ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2" The mean light curve for 86421. which has the clearest signal. is shown in Fig. Ἐν,"," The mean light curve for S6421, which has the clearest signal, is shown in Fig. \ref{lcmeanddcir},"3 where the amplitude is 0.026 mae., where the amplitude is 0.026 mag.4 The EF for the entire data set. excluding 86404. naturally has an alias problem: the two highest peaks are at 666.08 s and its one day alias 671.28 s. both with amplitudes of 0.017 mag.," The FT for the entire data set, excluding S6404, naturally has an alias problem; the two highest peaks are at 666.08 s and its one day alias 671.28 s, both with amplitudes of 0.017 mag."5 The —670 s signal is indicative of the rotation period of the primary or its orbital sideband., The $\sim$ 670 s signal is indicative of the rotation period of the primary or its orbital sideband.6 It would be valuable to extend observations of DD Cir. with larger telescopes. before it faces further.," It would be valuable to extend observations of DD Cir, with larger telescopes, before it fades further."7 TY Cry is an SU UMa type dwarf nova with à quiescent magnitude V  19 and superoutbursts spaced about a vear apart (Levy ct al., TV Crv is an SU UMa type dwarf nova with a quiescent magnitude V $\sim$ 19 and superoutbursts spaced about a year apart (Levy et al.8 1990)., 1990).9" During the superoutburst in June 1994 superhumps were observed with a period £P, of 1.56 4 0.02 h (Llowell et al.", During the superoutburst in June 1994 superhumps were observed with a period $P_{sh}$ of 1.56 $\pm$ 0.02 h (Howell et al.10 1996)., 1996).11 Superhumps usually have periods, Superhumps usually have periods12In 1919 a star was noticed to brighten in the constellation of Aquila (?)..,In 1919 a star was noticed to brighten in the constellation of Aquila \citep{Wolf1920}.13 A spectrum of the central source revealed it lo bea werogen-delicient eiant (7).., A spectrum of the central source revealed it to be a hydrogen-deficient giant \citep{Lundmark1921}.14" Shortly after the nova-like outburst. V605 Aql brightened over a period of 2 vears lo a peak of mj,=10.2 in 1919."," Shortly after the nova-like outburst, V605 Aql brightened over a period of 2 years to a peak of $m_{pg}=10.2$ in 1919."15 The surface temperature of he star was 75.000 Ix. and its spectrum in 1921 was very similar o that of R. Coronae Borealis (HCD) stars. hvdrogen-deficient. helium-rich supergiants (22)," The surface temperature of the star was $\sim$ 5,000 K, and its spectrum in 1921 was very similar to that of R Coronae Borealis (RCB) stars, hydrogen-deficient, helium-rich supergiants \citep[]{Clayton96,Clayton97}."16 Νους Aql was later noticed to be in the middle of an old ancl faint planetary nebula (DN: ?2)). Abell 58 CX 58) with a dynamical age of 200000 vr (2)...," V605 Aql was later noticed to be in the middle of an old and faint planetary nebula (PN; \citealt{Bidelman1971}) ), Abell 58 (A 58), with a dynamical age of 000 yr \citep{Pollacco92}."17 X bright hyelrogen-delicient knot was noticed erowing at its &cometric centre hy 2.., A bright hydrogen-deficient knot was noticed growing at its geometric centre by \citet{Seitter1987}.18 2. estimated. today's surface temperature of the central star to be 95.0001. The stellar spectrum and chemical abundances place thiscentral star of PN in the WollRavet spectral class (also called WR] by ο. to distinguish these stars from their massive counterparts)," \citet{Clayton06} estimated today's surface temperature of the central star to be 95,000K. The stellar spectrum and chemical abundances place thiscentral star of PN in the Wolf-Rayet spectral class (also called [WR] by \citet{vanderHucht1981}, to distinguish these stars from their massive counterparts)."19 Todas. the explanation for the observations of A 58 and its central star is that the central star. alter the formation of its surrounding PN. underwent a very late helium shell Hash. also called a final Dash. which ejected freshly processed. stellar material into the centre of the nebula (?7)..," Today, the explanation for the observations of A 58 and its central star is that the central star, after the formation of its surrounding PN, underwent a very late helium shell flash, also called a final flash, which ejected freshly processed stellar material into the centre of the nebula \citep{Iben83, Herwig01}."20 V605 Aql is considered. an older twin of Sakurai's object that underwent a similar outburst in 1995 (?).., V605 Aql is considered an older twin of Sakurai's object that underwent a similar outburst in 1995 \citep{Nakano1996}.21 Other PN consisting of (or containing) hydrogen-deficient ejecta have been found (e.g. A 30 and A T8: ?2)) and they too are considered. final Dash objects.," Other PN consisting of (or containing) hydrogen-deficient ejecta have been found (e.g., A 30 and A 78; \citealt{Jacoby1983}) ) and they too are considered final flash objects."22 The extent of the hvdrogen deficiency. of their stellar atmospheres or ejecta is explained by the timing of the final Hash (?).., The extent of the hydrogen deficiency of their stellar atmospheres or ejecta is explained by the timing of the final flash \citep{Herwig01}. .23 The central star of A 58 has a Woll-Rayet spectral, The central star of A 58 has a Wolf-Rayet spectral24zero except near the nebular lines.,zero except near the nebular lines.25 We used the best fit ligh-pass model. so as to eet the best match to absorption features. aud normalize it to the plivsical cosmic spectruuui using a smoothing filter.," We used the best fit high-pass model, so as to get the best match to absorption features, and normalize it to the physical cosmic spectrum using a smoothing filter."26 We show the example coutiuuau subtracted spectitm in Figure 11.., We show the example continuum subtracted spectrum in Figure \ref{fig:abs-spec}.27 The subtraction is excellent in the iregion. the priucipal discrepaucy is for wavelengths >δ000Α where the Cale triplet absorption lines are not well fit by anv of our models: this effect can also be seen in Figure 5..," The subtraction is excellent in the region, the principal discrepancy is for wavelengths $>8000$ where the Calcium triplet absorption lines are not well fit by any of our models; this effect can also be seen in Figure \ref{fig:residuals}."28 The line huninosity densities are simply calculated by intcerating the cosmic spectrum for each line frou AδΑ tto A|SAL., The line luminosity densities are simply calculated by integrating the cosmic spectrum for each line from $\lambda-8$ to $\lambda+8$.29 The box width is chosen to be 3« the typical hue EWIIM so the fixes are very close to total., The box width is chosen to be $\times$ the typical line FWHM so the fluxes are very close to total.30 The resulting line hunuinositv densities aro eiven 1u Table 3.., The resulting line luminosity densities are given in Table \ref{tab:lines}.31 We quote values for region A aud D. as the latter includes [OTI] and for comparative purposes.," We quote values for region A and B, as the latter includes [OII] and for comparative purposes."32 Both are normalized to the same kc Ipuninositv deusitv., Both are normalized to the same $r$ luminosity density.33 There are two sources of error: firstly the imperfection of the continu subtraction., There are two sources of error: firstly the imperfection of the continuum subtraction.34 Visually we checked the region around cach hue. particularly the Baler lines. aud found no evidence of significant residuals. ic. the plot appears as al emission hue with zero contimmiuiu plus ‘noise’ due to the mismatch in resolution between raw data aud model spectrum.," Visually we checked the region around each line, particularly the Balmer lines, and found no evidence of significant residuals, i.e. the plot appears as an emission line with zero continuum plus `noise' due to the mismatch in resolution between raw data and model spectrum."35 To quantify this for cach line we similarly extract two regions. either side of the line. of the same width where there is only blank continuum. ttypically a ooftset. (," To quantify this for each line we similarly extract two regions, either side of the line, of the same width where there is only blank continuum, typically a offset. ("36These are optimized for each line particularly in the crowded Πα region).,These are optimized for each line particularly in the crowded $\alpha$ /[NII] region).37 These give typically the sale error aud we /[NII|quote the maxinuun iu the table., These give typically the same error and we quote the maximum in the table.38 There is also an additional systematic error due to the uncertaintv in the ¢ Inuünositv density which we estimate as10., There is also an additional systematic error due to the uncertainty in the $r$ luminosity density which we estimate as.39. The line hunuinositv densities lead to some interesting results: first the Balmer decrement Πα) is 6.1+0.9 (reeion A but region D is similar). if we take an uureddened case D recombination value of 2.86 (Tuner&Storey1987) aud a Milkv Wavy dust law from Pei(1992). (the SAIC law eives simular nunboers as the two are close in the optical) we derive a nebular extinction Ay-=2.140.1.," The line luminosity densities lead to some interesting results: first the Balmer decrement $\alpha$ $\beta$ is $6.4\pm 0.9$ (region A but region B is similar), if we take an unreddened case B recombination value of 2.86 \citep{HummerStorey} and a Milky Way dust law from \cite{Pei} (the SMC law gives similar numbers as the two are close in the optical) we derive a nebular extinction $A_V=2.4\pm 0.4$."40 The Πα bhuuinositv density thus requires a correction. factor of (5.8c L8) , The $H\alpha$ luminosity density thus requires a correction factor of $\times (5.8\pm1.8)$ .41This is consistent with other workers findines for example we have re-analvzed the sample of Callegoet—al.(1995) looking at the fa correction factor as a function of luminosity and fud a volhune averaged value of «{οι , This is consistent with other workers findings — for example we have re-analyzed the sample of \cite{Gallego95} looking at the $H\alpha$ correction factor as a function of luminosity and find a volume averaged value of $\times 4.6$.42Thus it makes little difference whether one dereddens before taking the mean or simply cereddens the mean (Which is the approach we are taking here with the cosnde spectuni) even for these huge nebular extinction values., Thus it makes little difference whether one dereddens before taking the mean or simply dereddens the mean (which is the approach we are taking here with the cosmic spectum) even for these large nebular extinction values.43 The dereddened fe buuinositv deusitv is thus [1+ W ? for hi=0.7.," The dereddened $H\alpha$ luminosity density is thus $4.1\pm 1.344\times10^{32}$ W $^{-3}$ for $h=0.7$."45 Converting to ces units and fh=0.5 this gives 2.940.9ς107 eves + ? which is the same as that fouud by from the Canada FranceRedshift Survey (Tresse&Maddox1998b) at low redshift (2~ 0.2)., Converting to cgs units and $h=0.5$ this gives $2.9 \pm 0.9 \times10^{39}$ ergs $^{-1}$ $^{-3}$ which is the same as that found by from the Canada FranceRedshift Survey \citep{TresseMaddox98} at low redshift $z\sim 0.2$ ).46 Tt is twice as ligh as that found by the objective wisn survey of Gallegoetal. (1995). , It is twice as high as that found by the objective prism survey of \cite{Gallego95}. .47From our models we can also work out the conversion of Πα huninosity iuto SFR (from the uuuboer of iouizine ohotons). the mean conversion factor is 1:36«10! cress + + yr and the range in the models is 15% (it varies with metallicity).," From our models we can also work out the conversion of $\alpha$ luminosity into SFR (from the number of ionizing photons), the mean conversion factor is $1.36\times 10^{41}$ ergs $^{-1}$ $^{-1}$ yr and the range in the models is $\pm 15$ (it varies with metallicity)."48 This allows us toderive a SER deusity oday of 0.030 0.056 ὃ, This allows us toderive a SFR density today of $0.030$ – $0.056$ .49"ν, It is remarkable onote that this is eutirely consistent with the derived incdependcutly from the starformation listory fitting", It is remarkable tonote that this is entirely consistent with the derived independently from the star-formation history fitting50 ονwords: Stars: white Dwarfs. Stars: dwarf uovae (WW Ceti) Cataclysinic variables (CVs) are short-period. semi-detached binary systems consisting of au accretiug white dwarf (WD) primary star aud a low-lass malü-sequence secondary star as the Roche lobe-filling mass donor (Warner1995).," Keywords: Stars: white Dwarfs, Stars: dwarf novae (WW Ceti) Cataclysmic variables (CVs) are short-period, semi-detached binary systems consisting of an accreting white dwarf (WD) primary star and a low-mass main-sequence secondary star as the Roche lobe-filling mass donor \citep{war95}."51. The binary orbital period iu these systems ranges rou about zz Lh to a few days., The binary orbital period in these systems ranges from about $\approx 1$ h to a few days.52 However. there is a gap in orbital period between 2 aud 3 hours where almost πο systems are fouud.," However, there is a gap in orbital period between 2 and 3 hours where almost no systems are found."53 [tis not known whether the systems are evolving [rom a longer yerlod to a shorter period (across the gap) or whether the systems above tlie gap are all together different (rom the systems below the gap., It is not known whether the systems are evolving from a longer period to a shorter period (across the gap) or whether the systems above the gap are all together different from the systems below the gap.54 Dwarf novae (DN) are a subset of CVs that undergo lar eruptious called outbursts which last for days to weeks. separated by intervals of quiescence asting weeks to mouths.," Dwarf novae (DN) are a subset of CVs that undergo regular eruptions called outbursts which last for days to weeks, separated by intervals of quiescence lasting weeks to months."55 The now widely accepted interpretation of the quiescence/outburst cycle is that of the disk instability mocel (DIM. Canuizzo|. (1998))).," The now widely accepted interpretation of the quiescence/outburst cycle is that of the disk instability model (DIM, \citet{can98}) )."56 It is assumed that curing the quiescent phase the matter in the disk is cold and ueutral auc the disk is optically thin because of its low density. while during outburst. as the mass accretion rate increases. the matter in the disk is ionized aud becomes optically thick.," It is assumed that during the quiescent phase the matter in the disk is cold and neutral and the disk is optically thin because of its low density, while during outburst, as the mass accretion rate increases, the matter in the disk is ionized and becomes optically thick."57 The basic principle of the DIM theory clepeuds heavily, The basic principle of the DIM theory depends heavily58V. dRyju)34. yielding. an expansion: velocity: of about ~ 5 km .,"$_s$ $\left( \frac{R_{\rm HII}}{R_s} \right)^{-3/4}$, yielding an expansion velocity of about $\sim$ 5 km $^{-1}$."59 The obtained dynamical age and expansion velocity are in with those obtained in typical regions (Gum 31. ;: agreementSh2-173. 2) ," The obtained dynamical age and expansion velocity are in agreement with those obtained in typical regions (Gum 31, \citealt{cn08}; Sh2-173, \citealt{ci09}) )."60The total number of tonizing Lyman continuum photons needed to sustain the ionization. in. MBO is', The total number of ionizing Lyman continuum photons needed to sustain the ionization in MBO is.61 To search for stars that can provide the necessary UV photons. we used the available VIZIER catalogues.," To search for stars that can provide the necessary UV photons, we used the available VIZIER catalogues."62 CP-59 295] is a BI V star placed at (2).., CP-59 2951 is a B1 V star placed at \citep{bu99}.63 Using the catalogued spectral type. the visual magnitude. and the calibration of ?.. we estimated a distanced=2.," Using the catalogued spectral type, the visual magnitude, and the calibration of \citet{sk82}, we estimated a distance."647+0.8kpe.. The continuum ionizing photons emitted by the star are (?).., The continuum ionizing photons emitted by the star are \citep{sm02}.65 Although the distance of this star is 1n agreement (within errors) with the distance of.. the value of ΔΙ is almost one order of magnitude lower than the required to ionize MBO.," Although the distance of this star is in agreement (within errors) with the distance of, the value of $N^*_{\rm Lyc}$ is almost one order of magnitude lower than the required to ionize MBO."66 The presence of Pis!7 at a projected distance of3.4 pe ( 4’ at a distance of 2.9 kpc) indicates that the contribution of the star cluster to the ionization of MBO can not be ruled out., The presence of Pis17 at a projected distance of 3.4 pc $\sim$ $'$ at a distance of 2.9 kpc) indicates that the contribution of the star cluster to the ionization of MBO can not be ruled out.67" The presence of 12 candidate YSOs projected onto the --region suggests that they may have been triggered by the expansion of the Hitregion through the ""collect and collapse"" model. which indicates that expanding nebulae compress gas between the ionization and the shock fronts. leading to the formation of molecular cores where new stars can be embedded."," The presence of 12 candidate YSOs projected onto the -region suggests that they may have been triggered by the expansion of the region through the “collect and collapse” model, which indicates that expanding nebulae compress gas between the ionization and the shock fronts, leading to the formation of molecular cores where new stars can be embedded."68" Using the analytical model of ? for the case of expanding Hirregions. we derived the time when the fragmentation may have occurred (έρως). and the size of the region at £z, (Roe). which are given by where «d» is the sound velocity in units of 0.2 μα...ny,1000. and Ni,=N;/107."," Using the analytical model of \citet{wi94} for the case of expanding regions, we derived the time when the fragmentation may have occurred $t_{frag}$ ), and the size of the region at $t_{frag}$ $R_{frag}$ ), which are given by where $a_2$ is the sound velocity in units of 0.2, $n_3 \equiv n_{H_2}/1000$, and $N_{49}\equiv N_{Lyc}^*/10^{49}$."69 Adopting for this region 0.3 for the sound velocity. which corresponds to temperatures of 10-15 K in the surrounding molecular clouds (see Section 3.1.2). we obtainedyr. andpe.," Adopting for this region 0.3 for the sound velocity, which corresponds to temperatures of 10-15 K in the surrounding molecular clouds (see Section 3.1.2), we obtained, and."70". Considering that the values of r5, and Reo. are larger than ty, and Ay, (see Section 4.1). we can conclude that the fragmentation in the edge of 33503 is doubtful."," Considering that the values of $t_{frag}$ and $R_{frag}$ are larger than $t_{dyn}$ and $R_{HII}$ (see Section 4.1), we can conclude that the fragmentation in the edge of 3503 is doubtful."71 In section. 3.2 we reported the existence of a velocity gradient across clump A. Velocity gradients in. molecular cores/clumps were usually interpreted as gravitationally bound rotation motions (particulary in dense and small molecular cores)., In section 3.2 we reported the existence of a velocity gradient across clump A. Velocity gradients in molecular cores/clumps were usually interpreted as gravitationally bound rotation motions (particulary in dense and small molecular cores).72 Several theoretical models predict cloud flattening perpendicular to the rotation axis in response to centrifugal stress. which at first glance seems to be suitable for clump A. In order to investigate the dynamical stability of clump A. we use the parameter £ defined by ? to quantify the dynamical role of rotation by comparing the rotational kinetic energy to the gravitational energy.," Several theoretical models predict cloud flattening perpendicular to the rotation axis in response to centrifugal stress, which at first glance seems to be suitable for clump A. In order to investigate the dynamical stability of clump A, we use the parameter $\beta$ defined by \citet{go93} to quantify the dynamical role of rotation by comparing the rotational kinetic energy to the gravitational energy."73 Thus. 6 can be written as where / is the moment of inertia (/= pMR?*). MMJR is the gravitational potential energy. and w’=w/sii. Where/ 1s the inclination of the cloud along the line of sight.," Thus, $\beta$ can be written as where $I$ is the moment of inertia $I=pMR^2$ ), $q G M^2/R$ is the gravitational potential energy, and $\omega'=\omega/sin(i)$, where $i$ is the inclination of the cloud along the line of sight."74 considering (see ?)).I. (see Sect 3.1.2).pe. and a lower limit mass to clump AV. we obtain0.," Considering (see \citealt{go93}) ), (see Sect 3.1.2), and a lower limit mass to clump A, we obtain."7502.. This extremely low value of £ indicates that the effect of rotation. If exists. is not significant in. mantaining the dynamical stability of," This extremely low value of $\beta$ indicates that the effect of rotation, if exists, is not significant in mantaining the dynamical stability of"76"0.2 kpc, respectively.","0.2 kpc, respectively."77 The disk is rotationally supported and has a Toomre-Q of 1.2., The disk is rotationally supported and has a Toomre-Q of 1.2.78 The amplitude of the final bar is intermediate between the weakest and strongest bars observed in galaxies., The amplitude of the final bar is intermediate between the weakest and strongest bars observed in galaxies.79" The bar's minor-to-major axial ratio is about 0.5 to 0.6, and its half-length is ~ 4 kpc."," The bar's minor-to-major axial ratio is about 0.5 to 0.6, and its half-length is $\sim$ 4 kpc."80 Figure 1 (top three panels) shows face-on and side-on views of the projected density of the best-fitting model., Figure 1 (top three panels) shows face-on and side-on views of the projected density of the best-fitting model.81 A distinctly peanut shaped bulge is apparent in the edge-on projection., A distinctly peanut shaped bulge is apparent in the edge-on projection.82 Figure 1 (bottom panel) shows the surface brightness distribution in Galactic coordinates as seen from the Sun's vantage point., Figure 1 (bottom panel) shows the surface brightness distribution in Galactic coordinates as seen from the Sun's vantage point.83" disk stars dilute the peanut shape, but the bar still looks Nearbyboxy."," Nearby disk stars dilute the peanut shape, but the bar still looks boxy."84" Moreover, from close up, an asymmetry in the longitudinal direction is apparent; this means that the bar cannot be aligned with the direction from the Sun to the Galactic center."," Moreover, from close up, an asymmetry in the longitudinal direction is apparent; this means that the bar cannot be aligned with the direction from the Sun to the Galactic center."85" Rather, its near end is at positive Galactic longitude, so it looks taller in that quadrant, and it extends farther from the Galactic center on the near side than on the far side."," Rather, its near end is at positive Galactic longitude, so it looks taller in that quadrant, and it extends farther from the Galactic center on the near side than on the far side."86 Both the boxy shape and the asymmetry are in good agreement with the morphology revealed by the COBE satellite near-infrared images (Weilandetal.1994;Dwek1995).," Both the boxy shape and the asymmetry are in good agreement with the morphology revealed by the COBE satellite near-infrared images \citep{wei_etal_94,dwe_etal_95}."87. Figure 2 compares the best-fitting model kinematics (solid lines) with the mean velocity and velocity dispersion data from theBRAVA and other surveys (Rangwalaetal. 2009)., Figure 2 compares the best-fitting model kinematics (solid lines) with the mean velocity and velocity dispersion data from the and other surveys \citep{ran_etal_09}.88. All velocities presented here have been converted to Galactocentric values (the velocity that would be observed by a stationary observer at line-of-sightthe Sun's position)., All velocities presented here have been converted to Galactocentric values (the line-of-sight velocity that would be observed by a stationary observer at the Sun's position).89" For the first time, our model is able simultaneously to match the mean velocities and velocity dispersions along two Galactic latitudes (—4? and —8?) and along the minor axis."," For the first time, our model is able simultaneously to match the mean velocities and velocity dispersions along two Galactic latitudes $-4^\circ$ and $-8^\circ$ ) and along the minor axis."90 Figure 3 constrains the angle between the bar and the line that connects the Sun to the Galactic center., Figure 3 constrains the angle between the bar and the line that connects the Sun to the Galactic center.91 It compares the model results with the data in the b2—4? major-axis strip as we vary the above angle., It compares the model results with the data in the $b=-4^\circ$ major-axis strip as we vary the above angle.92 Clearly the smallest bar angles give the best match to the velocity dispersions., Clearly the smallest bar angles give the best match to the velocity dispersions.93" Intriguingly, we find that the velocity dispersions provide much stronger constraints than the mean velocity profile."," Intriguingly, we find that the velocity dispersions provide much stronger constraints than the mean velocity profile."94 A bar angle of 0? also matches the kinematics well., A bar angle of $0^\circ$ also matches the kinematics well.95" However, the photometric asymmetry excludes a bar that is pointed at the Sun."," However, the photometric asymmetry excludes a bar that is pointed at the Sun."96 We therefore conclude that the overall best-fitting model has a bar angle of ~20°., We therefore conclude that the overall best-fitting model has a bar angle of $\sim 20^\circ$ .97" Other studies converged on a similar bar angle (Staneketal.1997;Freudenreich1998;Fux1997,1999;Bis-Gerhard2002)."," Other studies converged on a similar bar angle \citep{sta_etal_97,freude_98,fux_97,fux_99,bis_ger_02}."98". The excellent match to the data in Figures 1 — 3 strongly supports the suggestion that the boxy pseudobulge of the Milky Way is an edge-on, buckled bar that evolved from a cold, massive disk."," The excellent match to the data in Figures 1 – 3 strongly supports the suggestion that the boxy pseudobulge of the Milky Way is an edge-on, buckled bar that evolved from a cold, massive disk."99" The thickened disk in the pseudobulge-forming process may have contributed to the thick disk of the Milk Way, as hintedfrom chemical similarities of Galactic bulge and local thick disk stars Britoetal.2010; 2010)."," The thickened disk in the pseudobulge-forming process may have contributed to the thick disk of the Milk Way, as hintedfrom chemical similarities of Galactic bulge and local thick disk stars \citep{alv_etal_10,ben_etal_10}."100. The model in BensbyFigures 1 — 3 contains no classical bulge component., The model in Figures 1 – 3 contains no classical bulge component.101 Could a small classical bulge also be present?, Could a small classical bulge also be present?102" Could it have been spun up by the formation of a bar, flattened thereby and made hard to detect?"," Could it have been spun up by the formation of a bar, flattened thereby and made hard to detect?"103" To constrain such multi-component models with kinematics, we also constructed models with a pre-existing classical bulge."," To constrain such multi-component models with kinematics, we also constructed models with a pre-existing classical bulge."104" The distribution function for the live classical bulge component was generated iteratively (Debattista&Sellwood2000) to ensure that both the disk and the classical bulge were initially in equilibrium, and we required that the bulge parameters are close to the fundamental plane for classical bulges and ellipticals (Kormendyetal.2009)."," The distribution function for the live classical bulge component was generated iteratively \citep{deb_sel_00} to ensure that both the disk and the classical bulge were initially in equilibrium, and we required that the bulge parameters are close to the fundamental plane for classical bulges and ellipticals \citep{kor_etal_09}."105. The setup of the disk is the same as in the disk-only model., The setup of the disk is the same as in the disk-only model.106 We show in Figure 4 that inclusion of a classical bulge — one widely thought to be typical of Sbc spiral galaxies like our own — greatly worsens the model fit to the data., We show in Figure 4 that inclusion of a classical bulge – one widely thought to be typical of Sbc spiral galaxies like our own – greatly worsens the model fit to the data.107 The degradation is especially obvious along the Galaxy's minor axis., The degradation is especially obvious along the Galaxy's minor axis.108 Including a classical bulge with just of the disk mass considerably worsens the fit of the model to the data., Including a classical bulge with just of the disk mass considerably worsens the fit of the model to the data.109 Our models rule out that the Milky Way has a significant classical bulge whose mass is >~ 15 of the disk mass., Our models rule out that the Milky Way has a significant classical bulge whose mass is $>\sim$ 15 of the disk mass.110" Could a smaller, merger-built bulge hide inside the boxy bar?"," Could a smaller, merger-built bulge hide inside the boxy bar?"111 The only result that we are aware of that might point to such a conclusion is the observed drop in stellar metal abundances with increasing height above the Galactic plane (Zoccalietal.2008;Zoccali201," The only result that we are aware of that might point to such a conclusion is the observed drop in stellar metal abundances with increasing height above the Galactic plane \citep{zoc_etal_08,zoccal_10}."1120).. Zoccalietal.(2008) argue that this means that the bulge must consist of both a classical and an edge-on bar component., \citet{zoc_etal_08} argue that this means that the bulge must consist of both a classical and an edge-on bar component.113" However, no kinematic gradient or transition corresponding to the abundance gradient is observed."," However, no kinematic gradient or transition corresponding to the abundance gradient is observed."114" Moreover, an abundance gradient can be produced within the context of secular pseudobulge formation if some of the vertical thickening is produced by resonant heating of stars that scatter off the bar (Pfenniger&Norman1990)."," Moreover, an abundance gradient can be produced within the context of secular pseudobulge formation if some of the vertical thickening is produced by resonant heating of stars that scatter off the bar \citep{pfe_nor_90}."115". If the most metal-poor stars are also the oldest stars, then they have been scattered for the longest time and now reach the greatest heights."," If the most metal-poor stars are also the oldest stars, then they have been scattered for the longest time and now reach the greatest heights."116 Our results have important for galaxy formation., Our results have important implications for galaxy formation.117 We demonstrate that the boxy implicationspseudobulge is not a separate component of the Galaxy but rather is an edge-on bar., We demonstrate that the boxy pseudobulge is not a separate component of the Galaxy but rather is an edge-on bar.118 Bars are parts of disks., Bars are parts of disks.119" To be sure, the stars in our Galactic bar are older than most disk stars."," To be sure, the stars in our Galactic bar are older than most disk stars."120" But those stars could have formed over a short period of time but long before the bar structure formed(Wyse1999;Freeman 2008),, their old age"," But those stars could have formed over a short period of time but long before the bar structure formed\citep{wyse_99,freema_08_IAU}, , their old age"121effect has been seeu in muuerical μαος where a cynically hotter center results when a bar dissolves (ποια Beng 1993: Hasan. Pteuniger Norman 1993) or weakeus (Athanassoula. Lambert Dehucu 2005).,"effect has been seen in numerical simulations where a dynamically hotter center results when a bar dissolves (Friedli Benz 1993; Hasan, Pfenniger Norman 1993) or weakens (Athanassoula, Lambert Dehnen 2005)."122 Iu this paper we investigate whether there is any observational evidence for this heating effect bv exanuning the correlation between the central velocity dispersion in bars aud the bar strength., In this paper we investigate whether there is any observational evidence for this heating effect by examining the correlation between the central velocity dispersion in bars and the bar strength.123 The σι values used in this paper are from published inteeralfield spectroscopy (IFS) observations of the unclear regious of galaxies., The $\sigma_{v}$ values used in this paper are from published integral-field spectroscopy (IFS) observations of the nuclear regions of galaxies.124 We have thirty oue galaxies in our sample (Table 1)., We have thirty one galaxies in our sample (Table 1).125" The majority of 6, values are from the SAURON survey of nearby. galaxies. (de Zeoewmw et al.", The majority of $\sigma_{v}$ values are from the SAURON survey of nearby galaxies (de Zeeuw et al.126 2002: Gauda ct al., 2002; Ganda et al.127 2006: Falcou-Darroso et al., 2006; Falcon-Barroso et al.128 2006: Peletier et al., 2006; Peletier et al.129 2007): a smaller number are from the INTEGRAL aud SPIRAL instruments ou the Willn IHerschel aud Anelo-Autralian Telescopes respectively (Batcheldor et al., 2007); a smaller number are from the INTEGRAL and SPIRAL instruments on the William Herschel and Anglo-Autralian Telescopes respectively (Batcheldor et al.130 2005)., 2005).131 The σι values for the remaining four galaxies are from observatious usiug the GAIOS instruneut at the Cemini North Telescope (Barbosa et al., The $\sigma_{v}$ values for the remaining four galaxies are from observations using the GMOS instrument at the Gemini North Telescope (Barbosa et al.132 2002)., 2002).133 The velocity dispersion values that we have used are derived frou two dimensional stellar velocity fields aud not gas kinematics., The velocity dispersion values that we have used are derived from two dimensional stellar velocity fields and not gas kinematics.134" One drawback of using these 6, values is that the aperture size is not unifori across the sample.", One drawback of using these $\sigma_{v}$ values is that the aperture size is not uniform across the sample.135 Heucewe have tried to bring the apertures to a common svsteni using the aperture correction formula of Jorseusen. Eaux Isjacreaard (1995).," Hence we have tried to bring the apertures to a common system using the aperture correction formula of Jorgensen, Franx Kjaergaard (1995)."136" The velocity dispersions were corrected to a radius R/S. where R, is the effective bulee radius of a galaxy."," The velocity dispersions were corrected to a radius $R_{e}/8$, where $R_{e}$ is the effective bulge radius of a galaxy."137 Thus σι was assumed equal to the average velocity dispersion witlin a radius RFs of the bulee of a galaxy., Thus $\sigma_{v}$ was assumed equal to the average velocity dispersion within a radius $R_{e}/8$ of the bulge of a galaxy.138 For five galaxies it was not possible to determine Z7. either because the bulee was not distinguishable or the tuaege quality was poor., For five galaxies it was not possible to determine $R_{e}$ either because the bulge was not distinguishable or the image quality was poor.139" Also. since the galaxies span a wide varicty of size and lass. we normalised the new aperture corrected velocity. cispersions (0,) with the III eas rotation velocity cy for cach galaxy."," Also, since the galaxies span a wide variety of size and mass, we normalised the new aperture corrected velocity dispersions $\sigma_{e}$ ) with the HI gas rotation velocity $v_{g}$ for each galaxy."140 Tus also takes out sole of the Iuninuositv/size effects for the galaxies., This also takes out some of the luminosity/size effects for the galaxies.141" The ce, values were derived from the iuaxiumuu Π1 rotation velocities (075) using the galaxy axes ratios (q) to correct for incliuatiou (i.e. ty=cyVi qo) ey was obtained from the Iperleda database.", The $v_{g}$ values were derived from the maximum HI rotation velocities $v_{H}$ ) using the galaxy axes ratios $q$ ) to correct for inclination (i.e. $v_{g}=v_{H}/\sqrt{1-q^{2}}$ ); $v_{H}$ was obtained from the Hyperleda database.142 The ratio σιοι is thus an indicator of how kinematically hot the center is for each galaxw relative to its disk rotation speed., The ratio $\sigma_{e}/v_{g}$ is thus an indicator of how kinematically hot the center is for each galaxy relative to its disk rotation speed.143 There are several wavs to quautify the streneth of a bar iu a galaxy., There are several ways to quantify the strength of a bar in a galaxy.144" In this paper we have derived the bar streneth in two wave: bar streueth is assumed to be the luaxinunu relative bar torque (Q,) derived from the eravitational potential of a galaxy.", In this paper we have derived the bar strength in two ways; bar strength is assumed to be the maximum relative bar torque $Q_g$ ) derived from the gravitational potential of a galaxy.145 This is probably the most robust estimate of bar strength but it is sensitive to the bulge mass or bhunuinositv., This is probably the most robust estimate of bar strength but it is sensitive to the bulge mass or luminosity.146 The secouc wav of estimating bar strength is to use the τακτά of the relative intensity amplitude of the bar in the uecar-IR image C15)., The second way of estimating bar strength is to use the maximum of the relative intensity amplitude of the bar in the near-IR image $A_2$ ).147 Both methods require that the images be deprojected before analysis., Both methods require that the images be deprojected before analysis.148" This assumes the disks are thin. but the presence of a less flattened bulec component could lead to artificial stretching of bulgex""p isophotes."," This assumes the disks are thin, but the presence of a less flattened bulge component could lead to artificial stretching of bulge isophotes."149" To minuuize this effect. we decomposed the »ilge from the disk. subtracted it from the image before deprojection. aud added it back (assuniug that bulec ight is spherically svaunietric) after deprojecting the disk/bar ποτ,"," To minimize this effect, we decomposed the bulge from the disk, subtracted it from the image before deprojection, and added it back (assuming that bulge light is spherically symmetric) after deprojecting the disk/bar light."150 The bulee components were separated roni the disks using a two-dimensional niulticoniponeut decomposition code which uses a Sersic mocel for the nlee. au exponential function for the disk. aud either Ferrers’ or Sersic’s fictions for the bar (Limikainen. Salo. and Buta 2005).," The bulge components were separated from the disks using a two-dimensional multicomponent decomposition code which uses a Sersic model for the bulge, an exponential function for the disk, and either Ferrers' or Sersic's functions for the bar (Laurikainen, Salo, and Buta 2005)."151 Effects of κοπο were taken into account. using the values of the full width at wf maxiuun stored i nuage headers or provided in articles.," Effects of seeing were taken into account, using the values of the full width at half maximum stored in image headers or provided in articles."152 The effective radius of the bulge (A) was estimated. by iutegratiug the flux of the fitted bulee uodel., The effective radius of the bulge $R_e$ ) was estimated by integrating the flux of the fitted bulge model.153 The images were obtained mainly frou the 2MASS survev and some frou previous studies., The images were obtained mainly from the 2MASS survey and some from previous studies.154 The fiters used were either IS or IT baud., The fiters used were either K or H band.155 The bar parameters were derived as follows., The bar parameters were derived as follows.156 The gravitational potentials (2) were inferred your near-IR helt distributious assunüug that the ight traces the mass., The gravitational potentials $\Phi$ ) were inferred from near-IR light distributions assuming that the light traces the mass.157 Bar induced taugeutial forces were calculated using a Polar method. as described iu Laurikainen Salo (2002) aud Lauriküneu. Salo Buta (2001).," Bar induced tangential forces were calculated using a Polar method, as described in Laurikainen Salo (2002) and Laurikainen, Salo Buta (2004)."158 In particular. the calculation applies au azimuthal Fourier decomposition of intensity. iuncludiug he even components up to m=20. which are then converted to the corresponding potential componcuts (Salo et al.," In particular, the calculation applies an azimuthal Fourier decomposition of intensity, including the even components up to m=20, which are then converted to the corresponding potential components (Salo et al."159 1999)., 1999).160 Two dimensional maps of the radial orce (Fy) aud taugeutial force (Fr) were calculated., Two dimensional maps of the radial force $F_R$ ) and tangential force $F_T$ ) were calculated.161 The radial profile of the maxima tanecutial force at cach distance is given by. where «|Fg(G0)|> denotes the azimuthally averaged axisviunietrie force at cach radius.," The radial profile of the maximum tangential force at each distance is given by, where $<|F_{R}(r,\phi)|>$ denotes the azimuthally averaged axisymmetric force at each radius."162 The maxim in the Qr profile at the region of the bar then, The maximum in the $Q_T$ profile at the region of the bar then163Still considering our caleulations. note that. using moclel 26 with 3e perturbations for LOMAL.. void regions with diameters of up to 62h.!Mpe (barvonie component) with density contrast Opp=0.756 could be produced.,"Still considering our calculations, note that, using model 26 with $3\sigma$ perturbations for $10^{15}{\rm M}_\odot$, void regions with diameters of up to $62 h^{-1}{\rm Mpc}$ (baryonic component) with density contrast $\delta_{\rm BF} = -0.756$ could be produced."164 In this case. the dark matter void would have a diameter of Dr=69h“Alpe (with opp=0.7 65).," In this case, the dark matter void would have a diameter of $D_{\rm165DF}=69 h^{-1}{\rm Mpc}$ (with $\delta_{\rm DF}= - 0.765$ )."166 Vhis result is roughly tha inferred to the diameter of the 3o0ttes. void., This result is roughly that inferred to the diameter of the Boöttes void.167 An interesting issue has to do with the fact tha the post-recombination Jeans mass ds ~10M. a recombination and it decreases later on. and that the niass scales studied here are in the range of 1077M... to 10715M...," An interesting issue has to do with the fact that the post-recombination Jeans mass is $\sim 10^6 {\rm M}_\odot$ at recombination and it decreases later on, and that the mass scales studied here are in the range of $10^{12}{\rm M}_\odot$ to $10^{15}{\rm M}_\odot$."168 WsThus. one could argue that collapse ancl eventua fragmentation should take place in the evolving (expanding) shells.," Thus, one could argue that collapse and eventual fragmentation should take place in the evolving (expanding) shells."169 To address this issue properly one should. study. in detail how density. perturbations evolve in the expanding shells., To address this issue properly one should study in detail how density perturbations evolve in the expanding shells.170 Note that it is not enough that a perturbation be Jeans unstable to guarantee that it will collapse and fragment., Note that it is not enough that a perturbation be Jeans unstable to guarantee that it will collapse and fragment.171 Consider the following example., Consider the following example.172 Let us think of the evolution of primorclial clouds after the recombination era (that is. the evolution of positive density perturbations).," Let us think of the evolution of primordial clouds after the recombination era (that is, the evolution of positive density perturbations)."173 Even the clouds that are already Jeans unstable at the recombination era will initially expand before collapsing., Even the clouds that are already Jeans unstable at the recombination era will initially expand before collapsing.174 For a cloud that. stops expanding. its mean density (ρο) relative to the background is given hy (see. ee. Peebles 1993: Coles Lucehin 1995) which corresponds to This result is a lower limit since it depends only on the expansion rate of the Universe (the above result. is taken for an Einstein-de Sitter universe) and on the gravity of the cloud.," For a cloud that stops expanding, its mean density $\bar \rho_{\rm c}$ ) relative to the background is given by (see, e.g., Peebles 1993; Coles Lucchin 1995) which corresponds to This result is a lower limit since it depends only on the expansion rate of the Universe (the above result is taken for an Einstein-de Sitter universe) and on the gravity of the cloud."175 For the cases in which other physical processes are relevant for the evolution of the cloud. the turnaround should occurr for In particular. we refer the reader to the papers by Oliveira et al. (," For the cases in which other physical processes are relevant for the evolution of the cloud, the turnaround should occurr for In particular, we refer the reader to the papers by Oliveira et al. ("1761998a.b) who studied the collapse of Population IL objects and consider such issues in detail.,"1998a,b) who studied the collapse of Population III objects and consider such issues in detail."177 Concerning the voic regions. their density contrast. is always negative and they never stop expanding.," Concerning the void regions, their density contrast is always negative and they never stop expanding."178 As a result he condition given by equation (35) is never fulfilled and so he evolving shels do no collapse., As a result the condition given by equation (35) is never fulfilled and so the evolving shells do not collapse.179 Density perurbations that could. be present in. the evolving shells. lOWOCVOLD. could in principle collapse and ragment if they jc the ime to stop expanding and evolve.," Density perturbations that could be present in the evolving shells, however, could in principle collapse and fragment if they had the time to stop expanding and evolve."180 ote that this issue concerning the collapse and eventual ragmentation in the evolving shells is by itself so interesting hat it deserves to be investigated. in. detail., Note that this issue concerning the collapse and eventual fragmentation in the evolving shells is by itself so interesting that it deserves to be investigated in detail.181 We leave.," We leave,"182 In order to make comparisons with observational data. and o explore the evolution of scaling relations over cosmological ime scales. we apply the new merger model to progenitor ooperties [rom two SAMs: the ? SAAT (hereafter. SOS) and a SAM. based on the Millennium Simulation (?)..," In order to make comparisons with observational data, and to explore the evolution of scaling relations over cosmological time scales, we apply the new merger model to progenitor properties from two SAMs: the \citet{S08} SAM (hereafter S08) and a SAM based on the Millennium Simulation \citep{Croton06}."183 We implement the merger model externally (icc... by post-oocessing) rather than incorporating it within each of he SAAIs.," We implement the merger model externally (i.e., by post-processing) rather than incorporating it within each of the SAMs."184 This provides an expedient means of exploring he properties of new elliptical galaxies arriving into the population via the merging ofcisk-dominated galaxies., This provides an expedient means of exploring the properties of new elliptical galaxies arriving into the population via the merging of disk-dominated galaxies.185 We restrict our analysis to mergers of disk galaxies because the current generation SAAIs do not have a reliable method for calculating bulge sizes. ancl we need stellar radii in order to calculate initial internal energies.," We restrict our analysis to mergers of disk galaxies because the current generation SAMs do not have a reliable method for calculating bulge sizes, and we need stellar radii in order to calculate initial internal energies."186 Furthermore. Consequently. we only analyze mergers in cach SAAL where both progenitors have a stellar clisk more massive than their bulge.," Furthermore, Consequently, we only analyze mergers in each SAM where both progenitors have a stellar disk more massive than their bulge."187 Acdcditionallv. since we are comparing the remnants to observations of elliptical galaxy populations. we only include major mergers with a mass ratio of 1:3 or greater. as these are the mergers expected to create elliptical galaxies.," Additionally, since we are comparing the remnants to observations of elliptical galaxy populations, we only include major mergers with a mass ratio of 1:3 or greater, as these are the mergers expected to create elliptical galaxies."188 Each SAAL directly provides the stellar mass. disk radius. and mass of cold gas for each progenitor.," Each SAM directly provides the stellar mass, disk radius, and mass of cold gas for each progenitor."189 In addition. the model requires information about the dark matter halo of cach progenitor galaxy.," In addition, the model requires information about the dark matter halo of each progenitor galaxy."190 Specifically. we need to be able to calculate mass as a function. of radius in order to caleulate both the halo half-mass radius and the central dark matter mass.," Specifically, we need to be able to calculate mass as a function of radius in order to calculate both the halo half-mass radius and the central dark matter mass."191 SOS and. Millennium provide the masses of the dark matter halos. but specify the halo mass distributions using cilferent quantities.," S08 and Millennium provide the masses of the dark matter halos, but specify the halo mass distributions using different quantities."192 SOS provides halo concentrations., S08 provides halo concentrations.193 The Millennium. SAAL provides μας and Yon. from which concentration can be caleulated.," The Millennium SAM provides $V_{\rm max}$ and $V_{\rm vir}$, from which concentration can be calculated."194 For both cases the concentration. virial mass. and redshift are used to calculate the distribution of mass within the halo.," For both cases the concentration, virial mass, and redshift are used to calculate the distribution of mass within the halo."195 For SOs the spherical top-hat collapse moclel is used to calculate the virial overdensity. using the approximation from ?.. whereas for Millennium the virial overdensity is assumed to be 200.," For S08 the spherical top-hat collapse model is used to calculate the virial overdensity, using the approximation from \citet{Bryan98}, whereas for Millennium the virial overdensity is assumed to be 200."196" Alb of these calculations assume the ACDAL concordance cosmology. with ,,=0.3. O4—0.7. and h=0.7."," All of these calculations assume the $\Lambda$ CDM concordance cosmology, with $\Omega_{\rm m}=0.3$, $\Omega_{\rm197 \Lambda}=0.7$, and $h=0.7$."198 ‘To gain a better intuitive grasp of the behavior of the merger nmiodel. we systematically explore the effects of variations in the progenitor properties and. mocdoel. parameters.," To gain a better intuitive grasp of the behavior of the merger model, we systematically explore the effects of variations in the progenitor properties and model parameters."199 For this study we introduce a series of four idealized: progenitor ealaxy models., For this study we introduce a series of four idealized progenitor galaxy models.200 In. order to isolate the cllects of various progenitor properties we begin with a fiducial progenitor aud scale the progenitor properties in such as way as to keep barvon fraction. average density. and halo concentration constant.," In order to isolate the effects of various progenitor properties we begin with a fiducial progenitor and scale the progenitor properties in such as way as to keep baryon fraction, average density, and halo concentration constant."201 The fiducial galaxy with which we begin our series is the G3 galaxy [rom. 7.. whose properties are designed to fit the average properties of observed. nearby. disk. galaxies in the Sloan Digital Sky Survey.," The fiducial galaxy with which we begin our series is the G3 galaxy from \citet{Cox08}, whose properties are designed to fit the average properties of observed nearby disk galaxies in the Sloan Digital Sky Survey."202 The G3 has a dark matter halo mass of 1.11072NI. a stellar mass of 5.0«101M... an initial half-mass racius of 3.8 kpe. and a halo concentration of 6.0.," The G3 has a dark matter halo mass of $1.1 \times 10^{12}203\msun$, a stellar mass of $5.0\times 10^{10} \msun$, an initial half-mass radius of 3.8 kpc, and a halo concentration of 6.0."204 Each subsequent. galaxy in the series is created by reducing the mass by 1/3. keeping the average densities. concentration. and barvon fraction Previous work has shown that eas can have a significant cllect on merger remnants (227772)...," Each subsequent galaxy in the series is created by reducing the mass by $1/3$, keeping the average densities, concentration, and baryon fraction Previous work has shown that gas can have a significant effect on merger remnants \citep{Barnes:1996a,RobertsonFP, Dekel06,Springel:2005c, Naabgas}."205 2 suggest. that a systematic variation in gas fraction with mass could be responsible for the tilt in the Fundamental plane of elliptical ealaxies. and ? demonstrate observational evidence for this hypothesis.," \citet{Dekel06} suggest that a systematic variation in gas fraction with mass could be responsible for the tilt in the fundamental plane of elliptical galaxies, and \citet{HopkinsFP} demonstrate observational evidence for this hypothesis."206 Phus. we examine the effect of progenitor gas fraction. defined here as the ratio of eas to stellar mass. on the properties of cqual-mass merger remnants.," Thus, we examine the effect of progenitor gas fraction, defined here as the ratio of gas to stellar mass, on the properties of equal-mass merger remnants."207 In our first experiment we set the gas mass of cach progenitor such that gas fraction is constant as a function of mass., In our first experiment we set the gas mass of each progenitor such that gas fraction is constant as a function of mass.208 We run the model for several gas fractions. setting the ratio of gas mass to stellar mass to 0.0. 0.25. 0.5. 1.0. and 2.0.," We run the model for several gas fractions, setting the ratio of gas mass to stellar mass to 0.0, 0.25, 0.5, 1.0, and 2.0."209 The size-tellar mass relation. stcllar-mass Faber-Jackson relation (EJ). and virial projection of the Fundamental plane (FP) of the merger remnants are shown in Figure 2(a)..," The size-stellar mass relation, stellar-mass Faber-Jackson relation (FJ), and virial projection of the fundamental plane (FP) of the merger remnants are shown in Figure \ref{fig:toyGasConst}."210 Several observations are worth noting about the size-mass relations plotted. in. Figure 2(a).., Several observations are worth noting about the size-mass relations plotted in Figure \ref{fig:toyGasConst}.211 First. for all gas fractions the remnant relations (crosses) are just. shifted horizontally and. vertically from. the progenitor relation (stars) without any significant rotation (Le. change of slope).," First, for all gas fractions the remnant relations (crosses) are just shifted horizontally and vertically from the progenitor relation (stars) without any significant rotation (i.e., change of slope)."212 Phat is. the vector between progenitor and remnant is constant for any given gas fraction.," That is, the vector between progenitor and remnant is constant for any given gas fraction."213 This means that Z2/f and Aat/Mausa are also constant for any particular gas fraction.," This means that $R_{\rm f}/R_{\rm i}$ and $M_{\rm214 star,f}/M_{\rm star,i}$ are also constant for any particular gas fraction."215 This is worth noting because the observed size-mass relations for disks and ellipticals are significantly rotated from one another with the relation for ellipticals being much steeper., This is worth noting because the observed size-mass relations for disks and ellipticals are significantly rotated from one another with the relation for ellipticals being much steeper.216 A realistic mechanism for the production of ellipticals must account for this steepening., A realistic mechanism for the production of ellipticals must account for this steepening.217 Remember that. the progenitors are constructed: so that they have a constant density. inside their. half-mass radius., Remember that the progenitors are constructed so that they have a constant density inside their half-mass radius.218 Thus one can quickly see from the plot that dry? mergers. with no gas. will produce remnants with densities less than their progenitors and sizes larger than their progenitors. whereas gas-rich mergers will produce remnants with densities higher than their progenitors.," Thus one can quickly see from the plot that `dry' mergers, with no gas, will produce remnants with densities less than their progenitors and sizes larger than their progenitors, whereas gas-rich mergers will produce remnants with densities higher than their progenitors."219 The sizes of the remnants of eas-rich mergers can be similar to or even smaller than the sizes of their progenitors., The sizes of the remnants of gas-rich mergers can be similar to or even smaller than the sizes of their progenitors.220 For this set of modelparameters. constant density evolution occurs at roughly a gas-to-stellar-mass ratio of 0.25. (light-blue CLOSSCS).," For this set of modelparameters, constant density evolution occurs at roughly a gas-to-stellar-mass ratio of 0.25 (light-blue crosses)."221 The stellar-mass EJ. plot. in the second panel of Figure 2(a). demonstrates a similar effect.," The stellar-mass FJ plot, in the second panel of Figure \ref{fig:toyGasConst}, demonstrates a similar effect."222 Progenitors are not shown because they have no values for e. however one can see that remnants of mergers with each eas fraction follow parallel lines.," Progenitors are not shown because they have no values for $\sigma$, however one can see that remnants of mergers with each gas fraction follow parallel lines."223 No rotation is introduced. between one. gas [raction series and the next., No rotation is introduced between one gas fraction series and the next.224 Lf elliptical. galaxies followed an exact virial relation. then one would expect that Maaxe BR.," If elliptical galaxies followed an exact virial relation, then one would expect that $M_{\rm star}\propto\sigma^2R$ ."225 Thus plotting these quantities. againstcach other gives us a ‘virial’, Thus plotting these quantities againsteach other gives us a `virial'226observed column densities.,observed column densities.227 Thev found that photodesorption can maintain a laver of water vapor above the midplane with a fractional abundance of ~ 3 x '., They found that photodesorption can maintain a layer of water vapor above the midplane with a fractional abundance of $\sim$ 3 $\times$ $^{-7}$.228 The average calculated value . ο ↜⋅ in their⋅ model was ~1.6 ⋅ x LO’? E7. and usingκ this. combinedκ with. the observed N(IIDO) they deduce Ο = 0.01 in DM Tan.," The average calculated value of $_2$ O) in their model was $\sim$ 1.6 $\times$ $^{15}$ $^{-2}$, and using this combined with the observed N(HDO) they deduce $_2$ O = 0.01 in DM Tau."229 We have previously investigated the effects of photodesorption on the chemistry ol disks (?) and found that it can retain high abundances of many molecules in a laver above the midplane. even in cold disks.," We have previously investigated the effects of photodesorption on the chemistry of disks \citep{wl00} and found that it can retain high abundances of many molecules in a layer above the midplane, even in cold disks."230 Ilere we revisit (he idea of photodesorption and investigate not only how it affects the abunelances but also how it impacts the deuteration of molecules (Models C and D) The rate of photodesorption is given by where Gy is the radiation field in units of the Habing field (105 photons 7s 1). Ay is the visual extinction and Y. is (he photodesorption vield.," Here we revisit the idea of photodesorption and investigate not only how it affects the abundances but also how it impacts the deuteration of molecules (Models C and D) The rate of photodesorption is given by where $G_0$ is the radiation field in units of the Habing field $^8$ photons $^{-2}$ $^{-1}$ ), $A_V$ is the visual extinction and $Y$ is the photodesorption yield."231 We use the temperature dependent value of Y! as determined experimentally by. τν From Figure 2 of ? YY = 0.003 molecules per photon at 7 « 50 Ix and rises to 0.075 al T= LOO kx. We include the effects of desorption caused by photons from the interstellar radiation lied. the stellar field and from the cosmic ray induced photon field (?)..," We use the temperature dependent value of $Y$ as determined experimentally by \citet{westley95}; From Figure 2 of \citeauthor{westley95} Y = 0.003 molecules per photon at $T$ $<$ 50 K and rises to 0.075 at $T$ = 100 K. We include the effects of desorption caused by photons from the interstellar radiation field, the stellar field and from the cosmic ray induced photon field \citep{pt83}."232 Previous models of deuterium chemistry in disks have ignored. grain. surface reactions and thereby have excluded a potentially very important contribution to the molecular D/1I ratios., Previous models of deuterium chemistry in disks have ignored grain surface reactions and thereby have excluded a potentially very important contribution to the molecular D/H ratios.233 The inclusion of erain chenmüsirv is problematic. as (he simplest wav is to use the rate equation method. but this gives very different surface abundances than (he more exact Monte Carlo model.," The inclusion of grain chemistry is problematic, as the simplest way is to use the rate equation method, but this gives very different surface abundances than the more exact Monte Carlo model."234 ?. found that using the ILatom sean rates of 2.. which are much lower than usually assumed. produces grain mantle abundances in better agreement wilh Monte Carlo models than the results from stanclarcl rate equation models.," \citet{caselli02}235 found that using the H–atom scan rates of \citet{katz99}, which are much lower than usually assumed, produces grain mantle abundances in better agreement with Monte Carlo models than the results from standard rate equation models."236 The work of Katz ETA hhas been disputed. bby ? who find (hat HH» forms very efficiently on erains. possibly by lIatoms tunneling through barriers on the graim surface.," The work of Katz ETA has been disputed, by \citet{horn03} who find that $_2$ forms very efficiently on grains, possibly by H–atoms tunneling through barriers on the grain surface."237 However. because of the advantage in going some wav to correcting (he short-comings of the rate equation method we use the ]Xatz wt ssean rates here. and assume that the scan rate lor Datoms is also slow.," However, because of the advantage in going some way to correcting the short-comings of the rate equation method we use the Katz wt scan rates here, and assume that the scan rate for D–atoms is also slow."238 We assume (hat reactions on grain surfaces can occur only if one of the reactants is an atom., We assume that reactions on grain surfaces can occur only if one of the reactants is an atom.239 All other species are assumed to be immobile., All other species are assumed to be immobile.240 The reaction set is taken from ? with the addition of the equivalent deuteration reactions., The reaction set is taken from \citet{hh93} with the addition of the equivalent deuteration reactions.241 Activation barriers for the deuterium, Activation barriers for the deuterium242For this study we chose to observe the open cluster NGC 6791.,For this study we chose to observe the open cluster NGC 6791.243 This cluster has been studied extensively for variability by the PISCES project (Mochejskaetal.2002.2005.. actcdlitioual variability surveys of this cluster iuclude those by Ixaluzny&Rucitiski1993.. Iuciáüski.Ixaluzuy. 1996.. Mochejska.Stanek.&Waluzny 2003.. and Brunttetal.2003)).," This cluster has been studied extensively for variability by the PISCES project \citealt{mochejs02,mochejs05}, additional variability surveys of this cluster include those by \citealt{kaluzny93}, , \citealt{rucinski96}, \citealt{mochejs03}, and \citealt{bruntt03}) )."244 As noted in 2005.. the cluster is populous (Ixaluzuy&Udalski1992).. old (7=8G yr). metal richpa ([Fe/HJ=+0.I). auc located at a distance modulus of Qu-M):=13.12 (Chaboyer.Green.&Liebert1999).," As noted in \citealt{mochejs05}, the cluster is populous \citep{kaluzny92}, old $\tau=8$ Gyr), metal rich $+0.4$ ), and located at a distance modulus of $_{V}=13.42$ \citep{chaboyer99}."245. We obtained 71 exposures centered on the cluster (a5)=(192205320.4-377163070) C12000.0) using a Sloan-r’ filter.," We obtained 71 exposures centered on the cluster $(\alpha,\delta)=(19^{\rm h}20^{\rm m}53\fs0,246+37\arcdeg46\arcmin30\farcs0)$ (J2000.0) using a $r^{\prime}$ filter."247 Of these exposures. 20 were obtained ou Oct. OL 206u with a two minute exposure time. L7 on Oct. 09. 2001 with a two minute exposure time. and 36 oun Oct. 20. 2001 with a oue iuinute exposure time.," Of these exposures, 20 were obtained on Oct. 04, 2004 with a two minute exposure time, 17 on Oct. 09, 2004 with a two minute exposure time, and 36 on Oct. 20, 2004 with a one minute exposure time."248 The data on the first two nights were obtained with a gain settine of 10e /ADU. alter notius the possibility of nonlinearity in pixels with more than 2x10? we switched to a gain of3.5 /ADU for the last night.," The data on the first two nights were obtained with a gain setting of 10 $^{-}$ /ADU, after noting the possibility of nonlinearity in pixels with more than $2\times 10^{5}$ $^{-}$ we switched to a gain of 3.5 $^{-}$ /ADU for the last night."249 In. both cases we were not limited by the A/D converter., In both cases we were not limited by the A/D converter.250" Allimages were read-out using 2x2 binning (yielding a pixel scale 0.16""). but this did not limit the uumber of electrous in the detector."," All images were read-out using 2x2 binning (yielding a pixel scale $0.16\arcsec$ ), but this did not limit the number of electrons in the detector."251 For relereuce. we present a Megacanm mosaic image of the field in Fig. 1," For reference, we present a Megacam mosaic image of the field in Fig. \ref{fov}."252 For the first night the seeing was highly variable. ranging from 1” to 37.," For the first night the seeing was highly variable, ranging from $1\arcsec$ to $3\arcsec$."253" On the second and hird nights the seeing was relatively stable. but not exceptional. aud ranged [rom 1"" to as high as 2"" in a handful of images."," On the second and third nights the seeing was relatively stable, but not exceptional, and ranged from $1\arcsec$ to as high as $2\arcsec$ in a handful of images."254 The poor conditions on the first night make the data unusable for oecision photometry using our reduction techuiques. though we include data from this uight. iu he Leht curves preseutec in 825.," The poor conditions on the first night make the data unusable for precision photometry using our reduction techniques, though we include data from this night in the light curves presented in 5."255 The preliminary CCD reductious. including overscan. zero level correction. aud flat-fieldiug were performed using the standard routines in the IRAF MSCREDpackage?.," The preliminary CCD reductions, including overscan, zero level correction, and flat-fielding were performed using the standard routines in the IRAF MSCRED."256. For each night we constructed a iuaster twilight [Iat-fiekl from 5. 19. and 5 individual twilight flat-Lielcl exposures. respectively.," For each night we constructed a master twilight flat-field from 5, 19, and 5 individual twilight flat-field exposures, respectively."257 Το obtain photometry we used the image subtraction methods due to Alard Lupton (1998: see also Alard 2000) as implemented in the ISIS2.1, To obtain photometry we used the image subtraction methods due to Alard Lupton (1998; see also Alard 2000) as implemented in the ISIS 2.1.258 The procedure we followed is similar tothat describec in e.g. Hartiuanetal.(2001): here we ouly highlight differences (rom the procedure discussed there., The procedure we followed is similar to that described in e.g. \citet{hartman04}; here we only highlight differences from the procedure discussed there.259 The basic scheme is to match the PSF auc background of a relereuce image to another image. subtract them. aud perforin photometry ou the subtracted image.," The basic scheme is to match the PSF and background of a reference image to another image, subtract them, and perform photometry on the subtracted image."260 The photometry routine that comes with the ISIS package convolves a PSF determiued empirically ou tlie reference nage with the convolution kernel used tomatch theimages. and then performs fixed-positiou. PSF," The photometry routine that comes with the ISIS package convolves a PSF determined empirically on the reference image with the convolution kernel used tomatch the images, and then performs fixed-position, PSF"261in publications ciring the first ten vears of CFHT to the increase in the reliability of both the instruments and tje. telescope aud to the development of more competitive instruments.,in publications during the first ten years of CFHT to the increase in the reliability of both the instruments and the telescope and to the development of more competitive instruments.262 There are wo possible reasous the uuumber of CFHT publications may be i a slow decline., There are two possible reasons the number of CFHT publications may be in a slow decline.263 First. as more 8-10 meter telescoyes cole Ou-line. CEHT is uo lounger a forefrout acility.," First, as more 8-10 meter telescopes come on-line, CFHT is no longer a forefront facility."264 Second. the use of large nosaic CCD cameras has increased al CFHT.," Second, the use of large mosaic CCD cameras has increased at CFHT."265 These generate a treimmendous amount of data. and he time [rom accusition of data to the publication of results has ikely increasect.," These generate a tremendous amount of data, and the time from acquisition of data to the publication of results has likely increased."266 Trimble (1995) studied he productivity of large. American optical telescopes including CEHT.," Trimble (1995) studied the productivity of large, American optical telescopes including CFHT."267 She compiled publication daa for an eighteen mouth period begiuniug January 1990. by examiine the major North American journals:Ap... ApJL.ApJS..AJ.. PASP.," She compiled publication data for an eighteen month period beginning January 1990, by examining the major North American journals:, ApJL, ."268. According to Trimble's ist. CFHT ranked fourth in procluctivity behiud the CTIO [-1ueter. Palomar axl tle IXPNO Lineer: amd. as Trinible notes. maty CFHT publications appear in journals uot inchded in her stily.," According to Trimble's list, CFHT ranked fourth in productivity behind the CTIO 4-meter, Palomar and the KPNO 4-meter; and, as Trimble notes, many CFHT publications appear in journals not included in her study."269 Taking all o| ihe 1990 papers and half of the 1991 papers. we count sixN-SeVren. CFHT papers (Timble couuted 28.6) tha were published in the major North Americauj wnals during this Je‘ioc. (," Taking all of the 1990 papers and half of the 1991 papers, we count sixty-seven CFHT papers (Trimble counted 58.6) that were published in the major North American journals during this period. ("270Triable |oo-rated each payer based upon the nuiuber of telescoyes 1sed iu the paper. which we bhave not do1e.),"Trimble pro-rated each paper based upon the number of telescopes used in the paper, which we have not done.)"271 Our database contaius oue huncdre oue CFHT yape* published italt ‘eltereed jot‘nals duri& this period., Our database contains one hundred one CFHT papers published in refereed journals during this period.272" [If we correct this uumber by the same aci«Y tha OUL ealier ""n""uber ciíTe‘'s from Trimble's for ouly Nortl American journals. we end iIp wihat otal of 88.3 yape""8s."," If we correct this number by the same factor that our earlier number differs from Trimble's for only North American journals, we end up with a total of 88.3 papers."273 The total uu1ο of CFHT publicaion chauged siguificantly by inchding publications roni all jouτας., The total number of CFHT publication changed significantly by including publications from all journals.274 Wlile the other teescopes uudoubtedly had| publicatious ihl Ho-North American journals. except. fy» lthe Anelo-Australian Telescope. their numbers would 101 lave increaseLas sienicantly.," While the other telescopes undoubtedly had publications in non-North American journals, except for the Anglo-Australian Telescope, their numbers would not have increased as significantly."275 Thus. auy1N future study of papers and citations. especially those hat compare different aciliies. should inchde all major journals.," Thus, any future study of papers and citations, especially those that compare different facilities, should include all major journals."276 The average CPP fo “all papers in a given vear. by vear oL ptblicatiou. is shown in Figure 5.," The average CPP for all papers in a given year, by year of publication, is shown in Figure 5."277 Oue woucl expect the average CPP to grow smoothly. with lune since publication., One would expect the average CPP to grow smoothly with time since publication.278 However. due to the relatively sinall nuiyer of papers ini alw given year. the average CPP can be influenced by a small uuuber of highly cited papers.," However, due to the relatively small number of papers in any given year, the average CPP can be influenced by a small number of highly cited papers."279 For exaiple. the bump in 1996 is due to two highly cited papers (Lilly et al.," For example, the bump in 1996 is due to two highly cited papers (Lilly et al."280 1996. Carlvere et al.," 1996, Carlberg et al."281 1996) hat are based on data taken with ÀLOS. the Multi-Object Spectrograph.," 1996) that are based on data taken with MOS, the Multi-Object Spectrograph."282 The flictuations in citaion numbers are uuch higher in earlier vears when the number of papers was smaller., The fluctuations in citation numbers are much higher in earlier years when the number of papers was smaller.283 Most CEHT «observers are from Catada. Frauce or the Uuiversity of Hawaii (UH).," Most CFHT observers are from Canada, France or the University of Hawaii (UH)."284 The French tend to publish in European journals. nainlyΔΑ... while Canadian and UH researchers favor North American journals.," The French tend to publish in European journals, mainly, while Canadian and UH researchers favor North American journals."285 How are CFHT publications distributed across the major journals?, How are CFHT publications distributed across the major journals?286 The cistributiou of pullications across eight jouruals (we include ApJL with ApJ)) is shown on the left side of Table 1., The distribution of publications across eight journals (we include ApJL with ) is shown on the left side of Table 1.287 Iu addition. each paper las been tageedMD as belouging to one of the three partuers based upon the affiliation of the first author or the ageuey that granted time for the observatious. (," In addition, each paper has been tagged as belonging to one of the three partners based upon the affiliation of the first author or the agency that granted time for the observations. ("288Canada grants some time to International researchers).,Canada grants some time to international researchers).289 The majority of CFHT papers have been published in the three major journals -A," The majority of CFHT papers have been published in the three major journals -,"290 The majority of CFHT papers have been published in the three major journals -Ap," The majority of CFHT papers have been published in the three major journals -,"291 The majority of CFHT papers have been published in the three major journals -ApJ," The majority of CFHT papers have been published in the three major journals -,"292 The majority of CFHT papers have been published in the three major journals -ApJ.," The majority of CFHT papers have been published in the three major journals -,"293 The majority of CFHT papers have been published in the three major journals -ApJ..," The majority of CFHT papers have been published in the three major journals -,"294perturbation theory was used for this purpose: where D is the linear erowth factor (?)..,perturbation theory was used for this purpose: where $D$ is the linear growth factor \citep{pjep}.295 As we show below. ignoring higher order terms in the above expression iutroduces a systematic error of order of 10 to.," As we show below, ignoring higher order terms in the above expression introduces a systematic error of order of 10 to."296. With the latest improvements iu the quality of observations. such efects should uot be neglected aud we provide a simple recipe how to take them iuto account.," With the latest improvements in the quality of observations, such efects should not be neglected and we provide a simple recipe how to take them into account."297" We focus on the comparison of oy, estimated from the peculiar velocity field at an effective redshift +=0. to ays inplied by the CAIB (effective redshift + 1100)."," We focus on the comparison of $\sigma_8$ estimated from the peculiar velocity field at an effective redshift $z=0$, to 8 implied by the CMB (effective redshift $z \approx 1100$ )."298" Relative motions of pais of galaxies (2) as well as bulk flows (27). and velocityshear (27) lmucasurements have been used to estimate σς aud Q,,. the deusitv of the nonrelativistic matter."," Relative motions of pairs of galaxies \citep{pairwise} as well as bulk flows \citep{pikhud05,sarfelwat07} and velocityshear \citep{watfel07,felwat08} measurements have been used to estimate $\sigma_8$ and $\Omega_m$, the density of the nonrelativistic matter."299" Iu particular. frou pairwise velocities we fouud in ? From CMD temperature fiuctuatious. the WALAP collaboration (7) fouud deseribed as the ""linear theory. amplitude” (see their Table 1)."," In particular, from pairwise velocities we found in \citet{pairwise} From CMB temperature fluctuations, the WMAP collaboration \citep{WMAP5} found described as the “linear theory amplitude” (see their Table 1)."300 The above two estimates differ oulv slightly. at the level of 15-0. aud it is a success of the model that inferences by such differcut methods applied at two ereatlv different epochs are in good agreement.," The above two estimates differ only slightly, at the level of $\sigma$, and it is a success of the model that inferences by such different methods applied at two greatly different epochs are in good agreement."301 Iun this paper we bring the two estinates even closer by taking nonlinear clvnamics iuto account., In this paper we bring the two estimates even closer by taking nonlinear dynamics into account.302 We find that the nonlinear correction is uodestly siguificaut. given the inproviug accuracy in cosinoloev: the linear value of ex. hereafter denoted σε. can be simaller by ~105€ than the ronlinear value. a systematic difference that is comparable to the current statistical uncertainties.," We find that the nonlinear correction is modestly significant, given the improving accuracy in cosmology: the linear value of $\sigma_8$, hereafter denoted $\sigma_L$, can be smaller by $\sim10$ than the nonlinear value, a systematic difference that is comparable to the current statistical uncertainties."303 Iu section 2. we describe the spatial window πο[Ίος used to define oy8., In section \ref{sec:window} we describe the spatial window functions used to define 8.304 In section 3. we oxovide the recipe for recovering σι from σ.," In section \ref{sec:linear_and_nonlinear_amplitudes}305 we provide the recipe for recovering $\sigma_L$ from $\sigma$."306 Iu section L we compare our revised σκδ paranietors o other observational estimates of aa., In section \ref{sec:discussion} we compare our revised 8 parameters to other observational estimates of 8.307 We sunnuaurze our results iu section 5.., We summarize our results in section \ref{sec:conc}.308" Like many cosinological[m] experiments, nieasurements of cosmic flows are sensitive to awindowed iuteeral of the matter power spectrum."," Like many cosmological experiments, measurements of cosmic flows are sensitive to awindowed integral of the matter power spectrum."309" Iu general. such an observable can be characterized as where P,(&) gives the primordial power spectra. kis the comoving wavemunber. T?(k) gives the transfer function which contains the plwvsics of the evolution of the particular observable from the primordial spectrum."," In general, such an observable can be characterized as where $P_p(k)$ gives the primordial power spectrum, $k$ is the comoving wavenumber, $T_i^2(k)$ gives the transfer function which contains the physics of the evolution of the particular observable from the primordial spectrum."310 The window function. (4). describes theexperimental setup (sky coverage. depth. errors etc.}.," The window function, $W(k)$, describes theexperimental setup (sky coverage, depth, errors etc.)."311 This formali describes straightforward measurements of the galaxy power spectrum m which case Q;=Pa(;). the CAIB spectrum for which Q;=ον aud the amplitucle of 16 cosinological velocity field where Q;=οκ). je velocity power spectrum.," This formalism describes straightforward measurements of the galaxy power spectrum, in which case $Q_i=P_{\rm gal} (k_i)$, the CMB spectrum for which $Q_i = C_{\ell_i}$, and the amplitude of the cosmological velocity field where $Q_i=P_{v} (k_i)$, the velocity power spectrum."312 It is crucial to note iat the trauster function depends implicitly upo- i6 other cosmological parameters and hence any lack of knowledee thereof will (or at leas+ should) trauslate to iucreased uucertaiuty ipo- 1e amplitude., It is crucial to note that the transfer function depends implicitly upon the other cosmological parameters and hence any lack of knowledge thereof will (or at least should) translate to increased uncertainty upon the amplitude.313" Bulk flow and shear measure the velocitv- power spectrum jor covariance, ο). whereas pairwise velocities measure the deusitv-velocity cross-spectrui (7).."," Bulk flow and shear measure the velocity-velocity power spectrum [or covariance, \cite{WatFelHud09,FelWatHud09}] ], whereas pairwise velocities measure the density-velocity cross-spectrum \citep{pairwise}."314 Uuder evolution. the density contrast is proportional to the divergeuce of the peculiar velocity in real space. or vxkp in Fourier space. so these power spectra differ bv powers of wavenunber & frou the deusity power spectrum. which can be absorbed into the appropriate trausfer function.," Under evolution, the density contrast is proportional to the divergence of the peculiar velocity in real space, or $\mathbf{v}\propto\mathbf{k}\rho$ in Fourier space, so these power spectra differ by powers of wavenumber $k$ from the density power spectrum, which can be absorbed into the appropriate transfer function."315 Au amplitude parameter such as oy is n essence a spectral observable as well., An amplitude parameter such as $\sigma_8$ is in essence a spectral observable as well.316 We define the Wa(x.x’)=Ἠμιx’). normalized so that fPeμα= d ," We define the $W_R(\mathbf{x}, \mathbf{x'})=W_R(\mathbf{x-x'})$, normalized so that $\int d^3x \; W_R(x) = 1$ ."317For our spherical top hat. Wri)=L/V where V= IxR/3. when r= Π 0 otherwise.," For our spherical top hat, $W_R(r) = 1/V$ where $V = 4\pi R^3/3$ , when $r=|\mathbf{x'-x}|\le R$ , 0 otherwise."318 Hence. the density contrast. spatially averaged over a sphere around a particular point x is simply The eusenible avarage of ορ at redshift + is eiven bv," Hence, the density contrast, spatially averaged over a sphere around a particular point $\mathbf{x}$ is simply The ensemble avarage of $\delta_R^2$ at redshift $z$ is given by"319is certainly allected by incompleteness aud blending.,is certainly affected by incompleteness and blending.320 Iu order to quantify these factors as a function of ruagnitude. we have performed a series of artificial stars experiments. following the procedure brielly described here.," In order to quantify these factors as a function of magnitude, we have performed a series of artificial stars experiments, following the procedure briefly described here."321 Artificial star experiments have to probe the observational effects associated with the whole srocess of data reduction of a given frame. Le.. for instance. the accuracy of the photometric ueasures. the crowding conditions. the ability of the PSE-fittiug code iu estimating the sky level or in resolving partially overlapped sources. etc.," Artificial star experiments have to probe the observational effects associated with the whole process of data reduction of a given frame, i.e., for instance, the accuracy of the photometric measures, the crowding conditions, the ability of the PSF-fitting code in estimating the sky level or in resolving partially overlapped sources, etc."322 It is of the utmost inportauce that the artificial stars do not interfere with each other since in that case the output of the experiments would be biased ywartificial crowding. not present in the original frame.," It is of the utmost importance that the artificial stars do not interfere with each other since in that case the output of the experiments would be biased by crowding, not present in the original frame."323 To avoid this poteutially serious bias we ave divided the frames in grids of cells of known width. aud we have randomly. positioned.cell at each run (a similar procedure has recently been adopted by Piotto Zoccali 1999).," To avoid this potentially serious bias we have divided the frames in grids of cells of known width, and we have randomly positioned at each run (a similar procedure has recently been adopted by Piotto Zoccali 1999)."324 The additional constr:int is that each star must have a distance from the cell edges sulliciently large to guarantee that all its flux aud background measuriug regious fall within the cell., The additional constraint is that each star must have a distance from the cell edges sufficiently large to guarantee that all its flux and background measuring regions fall within the cell.325 lu this way we can control the minimum cdistauce between adjacent stars., In this way we can control the minimum distance between adjacent stars.326 At each run the absolute position of the grid is raudomly chauged iu à way that. after a large number of experiments. the W.ars are uniformly. distributed in coordinates.," At each run the absolute position of the grid is randomly changed in a way that, after a large number of experiments, the stars are uniformly distributed in coordinates."327 The stars were distributed in maguitudee with a function similar to the observed. luminosity uuctiou (LE). except for an excess of [aint stars below the detection limit of our observations.," The stars were distributed in magnitude with a function similar to the observed luminosity function (LF), except for an excess of faint stars below the detection limit of our observations."328 This was to probe with sufficieut statistics the (faint) range of magnitudes where the incompleteness is expected to be most severe., This was to probe with sufficient statistics the (faint) range of magnitudes where the incompleteness is expected to be most severe.329" We have simulated about LO? stars for each. WEPC2 camera and ilter. and about 2x10"" for each NIC2 image."," We have simulated about $10^5$ stars for each WFPC2 camera and filter, and about $2\,\times\,10^5$ for each NIC2 image."330 The whole series of perforimed experiments provides 1.2x10* artificial stars. for which we have memorized input and output magnitudes. aud any other iseful parameter.," The whole series of performed experiments provides $1.2\,\times\,10^6$ artificial stars, for which we have memorized input and output magnitudes, and any other useful parameter."331 Stars with input-output magnitude Am>0.75 were cousidered because such a difference lmplies that they fell on a real star of their saine luminosity or brighter., Stars with input–output magnitude $\Delta m > 0.75$ were considered because such a difference implies that they fell on a real star of their same luminosity or brighter.332 The artificial stars have been projected outo the same reference [raiue of Fig., The artificial stars have been projected onto the same reference frame of Fig.333 LL and separated in the corresponding radial regions (six aunuli for the F555W aud. FESLIW filters. aud three [or the FLIOW and FI60W filters) to allow the characterization of incompleteness aud bleucdiug iu the different regious of the images.," \ref{mosaico_bw} and separated in the corresponding radial regions (six annuli for the F555W and F814W filters, and three for the F110W and F160W filters) to allow the characterization of incompleteness and blending in the different regions of the images."334 The frames have been re-reduced following exactly the same ⋅ ↥↽∐⋅∩∢∙≺↵⋔⊔⋅↩⋜↕⊳∖↥∩↥⋅↕⇂≺↵↥⋅≺↵⋜↕↥⊳∖↕⋜⋃⋅⊳∖⋅⋜↕∐≺⊔∐≺↵⊳∖⋜⋃∐≺↵⊳∖↩↥≺↵∢∙⋃∩∐∢∙↕⋅∐≺↵↥⋅⋜↕↥∩↕⋅∖−⋜↕∐≺⇂⊽↦⋅∕∣↙∣∣⋅∣↗∣∣∤⊽↦⋅⇁↦⋅⋖⋝↠∖≺↲≺↲⊱≺↲∢∙⋃∪∐⊳∖ ⋅ ⋅ ⋅ ⋅↽≻ ∣ ↿⋅ 2.1 aud 2.2) have been applied.," The frames have been re-reduced following exactly the same procedure as for the real stars, and the same selection criteria for $\chi^2$ and (see Sections 2.1 and 2.2) have been applied."335 Fie., Fig.336e 19 aud Fie., \ref{dm_v} and Fig.337e 20 show the input-output magnitudee of the artificial stars resultinge from our tests., \ref{dm_i} show the input–output magnitude of the artificial stars resulting from our tests.338 Aun πο are plotted as a function of and nmigwiiw-- respectively. for each Region from 0 to 7.," $\Delta$ and $\Delta$ are plotted as a function of and , respectively, for each Region from 0 to 7."339 Fig., Fig.340 21. shows imsteack «Αμ and «μι as a Dunction of the input and for the three inner Reeious., \ref{dm_jh} shows instead $\Delta$ and $\Delta$ as a function of the input and for the three inner Regions.341" The solid lines superimposed to the plotted. distributious report the mean Am (ceutral lines) aud the z1o,, arouud the mean.", The solid lines superimposed to the plotted distributions report the mean $\Delta m $ (central lines) and the $\pm 1 \sigma_m$ around the mean.342 The, The343in the CNOC2 galaxy catalogs.,in the CNOC2 galaxy catalogs.344" The luminosities were not corrected for evolution, but were k-corrected."," The luminosities were not corrected for evolution, but were k-corrected."345 The mass-to-light ratio of the galaxy groups as a function of radius is plotted in Figure 2., The mass-to-light ratio of the galaxy groups as a function of radius is plotted in Figure 2.346" We obtain an integrated mass-to-light ratio to 1.0 h! Mpc of 185+28hMo/Lgo, consistent with the value of 191+81hMo/Lae found by Hoekstra et al. ("," We obtain an integrated mass-to-light ratio to 1.0 $^{-1}$ Mpc of $185\pm28 h$ $_\odot$ $_{B\odot}$, consistent with the value of $191\pm81 h$ $_\odot$ $_{B\odot}$ found by Hoekstra et al. ("3472001) using a subset of the groups.,2001) using a subset of the groups.348 The method employed by Hoekstra et al., The method employed by Hoekstra et al.349 was slightly different in that the mass-to-light ratio was estimated by calculating the ratio between the measured shear signal and the expected shear derived from the luminosity profile., was slightly different in that the mass-to-light ratio was estimated by calculating the ratio between the measured shear signal and the expected shear derived from the luminosity profile.350 This method requires the assumption that the mass-to-light ratio is constant across the groups and was necessary because of the smaller data set and low signal-to-noise ratio., This method requires the assumption that the mass-to-light ratio is constant across the groups and was necessary because of the smaller data set and low signal-to-noise ratio.351" As is clear in Figure 2, the M/L is remarkably flat as a function of distance from the group center."," As is clear in Figure 2, the $M/L$ is remarkably flat as a function of distance from the group center."352" This is in contrast to what was found by the dynamical study of the CNOC2 groups, as will be discussed in Section 4."," This is in contrast to what was found by the dynamical study of the CNOC2 groups, as will be discussed in Section 4."353 If the M/L is calculated using the NFW mass profile the results are statistically equivalent., If the M/L is calculated using the NFW mass profile the results are statistically equivalent.354" It is important to note that the tangential shear signal is sensitive to all matter along the line-of-sight, and as the distance from the group center increases more of the signal is coming from other mass that is correlated with the group (like a 2-halo term in a cross-correlation function)."," It is important to note that the tangential shear signal is sensitive to all matter along the line-of-sight, and as the distance from the group center increases more of the signal is coming from other mass that is correlated with the group (like a 2-halo term in a cross-correlation function)."355" In addition to calculating the M/L of of the galaxy groups using the known group members from the CNOC2 groups catalog, we also calculated the M/L for all galaxies in the CNOC2 galaxy catalog projected to be within a small distance of the group center (1200 km s! along the "," In addition to calculating the M/L of of the galaxy groups using the known group members from the CNOC2 groups catalog, we also calculated the M/L for all galaxies in the CNOC2 galaxy catalog projected to be within a small distance of the group center (1200 km $^{-1}$ along the line-of-sight)."356The mass model does not change but the luminosity line-of-sight).profile is altered by including more galaxies., The mass model does not change but the luminosity profile is altered by including more galaxies.357" The total M/L is lower by8%,, which is within the lo errors, and is still flat with distance from the group center."," The total M/L is lower by, which is within the $\sigma$ errors, and is still flat with distance from the group center."358" Assuming a constant M/L with distance from the group center, the best fit M/L using this larger sample of galaxies can be observed as the heavy dashed line in Figure 2."," Assuming a constant M/L with distance from the group center, the best fit M/L using this larger sample of galaxies can be observed as the heavy dashed line in Figure 2."359" We wanted to examine the difference in the shear signal from the rich and poor groups, and to this end we divided the galaxy group catalog into two subsamples."," We wanted to examine the difference in the shear signal from the rich and poor groups, and to this end we divided the galaxy group catalog into two subsamples."360" We split the sample by the median dynamical velocity dispersion (190 km s~+), although results were similar regardless of whether the groups were divided by their luminosities or velocity dispersions."," We split the sample by the median dynamical velocity dispersion (190 km $^{-1}$ ), although results were similar regardless of whether the groups were divided by their luminosities or velocity dispersions."361 The same source catalog was used to study the two group subsets., The same source catalog was used to study the two group subsets.362 The only difference from the technique outlined in the sections above is that the input group catalogs have half the number of groups., The only difference from the technique outlined in the sections above is that the input group catalogs have half the number of groups.363 The resulting tangential and cross shear for the two group subsets are shown in Figure 3., The resulting tangential and cross shear for the two group subsets are shown in Figure 3.364 'The results clearly indicate that the lensing signal is dominated by the larger groups., The results clearly indicate that the lensing signal is dominated by the larger groups.365 A few of the galaxy groups identified in the CNOC2 fields had measured velocity dispersions in excess of 500 km s-!., A few of the galaxy groups identified in the CNOC2 fields had measured velocity dispersions in excess of 500 km $^{-1}$.366 To be certain that the tangential shear signal measured was not coming solely from these groups we measured the tangential shear around only those groups with velocity dispersions greater than 500 km s-!., To be certain that the tangential shear signal measured was not coming solely from these groups we measured the tangential shear around only those groups with velocity dispersions greater than 500 km $^{-1}$.367" In addition, we also repeated the measurement of the tangential shear around all galaxies except those with velocity dispersions greater than 500 km s~!."," In addition, we also repeated the measurement of the tangential shear around all galaxies except those with velocity dispersions greater than 500 km $^{-1}$."368 The results indicated that there is à substantial signal coming from the most massive galaxy groups (small clusters) but that the tangential shear profile is not dominated by these for the sample as a whole., The results indicated that there is a substantial signal coming from the most massive galaxy groups (small clusters) but that the tangential shear profile is not dominated by these for the sample as a whole.369" After the massive groups are removed an isothermal tangential shear profile with an Einstein radius of roughly 0.8"" remains.", After the massive groups are removed an isothermal tangential shear profile with an Einstein radius of roughly $''$ remains.370 'The shear profiles for the two subsamples were fit with isothermal spheres and their mass-to-light ratios were estimated., The shear profiles for the two subsamples were fit with isothermal spheres and their mass-to-light ratios were estimated.371" The mean velocity dispersion of the “poor” groups is <o? >!/2=193+38 km s7!, while the “rich” groups have a velocity dispersion of «o? »1/2—2704-39 km s-!."," The mean velocity dispersion of the “poor” groups is $<\sigma^{2}>^{1/2}=$ $\pm$ 38 km $^{-1}$, while the “rich” groups have a velocity dispersion of $<\sigma^{2}>^{1/2}=$ $\pm$ 39 km $^{-1}$."372" The mass-to-light ratios of the “rich” and “poor” galaxy groups are flat with radius, as can be seen in Figure 4."," The mass-to-light ratios of the “rich” and “poor” galaxy groups are flat with radius, as can be seen in Figure 4."373" The weighted mean mass-to-light ratio of the “poor” groups is 134+26 hMo/Lgo, while the mass-to-light ratio of the “rich” groups is 278-42 hMo/Lngo."," The weighted mean mass-to-light ratio of the “poor” groups is $\pm$ 26 $_{\odot}$ $_{B\odot}$, while the mass-to-light ratio of the “rich” groups is $\pm$ 42 $_{\odot}$ $_{B\odot}$."374" Once again, the were also calculating using a catalog of galaxies M/Lsprojected to be close to the group center and the best fit results are shown with the heavy"," Once again, the M/Ls were also calculating using a catalog of galaxies projected to be close to the group center and the best fit results are shown with the heavy"375the characteristics of the stars that are not being observed are provided [ον prospective Guest Observers.,the characteristics of the stars that are not being observed are provided for prospective Guest Observers.376 Funding for this Discovery mission is provided bv NASA's Science Mission Directorate., Funding for this Discovery mission is provided by NASA's Science Mission Directorate.377asviuuetnes observed in Figure 3. however. it is difficult to wnderstand why such racial dust lanes have not Όσοι cdestroved by rotation.,"asymmetries observed in Figure 3, however, it is difficult to understand why such radial dust lanes have not been destroyed by rotation."378 The second possible explanation for the dark lanes is that they are shadows cast from a partially obscured ACN., The second possible explanation for the dark lanes is that they are shadows cast from a partially obscured AGN.379 Such a possibility would require that the ACN be visible along lines ofsight that lie within the plane of the sky. but also require that certain lines of sight toward the ACN in he plane of the sky are blocked. perhaps by the presence of molecular clouds.," Such a possibility would require that the AGN be visible along lines of sight that lie within the plane of the sky, but also require that certain lines of sight toward the AGN in the plane of the sky are blocked, perhaps by the presence of molecular clouds."380 These two possibilities can be tested., These two possibilities can be tested.381 First. if AGN ight is visible along lines of sights within the plane of the sky then near-infrared. low surface-brightuess ight surrounding the inner nucleus should be polarized.," First, if AGN light is visible along lines of sights within the plane of the sky, then near-infrared, low surface-brightness light surrounding the inner nucleus should be polarized."382 Second. if the dark lanes are nuclear dust lanes. (οι» ) observations of NGC Llls should reveal evidence of molecular gas coindeut with the lanes.," Second, if the dark lanes are nuclear dust lanes, $1\to0$ ) observations of NGC 4418 should reveal evidence of molecular gas coindent with the lanes."383 Such CO observations would be useful in them own right as a confirmation of the high extinction to the nucleus calculated via the silicate absorption feature., Such CO observations would be useful in their own right as a confirmation of the high extinction to the nucleus calculated via the silicate absorption feature.384 Given the new data presented in this paper and colpiled from the literature. NGC 1118 appears to be a ealaxy with nuclear power source(s) which has(have) beeu trigecred via interactions with a companion galaxy 21 kpe away.," Given the new data presented in this paper and compiled from the literature, NGC 4418 appears to be a galaxy with nuclear power source(s) which has(have) been triggered via interactions with a companion galaxy 24 kpc away."385 The ealaxy NCC 1118 has the following ucar- to nuid-intrared properties: A compact. ucar-infrared nucleus cousisting of a 100200 pe hiel-surface brightuess linear feature surrounded by radial extensions. and ucar-infrared colors consisteut with moderately extinenished supergiaut stellar helt. No nuclear star clusters at near-infrared waveleugthls. which are conuuonlv seen in starburst ufrared galaxies. and uo Ms commonlyseen i AGN. brightfF poiut-like unele ultralunünunous infrared galaxies aud cool ultraluuiuous infrared galaxies such as Arp 220 and UCC 5101. Eanission of most of its mid to far-infrared light from a region <SO pe across. A deep silicate absorption feature. which translates iuto ο50 mag of visual extinction to the central cucrey source(s) (see also Roche et al.," The galaxy NGC 4418 has the following near- to mid-infrared properties: A compact, near-infrared nucleus consisting of a 100--200 pc high-surface brightness linear feature surrounded by radial extensions, and near-infrared colors consistent with moderately extinguished supergiant stellar light, No nuclear star clusters at near-infrared wavelengths, which are commonly seen in starburst infrared galaxies, and no bright point-like nucleus commonly seen in AGN, An infrared surface brightness comparable to warm ultraluminous infrared galaxies and cool ultraluminous infrared galaxies such as Arp 220 and UGC 5101, Emission of most of its mid to far-infrared light from a region $\lesssim 80$ pc across, A deep silicate absorption feature, which translates into $>50$ mag of visual extinction to the central energy source(s) (see also Roche et al."386 1986: Dudley Williams 1997: Spoon et al., 1986; Dudley Wynn-Williams 1997; Spoon et al.387 2001). No evidence of strong PAIL features. which are conunon to mildly extinguished starburst galaxies like M 82 (Cenzel et al.," 2001), No evidence of strong PAH features, which are common to mildly extinguished starburst galaxies like M 82 (Genzel et al."388 1998: Spoon et al., 1998; Spoon et al.389 2001). and Wari infrared colors (foss/foges=00.23) consistent with those observedo for infrared galaxies with Sevtert-like emission line spectra.," 2001), and Warm infrared colors $f_{25\mu m} / f_{60\mu m} = 0.23$ ) consistent with those observed for infrared galaxies with Seyfert-like emission line spectra."390 The basic picture of NGC LLLS is one in which a stellar core/disk approximately 150 pc in extent surrounds au imbedded ACN or a cou starburst., The basic picture of NGC 4418 is one in which a stellar core/disk approximately 150 pc in extent surrounds an imbedded AGN or a compact starburst.391 So deeply buried is the central cueie(s)nethe. that even probing the galaxy at near-infrared wavele where extinction is 510 mae rather than 50100 mag at optical wavelength. provides little information about the primary energy source idu NGC Libs.," So deeply buried is the central engine(s) that even probing the galaxy at near-infrared wavelengths, where extinction is 5–10 mag rather than 50–100 mag at optical wavelength, provides little information about the primary energy source in NGC 4418."392 Observatious at longer wavelengths. using iustrunents such as MIRLIN. Satellite InfraRed Telescope Facility (SIRTF). and the Stratospheric Observatory For Tnfrared Astronomy (SOFIA). will be required to determine the fundamental nature of this galaxy. class.," Observations at longer wavelengths, using instruments such as MIRLIN, Satellite InfraRed Telescope Facility (SIRTF), and the Stratospheric Observatory For Infrared Astronomy (SOFIA), will be required to determine the fundamental nature of this galaxy class."393 We thank D. Stobie. J. Mazzarella. D. Dale. A. Sargent. and L. Armus for useful discussions and assistance. aud the anonviuous referee for a careful reading of the manuscript.," We thank B. Stobie, J. Mazzarella, D. Dale, A. Sargent, and L. Armus for useful discussions and assistance, and the anonymous referee for a careful reading of the manuscript."394 ASE also thanks II. Spoon for providing ISO-PIIT-S data for inclusion in Figure lL., ASE also thanks H. Spoon for providing ISO-PHT-S data for inclusion in Figure 4.395 ASE and NZS were supported by NASA eraut NAC 5-3012., ASE and NZS were supported by NASA grant NAG 5-3042.396 ASE was also supported by NSF eraut AST 02-06262., ASE was also supported by NSF grant AST 02-06262.397 This research has made use of the NASA/TIPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory., This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory.398 0.31 ieure[m] 1., 0.3in Figure 1.399" The deconvolved/Caussian smoothed images of unclear regions[m] of NGC 11I8 at (a) l.l pan. (b) 1.6 pan. (c) 2.2 nu. The resolution of each inuageo is 1"", aud the associated[m] scale bars are in units of piv Ll "," The deconvolved/Gaussian smoothed images of nuclear regions of NGC 4418 at (a) 1.1 $\mu$ m, (b) 1.6 $\mu$ m, (c) 2.2 $\mu$ m. The resolution of each image is $\arcsec$, and the associated scale bars are in units of $\mu$ Jy $^{-1}$."400Note the morpholoeicalo similarities of the three images. (, Note the morphological similarities of the three images. (401d) À miasHH Mae of the nuclear region of NGC £115.,d) A $m_{1.1 \mu{\rm m}} - m_{1.6 \mu{\rm m}}$ image of the nuclear region of NGC 4418.402 The erecu lines outline the edges of the structure of the dark lanes visible iu 1.60n.Figures lac aud Figure 2. aud the scale bar represeuts the ratio of the 1.6 jan anc 1.1 pan fux densities provided in (a) aud (b," The green lines outline the edges of the structure of the dark lanes visible in Figures 1a–c and Figure 2, and the scale bar represents the ratio of the 1.6 $\mu$ m and 1.1 $\mu$ m flux densities provided in (a) and (b)."403"Berustein.Freecdauan.&Madore(2002a.b).. hereafter BFAIO2a. BFALIO2b. or DEMO2 comiued. have announced the first detection of the Extrwalactie Dackerouud Light (EBL) from absolute photometry.| with the mean values of LO(42.5). 2741.1). aud 2.2(E1.0) «10 Jat 3000. 5500. and SOOO respectively,","\citet[]{bfm02a, bfm02b}, hereafter BFM02a, BFM02b, or BFM02 combined, have announced the first detection of the Extragalactic Background Light (EBL) from absolute photometry, with the mean values of $\pm2.5$ ), $\pm1.4$ ), and $\pm1.0$ ) $\times$ at 3000, 5500, and 8000, respectively."404 The errors quoted ave lo uncertainties., The errors quoted are $\sigma$ uncertainties.405 Their method is based on the formula: where [yor is the total sky surface xiehtuess outside the atinosphere. {νι is the Zodiacal Ligit (ZL). and pe is the Diffuse Caactic Light (DCL) surface brieltucss. all to be determined in the direction of the DEMU2 target ficld at /=206.6.59.8 deg.," Their method is based on the formula: where $I_{\rm tot}$ is the total sky surface brightness outside the atmosphere, $I_{\rm ZL}$ is the Zodiacal Light (ZL), and $I_{\rm DGL}$ is the Diffuse Galactic Light (DGL) surface brightness, all to be determined in the direction of the BFM02 target field at $l = 206.6, 406b = -59.8$ deg."407 Each one of the three components is deriveκα in BFAIO2 with a cliffereit method., Each one of the three components is derived in BFM02 with a different method.408 Jpop is measured above the atmosphere with theTelescope (LIST) uus broad-baud CCD photometry: {γι is micasured from the erouncd. with t1ο 2.5an du Pont telescope at t1 Las. Campanas Observatory (LCO). using spectropliotoinetry: aud Jp js estimated by using a inodol Or the scattering of starligit by interstellar dust.," $I_{\rm tot}$ is measured above the atmosphere with the ) using broad-band CCD photometry; $I_{\rm ZL}$ is measured from the ground, with the 2.5-m du Pont telescope at the Las Campanas Observatory (LCO), using spectrophotometry; and $I_{\rm DGL}$ is estimated by using a model for the scattering of starlight by interstellar dust."409 A verv demanding task for the BEMO2 aethod is set by the requirenient that. for cach X the two telescopes with different properties ik different observing methods. the mie:wured fux. Zzj or £4. has to be separately calibrated to tjo same scale.," A very demanding task for the BFM02 method is set by the requirement that, for each of the two telescopes with different properties and different observing methods, the measured flux, $I_{\rm ZL}$ or $I_{\rm tot}$, has to be separately calibrated to the same scale."410" πο, ds ouly a σα. fraction. a few per cent at most. of {των are Ty..."," $I_{\rm EBL}$ is only a small fraction, a few per cent at most, of $I_{\rm tot}$ and $I_{\rm ZL}$."411 Theretore. the BFALO2 methoc crucially depends ο- whether or not the verv high aloslute accuracy. of Z1Vou.. needed in the measurement. calibration. axd scattere helt corrections for {γι aud separately for £4 is achieved.," Therefore, the BFM02 method crucially depends on whether or not the very high absolute accuracy, of $\lesssim$ 1, needed in the measurement, calibration, and scattered light corrections for $I_{\rm ZL}$ and separately for $I_{\rm tot}$ is achieved."412 Iu this paper a critical discussion will be oesented of the calibration aud the atmospheric corrections applied i- BEALO2b to the erouud based measurement of he Zodiaca Light., In this paper a critical discussion will be presented of the calibration and the atmospheric corrections applied in BFM02b to the ground based measurement of the Zodiacal Light.413 The assuniptious for estimating {ροι are critically reviewed., The assumptions for estimating $I_{\rm DGL}$ are critically reviewed.414 Iu addition. I point out a puzzliig situatioTO which emiergerges from Comparison. between tjo results o BFALO2 aud of the widely cited previous preseutations of the same observations.," In addition, I point out a puzzling situation which emergerges from comparison between the results of BFM02 and of the widely cited previous presentations of the same observations."415 Two amospheric corrections have to be applied: (1) extinctio1i and (2) tropospheric scattered lieht.," Two atmospheric corrections have to be applied: (1) extinction, and (2) tropospheric scattered light."416" The observed uieht skv brightness. L4,À.f..X). towards the tarect fle dis given by where Ais the waveleneth. f he time of the observation. X the airnass. r(À) the atiuosphlieric extinction coefficient for unit auass. [aoa the tropospheric scattered light. aud fou the airelow as observed from the ground (iucliding atmospheric attenuation ac scattered airglow)."," The observed night sky brightness, $I_{\rm obs}(\lambda,t,X)$, towards the target field is given by where $\lambda$ is the wavelength, $t$ the time of the observation, $X$ the airmass, $\tau(\lambda)$ the atmospheric extinction coefficient for unit airmass, $I_{\rm sca}$ the tropospheric scattered light, and $I_{\rm agl}$ the airglow as observed from the ground (including atmospheric attenuation and scattered airglow)."417 The DFM2h» method of separating the ZL from the airelow Con»oneut is basec ou the assumptions that (1) the depths of the Frauuhofer lues in the spectrum of the Zodiacal Light are icdeutica to those in the solar spectrum. and (2) the aireow spectrum is uncorrelated with the solar Fuuhofer spectitmn.," The BFM02b method of separating the ZL from the airglow component is based on the assumptions that (1) the depths of the Fraunhofer lines in the spectrum of the Zodiacal Light are identical to those in the solar spectrum, and (2) the airglow spectrum is uncorrelated with the solar Fraunhofer spectrum."418" The tropospleric scattered light. Lue,(A.t.NX). is f lua1 obstace iu conducΠιο accurate diffuse sky phooletIV from he eround."," The tropospheric scattered light, $I_{\rm sca}(\lambda,t,X)$, is the main obstacle in conducting accurate diffuse sky photometry from the ground."419 Uulike the photometry of stars or μα] extcuded sources. no differential ON/OFF lüeasurenielrs are possible. aud one nmst calculate the scattered helt contribution comine from all the light sotrces alvove the horizon.," Unlike the photometry of stars or small extended sources, no differential ON/OFF measurements are possible, and one must calculate the scattered light contribution coming from all the light sources above the horizon."420" The scattered ποτ coumpoucuts which coitribute to the ""ZL-like (Fraunhofer spectrum) sienal are die to the all-sky distributions of the ZL itself. the Iuteerated Starlight (ISL). aud the DGL."," The scattered light components which contribute to the “ZL-like” (Fraunhofer spectrum) signal are due to the all-sky distributions of the ZL itself, the Integrated Starlight (ISL), and the DGL."421 Each one of these components has the Ravleigh (RB) and the Mie or acrosol (M) scattering part:, Each one of these components has the Rayleigh (R) and the Mie or aerosol (M) scattering part:422source of error in the SD estimate. but this ellect is bevond the scope of this paper.,"source of error in the SB estimate, but this effect is beyond the scope of this paper."423" HE we assume a given profile. then we can discuss the ""intrinsic error in the APM SB caused bv the observational errors in (Jis. dis)."," If we assume a given profile, then we can discuss the “intrinsic” error in the APM SB caused by the observational errors in $I_{\rm iso}$ $A_{\rm iso}$ )."424 The errors in (finn. chin.) come from a complex combination of sources which we consider in two main categories.," The errors in $I_{\rm iso}$, $A_{\rm iso}$ ) come from a complex combination of sources which we consider in two main categories."425" First is the observing process. which includes a mixture of weather conditions ancl instrumental ellects. including the residual calibration dillerences between the survey plates that are not corrected by the field correction ""unction ancl overall plate matching."," First is the observing process, which includes a mixture of weather conditions and instrumental effects, including the residual calibration differences between the survey plates that are not corrected by the field correction function and overall plate matching."426 “Phis category also inclucles photon noise., This category also includes photon noise.427 Second are the errors. from. the ADPM sean itself, Second are the errors from the APM scan itself.428 VPhese errors can be estimated. cirectly rom repeat scans of selected plates., These errors can be estimated directly from repeat scans of selected plates.429" Por di, we find. this source contributes only about 0.04 mag uncertainty. and for Aus we find about5%."," For $I_{\rm iso}$ we find this source contributes only about 0.04 mag uncertainty, and for $A_{\rm iso}$ we find about."430. These errors could be analytically: ransformed to pro following a standard. propagation of errors procedure. but even if the resulting uncertainty in fio is slightly larger. it will be negligible compared to the observational errors.," These errors could be analytically transformed to $\mu_{0}$ following a standard propagation of errors procedure, but even if the resulting uncertainty in $\mu_{0}$ is slightly larger, it will be negligible compared to the observational errors."431 The overlapping areas of neighbouring plates provide a direct Opportunity to estimate the combined. errors in our SB estimates., The overlapping areas of neighbouring plates provide a direct opportunity to estimate the combined errors in our SB estimates.432 Figure 5((e) shows the residual errors Lor the overlapping field of F409 and E471. after applying the field correction and the overall matching correction. and it can rc seen that there is still anms scatter of about 0.25 mag )etween the two independent measurements for each galaxy.," Figure \ref{fig_us409471}( (c) shows the residual errors for the overlapping field of F409 and F471, after applying the field correction and the overall matching correction, and it can be seen that there is still an scatter of about 0.25 mag between the two independent measurements for each galaxy."433 This implies the error in each py will be =0.18 mag., This implies the error in each $\mu_{0}$ will be $\simeq 0.18 $ mag.434 We rave calculated the scatter for each one of the SOO plate overlaps. independently. and show the frequency distribution of these values in Figure S..," We have calculated the scatter for each one of the 809 plate overlaps, independently, and show the frequency distribution of these values in Figure \ref{fig_rmsdu}."435 For most of these overlaps. he of Agro is less than 0.3 mag. and the mode is at 0.21 mag. corresponding to a tvpical uncertainty of 0.15 mae for an individual SB measurement.," For most of these overlaps, the of $\Delta\mu_{0}$ is less than 0.3 mag, and the mode is at 0.21 mag, corresponding to a typical uncertainty of 0.15 mag for an individual SB measurement."436 If we consider all of the plate overlaps as à whole. therms Apy over all 1.282.600 galaxy. pairs is 0.23 mag. so the overall uncertainty for an individual SB measurement has an of 0.10.," If we consider all of the plate overlaps as a whole, the $\Delta\mu_{0}$ over all 1,282,600 galaxy pairs is 0.23 mag, so the overall uncertainty for an individual SB measurement has an of 0.16."437 This value includes both the random: error on each SD measurement. and the residual dillerence between the zero-points for all plates after applving the matching corrections.," This value includes both the random error on each SB measurement, and the residual difference between the zero-points for all plates after applying the matching corrections."438 The dillerence between thisrms. and the within each overlap suggests iat the residual error in the zero-point matching has an of 0.07 mag per plato. consistent with the overlap residuals.," The difference between this, and the within each overlap suggests that the residual error in the zero-point matching has an of 0.07 mag per plate, consistent with the overlap residuals."439 Ackdütionally. we have considereἱ 10error as a function of fio.," Additionally, we have considered theerror as a function of $\mu_{0}$."440 Table. 1 lists the difference between the si measurements in overlaps for a series of μυ ranges., Table 1 lists the difference between the $\mu_{0}$ measurements in overlaps for a series of $\mu_{0}$ ranges.441 Galaxies with yy about 21.0 ~ 22.0 mag have the smallest. error at 0.16 mag., Galaxies with $\mu_{0}$ about 21.0 $\sim$ 22.0 mag have the smallest error at 0.16 mag.442 At both [ow and high surface brightness the error increases up to 2 0.23., At both low and high surface brightness the error increases up to $\simeq$ 0.23.443 This tendency could. also be seen in Figure 5((c)., This tendency could also be seen in Figure \ref{fig_us409471}( (c).444 Vhe reason for the increased. error is that fio depends on the profile of a galaxy (see Section 5.2)). and when we estimate the total intensity of the galaxy. Zi (eqs. (10))," The reason for the increased error is that $\mu_{0}$ depends on the profile of a galaxy (see Section \ref{sec_profiles}) ), and when we estimate the total intensity of the galaxy, $I_{\rm tot}$ (eqs. \ref{eq_itot}) )"445 to (132). only fi; is directly constrained: by the observational data. while Zia and Joa. the other two contributions to {μι involve extrapolations that are more extreme at low or high SD.," to \ref{eq_ifield}) )), only $I_{\rm iso}$ is directly constrained by the observational data, while $I_{\rm field}$ and $I_{\rm446sat}$, the other two contributions to $I_{\rm tot}$, involve extrapolations that are more extreme at low or high SB."447" So in summary. the overall ""intrinsic uncertainty in fo including measurement errors. and. zero-point errors. ds tvpically 0.2 mag."," So in summary, the overall “intrinsic” uncertainty in $\mu_{0}$ including measurement errors, and zero-point errors is typically 0.2 mag."448 Comparing galaxies measured on one plate. the relative uncertainty is about 0.16. (also see the next subsection)," Comparing galaxies measured on one plate, the relative uncertainty is about 0.16 (also see the next subsection)."449 After applving the corrections to the individual plate data. we should be able to define galaxy. catalogues selected with uniform SD. criteria.," After applying the corrections to the individual plate data, we should be able to define galaxy catalogues selected with uniform SB criteria."450 We can make a simple. test. of the uniformity of the sample by caleulating the mean SB for galaxies on cach plate., We can make a simple test of the uniformity of the sample by calculating the mean SB for galaxies on each plate.451" Cosmic structure will introduce some intrinsic variation in the mean SB in dillerent directions on he sky. but this is likely to be small: indeed the variation in ealaxy numbers from plate to plate at 6,=20 is only 12% (Alaclelox. Efstathiou Sutherland 1996)."," Cosmic structure will introduce some intrinsic variation in the mean SB in different directions on the sky, but this is likely to be small; indeed the variation in galaxy numbers from plate to plate at $b_J = 20$ is only $12\%$ (Maddox, Efstathiou Sutherland 1996)."452 Figure 9 shows a plot of the mean fio For cach plate in the survey.before ancl after applying he matching corrections.," Figure \ref{fig_meanmu0} shows a plot of the mean $\mu_0$ for each plate in the survey,before and after applying the matching corrections."453 Using all fields. the scatter xore correction is 0.25 mag. and alter correction it reduces o 0.005 mae.," Using all fields, the scatter before correction is 0.25 mag, and after correction it reduces to 0.095 mag."454 Llowever. it is clear that. fields. centred," However, it is clear that fields centred"455absorbed population: filled circles).,absorbed population: filled circles).456" It is clear that the two populations are characterized by two different XLF with the absorbed AGN population being described by a steeper XLF, if compared with the unabsorbed ones, at all luminosities."," It is clear that the two populations are characterized by two different XLF with the absorbed AGN population being described by a steeper XLF, if compared with the unabsorbed ones, at all luminosities."457 The binned representation of the XLFs reported in Figure 5 have been fitted by a smoothly connected two power-laws function of the form taking into account the error bars of each data point and by minimizing y? using the routines in the QDP software package., The binned representation of the XLFs reported in Figure \ref{XLF_2} have been fitted by a smoothly connected two power-laws function of the form taking into account the error bars of each data point and by minimizing $\chi^2$ using the routines in the QDP software package.458 Best fit XLF parameters and 1 o errors are reported in Table 2., Best fit XLF parameters and 1 $\sigma$ errors are reported in Table 2.459" For the unabsorbed AGN population the value of y; and γ2 are consistent, within the errors, with those reported in Sazonov&Revnivtsev(2004) and in Shinozakietal.(2006)."," For the unabsorbed AGN population the value of $\gamma_1$ and $\gamma_2$ are consistent, within the errors, with those reported in \cite{sazonov2004} and in \cite{shinozaki2006}."460. For the absorbed AGN population the y; (y2) derived here is slightly steeper (flatter) than that reported in Shinozakietal.(2006) (σι=1121019: γ2= 3.347920). Sazo, For the absorbed AGN population the $\gamma_1$ $\gamma_2$ ) derived here is slightly steeper (flatter) than that reported in \cite{shinozaki2006} $\gamma_1=1.12^{+0.17}_{-0.19}$; $\gamma_2=3.34^{+0.90}_{-0.65}$ ).461nov&Revnivtsev(2004) does not quote the XLF parameters for the absorbed AGN population., \cite{sazonov2004} does not quote the XLF parameters for the absorbed AGN population.462 As discussed in section 2 two HBSS sources (XBSJ080411.3+650906 and XBSJ110050.6-344331) are still unidentified at the time of this writing., As discussed in section 2 two HBSS sources (XBSJ080411.3+650906 and XBSJ110050.6-344331) are still unidentified at the time of this writing.463 Can their inclusion in the AGN sample substantially change the results discussed above?, Can their inclusion in the AGN sample substantially change the results discussed above?464 In particular their inclusion could be important if these sources were high luminosity absorbed AGN where we measure a deficit of absorbed sources., In particular their inclusion could be important if these sources were high luminosity absorbed AGN where we measure a deficit of absorbed sources.465 To answer to this question we have examined in detail their X-ray spectral properties as well as the optical (photometric) properties of the most likely optical counterpart., To answer to this question we have examined in detail their X-ray spectral properties as well as the optical (photometric) properties of the most likely optical counterpart.466 XBSJ110050.6-344331 is well described (fixing z=0) by a power-law model having T=1.80x0.16 and Ny=1x0.510?! cm”., XBSJ110050.6-344331 is well described (fixing z=0) by a power-law model having $\Gamma = 1.80\pm 0.16$ and $N_H=1\pm0.5 \times 10^{21}$ $^{-2}$.467" Its 2-10 keV X-ray flux (~3x107? )), optical magnitude (mg = 18.0), X-ray to optical flux ratio (X/O~ 1) and X-ray spectral properties strongly suggest a type 1 (unabsorbed) object."," Its 2-10 keV X-ray flux $\sim 3 \times 10^{-13}$ ), optical magnitude $_R$ = 18.0), X-ray to optical flux ratio $X/O \sim 1$ ) and X-ray spectral properties strongly suggest a type 1 (unabsorbed) object."468 On the contrary XBSJ080411.34-650906 is most likely an absorbed AGN., On the contrary XBSJ080411.3+650906 is most likely an absorbed AGN.469" Its X-ray spectra is described (at z=0) by a power-law model having =1.7+0.4 and Ny=8.4+4.3x10?! cm?, so with an intrinsic Ny (at the source z) well above 4x10?! cm""?,"," Its X-ray spectra is described (at z=0) by a power-law model having $\Gamma = 1.7\pm 0.4$ and $N_H=8.4\pm 4.3 \times 10^{21}$ $^{-2}$, so with an intrinsic $N_H$ (at the source z) well above $4\times 10^{21}$ $^{-2}$."470" The optical magnitude of the counterpart (mg = 21.10) combined with its 2-10 keV X-ray flux (2.1x107-8 )) implies an X/O flux ratio of ~17.5, strongly supporting the absorbed AGN hypothesis (e.g. Severgniniet 2006))."," The optical magnitude of the counterpart $_R$ = 21.10) combined with its 2-10 keV X-ray flux $\sim 2.1471\times 10^{-13}$ ) implies an X/O flux ratio of $\sim 17.5$, strongly supporting the absorbed AGN hypothesis (e.g. \citealt{severgnini2006}) )."472" If we use the relationship between X/O flux ratio and intrinsic luminosity reported in Fioreetal.(2003) the most likely redshift of this object is ~0.55 (consistent with a poor quality optical spectrum of the optical counterpart) and its intrinsic luminosity is L,~1.9x10“..", If we use the relationship between X/O flux ratio and intrinsic luminosity reported in \cite{fiore2003} the most likely redshift of this object is $\sim 0.55$ (consistent with a poor quality optical spectrum of the optical counterpart) and its intrinsic luminosity is $L_x\simeq 1.9\times 10^{44}$.473" The addition of this object to the HBSS absorbed AGN sample produce an increase of ~8% of the space density of the absorbed AGN population at L,~10“,, a very marginal difference that is well within the error bar reported in Figure 5.."," The addition of this object to the HBSS absorbed AGN sample produce an increase of $\sim 8\%$ of the space density of the absorbed AGN population at $L_x\simeq 10^{44}$, a very marginal difference that is well within the error bar reported in Figure \ref{XLF_2}. ."474 It is, It is475have only a very minor effect on the C11 dwarf/giant cut which we used.,have only a very minor effect on the C11 dwarf/giant cut which we used.476" One of the most interesting results in this work is the period distribution for each spectral type, displayed in Figure 11.."," One of the most interesting results in this work is the period distribution for each spectral type, displayed in Figure \ref{fig:per_plot}."477" Although this should be considered a preliminary test due to the short timespan of the dataset, there is clear evidence that, for light curves with a clear periodic component, the period increases towards later spectral types."," Although this should be considered a preliminary test due to the short timespan of the dataset, there is clear evidence that, for light curves with a clear periodic component, the period increases towards later spectral types."478" The fraction of periodic stars also varies with spectral class, increasing towards later types to a maximum in the K stars, before reducing again in M stars."," The fraction of periodic stars also varies with spectral class, increasing towards later types to a maximum in the K stars, before reducing again in M stars."479" The relatively high number of stars in which we were able to identify a periodic or quasi periodic modulation in this dataset alone suggests that, when further quarters of data are added, it should be possible to measure periods for a significant fraction of all stars — and thus calibrate the evolution of angular momentum for intermediate and low-mass stars on the main sequence to an unprecedented level."," The relatively high number of stars in which we were able to identify a periodic or quasi periodic modulation in this dataset alone suggests that, when further quarters of data are added, it should be possible to measure periods for a significant fraction of all stars – and thus calibrate the evolution of angular momentum for intermediate and low-mass stars on the main sequence to an unprecedented level."480 We also investigated the stochastic component of the variability in two different ways., We also investigated the stochastic component of the variability in two different ways.481" First, we measured the number of periodogram peaks with power greater than of the maximum for the stars which pass our periodicity selection threshold."," First, we measured the number of periodogram peaks with power greater than of the maximum for the stars which pass our periodicity selection threshold."482" For all spectral type, the distribution of this statistic, which we call Nox, has a peak at low values, corresponding to clearly periodic light curves dominated by a single frequency, or a small number of frequencies, However, there is also another peak at high Ny, Whose amplitude increases towards later spectral types, reaching a maximum in the K stars and decreasing slightly in the M stars (as did the periodicity fraction)."," For all spectral type, the distribution of this statistic, which we call $N_{\rm pk}$, has a peak at low values, corresponding to clearly periodic light curves dominated by a single frequency, or a small number of frequencies, However, there is also another peak at high $N_{\rm pk}$, whose amplitude increases towards later spectral types, reaching a maximum in the K stars and decreasing slightly in the M stars (as did the periodicity fraction)."483" This peak corresponds to quasi-periodic light curves, as expected for rotational variables with evolving active regions."," This peak corresponds to quasi-periodic light curves, as expected for rotational variables with evolving active regions."484 We also parameterised the stochastic component of variability was performed by fitting auto-regressive models (also known as Harvey models) to the median power spectrum for each spectral type., We also parameterised the stochastic component of variability was performed by fitting auto-regressive models (also known as Harvey models) to the median power spectrum for each spectral type.485" Because of the relatively limited frequency resolution (caused by the short duration of the dataset used in this study), the fitted model parameters cannot be considered definitive, but they enable a preliminary inter-comparison."," Because of the relatively limited frequency resolution (caused by the short duration of the dataset used in this study), the fitted model parameters cannot be considered definitive, but they enable a preliminary inter-comparison."486" We find that the typical amplitude, timescale and power-law index all increase towards later types."," We find that the typical amplitude, timescale and power-law index all increase towards later types."487" This is consistent with our other tests, and supports a broadly coherent picture of main-sequence variability."," This is consistent with our other tests, and supports a broadly coherent picture of main-sequence variability."488" The hotter, earlier spectral classes show a lower variability level on the whole, and the variables tend to show clearly periodic behaviour on short time-scales, as expected from pulsations."," The hotter, earlier spectral classes show a lower variability level on the whole, and the variables tend to show clearly periodic behaviour on short time-scales, as expected from pulsations."489 The shape of their power spectra suggest that these stars possess smaller active regions that evolve more quickly., The shape of their power spectra suggest that these stars possess smaller active regions that evolve more quickly.490" By contrast, the cooler, later type stars show larger amplitude"," By contrast, the cooler, later type stars show larger amplitude"491show in Figure 10. the various mass-solutions we obtain for this galaxy. resulting from our assumptions about the nature of the NGC 524 cluster orbits.,"show in Figure \ref{fig:mass} the various mass-solutions we obtain for this galaxy, resulting from our assumptions about the nature of the NGC 524 cluster orbits."492 We have obtained low-resolution spectra for 41 GC candidates associated with the lenticular galaxy NGC 524., We have obtained low-resolution spectra for 41 GC candidates associated with the lenticular galaxy NGC 524.493 From this sample. 29 candidates are identified: as genuine GCs on the basis of their racial velocities.," From this sample, 29 candidates are identified as genuine GCs on the basis of their radial velocities."494 Deriving mean metallicities for the NGC 524 GC's. we find our sample spans a wide range in metallicity. with 240 < Fel] < 0.," Deriving mean metallicities for the NGC 524 GCs, we find our sample spans a wide range in metallicity, with –2.0 $\leq$ [Fe/H] $\leq$ 0."495 The individual S/N. of our spectra are &enerally insullicient to derive useful age constraints. since we rely on age discrimination to come from individual indices L3).," The individual S/N of our spectra are generally insufficient to derive useful age constraints, since we rely on age discrimination to come from individual indices $\beta$ )."496" Therefore we have. co-added the GCs into metal-poor CFefl] < 1.0) and metal-rich (Fe/1] 1.0) composite"" GCs.", Therefore we have co-added the GCs into metal-poor ([Fe/H] $<$ –1.0) and metal-rich ([Fe/H] $\geq$ –1.0) 'composite' GCs.497 From comparison with the stellar population mocdels of Maraston&Thomas. (2000). we find that the composite metal-rich and metal-poor GC sub-populations both appear old. and are coeval within the 2 & uncertainties.," From comparison with the stellar population models of \citeANP{Maraston00} (2000), we find that the composite metal-rich and metal-poor GC sub-populations both appear old, and are coeval within the 2 $\sigma$ uncertainties."498 We have examined the abundance ratios of the NGC 524 GCs using the a-enhanced stellar population models of Milone.Xwbuv.&Sehiavon (2000)., We have examined the abundance ratios of the NGC 524 GCs using the $\alpha$ -enhanced stellar population models of \citeANP{Milone00} (2000).499 The calibration of these models was first tested. usinge a sample of high> S/N Galactic GC integrated: spectra (Cohen.Blakeslee.&Ryzhov1905). which have independently: determine fe] ratios [rom high resolution spectroscopy.," The calibration of these models was first tested using a sample of high S/N Galactic GC integrated spectra \cite{Cohen98}, which have independently determined $\alpha$ /Fe] ratios from high resolution spectroscopy."500 We lind tha he model predictions are in good agreement with these iterature values., We find that the model predictions are in good agreement with these literature values.501 Comparing the Milone.Darbuy.&Schi-avon (2000) models to our data. we find a weak trend of decreasing o Fe] with increasing Fe/ll].," Comparing the \citeANP{Milone00} (2000) models to our data, we find a weak trend of decreasing $\alpha$ /Fe] with increasing [Fe/H]."502 This is supporte w the co-added. data. with the composite metal-poor GC possessing a Fe] ~ 0.3. whereas the metal-rich composite GC shows a/Fe] ~ 0.1.," This is supported by the co-added data, with the composite metal-poor GC possessing $\alpha$ /Fe] $\sim$ 0.3, whereas the metal-rich composite GC shows $\alpha$ /Fe] $\sim$ 0.1."503 The lower a/LFe] ratios of the metal-rich clusters may in fact reflect a mix of a /Fe] ratios sub-populations. amongst the metal-rich clusters) as ound by Ixuntschneretal. (2002) for the lenticular galaxy GC 3115., The lower $\alpha$ /Fe] ratios of the metal-rich clusters may in fact reflect a mix of $\alpha$ /Fe] ratios sub-populations amongst the metal-rich clusters) as found by \citeANP{Kuntschner02} (2002) for the lenticular galaxy NGC 3115.504 We have also investigated the kinematics of the (ας 524 GC system., We have also investigated the kinematics of the NGC 524 GC system.505 After the removal of one outlying GC. we obtain a velocity cispersion of 186429kms.+.," After the removal of one outlying GC, we obtain a velocity dispersion of $186\pm29 \kms$."506 Phe entire cluster svsten shows a rotation of 1442560kms+ (exeluding he outlving cluster). around a position angle of 22+27 deg.," The entire cluster system shows a rotation of $114\pm60 \kms$ (excluding the outlying cluster), around a position angle of $22\pm27 \deg$ ."507 By separating the GC systems into metal-rich and metal-poor components (at. Fe/1I]2.1.0). we find that the GO 524 GC sub-populations potentially exhibit dilferent kinematics.," By separating the GC systems into metal-rich and metal-poor components (at [Fe/H]=–1.0), we find that the NGC 524 GC sub-populations potentially exhibit different kinematics."508 30th sub-populations have similar (neglecting rotation) velocity dispersions (197c40kms and 169+49kms respectively). but the metal-poor clusters show signs of rotation (147+75kms Ly whereas the metal-rich clusters do not (GSSAknis 1)," Both sub-populations have similar (neglecting rotation) velocity dispersions $197\pm40 \kms$ and $169\pm 49 \kms$ respectively), but the metal-poor clusters show signs of rotation $147\pm75 \kms$ ), whereas the metal-rich clusters do not $68\pm84 \kms$ )."509 Finally. using tje entire GC system. we derive a virial ancl projected. mass esimation for NGC 524 of between 4 10 M. and 13 0H ML. (depending on the assumed orbital cüstribution) interior to  2 ellective radii of this ealaxy.," Finally, using the entire GC system, we derive a virial and projected mass estimation for NGC 524 of between 4 $\times$ $^{11}$ $\Msun$ and 13 $\times$ $^{11}$ $\Msun$ (depending on the assumed orbital distribution) interior to $\sim$ 2 effective radii of this galaxy."510 We thank Soeren Larsen and Alichacl Pierce. Lor useful comments and suggestions. John Blakeslee for supplying the Galactic GC data and the anonymous. referees. who greatly improved. the presentation of the paper. and noticed an error in the original manuscript.," We thank Soeren Larsen and Michael Pierce for useful comments and suggestions, John Blakeslee for supplying the Galactic GC data and the anonymous referee, who greatly improved the presentation of the paper, and noticed an error in the original manuscript."511 Part of this research was funded o» NSE grant AST 9900732 and. AS'T-0206139., Part of this research was funded by NSF grant AST 9900732 and AST-0206139.512 The data presented. herein were obtained at the WAL Keck Observaory. which is operated. as a scientific partnership among t1e California Institute of Technology. the University of California and the National Acronautics ancl Space Administration.," The data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration."513 The Observatory was made possible by the generous financial support of the WAL. Ixeck, The Observatory was made possible by the generous financial support of the W.M. Keck514Maenuoetoeraums provide the radial magnetic field ou the visible surface of the Sun.,Magnetograms provide the radial magnetic field on the visible surface of the Sun.515 The actual measurement is for the line-of-sight component of the maenetic field. which is then transformed iuto the radial commpoucut assinuiue au (approximately) radial field wear the solar surface.," The actual measurement is for the line-of-sight component of the magnetic field, which is then transformed into the radial component assuming an (approximately) radial field near the solar surface."516 As the Sun rotates. the individual maguetograms can be combined into a svuoptic maguetoeram that covers the whole spherical surface.," As the Sun rotates, the individual magnetograms can be combined into a synoptic magnetogram that covers the whole spherical surface."517 Synoptic maenetoeraus are provided by many observatorics. including Wilcox Solax Observatory (WSO). the Michelson. Doppler Duager (MDI) instrament ou the Solar aud Heliospherie Observatory (SOMO). the Global Oscillation Network Croup (CONC). Solar Dynamic Observatory (SDO) and the Synoptic Optical Long-term Iunvestieations of the Sun (SOLIS) observatory.," Synoptic magnetograms are provided by many observatories, including Wilcox Solar Observatory (WSO), the Michelson Doppler Imager (MDI) instrument on the Solar and Heliospheric Observatory (SOHO), the Global Oscillation Network Group (GONG), Solar Dynamic Observatory (SDO) and the Synoptic Optical Long-term Investigations of the Sun (SOLIS) observatory."518 Today's magnetoerams contain huudreds to thousands of pixels along cach coordinate direction., Today's magnetograms contain hundreds to thousands of pixels along each coordinate direction.519 These magnetograms cau be used to extrapolate the magnetic field iuto the solar corona., These magnetograms can be used to extrapolate the magnetic field into the solar corona.520 The simplest model (Schatten.Wilcox.&Ness1969). assumes a current-firee. in other words potential. magnetic field that matches the radial field of the maguetoeram on the surface. while it satisfies a simple boundary condition at the outer boundary at some radial distance HR.," The simplest model \citep{Schatten:1969}521 assumes a current-free, in other words potential, magnetic field that matches the radial field of the magnetogram on the surface, while it satisfies a simple boundary condition at the outer boundary at some radial distance $R$."522" The outer boundary condition is usuallv taken at A— 2.5R, (solar radii. and a purely racial Ποια is assmmed at this ""source surface”."," The outer boundary condition is usually taken at $R=2.5\,$ $_s$ (solar radii), and a purely radial field is assumed at this “source surface”."523 Mathematically the problem is the following: eiveu the maenetogram data that defines the radial component, Mathematically the problem is the following: given the magnetogram data that defines the radial component524to the other with a slope that changes in the inner longitudes |/|<4°.,to the other with a slope that changes in the inner longitudes $|l|<4^\circ$.525 These particular properties for the stellar populations of the Milky Way bar are very unlikely., These particular properties for the stellar populations of the Milky Way bar are very unlikely.526 A second point to consider is the adopted extinction law for the determination of dereddened ΚΑ magnitudes., A second point to consider is the adopted extinction law for the determination of dereddened $K_{s_0}$ magnitudes.527 For a consistent comparison with NOS measurements. we have used the same extinction law based on ?..," For a consistent comparison with N05 measurements, we have used the same extinction law based on \citet[][]{nishiyama09}."528 However. we note that this extinction law. which differs from the more commonly adopted laws (e.g.222).. was derived for the highly reddened inner bulge fields (|b]« 2°). while this does not seem to be the case for the whole bulge.," However, we note that this extinction law, which differs from the more commonly adopted laws \citep[e.g.][]{cardelli89,savage79,rieke85}, was derived for the highly reddened inner bulge fields $|b|<2^\circ$ ), while this does not seem to be the case for the whole bulge."529 In the study of RR Lyrae in the bulge from ?.. variations with respect to the standard reddening law were observed in à few directions.," In the study of RR Lyrae in the bulge from \citet[][]{kunder08}, variations with respect to the standard reddening law were observed in a few directions."530 However. they conclude that. on average. the extinction law of Ry~3.1 is consistent with the observations of the bulge at larger distances from the Galactic plane.," However, they conclude that, on average, the extinction law of $R_V\sim3.1$ is consistent with the observations of the bulge at larger distances from the Galactic plane."531 Given this uncertainty in the correct extinction law with line of sight. a variation of it from standard values to that of ? could produce a change of up to 0.1 magnitudes in Κι for the regions with the highest reddening (A;~ 2.5). as seen in Fig. ]..," Given this uncertainty in the correct extinction law with line of sight, a variation of it from standard values to that of \citet[][]{nishiyama09} could produce a change of up to 0.1 magnitudes in $K_{s_0}$ for the regions with the highest reddening $A_k\sim 2.5$ ), as seen in Fig. \ref{red}."532 However. these variations are likely to be randomly distributed along different lines of sight.," However, these variations are likely to be randomly distributed along different lines of sight."533 That the same change in the bar orientation is now observed at both positive and negative latitudes. where reddening patterns differ greatly (Fig. 1).," That the same change in the bar orientation is now observed at both positive and negative latitudes, where reddening patterns differ greatly (Fig. \ref{red}) ),"534 leads us to conclude that our results are not an effect of extinction., leads us to conclude that our results are not an effect of extinction.535 At larger Galactic latitudes (||> 3°). the flattening of the bar within |/|<4° is not observed.," At larger Galactic latitudes $|b|>3^\circ$ ), the flattening of the bar within $|l|<4^\circ$ is not observed."536 This. combined with the symmetric change in slope. leads us to suggest that we are detecting an inner second bar in the Milky Way.," This, combined with the symmetric change in slope, leads us to suggest that we are detecting an inner second bar in the Milky Way."537 We cannot however exclude that the observed flattening is due to à particular change in the density distribution of RC stars in the inner bulge., We cannot however exclude that the observed flattening is due to a particular change in the density distribution of RC stars in the inner bulge.538" We have used the VVV data at b=+1° to build the bulge Juminosity functions along different lines of sight. and to measure the mean dereddened K,, magnitude. which can be used as a distance indicator."," We have used the VVV data at $b=\pm1^\circ$ to build the bulge luminosity functions along different lines of sight, and to measure the mean dereddened $K_{s_0}$ magnitude, which can be used as a distance indicator."539 The RC ts clearly detected in all fields. and within |/|<5° a second component is detected in the K-band luminosity function.," The RC is clearly detected in all fields, and within $|l|<5^\circ$ a second component is detected in the K-band luminosity function."540 Given that the average magnitude shift of this second peak does not follow the primary RC. it could be an independent structure detected at ~11.2 kpe from the Sun e.g. a spiral arm behind the bulge.," Given that the average magnitude shift of this second peak does not follow the primary RC, it could be an independent structure detected at $\sim11.2$ kpc from the Sun e.g. a spiral arm behind the bulge."541" The main RC traces the mean orientation for the Galactic bar. which produces a magnitude variation from K,, ~13.4(~9.6 kpe) at/2-10 to K,,~12.4(~ "," The main RC traces the mean orientation for the Galactic bar, which produces a magnitude variation from $K_{s_0}\sim $ 13.4 $\sim9.6$ kpc) at $l=-10$ to $K_{s_0}\sim $ "542Gamma ray burst (GRB) outflows represent the most extreme variant of relativistic jets.,Gamma ray burst (GRB) outflows represent the most extreme variant of relativistic jets.543 That they represent finite opening angle flows ts supported by the appearance of Jet breaks in GRB afterelows (Frailetal.1997) (insights provided by a coupled simulation and light-curve synthesis point out subtle chromatic effects. van Eerten et al.," That they represent finite opening angle flows is supported by the appearance of jet breaks in GRB afterglows \citep{Frailetal97} (insights provided by a coupled simulation and light-curve synthesis point out subtle chromatic effects, van Eerten et al."544 2010)., 2010).545 Other convincing arguments rely on the polarization in prompt emission (Lazzatietal. 2004).. as well as theoretical reasoning to invoke physically plausible explosion energies (Bloometal.2003).," Other convincing arguments rely on the polarization in prompt emission \citep{Lazzatietal04}, as well as theoretical reasoning to invoke physically plausible explosion energies \citep{Bloometal03}."546. However. despite the progress in GRB_ understanding allowed by current detailed observations. various questions remain.," However, despite the progress in GRB understanding allowed by current detailed observations, various questions remain."547 [n particular. for the (micro and maero) physics occurring within the relativistic shock fronts.," In particular, for the (micro and macro) physics occurring within the relativistic shock fronts."548 To improve constraints on GRB progenitor. stars and overall GRB energies. We need to develop improved modeling. targeting the interaction of collimated relativistic blast. waves. with circumburst progenitor surroundings.," To improve constraints on GRB progenitor stars and overall GRB energies, we need to develop improved modeling, targeting the interaction of collimated relativistic blast waves with circumburst progenitor surroundings."549 This interaction Is subject to non-linear physics affecting the details of how energy is transferred from the collimated ejecta to the circumburst medium., This interaction is subject to non-linear physics affecting the details of how energy is transferred from the collimated ejecta to the circumburst medium.550 Studies of this interaction rely on accurate. shock-capturing high resolution simulations.," Studies of this interaction rely on accurate, shock-capturing high resolution simulations."551 Previous 1D. studies using Lorentz factor 100 shells in either uniform al.2007) or fully wind-structured surroundings (Meliani&Keppens2007) quantified the need to resolve a scale ratio of up to 6 orders of magnitude between shell width and traversed distance. to study the blastwave until the Sedov phases.," Previous 1D studies using Lorentz factor 100 shells in either uniform \citep{Melianietal07} or fully wind-structured surroundings \citep{zaklet07} quantified the need to resolve a scale ratio of up to $6$ orders of magnitude between shell width and traversed distance, to study the blastwave until the Sedov phases."552 Pioneering work in GRB dynamics in afterglow phases was perfomed analytically. e.g. Mészáros&Rees(1997). and numerically. e.g. Kobayashietal.(1999).. using isotropic explosion models.," Pioneering work in GRB dynamics in afterglow phases was perfomed analytically, e.g. \cite{Meszaros&Rees97}, and numerically, e.g. \cite{Kobayashietal99}, using isotropic explosion models."553 Rhoads(1999) studied GRB outflow in two-dimensional settings analytically. by making assumptions anout sideways jet-expansion speeds.," \cite{Rhoads99} studied GRB outflow in two-dimensional settings analytically, by making assumptions anout sideways jet-expansion speeds."554 In the past decade. two and even three-dimensional relativistic simulations emerged. necessarily sacrificing in resolution (Granotetal.2001:Can-nizzoetal. 2004).. grid-adaptive studies at very high effective resolution (Zhang&MacFadyen2009;vanEertenetal. as well as high initial Lorentz factors (up to y2100 Meliani et al.," In the past decade, two and even three-dimensional relativistic simulations emerged, necessarily sacrificing in resolution \citep{Granotetal01, cannizzoetal04}, grid-adaptive studies at very high effective resolution \citep{ZhangMacFadyen09,eerten10} as well as high initial Lorentz factors (up to $\gamma=100$ Meliani et al."555 2007) became feasible., 2007) became feasible.556 In. contrast to earlier analytic assumptions. these simulations found a slow lateral expansio=) of the GRB jet. in accord with semi-analytical works (Kumar&Granot 2003).," In contrast to earlier analytic assumptions, these simulations found a slow lateral expansion of the GRB jet, in accord with semi-analytical works \citep{Kumar&Granot03}."557 However. the stability properties of the decelerating relativistic blast wave have not yet been addressed.," However, the stability properties of the decelerating relativistic blast wave have not yet been addressed."558 in contrast. to the Newtonian regime. where the self-similar Sedov blast-wave structure is known to be unstable (Vishniac1983) when the compression rate is high (in turn a funetion of polytropic index Γ«1.3). the relativistic regime is more complex since the compression rate depends on effective polytropic index. as well as on the Lorentz factor.," in contrast, to the Newtonian regime, where the self-similar Sedov blast-wave structure is known to be unstable \citep{Vishniac83} when the compression rate is high (in turn a function of polytropic index $\Gamma<1.3$ ), the relativistic regime is more complex since the compression rate depends on effective polytropic index, as well as on the Lorentz factor."559 Relativistic blast-wave stability has to be studied in a single dimension. and can only be performed at extreme resolutions. as demonstrated here.," Relativistic blast-wave stability has to be studied in a single dimension, and can only be performed at extreme resolutions, as demonstrated here."560 epu labelmodelonetwo-dimensional|.. hydrodynamics blast wave simulation in this paper was performed with the special relativistic hydro-module of the adaptive-mesh refinement code AMRVAC (Melanietal.2007)., The two-dimensional hydrodynamics blast wave simulation in this paper was performed with the special relativistic hydro-module of the adaptive-mesh refinement code AMRVAC \citep{Melianietal07}.561. We use a Synge-type equation of state (Melanietal.2004) that takes full account of the change in effective polytropic index., We use a Synge-type equation of state \citep{Melianietal04} that takes full account of the change in effective polytropic index.562 In the present paper we neglect the effect of magnetic fields and radiative losses., In the present paper we neglect the effect of magnetic fields and radiative losses.563" As an initial condition. a self-similar relativistic Blandford&MeKee(1976) blast wave structure. given by their equations Eqs (28)-(30). is assumed to have a half-opening angle 6=20°. energy Ej4=Ej,,27/2ergs. and equivalent isotropic energy Fj=2.6%IO?ergs."," As an initial condition, a self-similar relativistic \cite{BlandfordMcKee76} blast wave structure, given by their equations Eqs (28)-(30), is assumed to have a half-opening angle $\theta=20^{\circ}$, energy $E_{\rm jet}\,=\,E_{\rm iso} \theta^2/2 \,{\rm ergs}$, and equivalent isotropic energy $E_{\rm iso}\,=\,2.6\times10^{51} \,{\rm ergs}$."564 The blast wave propagates in a constant density medium nn=0.78em™.," The blast wave propagates in a constant density medium $n\,=\,0.78 {\rm cm^{-3}}$."565" We begin the simulation at a shock Lorentz factor y,,=25 (implying a local Lorentz factor of y=25/νοx 17.7). making the initial radius of the blast wave Ry52.68x107pe at local time focao=51.68days and observer time fom=Ro/2y7cIDhour."," We begin the simulation at a shock Lorentz factor $\gamma_{sh}\,=\,25$ (implying a local Lorentz factor of $\gamma\simeq 25/\sqrt{2}\simeq 17.7$ ), making the initial radius of the blast wave $R_{0}\,\simeq\, 2.68\, \times\, 10^{-2}\,{\rm pc}$ at local time $t_{\rm local,0}\,\simeq\, 51.68\, {\rm days}$ and observer time $t_{\rm obs,0}\,=R_0/2\gamma^2 c \simeq 1 \,{\rm hour}$."566 At that time. the blast wave energy is mostly concentrated in a thin layer AR=Ro/y-8.5xIO?pe.," At that time, the blast wave energy is mostly concentrated in a thin layer $\Delta R\,\simeq \,R_0/\gamma^2=8.5\times 10^{-5} {\rm pc}$."567 To follow the evolution of this blast wave from relativistic to Newtonian phases. we use a spherical domain spanning [1.57107.157].pe in radius and [0.45°] in meridional angle.," To follow the evolution of this blast wave from relativistic to Newtonian phases, we use a spherical domain spanning $\left[1.57\times 10^{-2},\,1.57\right]\;{\rm pc}$ in radius and $\left[0,45^{\circ}\right]$ in meridional angle."568 To simulate this blast wave over this large dynamical range. we need adaptive mesh refinement (AMR).," To simulate this blast wave over this large dynamical range, we need adaptive mesh refinement (AMR)."569 This AMR run exploits 13 grid levels and uses an error estimator for normalized second derivatives on, This AMR run exploits 13 grid levels and uses an error estimator for normalized second derivatives on570Cataclysiic variable stars (CVs) are close binary systems in which a low-mass secoucdary transfers mass outo a white dwarl: Warner(1995) wrote au excellent mouograph ou CVs.,Cataclysmic variable stars (CVs) are close binary systems in which a low-mass secondary transfers mass onto a white dwarf; \citet{warn} wrote an excellent monograph on CVs.571 Because CVs are discovered by a variety of methods with idiosvucratic aud varying efficiency. their space deusity remains uncertain.," Because CVs are discovered by a variety of methods with idiosyncratic and varying efficiency, their space density remains uncertain."572 This is uulortunate. since an accurate kuowledge of the space density would serve as a strong coustraint on evolutiouary scenarios.," This is unfortunate, since an accurate knowledge of the space density would serve as a strong constraint on evolutionary scenarios."573 CV evolution is driven by the gradual loss of angular momentum., CV evolution is driven by the gradual loss of angular momentum.574 As the Roche lobe around the secoudary star sluiuks. matter is transferred to the white dwarf. giving rise to the rich observed pheuoimenology.," As the Roche lobe around the secondary star shrinks, matter is transferred to the white dwarf, giving rise to the rich observed phenomenology."575 The mass trausfer rate is observed to decline with declining orbital period 1981).. so there should be a prepo[undlerauce of short-period. slowly-evolving CVs. unless short-period CVs are somehow destroyed (Patterson1998. cliscusses these issues vividly).," The mass transfer rate is observed to decline with declining orbital period \citep{patterson84}, so there should be a preponderance of short-period, slowly-evolving CVs, unless short-period CVs are somehow destroyed \citealt{patlate98} discusses these issues vividly)."576 In adclition. (1986) suggest that old novae ‘hibernate’. that is. render themselves faint and iucouspicuous by lacing iuto exteuded states of little or no mass trausler between nova outbursts.," In addition, \citet{shara86} suggest that old novae `hibernate', that is, render themselves faint and inconspicuous by fading into extended states of little or no mass transfer between nova outbursts."577 The closer au object is. the easier it is to discover. so representatives of these hard-to-find Classes would be expected to show up relatively nearby.," The closer an object is, the easier it is to discover, so representatives of these hard-to-find classes would be expected to show up relatively nearby."578 Sclhiwopeetal.(2002). sumunarize the properties of CVs discovered in the ROSAT bright source (RBS) survey., \citet{rbsid} summarize the properties of CVs discovered in the ROSAT bright source (RBS) survey.579 The RBS was a program to identify optical counterparts of more than 2000 of the brightest X-ray sources. CLR>0.2 detected at high latitudes (|b]> 307) during the ROSAT all-sky survey.," The RBS was a program to identify optical counterparts of more than 2000 of the brightest X-ray sources, $CR > 0.2$ $^{-1}$, detected at high latitudes $|b| > 30\degr$ ) during the ROSAT all-sky survey."580 The optical spectrum of oue of these. since namec V105 Peg (Ixazarovetsetal. 2006).. shows a stroug contribution [rom au M-type secondary.," The optical spectrum of one of these, since named V405 Peg \citep{namelist78}, , shows a strong contribution from an M-type secondary."581 This led Sclhiwopeetal.(2002) to suggest it was eitlier a syimbiotic-like object or a CV:for the latter case they estimated a distance of ouly 30 pc., This led \citet{rbsid} to suggest it was either a symbiotic-like object or a CV;for the latter case they estimated a distance of only 30 pc.582 Ixato&Yamaoka(2002) estimated a proper motion of 69—£12 milli-aresee (mas) + from catalog positions. which coustrains the distance to <300 pe for transverse velocity ο<100 kms !.," \citet{kato-rbs1955} estimated a proper motion of $69 \pm 12$ milli-arcsec (mas) $^{-1}$ from catalog positions, which constrains the distance to $< 300$ pc for transverse velocity $v_t < 100$ km $^{-1}$."583 A 30 pe distance would make V105 Pee the nearest known CV. and would suggest that a large space deusity of such objects remains uucetected.," A 30 pc distance would make V405 Peg the nearest known CV, and would suggest that a large space density of such objects remains undetected."584 We therefore observed this object to find its orbital period. explore its uature. ancl constrain its distance.," We therefore observed this object to find its orbital period, explore its nature, and constrain its distance."585 We obtained spectra at the 2.lin Hiltuer telescope at MDM Observatory on Ixitt Peak. using the moctlar spectrograph.," We obtained spectra at the 2.4m Hiltner telescope at MDM Observatory on Kitt Peak, using the modular spectrograph."586 Most of the spectra are from 2002 October. with sparser coverage curing other observing runs extending up to 2005 September (see Table 1}.," Most of the spectra are from 2002 October, with sparser coverage during other observing runs extending up to 2005 September (see Table 1)."587 The instrument configuration and protocols were as described iu Thorsteuseuetal.(1998):: briefly. the setup yielded 2," The instrument configuration and protocols were as described in \citet{t98}; briefly, the setup yielded 2"588 The instrument configuration and protocols were as described iu Thorsteuseuetal.(1998):: briefly. the setup yielded 2A," The instrument configuration and protocols were as described in \citet{t98}; briefly, the setup yielded 2"589When studying the properties and evolution of galaxies it is necessary to have a proper census of all types of galaxies.,When studying the properties and evolution of galaxies it is necessary to have a proper census of all types of galaxies.590 Deep photographie surveys have shown the existence of a large number of galaxies with surface brightnesses much fainter than the night sky., Deep photographic surveys have shown the existence of a large number of galaxies with surface brightnesses much fainter than the night sky.591 The severe selection effects caused by the brightness of the night sky ensures that these galaxies are very much under-represented in conventional galaxy catalogs., The severe selection effects caused by the brightness of the night sky ensures that these galaxies are very much under-represented in conventional galaxy catalogs.592 However. in the last 20 years it has become clear that these low surface brightness (LSB) galaxies may constitute à major fraction of the total galaxy population.," However, in the last 20 years it has become clear that these low surface brightness (LSB) galaxies may constitute a major fraction of the total galaxy population."593 Clearly. LSB galaxies show us an alternative path of galaxy evolution which does not lead to the classical Hubble sequence and offer us a new window onto galaxy evolution (Impey Bothun 1907:: Bothun et al. 1997)).," Clearly, LSB galaxies show us an alternative path of galaxy evolution which does not lead to the classical Hubble sequence and offer us a new window onto galaxy evolution (Impey Bothun \cite{impey}; Bothun et al. \cite{bothun}) )."594 Most of the LSB galaxies investigated in any detail are either late-type and disk dominated (de Blok et al. 1995.. ," Most of the LSB galaxies investigated in any detail are either late-type and disk dominated (de Blok et al. \cite{de blok et al},"595hereafter dB95;: MeGaugh Bothun 1994)). or giant. Malin-]-like galaxies (Sprayberry et al. 1995:;," hereafter dB95; McGaugh Bothun \cite{mc gaugh}) ), or giant, Malin-1-like galaxies (Sprayberry et al. \cite{sprayberry};"596 Pickering et al. 1997))., Pickering et al. \cite{pickering}) ).597 The disk dominated LSB galaxies have only small traces of star formation (de Blok et al., The disk dominated LSB galaxies have only small traces of star formation (de Blok et al.598 1996aa). are very gas-rich (de Blok et al.," \cite{db}a a), are very gas-rich (de Blok et al."599 1996bb). and appear quite unevolved (van der Hulst et al. 1993)).," \cite{db2}b b), and appear quite unevolved (van der Hulst et al. \cite{vdhulst}) )."600 The masses are a few times 10°A. (de Blok et al., The masses are a few times $10^9 M_{\odot}$ (de Blok et al.601 1996bb) and the surface densities are usually close to the critical density for star formation (van der Hulst et al. 1993::, \cite{db2}b b) and the surface densities are usually close to the critical density for star formation (van der Hulst et al. \cite{vdhulst};602 de Blok et al., de Blok et al.603 1996bb: Kennicutt 1989))., \cite{db2}b b; Kennicutt \cite{kennicutt}) ).604 They also have color gradients. the outer parts of the disks are bluer than the inner parts.," They also have color gradients, the outer parts of the disks are bluer than the inner parts."605 Apart from this the LSB galaxies investigated by de Blok. MeGaugh and van der Hulst tend to be bluer than classical Hubble sequence HSB galaxies.," Apart from this the LSB galaxies investigated by de Blok, McGaugh and van der Hulst tend to be bluer than classical Hubble sequence HSB galaxies."606 There has been some discussion on whether this was an intrinsic property of LSB galaxies or yet another selection effect. due to the blue-sensitive plates used for the LSB surveys.," There has been some discussion on whether this was an intrinsic property of LSB galaxies or yet another selection effect, due to the blue-sensitive plates used for the LSB surveys."607 The discovery of a large number of red LSB galaxies (ONeil et al. 1997)), The discovery of a large number of red LSB galaxies (O'Neil et al. \cite{o'neil}) )608 showed that there is also a red > 0.9) component of the LSB population., showed that there is also a red $>$ 0.9) component of the LSB population.609 The continuous range of colors from the very blue to the very red clearly shows that LSB galaxies define a wide range of evolutionary states., The continuous range of colors from the very blue to the very red clearly shows that LSB galaxies define a wide range of evolutionary states.610" The fact that most LSB galaxies discovered so far are either bulgeless. late-type ""normal-sized"" galaxies or giant galaxies with a significant bulge component. raises the question whether there are any ""normal-sized"". bulge dominated LSB galaxies."," The fact that most LSB galaxies discovered so far are either bulgeless, late-type “normal-sized” galaxies or giant galaxies with a significant bulge component, raises the question whether there are any “normal-sized”, bulge dominated LSB galaxies."611 Are there LSB galaxies with disks with scale lengths of a few kpe and a low surface brightness that have a significant bulge component?, Are there LSB galaxies with disks with scale lengths of a few kpc and a low surface brightness that have a significant bulge component?612 If these galaxies do indeed exist then the fact that they are not turning up in LSB galaxy surveys can only mean that there are severe selection effects against them. or that we already found them and included them in our catalogs.," If these galaxies do indeed exist then the fact that they are not turning up in LSB galaxy surveys can only mean that there are severe selection effects against them, or that we already found them and included them in our catalogs."613 Because of their obvious bulge components it is hard to see which of the known selection effects could make us very much biased against them., Because of their obvious bulge components it is hard to see which of the known selection effects could make us very much biased against them.614 We have therefore assumed that at least a fraction of the bulge dominated LSB galaxies, We have therefore assumed that at least a fraction of the bulge dominated LSB galaxies615close to estimate.,close to Bondi-Hoyle estimate.616 In Fig. we Bondi-Hoyle," In Fig. \ref{fig:miratime},"617"show the density contours for a binary separation of [I0],70AU for several values of the dust formation radius where the wind is accelerated.", we show the density contours for a binary separation of $70 \mathrm{AU}$ for several values of the dust formation radius where the wind is accelerated.618 In these simulations we include the full gravity of the primary., In these simulations we include the full gravity of the primary.619 For a dust formation radius of 5AU the wind geometry is almost spherical., For a dust formation radius of $5 \mathrm{AU}$ the wind geometry is almost spherical.620 A bow shock forms as the wind is decelerated by the gravity from the companion and the accretion ratio is close to the Bondi-Hoyle value., A bow shock forms as the wind is decelerated by the gravity from the companion and the accretion ratio is close to the Bondi-Hoyle value.621 A small accretion disk is formed around the secondary., A small accretion disk is formed around the secondary.622 As we move the dust formation radius outwards the temperature for dust condensation decreases according to Fig , As we move the dust formation radius outwards the temperature for dust condensation decreases according to Fig \ref{fig:wind_temp}.623When we place the dust formation radius at 10AU the flow 5].structure is clearly elongated and the accretion rates are a few times larger than the Bondi-Hoyle theoretical estimate., When we place the dust formation radius at $10 \mathrm{AU}$ the flow structure is clearly elongated and the accretion rates are a few times larger than the Bondi-Hoyle theoretical estimate.624 This is consistent with, This is consistent with625With the discovery of the first ‘millisecond’ pulsar. B1937+21 (P=1.56 ms: Backeretal. 1982)). it became clear that neutron stars can achieve very rapid rotation rates.,"With the discovery of the first `millisecond' pulsar, B1937+21 $P=1.56$ ms; \citealt{bkh+82}) ), it became clear that neutron stars can achieve very rapid rotation rates."626 This period is close to but still somewhat greater than the minimum rotation period for a neutron star. below which the star becomes unstable to mass shedding at the equator (see e.g. Cook.Shapiro.&Teukolsky 1994)).," This period is close to but still somewhat greater than the minimum rotation period for a neutron star, below which the star becomes unstable to mass shedding at the equator (see e.g. \citealt{cst94}) )."627 Various equations of state have been proposed for nuclear matter and due to the differences in density under such equations. the limiting spin period of neutron stars depends on the choice of equation of state.," Various equations of state have been proposed for nuclear matter and due to the differences in density under such equations, the limiting spin period of neutron stars depends on the choice of equation of state."628 The discovery of a pulsar with P<1 ms would be of great value in eliminating potential equations of state., The discovery of a pulsar with $P < 1$ ms would be of great value in eliminating potential equations of state.629 The distribution of periods of known pulsars cuts off quite sharply below about P=2 ms. however it is not clear whether this cut-off is intrinsic to the pulsar population (see Lorimeretal. 1996)).," The distribution of periods of known pulsars cuts off quite sharply below about $P=2$ ms, however it is not clear whether this cut-off is intrinsic to the pulsar population (see \citealt{llb+96}) )."630 Most previous pulsar surveys had a time resolution of ~300 jus for nearby pulsars. resulting in a strong decline in sensitivity for periods less than a few milliseconds. indicating that the short-period cut-off may in fact be a selection effect.," Most previous pulsar surveys had a time resolution of $\sim 300$ $\mu$ s for nearby pulsars, resulting in a strong decline in sensitivity for periods less than a few milliseconds, indicating that the short-period cut-off may in fact be a selection effect."631 The only effective way to answer this question is to conduct surveys with sufficient time resolution to be well-sensitive to pulsars with P«| ms. and preferably with a flat sensitivity response to periods well below a millisecond in order to eliminate any bias towards longer pulse periods.," The only effective way to answer this question is to conduct surveys with sufficient time resolution to be well-sensitive to pulsars with $P <6321$ ms, and preferably with a flat sensitivity response to periods well below a millisecond in order to eliminate any bias towards longer pulse periods."633 For a traditional analog filterbank system this would require a large number of channels with fast sampling and would involve considerable cost., For a traditional analog filterbank system this would require a large number of channels with fast sampling and would involve considerable cost.634 An alternative is to record the raw receiver voltages at baseband and to perform all frequeney decimation and detection in software for the best possible time and frequency resolution., An alternative is to record the raw receiver voltages at baseband and to perform all frequency decimation and detection in software for the best possible time and frequency resolution.635 Until recently this approach has been little used due to the formidable data storage and processing requirements. however the rapid development that has occured in these areas in the last decade means that the required hardware is now relatively affordable.," Until recently this approach has been little used due to the formidable data storage and processing requirements, however the rapid development that has occured in these areas in the last decade means that the required hardware is now relatively affordable."636 We report here for the first time the use of baseband processing in a pulsar survey., We report here for the first time the use of baseband processing in a pulsar survey.637 Historically approximately half of all millisecond pulsar discoveries Were made in Globular clusters. with most of the remainders found in large scale surveys of the Galaxy.," Historically approximately half of all millisecond pulsar discoveries were made in Globular clusters, with most of the remainders found in large scale surveys of the Galaxy."638 Since the cores of most Globular clusters are easily contained in a single telescope beam for low to intermediate observing frequencies. globular cluster searches are very efficient in their return of millisecond pulsars for observing campaigns of limited duration.," Since the cores of most Globular clusters are easily contained in a single telescope beam for low to intermediate observing frequencies, globular cluster searches are very efficient in their return of millisecond pulsars for observing campaigns of limited duration."639 Due to the large amounts of data to be processed from observations of high time and frequency resolution. globular clusters are a logical place to begin the search for sub-millisecond pulsars.," Due to the large amounts of data to be processed from observations of high time and frequency resolution, globular clusters are a logical place to begin the search for sub-millisecond pulsars."640 We conducted several observations of each of 19 southern globular clusters with the CPSR baseband recording system (vanStraten.Britton.&Bailes2000) at the Parkes radio telescope., We conducted several observations of each of 19 southern globular clusters with the CPSR baseband recording system \citep{vbb00} at the Parkes radio telescope.641 This paper describes the searches and their results., This paper describes the searches and their results.642 In an observing run of four days from 2000 March 17-20 we conducted observations of 19 southern Galactic globular pulsars with the Parkes 64-m radio telescope., In an observing run of four days from 2000 March 17–20 we conducted observations of 19 southern Galactic globular pulsars with the Parkes 64-m radio telescope.643 The signals from two orthogonal linear polarizations of the 50-cm receiver were mixed to baseband in a quadrature down-convertor and filtered to provide a 20 MHz band centered at a sky frequency of 660 MHz., The signals from two orthogonal linear polarizations of the 50-cm receiver were mixed to baseband in a quadrature down-convertor and filtered to provide a 20 MHz band centered at a sky frequency of 660 MHz.644 The in-phase and quadrature components in each polarization were 2-bit sampled at a sample rate of 20 Msamples s! in accordance with the Nyquist theorem for complete description of the band-limited signal., The in-phase and quadrature components in each polarization were 2-bit sampled at a sample rate of 20 Msamples $^{-1}$ in accordance with the Nyquist theorem for complete description of the band-limited signal.645 Sampler thresholds were set at the beginning of the observation in accordance with the prescriptions of (Jenet&Anderson1998) and were held at these values for the duration of each observation., Sampler thresholds were set at the beginning of the observation in accordance with the prescriptions of \citep{ja98} and were held at these values for the duration of each observation.646 The resultant data stream had a bit-rate of 160 Mbit s! and was written in segments of ~53.7 s (corresponding to | GB of data) to DLT 7000 tapes., The resultant data stream had a bit-rate of 160 Mbit $^{-1}$ and was written in segments of $\sim53.7$ s (corresponding to 1 GB of data) to DLT 7000 tapes.647 The recording system consisted of four DLT 7000 drives. a large disk array and a Sun Ultra 60 workstation and in conjunction with the down-conversion and sampling systems is known as the Caltech-Parkes-Swinburne Recorder (CPSR) (van Straten.. in preparation).," The recording system consisted of four DLT 7000 drives, a large disk array and a Sun Ultra 60 workstation and in conjunction with the down-conversion and sampling systems is known as the Caltech-Parkes-Swinburne Recorder (CPSR) (van Straten, in preparation)."648 A total of 55 observations of 30 minutes? duration each were recorded. resulting in a 1.8 TB data-set.," A total of 55 observations of 30 minutes' duration each were recorded, resulting in a 1.8 TB data-set."649 The observations were processed on the 64-node Swinburne workstation cluster., The observations were processed on the 64-node Swinburne workstation cluster.650 Each observation could be processed by one of the schemes described below in about 12 hours using 12 500 MHz Compaq EV6 processors., Each observation could be processed by one of the schemes described below in about 12 hours using 12 500 MHz Compaq EV6 processors.651 Tapes were unloaded to a 1-TB RAID array to facilitate the reassembly of full, Tapes were unloaded to a 1-TB RAID array to facilitate the reassembly of full652Figure 3.,Figure 3.653 z=0.1 and z=1.1 sections of a chaotic trajectory associated with the dynamical system defined by the invariant distribution and the 1-form(3., $z=0.1$ and $z=1.1$ sections of a chaotic trajectory associated with the dynamical system defined by the invariant distribution and the 1-form.654"25).. Consider the invariant polynomial probability distribution up to a normalization factor, in the region where are all positive, with p=0 elsewhere."," Consider the invariant polynomial probability distribution up to a normalization factor, in the region where are all positive, with $\rho=0$ elsewhere."655" To uniquely specify a corresponding dynamical system, we choose a two-form"," To uniquely specify a corresponding dynamical system, we choose a two-form"656shorteitekau03e have been adopted and only galaxies with redshifts in the range 0.0350.10 have been plotted: the lowest redshifts are excluded because aperture corrections are substantial. whilst beyond :0.1 the sensitivity to emission lines is low. hampering classification by emission-line diagnostics.,"\\shortcite{kau03c} have been adopted and only galaxies with redshifts in the range $0.03 \le z \le 0.10$ have been plotted; the lowest redshifts are excluded because aperture corrections are substantial, whilst beyond $z=0.1$ the sensitivity to emission lines is low, hampering classification by emission–line diagnostics."657 Radi luminosities have been calculated from the fluxes assuming a radi spectral index of 0.7., Radio luminosities have been calculated from the fluxes assuming a radio spectral index of 0.7.658 Overlaid on this are theoretical predictions. derived using t Bruzual Charlot (2) stellar synthesis models. for the location of galaxies with different star formation histories.," Overlaid on this are theoretical predictions, derived using the Bruzual Charlot \shortcite{bru03} stellar synthesis models, for the location of galaxies with different star formation histories."659 For these models. the radio luminosities have been calculated using the prescription of Hopkins shorteitehopOl:: L446g;LsJOGER/AL.\WHHz +. where SFR is the average star formation rate in the past 10 years.," For these models, the radio luminosities have been calculated using the prescription of Hopkins \\shortcite{hop01}: $L_{\rm 1.4GHz} = 1.8 \times 10^{21} ({\rm660SFR}/M_{\odot})$ $^{-1}$, where SFR is the average star formation rate in the past $10^8$ years."661 Three of the models are for galaxies with exponentially-decaying star formation rates. of characteristic timescales 1.3 and 5 Gyrs: the tracks indicate how these galaxies move across this plane as they age.," Three of the models are for galaxies with exponentially–decaying star formation rates, of characteristic timescales 1,3 and 5 Gyrs; the tracks indicate how these galaxies move across this plane as they age."662 A fourth model shows the track for a galaxy with a constant star formation rate., A fourth model shows the track for a galaxy with a constant star formation rate.663 Two further models consider an old Ον) galaxy which has undergone a recent burst of star formation (10 and 10 years ago). as might be the case for à merger-triggered event.," Two further models consider an old Gyr) galaxy which has undergone a recent burst of star formation $10^7$ and $10^8$ years ago), as might be the case for a merger-triggered event."664 Here. the loci of the tracks show what happens if different fractions of the total galaxy mass are converted into stars in the burst.," Here, the loci of the tracks show what happens if different fractions of the total galaxy mass are converted into stars in the burst."665 These theoretical tracks largely cover the location of the data points., These theoretical tracks largely cover the location of the data points.666 The middle left panel of Figure 9 shows the same plot. but now includes all radio-emitting galaxies in this redshift range.," The middle left panel of Figure \ref{sfagncut} shows the same plot, but now includes all radio–emitting galaxies in this redshift range."667 The different colours represent different galaxy classifications based upon their locations in the BPT diagram (black — star forming galaxy: red — composite systems with both star formation and an AGN: orange — Seyfert AGN: green — LINER AGN: purple —, The different colours represent different galaxy classifications based upon their locations in the BPT diagram (black – star forming galaxy; red – composite systems with both star formation and an AGN; orange – Seyfert AGN; green – LINER AGN; purple –668The shape of the initial mass function. (LAIP) is. well established and. constrained for stars greater than O.5AL..,The shape of the initial mass function (IMF) is well established and constrained for stars greater than $M_{\sun}$.669 In comparison. determining the low mass part of the IME. particularly in the substellar regime below 70.0844;. has proven more challenging.," In comparison, determining the low mass part of the IMF, particularly in the substellar regime below $\sim $ $M_{\sun}$, has proven more challenging."670 In this mass range. the mass function may be allectec by turbulent fragmentation. dvnamical interactions. [fragmentation of massive disks. photo-crosion of cores or other processes. (see reviews by Whitworthetal.(2007):Bonnellοἱ (2007))).," In this mass range, the mass function may be affected by turbulent fragmentation, dynamical interactions, fragmentation of massive disks, photo-erosion of cores or other processes (see reviews by \citet{whi07,bon07}) )."671 Hence. in some theoretical scenarios. there could be wide variations in the form of the EME below about 0.337; depending on the environment.," Hence, in some theoretical scenarios, there could be wide variations in the form of the IMF below about $M_{\sun}$ depending on the environment."672 To test these ideas. it is essential to carry out surveys for brown cwarfs in civerse environments.," To test these ideas, it is essential to carry out surveys for brown dwarfs in diverse environments."673 Brown ενας are dillicult to observe because. they cool down rapidlv with age., Brown dwarfs are difficult to observe because they cool down rapidly with age.674 After 1 Myr a very. low-mass star near the hydrogen burning boundary. will have a luminosity only slightly greater than that of the highest mass brown να but after. 1 Gyr the brown cwarl will have a luminosity an order of magnitude below the star (Oppenheimeretal.1999).," After 1 Myr a very low-mass star near the hydrogen burning boundary will have a luminosity only slightly greater than that of the highest mass brown dwarf, but after 1 Gyr the brown dwarf will have a luminosity an order of magnitude below the star \citep{opp99}."675.. Because of their low temperatures and Luminosity. searching for then is best done in the near infra-red in nearby. young open clusters and star forming regions.," Because of their low temperatures and luminosity, searching for them is best done in the near infra-red in nearby young open clusters and star forming regions."676 The availability of wide-field near-infrared surveys such as 2ALASS and UlXIDSS thus greatly facilitates searches for substellar objects., The availability of wide-field near-infrared surveys such as 2MASS and UKIDSS thus greatly facilitates searches for substellar objects.677 Most nearby star forming regions have been searched for own cdwarfs over the past decade (see review by Luhmanetal. (2007)))., Most nearby star forming regions have been searched for brown dwarfs over the past decade (see review by \citet{luh07}) ).678 In some clusters. the surveys have revealed a population of objects with masses below the Deuterium runing limit of AL. (ZapteroOsorioetal.2000:Lucas&Roche 2000).," In some clusters, the surveys have revealed a population of objects with masses below the Deuterium burning limit of $M_{\sun}$ \citep{zap00,lar00}."679. The ratio between the number of low-mass stars (O.0S-L.04A/.) and the number of brown cwarfs ALI) an empirical constraint on the IME has been determined to be between 3.3 and 8.5 (Andersenetal.2008) and in one region 1540.3 (Scholzetal.2009).," The ratio between the number of low-mass stars $\,M_{\sun}$ ) and the number of brown dwarfs $\,M_{\sun}$ ) – an empirical constraint on the IMF – has been determined to be between 3.3 and 8.5 \citep{and08} and in one region $\pm$ 0.3 \citep{sch09}."680. This might » à first indication for environmental elfects on the LAL., This might be a first indication for environmental effects on the IMF.681 As of today. the brown να surveys in star forming regions suller from two problems: a) The surveys are incomplete at the low mass end. primarily cue to strong anc variable extinction in the molecular clouds.," As of today, the brown dwarf surveys in star forming regions suffer from two problems: a) The surveys are incomplete at the low mass end, primarily due to strong and variable extinction in the molecular clouds."682 b) Most nearby star forming regions are rather similar in their physica characteres. lor example. most of them do not. harbour massive stars.," b) Most nearby star forming regions are rather similar in their physical characterics, for example, most of them do not harbour massive stars."683 Llere we report on a new brown dwarf survey in a part of the Upper Scorpius (hereafter UpSco) star forming region., Here we report on a new brown dwarf survey in a part of the Upper Scorpius (hereafter UpSco) star forming region.684 UpSco is a favorable area for such a project. because i sullers from negligible extinction.," UpSco is a favorable area for such a project, because it suffers from negligible extinction."685 At a distance of 145+ 2pc (cleZeeuwctal.1999). it is the nearest OB assocation. ancl it represents our best chance of constraining the impac of massive stars on the formation of very low mass objects.," At a distance of $145\pm2$ pc \citep{dez99} it is the nearest OB assocation, and it represents our best chance of constraining the impact of massive stars on the formation of very low mass objects."686 With an age of about 5 Myr (Preibischetal.2002). UpSco is the voungest part of the Scorpius Centaurus Association. i.c.," With an age of about 5 Myr \citep{pre02} UpSco is the youngest part of the Scorpius Centaurus Association, i.e."687distribution of the low-redshift Ίο clouds.,distribution of the low-redshift $\alpha$ clouds.688 It secius likely that future studies lav uncover valuable information about their counectiou to large-scale structure and to the processes of galaxy formation aud evolution., It seems likely that future studies may uncover valuable information about their connection to large-scale structure and to the processes of galaxy formation and evolution.689keV. Therefore. we compared (he azimuthally averaged radial profiles of (hese sources in (his energv range wilh PSFs evaluated at. 1.0 keV. This comparison (Figure 4)) shows that the soft. N-ray emission is unresolved or. at best. marginally resolved.,"keV. Therefore, we compared the azimuthally averaged radial profiles of these sources in this energy range with PSFs evaluated at 1.0 keV. This comparison (Figure \ref{fig:psf}) ) shows that the soft X-ray emission is unresolved or, at best, marginally resolved."690 Most of the remaining 10 sources appear to be unresolved. with the exceptions of and F17208-0014.," Most of the remaining 10 sources appear to be unresolved, with the exceptions of F16090-0139 and F17208-0014."691 E16090-0139 appears to be extended in the NWSE direction., F16090-0139 appears to be extended in the NW–SE direction.692 Its linear extent is approximately 8.2 kpe (3200)., Its linear extent is approximately 8.2 kpc 0).693 F17208-0014 seems to be resolved with a linear diameter of approximately 5.2 kpe (6722)., F17208-0014 seems to be resolved with a linear diameter of approximately 5.2 kpc 2).694 The upper limits to the linear sizes of the rest of the sources fall in (he range of 0.56.3 kpc., The upper limits to the linear sizes of the rest of the sources fall in the range of 0.5–6.3 kpc.695 It is not surprising that FOL5S72+0009 and Z11598-0112 are bright X-ray sources: they are the only (wpe 1 Sevlerts in our sample., It is not surprising that F01572+0009 and Z11598-0112 are bright X-ray sources: they are the only type 1 Seyferts in our sample.696 Using the 15 counts per bin data. one can use V statistics (to evaluate models of the continuum emission of these sources.," Using the 15 counts per bin data, one can use $\chi^2$ statistics to evaluate models of the continuum emission of these sources."697 The spectra were [ist modeled with single power laws., The spectra were first modeled with single power laws.698 Due to the high flix of the soft component and consequently (the high signal-to-noise ratio in the soft enerey bins. such single power law models underestimate the flux in the hard energy band.," Due to the high flux of the soft component and consequently the high signal-to-noise ratio in the soft energy bins, such single power law models underestimate the flux in the hard energy band."699 Therefore. a two component model was needed (to describe (he continuum spectra: a hard power law and a soft. component represented by another power law or a MEINAL model were used.," Therefore, a two component model was needed to describe the continuum spectra: a hard power law and a soft component represented by another power law or a MEKAL model were used."700 If most of the flux in the soft band is produced by starbursts. then the soft band flux could plausibly be represented bv à MEIXAL model (for a hot diffuse gas).," If most of the flux in the soft band is produced by starbursts, then the soft band flux could plausibly be represented by a MEKAL model (for a hot diffuse gas)."701 The results of our modeling are listed in Table 3.. and the spectrum and the double power law model of FOL572+0009 are shown in Figure 5..," The results of our modeling are listed in Table \ref{tab:fits}, and the spectrum and the double power law model of F01572+0009 are shown in Figure \ref{fig:f01572}."702 The 3 counts per bin data were used to determine if there are weak emission lines in the spectra., The 3 counts per bin data were used to determine if there are weak emission lines in the spectra.703 The continua of the data were first modeled using (wo power laws., The continua of the data were first modeled using two power laws.704 The spectral indices from these fits are consistent with those obtained from binning the data to at least 15 counts per bin and using X7 statistics (see Table 3))., The spectral indices from these fits are consistent with those obtained from binning the data to at least 15 counts per bin and using $\chi^2$ statistics (see Table \ref{tab:fits}) ).705 This agreement indicates (hat binning the data to at least 2 counts per bin did not introduce any biases., This agreement indicates that binning the data to at least 3 counts per bin did not introduce any biases.706 The FO1572+0009 spectrum shows an excess above (he power law continuum al around 6.0 keV (Figure 5)). but (his suggestion of an emission line(s) is not significant.," The F01572+0009 spectrum shows an excess above the power law continuum at around 6.0 keV (Figure \ref{fig:f01572}) ), but this suggestion of an emission line(s) is not significant."707 The spectrum of Z11595-0112 has a possible emission line al an energy consistent with redshifted Fe Ίνα (Figure 6))., The spectrum of Z11598-0112 has a possible emission line at an energy consistent with redshifted Fe $\alpha$ (Figure \ref{fig:z11598}) ).708 We modeled the spectrum with a double power law as we had previously done with the 15 counts per bin data., We modeled the spectrum with a double power law as we had previously done with the 15 counts per bin data.709 Then a narrow Gaussian feature was added to the continuum to represent (he emission line., Then a narrow Gaussian feature was added to the continuum to represent the emission line.710 Using the οσα statistics option in NSPEC. the best fit model suggests that the line is located al a rest energv of 7.0 keV with an equivalent. width of iz keV (Table 3)).," Using the c-stat statistics option in XSPEC, the best fit model suggests that the line is located at a rest energy of 7.0 keV with an equivalent width of $^{+1.2}_{-0.7}$ keV (Table \ref{tab:fits}) )."711that in the Ας Way. but comparable to those fomnd in ULIRGs.,"that in the Milky Way, but comparable to those found in ULIRGs."712 In contrast. we find a characteristic deusity. pocdU P. which is lower than seen in ULIRGs. but comparable to values seen iu local star-forming galaxies and nuclei. as well as a πα nuuber of high-redshift systems where similar measurcments have been made.," In contrast, we find a characteristic density, $n\sim 10^{3}$ $^{-3}$, which is lower than seen in ULIRGs, but comparable to values seen in local star-forming galaxies and nuclei, as well as a small number of high-redshift systems where similar measurements have been made."713 Together these results sugeest that SMMEJJ2135 has a SFR intensity similar to that seen im local ULIRCs. but distributed over a larger vole.," Together these results suggest that J2135 has a SFR intensity similar to that seen in local ULIRGs, but distributed over a larger volume."714 This is consistent with the ~2-kpe distribution of star formation across this ealaxv (7) and previous suggestions of extended star formation in SMGs (e.g.?).., This is consistent with the $\sim$ 2-kpc distribution of star formation across this galaxy \citep[][]{swinbank10a} and previous suggestions of extended star formation in SMGs \citep[e.g.][]{biggs08}.715 Qur results show that SPIRE's FTS has the ability to measure the redshifts of suitably brielt aud distant. obscured galaxies via detection of atomic cooling lines such as [Cu].," Our results show that SPIRE's FTS has the ability to measure the redshifts of suitably bright and distant, obscured galaxies via detection of atomic cooling lines such as ."716 However. we estimate that z10-hr iutegratious will be required and this is not compctitive with blind. eround-based CO-line searches (ee.7). as evidenced by the ease with which the redshift of SAMALII2135 was determined using Zpectrometer on the Green Baul Telescope (?)..," However, we estimate that $\gs$ 10-hr integrations will be required and this is not competitive with blind, ground-based CO-line searches \citep[e.g.][]{weiss09}, as evidenced by the ease with which the redshift of J2135 was determined using Zpectrometer on the Green Bank Telescope \citep{swinbank10a}."717 Nevertheless. our results show that facilities such asZFerschel aud SCUBA-2 will allow detailed study of the integrated properties of ligh-redshift galaxies (through SED modelling). as wellas the chenustry of their ISM.," Nevertheless, our results show that facilities such as and SCUBA-2 will allow detailed study of the integrated properties of high-redshift galaxies (through SED modelling), as wellas the chemistry of their ISM."718llere. we prove that the estimator (7)) wilh weights ως and V. eiven by (8)) and (9)) is unbiased.,"Here, we prove that the estimator \ref{eqn:estimator}) ) with weights $\omega_\mathbf{x}$ and $V$ given by \ref{eqn:w}) ) and \ref{eqn:V}) ) is unbiased."719 Let £ represent the lines of sight. 9D4(x.) denote a shell with center x. radius h and thickness A.," Let $L$ represent the lines of sight, $\delta B_\Delta720(\mathbf{x}, h)$ denote a shell with center $\mathbf{x}$, radius $h$ and thickness $\Delta$ ."721 We write (/.5) for the polar coordinates of vector h. |+ for Euclidean distance. area or volume depending on the context. 4=zd|L| for the volume probed by the lines of sight and 1;(x) for the indicator function. with 15(x)=Lib x€£ and 0 otlierwise.," We write $(h,\gamma)$ for the polar coordinates of vector $\mathbf{h}$, $|\cdot |$ for Euclidean distance, area or volume depending on the context, $A=\pi d^2 |L|$ for the volume probed by the lines of sight and $1_L(\mathbf{x})$ for the indicator function, with $1_L(\mathbf{x})=1$ if $\mathbf{x}\in L$ and 0 otherwise."722 Write f(x.y.z)=liliΑμ-XDlusaesj(z-XDlo(Zyxziextlyxl.|z—.Q)V(ly—x].[Zz2xi. Q)). where Q=[ay.as] represents the range ofangles between ay and a».," Write $f(\mathbf{x},\mathbf{y},\mathbf{z}) =7231_L(\mathbf{x})1_L(\mathbf{y})1_L(\mathbf{z})1_{(0,R_1]}724(|\mathbf{y}-\mathbf{x}|)1_{(R_2,R_3]}(|\mathbf{z}-\mathbf{x}|)7251_\Omega(\angle \mathbf{yxz})726\omega_\mathbf{x}(|\mathbf{y}-\mathbf{x}|,|\mathbf{z}-\mathbf{x}|,\Omega)727V(|\mathbf{y}-\mathbf{x}|, |\mathbf{z}-\mathbf{x}|, \Omega))$ , where $\Omega = [\alpha_1, \alpha_2]$ represents the range ofangles between $\alpha_1$ and $\alpha_2$."728 Then the estimator in (7)) is 5°f[(x.y.z). with In the first equality above. we have expressed g@! in terms of three vector quantities x.X--h and x--k.," Then the estimator in \ref{eqn:estimator}) ) is $\sum_{\mathbf{x}\ne \mathbf{y}\ne \mathbf{z}}729f(\mathbf{x},\mathbf{y},\mathbf{z})$, with In the first equality above, we have expressed $g^{(3)}$ in terms of three vector quantities $\mathbf{x}, \mathbf{x}+\mathbf{h}$ and $\mathbf{x}+\mathbf{k}$ ."730 Il stationarity is assumed. the specilication of x in g is redundant.," If stationarity is assumed, the specification of $\mathbf{x}$ in $g^{(3)}$ is redundant."731 Thus we have removed the dependenceon x in g3) in the next line., Thus we have removed the dependenceon $\mathbf{x}$ in $g^{(3)}$ in the next line.732 We have also expressed h and k in polar coordinates., We have also expressed $\mathbf{h}$ and $\mathbf{k}$ in polar coordinates.733 Now. with the further assumption of isotropy. gh.k) depends onlv on the direction of h relative to K (or vice versa).," Now, with the further assumption of isotropy, $g^{(3)}(\mathbf{h},\mathbf{k})$ depends only on the direction of $\mathbf{h}$ relative to $\mathbf{k}$ (or vice versa)."734 This simplifies the expression above. so Chat where a denotesthe angle on the sphere relative to (. 2).," This simplifies the expression above, so that where $\alpha$ denotesthe angle on the sphere relative to $(k,\beta)$ ."735 Under the assumption that gU ds slowlyvarving over Q. the expression in the square bracket above is equal to," Under the assumption that $g^{(3)}$ is slowlyvarying over $\Omega$ , the expression in the square bracket above is equal to"736is 15 per cent that of unabsorbed QSOs (Pageetal.2004:Silvermanetal..2005:Pageal. 2006).. implving iat if all QSOs eo through an N-rav. absorbed. phase in reir evolution. this phase lasts only ~15 per cent as long as the unabsorbecl phase.,"is $\sim15$ per cent that of unabsorbed QSOs \citep{page04,silverman05,page06}, implying that if all QSOs go through an X-ray absorbed phase in their evolution, this phase lasts only $\sim15$ per cent as long as the unabsorbed phase."737 Vhese relative lifetimes may be a natural consequence of the high mass outflow rates in 1ο X-ray absorbed. QSOs: for the majority of our X-ray absorbed QSOs we estimate à mass outflow rate which is ~10 times higher than the accretion rate. implying that 1¢ Fuel supply will be depleted LO times faster in an X-ray absorbed QSO than in an unabsorbed QSO for the same accretion rate and fuel reservoir.," These relative lifetimes may be a natural consequence of the high mass outflow rates in the X-ray absorbed QSOs: for the majority of our X-ray absorbed QSOs we estimate a mass outflow rate which is $\sim10$ times higher than the accretion rate, implying that the fuel supply will be depleted 10 times faster in an X-ray absorbed QSO than in an unabsorbed QSO for the same accretion rate and fuel reservoir."738 However. this argument is more complicated if the two types of QSO [it within the evolutionary sequence discussed above. because in this case the fuel supply for an unabsorbed QSO will consist only of the fuel that remains after the X-ray absorbed phase.," However, this argument is more complicated if the two types of QSO fit within the evolutionary sequence discussed above, because in this case the fuel supply for an unabsorbed QSO will consist only of the fuel that remains after the X-ray absorbed phase."739 Nonetheless. if material is ejected. at  LO times the accretion rate for  15 per cent of the (X-ray absorbed | unabsorbed) QSO Lifetime. the total mass of material ejected by the QSO will be of the same order as that accreted.," Nonetheless, if material is ejected at $\sim$ 10 times the accretion rate for $\sim$ 15 per cent of the (X-ray absorbed + unabsorbed) QSO lifetime, the total mass of material ejected by the QSO will be of the same order as that accreted."740 The origin of the ionized. absorbing eas is then a fundamental issue for the physics of X-ray absorbed QSOs and their evolution.," The origin of the ionized, absorbing gas is then a fundamental issue for the physics of X-ray absorbed QSOs and their evolution."741 Assuming that N-rav absorbed QSOs have the usual AGN structure envisaged in. geometric unification schemes. the two obvious sources of material are the accretion disc and the clusty torus.," Assuming that X-ray absorbed QSOs have the usual AGN structure envisaged in geometric unification schemes, the two obvious sources of material are the accretion disc and the dusty torus."742 IH£ the wind is driven from the accretion disc. the ejeeted material niust xwss through the accretion disc during the X-ray absorbed hase: in this case it is dillieult to understand why this iippens on a timescale which is short compared. to the ifetime of the QSO.," If the wind is driven from the accretion disc, the ejected material must pass through the accretion disc during the X-ray absorbed phase; in this case it is difficult to understand why this happens on a timescale which is short compared to the lifetime of the QSO."743 On the other hand. if the ionized wind is driven from the torus then the timescale for the X-ray absorbed phase corresponds to the time required to erode he inner part of the torus ancl so enlarge substantially its opening angle: as shown by Ixrolik.&Ixriss.(2001) his timescale can be much shorter than the lifetime of he QSO.," On the other hand, if the ionized wind is driven from the torus then the timescale for the X-ray absorbed phase corresponds to the time required to erode the inner part of the torus and so enlarge substantially its opening angle; as shown by \citet{krolik01} this timescale can be much shorter than the lifetime of the QSO."744 For accretion at the Ecelington rate. the escape velocities at the distances of the inner edge of the torus (as eiven in Table 4)) are between 900 and 1500 1. and scale inversely with the square root of the accretion rate in I5ddington units.," For accretion at the Eddington rate, the escape velocities at the distances of the inner edge of the torus (as given in Table \ref{tab:physics}) ) are between 900 and 1500 $^{-1}$, and scale inversely with the square root of the accretion rate in Eddington units."745 Hence. of our X-ray absorbed: QSOs. only the BALQSO thas outllow velocities which are too high to plausibly oe associated with an outflow from the inner edge of the orus. implving an accretion disc origin for its outflow.," Hence, of our X-ray absorbed QSOs, only the BALQSO has outflow velocities which are too high to plausibly be associated with an outflow from the inner edge of the torus, implying an accretion disc origin for its outflow."746 Viable AGN feedback: models which reproduce the Alσ relation generally incorporate the feedback in the orm of kinetic energy. given to gas within the immediate (100 pe) environment of the AGN (e.g.Fabian.1999:2005:Llopkinsetal.2006:Sijacki 2007). which hen interacts with gas on a larger scale to terminate star ormation in the host spheroid.," Viable AGN feedback models which reproduce the $M-\sigma$ relation generally incorporate the feedback in the form of kinetic energy given to gas within the immediate $\sim$ 100 pc) environment of the AGN \citep[e.g. ][]{fabian99,granato04,dimatteo05,hopkins06,sijacki07}, which then interacts with gas on a larger scale to terminate star formation in the host spheroid."747 Lt is generally agreed that of order 5 per cent of the ACN radiative output must oe foc back as kinetic energy in order for the mocels to succeed (Silk&Rees.1998:WryitheLoeb.2003:DiMat-eo.Springel&Llernquist. 2005).," It is generally agreed that of order 5 per cent of the AGN radiative output must be fed back as kinetic energy in order for the models to succeed \citep{silk98,wyithe03,dimatteo05}."748. We can make a simple estimate for the kinetic energy. of the outllows compared o the radiative output of the N-rav absorbed. QSOs as ollows., We can make a simple estimate for the kinetic energy of the outflows compared to the radiative output of the X-ray absorbed QSOs as follows.749" We take the total energy. raciated during the X-rav absorbed phase to be fr=CAL where e is the racdiative cllicicney. ¢ is the speed. of light and AZ, is the mass accreted during the X-ray. absorbed. phase."," We take the total energy radiated during the X-ray absorbed phase to be $E_{T}=\epsilon M_{acc} c^{2}$ where $\epsilon$ is the radiative efficiency, $c$ is the speed of light and $M_{acc}$ is the mass accreted during the X-ray absorbed phase."750" The kinetic enerey built up by the outllow is £o=05M,07 where Alaa: is the mass supplied to the outflow during the X-ray absorbed phase and ο is the velocity of the outfTow.", The kinetic energy built up by the outflow is $E_{O}=0.5 M_{out} v^{2}$ where $M_{out}$ is the mass supplied to the outflow during the X-ray absorbed phase and $v$ is the velocity of the outflow.751 The fraction of the radiated output of the QSO which is fed. back to the surrounding gas as kinetic energv of the outllow is then [we take AlvaLAMm Mou Mouse~10 for the X-ray absorbed. phase (as we find for the majority of our X-ray absorbed QSOs). and a tvpical outflow velocity of SOOO kim + (see Table 2)). we obtain ος~4 per cent.," The fraction of the radiated output of the QSO which is fed back to the surrounding gas as kinetic energy of the outflow is then If we take $M_{out}/M_{acc} = $ $_{out}/$ $_{acc}\sim 10$ for the X-ray absorbed phase (as we find for the majority of our X-ray absorbed QSOs), and a typical outflow velocity of 8000 km $^{-1}$ (see Table \ref{tab:uvlines}) ), we obtain $E_{O}/E_{T} \sim 4$ per cent."752 The value of LeoIr so derived is independent of the radiative ellicieney e. because the c in Equation 6. cancels with that in Equation 5. [rom which AZ;/ ML is obtained.," The value of $E_{O}/E_{T}$ so derived is independent of the radiative efficiency $\epsilon$, because the $\epsilon$ in Equation \ref{eq:feedback} cancels with that in Equation \ref{eq:outflow} from which $_{out}/$ $_{acc}$ is obtained."753 On the other hand. the uncertainty on Moutf Mau is in truth Very laree (27 a factor of 10). depending on the unknown filling [actor f. and the square of the outllow velocity 0. which mav not be the same for the X-ray absorbing phase as the UN. absorber.," On the other hand, the uncertainty on $_{out}/$ $_{acc}$ is in truth very large $>$ a factor of 10), depending on the unknown filling factor $f$, and the square of the outflow velocity $v$, which may not be the same for the X-ray absorbing phase as the UV absorber."754 Nonetheless. Loflay4 per cent is quite consistent with the level of feedback required to terminate star formation and produce the Af@ relation. implving that the ionized outllows in N-ray. absorbed. QSOs could plausibly be the mechanism through which star formation is terminated in massive galaxies.," Nonetheless, $E_{O}/E_{T}755\sim 4$ per cent is quite consistent with the level of feedback required to terminate star formation and produce the $M-\sigma$ relation, implying that the ionized outflows in X-ray absorbed QSOs could plausibly be the mechanism through which star formation is terminated in massive galaxies."756 We have presented: X-ray spectra from EEPIC ancl rest-frame ultraviolet spectra from. based. telescopes for five X-ray absorbed. submillimetre-luminous QSOs.," We have presented X-ray spectra from EPIC and rest-frame ultraviolet spectra from ground-based telescopes for five X-ray absorbed, submillimetre-luminous QSOs."757 All five QSOs exhibit strong CLV absorption lines in their ultraviolet spectra with equivalent width 5A., All five QSOs exhibit strong IV absorption lines in their ultraviolet spectra with equivalent width $> 5$.758 Phe X-ray spectra can be modelled successfully in terms of 47. with either cole or ionized absorbers., The X-ray spectra can be modelled successfully in terms of $\chi^{2}$ with either cold or ionized absorbers.759 The cold. X-ray absorber mocdoel requires that the QSOs have unusually Dat N-ray continuum shapes and unusual optical to X-ray spectral energy distributions. while the 1onized. absorber model does not. require abnormal underlying continuum properties.," The cold X-ray absorber model requires that the QSOs have unusually flat X-ray continuum shapes and unusual optical to X-ray spectral energy distributions, while the ionized absorber model does not require abnormal underlying continuum properties."760 This finding. coupled with the presence. of strong ΗΝ absorption lines in the UY leads us to favour the ionizecl absorber model over the cold absorber model.," This finding, coupled with the presence of strong IV absorption lines in the UV leads us to favour the ionized absorber model over the cold absorber model."761 Assuming that the X-ray absorbing gas is outllowing with the same velocities as the LIV. absorbers. we are able to investigate the likely location. mass outflow rates and energetics of the ionizecl absorbers.," Assuming that the X-ray absorbing gas is outflowing with the same velocities as the IV absorbers, we are able to investigate the likely location, mass outflow rates and energetics of the ionized absorbers."762 We find that the X-ray absorbing gas is likely to be located within LOppe of the continuum source. and so is associated with the active nucleus rather than the surrounding host. galaxys interstellar medium.," We find that the X-ray absorbing gas is likely to be located within pc of the continuum source, and so is associated with the active nucleus rather than the surrounding host galaxy's interstellar medium."763 We estimate that the fraction of racliated power that. is converted into kinetic luminosity of the outllowing wines is twpically ~ 4 per cent. in agreement with estimates [or the kinetic feedback. from QSOs that is required. to produce the AJe relation.," We estimate that the fraction of radiated power that is converted into kinetic luminosity of the outflowing winds is typically $\sim$ 4 per cent, in agreement with estimates for the kinetic feedback from QSOs that is required to produce the $M - \sigma$ relation."764 This finding is thus consistent with the hypothesis that A-ray absorbed. QSOs represent the transition phase between obscurecl accretion ancl the Iuminous QSO phase in the evolution of massive galaxies., This finding is thus consistent with the hypothesis that X-ray absorbed QSOs represent the transition phase between obscured accretion and the luminous QSO phase in the evolution of massive galaxies.765solution of finite size. For which the integrals representing the total mass. angular momentum and energy. ave all convergent.,"solution of finite size, for which the integrals representing the total mass, angular momentum and energy, are all convergent."766 The central object is considered to be arbitrarily small and to act as a sink for mass and (negative) energy but not as a source for angular momentum., The central object is considered to be arbitrarily small and to act as a sink for mass and (negative) energy but not as a source for angular momentum.767 Therefore J dis strictly conserved. but AZ and £ are not.," Therefore $J$ is strictly conserved, but $M$ and $E$ are not."768 The time-dependent self-similar. solution is found by a well-known procedure (e.g. Darenblatt/ 1979)., The time-dependent self-similar solution is found by a well-known procedure (e.g. Barenblatt 1979).769 In. the standard terminology the solution is of tvpe Lo which means that the similarity variable can be deduced. simply from dimensional considerations.," In the standard terminology the solution is of type I, which means that the similarity variable can be deduced simply from dimensional considerations."770 In this case the dimensional constants present are the quantity CM and the total angular momentum 4., In this case the dimensional constants present are the quantity $GM$ and the total angular momentum $J$.771 One therefore identifies the similarity variable and seeks a solution of the form In such a solution. each physical quantity retains a similar spatial form αν the Wow evolves. but the characteristic leneth-seale of the Low increases proportionally to f°?) ," One therefore identifies the similarity variable and seeks a solution of the form In such a solution each physical quantity retains a similar spatial form as the flow evolves, but the characteristic length-scale of the flow increases proportionally to $t^{2/3}$ ."772Note that the total mass. M. is proportional to é* and the total enerey £ (which is in [act negative) proportional to /1, Note that the total mass $M$ is proportional to $t^{-1/3}$ and the total energy $E$ (which is in fact negative) proportional to $t^{-1}$.773 Substitution into equations (1)) (4) vields the dimensionless equations and where a prime denotes differentiation with respect to £., Substitution into equations \ref{drho}) \ref{de}) ) yields the dimensionless equations and where a prime denotes differentiation with respect to $\xi$.774 The constraint provides a normalization condition for the density., The constraint provides a normalization condition for the density.775 This is a filth-orcer system of. non-linear ordinary differential equations., This is a fifth-order system of non-linear ordinary differential equations.776 Critical points occur wherever ie. wherever the radial velocity measured. with respect to a sell-similarly expanding coordinate system is equal to zero or to the local sound speed., Critical points occur wherever i.e. wherever the radial velocity measured with respect to a self-similarly expanding coordinate system is equal to zero or to the local sound speed.777" When 5«5/3. an appropriate asymptotic solution as c£.0 is of the form in which where while 21, is determined. subsequently [rom the density normalization."," When $\gamma<5/3$ , an appropriate asymptotic solution as $\xi\to0$ is of the form in which where while $A_\rho$ is determined subsequently from the density normalization."778" Phe parameter A (such that 0<A 1) and the vector. B,By.Bo.D,]T. satisfy a certain algebraic eigenvalue. problem."," The parameter $\lambda$ (such that $0<\lambda\le1$ ) and the vector $[B_\rho,B_u,B_\Omega,B_e]^{\rm T}$ satisfy a certain algebraic eigenvalue problem."779 At Leading order. we have essentially the solution of NY.," At leading order, we have essentially the solution of NY."780" This is reasonable because. for small £. the How has experienced. many orbits and. except. for the declining density. may. be expected to approach a steady state,"," This is reasonable because, for small $\xi$, the flow has experienced many orbits and, except for the declining density, may be expected to approach a steady state."781" When 5=5/3. we have insteac in which where The limit ο75/3 is a singular one because A>0 so that cf,zlim.i, and olzαινι."," When $\gamma=5/3$, we have instead in which where The limit $\gamma\to5/3$ is a singular one because $\lambda\to0$ so that $\tilde A_u\ne\lim A_u$ and $\tilde A_e\ne\lim A_e$."782 In other words. the NY solution is subject to fractional corrections. which become of order unity at all radii as ο05/3. and the Bondi solution is never attained.," In other words, the NY solution is subject to fractional corrections which become of order unity at all radii as $\gamma\to5/3$, and the Bondi solution is never attained."783 Phe further development ofthe inner solution consists in general ofan irregular power series which is bevond the scope of this paper., The further development ofthe inner solution consists in general ofan irregular power series which is beyond the scope of this paper.784The behavior rofthe stelar Inninositv fuuction (LE) aud lass fuuctio1 (ME) for ow-lnass stays (<<LAD.) ds still under debate.,"The behaviour of the stellar luminosity function (LF) and mass function (MF) for low-mass stars $\rm < 1\,M_{\odot}$ ) is still under debate."785 ect al. (1997 )), et al. \cite{Jahreiss97}) )786 derive i local stellis LF (witlu- 20 pc) from he Catalogιο of Nearby Stars revised with Tipparcos daa., derived a local stellar LF (within 20 pc) from the Catalogue of Nearby Stars revised with Hipparcos data.787 Reid et a. (20023) , Reid et al. \cite{Reid2002}) )788"derived the nearby star LF using the Palomar/Michigan State University sample (PMSU) coiiiued with t1e ITipparcos 25 pe sapο,", derived the nearby star LF using the Palomar/Michigan State University sample (PMSU) combined with the Hipparcos 25 pc sample.789 Both LFs are shown in Figure 11.., Both LFs are shown in Figure \ref{lf}.790 Error bars are large due to the small SULPVON VCDulies., Error bars are large due to the small survey volumes.791 For masses smaller than NE... the «eteriiinuatio1i of the AIF is hamperee by the incompleteness of the different samples (IHeury et a. 1991..," For masses smaller than $\rm M_{\odot}$, the determination of the MF is hampered by the incompleteness of the different samples (Henry et al. \cite{Henry97},"792 Chabrier Barafte 2 100)) aud by the unknown proportio- O “AL dwarfs in binaries., Chabrier Baraffe \cite{Chabrier2000}) ) and by the unknown proportion of M dwarfs in binaries.793 Chabrier (2003)) estinated that the 1iass function below 1AL. is consistent with a Yaction D of AI dwar EDITwies where 30 shouk lave ali dwarf companion and a brown dwarf secoidary.," Chabrier \cite{Chabrier2003}) ) estimated that the mass function below $\rm7941\,M_{\odot}$ is consistent with a fraction of $\sim$ of M dwarf binaries where 30 should have an M dwarf companion and a brown dwarf secondary."795 Also ou Figure 11 are supermiposed the hunosY filicions used for siuulatious with our standard Calaxy model. as well as a few other Iuniuosity fictions obtained by varviug the IME slope a low mass.," Also on Figure \ref{lf} are superimposed the luminosity functions used for simulations with our standard Galaxy model, as well as a few other luminosity functions obtained by varying the IMF slope at low mass."796 The hunos filicjon is made froli seements of à power law IME. as eiven in equation l.. and a amass Iuinositv relaki fro Deltose et al. (20003) ," The luminosity function is made from segments of a power law IMF, as given in equation \ref{imf}, and a mass luminosity relation from Delfosse et al. \cite{Delfosse2000}) )"797ii the nagnitude range 12«A<1i axl from theoretical models of DBaraffe et al. (1998]) , in the magnitude range $<M_V<17$ and from theoretical models of Baraffe et al. \cite{Baraffe98}) )798at lower masses., at lower masses.799 The cutoff]vetween absolute magnitu5 16 to l8 is mostly due to fτς ΠΕ relation aud only weakv dependent on the IME slope at the very low lass end., The cutoff between absolute magnitude 16 to 18 is mostly due to the mass-luminosity relation and only weakly dependent on the IMF slope at the very low mass end.800" Ilowever iu the range 13My<16 the huuinosity function strongly «epends on the asstmed IME slope and ou the mass at which the slope changes: o = 1.5 for im« 0.5 ({standard Calasxy o = 1.5 for im« 0.5 aand oo = 2 fori<i, o = 1.5 forim« 0.5 aand oo = 3 for i<i, o = 1.5 for im« 0.5 asnkd oo = d for 0)«oan. and a,0.15.0.20.0.25AT."," However in the range $<M_V<16$ the luminosity function strongly depends on the assumed IMF slope and on the mass at which the slope changes: $\alpha$ = 1.5 for $m <$ 0.5 (standard Galaxy $\alpha$ = 1.5 for $m <$ 0.5 and $\alpha$ = 2 for $m < m_{c}$ $\alpha$ = 1.5 for$m <$ 0.5 and $\alpha$ = 3 for $m < m_{c}$ $\alpha$ = 1.5 for $m <$ 0.5 and $\alpha$ = 4 for $m < m_{c}$ and $ m_{c}= 0.15, 0.20, 0.25$."801.. Iu the following the various tested IAIFs are denoted Τα.το. where alpha is the IME slope. aud a. is the mass where the slope chauges.," In the following the various tested IMFs are denoted $\alpha-m_{c}$, where alpha is the IMF slope, and $m_{c}$ is the mass where the slope changes."802 We note that simulated stars cousidered here are suele stars., We note that simulated stars considered here are single stars.803 Distant binary svstenis nav be not correctly identified as stars. although from a detailed analysis of the binary effect (a complete analysis of the binary effec 1s postpone to the next paper of luis series). we have estimated that at ri>1.6 (that is Aly>Lt) the correction for stars maissed for this reason is negligible.," Distant binary systems may be not correctly identified as stars, although from a detailed analysis of the binary effect (a complete analysis of the binary effect is postponed to the next paper of this series), we have estimated that at $r'-i'>1.6$ (that is $_V>14$ ) the correction for stars missed for this reason is negligible."804 A roeAS he correction would be ess than aud a Ίοi<<L.6 it is less than., At $r'-i'<1.5$ the correction would be less than and at $1.5 < r'-i' <1.6$ it is less than.805. Ucuce with respec to the verv aunt eud of the LF stuied here. the binary effect is expected to be negligible because these stars are too close to lave been niüssed even in binary svstenis.," Hence with respect to the very faint end of the LF studied here, the binary effect is expected to be negligible because these stars are too close to have been missed even in binary systems."806" We limit our furher comparison to io>LA,", We limit our further comparison to $r'-i'>1.5$.807 Figure 10. shows clearly a deficit of late type thin disc dwarfs iu model predictions at i”>1.6. for the standard Calaxy nocdel.," Figure \ref{histall} shows clearly a deficit of late type thin disc dwarfs in model predictions at $r'-i'> 1.6$, for the standard Galaxy model."808 We have attempted to fit the LF o the available €'FITTLS data in the 3 fields using the IAIF formula from eq. (, We have attempted to fit the LF to the available CFHTLS data in the 3 fields using the IMF formula from eq. (8091).,1).810 Figure 12. shows the difference of the predicted sar counts compared to observations for he three tested INFs: a=3 anda L with ne=020M.," Figure \ref{hist_newlf} shows the difference of the predicted star counts compared to observations for the three tested IMFs: $\alpha=2$, $\alpha=3$ and $\alpha=4$ with $\rm m_{c} = 0.20$."811 Tu Table L. 5 and 6 we give the number of stars’ i’ intervals from the DI. D2 and D3 field respectively. aud. or ΠΕ th uunubers simulated frou tested LEs. varving ms from 0.15 to 0.25 and a atm <mn. from 1.5 ol.," In Table 4, 5 and 6 we give the number of stars in $r'-i'$ intervals from the D1, D2 and D3 field respectively, and, for comparison, the numbers simulated from tested LFs, varying $m_{c}$ from 0.15 to 0.25 and $\alpha$ at $m<m_{c}$ from 1.5 to 4."812 The standard cleviation of the models relative to the data are estimated roni Poisson statistics: assumune that he main source of error in the data is Polsson nolse. we estimate the deviation of the model by computing : which gives the relative difference in the counts in wits of the Poissonian scatter.," The standard deviation of the models relative to the data are estimated from Poisson statistics: assuming that the main source of error in the data is Poisson noise, we estimate the deviation of the model by computing : which gives the relative difference in the counts in units of the Poissonian scatter."813" Acceptable models have 0,44 in the range "," Acceptable models have $\sigma_{model}$ in the range $-3,3$ ]."814From these Tables we can couclide that :, From these Tables we can conclude that :815dipole. has converged in. the 2MASSs sample and that anv flux we are missing in low luuinosity ealaxies js a 1uinor contribution.,dipole has converged in the 2MASS sample and that any flux we are missing in low luminosity galaxies is a minor contribution.816 To estimate the effect of shot noise ou our calculation we perform bootstrap resampling ou he galaxy catalog., To estimate the effect of shot noise on our calculation we perform bootstrap resampling on the galaxy catalog.817 We first biu the galaxies by heir fluxes aud then resample cach fiux biu to eusure that the resampled catalog. has the correct Hux distribution., We first bin the galaxies by their fluxes and then resample each flux bin to ensure that the resampled catalog has the correct flux distribution.818"∙∙∙ Performine:∙↜ the resampling E100 ines the standard deviatious of the clustering dipole direction is Al=0,57.Ab0:37 and in uaenitude it is 0.5%,"," Performing the resampling $100$ times the standard deviations of the clustering dipole direction is $\Delta l = 8190.5\arcdeg ,\Delta b = 0.3\arcdeg $ and in magnitude it is $0.5\%$."820 We find that the svstematic uncertainties: are umeh larger. than the slot noise:, We find that the systematic uncertainties are much larger than the shot noise.821 The most iniportaut. sources of. systematic. error iu our calculation are our treatinent of the mask and of dust corrections., The most important sources of systematic error in our calculation are our treatment of the mask and of dust corrections.822 Cloning the sky above aud below the mask gives a dipole poiutiug towards /—2807.5= 397.," Cloning the sky above and below the mask gives a dipole pointing towards $l=280\arcdeg, b=39\arcdeg$ ."823 If mstead of cloningthe adjaceut sky we fill the mask with randomly selected. ealaxies the direction of the dipole changes to7=2777.5 317.," If instead of cloning the adjacent sky we fill the mask with randomly selected galaxies the direction of the dipole changes to $l=277\arcdeg, b=37\arcdeg$ ."824 I£ we perform no dust correction ou the galaxy catalog. then the dipole: iioves to /=3-7252777.510 (Fieure. 1)).," If we perform no dust correction on the galaxy catalog then the dipole moves to $l=277\arcdeg,b=40\arcdeg$ (Figure \ref{fig:dip}) )."825" We- adopt the ceutroid: ofd these three Πο 745,4=2782.57.bijBSE2” as the best fit dipole with error bars reflecting the dust: correction∖ and5 masksede fillingGaye uncertainties."," We adopt the centroid of these three measurements $l_{dipole}=278 \pm 2.5 \arcdeg,b_{dipole}=38 \pm 2 \arcdeg$ as the best fit dipole with error bars reflecting the dust correction and mask filling uncertainties."826ΕΠΕΛjon Thehe dipole calculated ouly using galaxies brighter then IK=13 points to 7=2787.0407 verifving that the iiussing faimter galaxies are not introducing ⋅⋅⋅ ⋜⋯⋅↖↽↴∖↴↕∶↴∙⊾∐∏↸⊳⋜," The dipole calculated only using galaxies brighter then $K_s = 13$ points to $l=278\arcdeg, b=40\arcdeg$ verifying that the missing fainter galaxies are not introducing any significant error."827⊔↸∖↕⋅↕⋅∪↕⋅∙ The hecMustermgdove dipoleiας isτω TT11 froufe tlià OMB!3 velocity dipole. closer thou aay previous deteriination.," The clustering dipole is $11 \arcdeg$ from the CMB velocity dipole, closer then any previous determination."828". This‘lus dsi somewhatnewhat largerlareer thenthe the eaverage separatioseparation of fii found ini thο N-bodyvly sisiumlationations. but withinvithi 95A NUNAss Μην,"," This is somewhat larger then the average separation of $7\arcdeg$ found in the N-body simulations, but within $95\%$ confidence limits."829 “Therefore we conclude hat the 2)L determined clustering Προ]. is consistent with the direction of the Local Caoup uofion1 givenovo the5 πιουνsorte]αλαΊος cansedCATISC Wwby luear effects and svsteiiatic errors., Therefore we conclude that the 2MASS determined clustering dipole is consistent with the direction of the Local Group motion given the uncertainties caused by non-linear effects and systematic errors.830" luterestinelv.. our clustering. dipole. is ∙≓19"" from. . ∐↸∖≼∐↻∪↕↸∖⋯↸∖⋜↧↴∖↴↿∐⋅↸∖≼↧⋯∪↴∖↴↑↥⋅↸∖↸⊳↸∖∐↑↕⋅↖↽∏↴∖↴∐↕∶↴∙⊾↑∐↸∖ ∙ ∐⊰⊀≚≋↕⋟↴∖↴↸⊳∶↸⊳⋜↧↑⋜↧↕∪∶"," Interestingly, our clustering dipole is $19\arcdeg$ from the dipole measured most recently using the IRAS $z$ catalog \citep{rowan:00}."831↴⋁⋖∎∙↗⋝∙∙⊺∐↕↴∖↴↕↴∖↴↕⋜∐⋅∶↴⋁↸∖↥⋅↑∐⋜↧∐ he systematic errors in either calculation and MAN! UStsts differtnees either| cansed |by tli owsbund of the survey or in the methods used o calculate the clustering dipole., This is larger than the systematic errors in either calculation and therefore suggests differences either caused by the passband of the survey or in the methods used to calculate the clustering dipole.832 It is possible, It is possible833To compare with observations. we make use of observationally based. stellar spectra used for the extensive ISOCAAL and ISOPIIOT. calibrationprograms.,"To compare with observations, we make use of observationally based stellar spectra used for the extensive ISOCAM and ISOPHOT calibration."834.. We calculated near- and mid-LR colours of stars with a range of spectral types from these spectra., We calculated near- and mid-IR colours of stars with a range of spectral types from these spectra.835 Phe models are estimatec to be aecurate within 5 per cent., The models are estimated to be accurate within 5 per cent.836" In the mid-IR. the Iluxes were colour-corrected (maximally a 7 per cent elect) Following the convention of £5O-Lluxes which are determine using a constant energy spectrum (note that for L3 the ""weference wavelength! is 14.3 tun).", In the mid-IR the fluxes were colour-corrected (maximally a 7 per cent effect) following the convention of -fluxes which are determined using a constant energy spectrum (note that for LW3 the `reference wavelength' is 14.3 $\umu$ m).837 From our own sample of stars. defined in Section 2.5.. we use only those with the REL-2 status.," From our own sample of stars, defined in Section \ref{stargal}, we use only those with the REL=2 status."838 In. addition. we exclude stars which have tyS mag. because of probable saturation in our near-LR images.," In addition, we exclude stars which have $K < 8$ mag, because of probable saturation in our near-IR images."839 Lig., Fig.840 Alashowsthestarsdelecledal tum plotted as 23/6.1] Ix. wilhthemodelstarsover plottedassolidsymbols," \ref{lw2_stars}$ $a$ shows the stars detected at $6.7 \umu$ m plotted as $[2.2/6.7]$ $J-K$ , with the model stars overplotted as solid symbols."841" from themodcl pqitlorsQucaE consistency. unnoticed multipliedNote snhlcoloi,γαι wherethelaterspeelrallypeswilhredders- 1ο Ixhevestighllylower2.2/6.7]."," From the model points one can notice a slight colour-term, where the later spectral types with redder $J-K$ have slightly lower $[2.2/6.7]$."842 Egnoringlhenegligiblecolour intoaccountΓΗ. fromtheaveragedif ferenccof 2.2/6.7|ralioso fobservalfon shi pergola Ayasdefeon qedueed veins Ue? NidGNSiuo lluxes of the ο”. ELAIS catalogue.," Ignoring the negligible colour-term, from the average difference of $[2.2/6.7]$ ratios of observations and models, we derive a correction of 1.22 to the $6.7\umu$ m fluxes of the v.1.3 ELAIS catalogue."843 Fig., Fig.844 Albshowstheequivalentplotforthel5 qum stars there are much less stars here. but the overall calibration of the v.1.3 ELAIS catalogue seems quite accurate.," \ref{lw2_stars}$ $b$ shows the equivalent plot for the $15 \umu$ m stars – there are much less stars here, but the overall calibration of the v.1.3 ELAIS catalogue seems quite accurate."845 We derive a 1.05. ADUfeain/s/mJdy calibration for the L\W3 data., We derive a 1.05 ADU/gain/s/mJy calibration for the LW3 data.846 Specifically. we doof lind evidence for the factor of 2 (or 1.75) scaling used in Serjeant ct ((2000).," Specifically, we do find evidence for the factor of 2 (or 1.75) scaling used in Serjeant et (2000)."847 Since we are using the same ELALS data. from the same reduction process and the same photometric aperture corrections. the diserepaney has to come from the adopted method. of extrapolating near-LR (our case) or optical magnitudes to the mic-LR.," Since we are using the same ELAIS data, from the same reduction process and the same photometric aperture corrections, the discrepancy has to come from the adopted method of extrapolating near-IR (our case) or optical magnitudes to the mid-IR."848 The J-band data can be used as well: panels e and d show the equivalent. colour-colour plots with J-Iux., The $J$ -band data can be used as well: panels $c$ and $d$ show the equivalent colour-colour plots with $J$ -flux.849 The calibration factors are. confirmed. as we find 1.24 and 1.06 ADU/gain/s/m.Jv for the LW2 and LAWS filters. respectively.," The calibration factors are confirmed, as we find 1.24 and 1.06 ADU/gain/s/mJy for the LW2 and LW3 filters, respectively."850 To compare with figures in Missoulis et ((1999) and Serjeant ct al. (, To compare with figures in Missoulis et (1999) and Serjeant et al. (8512000). Fig.,"2000), Fig."852 A3. shows theprediefed 6.7 and 15jum stellar Duxes (derived rom the observed. A magnitude of the star using the corresponding model colour ratio) against the observed and re-calibrated ELAIS 6.7 and L5pum , \ref{lw2_stars_corr} shows the 6.7 and $15 \umu$ m stellar fluxes (derived from the observed $K$ -magnitude of the star using the corresponding model colour ratio) against the observed and re-calibrated ELAIS 6.7 and $15 \umu$ 853with those observed over louger time intervals. where the effects of evolutionary changes iu mca radius become dominuaut (Turneretal.,"with those observed over longer time intervals, where the effects of evolutionary changes in mean radius become dominant \citep{15}."854200Ga).. The M supereiant variable BC Ce (M3 Ia) is an interesting example of random fluctuations iu period for the SRC class of long-period variables. a small group of pulsating stars often overlooked by variable star observers.," The M supergiant variable BC Cyg (M3 Ia) is an interesting example of random fluctuations in period for the SRC class of long-period variables, a small group of pulsating stars often overlooked by variable star observers."855 Thies of elt[m] maxima for BC Crevg can 8generally be established to within ⋜↧↖↖⇁↸∖↸∖↨↘↽∪↥⋅↴∖↴∪⋖∿∩∙∩↕∫≽⋟∙↴∏↕↑↑∐↸∖≼≓≽≼⊲↖⇁⋜∐⋅↕⋜↧↑↕∪∐↴∖↴ ⋖⊟∶↴∙⊾∙∶≩⊔≼∐↴," Times of light maxima for BC Cyg can generally be established to within a week or so $\sim0.01 P$ ), but the O–C variations (Fig. \ref{fig3}) )"856∖↴↻↕⋜↧⋅↖↽↴∖↴↸⊳⋜↧⇈↸∖↥⋅⋜∐⊔≺∏⋯↑↕∐∶↴⋁↑∪⋜↧↴∖↴⊔⋯⊳∐⋜↧↴∖↴ ⋜↧↕≯↸∖↖↖↽↕∐⊔≼, display scatter amounting to as much as a few hundred days.857⊔⋅↸∖≼↧≼↧⋜↧⋅↖↰∖↴∙↽∕∏∐∖↴⋝↸∖↴∖↴↑≓∐⇈↕∐∶↴⋁≼↧∪↖↖↽∐↖↖↽⋜∐⋅≼↧↴∖↴ sloped parabolic treud is otherwise consistent with the established period decrease in BC Cye between 1900 and 2000 (Turneretal.2006b)., The best-fitting downwards sloped parabolic trend is otherwise consistent with the established period decrease in BC Cyg between 1900 and 2000 \citep{16}.858. A test of the OC deviatious for BC Cre using the Eddiugton-Plakidis technique is displaved iu Fie. L., A test of the O–C deviations for BC Cyg using the Eddington-Plakidis technique is displayed in Fig. \ref{fig4}.859 The deduced raudonmmnoess parameter in this case of ©=12.88 is consistent with the recognized dependence of the parameter ou pulsation periodP., The deduced randomness parameter in this case of $e = 12.88$ is consistent with the recognized dependence of the parameter on pulsation period.860" In general. all existing results suggest that the ""OC paraimneter mereases with period P (Turucr&Berduikov2001).. as shown in Fig. 5.."," In general, all existing results suggest that the “e” parameter increases with period \citep{7}, as shown in Fig. \ref{fig5}."861 A workine relationship for the dependence is given by: It was noted by Eddington&Plakidis(1929) that the observed random fluctuations im period for o Cot (Mira) and à. Cre amounted to of the pulsation period. a parameter that in turn depends directly on stellar radius.," A working relationship for the dependence is given by: It was noted by \citet{1} that the observed random fluctuations in period for $o$ Cet (Mira) and $\chi$ Cyg amounted to of the pulsation period, a parameter that in turn depends directly on stellar radius."862 Iu other words. a better parameter for describing stochastic processes in pulsating stars should be the ratio οὐ. which mast be independent of radius if the variables obey a period-radius relation.," In other words, a better parameter for describing stochastic processes in pulsating stars should be the ratio $e/P$, which must be independent of radius if the variables obey a period-radius relation."863 Results to date for all Edciugtou-Plakidis analyses of pulsating stars (shown in Fie. 6)), Results to date for all Eddington-Plakidis analyses of pulsating stars (shown in Fig. \ref{fig6}) )864 confirm that assumption., confirm that assumption.865- The parameter c/P is iudeed relatively independent of pulsation period. Ae. indepeudent of stellar radius.4 aud has a mean value of 0.0136+0.0005 (0.0069 s.d.).," The parameter $e/P$ is indeed relatively independent of pulsation period, , independent of stellar radius, and has a mean value of $0.0136 \pm0.0005$ $\pm0.0069$ s.d.),"866 identicalto what Eddington&Plasicdis(1929). concluded SÜvears ago., identicalto what \citet{1} concluded 80years ago.867ina quark nova (QN:Ouvedetal.2002:Keranen2005).. releases up to 107 eres that mieht help power the explosion of the star.,"in a quark nova \citep[QN;][]{ouyed02, keranen05}, releases up to $10^{53}$ ergs that might help power the explosion of the star."868 This cau possibly explain wliv GRBs associated superuovae are often very energetic (sceOuvedetal.2007:Leaby&Ouved2007).," This can possibly explain why GRBs associated supernovae are often very energetic \citep[see][]{ouyed07, leahy07}."869. If a QS is formed directly in the core collapse. stage 1 will be bypassed aud the process starts frou stage 2.," If a QS is formed directly in the core collapse, stage 1 will be bypassed and the process starts from stage 2."870 Stage 2 is accretion onto the QS from the surrouudiug lyperaccreting debris disk. which is formed from material left over from the collapse of the progenitor.," Stage 2 is accretion onto the QS from the surrounding hyperaccreting debris disk, which is formed from material left over from the collapse of the progenitor."871 This launches a highly variable ultra-xclativistie jet. in which internal shocks cau give rise to the eamuna radiatiou secu iu à GRB (Ouvedctal.2005).," This launches a highly variable ultra-relativistic jet, in which internal shocks can give rise to the gamma radiation seen in a GRB \citep{ouyed05}."872. This jet will eventually interact with the suroundius medium creating an external shock that eives rise to the GRB afterelow., This jet will eventually interact with the surrounding medium creating an external shock that gives rise to the GRB afterglow.873" The afterglow light curve would follow a powcerlaw £,~ff)2) (Sarietal.1998)."," The afterglow light curve would follow a powerlaw $F_\nu\sim874t^{-(1-2)}$ \citep{sari98}."875 Tlowever. slower shells can catch up with the external shock at later times and refresh it.," However, slower shells can catch up with the external shock at later times and refresh it."876 This can lead to a flatter segment in the N-rav afterglow (e.g.Rees&Moészáros1998) which is cohmmonly seeu in CRB afterelows (O'Brienetal.2006:Liangetal. 2007).," This can lead to a flatter segment in the X-ray afterglow \citep[e.g.][]{reesmeszaros98} which is commonly seen in GRB afterglows \citep{obrien06, liang07}."877. Stage 3. which occurs if the QS. accreted. sufficiently that it collapsed to à DIT. is accretion outo the BIT which launches another ultra-relativistic jet. as described iu DeVilliers.Staff.&Ouved(2005).," Stage 3, which occurs if the QS accreted sufficiently that it collapsed to a BH, is accretion onto the BH which launches another ultra-relativistic jet, as described in \citet{devilliers05}."878. Interaction between this jet aud the QS jet or internal shocks in the BIT jet itself cau give rise to faring conunonly secu in the N-rav afterglow of GRBs., Interaction between this jet and the QS jet or internal shocks in the BH jet itself can give rise to flaring commonly seen in the X-ray afterglow of GRBs.879 The DIT jet has the potential to be very powerful. so if it catches up with the external shock a bmp uieht be seen in the helt curve.," The BH jet has the potential to be very powerful, so if it catches up with the external shock a bump might be seen in the light curve."880 The relevant features and cussion have been discussed in details iu SODOT., The relevant features and emission have been discussed in details in SOB07.881 Alternatively. if the QS did not collapse to a DII. continued accretion outo the QS after the prompt phase nuelt also be able to explain N-rav flaring.," Alternatively, if the QS did not collapse to a BH, continued accretion onto the QS after the prompt phase might also be able to explain X-ray flaring."882 Iu our model the prompt enuüssiou is produced by internal shocks in à QS jet launched by. livperaccretion onto a QS (Ouvedetal.2005)., In our model the prompt emission is produced by internal shocks in a QS jet launched by hyperaccretion onto a QS \citep{ouyed05}.883. Iu this section we will first explain that for the accreting material to be chauneled to the polar cap region. this requires a very high maeuetic field.," In this section we will first explain that for the accreting material to be channeled to the polar cap region, this requires a very high magnetic field."884 Tf the QS survives the acerction aud is rapidly rotating. this magnetic field can then spin the QS down.," If the QS survives the accretion and is rapidly rotating, this magnetic field can then spin the QS down."885 We will show that a sinularly strong magnetic field is what is needed to ect the right spin-cdown time to explain the observed flattening., We will show that a similarly strong magnetic field is what is needed to get the right spin-down time to explain the observed flattening.886 The proupt gamuna ταν cmission corresponds to svuchrotron emission by electrous accelerated i internal shocks in the QS jet., The prompt gamma ray emission corresponds to synchrotron emission by electrons accelerated in internal shocks in the QS jet.887 This jet forms an external shock upon interacting with the surroundius medi. and svuchrotron cussion from this external shock is responsible for the afterelow.," This jet forms an external shock upon interacting with the surrounding medium, and synchrotron emission from this external shock is responsible for the afterglow."888 Iu order to explain the euergy observed iu the prompt gala radiation. ΟΡΟΥ found that the accretion rate onto the QS nust be of the order M~10%10PAL/s.," In order to explain the energy observed in the prompt gamma radiation, SOB07 found that the accretion rate onto the QS must be of the order $\dot{M}\sim10^{-5}-10^{-3}M_\odot/{\rm s}$."889 Iu order to create a jet. the accretion has to be chauncled outo the polar cap.," In order to create a jet, the accretion has to be channeled onto the polar cap."890 This can occur if the magnetic radius is at least twice the radius of the star., This can occur if the magnetic radius is at least twice the radius of the star.891 With the before mentioned accretion rate. a magnetic Ποια of the order B—lt!απο (seeOuved.Keriuenu.2005) Is It should be noted that this QS jet is much differcut than the typical MITD disk wind jets.," With the before mentioned accretion rate, a magnetic field of the order $B\sim10^{14}-10^{15}G$ \citep[see][]{ouyed05b} is It should be noted that this QS jet is much different than the typical MHD disk wind jets."892 A QS jet is created as the accreting material reaches the surface of the QS. it is converted iuto CFL quark matter. resulting iu the creation of a hot spot due to the release of excess binding enerev.," A QS jet is created as the accreting material reaches the surface of the QS, it is converted into CFL quark matter, resulting in the creation of a hot spot due to the release of excess binding energy."893 This region cools by enüttius photous. which collide with subsequent accreting material. resulting in the ejection of material with hieh Lorentz factors (fordetails.seeOuvedetal.2005).," This region cools by emitting photons, which collide with subsequent accreting material, resulting in the ejection of material with high Lorentz factors \citep[for details, see][]{ouyed05}."894. Given that the prompt cuission requires such high magnetic fields (because of the ligh accretion rates). one has to reconcile this with the plateaus observed in some helt curves at later times.," Given that the prompt emission requires such high magnetic fields (because of the high accretion rates), one has to reconcile this with the plateaus observed in some light curves at later times."895 A very Ligh magnetic field and a high accretion rate can iuaxe the QS find itself iu the propeller regime if it is also spinning very fast CP=2 ins)., A very high magnetic field and a high accretion rate can make the QS find itself in the propeller regime if it is also spinning very fast $P\lesssim2$ ms).896 If the QS is born in the propeller reginae. then we sugeest that there will be a delay between the formation of the QS and the lauuching of the jet. while the propeller spins the QS down.," If the QS is born in the propeller regime, then we suggest that there will be a delay between the formation of the QS and the launching of the jet, while the propeller spins the QS down."897 Panaitescu(2007) suggested that au outflow. ejected. w the engine after the initial blast. can scatter the orward-shiock svuchrotrou emission and thereby produce Hux that will outshine the primary oue. especially if he outflow is nearly barvou free aud highlvic?.," \citet{panaitescu07} suggested that an outflow, ejected by the engine after the initial blast, can scatter the forward-shock synchrotron emission and thereby produce flux that will outshine the primary one, especially if the outflow is nearly baryon free and highly."898. This reflected fux cau produce certain light-curve eatures such as flares. plateaus. aud chromatic breaks.," This reflected flux can produce certain light-curve features such as flares, plateaus, and chromatic breaks."899 For this to occur. the duration of this scattering outflow das to last as long as these observed features (modulo cosinological time-dilation).," For this to occur, the duration of this scattering outflow has to last as long as these observed features (modulo cosmological time-dilation)."900 We uext show that by using the rotational energy lost roni a QS spinning down. assuming a magnetic field of 101C. a spii-period of ~21s. a characteristic decay iue of the order 10° - 10! seconds is obtained.," We next show that by using the rotational energy lost from a QS spinning down, assuming a magnetic field of $10^{15}~{\rm901G}$, a spin-period of $\sim 2~{\rm ms}$, a characteristic decay time of the order $10^3$ - $10^4$ seconds is obtained."902 The observed flatteniug in the light-curves of certain GRBs cun last for several times 104 s aud fits well with the duration from the QS spin-down., The observed flattening in the light-curves of certain GRBs can last for several times $10^4$ s and fits well with the duration from the QS spin-down.903 Following the birth of a CFL QS. due the to onsetρα of color superconductivity the maeuetic flux inside the star ds forced into a vortex lattice that is aligne< with the rotation axis.," Following the birth of a CFL QS, due the to onset of color superconductivity the magnetic flux inside the star is forced into a vortex lattice that is aligned with the rotation axis."904 This subsequently forces the magnetic field outside the star to re-structure itself into a dipole configuration that is aligned with the rotation axis (Ouvedetal.2006)., This subsequently forces the magnetic field outside the star to re-structure itself into a dipole configuration that is aligned with the rotation axis \citep{ouyed_niebergal06}.905. Such an aligue rotator will spin down by maguetospheric curreuts escaping through the light exliuder., Such an aligned rotator will spin down by magnetospheric currents escaping through the light cylinder.906 Pair production from magnetic reconnection supplies these curreuts (Nicberea with a correspouding hDuuinositv given bv (Shapiro&Teukolsky 1983)::, Pair production from magnetic reconnection supplies these currents \citep{niebergal06} with a corresponding luminosity given by \citep{shapiroteukolsky83}: :907roughly appropriate for local star forming galaxies (Newleyctal.2001:Ίνρ&Mattsson 2011).,"roughly appropriate for local star forming galaxies \citep{Ke01,I06,L08,PM11}."908". The k-values used are Ay,=2.468 and Aq;=3.631 (Calzetti2001).. and represent the ratio of the extinction at a given wavelength to the intrinsic colour excess in the b-band relative to the v-band (Ay=AA/E(B— V);) (Calzetti1994)."," The k-values used are $k_{\textnormal{H}\alpha}=2.468$ and $k_{\textnormal{H}\beta}=3.631$ \citep{C01}, and represent the ratio of the extinction at a given wavelength to the intrinsic colour excess in the b-band relative to the v-band $k_{\lambda}=A_{\lambda}/E(B-V)_{i}$ ) \citep{C94}."909" It should be noted that these SFRs pertain to the region of the galaxy falling within the 3"" diameter SDSS fibre aperture, which probes the inner ~1-9 kpc of the galaxies in our samples."," It should be noted that these SFRs pertain to the region of the galaxy falling within the 3” diameter SDSS fibre aperture, which probes the inner $\sim$ 1-9 kpc of the galaxies in our samples."910 This method was used for Sample T1 in order to follow the procedure adopted by Mannuccietal.(2010) as closely as possible., This method was used for Sample T1 in order to follow the procedure adopted by \citet{M10} as closely as possible.911 The method used im Sample T2 instead estimates the total-SFR using the SDSS photometry to correct for the missing star formation in the outer regions of the galaxy (see Section Moe, The method used in Sample T2 instead estimates the total-SFR using the SDSS photometry to correct for the missing star formation in the outer regions of the galaxy (see Section \ref{Sample T2}) ).912talliitv was caleulated for Sanple Tl using two of the strong Ine diagnostics calibrated by Maiolinoetal (2008). , Metallicity was calculated for Sample T1 using two of the strong line diagnostics calibrated by \citet{M08}. .913"Such diagnostics are often used when direct measurcmeuts of the clectrou temperature 7, in the regions of a galaxy are not possible, or at high imetallicitics (Z= 8.55) where they no longer provide an accurate estimate of Z due to temperature fluctuations within individual regions and ACTOSS the whole galaxy (Stasiüska2005:Maiolimoetal.2008) (this is the case for essentially all the galaxies in our sample)."," Such diagnostics are often used when direct measurements of the electron temperature $T_{e}$ in the regions of a galaxy are not possible, or at high metallicities $Z \gtrsim 8.35$ ), where they no longer provide an accurate estimate of $Z$ due to temperature fluctuations within individual regions and across the whole galaxy \citep{St05,M08} (this is the case for essentially all the galaxies in our sample)."914" In such cases, either an empirical method, utilising other galaxies with measured 7; metallicities, or a theoretical method, utilising purely theoretical photoionisation models, can be used (xewley&Ellison2005).."," In such cases, either an empirical method, utilising other galaxies with measured $T_{e}$ metallicities, or a theoretical method, utilising purely theoretical photoionisation models, can be used \citep{KE08}. ."915 Maiolinooetal(20085) derived their strong line diagnostics using a combination of cimpirical and theoretical methods., \citet{M08} derived their strong line diagnostics using a combination of empirical and theoretical methods.916" 259 local galaxies of Z<835. with T, derived inctallicities compiled by Nagaoetal.(2006) were used, combined with 22.482 SDSS-DR4 galaxies of Z>8.4. with anetallicities derived using the photoiomisation model outlined in Ixewley&Dopita(2002)."," 259 local galaxies of $Z<8.35$, with $T_{e}$ derived metallicities compiled by \citet{N06} were used, combined with 22,482 SDSS-DR4 galaxies of $Z>8.4$, with metallicities derived using the photoionisation model outlined in \citet{KD02}."917. The resulting combined calibrations are given by equ., The resulting combined calibrations are given by eqn.918 ] and table 4 in the Maiolinoctal.(2008) paper., 1 and table 4 in the \citet{M08} paper.919 For our Sample Tl. we follow Mannuccietal.(2010) by taking the average of the metallicities given by the A6584/Ha calibration and the Hos calibration as the final metallicity estimate for each We also corrected all. hne fluxes for dust. following Cardellietal.(1989).," For our Sample T1, we follow \citet{M10} by taking the average of the metallicities given by the $\lambda6584$ $\alpha$ calibration and the $R_{23}$ calibration as the final metallicity estimate for each We also corrected all line fluxes for dust, following \citet{C89}."920".. This lowers the metallicities estimated viaHos by ~0.03 dex atthe highest masses, but makes very little difference to those estimated via [Ni1]| A6584/Ha because the two lines involved are of very sinilar wavelengths."," This lowers the metallicities estimated via$_{23}$ by $\sim0.03$ dex atthe highest masses, but makes very little difference to those estimated via $\lambda6584$ $\alpha$ because the two lines involved are of very similar wavelengths."921" Our second sample, Sample Τὸ."," Our second sample, Sample T2,"922-.6in,-.6in923It has long been believed that the absolute inaguitude of RR Lyrae stars could be deteruumed by their helt curves aud. to some still uuknown extent. their metallicity.,"It has long been believed that the absolute magnitude of RR Lyrae stars could be determined by their light curves and, to some still unknown extent, their metallicity."924 Fourier decompositions. were introduced by Simon Lee 1981.. as a means of qualitative description of lielit curves of pulsation variables in geucral. and they showed that amplitude ratios aud phase differcuces provide a useful description of the ITertzspruug progression for classical Cepheids.," Fourier decompositions, were introduced by Simon Lee \markcite{si81}, as a means of qualitative description of light curves of pulsation variables in general, and they showed that amplitude ratios and phase differences provide a useful description of the Hertzsprung progression for classical Cepheids."925 In addition. Simon Teays showed that the Fourier decomposition parameters of 70 RR Lxiae field stars are iore sensitive discrininators of the Bailey type (ab or c) than the traditionally. eiiploved. period-uuplitude diagram.," In addition, Simon Teays \markcite{si82} showed that the Fourier decomposition parameters of 70 RR Lyrae field stars are more sensitive discriminators of the Bailey type (ab or c) than the traditionally employed period-amplitude diagram."926 Several elobular clusters oc)) contain mauv RR Lyrae stars. and sce the variables iu a globular cluster probably coustitute a auch more uniforii sample than the field RR Lyrac’s. a considerably simaller scatter is expected in data fron oue cluster.," Several globular clusters ) contain many RR Lyrae stars, and since the variables in a globular cluster probably constitute a much more uniform sample than the field RR Lyrae's, a considerably smaller scatter is expected in data from one cluster."927 Petersen examined Fourier decompositions of RR Lyrae’s inCentauri. aud found that the scatter in the Fourier parameters was larger than expected for a uniformi sample.," Petersen \markcite{pe84} examined Fourier decompositions of RR Lyrae's in, and found that the scatter in the Fourier parameters was larger than expected for a uniform sample."928 Petersen concluded that the scatter was most likely duc to the large metallicity distribution (|FE/II] ranges from -2.3 to -0.5 (Butler 1978)). differences iu 1uass of the horizontal brauch stars. or differences iu effective temperature.," Petersen \markcite{pe84} concluded that the scatter was most likely due to the large metallicity distribution ([FE/H] ranges from -2.3 to -0.5 (Butler \markcite{bu78}) ), differences in mass of the horizontal branch stars, or differences in effective temperature."929 As Suudth pointed out. lis so unusual iu its rauge of Chemical compositiou that it is questionable whether lis the kev to the absolute imagnuitudeauctallicity relation. too unusual to be a representative of the RR Lyrac population. or just one more clue to an absolute magnitude-metallicity relation relatiouship which is more complicated than expected.," As Smith \markcite{sm95} pointed out, is so unusual in its range of chemical composition that it is questionable whether is the key to the absolute magnitude-metallicity relation, too unusual to be a representative of the RR Lyrae population, or just one more clue to an absolute magnitude-metallicity relation relationship which is more complicated than expected."930 See Sunith for a review on RR Lyrae stars in general., See Smith \markcite{sm95} for a review on RR Lyrae stars in general.931 According to two recent papers. Ἱνονάσος Jurcsik (83) aud Jurcsik IKováces (JI). the mctallicity and absolute magnitude of RR Lyrae ab stars can be described by a simple linear combination," According to two recent papers, Kováccs Jurcsik \markcite{ko96} (KJ) and Jurcsik Kováccs \markcite{ju96} (JK), the metallicity and absolute magnitude of RR Lyrae ab stars can be described by a simple linear combination"932in the FLIOW frame. and 3321 in the FIGOW (rame. were indepeudently detected by the routine DAOFIND at 1.5 σ above the local backgrouud.,"in the F110W frame, and 3321 in the F160W frame, were independently detected by the routine DAOFIND at 1.5 $\sigma$ above the local background."933 Τιe instrumental imagnitude of each object was estimated via PSF fitting with a zero point calculated within a 2 pixel radius aperture., The instrumental magnitude of each object was estimated via PSF fitting with a zero point calculated within a 2 pixel radius aperture.934 We adopted as PSF templates the [stars of the field which turted out to be more isolated aud uualIected by prolile distortions., We adopted as PSF templates the 4 stars of the field which turned out to be more isolated and unaffected by profile distortions.935" The iustrumental inaguitudes (rom the PSF-[itting technique were calibrated iu the HST VECGAMAG system with the formula given by Dickinson (1999): where Ca, is the aperture correction to convert the magnitudes within a 2 pixel radius in thedrizzled images into the magnitudes within the conventional 075 radius (iu ourdrizzled case it corresponds to 13.33 pixels aud uot to the staudard 7.6 pixels). ος --0.1252 mag is the quantity eiven by Dickinson to convert the magnitude at 075 into the nominal infinite aperture. aud ZIN: is the published zero point for the HST VEGAMACG system (22.381 for FLIOW aud. 21.750 for F160W)."," The instrumental magnitudes from the PSF-fitting technique were calibrated in the HST VEGAMAG system with the formula given by Dickinson (1999): where $C_{\rm ap}$ is the aperture correction to convert the magnitudes within a 2 pixel radius in the images into the magnitudes within the conventional $\farcs$ 5 radius (in our case it corresponds to 13.33 pixels and not to the standard 7.6 pixels), $C_\infty$ –0.152 mag is the quantity given by Dickinson to convert the magnitude at $\farcs$ 5 into the nominal infinite aperture, and $ZP_{\rm V}$ is the published zero point for the HST VEGAMAG system (22.381 for F110W and 21.750 for F160W)."936 The objects fouud in both nds were cross-identilied with the routines DAOMATCH and DAONLASTER. retaining only those identifications with a diflerence in their coordinates within a radius of 2.0 pixels (roughly half of the PSF FWHAL in FIGOW).," The objects found in both bands were cross-identified with the routines DAOMATCH and DAOMASTER, retaining only those identifications with a difference in their coordinates within a radius of 2.0 pixels (roughly half of the PSF FWHM in F160W)."937 In this way we selected 2373 objects having a measured magnitude in both FLIOW aud FLOOW. As for the WEPC? objects. to distinguish as much as possible single stars frou. extended. blended or spuriousH objects.. we have appliedH to our catalog the X> audsharpness criteria.," In this way we selected 2373 objects having a measured magnitude in both F110W and F160W. As for the WFPC2 objects, to distinguish as much as possible single stars from extended, blended or spurious objects, we have applied to our catalog the $\chi^2$ and criteria."938H Alter a visual screening of each iudividual object whieh could or could not be removed depending on the adopted limits [or acceptable and X7. we have retained all the objects with < 0.3.," After a visual screening of each individual object which could or could not be removed depending on the adopted limits for acceptable and $\chi^2$ , we have retained all the objects with $\,\leq$ $\,\leq\,$ 0.3."939 In this case a restriction in X would lave inevitably removed also bright single 3.ars., In this case a restriction in $\chi^2$ would have inevitably removed also bright single stars.940 OF these selected objects. 1707 stars have 65540«X 0.2 in both filters (see Fig. 16))," Of these selected objects, 1707 stars have $\sigma_{DAO}\leq\,$ 0.2 in both filters (see Fig. \ref{dao_sig}) )"941 aud 829 W.ars have opo <Q.1.," and 829 stars have $\sigma_{DAO}\leq\,$ 0.1."942 By inspecting the rejected objects. we have 'ecognized all the candidate star clusters fouud in e portion of the PC image falliug in the NIC?2 field.," By inspecting the rejected objects, we have recognized all the candidate star clusters found in the portion of the PC image falling in the NIC2 field."943 They are markecl in Fig., They are marked in Fig.944 15 as open circles., \ref{pc_nicmos_bw2} as open circles.945 Hf “=re assume that the ealactic barycenter is most lisely located near the center of Region 6 aud of all e other isophotal contours. except Region 7. it is interesting to note that the candidate clusters are -ot evenly distributed arouud the center and see nto avoid the area close to the SSC.," If we assume that the galactic barycenter is most likely located near the center of Region 6 and of all the other isophotal contours, except Region 7, it is interesting to note that the candidate clusters are not evenly distributed around the center and seem to avoid the area close to the SSC."946 We consider is as a real segregation siuce we have not [ouud any reason to ascribe it to selection ellects in e candidate cluster identificatiou., We consider this as a real segregation since we have not found any reason to ascribe it to selection effects in the candidate cluster identification.947 The properties of the candidate clusters will be discussed in a ortheoming paper (Monelli et al., The properties of the candidate clusters will be discussed in a forthcoming paper (Monelli et al.948 in preparation when the F38OW aud Ε139W. images will also be examined audthe colors will be measured., in preparation) when the F380W and F439W images will also be examined andthe colors will be measured.949To illustrate the enerey conservation and svmplecticitv perlormance of adaptive ancl non-adapiive varialional integrators. we perlormecl several one-dimensional simulations of the Ixepler problem. The particular parameters we chose were m=hf=2/9. and /=219/135. with initia conditions ry=2/45. e=py0.0.,"To illustrate the energy conservation and symplecticity performance of adaptive and non-adaptive variational integrators, we performed several one-dimensional simulations of the Kepler problem, The particular parameters we chose were $m = k = 2/9$, and $l =9502\sqrt{19}/135$, with initial conditions $r_0 = 2/45$, $v_0=p_0=9510.0$."952 With (these parameters and initial conditions the tota enerev of the svstem is £=—1/4. the eccentricity is €=9/10. and Che orbital period is T—2$(2/45)κο(0588716.," With these parameters and initial conditions the total energy of the system is $E = -1/4$, the eccentricity is $e = 9/10$ and the orbital period is $\tau = 2\pi \left(2/45\right)^{3/2} \approx9530.0588716$."954 We evolved the svstem for various limes. [rom 7/10 to 10τ in increments of 7/10.," We evolved the system for various times, from $\tau/10$ to $10 \tau$ in increments of $\tau/10$."955 The plots shown in Figures 4 ancl 5 use values computed at the end of a simulation over the appropriate total me interval. not snapshots of the corresponding values in an ongoing simulation: the clistineGon is important because of what it implies about the choices of adaptive (ümestepssee Section 4...," The plots shown in Figures \ref{OneDEnergyError} and \ref{OneDSymplecticityError} use values computed at the end of a simulation over the appropriate total time interval, not snapshots of the corresponding values in an ongoing simulation; the distinction is important because of what it implies about the choices of adaptive timesteps—see Section \ref{AdaptiveTimesteps}."956 We used three different integration algorithms based on equations(16): a constant. (imestep integrator. an adaptive Gimestep integrator where / is chosen at the beeinning of a step according to where q=r and we set 7=0.05. and a block-power-ol-6wo timestep integrator which uses the above for ils μας.," We used three different integration algorithms based on equations: a constant timestep integrator, an adaptive timestep integrator where $h$ is chosen at the beginning of a step according to where $q=r$ and we set $\eta = 0.05$, and a block-power-of-two timestep integrator which uses the above for its $h_{\rm{max}}$."957 For the constant. Gimestep integrator. we chose (he timestep h(rg.po).," For the constant timestep integrator, we chose the timestep $h\left( r_0, p_0 \right)$."958 All algorithms iterate equation to convergence; we thus expect the power-ol-(wo and constant. (nmestep algorithms to be exactly svinplectic., All algorithms iterate equation to convergence; we thus expect the block-power-of-two and constant timestep algorithms to be exactly symplectic.959 Figure 4. displavs the relative energy error accumulated over many simulated orbits by the three aleorithms., Figure \ref{OneDEnergyError} displays the relative energy error accumulated over many simulated orbits by the three algorithms.960 It is clear that the (hiree algorithms accumulate comparable energy error. wilh the adaptive timestep choice slightly worse than the others.," It is clear that the three algorithms accumulate comparable energy error, with the adaptive timestep choice slightly worse than the others."961 Given an evolution mapping fy:(q.p)—(ήp).P(g.p)). the pushlorward of the Poincaré integral invariant Z=dqAdp along the trajectory q(f).pl)=Fi(qu.po) is given by All three integration algorithms are evolution mappings.," Given an evolution mapping $F_t : (q,p) \mapsto (Q_t(q,p), P_t(q,p))$, the pushforward of the Poincaré integral invariant $\mathcal{I}962\equiv dq \wedge dp$ along the trajectory $q(t), p(t) = F_t\left(q_0,963p_0 \right)$ is given by All three integration algorithms are evolution mappings."964 An elegant algorithum (??) exists to compute derivatives of arbitrary computations.such as our evolution mappings. without the (runeation error whieh would result [rom finite differencing.," An elegant algorithm \citep{Sussman2006,Sussman2001} exists to compute derivatives of arbitrary computations,such as our evolution mappings, without the truncation error which would result from finite differencing."965 We used this, We used this966analysis of the rotation-activity relation for such stars.,analysis of the rotation–activity relation for such stars.967 In Section 5 we follow the method of to derive a new empirical estimate of 7 based on the ?)larger sample used in this work., In Section \ref{s-tau} we follow the method of \citet{pizz03} to derive a new empirical estimate of $\tau$ based on the larger sample used in this work.968" Figure 2 shows Rx as a function of Ro for all the stars in our sample, clearly demonstrating that the X-ray luminosity ratio increases with decreasing rotation period (or increasing rotation rate), as expected from qualitative arguments based on the a— w-type shell dynamo theory"," Figure \ref{allstars} shows $R_X$ as a function of $Ro$ for all the stars in our sample, clearly demonstrating that the X-ray luminosity ratio increases with decreasing rotation period (or increasing rotation rate), as expected from qualitative arguments based on the $\alpha-\omega$ -type shell dynamo theory."969" As noted by many previous observers, the X-ray emission level appears to saturate at the highest rotation rates, reaching an approximately constant level of Rx~107%."," As noted by many previous observers, the X-ray emission level appears to saturate at the highest rotation rates, reaching an approximately constant level of $R_X \sim 10^{-3}$."970" This effect clearly divides the rotation-activity relation into two regimes: asaturated regime at high rotation rates, and anunsaturated regime for slow rotators."," This effect clearly divides the rotation–activity relation into two regimes: a regime at high rotation rates, and an regime for slow rotators."971 The transition between these two regimes can be seen to occur at Πο”0.1., The transition between these two regimes can be seen to occur at $Ro \sim 0.1$.972" In the discussion that follows, the rotation-activity relation is divided into these two regimes in an attempt to reveal the different physical processes at work."," In the discussion that follows, the rotation–activity relation is divided into these two regimes in an attempt to reveal the different physical processes at work."973" Approximately linear relations in log-log space are immediately apparent from this figure, despite a spread in both Rx and Ro."," Approximately linear relations in log-log space are immediately apparent from this figure, despite a spread in both $R_X$ and $Ro$."974 This spread is likely to be caused by a number of different factors arising from the necessarily simplified analysis of the data performed here., This spread is likely to be caused by a number of different factors arising from the necessarily simplified analysis of the data performed here.975 Both the X-ray luminosity and the photometric rotation period are approximations of the real values due to the methods employed in measuring them., Both the X-ray luminosity and the photometric rotation period are approximations of the real values due to the methods employed in measuring them.976" X-ray luminosities will vary over the course of a stellar activity cycle, by up to an order of magnitude in the case of our Sun (?),, and will vary on shorter timescales due to the influence of coronal flares."," X-ray luminosities will vary over the course of a stellar activity cycle, by up to an order of magnitude in the case of our Sun \citep{pere00}, and will vary on shorter timescales due to the influence of coronal flares."977" Furthermore, the measured rotation period will be a latitudinal mean due to the unresolved nature of the stellar disk, and may also vary over the course of an activity cycle due to the varying starspot coverage."," Furthermore, the measured rotation period will be a latitudinal mean due to the unresolved nature of the stellar disk, and may also vary over the course of an activity cycle due to the varying starspot coverage."978 A further source of uncertainty is due to the effects of unresolved binaries in this sample., A further source of uncertainty is due to the effects of unresolved binaries in this sample.979" Photometrically, the presence of a lower mass binary companion will cause the star to appear redder and more luminous, resulting in a lower mass estimate and a smaller photometric distance."," Photometrically, the presence of a lower mass binary companion will cause the star to appear redder and more luminous, resulting in a lower mass estimate and a smaller photometric distance."980" Distance errors cancel out when deriving the X-ray-to-bolometric luminosity ratio, but uncertainties in the mass, and therefore spectral type, can affect a number of the parameters and quantities derived for each star."," Distance errors cancel out when deriving the X-ray-to-bolometric luminosity ratio, but uncertainties in the mass, and therefore spectral type, can affect a number of the parameters and quantities derived for each star."981" Literature spectral types were obtained for 225 of the 824 stars in the sample including 163 of the 168 binaries in our sample, reducing the influence of this effect."," Literature spectral types were obtained for 225 of the 824 stars in the sample including 163 of the 168 binaries in our sample, reducing the influence of this effect."982" Another influence of binary companions is the effect on the X-ray emission, the presence of a close secondary potentially elevating the level of emission due to tidal coupling or their orbits."," Another influence of binary companions is the effect on the X-ray emission, the presence of a close secondary potentially elevating the level of emission due to tidal coupling or their orbits."983 The 168 binaries in our samples are highlighted in Figure 2 and are concentrated in the unsaturated regime (which is dominated by older field stars)., The 168 binaries in our samples are highlighted in Figure \ref{allstars} and are concentrated in the unsaturated regime (which is dominated by older field stars).984" Their X-ray levels, in both the saturated and unsaturated regimes, all lie within the 1o spreads on the fits determined here, with no trend for either elevated or reduced X-ray emission."," Their X-ray levels, in both the saturated and unsaturated regimes, all lie within the $\sigma$ spreads on the fits determined here, with no trend for either elevated or reduced X-ray emission."985 We therefore include these sources in our subsequent study of the rotation-activity relation without fear that their presence will bias the results., We therefore include these sources in our subsequent study of the rotation–activity relation without fear that their presence will bias the results.986 The unsaturated regime in the rotation-activity relation is believed to probe the efficiency of the stellar dynamo in heating the corona., The unsaturated regime in the rotation–activity relation is believed to probe the efficiency of the stellar dynamo in heating the corona.987" ?) found that the X-ray luminosity of solar- and late-type stars scales with projected rotational velocity, to the first order, Lxος (vsini)?."," \citet{pall81} found that the X-ray luminosity of solar- and late-type stars scales with projected rotational velocity, to the first order, $L_X \propto (v \mathrm{sin} i)^2$ ."988" This relationship has since been investigated by many authors, more recently in the form of the Rx - Ro relationship, using photometric rotation periods as well as making the distinction between stars with saturated and unsaturated X-ray emission."," This relationship has since been investigated by many authors, more recently in the form of the $R_X$ - $Ro$ relationship, using photometric rotation periods as well as making the distinction between stars with saturated and unsaturated X-ray emission."989 The low level of scatter in the Rx—Ro diagram has been interpreted by many authors (e.g.??) as evidence for a strong underlying physical relationship.," The low level of scatter in the $R_X - Ro$ diagram has been interpreted by many authors \citep[e.g.][]{mont01,pizz03} as evidence for a strong underlying physical relationship."990(CL) (SES) (LII) Comunent: Definition #11 ieludes all of the disks described here.,(CL) (SES) (LH) Comment: Definition 1 includes all of the disks described here.991 Definition 2 excludes: cireumibinary disks. (, Definition 2 excludes circumbinary disks. (992LII) (DW) (NC),LH) (DW) (NC)993"Finding the best combination of the parameters that minimizes the differences between the observed and the model spectrum, is a non-linear problem, due to the presence of extinction.","Finding the best combination of the parameters that minimizes the differences between the observed and the model spectrum, is a non-linear problem, due to the presence of extinction."994" Furthermore, it is also underdetermined, which means that the number of constraints is lower than the number of parameters."," Furthermore, it is also underdetermined, which means that the number of constraints is lower than the number of parameters."995" In fact, in our case, we are using SSPs of 12 different ages, so that our task turns into finding the combination of 12 mass and extinction values that better fits the observed spectrum."," In fact, in our case, we are using SSPs of 12 different ages, so that our task turns into finding the combination of 12 mass and extinction values that better fits the observed spectrum."996" To find the set of 24 parameters that will yield the best fit model, we use the Adaptive Simulated Annealing algorithm, which randomly explores the parameters space, searching for an absolute minimum in the x? function."," To find the set of 24 parameters that will yield the best fit model, we use the Adaptive Simulated Annealing algorithm, which randomly explores the parameters space, searching for an absolute minimum in the $\chi^2$ function."997" This method is particulary suited to such problems, where the function to minimize has lots of local minima: once a promising zone for a minimum, in the parameter space, is found, the algorithm not only refines the search of the local minimum, but also checks for the presence of other, deeper minima, outside the local *low-x? valley""."," This method is particulary suited to such problems, where the function to minimize has lots of local minima: once a promising zone for a minimum, in the parameter space, is found, the algorithm not only refines the search of the local minimum, but also checks for the presence of other, deeper minima, outside the local $\chi^2$ valley”."998" All the physical parameters that are derived from the the spectral analysis, refer to a best fit model for an observed spectrum."," All the physical parameters that are derived from the the spectral analysis, refer to a best fit model for an observed spectrum."999" The limited wavelength range under analysis, the well known age-metallicity degeneracy, and the non-linearity of the problem, together with the fact that it is underdetermined, makes the solution non-unique."," The limited wavelength range under analysis, the well known age-metallicity degeneracy, and the non-linearity of the problem, together with the fact that it is underdetermined, makes the solution non-unique."1000 'This means that models with different characteristics may equally well reproduce the observed spectral features., This means that models with different characteristics may equally well reproduce the observed spectral features.1001" 'To account for this, we give error-bars related to mass, extinction and age values."," To account for this, we give error-bars related to mass, extinction and age values."1002" To compute such uncertainties, we exploit the characteristics of the minimisation algorithm: the path towards the best fit model (or the minimum x?) depends on the starting points so, in general, starting from different initial positions can lead to different minimum points, ie. to best fit models with different parameters."," To compute such uncertainties, we exploit the characteristics of the minimisation algorithm: the path towards the best fit model (or the minimum $\chi^2$ ) depends on the starting points so, in general, starting from different initial positions can lead to different minimum points, i.e. to best fit models with different parameters."1003" We hence perform 11 optimisations, each time starting from a different point in the parameters space."," We hence perform 11 optimisations, each time starting from a different point in the parameters space."1004 In this way we end up with 11 best fit models that we verified are well representative of the space of the solutions., In this way we end up with 11 best fit models that we verified are well representative of the space of the solutions.1005" We take, as a reference, the model with the median total mass among these 11."," We take, as a reference, the model with the median total mass among these 11."1006 All the errorbars are computed as the average difference between the values of the models with the highest and lowest total stellar mass., All the errorbars are computed as the average difference between the values of the models with the highest and lowest total stellar mass.1007" The similarity between an observed spectrum and its best fit model is measured, as explained in refsec:fit,, by means of a x? function taking into account both spectral continuum fluxes and the equivalent widths of significant lines."," The similarity between an observed spectrum and its best fit model is measured, as explained in \\ref{sec:fit}, by means of a $\chi^2$ function taking into account both spectral continuum fluxes and the equivalent widths of significant lines."1008" Our choice to use a wide range both in metallicity and SSP ages, and to let both extinction and mass vary freely, are the key ingredients that allow us to satisfactorily reproduce any galactic spectrum, at least in principle."," Our choice to use a wide range both in metallicity and SSP ages, and to let both extinction and mass vary freely, are the key ingredients that allow us to satisfactorily reproduce any galactic spectrum, at least in principle."1009" In practice, low quality spectra due to low S/N, bad flux calibration, bad subtraction of sky or telluric lines,"," In practice, low quality spectra due to low S/N, bad flux calibration, bad subtraction of sky or telluric lines,"1010 , 1011binary GX 13]1 shares several of the properties of the Z sources (lloman ct al.,binary GX 13+1 shares several of the properties of the Z sources (Homan et al.1012 1998 and. references. therein), 1998 and references therein).1013 In particular the svstem is know to be a relatively bright aux persistent radio source. supported by our strong detection at a level *| mJy.," In particular the system is know to be a relatively bright and persistent radio source, supported by our strong detection at a level $\geq 1$ mJy."1014 mThe radio. spectrum from⋅ this. source. unlike that of GX 17|2 and GX 5-1. was negative curing ou observations and Consistent with optically thin svnchrotron emission.," The radio spectrum from this source, unlike that of GX 17+2 and GX 5-1, was negative during out observations and consistent with optically thin synchrotron emission."1015 Combined with the relatively bright. state. this suggests the recent ejection of a radio-emitting componen which has expanded to an optically thin state.," Combined with the relatively bright state, this suggests the recent ejection of a radio-emitting component which has expanded to an optically thin state."1016 The limits on linearly polarised emission. of and at 6.3 and 3.5 em respectively. are fairly constraining as this level of linear polarisation is sometimes achieved by brighter racio transients associated with X-ray binaries. particularly when the emission is optically thin (as suggested in this case by the spectral index of 0.4 0.1).," The limits on linearly polarised emission, of and at 6.3 and 3.5 cm respectively, are fairly constraining as this level of linear polarisation is sometimes achieved by brighter radio transients associated with X-ray binaries, particularly when the emission is optically thin (as suggested in this case by the spectral index of $-0.4 \pm 0.1$ )."1017 Probably there is still a large contribution from a depolarised core and/or Faraday depolarisation in the ejecta., Probably there is still a large contribution from a depolarised core and/or Faraday depolarisation in the ejecta.1018 1t has been suggested that 28 0921-630 (V395 Car) is a Z-source viewed nearly edge-on. (Zwarthoed ct al., It has been suggested that 2S 0921-630 (V395 Car) is a Z-source viewed nearly edge-on (Zwarthoed et al.1019 1993. and references therein: see also Shahbaz ct al., 1993 and references therein; see also Shahbaz et al.1020 1999)., 1999).1021 As the Z sources have all been detected. at. one time or another as radio sources (Πομις Han 1995 and references therein). it is expected that 28 0921-630 should also be a radio source i it is one of these systems.," As the Z sources have all been detected at one time or another as radio sources (Hjellming Han 1995 and references therein), it is expected that 2S 0921-630 should also be a radio source if it is one of these systems."1022 Zwarthoed et al. (, Zwarthoed et al. (10231993). placed upper limits on the radio Hux density [from this source of 0.5 mJy at 4.8 Cllz.,1993) placed upper limits on the radio flux density from this source of $\sim 0.5$ mJy at 4.8 GHz.1024 Fender Hendrey (2000) have shown that the mean radio flux. density of the Z sources at cm wavelengths. when on the Horizontal Branch. is 55+13/47 ," Fender Hendry (2000) have shown that the mean radio flux density of the Z sources at cm wavelengths, when on the Horizontal Branch, is $55 \pm 13 / d^2$ "1025? developed a photometric calibration of M-dwarf metallicities based on the spectroscopic analysis of F/G/K-type components of wide binary systems. where the secondaries are M dwarfs.,"\citet{2005A_A...442..635B} developed a photometric calibration of M-dwarf metallicities based on the spectroscopic analysis of F/G/K-type components of wide binary systems, where the secondaries are M dwarfs."1026 They complemented their calibratior sample with spectroscopic metallicities derived for metal-poor early- dwarfs by ?.., They complemented their calibration sample with spectroscopic metallicities derived for metal-poor early-M-type dwarfs by \citet{2005MNRAS.356..963W}.1027 Based on these metallicities and 2MASS photometry for 46 stars. they derived an expression for the netallicity as a function of absolute K magnitude Mj and V-K colour.," Based on these metallicities and 2MASS photometry for 46 stars, they derived an expression for the metallicity as a function of absolute K magnitude $M_K$ and $V-K$ colour."1028 ? analysed optical spectra with R>50000 and signal-to-noise ratios between 200 and 400 of three stars., \citet{2006ApJ...653L..65B} analysed optical spectra with $R\ge50000$ and signal-to-noise ratios between 200 and 400 of three stars.1029 They used the nethods developed in ?.. fitting synthetic spectra for 16 atomic lines in the spectral intervals 8326 to 8427 and 8660 to 8693Á.. as well as a TiO bandhead at 7088 tto. their observations.," They used the methods developed in \citet{2006ApJ...652.1604B}, fitting synthetic spectra for 16 atomic lines in the spectral intervals 8326 to 8427 and 8660 to 8693, as well as a TiO bandhead at 7088 to their observations."1030 They simultaneously determined Tey. metallicity. broadening parameters. and continuum normalization factors from the spectra.," They simultaneously determined , metallicity, broadening parameters, and continuum normalization factors from the spectra."1031 ? used five wide binary stars with F/G/K primaries and M-dwarf secondaries to evaluate their method (amongst them GJ 105)., \citet{2006ApJ...652.1604B} used five wide binary stars with F/G/K primaries and M-dwarf secondaries to evaluate their method (amongst them GJ 105).1032 They found differences in derived metallicity between the M dwarf and solar-similar components ranging from —0.16 to —0.07 for four systems. and +0.03 dex for GJ 105.," They found differences in derived metallicity between the M dwarf and solar-similar components ranging from $-0.16$ to $-0.07$ for four systems, and +0.03 dex for GJ 105."1033 ? and ? both aimed to improve the ? photometric calibration. taking a slightly different approach.," \citet{2009ApJ...699..933J} and \citet{2010A&A...519A.105S} both aimed to improve the \citet{2005A_A...442..635B} photometric calibration, taking a slightly different approach."1034 First. they used a volume-limitec calibration sample of solar-type stars to derive the mean metallicity of the solar neighbourhood.," First, they used a volume-limited calibration sample of solar-type stars to derive the mean metallicity of the solar neighbourhood."1035 ? selected 109 GO-K2 dwarfs with spectroscopically determined metallicities and distances d.<18 pe from ?.., \citet{2009ApJ...699..933J} selected 109 G0-K2 dwarfs with spectroscopically determined metallicities and distances $d<18$ pc from \citet{2005ApJS..159..141V}.1036" ? selected a sample of F and G dwarfs with metallicity estimates based on Strómmgren photometry and d.«20 pe from ?.. which was kinematically matchec to the solar-neighbourhood M-dwarf population,"," \citet{2010A&A...519A.105S} selected a sample of F and G dwarfs with metallicity estimates based on Strömmgren photometry and $d<20$ pc from \citet{2009A&A...501..941H}, which was kinematically matched to the solar-neighbourhood M-dwarf population."1037 Next. these authors defined a main-sequence line in the (V—K)-My plane for a second calibration sample of late-K and M-type dwarfs.," Next, these authors defined a main-sequence line in the $(V-K) - M_K$ plane for a second calibration sample of late-K and M-type dwarfs."1038 ? defined the second calibration sample of nearby low-mass stars to be a volume-limited sample of single K-type dwarfs (4«20 pc) and single M-type dwarfs (4.« pe) based on parallaxes from Hipparcos and other sources., \citet{2009ApJ...699..933J} defined the second calibration sample of nearby low-mass stars to be a volume-limited sample of single K-type dwarfs $d<20$ pc) and single M-type dwarfs $d<10$ pc) based on parallaxes from Hipparcos and other sources.1039 They fit a fifth-degree polynomial to the V—K colours and My magnitudes of these stars., They fit a fifth-degree polynomial to the $V-K$ colours and $M_K$ magnitudes of these stars.1040 ? adopted the main-sequence line of ? for their study., \citet{2010A&A...519A.105S} adopted the main-sequence line of \citet{2009ApJ...699..933J} for their study.1041 A third calibration sample was used to find the variation of metallicity with horizontal or vertical distance from the main-sequence line (A(V—K) or AMg. respectively).," A third calibration sample was used to find the variation of metallicity with horizontal or vertical distance from the main-sequence line $\Delta(V-K)$ or $\Delta M_K$, respectively)."1042 2. used a set of six M dwarfs with FGK-companions with. metallicities >40.2 dex from ? and assigned to the main-sequence line the mean metallicity of the first calibration sample., \citet{2009ApJ...699..933J} used a set of six M dwarfs with FGK-companions with metallicities $>+0.2$ dex from \citet{2005ApJS..159..141V} and assigned to the main-sequence line the mean metallicity of the first calibration sample.1043" They derived a linear relationship between [Fe/H] and AM, with a dispersion of 0.06 dex.", They derived a linear relationship between [Fe/H] and $\Delta M_K$ with a dispersion of 0.06 dex.1044 ? extended this calibration set by adding 13 wide-binary stars with accurate V magnitudes from ? with -0.33< [Fe/H] <+0.32., \citet{2010A&A...519A.105S} extended this calibration set by adding 13 wide-binary stars with accurate $V$ magnitudes from \citet{2005A_A...442..635B} with $-0.33\le$ [Fe/H] $\le+0.32$.1045 They derived a linear relationship between [Fe/H] and A(V-K). based only on the third calibration sample and the main-sequence line.," They derived a linear relationship between [Fe/H] and $\Delta(V-K)$, based only on the third calibration sample and the main-sequence line."1046 In this case. the first calibration sample was used to verify that the zero-point. of this relationship ts close to the mean metallicity of the solar neighbourhood.," In this case, the first calibration sample was used to verify that the zero-point of this relationship is close to the mean metallicity of the solar neighbourhood."1047 The work of ? is based on low-resolution spectroscopy in the K-band., The work of \citet{2010ApJ...720L.113R} is based on low-resolution spectroscopy in the K-band.1048 They used a calibration sample of 17 M dwarfs in wide-binary systems with metallicities determined for the FGK primaries by ?.., They used a calibration sample of 17 M dwarfs in wide-binary systems with metallicities determined for the FGK primaries by \citet{2005ApJS..159..141V}.1049 From these metallicities and their observations. they derived a linear relationship between [Fe/H]. two metallicity-sensitive indices measured from Na | and Ca I features. and a temperature-sensitive water index.," From these metallicities and their observations, they derived a linear relationship between [Fe/H], two metallicity-sensitive indices measured from Na I and Ca I features, and a temperature-sensitive water index."1050 They estimate an uncertainty for their calibration of 0.15 dex., They estimate an uncertainty for their calibration of 0.15 dex.1051 We compiled a sample of M dwarfs in binary systems with a solar-type (FGK) primary companion and non-binary M dwarfs in the solar vicinity., We compiled a sample of M dwarfs in binary systems with a solar-type (FGK) primary companion and non-binary M dwarfs in the solar vicinity.1052 Some of the M dwarfs or systems we observed are known to harbour planets. others have no detection of any planet companions as yet.," Some of the M dwarfs or systems we observed are known to harbour planets, others have no detection of any planet companions as yet."1053 The programme stars were selected from the Catalogue of nearby wide binary and multiple systems (?) and from the Interactive Catalog of the on-line Extrasolar Planets Encyclopaedia (?)footnotehttp://exoplanet.eu.. as well as from à programme searching for stellar companions of exoplanet host stars (222)..," The programme stars were selected from the Catalogue of nearby wide binary and multiple systems \citep{1994RMxAA..28...43P} and from the Interactive Catalog of the on-line Extrasolar Planets Encyclopaedia \citep{2011A&A...532A..79S}, as well as from a programme searching for stellar companions of exoplanet host stars \citep{2004A&A...425..249M,2005A&A...440.1051M,2007MNRAS.378.1328M}."1054 The observations were carried out in service mode with the infrared spectrometer CRIRES at ESO-VLT (?).., The observations were carried out in service mode with the infrared spectrometer CRIRES at ESO-VLT \citep{2004SPIE.5492.1218K}.1055 In total 14 targets were observed during periods 82 (Ist of October 2008 to 31st of March 2009) and 84 (Ist of October 2009 to 31st of March 2010)., In total 14 targets were observed during periods 82 (1st of October 2008 to 31st of March 2009) and 84 (1st of October 2009 to 31st of March 2010).1056" A slit width of 0.4"" was used. resulting in a resolving power of R = 4/A4=50000."," A slit width of $\arcsec$ was used, resulting in a resolving power of R = $\lambda/\Delta\lambda = 50\,000$."1057 In addition a number of close binary systems with small separations (x 220”) were observed which will be discussed in à future paper., In addition a number of close binary systems with small separations $\leq$ $\arcsec$ ) were observed which will be discussed in a future paper.1058 In this article we present the analysis of three wide binary systems and eight single M dwarfs., In this article we present the analysis of three wide binary systems and eight single M dwarfs.1059" The binary systems are well separated and the angular separations are 73” for HD 101930 (?).. 165” for GJ 105 (2).. and 58.3"" for GJ 250 (?).."," The binary systems are well separated and the angular separations are $\arcsec$ for HD 101930 \citep{2007MNRAS.378.1328M}, $\arcsec$ for GJ 105 \citep{1938ApJ....88...27V}, and $\arcsec$ for GJ 250 \citep{2002yCat.1274....0D}."1060 The observations of our targets should therefore not be contaminated with light from the companion star., The observations of our targets should therefore not be contaminated with light from the companion star.1061 GJ. 105A has a faint. close-by (37) low-mass companion. GJ 105C (22)..," GJ 105A has a faint, close-by $\arcsec$ ) low-mass companion, GJ 105C \citep{1995ApJ...444L.101G,1995ApJ...452L.125G}."1062 The luminosity difference in the J band however is on the order of five magnitudes and the fainter companion is assumed not to affect the analysis., The luminosity difference in the J band however is on the order of five magnitudes and the fainter companion is assumed not to affect the analysis.1063 See Table | fora list of spectral types. binarity and planet detections of the stars treated in this paper.," See Table \ref{tab:targets} for a list of spectral types, binarity and planet detections of the stars treated in this paper."1064 Each target was observed with four different CRIRES wavelength settings. centered on 1177. 1181. 1204. and nnm in period 82. and 1177. 1205. 1258. and nnm in period 84 (see Figure 2. 4 for the total wavelength coverage).," Each target was observed with four different CRIRES wavelength settings, centered on 1177, 1181, 1204, and nm in period 82, and 1177, 1205, 1258, and nm in period 84 (see Figure \ref{fig:GJ250A} \ref{fig:GJ849} for the total wavelength coverage)."1065 For some of the fainter targets we obtained several exposures. which were co-added to reach a signal-to-noise ratio around 100.," For some of the fainter targets we obtained several exposures, which were co-added to reach a signal-to-noise ratio around 100."1066 The typical continuum signal-to-noise ratio spans between 70 and 150., The typical continuum signal-to-noise ratio spans between 70 and 150.1067 CRIRES contains four detectors. but unfortunately. only detectors #22 and #33 produced reliable data. as #11 and #44 are heavily vignetted and possibly contaminated by crosstalk between adjacent orders.," CRIRES contains four detectors, but unfortunately only detectors 2 and 3 produced reliable data, as 1 and 4 are heavily vignetted and possibly contaminated by crosstalk between adjacent orders."1068 Realizing the extent of this failure of the first and fourth detector we chose to rearrange the wavelength settingsbetween the observing periods., Realizing the extent of this failure of the first and fourth detector we chose to rearrange the wavelength settingsbetween the observing periods.1069 We re- one target from period 82 (GJ 849) in period 84 to assure consistency between the two observing runs., We re-observed one target from period 82 (GJ 849) in period 84 to assure consistency between the two observing runs.1070 As Is shown below (Section 5)). our analysis indeed gives the same," As is shown below (Section \ref{sect:results}) ), our analysis indeed gives the same"1071reclshit error estinmates (see Brunnerefad.1999a for an application of this tecliuique to the ntherecdshilt «istribution).,redshift error estimates (see \citealt{brunner99} for an application of this technique to the number-redshift distribution).1072 The quantiv of inte‘est is determiued as the mean of the nultip realizaious. aud he associated error is given by the correspoucline staudarc deviation.," The quantity of interest is determined as the mean of the multiple realizations, and the associated error is given by the corresponding standard deviation."1073 lu order to civicle our saije by intrinsic luminosity. we «eterined the absolute maguiti cdistribijon of the ealaxies lu our catalog in an ensemble apJrOac1.," In order to divide our sample by intrinsic luminosity, we determined the absolute magnitude distribution of the galaxies in our catalog in an ensemble approach."1074" ""n‘st. we created clifferent realizalous of ot ealaxy cataog."," First, we created different realizations of our galaxy catalog."1075 In order to minimize any systenatic errors. we selected the »paret|o magultu(e of each gaaxy [roin a Gaussian probability ἆistribiion {liction with mean ick signa given Im the origiual photometr alog meastremeus.," In order to minimize any systematic errors, we selected the apparent magnitude of each galaxy from a Gaussian probability distribution function with mean and sigma given from the original photometric catalog measurements."1076 51Similarly. the recshift of each galaxy was ¢rawu [ron a separate Ca srobability cist‘buion [uncetion wit1 mean aud signa given n1n the phoometric redshift and. correspoidiug reds1ift error estimate.," Similarly, the redshift of each galaxy was drawn from a separate Gaussian probability distribution function with mean and sigma given from the photometric redshift and corresponding redshift error estimate."1077 The h—correction was ceted1uined ussing the spectral classiication wlΙσ was par oft lle original ‘ectshift estimaion procedre., The $k-$ correction was determined using the spectral classification which was part of the original redshift estimation procedure.1078 For galaxies with large jlphotometric redslits. occasional ciscordaut redshifts were Caculated outside tle range of our «walibrajou sainple — (2 1.2) in which case the galaxy was dropped [rom lat particular realization.," For galaxies with large photometric redshifts, occasional discordant redshifts were calculated outside the range of our calibration sample — $z < 0$, or $z >10791.2$ ) in which case the galaxy was dropped from that particular realization."1080ali Together. these qlantities were used to cerniie the absolute imagniude for each galaxy iu 100 cifferent eusemble distribiTous.," Together, these quantities were used to determine the absolute magnitude for each galaxy in 100 different ensemble distributions."1081 The absolute iuagnitude for each galaxy was calculated as the inean over the clilferer1 realizatious. appropriately ormalized to account [or possible cdiscordanut redshifts as discussed above.," The absolute magnitude for each galaxy was calculated as the mean over the different realizations, appropriately normalized to account for possible discordant redshifts as discussed above."1082 Tjeresultant. distributious for the C aud B bands are displayed iu Figure 2.., Theresultant distributions for the $U$ and $B$ bands are displayed in Figure \ref{abs-mag}.1083 Before computiig the anelar correlation fuuction. we quantified our ellicieucy. in detectiug galaxies as a [unctio1 of pixel loxation.," Before computing the angular correlation function, we quantified our efficiency in detecting galaxies as a function of pixel location."1084 The primary areas where this effect is unportant are around bright sars. in char‘ee transfer rails. aud. near the edge of the [raue due to edge ellects or focus degradaious.," The primary areas where this effect is important are around bright stars, in charge transfer trails, and near the edge of the frame due to edge effects or focus degradations."1085 We. tjerefore. deined bounding boxes. for each of he four stacked images. which contaiued all of the observable 1lus for the saturated stars within tie image.," We, therefore, defined bounding boxes, for each of the four stacked images, which contained all of the observable flux for the saturated stars within the image."1086 Iu the enc. a total of 15 regloIs Were nasXe out in tie. frame. 1T regious were maske out iu the frame. 15 regions were rnasked out in the [raije. aud 36 'e0οςlous were masked out iu the [rame.," In the end, a total of 15 regions were masked out in the frame, 17 regions were masked out in the frame, 45 regions were masked out in the frame, and 36 regions were masked out in the frame."1087 We also maskecl both the edge aud corners of each [ratne in order to reduce the ellects of PSF variations on our object detectiou eflicieucy., We also masked both the edge and corners of each frame in order to reduce the effects of PSF variations on our object detection efficiency.1088 These {οι loliask files were coucatenated to produce a total mask file which was used Oo ‘the calculation of tje angular correlation function in dilferent redshift or absolute imaguitude iuervals., These four mask files were concatenated to produce a total mask file which was used for the calculation of the angular correlation function in different redshift or absolute magnitude intervals.1089 We used the optimalestimator Landy&Szalay(1903). (DD-2DR+RR)/RR. where D stands ( “data and & stands for raudom. to determine the angular correlation. function.," We used the optimalestimator \citet{landy93} $(DD - 2DR + RR)/RR$, where $D$ stands for data and $R$ stands for random, to determine the angular correlation function."1090" This required COuuting the μιοί of observed pairs (that were not within masked areas). which was donein 10 dLis of consiant width Ale(J)= 0.25. centered at 0= L3"". to 0— 759.6""."," This required counting the number of observed pairs (that were not within masked areas), which was donein 10 bins of constant width $\Delta\lg(\theta) = 0.25$ , centered at $\theta = 4.3\arcsec$ , to $\theta = 759.6\arcsec$ ."1091 One thousand objects, One thousand objects1092source.,source.1093 Therefore. it cannot be ruled out that the NMAM-Newton (anc ASCA) observations represent already its normal lux level.," Therefore, it cannot be ruled out that the XMM-Newton (and ASCA) observations represent already its normal flux level."1094 This work is based on observations obtained with NMAM-Newton. an ESA science mission. with instruments and contributions cirectly funded by ESA Member States and the USA (NASA).," This work is based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and the USA (NASA)."1095 The NMM-Newton Science. Operation Center is gratefully acknowledged for having produced with unprecedented speed. and made publicly available ODE for the observation described in this paper.," The XMM-Newton Science Operation Center is gratefully acknowledged for having produced with unprecedented speed, and made publicly available ODF for the observation described in this paper."1096Ostrowski 2003). where à is the Doppler factor.,"Ostrowski 2003), where $\delta$ is the Doppler factor."1097 Recent work by Sambruna et al. (, Recent work by Sambruna et al. (10982004) and Hardeastle et al. (,2004) and Hardcastle et al. (10992004) provide additional optical hotspot source detections and we were able to estimate G. for 8 additional hotspots in 6 radio sources as described By)above (Table 5)).,"2004) provide additional optical hotspot source detections and we were able to estimate $\nu_{\rm b}$, $B_{\rm eq}$ ) for 8 additional hotspots in 6 radio sources as described above (Table \ref{table-5}) )."1100 Although information for a large number of optical hotspots are provided by Hardeastle et al. (, Although information for a large number of optical hotspots are provided by Hardcastle et al. (11012004). only four of these hotspots (in three objects) were not previously considered in the study by Brunetti et al. (,"2004), only four of these hotspots (in three objects) were not previously considered in the study by Brunetti et al. ("11022003).,2003).1103 Of these four hotspots. we could not confirm the case in 3C 280 from our independent analysis of the same HST data (see also the radio/optical image overlay in Figure 3 of Ridgway et al.," Of these four hotspots, we could not confirm the case in 3C 280 from our independent analysis of the same HST data (see also the radio/optical image overlay in Figure 3 of Ridgway et al."1104 2004 — the radio and optical peaks were not clearly coineident as in our case in 3C 208: 3.1.1)) - this case Is omitted in our discussion., 2004 – the radio and optical peaks were not clearly coincident as in our case in 3C 208; \ref{sec:3c208}) ) – this case is omitted in our discussion.1105 We find that the derived (74. B) of the high radio power hotspots (Tables 5) lie near the extrapolation of the mX7 trend 4.traced by Brunetti et al. (," We find that the derived $\nu_{b}$, $B$ ) of the high radio power hotspots (Tables \ref{table-4} \ref{table-5}) ) lie near the extrapolation of the $\nu_{\rm b}\propto$$B^{-3}$ trend traced by Brunetti et al. ("11062003). which lends support to their simple picture (Figure 6)).,"2003), which lends support to their simple picture (Figure \ref{fig-6}) )."1107 This is a remarkable finding considering the hotspots span about 3 orders of magnitude in magnetic field energy density. while considering both radio galaxies and quasars.," This is a remarkable finding considering the hotspots span about 3 orders of magnitude in magnetic field energy density, while considering both radio galaxies and quasars."1108 In the scenario outlined by Brunetti et al. (, In the scenario outlined by Brunetti et al. (11092003). the proportionality is: τηνκ Gti/ups777B7. where τ is the dynamical age of the hotspot and the ratio of the energy densities of the lobe (9) and the hotspot (ys) accounts for adiabatic losses.,"2003), the proportionality is: $\nu_{\rm b}\propto$ $(u_{l}/u_{\rm HS})^{1/2}1110\tau^{-2} B^{-3}$, where $\tau$ is the dynamical age of the hotspot and the ratio of the energy densities of the lobe $u_{l}$ ) and the hotspot $u_{\rm HS}$ ) accounts for adiabatic losses."1111 More precise mapping of the high-power hotspot SEDs are necessary to confirm that the —3 slope indeed extends over 6 orders of magnitude in frequency (e.g. that there Is no change in the slope)., More precise mapping of the high-power hotspot SEDs are necessary to confirm that the –3 slope indeed extends over 6 orders of magnitude in frequency (e.g. that there is no change in the slope).1112 If confirmed. these observations could imply that that there is a single dynamical age for radio hotspots in radio galaxies and quasars over a wide range in power.," If confirmed, these observations could imply that that there is a single dynamical age for radio hotspots in radio galaxies and quasars over a wide range in power."1113" Spitzer Space Telescope observations. already approved for two of our new optical hotspot sources. will allow us to measure the high energy slope of the SED which will constrain 1, more robustly."," Spitzer Space Telescope observations, already approved for two of our new optical hotspot sources, will allow us to measure the high energy slope of the SED which will constrain $\nu_{b}$ more robustly."1114" While additional millimeter and sub-mm observations (in the future with ALMA) are required to map the shape of the high energy synchrotron spectrum. existing radio. optical. and new infrared data can constrain the break frequency adequately (to better than a decade) for the purpose of showing the extrapolation of the 14—B4, sequence determined from the theory."," While additional millimeter and sub-mm observations (in the future with ALMA) are required to map the shape of the high energy synchrotron spectrum, existing radio, optical, and new infrared data can constrain the break frequency adequately (to better than a decade) for the purpose of showing the extrapolation of the $\nu_{\rm b}-B_{\rm eq}$ sequence determined from the theory."1115 Perl seripts written by Dan Homan were essential for this work and we are grateful to him for providing them., Perl scripts written by Dan Homan were essential for this work and we are grateful to him for providing them.1116 We thank Harri Teriissranta for providing us Metsihhovi monitoring data in advance of publication. Samuel Hariton for his help in the early stages of this project. the staffs at NRAO and Jodrell Bank for supplying us the archival radio data. and the anonymous referee for useful comments.," We thank Harri Terässranta for providing us Metsähhovi monitoring data in advance of publication, Samuel Hariton for his help in the early stages of this project, the staffs at NRAO and Jodrell Bank for supplying us the archival radio data, and the anonymous referee for useful comments."1117 C. C. C. is grateful to the HETG group at the MIT Kavli Institute for hosting his fellowship., C. C. C. is grateful to the HETG group at the MIT Kavli Institute for hosting his fellowship.1118 Radio astronomy at Brandeis University is supported by the NSF through grant AST 00-98608., Radio astronomy at Brandeis University is supported by the NSF through grant AST 00-98608.1119 Further support to C. C. C. and J. F. C. W. came from NASA grant GO2-3195C from the Smithsonian Astrophysical Observatory. and HST-GO-09122.08-A from the Space Telescope Science Institute (STScl).," Further support to C. C. C. and J. F. C. W. came from NASA grant GO2-3195C from the Smithsonian Astrophysical Observatory, and HST-GO-09122.08-A from the Space Telescope Science Institute (STScI)."1120 The VLA is a facility of the National Radio Astronomy Observatory is operated by Associated Universities. Inc. under à cooperative agreement with the National Science Foundation (NSF).," The VLA is a facility of the National Radio Astronomy Observatory is operated by Associated Universities, Inc. under a cooperative agreement with the National Science Foundation (NSF)."1121 MERLIN is a National Facility operated by the University of Manchester at Jodrell Bank Observatory on behalf of PPARC., MERLIN is a National Facility operated by the University of Manchester at Jodrell Bank Observatory on behalf of PPARC.1122 Based on observations made with the NASA/ESA Hubble Space Telescope. obtained from the data archive at the STSel. STSel is operated by the Association of Universities for Research in Astronomy. Inc. under NASA contract NAS 5-26555.," Based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the STScI. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555."1123 This research has made use of NASA’s Astrophysics Data System Abstract Service and the NASA/IPAC Extragalactic Database which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the NASA.," This research has made use of NASA's Astrophysics Data System Abstract Service and the NASA/IPAC Extragalactic Database which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the NASA."1124argest moment of inertia. the angular moment axis directed along CG. with G the amplitude of the aneular nunonientun and a reference axis arbitrarly chosen as the axis perpendicular to the orbit of Phoebe at a given epoch (see Fie.1)).,"largest moment of inertia, the angular momentum axis directed along $\overrightarrow{G}$, with G the amplitude of the angular momentum and a reference axis arbitrarly chosen as the axis perpendicular to the orbit of Phoebe at a given epoch t (see \ref{fig1}) )."1125 The precession aud mutation notions are respectively the linear aud the quasi-periodic parts of the notion of the figure axis or of the angular momentum axis with respect to the reference axis., The precession and nutation motions are respectively the linear and the quasi-periodic parts of the motion of the figure axis or of the angular momentum axis with respect to the reference axis.1126 Asstuine that he angle J between the angular momentum axis aud the Beure axis is παπα] as it is the case of the Earth (for which its value is less than 1). only the motic1 of the angular nolentii axis is considered here.," Assuming that the angle $J$ between the angular momentum axis and the figure axis is small as it is the case of the Earth (for which its value is less than $1""$ ), only the motion of the angular momentum axis is considered here."1127 The notion ofthis axis with respect to the reference axis is described by the angles h.I (Audover.1923) where Z is the obliquity angle aud fis characterizing the precessioun-uutatiou in longitude which corresponds to the augle between the reference point 2; aud the node Q.," The motion of this axis with respect to the reference axis is described by the angles $h, I$ (Andoyer,1923) where $I$ is the obliquity angle and $h$ is characterizing the precession-nutation in longitude which corresponds to the angle between the reference point $\gamma_{t}$ and the node $Q$."1128 The reference point 2; is the intersection vetweenthe orbit aud the equator of Phoebe at the date t. so-called “departure poiut (Capitaine. 1986) aud Q is the ascending node between the aue normal to the angular nolentium aud the orbital au.," The reference point $\gamma_{t}$ is the intersection between the orbit and the equator of Phoebe at the date t, so-called ""departure point"" (Capitaine, 1986) and $Q$ is the ascending node between the plane normal to the angular momentum and the orbital plan."1129 The Audover variables g.l in the Fig.l are respectively the angle between the rode Q and the node P aud 1 anele between a meridian orien al the node P where P is itself the ascending node )etwoeenu the plane normal to he augular moment axis aud the equatorial plane.," The Andoyer variables $g, l$ in the \ref{fig1} are respectively the angle between the node $Q$ and the node $P$ and the angle between a meridian origin and the node $P$ where $P$ is itself the ascending node between the plane normal to the angular momentum axis and the equatorial plane."1130 The proper rotation of Phoebe is described by the angle /|g=©., The proper rotation of Phoebe is described by the angle $l+g=\Phi$.1131 The Hamiltonian related o the rotational motion of Phoebo is: Fis the Tamultonian for the free rotational motion defined by: where £ is the component of the augular 1no1ieutui axis along the figure axis and zd.B.C are the principal moment of inertia of Phoebe.," The Hamiltonian related to the rotational motion of Phoebe is: $F_{o}$ is the Hamiltonian for the free rotational motion defined by: where $L$ is the component of the angular momentum axis along the figure axis and $A, B, C$ are the principal moment of inertia of Phoebe."1132 E|E* Is à coniponent related to the motion of the orbit of Phoebe. which is caused by planetary perturbations and have been giveu in detail iu Cottereau aud Souchay (2009) when studving the rotation of Venus.," $E+E'$ is a component related to the motion of the orbit of Phoebe, which is caused by planetary perturbations and have been given in detail in Cottereau and Souchay (2009) when studying the rotation of Venus."1133 Ü is the disturbing poteutial duc to Saturn considered as a point mass and its disturbing potential is given by : where G is the eravitational constant. M is tle mass of Saturn. r js the clistance between its barveenter aud the barveenter of Phoebe.," $U$ is the disturbing potential due to Saturn considered as a point mass and its disturbing potential is given by : where $\mathtt{\textbf{G}}$ is the gravitational constant, $M'$ is the mass of Saturn, $r$ is the distance between its barycenter and the barycenter of Phoebe."1134 a and 9 are respectively the longitude aud latitude of Saturn (not to be confused with the usual equatorial coordinates). with respect to the inca equator of Phoebe aud a meridian origin.," $\alpha$ and $\delta$ are respectively the longitude and latitude of Saturn (not to be confused with the usual equatorial coordinates), with respect to the mean equator of Phoebe and a meridian origin."1135" The 2)"" are the classical Legeudre functions giveu by: Notice that the perturbations due to the other plants. satellites aud the Sun a priori of second order. will not be studied in this paper."," The $P_{n}^m$ are the classical Legendre functions given by: Notice that the perturbations due to the other planets, satellites and the Sun a priori of second order, will not be studied in this paper."1136 The variation of the obliquity aud the precession angle is given by: To solve these equations. Kinoshita (1977) used the Horis method.," The variation of the obliquity and the precession angle is given by: To solve these equations, Kinoshita (1977) used the Hori's method."1137 As the order of the disturbing function is the jue method cau be applied to Phoebe., As the order of the disturbing function is : the same method can be applied to Phoebe.1138 Neglecting the very snall contribution as the component £|E aud applving the first order of the Moris method. this vields: U4 given by (3)) cau be expressed as a functiou of the longitude A aud the latitude JJ of Saturn with respect to the orbit of Phoebe at the date t using the trausformatious described by Kiuoshita (1977) and based on the Jacobi polvuomials: Finally the motious of precession-nutation in longitude and iu obliquity aregiven starting from (8)). (9)) aud (10)) by," Neglecting the very small contribution as the component $E+E'$ and applying the first order of the Hori's method, this yields: $ U_{1}$ given by \ref{eq1}) ) can be expressed as a function of the longitude $\lambda$ and the latitude $\beta$ of Saturn with respect to the orbit of Phoebe at the date t using the transformations described by Kinoshita (1977) and based on the Jacobi polynomials: Finally the motions of precession-nutation in longitude and in obliquity aregiven starting from\ref{eq2}) ), \ref{eq3}) ) and \ref{eq4}) ) by"1139decreases by a [actor Joni/Jon9xLOH210)!,"decreases by a factor $J_{\rm{env,i}}/J_{\rm{env}}{\approx}\,9\times10^{4}(2\times10^{8})$!"1140 The loss of angular momentum through the stellar wind is therefore important., The loss of angular momentum through the stellar wind is therefore important.1141 Other means bv which the envelope may lose angular monmentum include magnetic breaking and expansion of the convective envelope on the AGB (IlegerandLanger1993).., Other means by which the envelope may lose angular momentum include magnetic breaking and expansion of the convective envelope on the AGB \citep{1998A&A...334..210H}.1142 sources ol angular momentum for (he envelope may be provided by companion stus/planets and the core of the star., Sources of angular momentum for the envelope may be provided by companion stars/planets and the core of the star.1143 First. at (hie expense of its orbital angular momentum. a low nass companion max [eed angular momentum to the envelope during a common envelope phase (e.g.HarpazandSoker1994:2000)..," First, at the expense of its orbital angular momentum, a low mass companion may feed angular momentum to the envelope during a common envelope phase \citep[e.g.][]{1994MNRAS.270..734H,2000MNRAS.317..861S}."1144 The angular momentum of a companion of mass My is given by (SokerandIHarpaz2000) where M; is Jupiters mass ancl e is (he initial orbital separation.," The angular momentum of a companion of mass $M_{\rm{p}}$ is given by \citep{2000MNRAS.317..861S}1145 where $M_{\rm{J}}$ is Jupiter's mass and $a$ is the initial orbital separation."1146 Following (2000).. we may express the envelopes angular momentum as where 5 is a constant (5=2/9 is appropriate lor the upper AGB).," Following \cite{2000MNRAS.317..861S}, we may express the envelope's angular momentum as where $\gamma$ is a constant $\gamma=2/9$ is appropriate for the upper AGB)."1147" Comparing ancl releq:Jenv shows that e.g. a MyzzLOOAL)—0.1M. companion star with an inital orbital separation of AAU may replace all of the rotational angular momentum lost by the envelope of a star with A,=IM... ΔΙΣΜΗ. R=LAU. and &=10s|."," Comparing \\ref{eq:Jp} and \\ref{eq:Jenv} shows that e.g. a $M_{\rm{p}}\approx100\,M_{\rm{J}}=0.1\,\rm{M_{\odot}}$ companion star with an inital orbital separation of AU may replace all of the rotational angular momentum lost by the envelope of a star with $M_{\rm{i}}=1\,\rm{M_{\odot}}$, $M_{\rm{env}}{\leq}0.45\,\rm{M_{\odot}}$, $R=1\,\rm{AU}$, and $\omega=10^{-8}\rm{s}^{-1}$."1148" Likewise. a companion star with an inital orbital separation of AAU may replace all of (he rotational angular momentum lost bv (he envelope of a star wilh M;=ΤΑ... Mle<5.O8M.. —LAU. and &=10s|,"," Likewise, a $M_{\rm{p}}\approx500\,M_{\rm{J}}=0.5\,\rm{M_{\odot}}$ companion star with an inital orbital separation of AU may replace all of the rotational angular momentum lost by the envelope of a star with $M_{\rm{i}}=7\,\rm{M_{\odot}}$, $M_{\rm{env}}{\leq}5.98\,\rm{M_{\odot}}$, $R=1\,\rm{AU}$, and $\omega=10^{-8}\rm{s}^{-1}$."1149 The above illustrates that (a substantial fraction of) the angular momentum lost by (he wind can in principle be replaced by a low niass companion star., The above illustrates that (a substantial fraction of) the angular momentum lost by the wind can in principle be replaced by a low mass companion star.1150 second. Garcia-Seeuraetal.(1999) argue thal although the envelope of low- and intermecdiate-mass stars may be devoid of angular momentum (i.e. non-rotating) at the beeinning of the thermally pulsing ACB phase. stars with main sequence masses 1.3M. can spin up their envelopes to rotational speeds of 1km/s just prior to the PN ejection.," Second, \cite{1999ApJ...517..767G} argue that although the envelope of low- and intermediate-mass stars may be devoid of angular momentum (i.e. non-rotating) at the beginning of the thermally pulsing AGB phase, stars with main sequence masses $1.3\,\rm{M_{\odot}}$ can spin up their envelopes to rotational speeds of ${\sim}1\,\rm{km/s}$ just prior to the PN ejection."1151the turbulence can be described by a standard viscous stress tensor.,the turbulence can be described by a standard viscous stress tensor.1152 We used cylindrical coordinates (φις) centered on the primary star where the disk lies in the equatorial. z=0 plane.," We used cylindrical coordinates $ (r, \varphi, z)$ centered on the primary star where the disk lies in the equatorial, $z = 0$ plane."1153 Because our modelis two-dimensional (7.4). we solved the vertically integrated versions of the hydrodynamical equations.," Because our modelis two-dimensional $(r, \varphi)$, we solved the vertically integrated versions of the hydrodynamical equations."1154 In this approximation the continuity equation is where v=(v.v)—G.O7) is the velocity. and X=[ὅόρα- the surface density.," In this approximation the continuity equation is where $ \vec{v} = (v_r, v_\varphi) = (v, \Omega r) $ is the velocity, and $ \Sigma = \int_{-\infty}^{\infty} \rho \,dz $ the surface density."1155 As indicated. in the following we will also use v and /Q for the radial and orbital velocity. respectively.," As indicated, in the following we will also use $v$ and $r \Omega$ for the radial and orbital velocity, respectively."1156" The vertically integrated equation of radial motion is then and for the azimuthal component Here p is the vertically integrated pressure. V. the gravitational potential of both stars. and f, and f. describe the radial and azimuthal forces due to the disk viscosity (?).."," The vertically integrated equation of radial motion is then and for the azimuthal component Here $p$ is the vertically integrated pressure, $ \Psi $ the gravitational potential of both stars, and $f_r $ and $ f_\varphi $ describe the radial and azimuthal forces due to the disk viscosity \citep[][]{2002A&A...387..605M}."1157 Owing to the motion of the primary star around the center of mass of the binary. the coordinate system Is non-inertial. and indirect terms. were included in the equations of motion to account for this.," Owing to the motion of the primary star around the center of mass of the binary, the coordinate system is non-inertial, and indirect terms were included in the equations of motion to account for this."1158 These are included in the potential V., These are included in the potential $ \Psi $.1159 The gravitational influence of the disk on the binary Is neglected. and the disk m non-self-gravitating.," The gravitational influence of the disk on the binary is neglected, and the disk in non-self-gravitating."1160 The vertically integrated energy equation reads where e is the internal energy density. Q_ the heating source term and Q_ the cooling source term.," The vertically integrated energy equation reads where $ e $ is the internal energy density, $ Q_+ $ the heating source term and $ Q_- $ the cooling source term."1161" To obtain a fully determined system. we additionally used the ideal gas law where 7 is the temperature in the midplane of the disk. y the adiabatic index and ® the universal gas constant divided by the mean molecular mass. which can be calculated by 'R=ky/(am,). where Kg is the Boltzmann constant. µ the mean molecular weight and η the unified atomie mass unit."," To obtain a fully determined system, we additionally used the ideal gas law where $ T $ is the temperature in the midplane of the disk, $ \gamma $ the adiabatic index and $\mathcal{R} $ the universal gas constant divided by the mean molecular mass, which can be calculated by $ \mathcal{R} = k_\mathrm{B} / (\mu m_u) $, where $ k_\mathrm{B} $ is the Boltzmann constant, $ \mu $ the mean molecular weight and $ m_u $ the unified atomic mass unit."1162" The adiabatic sound speed c, within the disk is then given where eiΡ/Σ. is the isothermal sound speed."," The adiabatic sound speed $ c_\mathrm{s} $ within the disk is then given as where $ c_\mathrm{s,iso} = \sqrt{p/\Sigma} $ is the isothermal sound speed."1163 The vertical pressure scale height H is then where Oy Vydenotes the Keplerian angular velocity around the primary and /i the aspect ratio., The vertical pressure scale height $ H $ is then where $ \Omega_\mathrm{K} $ denotes the Keplerian angular velocity around the primary and $h$ the aspect ratio.1164 For the heating term Q_ we assumed that this is solely given by viscous dissipation. and it then is given by where v is the kinematic viscosity and o denotes the viscous stress tensor. to be written m polar coordinates.," For the heating term $ Q_+ $ we assumed that this is solely given by viscous dissipation, and it then is given by where $ \nu $ is the kinematic viscosity and $ \sigma $ denotes the viscous stress tensor, to be written in polar coordinates."1165 The viscosity v Is given by v=acH (?).. , The viscosity $ \nu $ is given by $ \nu = \alpha c_\mathrm{s} H $ \citep{1973A&A....24..337S}. .1166The cooling term Q_ describes the radiative losses from the lower and upper disk surface. which can be written as where Toycq 1s the Stefan-Boltzmann. constant and ry an effective optical depth.," The cooling term $ Q_- $ describes the radiative losses from the lower and upper disk surface, which can be written as where $ \sigma_\mathrm{R} $ is the Stefan-Boltzmann constant and $ \tau_\mathrm{eff} $ an effective optical depth."1167 We followed the approach of ? and write. according to ?.. The optical depth follows from τ=[prds. that can be approximated by 7.=paH where p and Kp.T) are evaluated at the disks midplane.," We followed the approach of \citet{2008A&A...487L...9K} and write, according to \citet{1990ApJ...351..632H}, The optical depth follows from $\tau = \int \rho \kappa dz$, that can be approximated by $\tau \approx \rho \kappa H$ where $\rho$ and $\kappa(\rho, T)$ are evaluated at the disk's midplane."1168 The vertical density profile of a disk ts approximately given by a Gaussian and hence To account for the drop of opacity with vertical height we introduced a correction factor οἱ and write finally The constant ο=4 is obtained by comparing two-imensional disk models with the fully. three-dimensional nocalculations as presented in ?.., The vertical density profile of a disk is approximately given by a Gaussian and hence To account for the drop of opacity with vertical height we introduced a correction factor $ c_1 $ and write finally The constant $ c_1 = \frac{1}{2} $ is obtained by comparing two-dimensional disk models with the fully three-dimensional calculations as presented in \citet{2009A&A...506..971K}.1169 For the Rosseland mean opacity we adopted power-law dependencies on temperature and 0Censity described by ? and ?.. where for various opacity regimes.," For the Rosseland mean opacity $ \kappa $ we adopted power-law dependencies on temperature and density described by \citet{1985prpl.conf..981L} and \citet{1994ApJ...427..987B}, where for various opacity regimes."1170 Each opacity regime is described by a minimum temperature Τμ. and maximum temperature Τμ. Which depends on the density p.," Each opacity regime is described by a minimum temperature $ T_\mathrm{min} $ and maximum temperature $ T_\mathrm{max} $, which depends on the density $ \rho $."1171 Table | [ists the constants κο. ¢ and b for each regime of the ? model.," Table \ref{tab:opacity} lists the constants $ \kappa_0 $, $ a$ and $ b $ for each regime of the \citeauthor{1985prpl.conf..981L} model."1172 The temperature and density are taken from the midplane. where the density p is obtained from Eq. (11)).," The temperature and density are taken from the midplane, where the density $\rho$ is obtained from Eq. \ref{eq:sigma}) )."1173 In our model we did not consider presently any radiation transport within the disk plane., In our model we did not consider presently any radiation transport within the disk plane.1174 This contribution is potentially important when strong gradients m temperature and density Occur., This contribution is potentially important when strong gradients in temperature and density occur.1175 In our situation this may be the case around the periastron phase of the binary., In our situation this may be the case around the periastron phase of the binary.1176 However. in our simulations the observed contrast did not seem strong enough and we did not expect a large impact on the evolution.," However, in our simulations the observed contrast did not seem strong enough and we did not expect a large impact on the evolution."1177 In subsequent studies we plan to investigate this question further., In subsequent studies we plan to investigate this question further.1178" Because we are interested in the global evolution of the disk. we measured the disk eccentricity eq, and the disk periastron cuj, by first calculating for each grid. cell the eccentricity vector e. which is defined by where dwj=rxwv i the specific angular momentum. G the gravitational constant. M the total mass and r the relative vector."," Because we are interested in the global evolution of the disk, we measured the disk eccentricity $ e_\mathrm{disk} $ and the disk periastron $ \varpi_\mathrm{disk} $ by first calculating for each grid cell the eccentricity vector $ \vec{e} $ , which is defined by where $ \vec{j} = \vec{r} \times \vec{v} $ is the specific angular momentum, $ G $ the gravitational constant, $ M $ the total mass and $ \vec{r} $ the relative vector."1179" In our two-dimensional case the specific angular momentum only has à component in z direction and therefore the eccentricity e and the longitude of periastron c follow as The global disk eccentricity eq, and disk periastron (i, isthen caleulated by a mass-weighted average over the whole", In our two-dimensional case the specific angular momentum only has a component in $ z $ direction and therefore the eccentricity $ e $ and the longitude of periastron $ \varpi $ follow as The global disk eccentricity $ e_\mathrm{disk} $ and disk periastron $ \varpi_\mathrm{disk} $ isthen calculated by a mass-weighted average over the whole1180"emperature 310"" Ix is also observed in the central region of M31 (Bogdán&Cilfanov2008)..",temperature $\sim 3~10^6$ K is also observed in the central region of M31 \citep{2008MNRAS.388...56B}.1181 Phe origin of this gas is not clear., The origin of this gas is not clear.1182 For a long time observations of 6.7 and 6.9 keV ines of heavily ionized iron and an unresolved X-ray. elow (at energies above a lew keV) of the Galactic plane were regarded as evidence for a much hotter. ~10 Ix. plasma iling most of the bulge's volume (e.g.Kovamaetal.1986)..," For a long time observations of 6.7 and 6.9 keV lines of heavily ionized iron and an unresolved X-ray glow (at energies above a few keV) of the Galactic plane were regarded as evidence for a much hotter, $\sim 10^8$ K, plasma filling most of the bulge's volume \citep[e.g.][]{1986PASJ...38..121K}."1183 'ositrons injected. into such a medium will slow down and annihilate before the plasma is able to cool (Fig. 13)).," Positrons injected into such a medium will slow down and annihilate before the plasma is able to cool (Fig. \ref{fig:tcool}) ),"1184 and à very broad. annihilation line without an ortho-positroniunm continuum is expected. to be observed. in stark contrast with observations.," and a very broad annihilation line without an ortho-positronium continuum is expected to be observed, in stark contrast with observations."1185 However. recent observations (Revniviseyetal.2006:SazonovRevniviseyct2009) have convincingly demonstrated that the apparently dilfuse Galactic X-ray emission is in fact a superposition of millions of faint compact sources accreting white dwarfs and coronally active stars.," However, recent observations \citep{2006A&A...452..169R,2006A&A...450..117S,2009Natur.458.1142R}1186 have convincingly demonstrated that the apparently diffuse Galactic X-ray emission is in fact a superposition of millions of faint compact sources – accreting white dwarfs and coronally active stars."1187 This removes the problem of confining LO” W eas by the gravitational well of the Galaxy., This removes the problem of confining $\sim 10^8$ K gas by the gravitational well of the Galaxy.1188" Cooler. 10° few 10"" WK. gas can on the contrary be trapped in the Galaxy potential."," Cooler, $10^5$ – few $10^6$ K, gas can on the contrary be trapped in the Galaxy potential."1189 For instance. the density of 2 10?Ix eas in hyerostatic equilibrium in the Milky Way potential would drop by a [factor of ~310? at a distance of ~1.5 kpe above the plane.," For instance, the density of $2~10^6$ K gas in hydrostatic equilibrium in the Milky Way potential would drop by a factor of $\sim 3~10^{3}$ at a distance of $\sim1190 1.5$ kpc above the plane."1191 This means that such gas can accumulate in the Galactic bulge., This means that such gas can accumulate in the Galactic bulge.1192" Llowever. à self-consistent model explaining the few 10"" ΙΔ in the bulge of the Alilky Way or in AISI is still missing."," However, a self-consistent model explaining the few $10^6$ K ISM in the bulge of the Milky Way or in M31 is still missing."1193 Lf one takes the mass loss rate by evolving stars (e.g.Ciottictal.1991). and the total energy. and iron input rate from SNla (e.g.Mannuceictal.2008). then a “natural” temperature of the gas is of order Low keV (mean energy. per injected. particle) and the expected abundance of iron is about 5 times the Solar value.," If one takes the mass loss rate by evolving stars \citep[e.g.][]{1991ApJ...376..380C} and the total energy and iron input rate from SNIa \citep[e.g.][]{2008MNRAS.383.1121M}, then a “natural” temperature of the gas is of order few keV (mean energy per injected particle) and the expected abundance of iron is about 5 times the Solar value."1194" These parameters do not fit the properties of the observed. few 10"" Ix component of the ISM.", These parameters do not fit the properties of the observed few $10^6$ K component of the ISM.1195 Tangetal.(2009) and Tang&Wang(2010) argue that the account for non-uniformity and intermittence in enerev. injection by SNla leads to a broad eas distribution over temperature with a lower than the mean temperature component making largest contribution to the observed. X-ray emission., \citet{2009MNRAS.398.1468T} and \citet{2010MNRAS.tmp.1115T} argue that the account for non-uniformity and intermittence in energy injection by SNIa leads to a broad gas distribution over temperature with a lower than the mean temperature component making largest contribution to the observed X-ray emission.1196 lt is not vet clear if this provides a full explanation of the origin of 10° Ix. gas., It is not yet clear if this provides a full explanation of the origin of $10^6$ K gas.1197 We therefore make an ad. hoc assumption that a few million degree medium is widespread in the Milky. Way bulge., We therefore make an ad hoc assumption that a few million degree medium is widespread in the Milky Way bulge.1198 The positron annihilation in a cooling ISM refsee:cooling)) can resolve some of the issues mentioned at the beginning of this section., The positron annihilation in a cooling ISM \\ref{sec:cooling}) ) can resolve some of the issues mentioned at the beginning of this section.1199 Indeed. if the ISM is able to cool down to LO? 10! IX before the positrons annihilate. then the observer will always see a spectrum characteristic ol annihilation in a warm plasma.," Indeed, if the ISM is able to cool down to $10^5$ $10^4$ K before the positrons annihilate, then the observer will always see a spectrum characteristic of annihilation in a warm plasma."1200 This resolves the question of why positrons are apparentIy annihilating in a warm/cold medium even though such a medium should have a relatively small filling factor., This resolves the question of why positrons are apparently annihilating in a warm/cold medium even though such a medium should have a relatively small filling factor.

Showing the first 1,200 of 10467 lines. Download the file for the rest.