emission from those regions is partly due to voung stars (Ixnapen et al.,the $K$ emission from those regions is partly due to young stars (Knapen et al.532 1995a.b).," 1995a,b)."533 Our NIB. imaging confirms he location of dust lanes and suspected SE regions. shown * Ixnapen et al. (," Our NIR imaging confirms the location of dust lanes and suspected SF regions, shown by Knapen et al. ("5341995a) in their £A colour index map.,1995a) in their $I-K$ colour index map.535 The locus of the cireumnuclear ring-like structure shows up ominentlv in all racial. profiles., The locus of the circumnuclear ring-like structure shows up prominently in all radial profiles.536 Unfortunatelv. noA/S Jt images are available.," Unfortunately, no NIR images are available."537 NGC 5248 is a galaxy with anHii nucleus and a lot of SE activity in the CNR., NGC 5248 is a galaxy with an nucleus and a lot of SF activity in the CNR.538 Elmeereen et al. (, Elmegreen et al. (5391997) found very conspicuous central spiral arms. ancl several hotspots that form a ring-like spiral pattern.,"1997) found very conspicuous central spiral arms, and several hotspots that form a ring-like spiral pattern."540 Buta and Crocker (1993) detected a nuclear ring with a diameter of 10.17 aresec., Buta and Crocker (1993) detected a nuclear ring with a diameter of 10–17 arcsec.541 This activity shows up clearly in our broad-band NUR images. as well as in our colour index maps (Fig.," This activity shows up clearly in our broad-band NIR images, as well as in our colour index maps (Fig."542 2k)., 2k).543 Spiral structure with star-forming arms. accompanied by dust lanes. is the dominant feature.," Spiral structure with star-forming arms, accompanied by dust lanes, is the dominant feature."544 The western spiral arm has colours which are redder by about 0.1 mag in JA than its counterpart in the east., The western spiral arm has colours which are redder by about 0.1 mag in $J-K$ than its counterpart in the east.545 Our J.A image has been published: earlier bv Laine et al. (, Our $J-K$ image has been published earlier by Laine et al. (5461999).,1999).547 hey. compared it with the images obtained using adaptive optics. which show a nuclear erauxd-design spiral structure.," They compared it with the images obtained using adaptive optics, which show a nuclear grand-design spiral structure."548 This nuclear spiral. at scales of tens of pc. is not expected to show up in a single broad-band NIB image. even at.LEST resolution. and in fact does not. show up (Fig.," This nuclear spiral, at scales of tens of pc, is not expected to show up in a single broad-band NIR image, even at resolution, and in fact does not show up (Fig."549 1)., 1).550 PheAST H-band image does show a wealth of structure in the CNR. again in the form of emitting regions distributed along spiral arm fragments. and accompanied by less Luminous regions which mav well be dusty.," The $H$ -band image does show a wealth of structure in the CNR, again in the form of emitting regions distributed along spiral arm fragments, and accompanied by less luminous regions which may well be dusty."551 As in other galaxies. we can see the signature of the ring asa peak at a radius of 7 arcsec in all radial profiles.," As in other galaxies, we can see the signature of the ring as a peak at a radius of $\sim7$ arcsec in all radial profiles."552 Phere is no evidence for nested bars., There is no evidence for nested bars.553 The dust structure in the cireumnuclear ring is the mos conspicuous feature in our JA colour index map. bu the star-forming regions in the ring can also be seen in the broad-band images (Fig.," The dust structure in the circumnuclear ring is the most conspicuous feature in our $J-K$ colour index map, but the star-forming regions in the ring can also be seen in the broad-band images (Fig."554 2D., 2l).555 Phe bar dust lanes connect to this nuclear ring in the northeast and. southwest., The bar dust lanes connect to this nuclear ring in the northeast and southwest.556 Severa sites of SE are located along the ring. and its presence is also seen in the ellipticity and PA profiles. as well as in al other profiles (rig.," Several sites of SF are located along the ring, and its presence is also seen in the ellipticity and PA profiles, as well as in all other profiles (Fig."557 21)., 2l).558 We can also see à blue ring at about 2 aresec. within the red. nuclear ring surrounding it.," We can also see a blue ring at about 2 arcsec, within the red nuclear ring surrounding it."559 Εις blue ring shows up as a dip in the JJ.A profile., This blue ring shows up as a dip in the $J-K$ profile.560 Its nature is not. clear. and needs further study.," Its nature is not clear, and needs further study."561 Ehe /-band image. used also by Pérrez ct al. (," The $H$ -band image, used also by Pérrez et al. ("5622000). shows a picture also seen in. e.g.. NGC 3351 and NGC 4314. namely of bright emitting knots,"2000), shows a picture also seen in, e.g., NGC 3351 and NGC 4314, namely of bright emitting knots"563reaclions are taken from ?..,reactions are taken from \citet{caselli02}.564 The rates are temperature dependent and (he reaction rate between (wo species. / and j. is given by where 5;; = Los ο is the activation barrier to (he reaction). Vy is the total number of sites on the surface of the grain and vy is the grain number densitv.," The rates are temperature dependent and the reaction rate between two species, $i$ and $j$, is given by where $\kappa_{ij}$ = $^{-E_a/kT_{gr}}$ $E_a$ is the activation barrier to the reaction), $N_s$ is the total number of sites on the surface of the grain and $n_d$ is the grain number density."565 The rate at which 7 and j scan the surface of the grain is given by /; and /;: where £j is the binding energy (from Table 7)) aud i is given by Equation 5.., The rate at which $i$ and $j$ scan the surface of the grain is given by $t_i$ and $t_j$: where $E_D$ is the binding energy (from Table \ref{tab:be}) ) and $\nu_0$ is given by Equation \ref{eq:nu0}.566 Important parameters are (he binding energies of I1 and D atoms and (heir reaction rates on the grains., Important parameters are the binding energies of H and D atoms and their reaction rates on the grains.567 For the formation rate of I» we have used the work of ?? who developed a moclel of (his process that fits (he experimental data for the reaction of (vo hydrogen atoms on silicate and amorphous carbon grains.," For the formation rate of $_2$ we have used the work of \cite{ct02,ct04}568 who developed a model of this process that fits the experimental data for the reaction of two hydrogen atoms on silicate and amorphous carbon grains."569 Thev find that I» formation can be efficient. at temperatures up to 5500 Ix on these surfaces., They find that $_2$ formation can be efficient at temperatures up to 500 K on these surfaces.570 This model takes into account the possibility of both chemi- aud physi-sorption ancl assumes a high binding energy. of GOO Ix. [or atomic hvedrogen atoms adsorbed onto a silicate surface., This model takes into account the possibility of both chemi- and physi-sorption and assumes a high binding energy of 600 K for atomic hydrogen atoms adsorbed onto a silicate surface.571 This value of Ep(II) is rather higher than the 350 IN 72. which we have assumed in our previous work. and which results in a greatly reduced IH» formation rate at 7/2 15 IX. For deuterium atoms we follow ?. and take Ep(D) = Eph + 21 Ix (21 Ix is the zero point energy difference between the hydrogen and deuterium atoms).," This value of $E_D$ (H) is rather higher than the 350 K \cite{ta87} which we have assumed in our previous work, and which results in a greatly reduced $_2$ formation rate at $T$ $>$ 15 K. For deuterium atoms we follow \citet{caselli02} and take $E_D$ (D) = $E_D$ (H) + 21 K (21 K is the zero point energy difference between the hydrogen and deuterium atoms)."572 Recent caleulations of the binding energy of HE:atoms adsorbed onto water ice have founcl values ranging rom ~ 400 Ix (2). to ~ 575 Ix (2)..," Recent calculations of the binding energy of H–atoms adsorbed onto water ice have found values ranging from $\sim$ 400 K \citep{alh}573 to $\sim$ 575 K \citep{perets05}."574 Our choice of 600 IX is therefore a little high. but consistent with the larger of these calculatecl values.," Our choice of 600 K is therefore a little high, but consistent with the larger of these calculated values."575 Given the uncertainty in {11} we compare the results for Zp(Il) = 600 Ix with those for ZZp(Il) = 350 Ix in section 3.1.5 to determine the effects of our choice on the chemistry., Given the uncertainty in $E_D$ (H) we compare the results for $E_D$ (H) = 600 K with those for $E_D$ (H) = 350 K in Section \ref{sec:h_be} to determine the effects of our choice on the chemistry.576 lonization in the disk can arise from several sources:, Ionization in the disk can arise from several sources:577"multiplicity the smaller the distortion to the interloper distribution compared to the normal one, whether oblate or prolate.","multiplicity the smaller the distortion to the interloper distribution compared to the normal one, whether oblate or prolate."578 Another interesting outcome of these simulations is we find a hard limit for the observable ellipsoid as a function of multiplicity and interloper rate (see Figure 7 for the prolate limits)., Another interesting outcome of these simulations is we find a hard limit for the observable ellipsoid as a function of multiplicity and interloper rate (see Figure \ref{limits} for the prolate limits).579" The observable limit is smallest for groups with the lowest interloper rates and multiplicities, and worst for those with the highest interloper rates and highest multiplicities."," The observable limit is smallest for groups with the lowest interloper rates and multiplicities, and worst for those with the highest interloper rates and highest multiplicities."580" The dependence on interloper rates is how one might expect, but the relation to multiplicity might not be so obvious."," The dependence on interloper rates is how one might expect, but the relation to multiplicity might not be so obvious."581 'These trends are observed strongly for both prolate and oblate shapes., These trends are observed strongly for both prolate and oblate shapes.582" A significant issue is the confusion effect: does the presence of interlopers make a prolate distribution look oblate and vica-versa, and how does multiplicity and the interloper rate affect the possibility of confusion?"," A significant issue is the confusion effect: does the presence of interlopers make a prolate distribution look oblate and vica-versa, and how does multiplicity and the interloper rate affect the possibility of confusion?"583" When confusion occurs it is generally at the largest axial ratios, an understandable result since as prolate and oblate shapes move closer to spherical it requires à smaller amount of random distortion to transform one distribution into the other, and hence it doesn't affect prolate or oblate groups worse."," When confusion occurs it is generally at the largest axial ratios, an understandable result since as prolate and oblate shapes move closer to spherical it requires a smaller amount of random distortion to transform one distribution into the other, and hence it doesn't affect prolate or oblate groups worse."584" It becomes easier to distinguish populations when the axial ratios are lower ( 0.5), however this improvement is lost when axial ratios are very small (less than the effective observable limit) because the distributions become very hard to fit at all"," It becomes easier to distinguish populations when the axial ratios are lower $\sim0.5$ ), however this improvement is lost when axial ratios are very small (less than the effective observable limit) because the distributions become very hard to fit at all."585" The distortion is particularly evident for higher multiplicities, as can be seen in Figure 8.."," The distortion is particularly evident for higher multiplicities, as can be seen in Figure \ref{distortions}."586" Here all the input axial ratios are 0.1 and the interloper rate is only596,, and yet the amount of distortion becomes quite significant as a function of multiplicity."," Here all the input axial ratios are 0.1 and the interloper rate is only, and yet the amount of distortion becomes quite significant as a function of multiplicity."587" In contrast the quality of fitting for axial ratios of 0.7 is very good even when interloper rates are at20%,, as is evident from the QQ-plots in Figure 9.."," In contrast the quality of fitting for axial ratios of 0.7 is very good even when interloper rates are at, as is evident from the QQ-plots in Figure \ref{qqplots}."588" 'The last finding of note is that interloper rates alone account for some degree of distribution broadening, on top of the aforementioned shift to more spherical populations."," The last finding of note is that interloper rates alone account for some degree of distribution broadening, on top of the aforementioned shift to more spherical populations."589" T'his is understandable simply because we are modeling a binomial distribution (every Monte-Carlo galaxy has a chance of being an interloper as described by the interloper and as such there will be an associated spread in rate),observed shapes since when there are many interlopers a given group will appear more"," This is understandable simply because we are modeling a binomial distribution (every Monte-Carlo galaxy has a chance of being an interloper as described by the interloper rate), and as such there will be an associated spread in observed shapes since when there are many interlopers a given group will appear more"590as archival of large. photometric catalogues. gravitational ensing and image cde-projection.,"as archival of large photometric catalogues, gravitational lensing and image de-projection."591" .X precise method. to measure the shear induced by weak lensing on galaxy iniages is presented in an adjoining paper (Itefregier Bacon 2001. ""aper HD."," A precise method to measure the shear induced by weak lensing on galaxy images is presented in an adjoining paper (Refregier Bacon 2001, Paper II)."592 The application of Shapelets to interferometric images will be presented in Chang Itefregier (2001)., The application of Shapelets to interferometric images will be presented in Chang Refregier (2001).593 The analvtical results derived in this paper may also be useful or any application using the Edgeworth expansion. such as. for instance. the study of the growth. of cosmological »erturbations (Juskiewicg et al.," The analytical results derived in this paper may also be useful for any application using the Edgeworth expansion, such as, for instance, the study of the growth of cosmological perturbations (Juskiewicz et al."594 1995 and reference therein)., 1995 and reference therein).595 This paper is organised as follows., This paper is organised as follows.596" In refone,g. . wedeseribethemeainpropertiesofl dimensionalshapeletsanddiseusstheirconnectiontolhec(4 O."," In \\ref{one_d}, we describe the main properties of 1-dimensional shapelets and discuss their connection to the QHO."5971nt lwogquarlesian..weshowhow2 dimensionalshapelelscanbe formedandderiveanumberof practicalanalgl ical resulls.," In \\ref{two_d_cartesian}, we show how 2-dimensional shapelets can be formed and derive a number of practical analytical results."598dnt refeonvolulion.. wediscusshowlheshapeletstatesbehaveunderceonvolulions.," In \\ref{convolution}, we discuss how the shapelet states behave under convolutions."599IEnt wederivepolarshapeletsfromthecartesianbasisfunclionsanddescribesomcoftheirproperlics.," In \\ref{two_d_polar}, we derive polar shapelets from the cartesian basis functions and describe some of their properties."600 Int .wediscussseveraldirectapplicalionsofshapelelbs.," In \\ref{applications}, we discuss several direct applications of shapelets."601Ourconclusionsarepresentedint conclusion., Our conclusions are presented in \\ref{conclusion}.602 We [first consider the description. of a. localisecl object in l-dimension., We first consider the description of a localised object in 1-dimension.603" For this purpose. we first define the cimensionless basis functions where n is a non-negative integer and Z4,Gr) is a hermite polynomial of order η."," For this purpose, we first define the dimensionless basis functions where $n$ is a non-negative integer and $H_{n}(x)$ is a hermite polynomial of order $n$."604 These functions are orthonormal in the sense that where ον is the Kronecker delta symbol., These functions are orthonormal in the sense that where $\delta_{mn}$ is the Kronecker delta symbol.605 Phe first few functions are plotted on figure 1.., The first few functions are plotted on figure \ref{fig:hermite}.606 These functions. which we call “Shapelets’. can be thought of as shape perturbations around the gaussian Oy). Jo describe an object in. practice. we use the dimensional basis functions where 3 ds a characteristic scale. which is typically. chosen to be close to the size of the object.," These functions, which we call `Shapelets', can be thought of as shape perturbations around the gaussian $\phi_{0}(x)$, To describe an object in practice, we use the dimensional basis functions where $\beta$ is a characteristic scale, which is typically chosen to be close to the size of the object."607 These functions are also orthonormal. i.c. This infinite set of functions forms a complete basis for smooth and integrable Functions.," These functions are also orthonormal, i.e. This infinite set of functions forms a complete basis for smooth and integrable functions."608 Thus. a (sullicicntly well behaved) object. profile f(r) can be expanded as From the orthonormality condition (eq. 4].," Thus, a (sufficiently well behaved) object profile $f(x)$ can be expanded as From the orthonormality condition (Eq. \ref{eq:orthonorm}] ]),"609 the shapelet coellicients are given hy In practice. the series of Equation (5)) will converge quickly if the object f(re) is sullieiently localised. and if: and the origin. =0 are not too cdilferent [rom the size and location of the object.," the shapelet coefficients are given by In practice, the series of Equation \ref{eq:decompose}) ) will converge quickly if the object $f(x)$ is sufficiently localised, and if $\beta$ and the origin $x=0$ are not too different from the size and location of the object."610 This series representation is referred to as the Gram-Charlicr series. or. in its asymptotic form. as the I5dgeworth expansion (see eg.," This series representation is referred to as the Gram-Charlier series, or, in its asymptotic form, as the Edgeworth expansion (see eg."611 Juiszkiewicz 1995 and reference therein), Juiszkiewicz 1995 and reference therein).612 These basis functions have a number of useful. properties., These basis functions have a number of useful properties.613" Let us first consider their Fourier transform. which. for an arbitrary function. fr). is defined as With these conventions. the Fourier transform: of the dimensionless basis function ó,(£) is Thus. up to a phase factor. the dimensionless basis functions are invariant under Fourier transforms."," Let us first consider their Fourier transform, which, for an arbitrary function $f(x)$, is defined as With these conventions, the Fourier transform of the dimensionless basis function $\phi_{n}(\xi)$ is Thus, up to a phase factor, the dimensionless basis functions are invariant under Fourier transforms."614 This very useful property can be understood in physical terms from the analogy with the quantum harmonic oscillator (see relqho))., This very useful property can be understood in physical terms from the analogy with the quantum harmonic oscillator (see \\ref{qho}) ).615 The Fourier transform of the dimensional basis function (μη9) is given by ‘Thus. the Fourier transform acts on the basis Functions with an unsurprising change of scale ο tf.," The Fourier transform of the dimensional basis function $B_{n}(x;\beta)$ is given by Thus, the Fourier transform acts on the basis functions with an unsurprising change of scale $\beta \rightarrow \beta^{-1}$ ."616correction to the GJ4436 photometry with the linear trend determined from the average of both reference stars yielded marginally smaller residuals from the light curve fit so it was utilized in the primary reduction.,correction to the 436 photometry with the linear trend determined from the average of both reference stars yielded marginally smaller residuals from the light curve fit so it was utilized in the primary reduction.617 The next step was to normalize the 4436 data to the same relative flux scale., The next step was to normalize the 436 data to the same relative flux scale.618 We were not successful at this no matter which combination of reference star data we used and the differences in the relative flux levels between visits were obvious by eye., We were not successful at this no matter which combination of reference star data we used and the differences in the relative flux levels between visits were obvious by eye.619 We believe that the primary reason for this is due to the varying position of 4436 in the instrument’s FOV., We believe that the primary reason for this is due to the varying position of 436 in the instrument's FOV.620 This happened because the two gyro guiding mode for the prevented the same spacecraft roll angle to be used for all the visits., This happened because the two gyro guiding mode for the prevented the same spacecraft roll angle to be used for all the visits.621" The visit groups 1, 2, and 3 — 6 were each obtained at different rolls."," The visit groups 1, 2, and 3 – 6 were each obtained at different rolls."622" The FGS FOV must not have a flat photometric response at the level our data are sensitive to in addition to the well studied variance in position aberration (i.e.theopticalfieldangledistortion, ?).."," The FGS FOV must not have a flat photometric response at the level our data are sensitive to in addition to the well studied variance in position aberration \citep[i.e. the optical field angle distortion,][]{mcarthur02}."623" Examination of the un-normalized data for the multi-visit set obtained at the same roll show consistent, but still not perfect, relative flux levels."," Examination of the un-normalized data for the multi-visit set obtained at the same roll show consistent, but still not perfect, relative flux levels."624 This supports our hypothesis about the FOV variance., This supports our hypothesis about the FOV variance.625 The lower level disagreement for this group could be a result of still small variances in FOV position even among visits carried out with the same roll or the effects of stellar activity (?).., The lower level disagreement for this group could be a result of still small variances in FOV position even among visits carried out with the same roll or the effects of stellar activity \citep{demory07}.626 We see no way to distinguish between the these two effects with the current data., We see no way to distinguish between the these two effects with the current data.627" The reference stars were never placed in the same position in the FOV as 4436, and indeed this would not have been possible due to guiding and FGS pointing restrictions."," The reference stars were never placed in the same position in the FOV as 436, and indeed this would not have been possible due to guiding and FGS pointing restrictions."628" Therefore, the reference star data cannot be used to correct the relative flux levels of 4436."," Therefore, the reference star data cannot be used to correct the relative flux levels of 436."629 The time dependent response correction described above is still valid because that variance is most likely due to the thermal settling of the telescope itself and should be similar for all the targets., The time dependent response correction described above is still valid because that variance is most likely due to the thermal settling of the telescope itself and should be similar for all the targets.630 Our solution to the relative flux correction problem was to introduce normalization parameters for the data obtained in each of the visits that were solved for during the light curve analysis described in $3., Our solution to the relative flux correction problem was to introduce normalization parameters for the data obtained in each of the visits that were solved for during the light curve analysis described in 3.631 The relative flux levels for the visits determined from this analysis are given in Table 1.., The relative flux levels for the visits determined from this analysis are given in Table \ref{t1}.632 At this point in the reduction we had two time series (X and Y axes) for each of the six visits., At this point in the reduction we had two time series (X and Y axes) for each of the six visits.633 We summed the two sets to make a single time series and analyzed the data as described in $3., We summed the two sets to make a single time series and analyzed the data as described in 3.634 This analysis yielded very poor results., This analysis yielded very poor results.635 The residuals were much larger than expected from counting statistics and clearly correlated (trends and jumps) on ~ mminute timescales., The residuals were much larger than expected from counting statistics and clearly correlated (trends and jumps) on $\sim$ minute timescales.636 Inspection of the data revealed that the source for most of the unusual noise was the X axis data., Inspection of the data revealed that the source for most of the unusual noise was the X axis data.637" When the data from the two axes were analyzed separately, we found that X axis data had residuals twice as large as those from the Y axis despite nearly identical count rates."," When the data from the two axes were analyzed separately, we found that X axis data had residuals twice as large as those from the Y axis despite nearly identical count rates."638" Furthermore, the Y axis transit model residuals do not exhibit obvious correlations like the X axis data."," Furthermore, the Y axis transit model residuals do not exhibit obvious correlations like the X axis data."639 We don't have a definitive explanation for the lower quality of the X axis data., We don't have a definitive explanation for the lower quality of the X axis data.640 We note that since beginning science observations with the FGSIr in 2000 we have consistently (thousands of independent observations) obtained position residuals ~35% higher in X axis data compared to Y axis data when using the instrument for high-precision relative astrometry even though corrections determined from extensive calibration efforts are applied for this work (e.g.??)..," We note that since beginning science observations with the FGS1r in 2000 we have consistently (thousands of independent observations) obtained position residuals $\sim$ higher in X axis data compared to Y axis data when using the instrument for high-precision relative astrometry even though corrections determined from extensive calibration efforts are applied for this work \citep[e.g.][]{benedict07,bean07}."641 This discrepancy is similar in magnitude but opposite what was seen in data from FGS3 when it was used for science observations., This discrepancy is similar in magnitude but opposite what was seen in data from FGS3 when it was used for science observations.642" The effect we see in the 4436 photometry is likely related to this issue, but relatively larger possibly due to a lack of any sort of known applicable correction."," The effect we see in the 436 photometry is likely related to this issue, but relatively larger possibly due to a lack of any sort of known applicable correction."643 We ultimately decided to set aside the X axis data because the expected V2 reduction in counting noise from including these data is more than negatively compensated by the larger errors introduced by using it., We ultimately decided to set aside the X axis data because the expected $\sqrt{2}$ reduction in counting noise from including these data is more than negatively compensated by the larger errors introduced by using it.644" The final time series that we analyzed as described in $3 was created by binning only the Y axis HHz measurements to 60ss samples, which yielded 180 data points."," The final time series that we analyzed as described in 3 was created by binning only the Y axis Hz measurements to s samples, which yielded 180 data points."645 The adopted values for each bin were the average of the counts and the initial error estimate was the error in the mean., The adopted values for each bin were the average of the counts and the initial error estimate was the error in the mean.646" These data are given in Table 2, which is only available electronically from the CDS."," These data are given in Table 2, which is only available electronically from the CDS."647 We modeled the obtained photometric time series of 4436 using the exact analytic formulae given by ? for a planetary transit., We modeled the obtained photometric time series of 436 using the exact analytic formulae given by \citet{mandel02} for a planetary transit.648 To account for the stellar limb darkening we calculated flux-weighted theoretical spectra for 18 different angles from the central line of sight and integrated them over the unique bandpass of the FGS with the F583W filter., To account for the stellar limb darkening we calculated flux-weighted theoretical spectra for 18 different angles from the central line of sight and integrated them over the unique bandpass of the FGS with the F583W filter.649" We used the latest version of the PHOENIX model atmosphere code (?) for these calculations with the stellar parameters given by ? as determined from a spectral synthesis analysis (T.7 = KK, log g = 4.92, and [M/H] = -0.33)."," We used the latest version of the PHOENIX model atmosphere code \citep{hauschildt99} for these calculations with the stellar parameters given by \citet{bean06} as determined from a spectral synthesis analysis $T_{eff}$ = K, log g = 4.92, and [M/H] = -0.33)."650 We fitted the calculated, We fitted the calculated651(,.652"68) Here, we have multiplied the spectrum (52)) by normalization constant 32/9; such that the total energy radiated matches that given by Larmor’s formula (40)): ."," Here, we have multiplied the spectrum \ref{HyperAllmu}) ) by normalization constant $32/9\pi$ such that the total energy radiated matches that given by Larmor's formula \ref{larmor}) ):."653" If the details of the emission on angular scales a*/L are unimportant, a 6-function’ aapproximation can be used."," If the details of the emission on angular scales $\accel/L$ are unimportant, a $\delta$ approximation can be used."654" While the integration over solid angle cannot be found, a simple function that approximates the angular integrated spectrum is fracc3wa*),"," While the integration over solid angle cannot be found, a simple function that approximates the angular integrated spectrum is ),."655 The accuracy Lobof ATDthis approximation can be seen in Figure 2 where the function is plotted together with the numerically integrated value of (67)) for a range of L/a*.," The accuracy of this approximation can be seen in Figure \ref{HyperApproxFig}656 where the function is plotted together with the numerically integrated value of \ref{Hyperestimate}) ) for a range of $L/\accel$."657 The maximum photon energy produced can be reasonably approximated as mc2-LÉ[[a* =enspace., The maximum photon energy produced can be reasonably approximated as = = .658". As we discuss in section 5,, this that each electron that traverses the gap from x=0 to impliesx= produces on average ας photons of frequency ω~Wmax, Lwhere ar is the fine-structure constant."," As we discuss in section \ref{pulsars}, this implies that each electron that traverses the gap from $x=0$ to $x=L$ produces on average $\alpha_{\rm f}$ photons of frequency $\omega\sim\omega_{\rm max}$, where $\alpha_{\rm f}$ is the fine-structure constant."659 In this section we consider two special cases for which approximate or analytic expressions can be found., In this section we consider two special cases for which approximate or analytic expressions can be found.660 The first is an isolated structure containing a reversal of the the electric field., The first is an isolated structure containing a reversal of the the electric field.661" To facilitate the analysis, we choose a particle orbit of the form with ((Q,))75)|Bo|<1, i.e., the particle starts and finishes its orbit at rest, while its position suffers a displacement of 20β0/Ώρ."," To facilitate the analysis, we choose a particle orbit of the form _0 ) with $\left|\beta_0\right|<1$, i.e., the particle starts and finishes its orbit at rest, while its position suffers a displacement of $2c\beta_0/\Omega_0$."662 The maximum particle speed is co., The maximum particle speed is $c\beta_0$.663 The electric field at the position of the particle isenspace., The electric field at the position of the particle is.664". Of the many functions E(x,f) that can provide such a trajectory, those representing an isolated structure that is either static or moving at constant, subluminal velocity (which is nowhere equal to the particle speed) are perhaps the that are physically realistic."," Of the many functions $E(x,t)$ that can provide such a trajectory, those representing an isolated structure that is either static or moving at constant, subluminal velocity (which is nowhere equal to the particle speed) are perhaps the simplest that are physically realistic."665" In the static case, the electric simplestfield is simply E(x)="," In the static case, the electric field is simply E(x) ="666bimodal. aud this division is somewhat arbitrary.,"bimodal, and this division is somewhat arbitrary."667 More precise age estimates will be enabled with the use of UV and/or Ho imaging: such data already exist [or a portion of the observed fielcl and will be utilized in a future paper., More precise age estimates will be enabled with the use of UV and/or $\alpha$ imaging; such data already exist for a portion of the observed field and will be utilized in a future paper.668 Of the 2920 star cluster candidates in our sample. 1877 (051) are blue. with 0.45.," Of the 2920 star cluster candidates in our sample, 1877 ) are blue, with $(B-V)_0<0.45$ ."669 The effect of our 7=23.5 magnitude limit is such that our cluster sample contains [aint clusters only if they are red., The effect of our $I=23.5$ magnitude limit is such that our cluster sample contains faint clusters only if they are red.670 The bluest clusters in our sample have V—722—0.5. so (he sample is not color-biased above V.—23 (Ady=—6.1).," The bluest clusters in our sample have $V-I \approx -0.5$, so the sample is not color-biased above $V=23$ $(M_V=-6.1)$."671 To this limit. there are 1715 cluster candidates of which 1260 (73%)) are blue.," To this limit, there are 1715 cluster candidates of which 1260 ) are blue."672 Figure 4. shows the spatial distribution of the MIOLI candidates. both the complete sample and the bright (V.«23) red and blue subsamples.," Figure \ref{color-spat} shows the spatial distribution of the M101 candidates, both the complete sample and the bright $V<23$ ) red and blue subsamples."673 The spiral pattern of the galaxy is more apparent in the blue clusters., The spiral pattern of the galaxy is more apparent in the blue clusters.674 This is consistent with them being vounger and associated with star formation in (he spiral aruis. and indeed the bluest clusters ((2—V)< 0.2) trace the arms even more clearly.," This is consistent with them being younger and associated with star formation in the spiral arms, and indeed the bluest clusters $(B-V)<0.2$ ) trace the arms even more clearly."675 Observed color distributions for the candidates ave shown in Figure 5.., Observed color distributions for the candidates are shown in Figure \ref{2color}.676 The left panel of this ligure compares the colors lor M1OI clusters to those in other nearby spirals: M81 (Chandaretal.2001a).. M33 (Mochejskaetal.1993).. and M51. (Biketal.2003): these colors have not been corrected [or reddening.," The left panel of this figure compares the colors for M101 clusters to those in other nearby spirals: M81 \citep{cft1}, M33 \citep{m98}, and M51 \citep{bik03}; these colors have not been corrected for reddening."677 The color distribution of MIOLI candidates is most similar to that of the M33 candidates. which is unsurprising given that the (wo galaxies are the same IIubble type ancl have a similar specilic star formation rate.," The color distribution of M101 candidates is most similar to that of the M33 candidates, which is unsurprising given that the two galaxies are the same Hubble type and have a similar specific star formation rate."678 ALLOL has [fewer blue elusters than M51. and fewer red. clusters than M81., M101 has fewer blue clusters than M51 and fewer red clusters than M81.679 This is broadly consistent. with a picture in which the proportion of blue to red clusters reflects the recent star formation rate (M51 might be expected (to have enhanced star formation due to encounters will its companion). and the number of red clusters is proportional to the galaxy. bulge mass (which is larger for M81. an earlier-tvpe galaxy (han MIOL).," This is broadly consistent with a picture in which the proportion of blue to red clusters reflects the recent star formation rate (M51 might be expected to have enhanced star formation due to encounters with its companion), and the number of red clusters is proportional to the galaxy bulge mass (which is larger for M81, an earlier-type galaxy than M101)."680 Chandaretal.(2001b) interpret the separation of M81 cluster colors into (wo groups (al D—V220.5 and V—J£22 1.0) as a separation in age., \citet{cft2} interpret the separation of M81 cluster colors into two groups (at $B-V\approx0.5$ and $V-I\approx1.0$ ) as a separation in age.681 No such clear separation is apparent in the MIOLI cluster candidates., No such clear separation is apparent in the M101 cluster candidates.682 In the right panel of Figure 5. we compare colors of red. MIOL cluster candidates (o those of globular clusters in the Milky Way (ILarris1996).. M31 (Darmbyοἱal.2000)... and elobular cluster candidates in MIOI itself from Chandaretal.(2004).," In the right panel of Figure \ref{2color} we compare colors of red M101 cluster candidates to those of globular clusters in the Milky Way \citep{h96}, M31 \citep{b00}, and globular cluster candidates in M101 itself from \citet{cwl04}."683. The median colors ol MIOL cluster candidates are clearly consistent with those of the elobulars in the other ealaxies. indicating thal we have indeed detected a population of old elobular clusters in AI101.," The median colors of M101 cluster candidates are clearly consistent with those of the globulars in the other galaxies, indicating that we have indeed detected a population of old globular clusters in M101."684 The larger scatter of the ALLOL colors presumably reflects the larger photometric or recldenine-correction errors., The larger scatter of the M101 colors presumably reflects the larger photometric or reddening-correction errors.685enough ions are present in the dissipation region. as we show below. then a source of anomalous resistivity can be established.,"enough ions are present in the dissipation region, as we show below, then a source of anomalous resistivity can be established."686 We argue that the energy. released. during the precursor was enough to heat the crust to a point where a barvon [aver was evaporated into the magnetosphere., We argue that the energy released during the precursor was enough to heat the crust to a point where a baryon layer was evaporated into the magnetosphere.687 TD95 provide an upper limit to the mass of the barvon laver ablated during a burst by comparing the thermal energy of the burst to that of the potential energy of the mass laver where we have assumed a more conservative estimate of fey., TD95 provide an upper limit to the mass of the baryon layer ablated during a burst by comparing the thermal energy of the burst to that of the potential energy of the mass layer where we have assumed a more conservative estimate of $E_{\rm th}$.688 Then. assuming that AZ amount of barvonic mass. in the form of protons. was injected into the magnetospheric volume of ~2? vielding a barvon number density of Even with the large amount of barvons. (the magnetospheric plasma is still. collisionless.," Then, assuming that $\Delta M$ amount of baryonic mass, in the form of protons, was injected into the magnetospheric volume of $\sim R_{\star}^3$ yielding a baryon number density of Even with the large amount of baryons, the magnetospheric plasma is still collisionless."689" Phe Spitzer resistivity for a quasi-neutral clectron-ion plasma is only a function of the electron. temperature -x7, which for electron temperatures as high as 107 Ix vields a negligible resistivity."," The Spitzer resistivity for a quasi-neutral electron-ion plasma is only a function of the electron temperature $\propto T_e^{-3/2}$, which for electron temperatures as high as $\sim 10^8$ K yields a negligible resistivity."690" For plasma temperatures higher than T3510"" Is. he reconnecting current laver turns into a super-hot urbulent current laver. (SIEECL). for which the theory ix been well developed by and. documented. in. (Somov 2006.. pp."," For plasma temperatures higher than $T>3\times10^7$ K, the reconnecting current layer turns into a super-hot turbulent current layer (SHTCL), for which the theory has been well developed by and documented in \citealt{Somov2006}, pp."691 129-151)., 129-151).692 The anomalous resistivity in the current aver arises due to wave-particle interactions. where the ions interact with field [luctuations in the waves.," The anomalous resistivity in the current layer arises due to wave-particle interactions, where the ions interact with field fluctuations in the waves."693 As a result. the resistivity and other transport coellicients of the asma are altered.," As a result, the resistivity and other transport coefficients of the plasma are altered."694" “Phe electrons are the current. carriers and participate mainlv in the heat conductive cooling of he οο,", The electrons are the current carriers and participate mainly in the heat conductive cooling of the SHTCL.695" The current [laver is assumed to have been venetrated by a relatively weak transverse magnetic Lele component (transverse to the electric field in the current aver) where Dj,Bo with Do as the strength. of he external dipole field."," The current layer is assumed to have been penetrated by a relatively weak transverse magnetic field component (transverse to the electric field in the current layer), where $B_\perp\ll B_0$ with $B_0$ as the strength of the external dipole field."696 In the two temperature model. where the electrons and ions are allowed to have dissimilar emperatures. the ellective anomalous resistivity is generally a combination of two terms.," In the two temperature model, where the electrons and ions are allowed to have dissimilar temperatures, the effective anomalous resistivity is generally a combination of two terms."697 One resulting from the ion-acoustic turbulence and the other from the ion-evelotron urbulence., One resulting from the ion-acoustic turbulence and the other from the ion-cyclotron turbulence.698 In addition. cach turbulent instability has two separate regimes — marginal and saturated.," In addition, each turbulent instability has two separate regimes – marginal and saturated."699 The former applies when the wave-particle interactions are described by quasilinear equations. and the latter becomes important in the case of strong electric fields when the nonlinear contributions can no longer be ignored (see for e.g. Somov1992. pp.," The former applies when the wave-particle interactions are described by quasilinear equations, and the latter becomes important in the case of strong electric fields when the nonlinear contributions can no longer be ignored (see for e.g. \citealt{Somov1992} pp."700 115-217 for a detailed description)., 115-217 for a detailed description).701 For an equal. temperature plasma (Z5.~ 77). the saturated: ion-evelotron turbulent instability makes the dominant contribution to the cllective resistivity.," For an equal temperature plasma $T_e\sim T_i$ ), the saturated ion-cyclotron turbulent instability makes the dominant contribution to the effective resistivity."702 Thus. we ignore any other terms corresponding to the ion-acoustic instability.," Thus, we ignore any other terms corresponding to the ion-acoustic instability."703" Phe effective resistivity in the present case is given as (Somoy2006).. depending on the dimensionless temperature parameter 6—T,/1;. where a=rose is the cllective reconnection rate determined bv the inflow Εις velocity ey into the current [aver. and the rest of the variables in equation (12)) retain their usual meaning."," The effective resistivity in the present case is given as \citep{Somov2006}, depending on the dimensionless temperature parameter $\theta\equiv T_e/T_i$, where $\alpha\equiv v_0/c$ is the effective reconnection rate determined by the inflow fluid velocity $v_0$ into the current layer, and the rest of the variables in equation \ref{eq:effectiveEta}) ) retain their usual meaning."704 Equation (16)) conveys the frozen-in field condition., Equation \ref{eq:frozenin}) ) conveys the frozen-in field condition.705 Next. we write the magnetic diffusivity of the plasma due to the effective anomalous resistivity ↾↓∖∪≼⇍⋜↧↓≼⇍⊔↓⋜⋯⊾∣↓↕∢⋅⊲↓⊔∐∪∖∖⊽↓≻⇂⋜↧⊳∖⊔⋯∖⇁⋖⋅⇂∪≼⋰∐∙∖⇁⊳∖∖⊽∢⊾⋜↧⊳∖⊳∖⊔⊔↓⋖⋅ ↿↓⋯↿⇂↓↥∢⊾∺∐↾↓∖≺⊲∟↕⊳∖∢⋅⊔↓∣⋡⋯⇂∠⇂⋖⋅∠⇂∐↕⋜↧⊔↓⋯⇍↓⋅∪⊳∖≼∙∪↓≻⋠⊔∙∺∖∖⊽∢⋅∢⋅↥− Parker current. laver.," Next, we write the magnetic diffusivity of the plasma due to the effective anomalous resistivity To calculate the inflow plasma velocity, we assume that the SHTCL is embedded in a macroscopic Sweet-Parker current layer."706 The. primary. role of the. SITECIL is to provide enough resistivity in a collisionless plasma so that the magnetic field. lines can diffuse through it. and ultimately undergo reconnection., The primary role of the SHTCL is to provide enough resistivity in a collisionless plasma so that the magnetic field lines can diffuse through it and ultimately undergo reconnection.707 From equation. (7)) we know that for a Sweet-Parker current laver the inflow [uid velocity is regulated by the aspect ratio of the current Laver., From equation \ref{eq:vin}) ) we know that for a Sweet-Parker current layer the inflow fluid velocity is regulated by the aspect ratio of the current layer.708 The outllow: velocity is limited by the speed. of light., The outflow velocity is limited by the speed of light.709 By expressing the width of the Sweet-Parker current. [aver in terms of the magnetic dilfusivitv. we find that the inflow velocity has to be on the order of ej~10ems+ (so that ocx 1). with the width of the laver given as where the transverse magnetic field is By~10.Dy. and L is the length of the current laver.," By expressing the width of the Sweet-Parker current layer in terms of the magnetic diffusivity, we find that the inflow velocity has to be on the order of $v_0\sim10^3\mbox{ cm s}^{-1}$ (so that $\alpha\ll1$ ), with the width of the layer given as where the transverse magnetic field is $B_\perp\sim10^{-3}B_0$, and $L$ is the length of the current layer."710 The size of the SLUPCL can now be obtained from the following where e and b are. respectively. the half-width and the," The size of the SHTCL can now be obtained from the following where $a$ and $b$ are, respectively, the half-width and the"711Low-power radio galaxies appear to be tuned such that their average jet kinetic powers. which are dictated by the rate of accretion onto a central supermassive black hole. provide the heating and momentum input required to limit star formation in their host galaxies by keeping the gas hot (e.g.. 2007)..,"Low-power radio galaxies appear to be tuned such that their average jet kinetic powers, which are dictated by the rate of accretion onto a central supermassive black hole, provide the heating and momentum input required to limit star formation in their host galaxies by keeping the gas hot \citep[e.g.,][]{granato, kawata, best,712schawinski}."713 This adds to the interest in studying jets and their lifecycles. and one issue of importance in the study of this feedback process is how the kinetic power of individual sources varies with time.," This adds to the interest in studying jets and their lifecycles, and one issue of importance in the study of this feedback process is how the kinetic power of individual sources varies with time."714 Historically the radio emission has been used as a probe., Historically the radio emission has been used as a probe.715 However. the loss lifetimes of electrons responsible for the radiation exceed flow times along many resolvable jet structures. and thus the radiation that is observed holds only a time-averaged trace of changes to the central power output and local environmental effects along the jet.," However, the loss lifetimes of electrons responsible for the radiation exceed flow times along many resolvable jet structures, and thus the radiation that is observed holds only a time-averaged trace of changes to the central power output and local environmental effects along the jet."716 X-ray studies of low-power radio galaxies came into omruition withChandra. whose aresec-scale resolution (Weisskopfαal.2000). supports the common detection of resolved X-ray ynehrotron emission from their kpe-seale jets (Worrall.Birkin-ynaw&Hardeastle 20013..," X-ray studies of low-power radio galaxies came into fruition with, whose arcsec-scale resolution \citep{weisskopf} supports the common detection of resolved X-ray synchrotron emission from their kpc-scale jets \citep*{worrall01}. ."717 For X-ray emission the electron energy- lifetimes are short compared with light travel times over the Palructures that are detected. and a focus of much current work is therefore the use of X-ray emission as a probe of distributed particle acceleration (seeWorrall2009.forareview).," For X-ray emission the electron energy-loss lifetimes are short compared with light travel times over the structures that are detected, and a focus of much current work is therefore the use of X-ray emission as a probe of distributed particle acceleration \citep[see][for a review]{worrall}."718 Most resolved X-ray jets in low-power radio sources correspond to the brighter radio jet onlv. indicating that the X-rays are notdetected without the assistance of relativistic boosting," Most resolved X-ray jets in low-power radio sources correspond to the brighter radio jet only, indicating that the X-rays are notdetected without the assistance of relativistic boosting"719We have introduced and presented a method dubbed that removes instrumental artefacts from CoRoT data and demonstrated its usefulness in some practical applications.,We have introduced and presented a method dubbed that removes instrumental artefacts from CoRoT data and demonstrated its usefulness in some practical applications.720 We emphasize that the algorithm can be used to prepares CoRoT data for any transit detection but should not be used for transit analysis because it can remove real signal., We emphasize that the algorithm can be used to prepares CoRoT data for any transit detection but should not be used for transit analysis because it can remove real signal.721 This is not of course a problem for the detection inasmuch as instrumental jumps affect far more the light curve., This is not of course a problem for the detection inasmuch as instrumental jumps affect far more the light curve.722" From our study of 1030 light curves in the first CoRoT field (IRao01), we found that only very few light curves have no instrumentally caused features and remain as they are, while the vast majority of light curves are appreciably improved."," From our study of 1030 light curves in the first CoRoT field (IRao01), we found that only very few light curves have no instrumentally caused features and remain as they are, while the vast majority of light curves are appreciably improved."723 We have presented some examples that show how the algorithm affects the light curves., We have presented some examples that show how the algorithm affects the light curves.724" Our main conclusion is that instrumental jumps substantially affect the CoRoT light curves, making a transit detection in fainter stars impossible."," Our main conclusion is that instrumental jumps substantially affect the CoRoT light curves, making a transit detection in fainter stars impossible."725" To illustrate how the algorithm affect the data of the full sample, we calculated the median absolute deviation (MAD) before and after applying 13 "," To illustrate how the algorithm affect the data of the full sample, we calculated the median absolute deviation (MAD) before and after applying \ref{fig9} "726We solve equation at several resolutions.,We solve equation at several resolutions.727 The hieliest resolution uses 297 collocation points in each rectangular block. 29«2112 collocation points (radial. ϐ and o directions) iu the iucr spherical shells aud 29«1632 im the outer spherical shell.," The highest resolution uses $29^3$ collocation points in each rectangular block, $29\times 21\times 42$ collocation points (radial, $\theta$ and $\phi$ directions) in the inner spherical shells and $29\times 16\times 32$ in the outer spherical shell."728 We use the differeuce in the solutions at neieliboriug resolutious as a iucasure of the error., We use the difference in the solutions at neighboring resolutions as a measure of the error.729 We denote the pointwise maxinuun of this difference bv {νε aud the rootziueau-square of the grid point values by £o., We denote the pointwise maximum of this difference by $L_{inf}$ and the root-mean-square of the grid point values by $L_2$.730 We also compute at cach resolution the quantity which is the total mass of the binary black hole system., We also compute at each resolution the quantity which is the total mass of the binary black hole system.731 AL will be needed iu the comparison to a finite difference code below., $M$ will be needed in the comparison to a finite difference code below.732 The difference AM between AL at ucieliboriug resolutions is again a measure of the error of the solution., The difference $\Delta M$ between $M$ at neighboring resolutions is again a measure of the error of the solution.733 Figure 5. shows the couvergeuce of the solution c with increasing resolution., Figure \ref{fig:Convergence-BBH} shows the convergence of the solution $\psi$ with increasing resolution.734 Since the rectangular blocks aud the spheres have ciffereut ummbers of collocation points. the cube root of the total number of degrees of freedom. Nog is used to label the w-asis.," Since the rectangular blocks and the spheres have different numbers of collocation points, the cube root of the total number of degrees of freedom, $N_{DF}^{1/3}$ is used to label the $x$ -axis."735 The exponential convergence is apparent., The exponential convergence is apparent.736 Because of the exponcutial convergence. and because Linf. L2 and AA utilize differences to the next lower resolution. the errors given iu figure 5 are esseutially the errors of the nextlower resolution.," Because of the exponential convergence, and because Linf, L2 and $\Delta M$ utilize differences to the next lower resolution, the errors given in figure \ref{fig:Convergence-BBH} are essentially the errors of the next resolution."737" Note that at the highest resolutious the approximation of the outer boundary condition bv a Dirichlet bouudiryv coudition at finite outer radius 109 becomes appareut: If we move the outer boundary to 1010, AZ changes by 2-10.? which is of order 1/109 as expected."," Note that at the highest resolutions the approximation of the outer boundary condition by a Dirichlet boundary condition at finite outer radius $10^9$ becomes apparent: If we move the outer boundary to $10^{10}$, $M$ changes by $2\cdot 10^{-9}$ which is of order $1/10^9$ as expected."738 Ou the coarsest resolution c= Lis used as the initial euess;, On the coarsest resolution $\psi=1$ is used as the initial guess.739 Newtou-Raplsou then needs six iterations to converge., Newton-Raphson then needs six iterations to converge.740 On the finer resolutions we use the result of the previous level as the initial guess., On the finer resolutions we use the result of the previous level as the initial guess.741 These initial guesses are so good that one Newtou-Raplson iteration is sufficient on cach resolution., These initial guesses are so good that one Newton-Raphson iteration is sufficient on each resolution.742"No Stokes I or V variability has been found forJ1354-0206,, neither for the several sources close toVir.","No Stokes I or V variability has been found for, neither for the several sources close to."743. Dynamical spectra are shown in Fig. 1.., Dynamical spectra are shown in Fig. \ref{spe}.744" Heliocentric rotational phases, computed by using the ephemerisby Pyperetal.(1998),, indicate that the peak ""a"" of April 23rd and the ""b"" of April 30th occur at the same phase (¢z 0.55), when the star is oriented in space in the same way relatively to the Earth."," Heliocentric rotational phases, computed by using the ephemerisby \citet{pyp98}, indicate that the peak ""a"" of April 23rd and the ""b"" of April 30th occur at the same phase $\phi\approx 0.55$ ), when the star is oriented in space in the same way relatively to the Earth."745 Fig., Fig.746" 2 shows the polarized flux average in the two bands as a function of the rotational phase, stressing the coincidence in phase of ""à"" and ""b"" events and a significant level of variability between the two observations."," \ref{phase} shows the polarized flux average in the two bands as a function of the rotational phase, stressing the coincidence in phase of ""a"" and ""b"" events and a significant level of variability between the two observations."747" All the three events last approximately 1 hour each; ""c"" exhibits a single peak of flux levels of about 20 mJy; ""a"" and ""b"" lower and broader emission, with two components in the ""b"" event."," All the three events last approximately 1 hour each; ""c"" exhibits a single peak of flux levels of about 20 mJy; ""a"" and ""b"" lower and broader emission, with two components in the ""b"" event."748" The phase difference between ""a"" (or ""b"") and ""c"" events is about 0.4."," The phase difference between ""a"" (or ""b"") and ""c"" events is about 0.4."749" This allows to recognize the same peaks of emission reported by Trigilioetal. (2000),, Trigilioetal.(2008) and"," This allows to recognize the same peaks of emission reported by \citet{tri00}, , \citet{tri08} and"750We may relate the outer vertical scale of the turbulence L- to the height of the disk H by introducing yet another parameter L- = mss where #j-«I.,We may relate the outer vertical scale of the turbulence $L_z$ to the height of the disk $H$ by introducing yet another parameter L_z = H where $\eta_z< 1$ .751" Recalling that H/A,~7. the wave temperature becomestau;-2n."," Recalling that $H/\lambda_p \simeq \tau$, the wave temperature becomes."752 Now. we may write the turbulent v-parameter as ye _(64) where nduip<| and 7? was chosen since 7>| for thin disks.," Now, we may write the turbulent $y$ -parameter as ) ) where $\eta^{2r}_R\,\eta^{2s}_{\phi}\,\eta^{2n}_z\leq 1 $ and $\tau^2$ was chosen since $\tau > 1$ for thin disks."753 Interestingly. eq. (61))," Interestingly, eq. \ref{reducedtemp}) )"754" tells us that 744,9.»Z4) if ", tells us that $T_w(\lambda_p)\rightarrow T_w(\lambda_0)$ if 1.755This is only possible near the inner-edge since for thin disks., This is only possible near the inner-edge since for thin disks.756" Close to the hole. where a large fraction of the disk’s power is released. A, approaches Ao as long as 7/ and n are sufficiently large."," Close to the hole, where a large fraction of the disk's power is released, $\lambda_p$ approaches $\lambda_0$ as long as ${\dot m}$ and $\alpha$ are sufficiently large."757" When this is the case. v, is roughly given by the product of the wave temperature on the outer scale T.(Ao) and the square of the optical depth tau"," When this is the case, $y_w$ is roughly given by the product of the wave temperature on the outer scale $T_w(\lambda_0)$ and the square of the optical depth ^2."758 Equations (40)) and (68)) then allow us to writeC, Equations \ref{kerrwavetemp}) ) and \ref{tau}) ) then allow us to write.759"A*(72) That is. when A,~Ao. the turbulent y-parameter is approximatelyr"," That is, when $\lambda_p\sim\lambda_0$ , the turbulent $y$ -parameter is approximately."760"adius, Figure 1. shows turbulent wave temperatures for maximally spinning black holes of varying 7 and o.", Figure \ref{fig:wavetemp} shows turbulent wave temperatures for maximally spinning black holes of varying ${\dot m}$ and $\alpha$.761" The radius at which 7; reaches its maximum value coincides with the most luminous radius of the disk. a consequence of 7), directly scaling with the aceretion stress."," The radius at which $T_w$ reaches its maximum value coincides with the most luminous radius of the disk, a consequence of $T_w$ directly scaling with the accretion stress."762" The curves shown in Figure 1. are independent of black hole mass. a result of c, and 7 being independent of black hole mass."," The curves shown in Figure \ref{fig:wavetemp} are independent of black hole mass, a result of $c_s$ and $\tau$ being independent of black hole mass."763" The curve labeled ""c"" depicts turbulent wave temperatures for vi and a = 0.1.", The curve labeled “c” depicts turbulent wave temperatures for ${\dot m}$ and $\alpha$ = 0.1.764 For this particular case. the turbulence was confined to the upper-most 1/10 of the disk.," For this particular case, the turbulence was confined to the upper-most 1/10 of the disk."765 Confinement of the turbulence to a thin upper layer may be possible since regions of large magnetic pressure will be relatively buoyant., Confinement of the turbulence to a thin upper layer may be possible since regions of large magnetic pressure will be relatively buoyant.766 Identical wave temperatures and y-parameters may be attained for a given jn by reducing «| by afactor £ while confining the turbulence to a narrow upper layer whose optical thickness is 7/f. implying that the local turbulentstresses are f£ times larger than the vertically averaged value.," Identical wave temperatures and $y$ -parameters may be attained for a given ${\dot m}$ by reducing $\alpha$ by a factor $f$ while confining the turbulence to a narrow upper layer whose optical thickness is $\tau/f$, implying that the local turbulentstresses are $f$ times larger than the vertically averaged value."767 Of course. this onlyapplies for our constant density disk atmosphere model where each optical depth occupies an equal amount of height.," Of course, this onlyapplies for our constant density disk atmosphere model where each optical depth occupies an equal amount of height."768 (A1240) = 0.6 7+0.07 and Lyo (AL216) = 0.87 + 0.03.,$\lambda$ 1240) = 0.67 $\pm$ 0.07 and $\alpha$ $\lambda$ 1216) = 0.87 $\pm$ 0.03.769 Fhree important conclusions arise [rom these results., Three important conclusions arise from these results.770 First. we clo not obtain any [αἱ correlation between the DaA values and the waveleneth/ceeree of ionization.," First, we do not obtain any fair correlation between the $B/A$ values and the wavelength/degree of ionization."771 Second. the average of the five measurements is z 0.75. Le. totally consistent with the macrolens ratio.," Second, the average of the five measurements is $\approx$ 0.75, i.e., totally consistent with the macrolens ratio."772 Third. for each pair of lines. there are several individual channes (at some wavelenghs within the integrationD interval) leading5 to {ux ratios in disagreement with the macrolens ratio.," Third, for each pair of lines, there are several individual channels (at some wavelengths within the integration interval) leading to flux ratios in disagreement with the macrolens ratio."773" T""herefore. it is not suroising to infer an anomalous [ux ratio from a refatively small collection of channels."," Therefore, it is not surprising to infer an anomalous flux ratio from a relatively small collection of channels."774 For example. due o the resolution of the gratings and the presence of prominent absorption features and blending. theIL. and Lye lines are studied through 317 channels.," For example, due to the resolution of the gratings and the presence of prominent absorption features and blending, the, and $\alpha$ lines are studied through 13–17 channels."775 However. we use 3637 channels or the and lines (see Table 1).," However, we use 36–37 channels for the and lines (see Table 1)."776 We interpret the continuumemission lines results in the following wav: while the bro:wlline emission region (BLIZIU) does not experience cilerential extinction as a whole. the continuum source and some substructures of the BLER do suller it.," We interpret the continuum/emission lines results in the following way: while the broad–line emission region (BLER) does not experience differential extinction as a whole, the continuum source and some substructures of the BLER do suffer it."777 Thus. a network of com»wt clusty clouds in he lens galaxy secms to be involved.," Thus, a network of compact dusty clouds in the lens galaxy seems to be involved."778 The longimescale evolution of D/:A in the £2? optical filter agrees with our interpretation (Oscoz et al., The long–timescale evolution of $B/A$ in the $R$ optical filter agrees with our interpretation (Oscoz et al.779 2002)., 2002).780 Phe lack of microlensing in the continuum ratios suggests that no stars are present within the dusty regions crossing the A and D images., The lack of microlensing in the continuum ratios suggests that no stars are present within the dusty regions crossing the A and B images.781 Hence. the ckμις do not seem to be associated to stars and the network is probably embedded in the elliptical galaxy dark halo.," Hence, the clouds do not seem to be associated to stars and the network is probably embedded in the elliptical galaxy dark halo."782 Spectroscopy. and multiband photometry of lensecl quasars ave throwing light on the cdillerential extinction. and microlensing of the continuum and emission line regions., Spectroscopy and multiband photometry of lensed quasars are throwing light on the differential extinction and microlensing of the continuum and emission line regions.783 Apart from our concusions on the CER and BLER of QSO 0957|561 (there is clillerential extinction of the CLR and some substructures of the BLER. but no gravitational microlensing) there are other very recent results on the subject.," Apart from our conclusions on the CER and BLER of QSO 0957+561 (there is differential extinction of the CER and some substructures of the BLER, but no gravitational microlensing) there are other very recent results on the subject."784 For example. Wucknitz ct αἱ. (," For example, Wucknitz et al. ("7852003) analvzed data of QSO LE 3329.,2003) analyzed data of QSO HE $-$ 3329.786 Assuming that the emission line [lux ratios are only alfected by dillercntial extinction. the authors properly. corrected. the continuum flux ratios and found evidence for a microlensed CLR.," Assuming that the emission line flux ratios are only affected by differential extinction, the authors properly corrected the continuum flux ratios and found evidence for a microlensed CER."787 Wavth. ODowd Webster (2005) also reported [ux ratios of QSO 237|0305.," Wayth, O'Dowd Webster (2005) also reported flux ratios of QSO 2237+0305."788 After applying corrections for cilferential extinction. they argued that both the CER and BLER must be microlensed.," After applying corrections for differential extinction, they argued that both the CER and BLER must be microlensed."789 We note that the four images of the system cross the bulge of a faceon Sab spiral galaxy., We note that the four images of the system cross the bulge of a face–on Sab spiral galaxy.790 Finally. from data of," Finally, from data of"791of 400 s. We do this to avoid apparent Dux variations due to the ROSA wobble period of about 400 s. Brinkmann et al. (,of 400 s. We do this to avoid apparent flux variations due to the $ROSAT$ wobble period of about 400 s. Brinkmann et al. (7921994) have shown that [lux determination in wobble mocde is good to within  4 per cent when binning over integer multiples of the 400 s wobble period.,1994) have shown that flux determination in wobble mode is good to within $\sim$ 4 per cent when binning over integer multiples of the 400 s wobble period.793 Moreover. for each time scale a careful analysis of the background. was mace to ensure that observed. variability is not due to a change in the background rate.," Moreover, for each time scale a careful analysis of the background was made to ensure that observed variability is not due to a change in the background rate."794 The light curve of all the sources obtained with a bin of 3600 s are shown in Figure 1., The light curve of all the sources obtained with a bin of 3600 s are shown in Figure 1.795 For each observation we report the source light curve (top panel) and. [or comparison. the background light curve (lower panel).," For each observation we report the source light curve (top panel) and, for comparison, the background light curve (lower panel)."796 1n order to understand and to interpret the properties, In order to understand and to interpret the properties797"Unfortunately, |Zu/IE| estimates exist for only six DLAS of the sample aud for oulv one low T. syste (the :~0.395 absorber towards PISS 1229-021) (Boisséetal.1998.Pettiui1991.Pettini1997.Aleveretal.1989.Mever&York 1992)).","Unfortunately, [Zn/H] estimates exist for only six DLAS of the sample and for only one low ${\rm T_s}$ system (the $z \sim 0.395$ absorber towards PKS 1229-021) \cite{boisse98,pettini94,pettini97,meyer89,meyer92}) )."798 These values are plotted agaimst spin teniperature in Fie. 5:, These values are plotted against spin temperature in Fig. \ref{fig:znts};799 it can be seen that the low Ty system has the highest |Zu/II| ratio of all six absorbers., it can be seen that the low ${\rm T_s}$ system has the highest [Zn/H] ratio of all six absorbers.800 It would be very interesting to test whether this trend persists. for the other absorbers in the salple.," It would be very interesting to test whether this trend persists, for the other absorbers in the sample."801 Fies., Figs.802 6 and 7 plot the velocity spreac AV (ful width between uulls) of the syvstenus with detecte 21 cin absorption against redshift aud spin temperature. respectively. (," \ref{fig:vel} and \ref{fig:vel_ts} plot the velocity spread $\dV$ (full width between nulls) of the systems with detected 21 cm absorption against redshift and spin temperature, respectively. ("803The total velocity spread is used. imstead of the EFWIIM of the absorption profile. to account for the possibility that a sinele line of sight intersects multiple clouds. as is typical iu spiral οealaxics.),"The total velocity spread is used, instead of the FWHM of the absorption profile, to account for the possibility that a single line of sight intersects multiple clouds, as is typical in spiral galaxies.)"804 The plot of AV versus redshift indicates that aree velocity spreads (AV>100 lan ?) ave not found for :=2. while both large and simall spreads are seen at low redshift.," The plot of $\dV$ versus redshift indicates that large velocity spreads $\Delta V > 100$ km $^{-1}$ ) are not found for $z805\ga 2$, while both large and small spreads are seen at low redshift."806 Similarly. Fig.," Similarly, Fig."807 9. shows that. while both low aud high T. values are obtained at low redshift. oulv high values are obtained for 21.5.," \ref{fig:tvsz} shows that, while both low and high ${\rm T_s}$ values are obtained at low redshift, only high values are obtained for $z \ga 1.5$."808 This is qualitatively consistent with what is expected in hierarchical clustering models (e.g. Ixauffinaun 1996). in which svstems with low circular volocities dominate the absorption cross-section at high redshift. while svstenis with both high and low circular velocities are found at low :.," This is qualitatively consistent with what is expected in hierarchical clustering models (e.g. Kauffmann 1996), in which systems with low circular velocities dominate the absorption cross-section at high redshift, while systems with both high and low circular velocities are found at low $z$."809 Next. Fig.," Next, Fig."810 7 shows a possible correlation between the velocity width and the spin temperature of the absorbers. with oulv one svstei (the 2=0.3127 absorber towards PINS 1127-115) havine both a large 21 cin velocity spread aud a high temperature: all other systems with large (AV100 kins 1) velocity widths are identified with low T. spirals.," \ref{fig:vel_ts} shows a possible correlation between the velocity width and the spin temperature of the absorbers, with only one system (the $z = 0.3127$ absorber towards PKS 1127-145) having both a large 21 cm velocity spread and a high temperature; all other systems with large $\dV > 100$ km $^{-1}$ ) velocity widths are identified with low ${\rm T_s}$ spirals."811 The svsteia towards PISS 1127-115 is likely to be tidally disturbed, The system towards PKS 1127-145 is likely to be tidally disturbed812Old accreting neutron stars. NSs. in low mass ο binaries. LAINRBs. display a colmplex variety of quasi-periodic oscillation. QPO. modes in their N-ray flux.,"Old accreting neutron stars, NSs, in low mass X-ray binaries, LMXRBs, display a complex variety of quasi-periodic oscillation, QPO, modes in their X-ray flux."813 The QPOs (~1100 IIz) that were discovered and studied frou hieh huninosity Z-sources in the cighties ave further classified iuto horizoutal. normal aud flaring brauch oscillations (ITIBOs. NBOs iud FBOs. respectively). depending on the simultaneous position occupied by a source in the X-ray colour-colour diagram (for a review see van der Klis 1995).," The QPOs $\sim 1-100$ Hz) that were discovered and studied from high luminosity Z-sources in the eighties are further classified into horizontal, normal and flaring branch oscillations (HBOs, NBOs and FBOs, respectively), depending on the simultaneous position occupied by a source in the X-ray colour-colour diagram (for a review see van der Klis 1995)."814 The κ QPOs (~0.2 to ~1.3 kIIz) that were revealed aud investigated with RATE in a uuuber of NS LAUINRBs (see van der Iklis 1998. 1999. 2000 aud refereuces therein) involve timescales simular to the dvnamucal timescales close to the NS.," The kHz QPOs $\sim 0.2$ to $\sim 1.3$ kHz) that were revealed and investigated with RXTE in a number of NS LMXRBs (see van der Klis 1998, 1999, 2000 and references therein) involve timescales similar to the dynamical timescales close to the NS."815 A coununion phenomenon is the presence of a pair of kIlz QPOs (centroid fequencies of 24 aud v2) which drift in frequency while mantaining their frequeney difference AvSr.νι250.360 Tz roughly coustaut., A common phenomenon is the presence of a pair of kHz QPOs (centroid frequencies of $\nu_1$ and $\nu_2$ ) which drift in frequency while mantaining their frequency difference $\Delta\nu \equiv \nu_2 - \nu_1 \approx 250-360$ Hz roughly constant.816 Detailed studies showed that in four sources A» decreases siguificautlv (by up to 100 Tz) as po Increases: these are Sco N-1 (van der Klis et al., Detailed studies showed that in four sources $\Delta\nu$ decreases significantly (by up to $\sim 100$ Hz) as $\nu_2$ increases; these are Sco X-1 (van der Klis et al.817 1997). IU1608-52 (Mondez ot al.," 1997), 4U1608-52 (Mendez et al."818 1998a.b). IU1735-II (Ford et al.," 1998a,b), 4U1735-44 (Ford et al."819 1998) aud £U1728-31 (Mendez vau der Ilis 1999)., 1998) and 4U1728-34 (Mendez van der Klis 1999).820 Owing to poor statistics. a similar variation of A» in other sources would have remained undetected (Psaltis et al.," Owing to poor statistics, a similar variation of $\Delta\nu$ in other sources would have remained undetected (Psaltis et al."821 1998)., 1998).822 κας OPOs show remarkably similar properties across NS LAINRBs of the Z and, kHz QPOs show remarkably similar properties across NS LMXRBs of the Z and823GRBs column density of neutral gas can still be traced by weakly ionised. metal lines (e.g. Zn Hl. Si HD. which in fact is a more logical method of comparing absorption in N.rays and the optical. given that the XNrays are absorbed by metals and not neutral hydrogen (e.g.Schady et al.,"GRBs column density of neutral gas can still be traced by weakly ionised metal lines (e.g. Zn II, Si II), which in fact is a more logical method of comparing absorption in X–rays and the optical, given that the X–rays are absorbed by metals and not neutral hydrogen (e.g. Schady et al."824 2011)., 2011).825 The X-shooter instrument mounted at the ESO/VLET ollers the best opportunities for these studies., The X-shooter instrument mounted at the ESO/VLT offers the best opportunities for these studies.826 Alaking use of the sox computed by Melandri et al. (, Making use of the $\beta_{OX}$ computed by Melandri et al. (8272011). we found a strong correlation between GlIUD darkness and Xrav absorbing column densities.,"2011), we found a strong correlation between GRB darkness and X–ray absorbing column densities."828 Since metals. are a kev ingredient for dust production (Draine 2003). our findings are consistent with a picture in which the darkness ofa GRB is in most cases due to absorption by circumburst material.," Since metals are a key ingredient for dust production (Draine 2003), our findings are consistent with a picture in which the darkness of a GRB is in most cases due to absorption by circumburst material."829 SC thanks Darach Watson anc Phil Evans for useful conversations., SC thanks Darach Watson and Phil Evans for useful conversations.830 Fhis work has been supported by ASL erant Lfoo4/11/0., This work has been supported by ASI grant I/004/11/0.831 This work macle use of data supplied by the Ulx Science Data Centre at the University of Leicester., This work made use of data supplied by the UK Science Data Centre at the University of Leicester.832tell us iu qualitative teris wren the amount of absorber was hieher or lower. bu it is tot possible to interpret the column density values «)btaiued in a simple way.,"tell us in qualitative terms when the amount of absorber was higher or lower, but it is not possible to interpret the column density values obtained in a simple way."833 If the change in fiux is real then. given that f naguctospleric radius Sis a functio1r οἳ the acevetion rate (RinneονMPO )tus nuelt iauplv an iucrease in f uagnetospherie radiis by about 1tal.," If the change in flux is real then, given that the magnetospheric radius is a function of the accretion rate $R_{\rm mag} \propto 834\dot{M}^{-2/7}$ ) this might imply an increase in the magnetospheric radius by about $10\%$."835 That iu um nieht allow the lower nae’uctic pole of he white dwart to IO nore visible. as wel as reducing the contribution from he impact regio ua the outer οςoo of the «isc.," That in turn might allow the lower magnetic pole of the white dwarf to be more visible, as well as reducing the contribution from the impact region at the outer edge of the disc."836 These wo changes togeher could then coiceivablv explain some of the chauges iu he brond orvital modiation ad some of the chauges in the spin pulse profile that are seen., These two changes together could then conceivably explain some of the changes in the broad orbital modulation and some of the changes in the spin pulse profile that are seen.837 However. trose Modulatious do not simMv chauge svsteimnaticallv from before to afOr the outburst.," However, those modulations do not simply change systematically from before to after the outburst."838 We therefore couclude that there is no conipelliug evidence for a sienificautly altered X-rav flux or coluun density between auv of the various N-raxv observations of NY Avi in quiescence., We therefore conclude that there is no compelling evidence for a significantly altered X-ray flux or column density between any of the various X-ray observations of XY Ari in quiescence.839 So we iust look or other causes of the changes in orbital modulation aud spin pulse profile., So we must look for other causes of the changes in orbital modulation and spin pulse profile.840 The broad orbital modulation secu from NY Avi was prominent when the object was observed byGinga.ASCA. aud between 1989 aud 2000.," The broad orbital modulation seen from XY Ari was prominent when the object was observed by, and between 1989 and 2000."841 By the time of the second observation in 2001. the broad modulation was less apparent with a siguificaut decrease in the low energy modulation depth.," By the time of the second observation in 2001, the broad modulation was less apparent with a significant decrease in the low energy modulation depth."842 In the most recent observatious. withRATE. the broad modulation is," In the most recent observations, with, the broad modulation is"843subject of SSCs in external galaxies. we refer the reader to Whitmore (2000).,"subject of SSCs in external galaxies, we refer the reader to Whitmore (2000)."844 While a lot of effort is beiug devoted to understanding he properties of SSCs. /NICAIOS imaging has ouly recently revealed a population of bright regions iu two LIRGs. Arp 299 and NGC 1611 (CAATIO0: AATIOL).," While a lot of effort is being devoted to understanding the properties of SSCs, /NICMOS imaging has only recently revealed a population of bright regions in two LIRGs, Arp 299 and NGC 1614 (AAH00; AAH01)."845 A larec yaction of these regions show Iuninosities iu excess of hat of 30 Doradus. the prototypical giant region.," A large fraction of these regions show luminosities in excess of that of 30 Doradus, the prototypical giant region."846 One of the main difficulties in quautitving the age of the stellar xo»pulatious in LIRGs aud interacting galaxies is breaking he age-extinction degencracy., One of the main difficulties in quantifying the age of the stellar populations in LIRGs and interacting galaxies is breaking the age-extinction degeneracy.847 This usually translates iuto ouly rough age estimates for SSCs (from photometric data) ranging between 5 aud 900ATIr (sce the recent review x Whitmore 2000)., This usually translates into only rough age estimates for SSCs (from photometric data) ranging between 5 and Myr (see the recent review by Whitmore 2000).848 regions. on the other haud. will üehlieht the vouugest regions of star formation. with ages of«5 10XMvr. as these are the lifetimes of the O aud D stars required to ionize the eas.," regions, on the other hand, will highlight the youngest regions of star formation, with ages of $< 5-10\,$ Myr, as these are the lifetimes of the O and B stars required to ionize the gas."849 Clearly. understaudiug he properties of regions and SSCs. aud their relation at Ligh spatial resolution will provide further insight iuto he nature of the star formation processes in LIRCis.," Clearly, understanding the properties of regions and SSCs, and their relation at high spatial resolution will provide further insight into the nature of the star formation processes in LIRGs."850 Iu this paper we present a study of thedetailed (tens toa ew hundred parsecs) properties of the star forming regions regions aud star clusters) of a sample of 8 LIRGs., In this paper we present a study of the (tens to a few hundred parsecs) properties of the star forming regions regions and star clusters) of a sample of 8 LIRGs.851 This paper is organized as follows., This paper is organized as follows.852 Section (2) describes the observations. data reduction aud the production of the region aud star cluster catalogs.," Section (2) describes the observations, data reduction and the production of the region and star cluster catalogs."853 Iu Section (3) we establish the overall morphology of star forming regions i LIRCs and its relation with the dvuaimical stage of the galaxy., In Section (3) we establish the overall morphology of star forming regions in LIRGs and its relation with the dynamical stage of the galaxy.854 Iu Section (1) the statistical properties of regious iu LIRGs are analyzed and compared with those of normal ealaxies observed at comparable spatial resolutions., In Section (4) the statistical properties of regions in LIRGs are analyzed and compared with those of normal galaxies observed at comparable spatial resolutions.855 The spatial distribution of regions and star clusters. their relative numbers and the age sequence are analyzed in Section (5).," The spatial distribution of regions and star clusters, their relative numbers and the age sequence are analyzed in Section (5)."856 Our conclusions are preseuted in Section (6)., Our conclusions are presented in Section (6).857 The large amount of extinction routinely present in LIRGs. aud in particular. the fact that active star forming regions are expected to contain non-neelieible amounts of dust. prompted us to search theLEST archive for infrared observations.," The large amount of extinction routinely present in LIRGs, and in particular, the fact that active star forming regions are expected to contain non-negligible amounts of dust, prompted us to search the archive for infrared observations."858" The obvious choice was narrow-band Pan and broad-band continua duaecine to identity regions and star clusters respectively,", The obvious choice was narrow-band $\alpha$ and broad-band continuum imaging to identify regions and star clusters respectively.859 This resulted im a sample of cight LIRGs., This resulted in a sample of eight LIRGs.860" The sample covers a range of mfrared huninositices between logLy;=LOOLL.. and logLy;=11.82L.. aswellasa varietv of dynamical stages: isolated ealaxies. close pairs of interacting galaxies and advanced increers,"," The sample covers a range of infrared luminosities –between $\log L_{\rm IR} =86110.94\,{\rm L}_\odot$ and $\log L_{\rm IR} =86211.82\,{\rm L}_\odot$ – as well as a variety of dynamical stages: isolated galaxies, close pairs of interacting galaxies and advanced mergers."863 The sample is presented in Table in increasing order of tufrared Ininositv., The sample is presented in Table in increasing order of infrared luminosity.864 The observations of the LIRGS analyzed in this paper were obtained as part of a varietv of ZZST/NICMOS GTO and GO programs. listed in Table 1.," The observations of the LIRGS analyzed in this paper were obtained as part of a variety of /NICMOS GTO and GO programs, listed in Table 1."865 The Pao |continua inages were taken with the NIC2 aud NICS cameras (pixel size iid 1. respectively) using the narrow-band filter FLOON filter.," The $\alpha$ +continuum images were taken with the NIC2 and NIC3 cameras (pixel size $^{-1}$ and $^{-1}$, respectively) using the narrow-band filter F190N filter."866 At the distances of the ΤΠ sample. this filter (AA/Ac 1%) contains the Pao cussion line aud the adjacent coutinuuni at 1.90 gan. For the continua subtraction. inages through the F187N filter were usec. except for NCC 5653 and NGC. 6808 (from Bolsker et al.," At the distances of the LIRG sample, this filter $\Delta \lambda/\lambda867\simeq 1\%$ ) contains the $\alpha$ emission line and the adjacent continuum at $1.90\,\mu$ m. For the continuum subtraction, images through the F187N filter were used, except for NGC 5653 and NGC 6808 (from Bökker et al."868 1999 survey) for which broud-baud F160W filter observations were einiploved instead., 1999 survey) for which broad-band F160W filter observations were employed instead.869" The field of view of the images is 19.5""« and 51.2""« for the NIC2 and NIC3 observations. respectively."," The field of view of the images is $19.5\arcsec \times 19.5\arcsec$ and $51.2\arcsec \times 51.2\arcsec$ for the NIC2 and NIC3 observations, respectively."870 All the continuuni miaeses used to identify the star clusters were observed through the FIGOW filter which represeuts a eood compromise between the better spatial resolution at shorter wavelengths and lower extinction at longer wavelengths., All the continuum images used to identify the star clusters were observed through the F160W filter which represents a good compromise between the better spatial resolution at shorter wavelengths and lower extinction at longer wavelengths.871 Iu Table 1 for cach galaxy we list the iufrared Iunuinosity. distance (assunuüug Sty=Thkus!Mpe lj. lareo. scale morphology. cameras aud filters used. the corresponding linear scale iu parsec per pixel aud the MST program," In Table 1 for each galaxy we list the infrared luminosity, distance (assuming $H_0 = 75\,{\rm km\,s}^{-1}\,872{\rm Mpc}^{-1}$ ), large scale morphology, cameras and filters used, the corresponding linear scale in parsec per pixel and the program"873mechanisms that can produce such powerful AGN wines in El.,mechanisms that can produce such powerful AGN winds in \ref{sec:discussion}.874 In the subgrid LSAT model of SLIO3. gas with densities above the star formation threshold approaches an ellective thermal energy. Hepp. set by a balance between cooling. and. the feedback from star formation.," In the subgrid ISM model of SH03, gas with densities above the star formation threshold approaches an effective thermal energy, $u_{eff}$, set by a balance between cooling and the feedback from star formation."875 LW processes such as shocks or aciabatic expansion/compression cause the internal energy to deviate [rom ρε. the differences decay on the timescale given by eq. (," If processes such as shocks or adiabatic expansion/compression cause the internal energy to deviate from $u_{eff}$, the differences decay on the timescale given by eq. ("87612) of SLII03.,12) of SH03.877 This decay timescale is set by the προς! model rather than the true cooling time of the gas., This decay timescale is set by the subgrid model rather than the true cooling time of the gas.878 One consequence of SII03s. ISM. model. ijs that sullicienthy dense shock heated: gas does not cool on its cooling timescale., One consequence of SH03's ISM model is that sufficiently dense shock heated gas does not cool on its cooling timescale.879 In this paper we show that ACN winds can shock heat gas in the ISM to above the escape speed his contributes to driving a galactic wind., In this paper we show that AGN winds can shock heat gas in the ISM to above the escape speed – this contributes to driving a galactic wind.880" To ensure that he cooling of the shock heated. gas is correct. we mocified he ISM model of SLI03 to better match the expected cooling rate for gas with roughly a solar metallicity,"," To ensure that the cooling of the shock heated gas is correct, we modified the ISM model of SH03 to better match the expected cooling rate for gas with roughly a solar metallicity."881 To compute he local cooling rate we use a fit to 2? for gas with solar metallicity., To compute the local cooling rate we use a fit to \cite{sutherland93} for gas with solar metallicity.882 The fit is essentially eq. (, The fit is essentially eq. (88312) of 7. but with he cooling rate increased by a factor of two when the cmperature is between ~3103 I and 3.10* Ix (to account or solar metallicity).,12) of \cite{sharma10} but with the cooling rate increased by a factor of two when the temperature is between $\sim 3 \times 10^4$ K and $3 \times 10^7$ K (to account for solar metallicity).884 From this cooling rate we compute a cooling time. ἑρμως dillerences between the thermal energy and the subgrid Πρ decay on fi4455feoot.," From this cooling rate we compute a cooling time, $t_{cool}$; differences between the thermal energy and the subgrid $u_{eff}$ decay on $t_{relax} = t_{cool}$."885 lor most of the relevant range of temperature ancl density in our simulations. this cooling time is shorter than the relaxation time of SLLOS.," For most of the relevant range of temperature and density in our simulations, this cooling time is shorter than the relaxation time of SH03."886 1n addition to the above mocification to the cooling rale. we also consider the role. of. inverse Compton coolingheating.," In addition to the above modification to the cooling rate, we also consider the role of inverse Compton cooling/heating."887 To do so. we modify the cooling/relaxation timescale of the gas to be where the (non-relativistic) Compton time is given by ∖∖⋰↓↿↓↕∫↘⋟↿↓↥⋖⋅∠∐⊳∖⋜↧⊔≼∼⋖⋅↿∪⇂↓↥∢⊾∐∐⋜⋯∠⇂∠↿↓∐⋅⋜↧⊳∖⊳∖⋯∷↓⋜⋯⋅∠⇂ ⇀∖≺∶↓∖⊽↓⇂⇂↓," To do so, we modify the cooling/relaxation timescale of the gas to be where the (non-relativistic) Compton time is given by with $R$ the distance to the BH and $L$ the associated AGN luminosity."888↥↓↕↓↥∢≱≻↕⇂∙∖⇁⊳∖∖⊽∢⊾∠⇂∪⊔∪⇂≼⇍∪⊔⊳∖⊲⊔⇂⋖⊾↓⋅⋜⋯∙∖⇁↓⋅⋯⇂⊲↓⋜⊔⊲↓∖⇁⋖⋅↿↓⋅⋜⋯⊳∖⇂⋅∢⋅↓⋅ ⋖⋅∐⋅⋯∼⇂⊳∖↕↓↕↿↓↕↕≻↓≻⋜↧↓≻⋖⊾↓⋅⊳∖∖⋎↓↥↕≼∼↓↕↕↓↕↓⋅⋖⋅⋜↧↓↕↿∙∖⇁≼⇍⋜↧⊔⊔↓⋯⇂∐⋮∖⇁∣⋯↿↓⊔↓↕∢⋅ Iuminosity L seen at a given radius and the local Compton temperature at a given radius.," We do not consider any radiative transfer effects in this paper, which in reality can modify both the luminosity $L$ seen at a given radius and the local Compton temperature at a given radius."889 Instead. we take the Compton temperature to be that appropriate for the mean spectrum of luminous AGN. including the ellects of obscuration: 2.]0 K(T)," Instead, we take the Compton temperature to be that appropriate for the mean spectrum of luminous AGN, including the effects of obscuration: $T_C \simeq 2 \times 10^7$ K \citep{sazonov04}."890" In the limit that the Compton timescale is. short compared to the two-body cooling time. we no longer relax the thermal energy. of the gas to the elfective equation of state value for the energy. i,rg. but rather to ne:=MK. ‘T"," In the limit that the Compton timescale is short compared to the two-body cooling time, we no longer relax the thermal energy of the gas to the effective equation of state value for the energy, $u_{eff}$, but rather to $u_C = 3/2 k T_C$."891o transition between these two limits. we in general let the thermal energve of ogas relax to: For dense gas. atomic cooling dominates ancl the eas rather quickly approaches the sound: speed: associated with the effective. equation of state.," To transition between these two limits, we in general let the thermal energy of gas relax to: For dense gas, atomic cooling dominates and the gas rather quickly approaches the sound speed associated with the effective equation of state."892 For. gas. densities characteristic of the ESAL in the central kpe of our mocel galaxies (~10.10% 7) the sound speeds are 40knis and thus the gas is primarily rotationally supported rather than pressure supported., For gas densities characteristic of the ISM in the central kpc of our model galaxies $\sim 10-10^3$ $^{-3}$ ) the sound speeds are $\sim 40 \kms$ and thus the gas is primarily rotationally supported rather than pressure supported.893 This justifies our use of the viscous accretion rate in equation 1.., This justifies our use of the viscous accretion rate in equation \ref{eqn:Mdvisc}.894 Table. 1 lists the parameters of the galaxy merger simulations presented in this work., Table \ref{tab:simparm} lists the parameters of the galaxy merger simulations presented in this work.895 We consider a single galaxy mass and merger orbit (see 2.1)). ancl explore the elects of including ACN wind feedback. both with ancl without radiation. pressure.," We consider a single galaxy mass and merger orbit (see \ref{sec:ICs}) ), and explore the effects of including AGN wind feedback, both with and without radiation pressure."896 For the GN. winds. we vary both the total momentum Hux in the wind (τι) are the wind speed c. with ficucial values of τν=5 ane ry=10.000kms," For the AGN winds, we vary both the total momentum flux in the wind $\tau_w$ ) and the wind speed $v_w$, with fiducial values of $\tau_w = 5$ and $v_w = 10,000 \kms$."897 In varving the AGN wind. paranieters. we are no e&uaranteed that the resulting DII mass will be consisten with the AJeywoo relation.," In varying the AGN wind parameters, we are not guaranteed that the resulting BH mass will be consistent with the $M_{BH}-\sigma$ relation."898 In such cases. the effects of the AGN wind might not be realistic because of the unphysica Bll mass.," In such cases, the effects of the AGN wind might not be realistic because of the unphysical BH mass."899 To quantify this. we present results with ane without the radiation pressure feedback model explored. in DOM.," To quantify this, we present results with and without the radiation pressure feedback model explored in DQM."900 Our simple model of radiation. pressure. feedback xocduces model galaxies roughly on the observed Alpy0 correlation for 7~20. the value used. here (DOM.," Our simple model of radiation pressure feedback produces model galaxies roughly on the observed $M_{\rm BH}-\sigma$ correlation for $\tau \sim 20$, the value used here (DQM)."901 For he present purposes these calculations are useful primarily recause they allow us to study the ellects of AGN wind eedback for svstems in which the DII is guaranteed to be approximately on the lew—0 relation., For the present purposes these calculations are useful primarily because they allow us to study the effects of AGN wind feedback for systems in which the BH is guaranteed to be approximately on the $M_{BH}-\sigma$ relation.902 We also separately carey out simulations with wind feedback. alone., We also separately carry out simulations with wind feedback alone.903" Figure 1. shows the net accretion rate into the black hole. Al;,. and the star formation rate. Al,. as a function of time (summed over both galaxies) for three dillerent simulations: the ficlucial simulation (black curve) with radiation pressure (r= 20) and AGN wind feedback (7,=5 and e,=]0.000kms +). a run identical to the fiducial run but without the wind feedback (grav) and a run with both wind and radiation pressure feedback that includes Compton heating/cooling in the thermodyvnamics of the gas (blue)."," Figure \ref{fig:mdotfid} shows the net accretion rate into the black hole, $\dot{M}_{in}$ , and the star formation rate, $\dot{M}_{*}$, as a function of time (summed over both galaxies) for three different simulations: the fiducial simulation (black curve) with radiation pressure $\tau=20$ ) and AGN wind feedback $\tau_w = 5$ and $v_w = 10,000 \kms$ ), a run identical to the fiducial run but without the wind feedback (gray), and a run with both wind and radiation pressure feedback that includes Compton heating/cooling in the thermodynamics of the gas (blue)."904 We first describe the cllects of the AGN wind and later return to the role of Compton heating/cooling., We first describe the effects of the AGN wind and later return to the role of Compton heating/cooling.905 The inclusion of the wind feedback has little effect on either the accretion or star formation rate before the final coalescence of the two galaxies at /~1.7 Cyr., The inclusion of the wind feedback has little effect on either the accretion or star formation rate before the final coalescence of the two galaxies at $t \sim 1.7$ Gyr.906 This is surprising because equation (6)) implies that [or a given set of conditions at large radii (that determines Meise) the BLL accretion rate at small radii is a [actor of Loloreqefes=16 smaller for the simulation with ACN winds than for the run with just radiation pressure., This is surprising because equation \ref{eqn:Mdin}) ) implies that for a given set of conditions at large radii (that determines $\dot M_{\rm visc}$ ) the BH accretion rate at small radii is a factor of $1+ \tau_w\eta c/v_w =16$ smaller for the simulation with AGN winds than for the run with just radiation pressure.907 After a small number of time steps. however. the feedback due to radiation pressure is so effective in all of the simulations in ligure 1. that the physical conditions at small racii quickly adjust so that there is à balance between radiation pressure and eravity.," After a small number of time steps, however, the feedback due to radiation pressure is so effective in all of the simulations in Figure \ref{fig:mdotfid} that the physical conditions at small radii quickly adjust so that there is a balance between radiation pressure and gravity."908" This sets the BIL accretion. rate Ali, to be ~στ(one) (2) independent of the presence ofthe ACN wind removing mass from the nuclear region (where fjand"," This sets the BH accretion rate $\dot M_{in}$ to be $\sim f_g909\sigma^4/(\tau \eta c G)$ \citep{debuhr10} independent of the presence of the AGN wind removing mass from the nuclear region (where $f_g$and"910effect of the variable airmass and sky transparency in the NIR. we performed differential aperture photometry of CI against three comparison stars in its field.,"effect of the variable airmass and sky transparency in the NIR, we performed differential aperture photometry of C1 against three comparison stars in its field."911 The instrumental magnitude difference between the comparison stars was found to be constant within the photometric errors. hence to the accuracy of our photometry (~0.02 mag) these stars can be considered non-vartable.," The instrumental magnitude difference between the comparison stars was found to be constant within the photometric errors, hence to the accuracy of our photometry $\sim$ 0.02 mag) these stars can be considered non-variable."912 Their magnitudes were calibrated against a standard star observed at the same airmass as one of the frames., Their magnitudes were calibrated against a standard star observed at the same airmass as one of the frames.913 In Fig. 4..," In Fig. \ref{curves},"914 we present the light curves obtained., we present the light curves obtained.915 Both curves exhibit random variations that are fully consistent with photometric uncertainties., Both curves exhibit random variations that are fully consistent with photometric uncertainties.916 A Lomb-Scargle periodogram does not display any periodicity. indicating that the data are consistent with a constant source.," A Lomb-Scargle periodogram does not display any periodicity, indicating that the data are consistent with a constant source."917 We also searched for long-term variability. using. the observations on April 18. 21. and 28 and July 22 to monitor possible magnitude changes on scales of days or months.," We also searched for long-term variability, using the observations on April 18, 21, and 28 and July 22 to monitor possible magnitude changes on scales of days or months."918" Figure 5. shows that these changes do occur in Cl. which was brighter in the NIR in mid April. fading later by ~0.2 mag in both H and K,."," Figure \ref{longcurve} shows that these changes do occur in C1, which was brighter in the NIR in mid April, fading later by $\sim$ 0.2 mag in both $H$ and $K_{\mathrm s}$."919 The / band data present the opposite behavior. displaying a marginal brightening in this. band.," The $J$ band data present the opposite behavior, displaying a marginal brightening in this band."920 None of the other two counterpart candidates (C2—C3) shows magnitude variations between April and July 2005., None of the other two counterpart candidates (C2–C3) shows magnitude variations between April and July 2005.921" The long-term variability of Cl m the NIR bands is interesting. and in addition to the properties discussed in former sections of the present work. makes a strong case forJ16281083-4838560..G335.3268+00.1016.. and being different emissions of the same astrophysical system,"," The long-term variability of C1 in the NIR bands is interesting, and in addition to the properties discussed in former sections of the present work, makes a strong case for, and being different emissions of the same astrophysical system."922" NIR polarimetry in the A, band was performed using the observations taken with the Wollaston prism at different position. angles.", NIR polarimetry in the $K_{\mathrm s}$ band was performed using the observations taken with the Wollaston prism at different position angles.923 Images were reduced using the procedure described in the SOFI user manual., Images were reduced using the procedure described in the SOFI user manual.924 Aperture photometry was performed for candidate Cl and several stars in the field to determine their fluxes., Aperture photometry was performed for candidate C1 and several stars in the field to determine their fluxes.925 Standard unpolarized (HD 125184) and polarized stars (HD 150193. P=1.68+0.02% at a position angle of 60x 1°) were also observed to ensure that instrumental and sky polarization were appropriately removed.," Standard unpolarized (HD 125184) and polarized stars (HD 150193, $P =9261.68 \pm 0.02\%$ at a position angle of $60 \pm 1\degr$ ) were also observed to ensure that instrumental and sky polarization were appropriately removed."927 The measurement of field stars allowed us to estimate the foreground interstellar polarization. obtaining a value of P;=3.7+0.5% at a position angle (north through east) of 33+1," The measurement of field stars allowed us to estimate the foreground interstellar polarization, obtaining a value of $P_{\mathrm f} = 3.7 \pm 0.5\%$ at a position angle (north through east) of $33 \pm 1\degr$."928 A deviation of CI polarization from this value would indicate an intrinsic. polarization. of the source., A deviation of C1 polarization from this value would indicate an intrinsic polarization of the source.929 For Cl. we obtained," For C1, we obtained"930"where3;,j is the IXronecker delta. eT=Obrs,+ο dHobiloΊνα Ξαιfee. bao) is the Laplace coellicient. ∖∖⋎↓↥⋖⊾↓⋅∢⋅∣⋎∶∕∖⊥∕∖⊐⋡ bt This equation includes no secular terms since these are higher order in the eccentricity.","where$\delta_{i,j}$ is the Kronecker delta, $c^{\pm}_j=\partial_\alpha b^{(j)}_{1/2}\pm 2jb^{(j)}_{1/2}$ , $d^{\pm}_j=c^{\pm}_j+b^{(j)}_{1/2}(\alpha)$, $\alpha = a_1/a_2$, $b^{(j)}_{1/2}(\alpha)$ is the Laplace coefficient, where $\psi=\lambda_1-\lambda_2$, and This equation includes no secular terms since these are higher order in the eccentricity."931 Note that since we have only included the first order terms in the eccentricity. the resonant arguments which appear have ratios j|1:j and j:j 1 for the mean lonegituces.," Note that since we have only included the first order terms in the eccentricity, the resonant arguments which appear have ratios $j+1$ $j$ and $j$ $j+1$ for the mean longitudes."932" The perturbecl semi-major axis is given in ?.. and we compute the perturbed eccentricity and. longitude of periastron using P,=ejsinze, and Ay=e,cosz,."," The perturbed semi-major axis is given in \citet{mal93b}, and we compute the perturbed eccentricity and longitude of periastron using $h_1=e_1\sin{\varpi_1}$ and $k_1=e_1\cos{\varpi_1}$."933" Weeping all the resonance terms that exist to first order in the eccentricities gives the equations of motion for hj.Aj. Vo find the ciunge in the transit timing we use the orbital elements to compute the variation in 6,."," Keeping all the resonance terms that exist to first order in the eccentricities gives the equations of motion for $h_1, k_1$, To find the change in the transit timing we use the orbital elements to compute the variation in $\dot\theta_1$ ."934" ""To first order in e, Since we begin with zero eccentricitv. we ignore perturbations to A in the sin ancl cos terms in this equation."," To first order in $e_1$ Since we begin with zero eccentricity, we ignore perturbations to $\lambda$ in the $\sin$ and $\cos$ terms in this equation."935" As in equation (22)) where 060,—6,njo. we integrate this equation to find where p, and no are taken at their initial values. Ajo=ALU0). AsoAs(E—0). &=2/0(110). (4} is the complete elliptic integral. (0) is defined in the appendix of 7.. and we havedropped any terms which vary linearly. with time."," As in equation \ref{eclipsetime}) ) where $\delta \dot\theta_1 = \dot\theta_1 -n_{10}$, we integrate this equation to find where $n_1$ and $n_2$ are taken at their initial values, $\lambda_{10}=\lambda_1(t=0)$, $\lambda_{20}=\lambda_2(t=0)$, $k=2\sqrt{\alpha}/(1+\alpha)$, $K(k)$ is the complete elliptic integral, $Q(\psi)$ is defined in the appendix of \citet{mal93b}, , and we havedropped any terms which vary linearly with time."936 AX similar calculation canbe carried out for perturbations by a planet interior to the transitingὃν planet.," A similar calculation canbe carried out for perturbations by a planet interior to the transiting planet,"937A programme has been. started. using the recently commissioned. Nagova-South African. 14m Infrared Survey Facility (RSE) at SAO Sutherland. to study the stellar populations. evolution and structures of Local. Ciroup galaxies.,"A programme has been started, using the recently commissioned Nagoya-South African 1.4m Infrared Survey Facility (IRSF) at SAAO Sutherland, to study the stellar populations, evolution and structures of Local Group galaxies."938 One aim of this programme is to detect long period variables (Miras ancl other types) in these svstems aid to derive their infrared light curves., One aim of this programme is to detect long period variables (Miras and other types) in these systems and to derive their infrared light curves.939 “Phe programme will necessarily take several vears to complete., The programme will necessarily take several years to complete.940 In. the present communication we discuss the light that initial observations of the dwarf spheroidal galaxy. Leo lL. throw on the AGB star population of that galaxy.," In the present communication we discuss the light that initial observations of the dwarf spheroidal galaxy, Leo I, throw on the AGB star population of that galaxy."941 The IRSE is a 1.4-2m telescope constructed and operated in terms of an agreement. between SAAQO and the Ciraduate School of Science and School of Science. Nagova University. to carry out specialized. surveys of the southern sky. in the infrared.," The IRSF is a 1.4-m telescope constructed and operated in terms of an agreement between SAAO and the Graduate School of Science and School of Science, Nagoya University, to carry out specialized surveys of the southern sky in the infrared."942 Phe telescope is equipped with a 3-channel camera. SIRIUS. constructed jointly by Nagova University and the National Astronomical Observatory of Japan (Nagashima et al.," The telescope is equipped with a 3-channel camera, SIRIUS, constructed jointly by Nagoya University and the National Astronomical Observatory of Japan (Nagashima et al."943 1999). that allows and images to be obtained simultaneously.," 1999), that allows and images to be obtained simultaneously."944 The field of view is 7.8 arcmin square with a scale of 0.45 arcsec/pixel., The field of view is 7.8 arcmin square with a scale of 0.45 arcsec/pixel.945 Images centred on Leo LE (referred to hereafter as field A) were obtained at two epochs. 2001-01-16 ancl 2001-12-19. and processed by means of the standard. IRSE pipeline (Nakajima. private communication).," Images centred on Leo I (referred to hereafter as field A) were obtained at two epochs, 2001-01-16 and 2001-12-19, and processed by means of the standard IRSF pipeline (Nakajima, private communication)."946 A single image comprises 10 ditherecdl 30-5 exposures., A single image comprises 10 dithered 30-s exposures.947 Three such sets of frames were combined to give an elfective 900-8 exposure in each of and A. at both epochs., Three such sets of frames were combined to give an effective 900-s exposure in each of and $ K_{s}$ at both epochs.948 At this stage. the clleetive field. of view is reduced to 7.2 aremin square.," At this stage, the effective field of view is reduced to 7.2 arcmin square."949 Standard stars from Persson οἱ al. (, Standard stars from Persson et al. (9501998) were observed on each night and the results presented here are in the natural system of the SIRIUS camera. but with the zero point of the Persson ct al.,"1998) were observed on each night and the results presented here are in the natural system of the SIRIUS camera, but with the zero point of the Persson et al."951 standards., standards.952 At the first epoch. we obtained a supplementary set. of images of an adjacent.field. (field," At the first epoch, we obtained a supplementary set of images of an adjacentfield (field"953the cluster X-ray emission (Fig.,the cluster X-ray emission (Fig.954 1 and Fig., 1 and Fig.955 2)., 2).956 The optical spectrum. of nonstellar Light is characterized. by. weak. Iow-ionization emission lines (Baum et al 1988: Tadhbunter οἱ al 1993).," The optical spectrum of nonstellar light is characterized by weak, low-ionization emission lines (Baum et al 1988; Tadhunter et al 1993)."957 Fig., Fig.958 7 shows the radio image of 3€353 taken in the NRAO/VLA Sky Survey (NVSS. Condon et al 1998). in contour superposed on the SIS full band image.," 7 shows the radio image of 3C353 taken in the NRAO/VLA Sky Survey (NVSS, Condon et al 1998) in contour superposed on the SIS full band image."959 The radio image was taken bv the VLA at 20 em at resolution of 45 aresec., The radio image was taken by the VLA at 20 cm at resolution of 45 arcsec.960 In this low resolution image. the radio source appears to be triple while much higher resolution images such that in Morganti. Killeen Tacdhunter (1993) and Swain. Briclle Baum (1998) reveal more details in the radio structure as well as the weak radio core at the nucleus.," In this low resolution image, the radio source appears to be triple while much higher resolution images such that in Morganti, Killeen Tadhunter (1993) and Swain, Bridle Baum (1998) reveal more details in the radio structure as well as the weak radio core at the nucleus."961 point-like X-ray source coincides with the nucleus of the radio galaxy which is located at the centre between the radio lobes., A point-like X-ray source coincides with the nucleus of the radio galaxy which is located at the centre between the radio lobes.962 The brightero jet ὃνgoingo towards the cluster emission. terminates at à hot spot ancl the surface brightness of the jet-sicle Lobe steeply declines in front. of the bright cluster emission., The brighter jet going towards the cluster emission terminates at a hot spot and the surface brightness of the jet-side lobe steeply declines in front of the bright cluster emission.963 The cluster medium may be acting as a working surface of the radio jet. or it is merely an orientation elfect of the jet.," The cluster medium may be acting as a working surface of the radio jet, or it is merely an orientation effect of the jet."964 As suggested from the image analysis. the X-ray. spectrum of 30353 is very hard.," As suggested from the image analysis, the X-ray spectrum of 3C353 is very hard."965 A likely explanation is an absorbed X-ray source of an active nucleus in the radio galaxy., A likely explanation is an absorbed X-ray source of an active nucleus in the radio galaxy.966 To minimize the contamination from the cluster enission. we use the SIS data for a spectral study as the SIS provides better spatial resolution. and the data were collected. from. a small region with a radius of 1.5 aremin on the two SIS detectors centred on the hard X-ray source.," To minimize the contamination from the cluster emission, we use the SIS data for a spectral study as the SIS provides better spatial resolution, and the data were collected from a small region with a radius of 1.5 arcmin on the two SIS detectors centred on the hard X-ray source."967 Halt of the total photons from 3€C353 should be contained in the region. when the point spread. function of the ASCA ARP for a point source is assumed.," Half of the total photons from 3C353 should be contained in the region, when the point spread function of the ASCA XRT for a point source is assumed."968 The background. data were taken from a region where the cluster emission is weak., The background data were taken from a region where the cluster emission is weak.969 The obtained spectrum should. therefore contain some cluster emission in he soft. X-ray band., The obtained spectrum should therefore contain some cluster emission in the soft X-ray band.970 The SIS spectrum can be fitted with a very Hat. power- of DP-—0.60+0.24 (Fig., The SIS spectrum can be fitted with a very flat power-law of $\Gamma = 0.60\pm 0.24$ (Fig.971 5), 8).972 llowever. a realistic xeture of the spectrum is a sum of the cluster emission and an absorbed: power-law from an AGN.," However, a realistic picture of the spectrum is a sum of the cluster emission and an absorbed power-law from an AGN."973 Since soft. X-ray emission from the radio galaxy is very weak. as illustrated w the HERE imageὃν and the soft band GIS image.o the energye xuid below 2 keV in the spectrum. is dominated by. the diffuse cluster emission.," Since soft X-ray emission from the radio galaxy is very weak, as illustrated by the HRI image and the soft band GIS image, the energy band below 2 keV in the spectrum is dominated by the diffuse cluster emission."974 Fitting with a model consisting of a thermal emission spectrum (MISIAL) with A7=4.3 keV and metallicity of aand an absorbed power-law with a photon-index of 1.7 gives an absorption column density ης51070m, Fitting with a model consisting of a thermal emission spectrum (MEKAL) with $kT=4.3$ keV and metallicity of and an absorbed power-law with a photon-index of 1.7 gives an absorption column density $ = 5\times 10^{22}$.975 The contribution from the cluster emission (as modelled by the MISIAL component) is found to be about GO per cent in the 0.52 keV energy range., The contribution from the cluster emission (as modelled by the MEKAL component) is found to be about 60 per cent in the 0.5–2 keV energy range.976 The absorption-corrected 2.10 keV luminosity of the N-rav source is 8LO , The absorption-corrected 2–10 keV luminosity of the X-ray source is $8\times 10^{42}$.977An ASCA spectral study of a sample of radio galaxies including 3C353 will be reported. elsewhere. (see also Sambruna. Eracleous Mushotzky. 1999).," An ASCA spectral study of a sample of radio galaxies including 3C353 will be reported elsewhere (see also Sambruna, Eracleous Mushotzky 1999)."978 Compared. with the other “cnission-line selected radio. galaxies. ὃς2039 appears to be underluminous in N-ravs for its radio power.," Compared with the other `emission-line selected' radio galaxies, 3C353 appears to be underluminous in X-rays for its radio power."979 We have shown that the extended. emission. around. the powerful radio galaxy 3C35335 is a cluster. with highly disturbed: morphology of the X-ray emission. which might allect the radiojets of 80353., We have shown that the extended emission around the powerful radio galaxy 3C353 is a cluster with highly disturbed morphology of the X-ray emission which might affect the radio jets of 3C353.980 The large racio power of 3€353, The large radio power of 3C353981"With no clear optical association we cannot positively classify this source, but the time-scales between the NVSS detection and MOST detection and non-detection rule out RSNe and GRB afterglows.","With no clear optical association we cannot positively classify this source, but the time-scales between the NVSS detection and MOST detection and non-detection rule out RSNe and GRB afterglows."982 The light curve for SUMSS J062636—425807 (seeAppendix has a detection and a non-detection separated by almost a [B))year., The light curve for SUMSS $-$ 425807 (seeAppendix \ref{sec:light_curves_transients}) ) has a detection and a non-detection separated by almost a year.983" The optical counterpart is point like and the colours are red, with B-K — 5."," The optical counterpart is point like and the colours are red, with B-K = 5."984 The source is most likely an AGN scintillating above our noise threshold., The source is most likely an AGN scintillating above our noise threshold.985" The light curve for J135304—363726 (see Appendix [B)) is consistent with a flaring source, or a variable source occasionally appearing above our sensitivity limit."," The light curve for $-$ 363726 (see Appendix \ref{sec:light_curves_transients}) ) is consistent with a flaring source, or a variable source occasionally appearing above our sensitivity limit."986" It is marginally detected in the SuperCOSMOS R plates and not detected in B or I, or any 2MASS images."," It is marginally detected in the SuperCOSMOS R plates and not detected in B or I, or any 2MASS images."987 This source is likely an optically faint AGN scintillating above our noise threshold., This source is likely an optically faint AGN scintillating above our noise threshold.988" Some 25 per cent of the variable sources have a clear point- or marginally resolved optical counterpart most of which have red colours, with 0«B—R2."," Some 25 per cent of the variable sources have a clear point-like or marginally resolved optical counterpart most of which have red colours, with $0 < B-R < 2$."989" The optical point source and radio detection would typically imply AGN, but the colour distribution is unusual for AGN, for which the vast majority have B—R<1 (?).."," The optical point source and radio detection would typically imply AGN, but the colour distribution is unusual for AGN, for which the vast majority have $B-R<1$ \citep{Croom04}. ."990 The reddest sources are, The reddest sources are991"minimun racial bin. H,,5,. to x.","minimum radial bin, $R_{min}$, to $\infty$."992 In practice. one only has shear data covering a range from Ryriy lO μι.," In practice, one only has shear data covering a range from $R_{min}$ to $R_{max}$."993" Wereler to the parts of (he integrals Irom 10,4, lo x: as endpoint corrections: (hey must be added to the parts of the integrals (hat we can actually perform by interpolating the data.", We refer to the parts of the integrals from $R_{max}$ to $\infty$ as endpoint corrections; they must be added to the parts of the integrals that we can actually perform by interpolating the data.994 Consider Equation 12. as an example: we can rewrite il as where 75 and Te stand for Data ancl Correction., Consider Equation \ref{eq:delta-rho} as an example; we can rewrite it as where $T_D$ and $T_C$ stand for Data and Correction.995 To estimate the magnitude of each term. consider an isothermal sphere. AN~A1: in this case. the integrals can be computed analvticallv. leading to For the outermost data point. r=ει (he correction term gives the whole result. and one cannot learn anvihing about the density al this point.," To estimate the magnitude of each term, consider an isothermal sphere, $\Delta\Sigma \sim R^{-1}$; in this case, the integrals can be computed analytically, leading to For the outermost data point, $r=R_{max}$, the correction term gives the whole result, and one cannot learn anything about the density at this point."996" ILowever. lor smaller scales. r<B. the ratio Te/(Tp4Te)eG/B,4u,)/2."," However, for smaller scales, $r \ll R_{max}$, the ratio $T_C/(T_D+T_C) \simeq (r/R_{max})^2/2$."997" For example. for Sheldon et al.-size bins. (his implies that the correction is only about at the value of H2;=Ry. (vo radial bins inward of H,4,;=yy."," For example, for Sheldon et al.-size bins, this implies that the correction is only about at the value of $R_i=R_{16}$, two radial bins inward of $R_{max}=R_{18}$."998 The correction terms at the next bins inwarel (proceeding from larger to smaller scale) are.3%... and 2%.. while the remaining inner 12 bins are alfectecl by less than196.," The correction terms at the next bins inward (proceeding from larger to smaller scale) are, and , while the remaining inner 12 bins are affected by less than."999" In fact. it is only the error in estimating this correction term that concerns us. so we expect that even at the second bin inward of /2,,,. one could estimate Ap to an accuracy of a few percent."," In fact, it is only the error in estimating this correction term that concerns us, so we expect that even at the second bin inward of $R_{max}$, one could estimate $\Delta \rho$ to an accuracy of a few percent."1000" Around the virial radius of clusters. R~1h+ Mpe. the correction term itself is only half a percent of the total for R,,,,—10fh! Mpe."," Around the virial radius of clusters, $R \sim 1~ h^{-1}$ Mpc, the correction term itself is only half a percent of the total for $R_{max} =10~ h^{-1}$ Mpc."1001 Devond 105.! Ape. the halo densitv profile is expected to drop off more steeply than isothermal. so the correction [actor in this case should be less than the estimate in 27...," Beyond $10 h^{-1}$ Mpc, the halo density profile is expected to drop off more steeply than isothermal, so the correction factor in this case should be less than the estimate in \ref{eq:TCTD}."1002 At these large scales. it is probably a good assumption to use the shape of the linear. mass correlation function (i.e. the Fourier transform of the linear power spectrum). which is well understood. theoretically for a given cosmology. as the model with which to compute the endpoint correction.," At these large scales, it is probably a good assumption to use the shape of the linear mass correlation function (i.e. the Fourier transform of the linear power spectrum), which is well understood theoretically for a given cosmology, as the model with which to compute the endpoint correction."1003 This is the expected large scale behavior from the halo model., This is the expected large scale behavior from the halo model.1004 This requirement of providing endpoint corrections is the one part of this method which requires a model., This requirement of providing endpoint corrections is the one part of this method which requires a model.1005 ILowever. this model dependence only. allects the results at the largest scales for any reasonable exirapolation. guided by theoretical expectation and constrained by the scale galaxy autocorrelation function which is now measured to 175h.! Mpc 2005)..," However, this model dependence only affects the results at the largest scales for any reasonable extrapolation, guided by theoretical expectation and constrained by the large-scale galaxy autocorrelation function which is now measured to $175~ h^{-1}$ Mpc \citep{eisenstein:wiggles}."1006 It is left up to the experimenter to decide which points to omit and how to take (he error in the correction into account., It is left up to the experimenter to decide which points to omit and how to take the error in the correction into account.1007 In this context. for lensing data that extends to scales of order a few Alpe. the endpoint correction can be considered a manifestation of the mass sheet degeneracy.," In this context, for lensing data that extends to scales of order a few Mpc, the endpoint correction can be considered a manifestation of the mass sheet degeneracy."1008 In the current, In the current1009"3.7""7x11.3"" at and Long-High slit (18.737.250) is 11.17x22.3"". atPA=46.",$\times$ at and Long-High slit $\rm \mu m$ ) is $\times$ at.10101°.. We include mid-infrared data from the AKARI IRC Point Source Catalogue archive (2).., We include mid-infrared data from the AKARI IRC Point Source Catalogue archive \citep{2007PASJ...59S.369M}.1011 M2-9 has been observed with the InfraRed Camera (?) at two infrared bands. namely SOW l.6:m) and LISW (13.9-25.64m) with respective effective wavelengths at 9 and 18 jm (see Fig. 6)).," M2-9 has been observed with the InfraRed Camera \citep{2007PASJ...59S.401O} at two infrared bands, namely S9W $\rm\mu m$ ) and L18W $\rm\mu m$ ) with respective effective wavelengths at 9 and 18 $\rm \mu m$ (see Fig. \ref{fig:SED}) )."1012 The integrated flux. as detected by MIDI (field-of-view: ~O.4” with UTs). in Fig.," The integrated flux, as detected by MIDI (field-of-view: $\sim$ with UTs), in Fig."1013 6. clearly shows a difference between the MIDI and the ISO spectra., \ref{fig:SED} clearly shows a difference between the MIDI and the ISO spectra.1014 Since the rectangular aperture of ISO (1422) was positioned over the central area of M2-9 (excluding the largest part of the lobes) and it increased m size for bands larger than 124m (including part of the lobes near the central source). It is expected that ISO detected a more extended source than MIDI.," Since the rectangular aperture of ISO $\times$ ) was positioned over the central area of M2-9 (excluding the largest part of the lobes) and it increased in size for bands larger than $\rm \mu m$ (including part of the lobes near the central source), it is expected that ISO detected a more extended source than MIDI."1015 The fact that both spectra have similar shape and only slightly different flux levels. indicates that they both detectedalmost the same compact source.," The fact that both spectra have similar shape and only slightly different flux levels, indicates that they both detectedalmost the same compact source."1016 Both ISO and MIDI spectra. shown in Fig. 6..," Both ISO and MIDI spectra, shown in Fig. \ref{fig:SED},"1017 have been dereddened using the ? law for Ay=2.5 (?).., have been dereddened using the \citet{1979ARA&A..17...73S} law for $A_{V}=2.5$ \citep{1998RMxAC...7..171T}.1018 The two Spitzer slits were positioned on top of the northern lobe. but they have probed different parts of the nebula.," The two Spitzer slits were positioned on top of the northern lobe, but they have probed different parts of the nebula."1019 In more detail (Fig. 3)):, In more detail (Fig. \ref{fig:spitzer}) ):1020 Our VLTI observations of the core of M2-9 revealthe presence of a dusty flat-like structure., Our VLTI observations of the core of M2-9 revealthe presence of a dusty flat-like structure.1021 Visibilities decrease as the P.A. of the projected baselines increases (Fig. 5)).," Visibilities decrease as the P.A. of the projected baselines increases (Fig. \ref{fig:gauss}) ),"1022 suggesting an increase of the dust opacity., suggesting an increase of the dust opacity.1023 Thus. MIDI has probed the existence of a flattened structure along the equatorial plane of the nebula.," Thus, MIDI has probed the existence of a flattened structure along the equatorial plane of the nebula."1024 The core is significantly resolved by the 40-50m baselines. with visibilities ofthe order of 0.1-0.2.," The core is significantly resolved by the 40-50m baselines, with visibilities ofthe order of 0.1-0.2."1025 Our observations showed that the flattened structure is compact. typically 25x35 mas at Sum. and 37x46 mas at 134m (Fig. 5)).," Our observations showed that the flattened structure is compact, typically $\times$ 35 mas at $\rm \mu m$, and $\times$ 46 mas at $\rm \mu m$ (Fig. \ref{fig:gauss}) )."1026 The dusty structure is more elongated along the planetary nebula's equatorial plane. compared to the direction of the lobes.," The dusty structure is more elongated along the planetary nebula's equatorial plane, compared to the direction of the lobes."1027 Therefore. the disks geometrical size can be constrained (see Sections 4 6).," Therefore, the disk's geometrical size can be constrained (see Sections 4 6)."1028 Subtracting the continuum from each spectrally dispersed visibility. one may enhance subtle visibility fluctuations that could not be distinguished otherwise.," Subtracting the continuum from each spectrally dispersed visibility, one may enhance subtle visibility fluctuations that could not be distinguished otherwise."1029 Significant signatures of forsterite (Mg2S104) are observed as small (~5—10%) dips in the visibility curves (Fig. 4)), Significant signatures of forsterite $_{2}$ $_{4}$ ) are observed as small $\sim5-10\%$ ) dips in the visibility curves (Fig. \ref{fig:forst}) )1030 at 9.8 and l4gem (?).., at 9.8 and $\rm \mu m$ \citep{2002A&A...382..222M}.1031 We confirmed the validity of this. since both features were present in the uncalibrated visibilities and they were absent in the calibrator data.," We confirmed the validity of this, since both features were present in the uncalibrated visibilities and they were absent in the calibrator data."1032 In addition. the peaks nearly match the emission curves of forsterite grains measured in the lab by 990 ," In addition, the peaks nearly match the emission curves of forsterite grains measured in the lab by \citet{2000A&A...363.1115K, 2006A&A...449..583K}."1033The visibility decrease at typically shows that the forming regions of these features are resolved and thus slightly more extended than the continuum and amorphous silicate regions (as already observed in Young Stellar Objects. ?)).," The visibility decrease at typically shows that the forming regions of these features are resolved and thus slightly more extended than the continuum and amorphous silicate regions (as already observed in Young Stellar Objects, \citet{2004Natur.432..479V}) )."1034 In this section we present the modelled disk and the constraints introduced by the fitting procedure., In this section we present the modelled disk and the constraints introduced by the fitting procedure.1035 The 3D radiative transfer code MC3D. which is based on the Monte Carlo method and solves the radiative transfer problem self-consistently. has been used in this work (2?)..," The 3D radiative transfer code MC3D, which is based on the Monte Carlo method and solves the radiative transfer problem self-consistently, has been used in this work \citep{1999A&A...349..839W, 2003CoPhC.150...99W}."1036 It simulates the temperatures produced by dusty configurations and creates as observables spectral energy distributions and wavelength-dependent images of the dusty environments. as well as polarisation maps.," It simulates the temperatures produced by dusty configurations and creates as observables spectral energy distributions and wavelength-dependent images of the dusty environments, as well as polarisation maps."1037 The density law used in this model is where ris the radial distance in the disk midplane. R. is the stellar radius. £ is the vertical density parameter. a ts the density parameter in the midplane and /ij is the scale height at a given distance from the star (??) .," The density law used in this model is where is the radial distance in the disk midplane, $R_{*}$ is the stellar radius, $\beta$ is the vertical density parameter, $\alpha$ is the density parameter in the midplane and $h_{0}$ is the scale height at a given distance from the star \citep{1973A&A....24..337S,2002ApJ...564..887W} ."1038 We have used the distribution of 2? for the grain sizes: nib)x 57. where is the grain size. assuming that the dust grains have spherical symmetry.," We have used the distribution of \cite{1977ApJ...217..425M} for the grain sizes: $n(b)\propto b^{-3.5}$ , where is the grain size, assuming that the dust grains have spherical symmetry."1039Vokrouhblickv 2009: Lykawka et al.,Vokrouhlicky 2009; Lykawka et al.1040 2009)., 2009).1041 Both the L4 and L5 Neptune Trojan regions appear to have similar sized populations and dynamics., Both the L4 and L5 Neptune Trojan regions appear to have similar sized populations and dynamics.1042 The expected large number of hieh inclination Neptune Trojans in both the L4 and L5 regions of Neptune suggests (hal capture occurred with a dvnamically excited planetesimal population (Sheppard Trujillo 2010)., The expected large number of high inclination Neptune Trojans in both the L4 and L5 regions of Neptune suggests that capture occurred with a dynamically excited planetesimal population (Sheppard Trujillo 2010).1043 Observations were obtained in June 2008 and 2009 [or the L5 region and October [or the L4 region of Neptune., Observations were obtained in June 2008 and 2009 for the L5 region and October 2004-2009 for the L4 region of Neptune.1044 For the Subaru observations the Suprime-Cam with ten 2048x4096 pixel CCDs arranged in a 5x2 pattern was used., For the Subaru observations the Suprime-Cam with ten $2048 \times 4096$ pixel CCDs arranged in a $5 \times 2$ pattern was used.1045 Suprime-Cam has ΓΙ pixels that gives a pixel scale of 0.720 ! at prime focus and a field-ol-view (hat is about 34.x27' with the North-South direction aligned with the long axis.," Suprime-Cam has $151046\micron$ pixels that gives a pixel scale of $0.\arcsec 20$ $^{-1}$ at prime focus and a field-of-view that is about $34\arcmin \times 27\arcmin$ with the North-South direction aligned with the long axis."1047" Gaps between the chips are about. 16"" in the North-South direction and 3” in the East-West direction (Miyazaki et al.", Gaps between the chips are about $16 \arcsec$ in the North-South direction and $3 \arcsec$ in the East-West direction (Miyazaki et al.1048 2002)., 2002).1049 At Magellan the the INLACS camera on the Baacle telescope was used., At Magellan the the IMACS camera on the Baade telescope was used.1050 INLACS is a wide-lield CCD imager that has eight 2048x4096 pixel CCDs with a pixel scale of 0.720 pixel| and a field-ol-view of about 0.2 square degrees., IMACS is a wide-field CCD imager that has eight $2048\times4096$ pixel CCDs with a pixel scale of $0.\arcsec 20$ $^{-1}$ and a field-of-view of about 0.2 square degrees.1051 The eight CCDs are arranged in a 4x2 box pattern with four above and [our below and about 12 arcseconc gaps between chips., The eight CCDs are arranged in a $4 \times 2$ box pattern with four above and four below and about 12 arcsecond gaps between chips.1052 The images were bias-subtracted ancl then flat-fielded with twilight Hats., The images were bias-subtracted and then flat-fielded with twilight flats.1053 During exposures the telescope was autoguided sidereally on [ied stars., During exposures the telescope was autoguided sidereally on field stars.1054 Integration (mes were between 300 and 450 seconds and images of the same field were obtained on three visits with 1 to 1.5 hours between visits., Integration times were between 300 and 450 seconds and images of the same field were obtained on three visits with 1 to 1.5 hours between visits.1055 Observations were obtained while the Neptune Trojans were within 1 hour of opposition so the dominant apparent motion was lareely parallactic and thus is inversely related to distance., Observations were obtained while the Neptune Trojans were within 1 hour of opposition so the dominant apparent motion was largely parallactic and thus is inversely related to distance.1056 Objects al the heliocentric distance of Neptune. A~30 AU. will have an apparent motion of about ~4” hr.!.," Objects at the heliocentric distance of Neptune, $R\sim 30$ AU, will have an apparent motion of about $\sim 4\arcsec $ $^{-1}$."1057 Previous surveys for Neptune Trojans focused mostly on finding relatively bright objects (radii greater (han 40 km or brighter than 24th magnitude) (Chiang et al., Previous surveys for Neptune Trojans focused mostly on finding relatively bright objects (radii greater than 40 km or brighter than 24th magnitude) (Chiang et al.1058 2003: Shepparel Trujillo 2006: Decker et al., 2003; Sheppard Trujillo 2006; Becker et al.1059 2008)., 2008).1060 The Neptune Trojan regions cover thousands of square degrees on the skv as many Trojans have large inclinations and librate up to 430 degrees from the Lagrangian points over a ten thousand vear time scale (Chiang et al., The Neptune Trojan regions cover thousands of square degrees on the sky as many Trojans have large inclinations and librate up to $\pm 30$ degrees from the Lagrangian points over a ten thousand year time scale (Chiang et al.1061 2003)., 2003).1062 We obtained an ultra-deep. large area survey of the Neptune L5 and L4 Trojan regions.," We obtained an ultra-deep, large area survey of the Neptune L5 and L4 Trojan regions."1063 A total of 49 square degrees were searched of which 30 square degrees were in the L4 region while, A total of 49 square degrees were searched of which 30 square degrees were in the L4 region while10642000 transformation was computed with only 8 stars.,2000 transformation was computed with only 8 stars.1065 We checked that the quality of the transformation was not depending heavily ou the number of astrometric refercuce stars used., We checked that the quality of the transformation was not depending heavily on the number of astrometric reference stars used.1066 Since wart of the proper motion could be due to bulk motion of the reference stars we also computed the astrometric solution of the December 2000 VLT image using 78 USNO-À2 field stars., Since part of the proper motion could be due to bulk motion of the reference stars we also computed the astrometric solution of the December 2000 VLT image using 78 USNO-A2 field stars.1067 Reference stars do not show anv systematic difference in position in the tine interval from 1980 (USNO-A2) till 200, Reference stars do not show any systematic difference in position in the time interval from 1980 (USNO-A2) till 2000.1068 The accuracy with which reference stars coincide after raustormmation is rather good., The accuracy with which reference stars coincide after transformation is rather good.1069 Their maxinuun offset to uean positions after transformation are listed in Table , Their maximum offset to mean positions after transformation are listed in Table \ref{astroerrors}.1070Between December 2000 aud 2002-2003 VET observations. he mean residual of the LO reference stars is ouly 1.5 mas.," Between December 2000 and 2002-2003 VLT observations, the mean residual of the 10 reference stars is only 4.5 mas."1071 We plot in Fie., We plot in Fig.1072 3 the apparent displaceiieuts of the 17 zdut comparison stars together with those of aand of the astrometric references derived. from the wo FORSL/VLT observations., \ref{Bpm} the apparent displacements of the 17 faint comparison stars together with those of and of the astrometric references derived from the two FORS1/VLT observations.1073 Noue of the reference stars exhibit significant motion with respect to the rest of he eroup., None of the reference stars exhibit significant motion with respect to the rest of the group.1074 Compared to stars of simular brightuess. the apparent motion of Hs clearly of high sienificance.," Compared to stars of similar brightness, the apparent motion of is clearly of high significance."1075 We also corrected for differeutial refraction effects resulting from the laree colour difference between ((U-DB. = -ᾱ1) and the refercuee astrolctric stars (mean U-B = 0.17)., We also corrected for differential refraction effects resulting from the large colour difference between (U-B = -1.11) and the reference astrometric stars (mean U-B = 0.17).1076 Iu the D filter. this translates iuto a shift of ~ iin effective wavelcneth.," In the B filter, this translates into a shift of $\sim$ in effective wavelength."1077 Since all observations were clone at low aivimass. the corrections retain small of the order of 5 to 30 mas ancl are usally negligible compared to positioniug errors.," Since all observations were done at low airmass, the corrections remain small, of the order of 5 to 30 mas and are usually negligible compared to positioning errors."1078 Differential refraction effects are onlv significant in the case of the Deceiiber 2000 VET observation., Differential refraction effects are only significant in the case of the December 2000 VLT observation.1079 We ien fitted a proper motion solution expressed ln ternis of total motion and direction angle to the various positions of uusiug a miuimuiuu V? algorithin., We then fitted a proper motion solution expressed in terms of total motion and direction angle to the various positions of using a minimum $\chi^{2}$ algorithm.1080 The best fit shown in Fie., The best fit shown in Fig.1081 | is obtained for ΕΞ91x12 mas/vr., \ref{pm} is obtained for $\mu = 97\pm 12$ mas/yr.1082 The direction of motiou is oricuted tft iuorth of west (all errors are coufideuce level for one parameter)., The direction of motion is oriented $\pm$ north of west (all errors are confidence level for one parameter).1083 Tn the N-rav domain wwas observed with the ROSAT. SAN. NMME-Newton aud," In the X-ray domain was observed with the ROSAT, SAX, XMM-Newton and"1084through the use of stress-free boundary conditions. is worthy of consideration.,"through the use of stress-free boundary conditions, is worthy of consideration."1085 Dissipation within the core itself is vet another area of uncertainty., Dissipation within the core itself is yet another area of uncertainty.1086 A quite cillerent paradigm for tidal dissipation in rotating planets and stars could. emerge through a consideration of elliptical instabilities (Ixerswell2002.and.referencestherein).., A quite different paradigm for tidal dissipation in rotating planets and stars could emerge through a consideration of elliptical instabilities \citep[][and references therein]{2002AnRFM..34...83K}.1087 I£ the linear tidal response is considered to provide merely an elliptical. distortion of the streamlines of the rotating Bluid. as is true in the case of a full sphere of incompressible uid. then the secondary instabilities of the elliptical Dow can produce turbulence ancl enhanced tidal dissipation.," If the linear tidal response is considered to provide merely an elliptical distortion of the streamlines of the rotating fluid, as is true in the case of a full sphere of incompressible fluid, then the secondary instabilities of the elliptical flow can produce turbulence and enhanced tidal dissipation."1088 Analytical. numerical and. experimental investigations have been motivated. mainly by the case of the Earth's core but also by lo (Ixerswell&Alalkus1998) and by accretion disces in binary stars (Goodman.1993:Lubow.Pringle&Ixerswell1993:RyuGoodman 1994)..," Analytical, numerical and experimental investigations have been motivated mainly by the case of the Earth's core but also by Io \citep{1998GeoRL..25..603K} and by accretion discs in binary stars \citep{1993ApJ...406..596G,1993ApJ...419..758L,1994ApJ...422..269R}."1089 This nonlinear mechanism may m more relevant. for tides in extrasolar planets. while the much weaker tides in. solar-system planets may depend on linear mechanisms such as those described in this paper.," This nonlinear mechanism may be more relevant for tides in extrasolar planets, while the much weaker tides in solar-system planets may depend on linear mechanisms such as those described in this paper."1090 Since the linear response in à spherical annulus departs significantly: from a simple elliptical distortion. it would be of interest to. understand the nonlinear outcome in the presence of a core.," Since the linear response in a spherical annulus departs significantly from a simple elliptical distortion, it would be of interest to understand the nonlinear outcome in the presence of a core."1091 In this paper we have studied the tidal forcing. propagation and. dissipation of linear inertial waves in a rotating [uid body.," In this paper we have studied the tidal forcing, propagation and dissipation of linear inertial waves in a rotating fluid body."1092 The intentionally simplified mocel involves à perfectly rigid core surrounded. by a deep ocean consisting of homogeneous incompressible Huid., The intentionally simplified model involves a perfectly rigid core surrounded by a deep ocean consisting of a homogeneous incompressible fluid.1093 Centrifugal cllects are neglected. but. the Coriolis force is considered in full. and dissipation occurs through viscous or frictional forces.," Centrifugal effects are neglected, but the Coriolis force is considered in full, and dissipation occurs through viscous or frictional forces."1094 We introduced. a further simplification by replacing the free outer surface with a boundary on which the racial velocity is specified. which closely mimics the elfects of tidal forcing at low frequencies.," We introduced a further simplification by replacing the free outer surface with a boundary on which the radial velocity is specified, which closely mimics the effects of tidal forcing at low frequencies."1095 Various analytical results provide tests of the numerical methods for caleulating forced linear waves., Various analytical results provide tests of the numerical methods for calculating forced linear waves.1096 The dissipation rate exhibits a complicated dependence on the tidal frequency ancl generally. increases strongly with the size of the core., The dissipation rate exhibits a complicated dependence on the tidal frequency and generally increases strongly with the size of the core.1097 In certain intervals of frequency. elficien dissipation is found to occur even for very. small values of the coefficient. of viscosity. or [rietion. which is promising for astrophysical ancl planetary. applications.," In certain intervals of frequency, efficient dissipation is found to occur even for very small values of the coefficient of viscosity or friction, which is promising for astrophysical and planetary applications."1098 In restrictec intervals. the wave enerev is focused towards: relatively simple wave attractors and a well defined asvmptotic dissipation rate is achieved.," In restricted intervals, the wave energy is focused towards relatively simple wave attractors and a well defined asymptotic dissipation rate is achieved."1099 Llowever. a more typica behaviour is that the inertial waves propagate in a very complicated. way around the fluid annulus.," However, a more typical behaviour is that the inertial waves propagate in a very complicated way around the fluid annulus."1100 The critica Iatitucde on the inner boundary. plays an important role in the solutions., The critical latitude on the inner boundary plays an important role in the solutions.1101 While the dissipation rate is enhanced in a strongly frequencv-dependent manner. it may not converge in the limit of small viscosity in the same way as for à wave attractor.," While the dissipation rate is enhanced in a strongly frequency-dependent manner, it may not converge in the limit of small viscosity in the same way as for a wave attractor."1102 In the limit of a thin [uid shell. the dissipation rate can be ereathy enhanced through a traditional tvpe of resonance with a toroidal mode (r mode or Rosshy wave).," In the limit of a thin fluid shell, the dissipation rate can be greatly enhanced through a traditional type of resonance with a toroidal mode (r mode or Rossby wave)."1103 The model adopted. in this paper is deliberately oversiniplified. although it may be more or less applicable to planets or moons involving a deep ocean.," The model adopted in this paper is deliberately oversimplified, although it may be more or less applicable to planets or moons involving a deep ocean."1104 We have pointed. oul numerous avenues for further investigation. including aspects of internal wave propagation. reflection ancl dissipation. and nonlinear behaviour such as the elliptical instabilitv.," We have pointed out numerous avenues for further investigation, including aspects of internal wave propagation, reflection and dissipation, and nonlinear behaviour such as the elliptical instability."1105 l thank Jeremy Goodman and the referee. Leo Maas. [or helpful comments.," I thank Jeremy Goodman and the referee, Leo Maas, for helpful comments."1106decreases the mean errors in the positions for all sources to 12 mas in both àcos and à.,decreases the mean errors in the positions for all sources to 12 mas in both $\alpha \cos\delta$ and $\delta$.1107 The lower limit on the accuracy of the positions for the best ICRF calibrators is 0.25 mas (Maetal.1998).. well below the precision obtained from our VLA+PT measurements discussed above.," The lower limit on the accuracy of the positions for the best ICRF calibrators is 0.25 mas \citep{MA:98}, well below the precision obtained from our VLA+PT measurements discussed above."1108 The ICRF coordinates thus provide representative reference positions with which to compare our VLA+PT positions., The ICRF coordinates thus provide representative reference positions with which to compare our VLA+PT positions.1109 Figures 3. and 4. display the results of such a comparison., Figures \ref{ICRFVLARA} and \ref{ICRFVLADEC} display the results of such a comparison.1110 Differences between the ICRF positions and the VLA+PT positions for the calibrator sources are plotted as a function of source right ascension in Figure 3. and as a function of source declination in Figure 4..., Differences between the ICRF positions and the VLA+PT positions for the calibrator sources are plotted as a function of source right ascension in Figure \ref{ICRFVLARA} and as a function of source declination in Figure \ref{ICRFVLADEC}.1111 Error bars 1n the two figures are those derived for our VLA+PT measurements reported in Table 2.., Error bars in the two figures are those derived for our VLA+PT measurements reported in Table \ref{POSITIONS}.1112 Neither figure shows a clear dependence of position offset on source right ascension or declination., Neither figure shows a clear dependence of position offset on source right ascension or declination.1113 The means of the differences in ncosó and 9 are —0.3 mas and —1.0 mas respectively. indicating that systematic effects are negligible.," The means of the differences in $\alpha \cos\delta$ and $\delta$ are $-$ 0.3 mas and $-$ 1.0 mas respectively, indicating that systematic effects are negligible."1114 The standard deviations of the position differences are 17 mas and 11 mas in acosd and à respectively., The standard deviations of the position differences are 17 mas and 11 mas in $\alpha \cos\delta$ and $\delta$ respectively.1115 These values are roughly equivalent to the mean position errors for the stars derived above., These values are roughly equivalent to the mean position errors for the stars derived above.1116 If we again disregard the two calibrator sources associated with the star HD50896-N then the standard deviations of the differences fall to 10 mas in both acos? and o., If we again disregard the two calibrator sources associated with the star HD50896-N then the standard deviations of the differences fall to 10 mas in both $\alpha \cos\delta$ and $\delta$.1117 In addition to the comparison of calibrator positions. we also compared the positions of the 19 stars as derived from our VLA+PT observations with the corresponding Hipparcos positions updated to the epoch of our observations. Julian Day 2451889.," In addition to the comparison of calibrator positions, we also compared the positions of the 19 stars as derived from our VLA+PT observations with the corresponding Hipparcos positions updated to the epoch of our observations, Julian Day 2451889."1118 Figures 5. and 6 plot the position differences for the radio stars as a function of source right ascension (Figure 5)) and as a function of source declination (Figure 6))., Figures \ref{HIPVLARA} and \ref{HIPVLADEC} plot the position differences for the radio stars as a function of source right ascension (Figure \ref{HIPVLARA}) ) and as a function of source declination (Figure \ref{HIPVLADEC}) ).1119 Error bars are those derived from our VLA+PT observations., Error bars are those derived from our VLA+PT observations.1120 From Figures 5 and 6.. itis apparent that roughly half of the positions derived from our VLA+PT data do not agree with the Hipparcos positions to within the uncertainties in our measurements.," From Figures \ref{HIPVLARA} and \ref{HIPVLADEC}, it is apparent that roughly half of the positions derived from our VLA+PT data do not agree with the Hipparcos positions to within the uncertainties in our measurements."1121 The most obvious disagreement ts for the star UX Ari. for which the differences in ocosó and à are 84 mas and 42 mas respectively.," The most obvious disagreement is for the star UX Ari, for which the differences in $\alpha \cos\delta$ and $\delta$ are 84 mas and 42 mas respectively."1122 The large offsets for UX Ari are real. and are discussed in section 6 below.," The large offsets for UX Ari are real, and are discussed in section 6 below."1123 Optical (Hipparcos) minus radio (this paper) position differences (Ancosó. Ad) were calculated for the 18 stars on our list (excluding UX Ari) at our 2000.94 epoch.," Optical (Hipparcos) minus radio (this paper) position differences $\Delta \alpha \cos \delta, \Delta \delta$ ) were calculated for the 18 stars on our list (excluding UX Ari) at our 2000.94 epoch."1124 The three rotation angles between the optical and radio frames were determined from these data using a weighted least-squares adjustment (see Table 3)), The three rotation angles between the optical and radio frames were determined from these data using a weighted least-squares adjustment (see Table \ref{ROT_TAB}) ).1125 For the radio positions. we used the errors reported in Table 2.," For the radio positions, we used the errors reported in Table 2."1126 For the optical positions we used the Hipparcos errors at epoch (1991.25) updated to our epoch using the Hipparcos proper motion errors., For the optical positions we used the Hipparcos errors at epoch (1991.25) updated to our epoch using the Hipparcos proper motion errors.1127 No significant misalignment of the frames was found to within the formal errors of about 3 mas per axis., No significant misalignment of the frames was found to within the formal errors of about 3 mas per axis.1128 The reduced \7 for the solutions is 1.0. confirming the error estimates for the input data.," The reduced $\chi^2$ for the solutions is $\approx$ 1.0, confirming the error estimates for the input data."1129 The positions of the 19 radio stars from our VLA+PT observations were combined with previous VLA observations (Johnstonetal.1985:Johnston.deVeet&Gaume2003) to determine stellar proper motions. Εως and 4/45. for the 15 sources common to both programs.," The positions of the 19 radio stars from our VLA+PT observations were combined with previous VLA observations \citep{JWFD:85, JDG:03} to determine stellar proper motions, $\mu_{\alpha \cos\delta}$ and $\mu_{\delta}$, for the 15 sources common to both programs."1130 Although the data cover a long time range. 1978-2000. the sampling is not sufficient to enable the determination of source parallaxes.," Although the data cover a long time range, 1978–2000, the sampling is not sufficient to enable the determination of source parallaxes."1131 We therefore computed proper motions for the 15 stars using the parallaxes obtained from Hipparcos., We therefore computed proper motions for the 15 stars using the parallaxes obtained from Hipparcos.1132 The proper motions derived from the combined VLA and VLA+PT data are listed in Table 4.., The proper motions derived from the combined VLA and VLA+PT data are listed in Table \ref{PROP_MOT_TAB}.1133 The values listed in columns 3 and 4 of Table + were computed using a linear least-squares fit to the data weighted by the position errors for each observation., The values listed in columns 3 and 4 of Table \ref{PROP_MOT_TAB} were computed using a linear least-squares fit to the data weighted by the position errors for each observation.1134 Position errors for the previous VLA observations were estimated to be 30 mas in both acosà and à (Johnston.deVest&Gaume2003) and we have adopted these values in our proper motion analysis., Position errors for the previous VLA observations were estimated to be 30 mas in both $\alpha \cos\delta$ and $\delta$ \citep{JDG:03} and we have adopted these values in our proper motion analysis.1135 We did not attempt to melude accelerations or to model possible companions in wide orbits with the exception of the star UX Art discussed in the next section., We did not attempt to include accelerations or to model possible companions in wide orbits with the exception of the star UX Ari discussed in the next section.1136 In addition to our VLA/VLA+PT proper motions. Table 4 lists the proper motions derived from the Hipparcos mission and from long-term VLBI observations by Lestradeetal.(1999).," In addition to our VLA/VLA+PT proper motions, Table \ref{PROP_MOT_TAB} lists the proper motions derived from the Hipparcos mission and from long-term VLBI observations by \cite{LPJPRTRG:99}."1137. Comparing the various proper motions listed in the table. one can see that the VLA/VLA+PT values. with mean errors of 1.44 mas yr! IN 4os5 and 1.79 mas yr! In jis. are beginning to approach the accuracies of the Hipparcos proper motions with mean errors of 0.95 mas yr! and 0.87 mas yr! respectively.," Comparing the various proper motions listed in the table, one can see that the VLA/VLA+PT values, with mean errors of 1.44 mas $^{-1}$ in $\mu_{\alpha \cos\delta}$ and 1.79 mas $^{-1}$ in $\mu_{\delta}$, are beginning to approach the accuracies of the Hipparcos proper motions with mean errors of 0.95 mas $^{-1}$ and 0.87 mas $^{-1}$ respectively."1138 For a few of the stars listed in Table 4.. our proper motion errors are actually smaller than those derived from the Hippareos observations.," For a few of the stars listed in Table \ref{PROP_MOT_TAB}, our proper motion errors are actually smaller than those derived from the Hipparcos observations."1139 Comparisons of the VLA/VLA+PT proper motions with those derived from Hipparcos and VLBI data are shown in Figures 7 and 8.., Comparisons of the VLA/VLA+PT proper motions with those derived from Hipparcos and VLBI data are shown in Figures \ref{PROP_MOT_VLA} and \ref{PROP_MOT_VLBI}.1140" Figure 7. plots the differences between the proper motions in acos. (Agi,cos) and 6 (Ajis). as derived from our VLA/VLA+PT observations and those of Hipparcos."," Figure \ref{PROP_MOT_VLA} plots the differences between the proper motions in $\alpha \cos\delta$ $\Delta\mu_{\alpha \cos\delta}$ ) and $\delta$ $\Delta\mu_{\delta}$ ), as derived from our VLA/VLA+PT observations and those of Hipparcos."1141 The error bars are the root-sum-square of the uncertainties reported for the two sets of proper motions., The error bars are the root-sum-square of the uncertainties reported for the two sets of proper motions.1142 For six of the 15 stars common to both data sets. proper motions in both ocosd and ó are in agreement to within the error bars.," For six of the 15 stars common to both data sets, proper motions in both $\alpha \cos\delta$ and $\delta$ are in agreement to within the error bars."1143" An additional three stars agree in 7,44,5 only. four stars agree in iis only. and two stars do not agree at the Io level."," An additional three stars agree in $\mu_{\alpha \cos\delta}$ only, four stars agree in $\mu_{\delta}$ only, and two stars do not agree at the $\sigma$ level."1144 Figure 8 shows a similar comparison of the VLA/VLA+PT proper motions with those derived from VLBI observations of Lestradeetal. (1999)., Figure \ref{PROP_MOT_VLBI} shows a similar comparison of the VLA/VLA+PT proper motions with those derived from VLBI observations of \cite{LPJPRTRG:99}.1145. Although the errors reported for the VLBI proper motions are significantly smaller than those estimated for the VLA/VLA+PT data (see Table 4)). the computed proper motions are in complete agreement for four of the six stars common to both experiments.," Although the errors reported for the VLBI proper motions are significantly smaller than those estimated for the VLA/VLA+PT data (see Table \ref{PROP_MOT_TAB}) ), the computed proper motions are in complete agreement for four of the six stars common to both experiments."1146" The other two stars do not agree within the uncertainties in either j5,,,,5 Or 4/5.", The other two stars do not agree within the uncertainties in either $\mu_{\alpha \cos\delta}$ or $\mu_{\delta}$.1147 One of these stars is Algol a known ternary. for which we only have 6 data points.," One of these stars is Algol a known ternary, for which we only have 6 data points."1148 The other star is UX Ari which was mentioned previously as having large differences between our VLA+PT position and the Hipparcos position., The other star is UX Ari which was mentioned previously as having large differences between our VLA+PT position and the Hipparcos position.1149 UX Ari is discussed in more detail below., UX Ari is discussed in more detail below.1150 Finally. in columns 9 and 10 of Table 4. we combined the VLA/VLA+PT. Hipparcos. and VLBI values by computing weighted mean proper motions and associated errors for each of the 15 stars having VLA/VLA+PT data.," Finally, in columns 9 and 10 of Table \ref{PROP_MOT_TAB} we combined the VLA/VLA+PT, Hipparcos, and VLBI values by computing weighted mean proper motions and associated errors for each of the 15 stars having VLA/VLA+PT data."1151 The combined position was weighted by the errors in the individual proper motions derived from each of the three data sets: WLA/VLA+PT. Hippareos. and VLBI (when available).," The combined position was weighted by the errors in the individual proper motions derived from each of the three data sets: VLA/VLA+PT, Hipparcos, and VLBI (when available)."1152 The error in the combined position is just the WRMS of the available VLA/VLA+PT. Hipparcos. and/or VLBI errors.," The error in the combined position is just the WRMS of the available VLA/VLA+PT, Hipparcos, and/or VLBI errors."1153 Because of the relatively small errors in the VLBI derived proper motions. some of the combined proper motions are heavily weighted toward the VLBI value (see c CrB for example).," Because of the relatively small errors in the VLBI derived proper motions, some of the combined proper motions are heavily weighted toward the VLBI value (see $\sigma^2$ CrB for example)."1154" The accuracies of the averaged proper motions exceed those of the VLA/VLA+PT and Hipparcos data alone with average WRMS errors of 0.47 mas yr! IN £5,05,5 and 0.48 mas yr! In fis.", The accuracies of the averaged proper motions exceed those of the VLA/VLA+PT and Hipparcos data alone with average WRMS errors of 0.47 mas $^{-1}$ in $\mu_{\alpha \cos\delta}$ and 0.48 mas $^{-1}$ in $\mu_{\delta}$ .1155with. e.g.. Balletal.2008.. who achieve 7 = 0.0242 (without 1|Z normalization) and references therein.,"with, e.g., \citealt{Ball08}, who achieve $\sigma$ = 0.0242 (without $1+Z$ normalization), and references therein."1156 We find that he outlier rate is consistent from training set to validation set (increasing from to )). and that Z2c* increases w only when we use the Nvstr6muim extension as opposed to clirectly fitting the data. (," We find that the outlier rate is consistent from training set to validation set (increasing from to ), and that $\Rhat$ increases by only when we use the Nyströmm extension as opposed to directly fitting the data. ("1157Note that if we include the w xund. the estimate of€ increases by two orders of magnitude. indicating the scatter in colour space introduced. by. non- u-band data. although. fey itself only rises vom 5/4.),"Note that if we include the $u$ band, the estimate of $\epshat$ increases by two orders of magnitude, indicating the scatter in colour space introduced by non-constraining $u$ -band data, although $\Rhat$ itself only rises by $\approx$ .)"1158 The LRG redshift predictions. like their MS counterparts. are biased. with a similar downward trend in he bias as a Function of Z (left middle panel. Fig. 2)).," The LRG redshift predictions, like their MSG counterparts, are biased, with a similar downward trend in the bias as a function of $Z$ (left middle panel, Fig. \ref{fig:bias}) )."1159 We repeat our simple resampling experiment with LAC data and find that the bias slope increases upon resampling. demonstrating that attenuation bias also allects LRG data analysis (as expected: see Fig. 4)).," We repeat our simple resampling experiment with LRG data and find that the bias slope increases upon resampling, demonstrating that attenuation bias also affects LRG data analysis (as expected; see Fig. \ref{fig:comp_bias}) )."1160 The DEEP? Galaxy Redshift Survey (Davisctal.2003.. Davisetal. 2007)) studied both galaxy. properties and large-scale structure primarily at redshifts 0.7zz1.4. in four ficlds of total area ~ 3 square degrees.," The DEEP2 Galaxy Redshift Survey \citealt{Davis03}, \citealt{Davis07}) ) studied both galaxy properties and large-scale structure primarily at redshifts $0.7 \la z \la 1.4$, in four fields of total area $\sim$ 3 square degrees."1161 DELP? targets are selected to have Pagx 24.1 using CFU BRI photomoetric data (Coiletal. 2P004))., DEEP2 targets are selected to have $R_{AB} \leq$ 24.1 using CFHT BRI photometric data \citealt{Coil04}) ).1162 In three of the four DEEP? fields. colour cuts are used to select zz 0.7 objects for observation: however. in this paper we utilize the DEEP2 sample in the Extended Groth Strip. for which no colour cuts have been applied.," In three of the four DEEP2 fields, colour cuts are used to select $z >$ 0.7 objects for observation; however, in this paper we utilize the DEEP2 sample in the Extended Groth Strip, for which no colour cuts have been applied."1163 DEEP2 collected. spectra typically covering the wavelength range .1C)OA [or z 50.000 objects.," DEEP2 collected spectra typically covering the wavelength range $-$ 9,100 for $>$ 50,000 objects."1164 From the survey we select the 6.55552 ealaxies lor which single-system ugriz photometry exists from the ΕΙΤΙ) Legacy Survey (field and for which the DELP2ZQUALITY Lag is either 3 or dC or confidence that the redshift is correct. respectively).," From the survey we select the 6,552 galaxies for which single-system $ugriz$ photometry exists from the CFHT Legacy Survey (field and for which the DEEP2 flag is either 3 or 4 $>$ or confidence that the redshift is correct, respectively)."1165 Thus the dimensionality. of colour-space for these data is p = 4., Thus the dimensionality of colour-space for these data is $p$ = 4.1166 We further remove data for which the redshift error. or any magnitude or magnitude error. is not provided. leaving 6.418 galaxies: after outlier removal. the final sample size is 6.067.," We further remove data for which the redshift error, or any magnitude or magnitude error, is not provided, leaving 6,418 galaxies; after outlier removal, the final sample size is 6,067."1167 Lowe restrict ourselves to data for whichZQUALITY = 4. the sample size is 5.223.," If we restrict ourselves to data for which = 4, the sample size is 5,223."1168 Application of the algorithm outlined in. 882.1-2.2 vields tuning parameter estimates (6.71) = (0.002.850) for = 4 and (0.002.1050) forZQUALITY = 3.," Application of the algorithm outlined in 2.1-2.2 yields tuning parameter estimates $(\epshat,\mhat)$ = (0.002,850) for = 4 and (0.002,1050) for $\geq$ 3."1169 We display our results in Table 1. and Fig. 6:, We display our results in Table \ref{tab:results} and Fig. \ref{fig:deep2};1170 note that because we do not apply the Nystrómm extension here (but rather. fit to the data directly alter (ο.0i) are determined). the observed scatter is smaller than we would observe with a larger. Nystrómnmr-eextended dataset.," note that because we do not apply the Nyströmm extension here (but rather, fit to the data directly after $(\epshat,\mhat)$ are determined), the observed scatter is smaller than we would observe with a larger, Nyströmm-extended dataset."1171 In both cases. we exclude of the objects from analysis as outlicrs.," In both cases, we exclude of the objects from analysis as outliers."1172 In Fig. 6..," In Fig. \ref{fig:deep2},"1173" we observe that the quality of the fits below Zs 0.15 (Fic = 0.038 forZQUALITY = 4) is superior to that athigher redshifts ""Tom 0.064).", we observe that the quality of the fits below $Z \approx$ 0.75 $\Rhat$ = 0.038 for = 4) is superior to that athigher redshifts $\Rhat$ = 0.064).1174 To understand why this is so. we examine the DEEP? colour data (Eig. 7)).," To understand why this is so, we examine the DEEP2 colour data (Fig. \ref{fig:deep2colours}) )."1175" Pick an object at Zz0.75. and compute the Euclidean distance in colour-space to a random object at any other redshift, Z0.1.5]."," Pick an object at $Z \approx 0.75$, and compute the Euclidean distance in colour-space to a random object at any other redshift $Z \in [0,1.5]$."1176 This distance is a nearly constant function of AZ: thus for values o£ « similar to those chosen in the SDSS analyses. there is only a slightly lesser probability of cüllusing from Z= 0.75 to. eg. Z= (2asto. eg. Z= 0.74.," This distance is a nearly constant function of $\Delta Z$; thus for values of $\epsilon$ similar to those chosen in the SDSS analyses, there is only a slightly lesser probability of diffusing from $Z =$ 0.75 to, e.g., $Z =$ 0.2 as to, e.g., $Z =$ 0.74."1177 To achieve aceurate predictions at Ze0.75. « must be mace smaller (lessening the probability of large AZ jumps): this is what our optimization vields.," To achieve accurate predictions at $Z \approx 0.75$, $\epsilon$ must be made smaller (lessening the probability of large $\Delta Z$ jumps); this is what our optimization yields."1178 A consequence of a smaller € is that the weighted graph of the DEIEP2 objects is not fully connected (see diseussion around. equation 1))., A consequence of a smaller $\epshat$ is that the weighted graph of the DEEP2 objects is not fully connected (see discussion around equation \ref{eqn:weighted}) ).1179 One can discern connectedness by examining the vector of eigenvalues: for € = 0.002. the first zz 20 eigenvalues are all c 0.95. implvingthe presence of several disconnected. ebumps on the graph.," One can discern connectedness by examining the vector of eigenvalues; for $\epshat$ = 0.002, the first $\approx$ 20 eigenvalues are all $>$ 0.95, implyingthe presence of several disconnected clumps on the graph."1180 he most. visually obvious manifestation of disconnectedness in the DIZIEP2 analysis is the presence of a markecl knee in the predictions at Zz 0.75 for small values of m (see Fig. 8)):, The most visually obvious manifestation of disconnectedness in the DEEP2 analysis is the presence of a marked knee in the predictions at $Z \approx$ 0.75 for small values of $m$ (see Fig. \ref{fig:deep2ev}) );1181 the dominant eigenvectors describe the low redshift data well. but not the high redshift data.," the dominant eigenvectors describe the low redshift data well, but not the high redshift data."1182 As m increases. the knee straightens out: however. because of the bias-variance (ρασος i can only increase so much before Rey begins to increase as well. due to increasing variance.," As $m$ increases, the knee straightens out; however, because of the bias-variance tradeoff, $m$ can only increase so much before $\Rhat$ begins to increase as well, due to increasing variance."1183 For m = S50(ZQUALITY = +) we have not vet achieved an optimal description for the hieh-redshift data., For $\mhat$ = 850 = 4) we have not yet achieved an optimal description for the high-redshift data.1184 To demonstrate that we can achieve a better description of these data. we split the full dataset into Iow- and high-recshift sets (at. eg. Zou = 0.9) and compute diffusion maps for cach.," To demonstrate that we can achieve a better description of these data, we split the full dataset into low- and high-redshift sets (at, e.g., $Z_{\rm cut}$ = 0.9) and compute diffusion maps for each."1185 We find that we can achieve. e.g.. Rey8: 0.035 for hieh-redshift data with as [ew as 40 eigenvectors. while the predictions at low redshifts change only slightly.," We find that we can achieve, e.g., $\Rhat \approx$ 0.035 for high-redshift data with as few as 40 eigenvectors, while the predictions at low redshifts change only slightly."1186 While splitting the data vields better results for our DELP? sample. we do not propose such splitting as part of our general dilfusion map framework. for multiple reasons: (a) it acids a tuning parameter (Zou). (b) it complicates the Nystrómam extension (to which data split do we assign a new object?).," While splitting the data yields better results for our DEEP2 sample, we do not propose such splitting as part of our general diffusion map framework, for multiple reasons: (a) it adds a tuning parameter $Z_{\rm cut}$ ), (b) it complicates the Nyströmm extension (to which data split do we assign a new object?),"1187 and. most importantly (ο) a data split. can be rendered. moot with the inclusion of new data in other banclpasses (e.g.. the inclusion of near-It data in the DEEP? sample would mitigate the Iuclidean-cdistance issue seen at Ze 0.15).," and most importantly (c) a data split can be rendered moot with the inclusion of new data in other bandpasses (e.g., the inclusion of near-IR data in the DEEP2 sample would mitigate the Euclidean-distance issue seen at $Z \approx 0.75$ )."1188 Concentrating on the regime Z 0.75. we find that our result Rey80.035 with ηez compares favorably with that of bertetal. (2006).. who train a template-based photometric redshift code using 2.867 spectroscopic redshifts from the VIMOS VLE Deep Survey (VVDS) in the ΕΙΤὸ DI field and obtain σ= and 5g= (sce their. 86.3 and fig.," Concentrating on the regime $Z \la 0.75$ , we find that our result $\Rhat \approx 0.035$ with $\eta \approx$ compares favorably with that of \cite{Ilbert06}, , who train a template-based photometric redshift code using 2,867 spectroscopic redshifts from the VIMOS VLT Deep Survey (VVDS) in the CFHTLS D1 field and obtain $\sigma = 0.032$ and $\eta =$ (see their 6.3 and fig."1189 14)., 14).1190 Our, Our1191to a space-filling pattern of shorter LCSs that look more favourable for widespread reconnection.,to a space-filling pattern of shorter LCSs that look more favourable for widespread reconnection.1192 The observed velocity field is found to have comparable [V-v| and |Vxv]. and the observed c field is in qualitative agreement with a combined model incorporating both effects.," The observed velocity field is found to have comparable $|\nabla\cdot{\bf v}|$ and $|\nabla\times{\bf v}|$, and the observed $\sigma$ field is in qualitative agreement with a combined model incorporating both effects."1193 In the combined case. the appearance of the «c and Q fields follows that of the diverging flow model: the diverging part of the velocity acts to quickly stretch and deform the picture.," In the combined case, the appearance of the $\sigma$ and $Q$ fields follows that of the diverging flow model: the diverging part of the velocity acts to quickly stretch and deform the picture."1194" However. the rate of increase of integrated log,,Q in the combined model is double that of the original model. and we hypothesise that the vortical structure remains ""hidden"" in the magnetic field topology."," However, the rate of increase of integrated $\log_{10}Q$ in the combined model is double that of the original model, and we hypothesise that the vortical structure remains “hidden” in the magnetic field topology."1195" We have demonstrated how the vortical part may be extracted from an observed velocity field. but further study is required to determine whether the vortical part is a more appropriate predictor of subsequent reconnection,"," We have demonstrated how the vortical part may be extracted from an observed velocity field, but further study is required to determine whether the vortical part is a more appropriate predictor of subsequent reconnection."1196 Due to the limitations of the observational technique used for the demonstration in this paper. the typical flow speeds measured were only 0.1kms'. a factor of 5—10 slower than real granular flows.," Due to the limitations of the observational technique used for the demonstration in this paper, the typical flow speeds measured were only $0.1\,\textrm{km}\,\textrm{s}^{-1}$, a factor of $5-10$ slower than real granular flows."1197 From investigation of the analytical model. we predict that faster flow speeds (for the same size and lifetime of granules) will result in. significantly faster development of strong gradients in the magnetic field.," From investigation of the analytical model, we predict that faster flow speeds (for the same size and lifetime of granules) will result in significantly faster development of strong gradients in the magnetic field."1198 Our initial results are therefore very much a lower bound for the complexity that we expect to develop in the coronal magnetic field over this time., Our initial results are therefore very much a lower bound for the complexity that we expect to develop in the coronal magnetic field over this time.1199 The model also indicates that. if the real vorticity is also larger. then the combined c field will show greater infilling of LCSs.," The model also indicates that, if the real vorticity is also larger, then the combined $\sigma$ field will show greater infilling of LCSs."1200" In this case. the mixing of trajectories is sufficient that the model begins to show a process of ""homogenisation"" of the «c field as found in simulations of turbulence(?)."," In this case, the mixing of trajectories is sufficient that the model begins to show a process of “homogenisation” of the $\sigma$ field as found in simulations of turbulence."

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