ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2" Our results suggest that envelope pollution by icy planetesimals has the potential to make gas giant formation with small cores possible; for example, gas giants with cores smaller than 1Mg can capture disc gas by 1Myr when Zy>0.7 for f=1 or when Z,>0.5 for f=0.01."," Our results suggest that envelope pollution by icy planetesimals has the potential to make gas giant formation with small cores possible; for example, gas giants with cores smaller than $1M_\oplus$ can capture disc gas by 1Myr when $Z_\mathrm{h} \geq 0.7$ for $f = 1$ or when $Z_\mathrm{h} \geq 0.5$ for $f = 0.01$."3 We assumed that both Zi and 7i are constant with time., We assumed that both $Z_\mathrm{h}$ and $T_\mathrm{h}$ are constant with time.4" 'This may be oversimplification and questionable, especially in the phase of runaway gas accretion."," This may be oversimplification and questionable, especially in the phase of runaway gas accretion."5" When the critical core mass is attained, the accretion rate of disc gas is much higher than that of planetesimals."," When the critical core mass is attained, the accretion rate of disc gas is much higher than that of planetesimals."6" In an extreme case where the unpolluted outer envelope never exchanges material with the polluted lower envelope, the gas accretion results in increasing the mass only of the upper envelope."," In an extreme case where the unpolluted outer envelope never exchanges material with the polluted lower envelope, the gas accretion results in increasing the mass only of the upper envelope."7 The lower envelope behaves like a part of the “core”., The lower envelope behaves like a part of the “core”.8" In this case, the envelope pollution does not resolve the problem of the slow formation of gas giants with small cores."," In this case, the envelope pollution does not resolve the problem of the slow formation of gas giants with small cores."9" In the other extreme case where the inner and outer envelopes exchange material instantaneously between each other via eddy diffusion, accreting fresh disc gas dilutes the polluted lower envelope, which results in decelerating the disc-gas accretion."," In the other extreme case where the inner and outer envelopes exchange material instantaneously between each other via eddy diffusion, accreting fresh disc gas dilutes the polluted lower envelope, which results in decelerating the disc-gas accretion."10" On the other hand, the dilution is inevitably accompanied by mass growth of the envelope, which accelerates the disc-gas accretion."," On the other hand, the dilution is inevitably accompanied by mass growth of the envelope, which accelerates the disc-gas accretion."11" Unfortunately, it is uncertain whether or not mixing occurs effectively, as follows."," Unfortunately, it is uncertain whether or not mixing occurs effectively, as follows."12" A characteristic time-scale of eddy diffusion, Teaay, is givenby where Πρ is the pressure scale-height and K,, is the coefficient of eddy diffusion."," A characteristic time-scale of eddy diffusion, $\tau_\mathrm{eddy}$ , is givenby where $H_p$ is the pressure scale-height and $K_\mathit{zz}$ is the coefficient of eddy diffusion."13" Estimated values ofTeaayare listed in Table 4, where we have used our numerical values of H, at the tropopause when Moore= Merit."," Estimated values of$\tau_\mathrm{eddy}$are listed in Table 4, where we have used our numerical values of $H_p$ at the tropopause when $M_\mathrm{core} = M_\mathrm{crit}$ ."14 We have, We have15eo through transient outbursts. then 50 isolated. black holes per vear would be detectable as X-ray novae. so we reject this possibility since isolated X-ray novae have not been observed.,"go through transient outbursts, then 50 isolated black holes per year would be detectable as X-ray novae, so we reject this possibility since isolated X-ray novae have not been observed."16 The greatest. uncertainty in our predictions is the ellicicney of black-hole accretion. with which we have parameterized our results.," The greatest uncertainty in our predictions is the efficiency of black-hole accretion, with which we have parameterized our results."17 Most of the detectable black holes should reside in interstellar clouds that have higher densities: however. this leads to the problem of confusion with other X-ray sources such as the coronae of massive stars.," Most of the detectable black holes should reside in interstellar clouds that have higher densities; however, this leads to the problem of confusion with other X-ray sources such as the coronae of massive stars."18 Some tests for whether an acereting object is a black hole are the following: 1) Is there high-enerey emission?, Some tests for whether an accreting object is a black hole are the following: 1) Is there high-energy emission?19 Accreting black holes tend to show spectra which have power laws extending up to ~Q keV. (Grove et al., Accreting black holes tend to show spectra which have power laws extending up to $\sim 10^2$ keV (Grove et al.20 1998)., 1998).21 2) What is the nature of the variability?, 2) What is the nature of the variability?22 Accreting black holes show no pulsations. show only QPOs with v«1 kllz. and show power spectra that cut olf around 500 Lz (Sunvaev Revnivisey 2000).," Accreting black holes show no pulsations, show only QPOs with $\nu < 1$ kHz, and show power spectra that cut off around 500 Hz (Sunyaev Revnivtsev 2000)."23 3) What is the mass?, 3) What is the mass?24 Without a binary companion. the mass of an accreting object is cillicultἱ to measure: however. this might be achieved by carrying out astrometry of background stars to look for gravitational distortion bv the accreting object (Paczvisski 2001).," Without a binary companion, the mass of an accreting object is difficult to measure; however, this might be achieved by carrying out astrometry of background stars to look for gravitational distortion by the accreting object (Paczyńsski 2001)."25 4) What do other parts of the spectra look like?, 4) What do other parts of the spectra look like?26 Accreting black holes can produce relativistic radio jets CMirabel Itodr(eguez 1999). and photoionisation of the surrounding gas might result in observable infrared lines (Maloney. €olgan Lollenbach 1997).," Accreting black holes can produce relativistic radio jets (Mirabel Rodrígguez 1999), and photoionisation of the surrounding gas might result in observable infrared lines (Maloney, Colgan Hollenbach 1997)."27 There are several assumptions in our calculation that might. alleet the results., There are several assumptions in our calculation that might affect the results.28 We have assumed that the accretion low is one-dimensional. and that the sonic point is at the accretion radius.," We have assumed that the accretion flow is one-dimensional, and that the sonic point is at the accretion radius."29 We have also assumed that the accretion is ime steady: this may not be the case for higher accretion rates than we find for black holes accreting from the ISM. (c.g. Crindlay 1978)., We have also assumed that the accretion is time steady; this may not be the case for higher accretion rates than we find for black holes accreting from the ISM (e.g. Grindlay 1978).30 Lo the black hole is moving slower than the sound speed at the accretion radius then the preheated region outside the accretion radius may have a chance to expand into the ISM. reducing the number density. and. thus reducing he accretion rate.," If the black hole is moving slower than the sound speed at the accretion radius then the preheated region outside the accretion radius may have a chance to expand into the ISM, reducing the number density, and thus reducing the accretion rate."31 We have neglected mechanical feedback. which may occur if à jet or wind is developed.," We have neglected mechanical feedback, which may occur if a jet or wind is developed."32 Recent work on non-radiating accretion [lows indicates that strong winds can be formed. which carry the bulk of the energy. outwards as mechanical rather than radiative energy (Blandford DBegelman 1999. leumenshehey. Abramowicz Naravan 2000. Llawley. Balbus Stone 2001).," Recent work on non-radiating accretion flows indicates that strong winds can be formed which carry the bulk of the energy outwards as mechanical rather than radiative energy (Blandford Begelman 1999, Igumenshchev, Abramowicz Narayan 2000, Hawley, Balbus Stone 2001)."33 These authors argue that the acerction rate scales as Alxor., These authors argue that the accretion rate scales as $\dot M \propto r$.34 H£ the outer radius is taken as iy. hen ALGO)~1O(ecyALG)~?.10TePALA).," If the outer radius is taken as $r_A$, then $\dot M (10 r_g) \sim 10 (v/c)^2 \dot M(r_A) \sim 2\times 3510^{-7} v_{40}^{-2} \dot M(r_A)$."36" lU tbe outer radius is taken to be the cireularization radius. then Al(10r,)~10.CM9M.L)7707L?flkms+)U*?."," If the outer radius is taken to be the circularization radius, then $\dot M(10 r_g) \sim 10^{-3}37(M/9{\rm M}_\odot)^{-2/3} [(v^2+c_s^2)^{1/2}/40 {\rm km~s^{-1}}]^{-10/3}$."38 Either of these cireunistances will make black holes loss visible. which in the formalism of this paper corresponds to a further reduction in the aceretion ellieieney.," Either of these circumstances will make black holes less visible, which in the formalism of this paper corresponds to a further reduction in the accretion efficiency."39 Magnetic fields will likely av an important role as they are amplified by Hux-freezing. possibly heating the gas to virial temperatures (Leumenshchey Naravan 2001) and can transport angular momentum via the magnetorotational instability once the circularization radius is reached. mocdifving the dynamics of the accretion How.," Magnetic fields will likely play an important role as they are amplified by flux-freezing, possibly heating the gas to virial temperatures (Igumenshchev Narayan 2001) and can transport angular momentum via the magnetorotational instability once the circularization radius is reached, modifying the dynamics of the accretion flow."40 We have not explored the dependence of the ellicieney on other xwameters. which may. result. for example. from changes in the gas density ancl angular momentum as a function of the accretion rate. so our extrapolation from estimated ellieiencies of black-hole X-ray binaries may be too optimistic.," We have not explored the dependence of the efficiency on other parameters, which may result, for example, from changes in the gas density and angular momentum as a function of the accretion rate, so our extrapolation from estimated efficiencies of black-hole X-ray binaries may be too optimistic."41 The validity of these assumptions can be tested with 3-D radiation. SUID simulations of a black hole accreting from an inhomogeneous mecium. a daunting numerical problem.," The validity of these assumptions can be tested with 3-D radiation MHD simulations of a black hole accreting from an inhomogeneous medium, a daunting numerical problem."42 Lt is possible that a population of intermediate-mass black holes (ENMBIIS) exist with larger masses around ΟΔΙΕ. the remnants of the first generation of star formation (Aladau Rees 2001).," It is possible that a population of intermediate-mass black holes (IMBHs) exist with larger masses around $250 {\rm M}_\odot$, the remnants of the first generation of star formation (Madau Rees 2001)."43 The larger masses of these objects would result in vet larger aceretion rates ancl luminosities hy a factor of ~LO’. if they are distributed with same phase-space distribution as DAL. black holes.," The larger masses of these objects would result in yet larger accretion rates and luminosities by a factor of $\sim 10^3$, if they are distributed with same phase-space distribution as $9 {\rm M}_\odot$ black holes."44 owe assume that ~10° ΠΛΗΡΗΣ reside in our galaxy. then we find that the number of detectable objects at high fluxes may comparable to OAL. black holes accreting at the same ellicieney. (Figure 3).," If we assume that $\sim 10^6$ IMBHs reside in our galaxy, then we find that the number of detectable objects at high fluxes may comparable to $9 {\rm M}_\odot$ black holes accreting at the same efficiency (Figure 3)."45 However. if these objects reside in the halo or bulgee of the ogalaxy. the number detectable will be decreased significantInIv.," However, if these objects reside in the halo or bulge of the galaxy, the number detectable will be decreased significantly."46 We acknowledge D. Bennett. L. Bildsten. O. Blaes. It. Blandford. J. Carpenter. D. Chernoll. C. Dubus. A. Esin. €. Eryer. J. Cuaincdlav. T. Ixallman. L. Ixoopmans. J. Ixrolik. Y. Lithwick. A. Melatos. S. Phinney. M. Rees. 1. Rutledge. N. Scoville. aud Ix. Sheth for useful conversations and ideas which greatly improved this work.," We acknowledge D. Bennett, L. Bildsten, O. Blaes, R. Blandford, J. Carpenter, D. Chernoff, G. Dubus, A. Esin, C. Fryer, J. Grindlay, T. Kallman, L. Koopmans, J. Krolik, Y. Lithwick, A. Melatos, S. Phinney, M. Rees, R. Rutledge, N. Scoville, and K. Sheth for useful conversations and ideas which greatly improved this work."47 This work was supported in part by NSE AS'T-0096023. NASA NACG5-8506. and. Dol DI-EXGO3-92-I2140701.," This work was supported in part by NSF AST-0096023, NASA NAG5-8506, and DoE DE-FG03-92-ER40701."48 Support for the work done by LA was provided by the National Acronautics and Space Administration through Chandra Postdoctoral Fellowship Award Number PEO-10013 issued by the Chandra X-ray Observatory Center. which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Acronautics Space Administration under contract NASS-39073.," Support for the work done by EA was provided by the National Aeronautics and Space Administration through Chandra Postdoctoral Fellowship Award Number PF0-10013 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-39073."49state. which are ealeulated by simulations without magnetic field irregularities.,"state, which are calculated by simulations without magnetic field irregularities."50" Ten solid lines Irom the bottom to the top are density distributions caleulated by simulations with magnetic field irregularities for time /= 2.500 to 25.000 wy” with an interval of 2.500 cw,. respectively."," Ten solid lines from the bottom to the top are density distributions calculated by simulations with magnetic field irregularities for time $t=$ 2,500 to 25,000 $\omega_p^{-1}$ with an interval of 2,500 $\omega_p^{-1}$, respectively."51 Dotted vertical lines in Figures 11. and 12. show the forbidden distance. which are borders of the forbidden region calculated theoretically in Section 2.1. and shown in Figure 7..," Dotted vertical lines in Figures \ref{dhist6} and \ref{dhist18} show the forbidden distance, which are borders of the forbidden region calculated theoretically in Section \ref{sec:analy} and shown in Figure \ref{penet}."52 We can see from Figure 11.. which shows the case for 6 GY cosmic ταν particles. (hat the density distribution inside and outside the forbidden region is greatly different.," We can see from Figure \ref{dhist6}, which shows the case for 6 GV cosmic ray particles, that the density distribution inside and outside the forbidden region is greatly different."53 Out of (he region. there is a density bump around p=0.8 in the later time.," Out of the region, there is a density bump around $\rho=0.8$ in the later time."54" The densitv out of the forbidden region increases drastically with Gime and the bump is formed just outside the region,", The density out of the forbidden region increases drastically with time and the bump is formed just outside the region.55 The bump is formed in (he following processes., The bump is formed in the following processes.56 The particles penetrating [rom the outside of the flux rope edge are scattered by small-scale magnetic field irregularities between the Forbidden region aud (he [Iux rope edge. and changed their pitch angles.," The particles penetrating from the outside of the flux rope edge are scattered by small-scale magnetic field irregularities between the forbidden region and the flux rope edge, and changed their pitch angles."57 These pitch angle changes can make the particles Fall into the (rap region. which is expressed as Equation (21)) and diawn in Figure 5..," These pitch angle changes can make the particles fall into the trap region, which is expressed as Equation \ref{Dregion}) ) and drawn in Figure \ref{trap}."58 As a result. the particles are trapped between the forbidden region and the flux rope edge.," As a result, the particles are trapped between the forbidden region and the flux rope edge."59 As the solid angle of the trap region near the forbidden region is larger (han that near the flux rope edge (see Figure 6)). cosmic rav particles tend to fall in the (trap region near the forbidden region. not near the edge.," As the solid angle of the trap region near the forbidden region is larger than that near the flux rope edge (see Figure \ref{trap_area}) ), cosmic ray particles tend to fall in the trap region near the forbidden region, not near the edge."60 Accimulating these trapped particles. the bump in the density distribution is lormed.," Accumulating these trapped particles, the bump in the density distribution is formed."61 Moreover. there is a small density drop just inside the flux rope edge.," Moreover, there is a small density drop just inside the flux rope edge."62 The drop is formed in the following processes., The drop is formed in the following processes.63 Since the solid angle of trap region is verv small just inside the flix rope edge as shown in Figure 6.. nearly particles cannot be trapped in Chis region.," Since the solid angle of trap region is very small just inside the flux rope edge as shown in Figure \ref{trap_area}, nearly particles cannot be trapped in this region."64 Therefore. the cosmic ray particles in this region are distributed like (he steady state distribution without magnetic field irregularities (dashed line in Figure 11)).," Therefore, the cosmic ray particles in this region are distributed like the steady state distribution without magnetic field irregularities (dashed line in Figure \ref{dhist6}) )."65 As the density bump is formed near the forbidden region. this fills in much of the densitv drop just inside the edge of the flux rope. which is why the small densitv drop is formed just inside the flux rope edge.," As the density bump is formed near the forbidden region, this fills in much of the density drop just inside the edge of the flux rope, which is why the small density drop is formed just inside the flux rope edge."66 A major role of magnetic field inregularities outside of the forbidden region is to make the particles fall into the trap region by pitch angle scattering., A major role of magnetic field irregularities outside of the forbidden region is to make the particles fall into the trap region by pitch angle scattering.67 Outside of the forbidden region. the effect of a finite Larmor radius is significant for density distribution.," Outside of the forbidden region, the effect of a finite Larmor radius is significant for density distribution."68 Inside of (he forbidden region. the trapped particles just out of the forbidden region diffuse into the forbidden region by means of spatial diffusion due lo scattering bv magnetic field irregularities and a magnetic field line random walk. which is why the density distribution in the lorbidden region decreases monotonically toward the flux rope center.," Inside of the forbidden region, the trapped particles just out of the forbidden region diffuse into the forbidden region by means of spatial diffusion due to scattering by magnetic field irregularities and a magnetic field line random walk, which is why the density distribution in the forbidden region decreases monotonically toward the flux rope center."69 Thus. a major role of magnetic field irregularities inside (he forbidden region is spatial diffusion toward the flix rope Fieure 12. shows the results for the case of 18 GV cosmic ravs particles.," Thus, a major role of magnetic field irregularities inside the forbidden region is spatial diffusion toward the flux rope Figure \ref{dhist18} shows the results for the case of 18 GV cosmic rays particles."70 The bump in the density distribution appears while the peak of (he bump is located closer to the flux rope axis compared to the case of 6 GV cosmic ray. particles., The bump in the density distribution appears while the peak of the bump is located closer to the flux rope axis compared to the case of 6 GV cosmic ray particles.71 This is because the effect of, This is because the effect of72the core in PA~0°.,the core in $\sim0\degr$.73 Our VLBI image (Fig. 4)), Our VLBI image (Fig. \ref{fig:0749}) )74 reveals a dominant core. with an extension to the north. in roughly the direction of the previously detected VLBI jet.," reveals a dominant core, with an extension to the north, in roughly the direction of the previously detected VLBI jet."75 The core shows an unusually high fractional polarization of ~9%. while no polarization was detected in the jet.," The core shows an unusually high fractional polarization of $\sim 9\%$, while no polarization was detected in the jet."76 0829--046 or O.J 049 is a οταν loud blazar (2). which shows rapid and large optical variability (?).., 0829+046 or OJ 049 is a $\gamma$ -ray loud blazar \citep{Dondi95} which shows rapid and large optical variability \citep{LillerLiller75}.77 The 1.4 Gllz VLA images of ? and ο show a (wo-sided structure with an extended and curved region of emission (o (he southeast.," The 1.4 GHz VLA images of \citet{AntonucciUlv85} and \citet{Giroletti04a}78 show a two-sided structure with an extended and curved region of emission to the southeast."79 Previous VEDI images show a VLBI jet extending to the northeast (?).. clearly misaliened with the kpc-seale radio structure.," Previous VLBI images show a VLBI jet extending to the northeast \citep{Jorstad01}, clearly misaligned with the kpc-scale radio structure."80 Our VLBI images (Fig. 5)), Our VLBI images (Fig. \ref{fig:0829}) )81 reveal the rich polarization structure of the VLBI jet. whose inferred D field geometry has remained roughly constant over about five vears.," reveal the rich polarization structure of the VLBI jet, whose inferred $B$ field geometry has remained roughly constant over about five years."82 The predominant jel B field is longitudinal to the jet., The predominant jet $B$ field is longitudinal to the jet.83 The polarization position angle for the knot 4 changes dramatically over the roughly five vears covered by our observations. and seems lo swing to remain perpendicular to the VLBI jet as this component propagates rom the core (making the dominant D field longitudinal essentially throughout the jet).," The polarization position angle for the knot K4 changes dramatically over the roughly five years covered by our observations, and seems to swing to remain perpendicular to the VLBI jet as this component propagates from the core (making the dominant $B$ field longitudinal essentially throughout the jet)."84 Both Ix3 and Ix4 show appreciable increases in the degree of polarization accompanied by decreases in total intensity. suggesting Chis is associated with (he expansion of (hese components as thev evolve.," Both K3 and K4 show appreciable increases in the degree of polarization accompanied by decreases in total intensity, suggesting this is associated with the expansion of these components as they evolve."85These objects show significant polarization withpiv. > 1. except lor HE 1523-1155 lor which we have obtained pt = 0.349 + 0.08.,"These objects show significant polarization with$p$ ${\ge}$ 1, except for HE 1523-1155 for which we have obtained $p\%$ = 0.849 $\pm$ 0.08."86 Reddening estimates £(B—V) range from 0.03 to 0.08 for these stars: the values of E(D—V) for the HE stars are taken from (2007)., Reddening estimates $E(B-V)$ range from 0.03 to 0.08 for these stars; the values of $E(B-V)$ for the HE stars are taken from \citet{beers07}.87 A low carbon isotopic ratio (LC/PC < 10) for LEE 1027-2501 indicates that the star is on the first ascent of the giant braneh wherein the material (transferred. from the now unseen companion has been mixed into (he CN-burning region of the CI star or constitute a nuimor fraction of the envelop mass of the CIE star., A low carbon isotopic ratio $^{12}$ $^{13}$ C $<$ 10) for HE 1027-2501 indicates that the star is on the first ascent of the giant branch wherein the material transferred from the now unseen companion has been mixed into the CN-burning region of the CH star or constitute a minor fraction of the envelop mass of the CH star.88 Such low values are believed to be due to convection which dredges up the products of internal CNO evele to the stellar atmosphere in (he ascending red giant branch (RGB)., Such low values are believed to be due to convection which dredges up the products of internal CNO cycle to the stellar atmosphere in the ascending red giant branch (RGB).89 When the star reaches the AGB stage. fresh C may be supplied from the internal IHe-burning laver to the stellar surface. leading (to an increase of C/C ratio.," When the star reaches the AGB stage, fresh $^{12}$ C may be supplied from the internal He-burning layer to the stellar surface, leading to an increase of $^{12}$ $^{13}$ C ratio."90 TE 13052-0001 shows enhancement of both r- ancl s-process elements including lead., HE $+$ 0007 shows enhancement of both $r$ - and $s$ -process elements including lead.91 The second-peak s-process elements are more enhanced (han the first-peak s-process elements., The second-peak $s$ -process elements are more enhanced than the first-peak $s$ -process elements.92 This is a low-metallicity and high-velocity object (V — 4217.8 3 L5 kms. P)its atmospheric parameters are consistent wilh a present location on the RGB (Goswamietal. (2006)))., This is a low-metallicity and high-velocity object $V_{r}$ = $+$ 217.8 $\pm$ 1.5 km $^{-1}$ ); its atmospheric parameters are consistent with a present location on the RGB \citet{goswami06}) ).93 The star LP 625—44 is a carbon- ancl s-process-element-rich very metal-poor subgiant., The star LP $-$ 44 is a carbon- and $s$ -process-element-rich very metal-poor subgiant.94 Abundance estimate derived using the O 7 triplet around 7770 shows excess of oxvgen by a factor of 10 (Aoki et al., Abundance estimate derived using the O $I$ triplet around 7770 shows excess of oxygen by a factor of 10 (Aoki et al.95 2002): ancl Na enhancement by about a factor of 50 in comparison to ILD 140283 (a metal-poor subgiant with normal abundance ratio) and a high Mg abundance ([Mg/Fe| = 1.12 z 0.24)., 2002); and Na enhancement by about a factor of 50 in comparison to HD 140283 (a metal-poor subgiant with normal abundance ratio) and a high Mg abundance ([Mg/Fe] = 1.12 $\pm$ 0.24).96 High abundance of Na suggests. that hydrogen burning in the 7 Ne-rich laver in an AGB star must have produced (he abundance pattern of this object.," High abundance of Na suggests, that hydrogen burning in the $^{22}$ Ne-rich layer in an AGB star must have produced the abundance pattern of this object."97 The Pb enhancement shown by LP 625—44 is not high enough to be placed in the group of lead stars., The Pb enhancement shown by LP $-$ 44 is not high enough to be placed in the group of lead stars.98 The abundance ratio of s-process elements al (he second peak (La. Ce. and Nd) to that al the third peak (Pb) in LP 625-44 issignificantly higher (bv a factor of 5) than that in the s-process element-rich lead star TID 196944 (VanEcketal. (2001))).," The abundance ratio of $s$ -process elements at the second peak (La, Ce, and Nd) to that at the third peak (Pb) in LP 625-44 issignificantly higher (by a factor of 5) than that in the $s$ -process element-rich lead star HD 196944 \citet{van01}) )."99 Unlike CID stars. the radial velocity of this object is low (e 30 km +) and the variation of the radial velocity is expected to be for about 200 davs (Aokietal. 2000)..," Unlike CH stars, the radial velocity of this object is low ${\sim}$ 30 km $^{-1}$ ) and the variation of the radial velocity is expected to be for about 200 days \citep{aoki00}. ."100 Like LP 625-44. HE 1429-0551. and WE 1523-1155 are also low-velocity objects (~ —44.9 and ~ —46.03 kins +. respectively).," Like LP 625-44, HE 1429-0551, and HE 1523-1155 are also low-velocity objects ${\sim}$ $-$ 44.9 and ${\sim}$ $-$ 46.03 km $^{-1}$ , respectively)."101 Both show high abundances of C. N. and Mg relative to Fe.," Both show high abundances of C, N, and Mg relative to Fe."102 Estimated carbon isotopic ratio of C/C for LIE 1429-0551 is high ~30.τρ 200T).., Estimated carbon isotopic ratio of $^{12}$ $^{13}$ C for HE 1429-0551 is high $\sim ~30^{+20}_{-10}$ \citep{aoki07}. .103 Such high ratios are generally noticed inC-N stars., Such high ratios are generally noticed inC-N stars.104 With a marginal difference in the, With a marginal difference in the105Figure 4. presents a contour map of the outflow emission in theCO(6—5) line overlaved with the 8.6 GlIz radio continuum emission observed. toward IRAS 16562—3959 (?)..,Figure \ref{fig-outjet} presents a contour map of the outflow emission in the line overlayed with the 8.6 GHz radio continuum emission observed toward IRAS $-$ 3959 \citep{Guzman2010ApJ}.106 It appears (hat the SE-NW outflow is associated with the string of radio sources. the peak position of the blue-shilted and red-shifted lobes being svimmetrically displaced Irom the bright central radio source.," It appears that the SE-NW outflow is associated with the string of radio sources, the peak position of the blue-shifted and red-shifted lobes being symmetrically displaced from the bright central radio source."107" The SE blueshifted and NW redshilted lobes extend up to 27 and ~32"" from the central radio source. respectively."," The SE blueshifted and NW redshifted lobes extend up to $\sim 27\arcsec$ and $\sim 32\arcsec$ from the central radio source, respectively."108 The svmmetry axis of the SE-NW outflow is along a direction with a position angle of ~LO7*.. roughly the same as the PLA. of the svimmetry axis of the jet of 1107.," The symmetry axis of the SE-NW outflow is along a direction with a position angle of $\sim107$, roughly the same as the P.A. of the symmetry axis of the jet of $110$."109.. As noted in ?.. the radio lobes and the jet are not completely aligned. showing a small bending. which is also seen in the SE-NW outflow.," As noted in \citet{Guzman2010ApJ}, the radio lobes and the jet are not completely aligned, showing a small bending, which is also seen in the SE-NW outflow."110 Possible bending mechanisms of protostellar jets are discussed in 2.. bul with the available data we can not discern between the various alternatives.," Possible bending mechanisms of protostellar jets are discussed in \citet{Fendt1998AA}, but with the available data we can not discern between the various alternatives."111" The spectroscopic signatures of the(493) andC4O(332) transitions suggest that the bulk of the molecular gas toward IRAS 16562-3959 is undergoing large-scale inward motions (e.g.ο,", The spectroscopic signatures of the and transitions suggest that the bulk of the molecular gas toward IRAS $-$ 3959 is undergoing large-scale inward motions \citep[e.g.][]{Sanhueza2010ApJ}.112 Infalling motions traced by optically Chick molecular lines are expected to produce line profiles showing blue asvinimetry. whereas optically thin lines are expected to exhibit svamnietrical profiles (?)..," Infalling motions traced by optically thick molecular lines are expected to produce line profiles showing blue asymmetry, whereas optically thin lines are expected to exhibit symmetrical profiles \citep{Mardones1997ApJ}."113 Figure 7 presents an image of the Two Micron. All Sky Survey (2\LASS. ?)) ἰν band emission across an 8.x8' region of the sky. centered near IRAS 16562—3959.," Figure \ref{fig-2mass} presents an image of the Two Micron All Sky Survey (2MASS, \citealt{Skrustskie2006AJ}) ) $K_s$ -band emission across an $8\arcmin\times8\arcmin$ region of the sky, centered near IRAS $-$ 3959."114 Clearly seen toward (the center is diffuse emission along the SE-NW direction extending by more than 1.5 oon each side of the bright radio source., Clearly seen toward the center is diffuse emission along the SE-NW direction extending by more than $1.5$ on each side of the bright radio source.115 The position angle of this diffuse A.-band emission, The position angle of this diffuse $K_s$ -band emission116 6.55+0.98 AL). 2.68+ L87+0.10 cmn? atmosphere., $6.55\pm 0.98$ $M_\oplus$ $2.68\pm 0.13$ $R_\oplus$ $1.87\pm 0.40$ $^{-3}$ atmosphere.117 Another goal was to check for anv nou-periodicity iu the transit times. as a 1ieaus of discovering other plauets in the system. through the method of Tolman Murray (2005) aud Agol et al. (," Another goal was to check for any non-periodicity in the transit times, as a means of discovering other planets in the system, through the method of Holman Murray (2005) and Agol et al. ("1182005).,2005).119 Supor-carths have frequently been fouud im pairs or even triples in compact arrangements (Lo Curto et al., Super-earths have frequently been found in pairs or even triples in compact arrangements (Lo Curto et al.120 2010). aud it would be interesting to know if GJ 121Lb is another such example.," 2010), and it would be interesting to know if GJ 1214b is another such example."121 This paper is organized as follows., This paper is organized as follows.122 Section 2. describes the observations aud data reduction., Section \ref{sec:obsred} describes the observations and data reduction.123 Section 2. presents the licht. curve model. taking into account the effects of starspots.," Section \ref{sec:model} presents the light curve model, taking into account the effects of starspots."124 Section [.[ discusses the method by which we estimated the model parameters aud their coufideuce intervals., Section \ref{sec:analysis} discusses the method by which we estimated the model parameters and their confidence intervals.125 Section 5. discusses the results for the planet-to-star radius ratio., Section \ref{sec:radrat} discusses the results for the planet-to-star radius ratio.126 Section 6.— preseuts two different iethods for determining the stellar radius (ancl hence the planetary radius). which eive discrepant results.," Section \ref{sec:radplanet} presents two different methods for determining the stellar radius (and hence the planetary radius), which give discrepant results."127 Some possible resolutions of this discrepancy are discussed., Some possible resolutions of this discrepancy are discussed.128 Section F presents our analysis of the measured trausit times. and constraints on the properties of a hvpothoetical second planet.," Section \ref{sec:timing} presents our analysis of the measured transit times, and constraints on the properties of a hypothetical second planet."129 Finally. in Section &.. we discuss the nuplicatious of our analysis on the uuderstauding of CG 121tb and more broadly on ΑΓ dwarf trausit hosts.," Finally, in Section \ref{sec:disc}, we discuss the implications of our analysis on the understanding of GJ 1214b and more broadly on M dwarf transit hosts."130 Om data were gathered during the 2009 and 2010 observing seasons., Our data were gathered during the 2009 and 2010 observing seasons.131 Thirteen transits were observed witli the 1.212 telescope at the Fred WWhipple Observatory (FLWO) ou Mount IHopkius. Arizona. using Neplercam aud a Sloan z' filter.," Thirteen transits were observed with the 1.2m telescope at the Fred Whipple Observatory (FLWO) on Mount Hopkins, Arizona, using Keplercam and a Sloan $z'$ filter."132 The first two of the FIAVO transits were already presented by Charbonneau et 20001 those data havebeen, The first two of the FLWO transits were already presented by Charbonneau et (2009); those data havebeen133The star ΠΟ 81032 was observed and detected by the ROSAT PSPC detector duriue the ROSAT (RASS) phase over a 2-dav period from 1990 November 10 to 12.,The star HD 81032 was observed and detected by the ROSAT PSPC detector during the ROSAT All-Sky-Survey (RASS) phase over a 2-day period from 1990 November 10 to 12.134 The exposure tine was 50] s. and was accumulated im 26 separate short scans of this region of ska.," The exposure time was 501 s, and was accumulated in 26 separate short scans of this region of sky."135 The PSPC had an energy range from 0.1 - 2.1 keV with a (low) spectral resolution. (AL/Ez0.12 at 1 keV).," The PSPC had an energy range from 0.1 - 2.4 keV with a (low) spectral resolution $\Delta E/E 136\approx 0.42$ at 1 keV)."137 A full description of the X-ray telescope aud detectors cau be found in Trimnuper (1983) aud in Pfefferiiaun ct al.(1987)., A full description of the X-ray telescope and detectors can be found in Trümmper (1983) and in Pfeffermann et al.(1987).138 The ROSAT X-ray data for ΠΟ 81032 were obtained from the public archives. the relevant RASS dataset beige rs932025n00.," The ROSAT X-ray data for HD 81032 were obtained from the public archives, the relevant RASS dataset being rs932025n00."139 Source spectra for IID 81032 were accunmlated from ou-source counts obtained from a circular region on the sky centered ou the N-ray peak and having a radius of 3.85 arcuun., Source spectra for HD 81032 were accumulated from on-source counts obtained from a circular region on the sky centered on the X-ray peak and having a radius of 3.85 arcmin.140 The backeround was acctuuulated from several neighhborimg regions at ucarly the same offset from the source., The background was accumulated from several neighboring regions at nearly the same offset from the source.141 Photometric curves corresponding to the four ruis were taken., Photometric light curves corresponding to the four observing runs were taken.142 Figure 1. shows the V baxd differential lightlight. curves of he star ITD 81032 atobserving different 0ος»., Figure \ref{ligper.fig} shows the V band differential light curves of the star HD 81032 at different epochs.143 We did not fiud any siguificaut variatious m the comparison star (see below)., We did not find any significant variations in the comparison star (see below).144 The vearly mean of he staudard deviationte) between the ierent measures of comparison aud check stars iu he D. V alc R filters was found to be 0.011. 0.01 alc LOLOL. respectively.," The yearly mean of the standard $\sigma$ ) between the different measures of comparison and check stars in the B, V and R filters was found to be 0.011, 0.01 and 0.01, respectively."145 Each lieb curve shown in Fi, Each light curve shown in Fig.146e. 1 was allaIwsed for periodicity., \ref{ligper.fig} was analysed for periodicity.147 To find a period frou unequaIv spaced data. we used the CLEAN aexOxitlun (Rolxrts et al.," To find a period from unequally spaced data, we used the CLEAN algorithm (Roberts et al."148 1987) in Starlink’s PERIOD sotware., 1987) in Starlink's PERIOD software.149 The obtaiied this method is shown in the mset of cach panel of Fig., The power spectrum obtained using this method is shown in the inset of each panel of Fig.150 1 wit1 the power spectudetermined.," \ref{ligper.fig}151 along with the period determined."152 The usingCLEAN: power spectra presented were obtained after LOO iterationsalong wih a period of 0.1., The CLEANed power spectra presented were obtained after 100 iterations with a loop gain of 0.1.153 Tje period is fouxd to be constant within error for cach , The period is found to be constant within error for each epoch.154To nuprove the xeriod loopdeterminationgain of he star IID 810:32. the ¢sutire data from 2000 - 200[ wereepoch. analysed using the same algorithm.," To improve the period determination of the star HD 81032, the entire data from 2000 - 2004 were analysed using the same algorithm."155 Figure 2 shows the CLEANed power spectrum from the eutire dataset., Figure \ref{power.fig} shows the CLEANed power spectrum from the entire dataset.156 The highest peak in the CLEANed power spectrum corres»onds to a period of 18.502+0.07Ed., The highest peak in the CLEANed power spectrum corresponds to a period of $18.802 \pm 0.074 \rm{d}$.157 The 15.502 d period is much more plausible than tje 57 d perio reported earlier (Paudey et al., The 18.802 d period is much more plausible than the 57 d period reported earlier (Pandey et al.158 2002)., 2002).159 The previous determinatio was nadulv due to olbscαναολα. luitations as our carly data were too sparse and liehly uneven., The previous determination was mainly due to observational limitations as our early data were too sparse and highly uneven.160 Besides a subeiaut like this ojo ds unlikely o be svuchronized im a binary of 57-days period., Besides a subgiant like this one is unlikely to be synchronized in a binary of 57-days period.161" The Julian days of the observations were couverted to the phases using the eplemeris: Phasct))=JD252307.76118""NOSE where the initial epoch corresponds to the conjunction with the first nünimuiuu observed.", The Julian days of the observations were converted to the phases using the ephemeris: $ Phase(\theta) = JD 2452307.761 + 18^{d}.802 E$ where the initial epoch corresponds to the conjunction with the first minimum observed.162 Figure 3H shows the differentia D.V. Rand. V... light «irves iud. (B-V) aud (V-B) colour οrves of the star IID 81032.," Figure \ref{fold.fig} shows the differential B, V, R and $_c$, light curves and, (B-V) and (V-R) colour curves of the star HD 81032."163" Tere V, stas for the differential V baud lieht curve of the comparison aud the check stars.", Here $_c$ stands for the differential V band light curve of the comparison and the check stars.164 Each point im the| light. curves is iiean of 3 - [iudeoudeut observations taken over a nieht., Each point in the light curves is mean of 3 - 4 independent observations taken over a night.165 The light curve the 2001-2002 has a dense temporal coverage., The light curve during the observing years 2001-2002 has a dense temporal coverage.166" We. therefore. divided this licht curve chivingiuto wo observingdiffereut vearsepochs ο see anv variation in the 0,,5, aud the amyplitiue"," We, therefore, divided this light curve into two different epochs to see any variation in the $\theta_{min}$ and the amplitude."167" The mean epoch of the light curves. ιο observec maxiunn (AV), ,,) aud mininnuun (AV,,;,) iu fie V baud. peak to peak amplitude (AW=AlnarΔΙmin j. alc phase of nininia(0,,;,) are listed iu Table 1.."," The mean epoch of the light curves, the observed maximum $\Delta V_{max}$ ) and minimum $\Delta V_{min}$ ) in the V band, peak to peak amplitude $\Delta V = \Delta V_{max} - \Delta V_{min}$ ), and phase of $\theta_{min}$ ) are listed in Table \ref{ligper.tab}."168" The value of AV, Was constant curing each 1 indicatiug hat the ποιους of uuspot«€ photosphere was constant from epoch to eoch.", The value of $\Delta V_{max}$ was constant during each epoch indicating that the brightness of unspotted photosphere was constant from epoch to epoch.169" However. epocthe vedue of AV, παν reduced by 0.1 linag from epoch “a to epoch b. and remainect ¢constant durius he οoch ο wd aud e."," However, the value of $\Delta V_{min}$ was reduced by 0.14 mag from epoch 'a' to epoch 'b', and remained constant during the epoch 'c', 'd' and 'e'."170 The RS CVu systems usually show «ne or two well defined minima. thereby iuicating that the rotational modulations caised by oue or Wo pronineif spots or o of spots.," The RS CVn systems usually show one or two well defined minima, thereby indicating that the rotational modulations caused by one or two prominent spots or groups of spots."171 Ackitional may be present at other longitides. or im the circiupolar PC@IOUS but groucontribution to the overall spotsrotational modulation may not be apxeciable.," Additional spots may be present at other longitudes, or in the circumpolar regions but contribution to the overall rotational modulation may not be appreciable."172 The oiase of the liebt iniwn (μμ) directly 1idicates the mean longitude of the comunaut eroups of spos., The phase of the light minimum $\theta_{min}$ ) directly indicates the mean longitude of the dominant groups of spots.173 A sharp nininum was observed durius he epoch “a (see Fi, A sharp minimum was observed during the epoch 'a' (see Fig.174e. aa)., \ref{fold.fig}a a).175" At the same tiue the amplitude of the| V band light «""Uurve was fouud to be 0,288 nag. which Was mnaxinun ourybservatious."," At the same time the amplitude of the V band light curve was found to be 0.288 mag, which was maximum during our observations."176 T16 of the 111ii inuuiuimdicate that 1 is the latitudinal exteut of the groups durnuegof spos that may be responsible sharpucssrather than the longitudinal exteut., The sharpness of the minimum indicate that it is the latitudinal extent of the groups of spots that may be responsible rather than the longitudinal extent.177 Droad minima during the epochs b.c and d inedicate that he spots wei‘© spread over an appreciable longitudinal range (Fi," Broad minima during the epochs 'b', 'c' and 'd' indicate that the spots were spread over an appreciable longitudinal range (Fig."178e. 3 b to d)., \ref{fold.fig} b to d).179 It is interesting to see the light curve «ft the star ITD 81032 during the epoch e., It is interesting to see the light curve of the star HD 81032 during the epoch 'e'.180 Tere a single large spot. characterized by a broad maui ¢mine the epochs b. € aud d separated iuto two groups of spots.," Here a single large spot, characterized by a broad minimum during the epochs 'b', 'c' and 'd' separated into two groups of spots."181 Tus can be easilv seeu w two well «parated λάμα (see Fi, This can be easily seen by two well separated minima (see Fig.182e. 23 ο)., \ref{fold.fig} e).183 Siguificaut change iu (η (see Table 1)) is probably associated with a chaice iu the spot configuration on the surface of the star., Significant change in $\theta_{min}$ (see Table \ref{ligper.tab}) ) is probably associated with a change in the spot configuration on the surface of the star.184pile-up of mass.,pile-up of mass.185 We therefore retain terms involving pressure to first order in 3., We therefore retain terms involving pressure to first order in $\beta$.186 Velocity evolution is governed by a momentum equation with only these two forces., Velocity evolution is governed by a momentum equation with only these two forces.187 Conservation properties become apparent when arc-length is replaced with ji. the integrated mass per unit flux: Op/Ot=pj/D;.," Conservation properties become apparent when arc-length is replaced with $\mu$, the integrated mass per unit flux: $\partial\mu/\partial\ell=\rho_i/B_i$."188 The value of j(/ never changes for a given fluid element., The value of $\mu$ never changes for a given fluid element.189" The resulting momentum equation di DKt))1 = includes the parallel pressure gradient after use of pressure balance, D;=Dd4s(p.—pji)/be. valid to first order in 7."," The resulting momentum equation = ) = ), includes the parallel pressure gradient after use of pressure balance, $B_i=B_e + 4\pi(p_e-p_i)/B_e$, valid to first order in $\beta$."190" The momentum per unit flux of any section of tube, P= = changes only through forces (per unit flux) from the ends of the section, D;t/4z. directed parallel to the axis."," The momentum per unit flux of any section of tube, = =, changes only through forces (per unit flux) from the ends of the section, $B_i\that/4\pi$, directed parallel to the axis."191 Momentum conservation leads to a set of shock relations for thin flux tubes., Momentum conservation leads to a set of shock relations for thin flux tubes.192" Consider two straight sections with uniform properties (designated 1 and 2), separated by an abrupt change at coordinate µῃ."," Consider two straight sections with uniform properties (designated $1$ and $2$ ), separated by an abrupt change at coordinate $\mu_0$."193 The length-seale of this change is large compared to the tube radius but otherwise small enough that we hereafter call it a “discontinuity” and, The length-scale of this change is large compared to the tube radius but otherwise small enough that we hereafter call it a “discontinuity” and194"greatly reduce the required absorption column densities, is highly unlikely because of the agreement between absorption and emission, between J=13 and other direct ¢-type lines (Fig. 10)),","greatly reduce the required absorption column densities, is highly unlikely because of the agreement between absorption and emission, between $J$ =13 and other direct $\ell$ -type lines (Fig. \ref{fig:rd}) ),"195 and between the derived column densities and dust emission data., and between the derived column densities and dust emission data.196" Therefore, we consider LTE a good assumption for this transition."," Therefore, we consider LTE a good assumption for this transition."197" If we assume similar optical depth for the emission lines, say 0.3, and a temperaturea of 400 K, then the line intensity should be 100 K, which is just the noise level in 1 km s! channels and 0.13"" beams."," If we assume a similar optical depth for the emission lines, say 0.3, and a temperature of 400 K, then the line intensity should be 100 K, which is just the noise level in 1 km $^{-1}$ channels and $''$ beams."198" Owing to the strength of the free-free radiation, we are thus more sensitive to absorption than emission lines."," Owing to the strength of the free-free radiation, we are thus more sensitive to absorption than emission lines."199 Averaging over a larger region (Fig., Averaging over a larger region (Fig.200 1 and Table 3)) lowers both noise and peak intensities., \ref{fig:spectra} and Table \ref{tab:emlines}) ) lowers both noise and peak intensities.201" The latter reach up to 300 K in G10.47+0.03, suggesting that optical depth and temperature are higher than the above mentioned assumptions."," The latter reach up to 300 K in G10.47+0.03, suggesting that optical depth and temperature are higher than the above mentioned assumptions."202" Surprising is the detection of the line toward G10.47+0.03 A, since no NH3(4,4) satellites were detected by 9"," Surprising is the detection of the line toward G10.47+0.03 A, since no $_3$ (4,4) satellites were detected by \citet{Cesaroni10}."203" In the model for SgrB2-M, we have placed the regions F3 and Fle in front of and behind the bulk of the molecular gas, respectively."," In the model for SgrB2-M, we have placed the regions F3 and F1e in front of and behind the bulk of the molecular gas, respectively."204 This prevents absorption toward most of F3 and leads to stronger absorption toward Fle., This prevents absorption toward most of F3 and leads to stronger absorption toward F1e.205" The exact offsets in z are not well constrained, however."," The exact offsets in z are not well constrained, however."206" To obtain the very strong absorption toward K2 in SgrB2-N, we put a very dense core just in front of the region."," To obtain the very strong absorption toward K2 in SgrB2-N, we put a very dense core just in front of the region."207 This is of course not very satisfying as it is unlikely that such a core is exactly along the line-of-, This is of course not very satisfying as it is unlikely that such a core is exactly along the line-of-sight.208 It was however not possible to reproduce both emission and absorption with a more symmetric distribution., It was however not possible to reproduce both emission and absorption with a more symmetric distribution.209 Heating up large masses of molecular gas requires deeply embedded massive (proto)stars with high luminosities., Heating up large masses of molecular gas requires deeply embedded massive (proto)stars with high luminosities.210" Their radiation is either originally in the infrared (?),, not producing regions, or is quickly processed to the infrared by dust absorption of the UV radiation."," Their radiation is either originally in the infrared \citep{Hosokawa09}, not producing regions, or is quickly processed to the infrared by dust absorption of the UV radiation."211" Due to high column densities in all directions, the dust is optically thick even in the infrared and this radiation cannot escape, but diffuses outwards by multiple absorption/emission events until the dust is optically thin to its own radiation."," Due to high column densities in all directions, the dust is optically thick even in the infrared and this radiation cannot escape, but diffuses outwards by multiple absorption/emission events until the dust is optically thin to its own radiation."212 This diffusion (or radiative trapping) leads to, This diffusion (or radiative trapping) leads to213"Sealo. 1979... with Mj=0.1A to AL,=10 M) and with au exponent x=-1.35 (from M,=0.33AL: to AL,—10 Mj).","Scalo, \cite{miller}, with $\rm M_l=0.1~ M\odot$ to $\rm M_u = 10~ M\odot$ ) and with an exponent x=-1.35 (from $\rm M_l=0.33~ M\odot$ to $\rm M_u = 10~ M\odot$ ))."214 We select all objects whose colors are consistent with the envelope of the models adopting a 20 uncertainty on cach color given bv the DAOPIIOT software.," We select all objects whose colors are consistent with the envelope of the models adopting a $\rm 2152\sigma$ uncertainty on each color given by the DAOPHOT software."216 We use the models of Bertelli et al. (199 D):, We use the models of Bertelli et al. \cite{bertelli}) ):217 they cad to a similar selection of GC candidates., they lead to a similar selection of GC candidates.218The resulting range of acceptable colors is 0.80κV¥T<1.50.13<DIc2.7.05«DB.V<1.6 but our selection is more refined than adopting simple color ranges since we check he compatibility of the three colors by heir locus in color-color diagrams.,"The resulting range of acceptable colors is $\rm 2190.80<V-I<1.50,~ 1.3<B-I<2.7,~ 0.5<B-V<1.6$ but our selection is more refined than adopting simple color ranges since we check the compatibility of the three colors by their locus in color-color diagrams."220 For the objects which are not detected iu D of the sample) a range of plausible values for their D maguitude is estimated from the models aud their V-I colors., For the objects which are not detected in B of the sample) a range of plausible values for their B magnitude is estimated from the models and their V-I colors.221 Then we reject the objects which must be detected in D (the laniting D imaguitude is taken at 23.5 mae of completeness))., Then we reject the objects which must be detected in B (the limiting B magnitude is taken at 23.5 mag of completeness)).222" After these selections we are left with 89 GC candidates; out of which only 3 have no D micasurement,."," After these selections we are left with 89 GC candidates, out of which only 3 have no B measurement."223 We study the density profile of GCs using thes«nselected V detections down to V=23.9 mae. our completeness liuit.," We study the density profile of GCs using the V detections down to V=23.9 mag, our completeness limit."224 To compute this censity profile we biu the suuple iu elliptical times having the same inclination aud ellipticitv as NGC 7157 (e=0.11 and p.a.=1307. LEDA database).," To compute this density profile we bin the sample in elliptical rings having the same inclination and ellipticity as NGC 7457 $\rm \epsilon = 0.41$ and $\rm p.a. = 130\degr$, LEDA database)."225" The major axis step is about 25 "" and the minor 15 "". The", The major axis step is about 25 $\rm\arcsec$ and the minor 15 $\rm\arcsec$ The226recurrence times is (wolold.,recurrence times is twofold.227 Not only is the accretion rate per unit area smaller [or a larger star. but also (he amount of [uel per unit area required for a superburst to occur is larger.," Not only is the accretion rate per unit area smaller for a larger star, but also the amount of fuel per unit area required for a superburst to occur is larger."228 The effect of radius on superburst energelics is even stronger., The effect of radius on superburst energetics is even stronger.229 In. addition to the [actors stated above. the total surface area of the star is larger. so the total amount of fel available to burn al a given column depth is ereater.," In addition to the factors stated above, the total surface area of the star is larger, so the total amount of fuel available to burn at a given column depth is greater."230 Figure 16 (hus suggests that superburst observations max be useful lor constraining neutron star radii., Figure 16 thus suggests that superburst observations may be useful for constraining neutron star radii.231 As noted in 811. the nine superbursts that have been observed. excluding those rom GX 172-2. have integrated photon fluxes of &107 eres.," As noted in 1, the nine superbursts that have been observed, excluding those from GX 17+2, have integrated photon fluxes of $ \approx23210^{42}$ ergs."233 The paucity of data makes the recurrence time of superbursts difficult to determine. but observations imply a recurrence time of 1-2 vears.," The paucity of data makes the recurrence time of superbursts difficult to determine, but observations imply a recurrence time of $\sim 1$ $2$ years."234 All nine superbursts occurred in svstems with aceretion rates between LOY and 30% of the Eddington limit., All nine superbursts occurred in systems with accretion rates between $10\%$ and $30\%$ of the Eddington limit.235 Additionally. several superburst candidates have been observed in the near-Eddington accretor GX 1742 with energies of ~5x1011 eves.," Additionally, several superburst candidates have been observed in the near-Eddington accretor GX 17+2 with energies of $\sim 5 \times 10^{41}$ ergs."236 A successful theoretica moclel of superbursts must explain (hese facts., A successful theoretical model of superbursts must explain these facts.237 We beein by discussing the AM range over which superbursts are observed., We begin by discussing the $\dot M$ range over which superbursts are observed.238 The lack of superbursts for accretion rates AM.<OALgq arises naturally in our model and is rather simple to explain theoretically.," The lack of superbursts for accretion rates $\dot{M}239\lesssim 0.1 \dot{M}_{\mathrm{Edd}}$ arises naturally in our model and is rather simple to explain theoretically."240 As discussed in 844.3. at low AZ. either the carbon [ne burns stably via thermonuclear reactions before an instability is (rige@erecl (for high core temperatures. Cumming Bildsten 2001) or (the crust solidifies in (he superburst ienition region and the carbon burns stably via pyvenonuclear reactions (For low core temperatures).," As discussed in 4.3, at low $\dot M$, either the carbon fuel burns stably via thermonuclear reactions before an instability is triggered (for high core temperatures, Cumming Bildsten 2001) or the crust solidifies in the superburst ignition region and the carbon burns stably via pycnonuclear reactions (for low core temperatures)."241 In either case. (here is a cutoff of superbursts al low values of (M.," In either case, there is a cutoff of superbursts at low values of $\dot M$."242 The above discussion is invalid if (the erust is highly disordered. since then the thermal conductivity is low. causing the region in which superbursts are triggered to be hotter than if the crust were ordered.," The above discussion is invalid if the crust is highly disordered, since then the thermal conductivity is low, causing the region in which superbursts are triggered to be hotter than if the crust were ordered."243 Also. when the carbon ignites. the low thermal conductivity inhibits the diffusion of the nuclear οποίον generated there.," Also, when the carbon ignites, the low thermal conductivity inhibits the diffusion of the nuclear energy generated there."244 The nuclear energy generation rate exceeds (he rate at which thermal conduction can cool the region. so a thermonuclear runaway ensues and a superburst is triggered.," The nuclear energy generation rate exceeds the rate at which thermal conduction can cool the region, so a thermonuclear runaway ensues and a superburst is triggered."245 Therefore. as seen in Figure 15. superbursts occur down to accretion rates below 0.1Mp4.," Therefore, as seen in Figure 15, superbursts occur down to accretion rates below $0.1\dot M_{\rm246Edd}$."247 The lack of observed superbursts for accretion rates M<0.1Mia then needs to be explained.," The lack of observed superbursts for accretion rates $\dot{M}248\lesssim 0.1 \dot{M}_{\mathrm{Edd}}$ then needs to be explained."249 One possibility is (hat. for some reason. e.g.. lack of delaved mixed bursts (see below). carbon is not produced in sufficient quantiües to [nel a superburst.," One possibility is that, for some reason, e.g., lack of delayed mixed bursts (see below), carbon is not produced in sufficient quantities to fuel a superburst."250 Another explanation could be that at low accretion rates the recurrence times are so long that astronomers simply have not observed anv of the systems long enough to see superbursts., Another explanation could be that at low accretion rates the recurrence times are so long that astronomers simply have not observed any of the systems long enough to see superbursts.251different morphologies compared to those at low redshifts (Abraham van den Bergh 2001: Brinchmann et al.,different morphologies compared to those at low redshifts (Abraham van den Bergh 2001; Brinchmann et al.252 1998; van den Bergh 2001)., 1998; van den Bergh 2001).253 Dust and related extinction characteristics may certainlv depend on redshift (Totani Ixobavashi 1999)., Dust and related extinction characteristics may certainly depend on redshift (Totani Kobayashi 1999).254 Furthermore (he abundance ratios of the progenitor stars mav be different at different redshifts (Hófllich et al., Furthermore the abundance ratios of the progenitor stars may be different at different redshifts (Höfflich et al.255 2000)., 2000).256 Several studies emphasize that evolution effects cannot be ruled out (Falco et al., Several studies emphasize that evolution effects cannot be ruled out (Falco et al.257 1999; Aguirre 1999: Farrah et al., 1999; Aguirre 1999; Farrah et al.258 2004: Clements et al., 2004; Clements et al.259 2004)., 2004).260 In this paper we [ind evidence for evolution or bias in the extinction parameters used to pre-process the data., In this paper we find evidence for evolution or bias in the extinction parameters used to pre-process the data.261 If the effect is due to bias. extinctions have been overestimate. which makes supernovas appear more dim.," If the effect is due to bias, extinctions have been overestimated, which makes supernovas appear more dim."262 Yet just the same phenomenon could occur from a real physical effect in which (he actual host exünct(ons are correlated with the deviation ol magnitudes [rom moclel fits., Yet just the same phenomenon could occur from a real physical effect in which the actual host extinctions are correlated with the deviation of magnitudes from model fits.263" Traditional IIubble diagrams represent the relation of observed flux F to the luminosity ol the source £. >. where d, is the so-called Iuminosity distance."," Traditional Hubble diagrams represent the relation of observed flux ${\cal F}$ to the luminosity of the source ${\cal L}$, , where $d_{L}$ is the so-called luminosity distance."264 The distance modulus 4/j=m—M. where im and AM ave the apparent and absolute magnitudes respectively. is where the luminosity distance dj is in megaparsecs.," The distance modulus $\mu_p=m-M$, where $m$ and $M$ are the apparent and absolute magnitudes respectively, is where the luminosity distance $d_L$ is in megaparsecs."265 The process of converting observed data into the supernova magnitudes reported actually contains an additive parameter. called (he extinction coefficient ο.," The process of converting observed data into the supernova magnitudes reported actually contains an additive parameter, called the extinction coefficient $A$ ."266 Exünction max depend on lrequeney. designated by Ay. ly. ete.," Extinction may depend on frequency, designated by $A_{B}$, $A_{R}$, etc."267 The units of A are magnitude., The units of $A$ are magnitude.268" In practice A shifts (he supernova magnitude mo deduced from light-curves to a reported magnitude (""extinction corrected magnitude"") mi=my—d.", In practice $A $ shifts the supernova magnitude $m_{0}$ deduced from light-curves to a reported magnitude (“extinction corrected magnitude”) $m= m_{0}-A $.269 Our galaxy contributes extinction. as do (he additional extinctioneffects associated with supernova host galaxies.which are more model dependent.," Our galaxy contributes extinction, as do the additional extinctioneffects associated with supernova host galaxies,which are more model dependent."270of the individual random-phase fluxes measured of each variable. ancl converting (he average [Iuxes back into magnitudes.,"of the individual random-phase fluxes measured of each variable, and converting the average fluxes back into magnitudes."271 La principle a more accurate procedure to determine (le mean magnitudes in J and Ix would be (he recipy described by Soszvuski et al. (, In principle a more accurate procedure to determine the mean magnitudes in J and K would be the recipy described by Soszynski et al. (2722005) which uses the V and I light eurves of the variables and the known phases of the near-inlrared observations.,2005) which uses the V and I light curves of the variables and the known phases of the near-infrared observations.273 Ilowever. in the present case of WLM the epoch difference between the near-intrared data reported in this paper. ancl the previous VI data reported in Paper I is so large. typically some 200 pulsation eveles. that with the limited accuracy. of (he. periods of the variables derived in Paper I the phasing of the near-IR data becomes very. uncertain.," However, in the present case of WLM the epoch difference between the near-infrared data reported in this paper, and the previous VI data reported in Paper I is so large, typically some 200 pulsation cycles, that with the limited accuracy of the periods of the variables derived in Paper I the phasing of the near-IR data becomes very uncertain."274 While this is unfortunate. the simple taking of a straight average of several random-phase magnitudes in a near-IR. band of a Cepheid still does produce a rather accurate mean magnitude. given the ow light curve amplitudes of Cepheid variables at these wavelengths of (vpically 0.3 mas or stus with periods less than 10 davs (e.g. Persson et al.," While this is unfortunate, the simple taking of a straight average of several random-phase magnitudes in a near-IR band of a Cepheid still does produce a rather accurate mean magnitude, given the low light curve amplitudes of Cepheid variables at these wavelengths of typically 0.3 mag for stars with periods less than 10 days (e.g. Persson et al."275 2004)., 2004).276 For the one long-period Cephleid in WLM. cepOO1 with a period of 54 days. the amplitucle of the Ix-band light curve is expected to be about 0.5 mag. but for this variable we have obtained six observations al different phases which makes us expect that their mean value is verv close to the (rue mean nagnitude of the variable. in the two bands we observed.," For the one long-period Cepheid in WLM, cep001 with a period of 54 days, the amplitude of the K-band light curve is expected to be about 0.5 mag, but for this variable we have obtained six observations at different phases which makes us expect that their mean value is very close to the true mean magnitude of the variable, in the two bands we observed."277 Table 3 gives the intensity mean J and Ix magnitudes of the individual Cepheids. with their estimated. uncertainties from the number anc accuracy of the individual observations leading to the adopted mean magnitude.," Table 3 gives the intensity mean J and K magnitudes of the individual Cepheids, with their estimated uncertainties from the number and accuracy of the individual observations leading to the adopted mean magnitude."278 We also provide the periods (adopted [rom Paper D., We also provide the periods (adopted from Paper I).279 In Figures 4 and 5 we show the period-mean magnitude relations in the J and Ix bands as delined by the data in Table 3., In Figures 4 and 5 we show the period-mean magnitude relations in the J and K bands as defined by the data in Table 3.280 There is one Cepheid. cep038. which is clearly over-Iuminous in both PL diagrams. by about 1.5 mag in J and about 2 mag in Ix. We assume that (he very bright magnitude of this variable is caused by. a nearby. bright object which is not resolved in our images.," There is one Cepheid, cep038, which is clearly over-luminous in both PL diagrams, by about 1.5 mag in J and about 2 mag in K. We assume that the very bright magnitude of this variable is caused by a nearby bright object which is not resolved in our images."281 Since the V and I magnitudes of cep038 are normal for its period (see Paper 1) the blend must be a very red. object.," Since the V and I magnitudes of cep038 are normal for its period (see Paper I), the blend must be a very red object."282 The ocurrence of at least one strongly blended Cepheid in WLM in a sample of about 30 stars is «uite expected [rom (he result obtained by Bresolin et al. (, The ocurrence of at least one strongly blended Cepheid in WLM in a sample of about 30 stars is quite expected from the result obtained by Bresolin et al. (2832005) who studied the blending of Cepheids in NGC 300. al about twice the distance of WLM. from a comparison of ground-based and HST/ACS photometry. finding three strongly blended Cepheids in a sample of 16 Cepheids in this galaxy.,"2005) who studied the blending of Cepheids in NGC 300, at about twice the distance of WLM, from a comparison of ground-based and HST/ACS photometry, finding three strongly blended Cepheids in a sample of 16 Cepheids in this galaxy."284 For the following distance analysis. we exclude star cepü38.," For the following distance analysis, we exclude star cep038."285 For the reasons discussed in Paper L and in conformity with the approach adopted there. we adopt a period cutoff of log P. (days) = 0.5 lor the distance analvsis. retaining onlv the Cepheids with longer periods in the sample.," For the reasons discussed in Paper I, and in conformity with the approach adopted there, we adopt a period cutoff of log P (days) = 0.5 for the distance analysis, retaining only the Cepheids with longer periods in the sample."286 This ensures (hat possible overtone pulsators are likely to be excluded in the sample adopted for the distance determination. ancl it eliminates (he variables with the lowest signal-to-nolse ratio in the photometry.," This ensures that possible overtone pulsators are likely to be excluded in the sample adopted for the distance determination, and it eliminates the variables with the lowest signal-to-noise ratio in the photometry."287 The final sample consists of Cepheids 001-033 in Table 3 (24 stars)., The final sample consists of Cepheids 001-033 in Table 3 (24 stars).288 Note that the strongly blended Cepheicl cepO38 is eliminated from the final sample also on the basis of the adopted period, Note that the strongly blended Cepheid cep038 is eliminated from the final sample also on the basis of the adopted period289of view of the included. phyvsies. our previous onc-cinensioual simulations obwviouslv could not address +ιο inpact of eenuimelv two-dimensional phenomena u the feedback phenomenon.,"of view of the included physics, our previous one-dimensional simulations obviously could not address the impact of genuinely two-dimensional phenomena on the feedback phenomenon."290 We recall here the most iurportant of them. that will be discussed in this paper.," We recall here the most important of them, that will be discussed in this paper."291 The first one concerus the possible instabilities (e.g. RavleighTavlor. RT) that can affect the evolution of the cold shells that appear during the evolution of ouc-dimensional models.," The first one concerns the possible instabilities (e.g., Rayleigh–Taylor, RT) that can affect the evolution of the cold shells that appear during the evolution of one-dimensional models."292 The central bursts are caused by these shells. aud the shells have a two-fold origin.," The central bursts are caused by these shells, and the shells have a two-fold origin."293 At the beginning of each major burst. the classical Field cooling instability (Field1965). appears around 1 kpc from the center. due to the local critical balance between heating and cooling.," At the beginning of each major burst, the classical Field cooling instability \citep{field:65} appears around 1 kpc from the center, due to the local critical balance between heating and cooling."294 As the density increases. the shell starts to fall toward the ceuter and compresses the eas.," As the density increases, the shell starts to fall toward the center and compresses the gas."295 Whena burst first appears. shock waves are seut from the center toward the falling shell. aud a series of 3ub-bursts and consequent reflected shock waves impact on the cold shell. increasing its deusity still further.," When a burst first appears, shock waves are sent from the center toward the falling shell, and a series of sub-bursts and consequent reflected shock waves impact on the cold shell, increasing its density still further."296 As the bulk of star formation in the one-dimensional models happens in these cold shells. if is very important to understand the cold shell plivsies. not ouly from the poiut of view of central accretion. but also for the starburst which occurs Within the cold shell.," As the bulk of star formation in the one-dimensional models happens in these cold shells, it is very important to understand the cold shell physics, not only from the point of view of central accretion, but also for the starburst which occurs within the cold shell."297" From the short description above, a few obvious questions arise: for example. will the allowance of the additional deeree of freedom still lead to a formation of a cold shell near the ceuter in the case ofan aspherical galaxv?"," From the short description above, a few obvious questions arise: for example, will the allowance of the additional degree of freedom still lead to a formation of a cold shell near the center in the case of an aspherical galaxy?"298 What is the effect of non-zero aueular momentum in the gas?, What is the effect of non-zero angular momentum in the gas?299 Will the cold shell fall toward the center as iu the one-dineusional siuulationus or it will break up due to (RT) iustabilitv?, Will the cold shell fall toward the center as in the one-dimensional simulations or it will break up due to (RT) instability?300 Even more important. what is the fate of the multiple interacting shocks?," Even more important, what is the fate of the multiple interacting shocks?"301 Will the aceretion still be characterized by strong bursts separated by loueg time intervals or will the breaxup of the shells lead to cold finecrs of dense gas being acereted in a amore or less steady flow while hot gas flows outward. therefore resulting iu flows that at each radius are partially accretiug aud partially outflowiue?," Will the accretion still be characterized by strong bursts separated by long time intervals or will the breakup of the shells lead to cold fingers of dense gas being accreted in a more or less steady flow while hot gas flows outward, therefore resulting in flows that at each radius are partially accreting and partially outflowing?"302 The second reason to imove το two-dimensional siuulatious is to explore the interaction (and the consequent mechanical feedback) of the conical nuclear wind with the ealaxy ISM., The second reason to move to two-dimensional simulations is to explore the interaction (and the consequent mechanical feedback) of the conical nuclear wind with the galaxy ISM.303 In our previous onc-mensional sninulatious this interaction was necessarily described as a spherical average of au inhercuth non-spherical effect. even though we had taken iuto account several physical aspects of the phenomenon via a time-dependent differential equation.," In our previous one-dimensional simulations this interaction was necessarily described as a spherical average of an inherently non-spherical effect, even though we had taken into account several physical aspects of the phenomenon via a time-dependent differential equation."304 Clearly. a dimensional simulation is also needed to explore IelviuUehuholtz iustabilities at the interface between the outflowiueg conical wind aud the ISM.," Clearly, a two-dimensional simulation is also needed to explore Kelvin--Helmholtz instabilities at the interface between the outflowing conical wind and the ISM."305 Iu the preseut work. we focus on two-dimensional smnulatious of a galaxy wihn verv low specific angular moment iji order to niake close coutact with the existiue one-«nueusional siwulations.," In the present work, we focus on two-dimensional simulations of a galaxy with very low specific angular momentum in order to make close contact with the existing one-dimensional simulations."306 We would like to isolate the effect. of increasiug the dimensionality of the simulation., We would like to isolate the effect of increasing the dimensionality of the simulation.307 Tie adopted angular momentum profile is consisteut witi the slowest of he SAURON slow-rotators (Enuscllenetal.2001.., The adopted angular momentum profile is consistent with the slowest of the SAURON slow-rotators \citep{emsellem:04}.308. In fture work. we will expaud our treatiucut to include anegulay moment transport via the stateard oo prescription (Shakura&Suuvaev1973) and more recent nioccls based on exavitational torques (IHopkius&Quataert2010a)..," In future work, we will expand our treatment to include angular momentum transport via the standard $\alpha$ prescription \citep{shakura:73} and more recent models based on gravitational torques \citep{hopkins:10-analytic-preprint}."309 There have OCTL Wad nuierical simulations of SMDIT accretion auk the subsequeit effects on the galaxies containing the resulting ACN., There have been many numerical simulations of SMBH accretion and the subsequent effects on the galaxies containing the resulting AGN.310 Nearly all of the efforts to date can be classified into three broad categories. DiMatteoetal.(2005)... Debuhlretal.(2010.2011).," Nearly all of the efforts to date can be classified into three broad categories. \citet{dimatteo:05}, \citet{debuhr:10,debuhr:11},"311. and Johanssonetal.(2009). are examples where the siuulations cover leneth scales from z 100 pe to tens of kpe aud timescales from ai fraction of a Myr to several Cyr., and \citet{johansson:09} are examples where the simulations cover length scales from $\simeq$ 100 pc to tens of kpc and timescales from a fraction of a Myr to several Gyr.312 Galactic leugth aud timescales are resolved. but the SAIBID accretion aud. feedback processes are considered to be sub-resolutiou.," Galactic length and timescales are resolved, but the SMBH accretion and feedback processes are considered to be sub-resolution."313 Complementary studies by Iurosawa&Proga(2009a)) and Kurosawa&Prosa(2009b) are exaniples of iiulti-dineusional sinulatious that cover the leneth scales from a few AU to z 1 pe.," Complementary studies by \citet{kurosawa:09-2d}314 and \citet{kurosawa:09-3d} are examples of multi-dimensional simulations that cover the length scales from a few AU to $\simeq$ 1 pc."315 Leugth aud timescales relevant to SAIBIT accretion are resolved. aud the generation of radiativelv driven winds is computed. but these simulations do uot approach ealactic leneth or timescales. and imfall rates are taken as eiveu.," Length and timescales relevant to SMBH accretion are resolved, and the generation of radiatively driven winds is computed, but these simulations do not approach galactic length or timescales, and infall rates are taken as given."316 Hopkius&Quatacrt(20100) and Levineetal.(2008) are examples of a multi-resolution studies of SMDITI aceretion involving proeressively higher spatial resolution παος run for progressvelv shorter times., \citet{hopkins:10-simulation} and \citet{levine:08} are examples of a multi-resolution studies of SMBH accretion involving progressively higher spatial resolution simulations run for progressively shorter times.317 The highest spatial resolution simulations eo dowd to a fraction of à pc and are mun for about one Myr of sinulation time., The highest spatial resolution simulations go down to a fraction of a pc and are run for about one Myr of simulation time.318 These simulations spatially resolve the accretion process. but do not reach galactic timescales.," These simulations spatially resolve the accretion process, but do not reach galactic timescales."319 Therefore. they cannot selfconsistentlv calculate the effect of ACN feedback on the gas in the galaxy as a whole aud the subsequent SMDIT accretion.," Therefore, they cannot self-consistently calculate the effect of AGN feedback on the gas in the galaxy as a whole and the subsequent SMBH accretion."320 Finally. there have been several uumerical studies of accretion by diuteriuediate-nüass black holes (IMDIIs) with the goal of understanding BIT growth in the carly universe (Alvarezctal.2000:Park&Ricotti2010).," Finally, there have been several numerical studies of accretion by intermediate-mass black holes (IMBHs) with the goal of understanding BH growth in the early universe \citep{alvarez:09, park:10-preprint}."321. Tn tenus of dimensiouless leugth scales ¢/rpondai Or relSchwarzschild: ποιο of these simulations are simular to our snmulations.," In terms of dimensionless length scales $r/r_{\rm Bondi}$ or $r/r_{\rm322 Schwarzschild}$, some of these simulations are similar to our simulations."323 Towever. studies of IMDIT accretion focus ou DIIS with very small masses (1001000/7.) compared to those preseuted here.," However, studies of IMBH accretion focus on BHs with very small masses (100–1000 $M_\odot$ ) compared to those presented here."324 Therefore. the relevant plvsical leugth and timescales are uch sinaller and the physical sources of the infalling eas are very different from those considered iu the present work.," Therefore, the relevant physical length and timescales are much smaller and the physical sources of the infalling gas are very different from those considered in the present work."325 Our goal is to resolve both the relevant accretion leugth and timescales while at the same time resolving ealactic leneth aud timescales (e£.Levineetal.2008:Al-varezetal. 2009).," Our goal is to resolve both the relevant accretion length and timescales while at the same time resolving galactic length and timescales \citep[cf.][]{levine:08, alvarez:09}."326. There have been oulv a few attempts to perform iulti-dimensional simulations that bridge the gap between galactic and SAIBID scales. although several papers have examined the interaction between an outflowineg wind‘jet with specified properties aud the surrounding intergalactic mediu (cf.Metzler&EvrardAviclictal.2010) The preseu work is an attempt to sinultaneouslv resolve the duncr leneth scales relevant to SAIBIT accretion (a ew pe). outer leugth scales relevant to ealaxies (tens of Ispe)}. iuner timescales relevant to SAIBIT accretion (a few vears). aud outer timescales relevaut to galaxies and stellar evolution (10 Cer).," There have been only a few attempts to perform multi-dimensional simulations that bridge the gap between galactic and SMBH scales, although several papers have examined the interaction between an outflowing wind/jet with specified properties and the surrounding intergalactic medium \citep[cf.][]{metzler:94,omma:04,sijacki:07,sternberg:08,reeves:09,fabian:09,arieli:10}327 The present work is an attempt to simultaneously resolve the inner length scales relevant to SMBH accretion (a few pc), outer length scales relevant to galaxies (tens of kpc), inner timescales relevant to SMBH accretion (a few years), and outer timescales relevant to galaxies and stellar evolution (10 Gyr)."328 However. the region inside of 1l pe including the disk and the SMIDIT itself are still treated as sub-resolutiou plysics and we compute the output from these regions as tinic- functious of the input to them. utilizing formulae from the above quoted sources.," However, the region inside of 1 pc including the disk and the SMBH itself are still treated as sub-resolution physics and we compute the output from these regions as time-dependent functions of the input to them, utilizing formulae from the above quoted sources."329 We take particular care to resolve the inner scales where the rate of accretion is set (the Dondi radius) even, We take particular care to resolve the inner scales where the rate of accretion is set (the Bondi radius) even330showing different sub-samples.,showing different sub-samples.331 The problem is found in individual objects., The problem is found in individual objects.332 This cannot be accounted for by reddening effects., This cannot be accounted for by reddening effects.333 Correcting for reddening would produce higher [NeV]/[OTI] and [NeV]/[NeIII] that would result on larger ( values., Correcting for reddening would produce higher [NeV]/[OII] and [NeV]/[NeIII] that would result on larger $U$ values.334 On the other hand. [OIT/[OITII] would also become larger. implying lower (7 values.," On the other hand, [OII]/[OIII] would also become larger, implying lower $U$ values."335 Therefore. the discrepancy would be worse.," Therefore, the discrepancy would be worse."336 We have plotted in Fig., We have plotted in Fig.337 4 the temperature sensitive [OIII]AA3007.4959/[OTII] ratio vs. [OIITI/H-7., 4 the temperature sensitive $\lambda\lambda$ $\lambda$ 4363 ratio vs. $\beta$.338 The arrows correspond to objects for A4363which [OIIT[A4363 was not detected and only upper limits could be estimated., The arrows correspond to objects for which $\lambda$ 4363 was not detected and only upper limits could be estimated.339 For all objects the predicted and measured values of [OIIT[AA3007.4959/TOITI]A4363 are discrepant by at least a factor of 2 (a shift of 20.3 in 15)., For all objects the predicted and measured values of $\lambda\lambda$ $\lambda$ 4363 are discrepant by at least a factor of 2 (a shift of $>$ 0.3 in lg).340 This cannot be accounted for by measurement errors (see Fig., This cannot be accounted for by measurement errors (see Fig.341 +) or reddening effects. since correcting for this would result on even ower [OIIT[AA5007.4959/[OITII]44363 ratios.," 4) or reddening effects, since correcting for this would result on even lower $\lambda\lambda$ $\lambda$ 4363 ratios."342 Higher densities can explain low OMTAAS007.4959/[ONTA4363 values consistent with the data. but produce strong discrepancies with other line ratios.," Higher densities can explain low $\lambda\lambda$ $\lambda$ 4363 values consistent with the data, but produce strong discrepancies with other line ratios."343" As an example. models with n=l0""  produce [OIII]AA5007.4959/TOTII]A4363)::2.. as measured for many ype 2 quasars."," As an example, models with $n$ $^5$ $^{-3}$ produce $\lambda\lambda$ $\lambda$ $\le$ 2, as measured for many type 2 quasars."344 However. for such models [OITI]/[ONT]<0.02. ΟΠΗ: <0.3 (much lower than the measured values. Fig.," However, for such models $\le$ 0.02, $\beta\le$ 0.3 (much lower than the measured values, Fig."345 |) and [OIII/H2 18 ¢higher than measured. Fig.," 1) and $\beta\ge$ 18 (higher than measured, Fig."346 1)., 1).347 High densitiesonlv. therefore. in general do not solve the problem.," High densities, therefore, in general do not solve the problem."348" In the low density limit (Osterbrock 1989)). this discrepancy implies that the models prediet too low electron temperatures: T,x 11000 K for all models ofthe {ὁ sequence. while the measured line ratios imply 7; 15 000 K. being —20 000 in several cases. errors considered."," In the low density limit (Osterbrock \citeyear{ost89}) ), this discrepancy implies that the models predict too low electron temperatures: $T_e\le$ 11000 K for all models of the $U$ sequence, while the measured line ratios imply $T_e\ga$ 15 000 K, being $>$ 20 000 in several cases, errors considered."349 The same problem has been discussed in detail for other type 2 AGNS (e.g. Binette. Wilson Storchi-Beremann 1996.. Robinson et al. 1987).," The same problem has been discussed in detail for other type 2 AGNs (e.g. Binette, Wilson Storchi-Bergmann \citeyear{bin96}, Robinson et al. \citeyear{rob87}) )."350 The data present a large HeII/H.? scatter inconsistent with the standard AGN sequence (Fig., The data present a large $\beta$ scatter inconsistent with the standard AGN sequence (Fig.351 | bottom panel). which is not due to errors in the measurements. neither reddening effects.," 1 bottom panel), which is not due to errors in the measurements, neither reddening effects."352 There are objects with too high and objects with too low HeII/H:? ratios compared with the model predictions (see Fig., There are objects with too high and objects with too low $\beta$ ratios compared with the model predictions (see Fig.353 5)., 5).354 Such large scatter has been observed also in low z radio galaxies (e.g. Robinson et al., Such large scatter has been observed also in low $z$ radio galaxies (e.g. Robinson et al.355 1987)., 1987).356 The [NII/Ha vs. [OII]/JOIII]. diagram (Fig., The $\alpha$ vs. [OII]/[OIII] diagram (Fig.357 |) shows a very large scatter in the [NIT]/Hea ratio inconsistent with the standard AGN (solar metallicity) predictions which again cannot be explained by errors in the measurements or reddening effects., 1) shows a very large scatter in the $\alpha$ ratio inconsistent with the standard AGN (solar metallicity) predictions which again cannot be explained by errors in the measurements or reddening effects.358 For a large fraction of objects. the [NIT] emission is too strong.," For a large fraction of objects, the [NII] emission is too strong."359 Given that this ratio is a direct metallicity indicator. rather than being a problem for photoionization models. the large range of values suggests that the nitrogen/hydrogen ratio varies substantially within the sample.," Given that this ratio is a direct metallicity indicator, rather than being a problem for photoionization models, the large range of values suggests that the nitrogen/hydrogen ratio varies substantially within the sample."360 Nitrogen is likely to be overabundant in those objects with large [NIT]/Ha values (e.g. Robinson et al. 1987»)., Nitrogen is likely to be overabundant in those objects with large $\alpha$ values (e.g. Robinson et al. \citeyear{rob87}) ).361 Possible solutions to. these problems have been extensively discussed in the literature for more than 20 years., Possible solutions to these problems have been extensively discussed in the literature for more than 20 years.362 We present, We present363ln contrast with the local. universe. where only 30 of the bolometric Luminosity is released. in the HV/submum wavelength range (Soifer Neugebauer 1991). there is a erowing amount of evidence that the high.redshift universe was much more opaque.,"In contrast with the local universe, where only 30 of the bolometric luminosity is released in the IR/submm wavelength range (Soifer Neugebauer 1991), there is a growing amount of evidence that the high–redshift universe was much more opaque."364 Indeed. the discovery of the Cosmic Infrared. Background. (CIRB) at a level ten times higher than the noevolution preclictions based on the local LR Iuminosity function. and twice as high as the Cosmic Optical Background obtained from optical counts. has shown that dust extinction and emission are key processes for highredshift galaxies (Puget et al.," Indeed, the discovery of the Cosmic Infrared Background (CIRB) at a level ten times higher than the no–evolution predictions based on the local IR luminosity function, and twice as high as the Cosmic Optical Background obtained from optical counts, has shown that dust extinction and emission are key processes for high--redshift galaxies (Puget et al."365 1996: Cruiderconi et al., 1996; Guiderdoni et al.366 1997: Fixsen et al., 1997; Fixsen et al.367 1998: Hauser et al., 1998; Hauser et al.368 1998: Schlegel. Finkbeiner Davis 1998).," 1998; Schlegel, Finkbeiner Davis 1998)."369 Deep surveys with the180 satellite at 15 jum (Oliver et al., Deep surveys with the satellite at 15 $\mu$ m (Oliver et al.370 1997: Aussel et al., 1997; Aussel et al.371 1999: Elbaz et al., 1999; Elbaz et al.372 1999) and 175 yam (Ixawara et al., 1999) and 175 $\mu$ m (Kawara et al.373 1998: Puget et al., 1998; Puget et al.374 1999). and with the SCUBA instrument at S850 sam (Smail. Ivison Blain 1997: Barger et al.," 1999), and with the SCUBA instrument at 850 $\mu$ m (Smail, Ivison Blain 1997; Barger et al."375 1998: Hughes ct al., 1998; Hughes et al.376 1998: Eales et al., 1998; Eales et al.377 1999: Barger. Cowie Saunders 1999) have begun to resolve the CIHAD into its brightest contributors.," 1999; Barger, Cowie Saunders 1999) have begun to resolve the CIRB into its brightest contributors."378 Although identification and spectroscopic Follow:up of subnim sources are not easy. such studies seem to reach the conclusion that an important fraction of these sources are the highredshift counterparts of the local luminous anc ultraluminous LR ealaxies (LIRGs and ULLIiCs) discovered. by (Smiail et al.," Although identification and spectroscopic follow–up of submm sources are not easy, such studies seem to reach the conclusion that an important fraction of these sources are the high–redshift counterparts of the local luminous and ultraluminous IR galaxies (LIRGs and ULIRGs) discovered by (Smail et al."379 1998: Lilly et al., 1998; Lilly et al.380 1999: Barger et al., 1999; Barger et al.381 1999)., 1999).382 In the optical and nearLR window. careful examinations of the CanadaFrance Redshift Survey (CERS) galaxies at 2~ 1. and Lyman break galaxies at 2~3 and 4 have revealed a significant amount of extinction (Flores ct al.," In the optical and near–IR window, careful examinations of the Canada–France Redshift Survey (CFRS) galaxies at $z\sim 1$ , and Lyman break galaxies at $z \sim 3$ and 4 have revealed a significant amount of extinction (Flores et al."383 1999: Steicdel et al., 1999; Steidel et al.384 1999: Aleurer. Lleekman Calzetti 1999).," 1999; Meurer, Heckman Calzetti 1999)."385 This has leac to a reassessment of previous estimates of the UV Iluxes. and consequently of the star formation rates in these objects. which are now found to be higher by a factor 2 to 5.," This has lead to a reassessment of previous estimates of the UV fluxes, and consequently of the star formation rates in these objects, which are now found to be higher by a factor 2 to 5."386 In light of these observations. one can view the far infrared. background as a sink for the hidden aspects of galaxy formation.," In light of these observations, one can view the far infrared background as a sink for the hidden aspects of galaxy formation."387 At optical wavelengths. cllipticals aud spheroids are old. even at ο~I1. No evidence is seen for either the luminous formation phase. orthe early evolution," At optical wavelengths, ellipticals and spheroids are old, even at $z \sim 1.$ No evidence is seen for either the luminous formation phase, orthe early evolution"388"back-evolved masses as grey circles. and the ""true"" initial cluster masses as dots. using /;—8 Gyr in the top panel and /;=| Gyr in the bottom panel.","back-evolved masses as grey circles, and the “true” initial cluster masses as dots, using $t_4 = 8$ Gyr in the top panel and $t_4 = 1$ Gyr in the bottom panel."389 For us a larger /; seems to be more realistic. as the Small Magellanic Cloud has a similar value (logjo/4 =9.9. ?Y and more massive spiral galaxies with a deeper gravitational potential have smaller values.," For us a larger $t_4$ seems to be more realistic, as the Small Magellanic Cloud has a similar value \citep[$\log_{10} t_4 = 9.9, and more massive spiral galaxies with a deeper gravitational potential have smaller values."390 We will. however. discuss below the implications of both values when determining the star formation history from the most massive clusters.," We will, however, discuss below the implications of both values when determining the star formation history from the most massive clusters."391 Further features in the age-mass diagram besides the typical wedge-like shape were pointed out by ?:: (1) The large densities of clusters at logjo of 6.6 and 7.2: These are caused by the fitting procedure., Further features in the age-mass diagram besides the typical wedge-like shape were pointed out by \citet{degrijs+anders2006}: (1) The large densities of clusters at $\log_{10} \tau $ of 6.6 and 7.2: These are caused by the fitting procedure.392 There aret no isochrones for clusters younger than 4 Myr (log;t= 6.6). and at logjot=7.2 the isochrones are discrete due to rapid evolution.," There are no isochrones for clusters younger than 4 Myr $\log_{10} \tau = 6.6$ ), and at $\log_{10} \tau = 7.2$ the isochrones are discrete due to rapid evolution."393" This does not have a large influence on the determined (2) The under-density of data points between = 3 Gyr and 13 Gyr 629.5xlogygt= 10.1). which is the ""well-known LMC cluster (3). Overdensities at 7.8xlogygt<=80. 28log;(M/M.)x3.4 and 8.2<letS4. all masses."," This does not have a large influence on the determined (2) The under-density of data points between $\approx$ 3 Gyr and 13 Gyr $\approx 9.5 \le \log_{10} \tau \le 10.1$ ), which is the “well-known LMC cluster (3) Overdensities at $7.8 \le \log_{10} \tau \le 8.0$, $2.8 \le \log_{10} (M/\Msun) \le 3.4$ and $ 8.2 \le \lg \tau \le 8.4 $, all masses."394 These features could be caused by the last encounters between the Large and Small Magellanic Cloud. but this cannot be concluded with sufficient certainty because of the lack of better age resolution and lack of orbital information for the galaxies.," These features could be caused by the last encounters between the Large and Small Magellanic Cloud, but this cannot be concluded with sufficient certainty because of the lack of better age resolution and lack of orbital information for the galaxies."395 It has also to be noted that this star cluster sample does not contain the 30Dor region. containing the young star cluster R136.," It has also to be noted that this star cluster sample does not contain the 30Dor region, containing the young star cluster R136."396 It was classified as a newly formed star cluster (INC) by ? and so in a group of objects which were not selected by ?.., It was classified as a newly formed star cluster (“NC”) by \citet{bica-etal1999} and so in a group of objects which were not selected by \citet{hunter-etal2003}.397 However. R135 is a massive star cluster having a mass of zz5.5x10M. (2) and is the most massive star cluster recently formed.," However, R135 is a massive star cluster having a mass of $\approx 5.5 \times 10^4\ \Msun$ \citep{hunter-etal1995}, and is the most massive star cluster recently formed."398 The inclusion of this cluster is therefore crucial to the method used in the next Section., The inclusion of this cluster is therefore crucial to the method used in the next Section.399 In ὁ we presented and tested a method to derive the star formation history of a galaxy using the most massive clusters., In \citet{maschberger+kroupa2007} we presented and tested a method to derive the star formation history of a galaxy using the most massive clusters.400 This method is based on the observation that the brightness of the brightest young cluster in a galaxy is correlated with the (present) star formation rate (222)..," This method is based on the observation that the brightness of the brightest young cluster in a galaxy is correlated with the (present) star formation rate \citep{larsen2002,weidner-etal2004,bastian2008}."401 This can be understood following the argument of 2.., This can be understood following the argument of \citet{weidner-etal2004}.402 Within a certain time span of the galaxy’s lifetime. of. the amount of mass assembled in (long-lived) stellar clusters is proportional to the star formation rate. =A δ/ (A is the proportionality constant).," Within a certain time span of the galaxy's lifetime, $\delta t$, the amount of mass assembled in (long-lived) stellar clusters is proportional to the star formation rate, = A t $A$ is the proportionality constant)."403 This mass in clusters is related to a number of clusters that have formed. -= where a universal cluster mass function is assumed to calculate the average mass of a star cluster. 1.," This mass in clusters is related to a number of clusters that have formed, = where a universal cluster mass function is assumed to calculate the average mass of a star cluster, $\bar{M}$."404" Interpreting the star cluster mass function as a probability distribution. this then allows one to calculate the distribution of the most massive star cluster. Afia. that would be expected for the given Nuus,."," Interpreting the star cluster mass function as a probability distribution, this then allows one to calculate the distribution of the most massive star cluster, $M_\mathrm{max}$, that would be expected for the given $N_\mathrm{clusters}$."405 From this model follows a relation of the mass of the most massive star cluster with the star formation rate within 6/., From this model follows a relation of the mass of the most massive star cluster with the star formation rate within $\delta t$.406 This can be inverted to SFR=/(Minax) Which can be used to determine the star formation rate over time. discretised by oy.," This can be inverted to $SFR=f(M_\mathrm{max})$ which can be used to determine the star formation rate over time, discretised by $\delta t$."407" In general M, follows a probability distribution. related to the star cluster mass function. which has to be taken into account for the inversion (details of this can be found in 25)."," In general $M_\mathrm{max}$ follows a probability distribution, related to the star cluster mass function, which has to be taken into account for the inversion (details of this can be found in \citealp{maschberger+kroupa2007}) )."408 To minimise the number of assumptions. especially the exact form (pure power law or Schechter function as suggested by ?)) and. parameters of the cluster mass function. we use the relation of the mean mass of the most massive cluster and the star formation rate.," To minimise the number of assumptions, especially the exact form (pure power law or Schechter function as suggested by \citealp{gieles-etal2006b}) ) and parameters of the cluster mass function, we use the relation of the mean mass of the most massive cluster and the star formation rate."409 The Miyaxs-SFR relation can be directly calibrated with the observed relation of the brightest young cluster and the star formation rate in a galaxy Cassuming that the brightest cluster is also the most massive one of the most recent time interval. an assumption which is discussed in more detail below).," The $\bar{M}_\mathrm{max}$ –SFR relation can be directly calibrated with the observed relation of the brightest young cluster and the star formation rate in a galaxy (assuming that the brightest cluster is also the most massive one of the most recent time interval, an assumption which is discussed in more detail below)."410 This Minay-SFR relation is then applied to a mean mass of the observed most massive clusters over several 6¢ (choosing the number of used à such that during the whole time of averaging the star formation rate in the galaxy is not changing significantly)., This $\bar{M}_\mathrm{max}$ –SFR relation is then applied to a mean mass of the observed most massive clusters over several $\delta t$ (choosing the number of used $\delta t$ such that during the whole time of averaging the star formation rate in the galaxy is not changing significantly).411 By using a moving averaging window (moved in steps of à/ the time resolution of the obtained star formation history can be increased., By using a moving averaging window (moved in steps of $\delta t$ ) the time resolution of the obtained star formation history can be increased.412 The length of the averaging window is essentially constrained by the age uncertainties of the star clusters. which are constant in logarithmic space. so that we keep the averaging window also constant in logo.," The length of the averaging window is essentially constrained by the age uncertainties of the star clusters, which are constant in logarithmic space, so that we keep the averaging window also constant in $\log_{10}$."413 By using My and the empirical calibration we have avoided the need of the exact knowledge of the star cluster mass function., By using $\bar{M}_\mathrm{max}$ and the empirical calibration we have avoided the need of the exact knowledge of the star cluster mass function.414 However. another crucial ingredient in this method is the formation epoch. à. which needs more explanation.," However, another crucial ingredient in this method is the formation epoch, $\delta t$, which needs more explanation."415" In this context the often mentioned ""size-of-sample"" effect has to be discussed.", In this context the often mentioned “size-of-sample” effect has to be discussed.416" The ""size-of-sample"" effect is simply the statistical increase of the mass of the most massive cluster with increasing sample size.", The ``size-of-sample'' effect is simply the statistical increase of the mass of the most massive cluster with increasing sample size.417 With the general assumptions of an unchanging cluster mass function and constant cluster formation rate (number per time) a logarithmic age-mass diagram has the characteristic upper envelope of an increasing mass with time., With the general assumptions of an unchanging cluster mass function and constant cluster formation rate (number per time) a logarithmic age-mass diagram has the characteristic upper envelope of an increasing mass with time.418 Equally-spaced time intervals in logarithmie space contain more physical time. thus more clusters are formed and subsequently the mass increases.," Equally-spaced time intervals in logarithmic space contain more physical time, thus more clusters are formed and subsequently the mass increases."419" However. this is not the full picture as the cluster (or star-) formation rate can change with time. leading for example to the ""age gap"" in the Large Magellanic Cloud where barely clusters are found."," However, this is not the full picture as the cluster (or star-) formation rate can change with time, leading for example to the “age gap” in the Large Magellanic Cloud where barely clusters are found."420 A mathematically more correct deseription would be a star cluster mass function depending on both mass«nd time. which is however not very practical.," A mathematically more correct description would be a star cluster mass function depending on both mass time, which is however not very practical."421 Here the formation epoch. 6. comes into the play: this is the time by which the time evolution of a galaxy is discretised.," Here the formation epoch, $\delta t$, comes into the play: this is the time by which the time evolution of a galaxy is discretised."422 With a reasonable choice of à the star formation rate in the galaxy can be assumed to stay constant. simplifying the statistical treatment.," With a reasonable choice of $\delta t$ the star formation rate in the galaxy can be assumed to stay constant, simplifying the statistical treatment."423 The increasing envelope in the logtage)-logtmass) diagram is preserved with using 6/ (showninfig.3.toppanel.of.2)..," The increasing envelope in the log(age)-log(mass) diagram is preserved with using $\delta t$ \citep[shown in fig. 3, top panel, of ][]{maschberger+kroupa2007}."424" The difference to the established understanding of the ""size-of-sample"" effect is tha one does not increase the size of a single sample. but one instead increases the number of samples."," The difference to the established understanding of the “size-of-sample” effect is that one does not increase the size of a single sample, but one instead increases the number of samples."425 The question is now what a reasonable size for à is., The question is now what a reasonable size for $\delta t$ is.426 Already mentioned was the need for the star formation rate to be constan over Of. which gives an upper limit for 6; of ez 100 Myr. the dynamical time of a galaxy.," Already mentioned was the need for the star formation rate to be constant over $\delta t$, which gives an upper limit for $\delta t$ of $\approx$ 100 Myr, the dynamical time of a galaxy."427 In fact. the star formation rate should be constant over several 6/ so that it can be averaged over severa Minax.," In fact, the star formation rate should be constant over several $\delta t$ so that it can be averaged over several $M_\mathrm{max}$."428" We follow here the choice of ?. and ?. of 10 Myr. for the practical reason that most clusters are of this age in the observational Ada,SFR plot. as the luminosity of a star cluster peaks at about 10 Myr."," We follow here the choice of \citet{weidner-etal2004} and \citet{maschberger+kroupa2007} of 10 Myr, for the practical reason that most clusters are of this age in the observational $M_\mathrm{max}-\mathrm{SFR}$ plot, as the luminosity of a star cluster peaks at about 10 Myr."429 Thus the brightest cluster is in many cases of this age and at the same time the most massive., Thus the brightest cluster is in many cases of this age and at the same time the most massive.430 With, With431magnitude to (;/7; so as to be consistent with Equation 7.,magnitude to $v_{i}/\sigma_{G}$ so as to be consistent with Equation 7.432 The cloud line profile. ο0foe.ce£06). is thus A cloud with small οσο) (but still larger. than (ος σελ). has a relatively narrow width: ane makes a smaller small Uux contribution to the total line profile as compared to clouds with larger [οσο].," The cloud line profile, $g(v_{i}/\sigma_{G},v_{G}/\sigma_{G})$, is thus A cloud with small $|v_{i}/\sigma_{G}|$ (but still larger than $(v_{G}/\sigma_{G})_{cut}$ ), has a relatively narrow width and makes a smaller small flux contribution to the total line profile as compared to clouds with larger $|v_{i}/\sigma_{G}|$."433 For comparison Figure 1 also shows two cloud. profiles. namely gl0.32.0σε) and g(2.05.06/00).," For comparison Figure 1 also shows two cloud profiles, namely $g(-0.32,v_{G}/\sigma_{G})$ and $g(2.05,v_{G}/\sigma_{G})$."434 Both have been normalized to g(2.05.0.0)=1.0.," Both have been normalized to $g(2.05,0.0)=1.0$."435 It is apparent in the figure that. individually. clouds with high |e;fe.) outshine rose with low |e;/0e;].," It is apparent in the figure that, individually, clouds with high $|v_{i}/\sigma_{G}|$ outshine those with low $|v_{i}/\sigma_{G}|$."436 For the two cloud. profiles shown in Figure 1 the larger [o;/0;| cloud is 10 times more luminous., For the two cloud profiles shown in Figure 1 the larger $|v_{i}/\sigma_{G}|$ cloud is 10 times more luminous.437 (Jn the other hand there are many more low velocity clouds wn high velocity clouds due to the distribution {οςfae)., On the other hand there are many more low velocity clouds than high velocity clouds due to the distribution $f(v_{G}/\sigma_{G})$.438" The resulting profile. due to the accumulation of all 84.000 clouds is shown in Figure 2 though only SI. percent of the ‘louds actually contribute the line profile due to the οο,"," The resulting profile, due to the accumulation of all 84,000 clouds is shown in Figure 2 though only 81 percent of the clouds actually contribute the line profile due to the cutoff."439 The Profile represents the BLR contribution of an ACN emission line., The Profile represents the BLR contribution of an AGN emission line.440 Analvsis of this model shows that lowering the number of clouds to 300 has little ellect on the line profile though it does become somewhat [ess symmetric due to the sensitivity of the profile to large individual contributions from high velocity. clouds., Analysis of this model shows that lowering the number of clouds to 300 has little effect on the line profile though it does become somewhat less symmetric due to the sensitivity of the profile to large individual contributions from high velocity clouds.441 The. effect o£. MIID. wave broadening is apparent when the fall width at half. maximum. (EWILM) of the profile in Figure 2 is compared to the EWIIM of fleafoc)., The effect of MHD wave broadening is apparent when the full width at half maximum (FWHM) of the profile in Figure 2 is compared to the FWHM of $f(v_{G}/\sigma_{G})$.442 The line profile is 1.6 times wider than frefac)., The line profile is 1.6 times wider than $f(v_{G}/\sigma_{G})$.443 The same mocel with 84.000 clouds but using (eefoedenn=)43 (e.g. parameters for 3C°390.3) vields a similar profile o the one shown in Figure 2.," The same model with 84,000 clouds but using $(v_{G}/\sigma_{G})_{cut} = 0.43$ (e.g., parameters for 3C390.3) yields a similar profile to the one shown in Figure 2."444 It is somewhat wider (the J'EN is 1.7 times larger than the ENCIEM of fec fac) out has a flat. plateau nearly twice as wide., It is somewhat wider (the FWHM is 1.7 times larger than the FWHM of $f(v_{G}/\sigma_{G})$ ) but has a flat plateau nearly twice as wide.445" In the following section we interpret the above results in terms of current AGN research and make suggestions [or ""ture avenues of study.", In the following section we interpret the above results in terms of current AGN research and make suggestions for future avenues of study.446 This simple model brings a whole series of issues to the study of AGN phenomena., This simple model brings a whole series of issues to the study of AGN phenomena.447 Attempts to infer cloud numbers [rom broad line profiles need to include the possibility of MED wave line broadening before making conclusions abou whether BLE clouds are continuous or discrete., Attempts to infer cloud numbers from broad line profiles need to include the possibility of MHD wave line broadening before making conclusions about whether BLR clouds are continuous or discrete.448 Lf individua clouds are sought. the search. needs to be redirected: away from the lino wings and toward the line core since. bv Equation 4. the line broadening. ep. will be weaker a smaller values of ο," If individual clouds are sought, the search needs to be redirected away from the line wings and toward the line core since, by Equation 4, the line broadening, $\sigma_{\rm{B}}$, will be weaker at smaller values of $v$."449 An alternative approach to AGN cloud counting coul be to use a principle component analysis fitting approach., An alternative approach to AGN cloud counting could be to use a principle component analysis fitting approach.450 The gaussian basis functions. used. to fit a profile can be eiven widths proportional to their olfset from zero systemic velocity., The gaussian basis functions used to fit a profile can be given widths proportional to their offset from zero systemic velocity.451 The minimum number of gaussians required to find an acceptable fit to the line profiles will be an estimate of the minimum cloud number., The minimum number of gaussians required to find an acceptable fit to the line profiles will be an estimate of the minimum cloud number.452 Components may be tested in AGN that have had extensive spectral monitoring. c.g. NGC 5548. NGC 4151. 3€390.3 and. 3C2," Components may be tested in AGN that have had extensive spectral monitoring, e.g. NGC 5548, NGC 4151, 3C390.3 and 3C273."453 A sequence of spectra. covering a time span shorter than the 111 dynamical crossing time but longer than a characteristic continuum variability timescale. can be fit.," A sequence of spectra, covering a time span shorter than the BLR dynamical crossing time but longer than a characteristic continuum variability timescale, can be fit."454 I£ the component number ancl locations in the sequence do not significantly. vary. then that would. be evidence in favor of the components being actual clouds.," If the component number and locations in the sequence do not significantly vary, then that would be evidence in favor of the components being actual clouds."455 The ensemble could be further tested agains various kinematic models by tracking detected. clouds over a lew crossing times., The ensemble could be further tested against various kinematic models by tracking detected clouds over a few crossing times.456 There is already evidence to sugges that line profiles of clouds are a complex aumalgaum of emitters., There is already evidence to suggest that line profiles of clouds are a complex amalgam of emitters.457 Multiple components are often. required. to. [i line. profiles., Multiple components are often required to fit line profiles.458 For example. four or five components are required to fit the LL? line of Ark 120. (Ixorista. 1992) and 12 in NGC 5548 shows three seemingly. independen time variable components (Wanders and Peterson 1996).," For example, four or five components are required to fit the $\beta$ line of Ark 120 (Korista 1992) and $\beta$ in NGC 5548 shows three seemingly independent time variable components (Wanders and Peterson 1996)."459 We note. for clarity however. that it is not suggested that the components presented in those papers necessarily represen actual clouds since the fitting algorithms are designed. for cllicicney and have no physical meaning.," We note, for clarity however, that it is not suggested that the components presented in those papers necessarily represent actual clouds since the fitting algorithms are designed for efficiency and have no physical meaning."460 We do however. wish to emphasize the potential for future reanalysis of available clata.," We do however, wish to emphasize the potential for future reanalysis of available data."461" With regard. to magnetic broadening and long term wolile variability. consider the ""shoulders"" of the LL3 line of GC 5548 reported by Wanders and Peterson (1996)."," With regard to magnetic broadening and long term profile variability, consider the “shoulders” of the $\beta$ line of NGC 5548 reported by Wanders and Peterson (1996)."462 They note that shoulders “cdo not appear to move systematically in racial velocity but appear to come and go at approximately κος wavelengths.”, They note that shoulders “do not appear to move systematically in radial velocity but appear to come and go at approximately fixed wavelengths.”463 In terms of our simple model. this havior can be explained. by the movement of a few relatively high. velocity clouds., In terms of our simple model this behavior can be explained by the movement of a few relatively high velocity clouds.464 Since both the emission and ine width is large in these clouds we would expect that the wings vary on a time scale of the order of the BLK. crossing ime. which they estimate to be ~1.6vr.," Since both the emission and line width is large in these clouds we would expect that the wings vary on a time scale of the order of the BLR crossing time, which they estimate to be $\sim1.6\rm{~yr}$."465 This is indeed the case., This is indeed the case.466 The line core. in our model. however. is dominated by many cimmoer clouds.," The line core, in our model, however, is dominated by many dimmer clouds."467 Thus the profile core will be relatively stable since the addition or subtraction of a few clouds will not alfect. the overall shape of that segment. of the line., Thus the profile core will be relatively stable since the addition or subtraction of a few clouds will not affect the overall shape of that segment of the line.468 1n addition. the crossing time at a lower velocity will be longer than average.," In addition, the crossing time at a lower velocity will be longer than average."469 The net result is a stable line core with, The net result is a stable line core with470"a number of these sources (e.g.. Ohta et 11996: Omont et 11996: Carilli et 220022). unveiling massive molecular gas reservoirs of 1019.1! ML, and providing supporting evidence for massive starbursts at less than of the age of the Universe.","a number of these sources (e.g., Ohta et 1996; Omont et 1996; Carilli et 2002a), unveiling massive molecular gas reservoirs of $10^{10-11}$ $_\odot$, and providing supporting evidence for massive starbursts at less than of the age of the Universe."471 One of the most spectacular examples of this class of object is BR 0725. the most distant ες=4.695) and optically luminous (Mg=— 28.5) radio-quiet quasar of the BR(D quasars (Storrie-Lombardi et 11996).," One of the most spectacular examples of this class of object is BR $-$ 0725, the most distant $z=4.695$ ) and optically luminous $M_{B}=472-$ 28.5) radio-quiet quasar of the BR(I) quasars (Storrie-Lombardi et 1996)."473 The first z4 quasar to be detected at (subjmm wavelengths (McMahon et 11994: Isaak et 11994). BR 0725 was found to contain ~10° M. of dust ata temperature of 50K.," The first $z > 4$ quasar to be detected at (sub)mm wavelengths (McMahon et 1994; Isaak et 1994), BR $-$ 0725 was found to contain $\sim10^9$ $_\odot$ of dust ata temperature of $\sim 50$."474. CO observations. traced more than 10! . of molecular gas (assuming locally-determined conversion factors)., CO observations traced more than $10^{11}$ $_\odot$ of molecular gas (assuming locally-determined conversion factors).475 A multi-line LVG analysis by Ohta et (01998) using a range of CO transitions (COC7—-6): Omont et 11996: CO(S—4): Ohta et 11996: Omont et 11996: and CO(2—1: Ohta et 11998) suggested that the molecular gas density is 10 7., A multi-line LVG analysis by Ohta et (1998) using a range of CO transitions (CO(7–6): Omont et 1996; CO(5–4): Ohta et 1996; Omont et 1996; and CO(2--1): Ohta et 1998) suggested that the molecular gas density is $>10^4$ $^{-3}$.476 This conclusion was also reached by ΟΠΗ et (2002b) using data having a much higher signal-to-noise ratio., This conclusion was also reached by Carilli et (2002b) using data having a much higher signal-to-noise ratio.477 The modelling requires a number of assumptions. and it is clear that a direct measure of the dense gas is desirable in order to establish whether the host galaxies of high redshift quasars are indeed the analogues of nearby ULIRGs.," The modelling requires a number of assumptions, and it is clear that a direct measure of the dense gas is desirable in order to establish whether the host galaxies of high redshift quasars are indeed the analogues of nearby ULIRGs."478 With few exceptions. studies of the molecular interstellar medium in very distant galaxies have used the CO rotational ladder.," With few exceptions, studies of the molecular interstellar medium in very distant galaxies have used the CO rotational ladder."479 With a critical density of 107 >. the lowest of the HCN rotational line traces molecular gas at a much higher density than the corresponding CO transition.," With a critical density of $>10^4$ $^{-3}$, the lowest of the HCN rotational line traces molecular gas at a much higher density than the corresponding CO transition."480" In this paper we present a search for HCN(I-0) emission from BR 0725 using the Very Large Array (VLA) of the National Radio AstronomyΤοντ, with the aim of providing an independent measure of the dense gas component in its host galaxy. and to enable a direct comparison with the local ULIRGs observed by Solomon et (19923)."," In this paper we present a search for HCN(1–0) emission from BR $-$ 0725 using the Very Large Array (VLA) of the National Radio Astronomy, with the aim of providing an independent measure of the dense gas component in its host galaxy, and to enable a direct comparison with the local ULIRGs observed by Solomon et (1992a)."481 The mean rest frequency of the HCN(I-0). triplet is View=88.632 GHz. which is redshifted to 15.563 GHz in BR 0725.," The mean rest frequency of the HCN(1–0) triplet is $\nu_{\rm rest} = 88.632$ GHz, which is redshifted to 15.563 GHz in BR $-$ 0725."482 All quantities given here have been derived using a A-cosmology. with Hy=65 km | |.," All quantities given here have been derived using a $\Lambda$ -cosmology, with $H_0 = 65$ km $^{-1}$ $^{-1}$ ."483 For comparison. the same quantities derived for a flat. Einstein-de Sitter cosmology with Hp—50 km | | are included in parentheses.," For comparison, the same quantities derived for a flat, Einstein-de Sitter cosmology with $H_0 = 50$ km $^{-1}$ $^{-1}$ are included in parentheses."484" These cosmologies give a luminosity distance Dj,=46.6(39.6) Gpe for BR 0725."," These cosmologies give a luminosity distance $D_{\rm L}485= 46.6(39.6)$ Gpc for BR $-$ 0725."486 The VLA observations were made on 2000 August 26. September 2—L and in 2003 January 25—29.," The VLA observations were made on 2000 August 26, September 2–4, and in 2003 January 25–29."487 In 2000 the VLA was in the compact D configuration. while in 2003 it was in the DnC configuration.," In 2000 the VLA was in the compact D configuration, while in 2003 it was in the DnC configuration."488 The instantaneous bandwidth of the VLA is only 50 MHz. tuneable in finite steps of 20 or 30 MHz.," The instantaneous bandwidth of the VLA is only 50 MHz, tuneable in finite steps of 20 or 30 MHz."489 We therefore chose a set-up for the local oseillators that most closely centred the redshifted HCN¢!—0) line in the 50 MHz bandwidth. and covered the 50 MHz with 8 channels of 6.25 MHz (120 km s.) with both right and left circular polarizations.," We therefore chose a set-up for the local oscillators that most closely centred the redshifted HCN(1–0) line in the 50 MHz bandwidth, and covered the 50 MHz with 8 channels of 6.25 MHz (120 km $^{-1}$ ) with both right and left circular polarizations."490 The narrow total bandwidth of the current 15 GHz receivers at the VLA esulted in the sensitivity achieved the frequency of the redshifted HCN line being degraded by a factor of about 2 relative to the centre of the band., The narrow total bandwidth of the current 15 GHz receivers at the VLA esulted in the sensitivity achieved the frequency of the redshifted HCN line being degraded by a factor of about 2 relative to the centre of the band.491 Antenna- complex gains were monitored every |5 minutes through observations of the quasar PMN 0740., Antenna-based complex gains were monitored every 15 minutes through observations of the quasar PMN $-$ 0740.492 The bandpass anc absolute flux density scale were determined through observations of 3C273 and 3C286 respectively., The bandpass and absolute flux density scale were determined through observations of 3C273 and 3C286 respectively.493 The total uncertainty in the flux density calibration is estimated to be less than 5 per cent., The total uncertainty in the flux density calibration is estimated to be less than 5 per cent.494 The tropospherie phase stability was relatively. poor for the observations made during 2000 late summer. and the data with particularly bad phase coherence (typically those on the longest baselines in the D configuration) have been edited.," The tropospheric phase stability was relatively poor for the observations made during 2000 late summer, and the data with particularly bad phase coherence (typically those on the longest baselines in the D configuration) have been edited."495 The weather during 2003 January was excellent., The weather during 2003 January was excellent.496 The data were reduced and imaged using the Astronomical Image Processing System (AIPS)., The data were reduced and imaged using the Astronomical Image Processing System (AIPS).497 After combining the data from both sets of observations. the resulting naturally-weighted synthesized beam is 4.6x4.4 aresec? at position angle 660.," After combining the data from both sets of observations, the resulting naturally-weighted synthesized beam is $4.6 \times 4.4$ $^2$ at position angle $-60^\circ$."498The rms noise per channel in the final image is 60 gly ], The rms noise per channel in the final image is 60 $\mu$ Jy $^{-1}$.499 No redshifted HCN(I-0). emission is detected., No redshifted HCN(1–0) emission is detected.500 The central six channels are displayed in Fig. |..," The central six channels are displayed in Fig. \ref{map},"501 with 2-6 contours of 120 ulJy |. and crosses denoting the positions of the two millimetre sources detected by Omont et (1996).," with $\sigma$ contours of 120 $\mu$ Jy $^{-1}$ , and crosses denoting the positions of the two millimetre sources detected by Omont et (1996)."502 The CO lines reported by Omont et hhave line widths of 190 and 350 kms. |: assuming an intrinsic line width AV. for any HCN emission of  250kms | we find à 3-6 upper limit to the HCN¢1-0) emission of (3(Ανω/AVenamet}!σε rms per channel) = 31 mJy km »," The CO lines reported by Omont et have line widths of 190 and 350 km $^{-1}$; assuming an intrinsic line width $\Delta V_{\rm line}$ for any HCN emission of $\sim 250$ km $^{-1}$ we find a $\sigma$ upper limit to the HCN(1–0) emission of $3 \cdot (\Delta V_{\rm line}/\Delta V_{\rm503channel})^{1/2} \cdot$ rms per channel) = 31 mJy km $^{-1}$."504 Using equations | and 3 from Solomon et ((1992b). we derive a 3-G upper limit to the line luminosity of lo Kkms | per.," Using equations 1 and 3 from Solomon et (1992b), we derive a $\sigma$ upper limit to the line luminosity of $L'_{\rm HCN} < 4.9(3.6) \times50510^{10}$ K km $^{-1}$ $^{2}$."506 In order to compare the molecular properties of BR 0725 with those of local (UILIRGs we include it in plots of Luen Lig. and Ler/Leg Luen/Leo. in Fig. 2..," In order to compare the molecular properties of BR $-$ 0725 with those of local (U)LIRGs we include it in plots of $L'_{\rm HCN}$ $L_{\rm FIR}$, and $L_{\rm FIR}/L'_{\rm CO}$ $L'_{\rm HCN}/L'_{\rm507CO}$, in Fig. \ref{plots}."508 The value for the far-infrared luminosity. £ya=6.3(4.6)xI0 1... has been calculated by integrating under the thermal greybody spectral energy distribution as detailed by Isaak et (2002).," The value for the far-infrared luminosity, $L_{\rm FIR} = 6.3(4.6) \times 10^{13}$ $_\odot$, has been calculated by integrating under the thermal greybody spectral energy distribution as detailed by Isaak et (2002)."509 The COtl—O) luminosity comes from a recent measurement of the COtI-0) line flux. Seg=0.170:05 Jy kms.! (C. Henkel. private communication).," The CO(1–0) luminosity comes from a recent measurement of the CO(1–0) line flux, $S_{\rm CO} = 0.17 \pm5100.05$ Jy km$^{-1}$ (C. Henkel, private communication)."511 The upper limit of Luc or BR 0725 is consistent with the correlations between LCN Log. and Ly/Leo L'ueN/Leo. observed in more local (UJLTRGs.," The upper limit of $L'_{\rm HCN}$ for BR $-$ 0725 is consistent with the correlations between $L'_{\rm HCN}$ $L_{\rm FIR}$, and $L_{\rm FIR}/L'_{\rm CO}$ $L'_{\rm HCN}/L'_{\rm CO}$, observed in more local (U)LIRGs."512 Our measured upper limit suggests that the globally-averaged molecular properties of the host galaxy of BR 0725 are consistent with those found in more local ULIRGs., Our measured upper limit suggests that the globally-averaged molecular properties of the host galaxy of BR $-$ 0725 are consistent with those found in more local ULIRGs.513 Furthermore. it is consistent with the interpretation that a large fraction of the far-infrared luminosity originates from dust heated by star formation.," Furthermore, it is consistent with the interpretation that a large fraction of the far-infrared luminosity originates from dust heated by star formation."514 We note. however. that a significant fraction of ULIRGs show signs of both starburst and AGN activity (Genzel et 11998).," We note, however, that a significant fraction of ULIRGs show signs of both starburst and AGN activity (Genzel et 1998)."515 This has also been found to be the case in many of the high-redshift sources identified in submillimetre surveys that have exploited the lensing effect of galaxy clusters (e.g.. Smail. Ivison Blain 1997).," This has also been found to be the case in many of the high-redshift sources identified in submillimetre surveys that have exploited the lensing effect of galaxy clusters (e.g., Smail, Ivison Blain 1997)."516 Tt is therefore not surprising that a naked AGN residing in a young host galaxy might show similarities with ULIROs., It is therefore not surprising that a naked AGN residing in a young host galaxy might show similarities with ULIRGs.517 A deeper limit to the HCN emission from BR 0725 will only be possible with the EVLA-.. when an improvement in sensitivity of a factor of about 6 is anticipated for spectral linework at this frequency.," A deeper limit to the HCN emission from BR $-$ 0725 will only be possible with the , when an improvement in sensitivity of a factor of about 6 is anticipated for spectral linework at this frequency."518 With our current limit we do. however. exclude a low {με{μονratio.," With our current limit we do, however, exclude a low $L_{\rm FIR}/L_{\rm HCN}$ratio."519 Such a ratio would be interpreted as a host galaxy with a high molecular gas density with little ongoing star formation or AGN activity. that is. gas that is to form stars," Such a ratio would be interpreted as a host galaxy with a high molecular gas density with little ongoing star formation or AGN activity, that is, gas that is to form stars"520cosmological models (Samushia&Ratra2006:YiZhang2007) and some other relevant works include Wei&Zhang(2007Ta.b);WuYu(2007a.b):Lazkoz]xurek&Szvellowski(2008):SenScherrerXuetal.ZhangZhu(2003) for examples.,"cosmological models \citep{Samushia06,Yi07} and some other relevant works include \citet{Wei07a,Wei07b,Wu07a,Wu07b,Lazkoz07,Kurek08,Sen08,Xu08,Zhang08}521 for examples."522 Recently. Sternοἱal.(2010) obtained the £(z) data at 11 different redshifts obtained [rom the differential ages of red-envelope galaxies: ancl other two Hubble parameter data al z=0.24 and z=0.43 were determined by Gaztanagaοἱal.(2009) [rom observations olBAO peaks.," Recently, \citet{hz2} obtained the $H(z)$ data at 11 different redshifts obtained from the differential ages of red-envelope galaxies; and other two Hubble parameter data at $z=0.24$ and $z=0.43$ were determined by \citet{hz3} from observations ofBAO peaks."523 Some recent works using these newly /7(z:) data for cosmological constraint can be found in Gongetal.(2010);Liang.Wu&ZhangCao.ZhuLiane(2011):Aa&Zhang(2011);XuWang(2010):Zhaietal.(2010);Zhang.MaLan (2010).," Some recent works using these newly $H(z)$ data for cosmological constraint can be found in \citet{Gong10,Liang2010,Cao11a,Ma11,Xu10,Zhai10,ZML10}."524. In the previous works. Wei&Zhang(2007a) compared the 9 observational Lf(2) data wilh some cosmological models with/without interaction between dark energv and dust matter and found that the Z7(2) data points with fairly large errors cannot severely constrain model parameters alone.," In the previous works, \citet{Wei07a} compared the 9 observational $H(z)$ data with some cosmological models with/without interaction between dark energy and dust matter and found that the $H(z)$ data points with fairly large errors cannot severely constrain model parameters alone."525 In this paper. we focus on the newly (2) data to study the interaction between the dust matter and dark energy and test ihe cosmic coincidence problem.," In this paper, we focus on the newly $H(z)$ data to study the interaction between the dust matter and dark energy and test the cosmic coincidence problem."526 Ii order to break the degeneracy of model parameters. we also add the barvonic acoustic oscillation (BAO) peak detected by large-scale correlation function. of luminous red galaxies [rom Sloan Digital Skv Survey (SDSS) (Eisensteinetal.2005).. the cosmic microwave background (CAIB) detected by the 7-vear WAIAP data (Ixomatsu and the newly revised Union2 SNe Ia data set (Amanullahetal.," In order to break the degeneracy of model parameters, we also add the baryonic acoustic oscillation (BAO) peak detected by large-scale correlation function of luminous red galaxies from Sloan Digital Sky Survey (SDSS) \citep{Eisenstein05}, the cosmic microwave background (CMB) detected by the 7-year WMAP data \citep{Komatsu10} and the newly revised Union2 SNe Ia data set \citep{Amanullah}."5272010).. This paper is organized as follows: In section ??.. we introduce the observational data including the /7(:). BAO. CAIB and SNe Ia data.," This paper is organized as follows: In section \ref{sec2}, we introduce the observational data including the $H(z)$, BAO, CMB and SNe Ia data."528 In section ??.. we derive two Hubble parameters and perform a Markov Chain Monte Carlo analvsis spanning the full parameter space of the model using different data sets.," In section \ref{sec3}, we derive two Hubble parameters and perform a Markov Chain Monte Carlo analysis spanning the full parameter space of the model using different data sets."529 Finally. we summarize the main conclusions in Section ??..," Finally, we summarize the main conclusions in Section \ref{sec4}."530 In this sectionwe will list the cosmological observations used in our ealeulations: 7 (2). BAO. CMD as well as the SNe Ia observations.," In this sectionwe will list the cosmological observations used in our calculations: $H(z)$ , BAO, CMB as well as the SNe Ia observations."531 We adopt the (z) data at 11 different redshillsobtained in Ref. Sternetal. (2010)," We adopt the $H(z)$ data at 11 different redshiftsobtained in Ref. \cite{hz2}, ,"532.. and two I7(2) data (7(2=0.24)τοσο 2993. and£(2=0.43) 86.4543.27) determined by Gaztanagaetal. (2009).," and two $H(z)$ data $H(z=0.24)=76.69\pm2.32$ , and$H(z=0.43)=86.45\pm3.27$ ) determined by \citet{hz3}. ."533. The corresponding V can be defined as where o5; is (he lo uncertainty in the //(2) data., The corresponding $\chi^2$ can be defined as where $\sigma_{hi}$ is the $1\sigma$ uncertainty in the $H(z)$ data.534To a very good. approximation. the equivalent. width of an absorption line in the specific intensity profile [rom any part of the stellar disc is the same as the equivalent width of the rotationallv-broadened line profile considered as a whole.,"To a very good approximation, the equivalent width of an absorption line in the specific intensity profile from any part of the stellar disc is the same as the equivalent width of the rotationally-broadened line profile considered as a whole."535" The ratio of the equivalent. width of a small starspot bump at disc centre to that of the entire line profile is therefore just the ratio of the Dux. ""missing in the spot (Piu&RoBaua d)*) to the total Dux from the remaining limb- photosphere. {ρω=wl,τςuf)Pa."," The ratio of the equivalent width of a small starspot bump at disc centre to that of the entire line profile is therefore just the ratio of the flux “missing” in the spot $F_{spot} 536\simeq 537\pi I_0 (R_{spot}/d)^{2}$ ) to the total flux from the remaining limb-darkened photosphere, $F_{phot} = \pi I_0 (R_{\star}/d)^2 (1-u/3)-F_{spot}$."538" Llere fy is the specific intensity of the photosphere at. disc centre. /2,,,; and £2, are the radit of the spot and the star respectively. and d is the distance to the star."," Here $I_{0}$ is the specific intensity of the photosphere at disc centre, $R_{spot}$ and $R_{\star}$ are the radii of the spot and the star respectively, and $d$ is the distance to the star."539 Hence for a small. isolated. spot viewed at the centre of the stellar clise.," Hence for a small, isolated spot viewed at the centre of the stellar disc."540 In reality the spots are neither isolated. nor completely dark., In reality the spots are neither isolated nor completely dark.541 At the τος waveleneths observed. the continuum surface brightness of the spots is expected to be about 0.25 ο 0.3 times the photospheric value.," At the red wavelengths observed, the continuum surface brightness of the spots is expected to be about 0.25 to 0.3 times the photospheric value."542 The bump amplitude or a spot of given area is thus expected to be diminished by his amount relative to the bump amplitude fora completely dark spot., The bump amplitude for a spot of given area is thus expected to be diminished by this amount relative to the bump amplitude for a completely dark spot.543 However. the fractional coverage of spots on AB Dor is probably of order 30 percent. which serves to increase he loss of light from an individual spot as a fraction of the otal amount of 7clean photosphere.," However, the fractional coverage of spots on AB Dor is probably of order 30 percent, which serves to increase the loss of light from an individual spot as a fraction of the total amount of “clean” photosphere."544 Overall. the ellects of inito spot surface brightness and a high spot filling factor will tend to cancel cach other out.," Overall, the effects of finite spot surface brightness and a high spot filling factor will tend to cancel each other out."545 The spots listed in Table 1. have equivalent: widths ranging [rom W—0.0016 to M=0.0071 km +., The spots listed in Table \ref{tab:spotpar} have equivalent widths ranging from $W=0.0016$ to $W=0.0071$ km $^{-1}$.546 Since the equivalent width of the deconvolved. stellar. profile is approximately 4.5 kms 1 (ef., Since the equivalent width of the deconvolved stellar profile is approximately 4.5 km $^{-1}$ (cf.547 Fig. 1)).," Fig. \ref{fig:tellurics}) ),"548 the inferred fractional areas. (Rojo1)? of individual spots range [rom 0.00026, the inferred fractional areas $(R_{spot}/R_{\star})^{2}$ of individual spots range from 0.00026549A sumnmarv of the number of stars and exposures that met each flare criterion is presented in Table 4. which also shows that the majority of flares come from the MSN sample.,"A summary of the number of stars and exposures that met each flare criterion is presented in Table 4, which also shows that the majority of flares come from the MSN sample."550 This is not unexpected. since there are many more stars in (hat sample.," This is not unexpected, since there are many more stars in that sample."551 Our results sugeest Chat flares in this sparsely sampled spectroscopic data set are most easily identified through emission line variability rather than the absolute strength of the emission lines., Our results suggest that flares in this sparsely sampled spectroscopic data set are most easily identified through emission line variability rather than the absolute strength of the emission lines.552 We first analvzed our flare sample to verily that the properties of the Mares we identified are consistent with the characteristic time evolution seen in continuous monitoring observations., We first analyzed our flare sample to verify that the properties of the flares we identified are consistent with the characteristic time evolution seen in continuous monitoring observations.553 Because our data might capture any. or all phases of a flare. we expected to see examples of flares in the rise. peak. and decay pliases as well as a few laree impulsive phase flares (hat show blue continuum flix enhancement.," Because our data might capture any or all phases of a flare, we expected to see examples of flares in the rise, peak, and decay phases as well as a few large impulsive phase flares that show blue continuum flux enhancement."554 We defined decay-phase flares as those showing both Ho and IL? in at least two consecutive exposures with diminishing FLI values., We defined decay-phase flares as those showing both $\alpha$ and $\beta$ in at least two consecutive exposures with diminishing FLI values.555 Rise-phase flares were delined in (he opposite sense. with (wo or more consecutive exposures having increasing FLI values for both Ila aud IL3.," Rise-phase flares were defined in the opposite sense, with two or more consecutive exposures having increasing FLI values for both $\alpha$ and $\beta$."556 There were ten rise phase flares and 11 decav phase flares in the sample., There were ten rise phase flares and 11 decay phase flares in the sample.557 Additionally. we saw five “peak” [lares (hat show first increasing and (hen decreasing ELI values. which we interpret as [lares that were seen through most of their evolution.," Additionally, we saw five “peak” flares that show first increasing and then decreasing FLI values, which we interpret as flares that were seen through most of their evolution."558 We also identified Πάγος that occurred in only a subset of the exposures. either in the final exposure of a sequence. or in cases where some of (he exposures are separated by many hours or clavs from (he other exposures.," We also identified flares that occurred in only a subset of the exposures, either in the final exposure of a sequence, or in cases where some of the exposures are separated by many hours or days from the other exposures."559 In 19 cases. at least one exposure was obtained that showed a quiescent spectrum wilh no sien of flaring.," In 19 cases, at least one exposure was obtained that showed a quiescent spectrum with no sign of flaring."560 Flares with quiescent spectrum. as well as rise. decay. and peak phase flares are noted in (he final column of Table 3.," Flares with quiescent spectrum, as well as rise, decay, and peak phase flares are noted in the final column of Table 3."561 The time evolution of the flares we have identified is consistent with the known characteristics of Hares., The time evolution of the flares we have identified is consistent with the known characteristics of flares.562 Previous observations using time resolved spectroscopic monitoring have shown that the higher order Balmer lines show larger increases in flux during Hares than the lower order lines., Previous observations using time resolved spectroscopic monitoring have shown that the higher order Balmer lines show larger increases in flux during flares than the lower order lines.563 This results in the observed. Balner clecrement (ratio of individual lines to a fiducial. often. IL? as we adopt here) becoming flatter. since H and the higher order lines," This results in the observed Balmer decrement (ratio of individual lines to a fiducial, often $\beta$ as we adopt here) becoming flatter, since $\gamma$ and the higher order lines"564broken lines indicate galaxies before they are recognized as early-type galaxies.,broken lines indicate galaxies before they are recognized as early-type galaxies.565 It can easily be seen that the sample of early-type galaxies at high redshift is a small subsample of all galaxies which are classified as early-type galaxies at z=0., It can easily be seen that the sample of early-type galaxies at high redshift is a small subsample of all galaxies which are classified as early-type galaxies at $z=0$.566 The two samples are therefore not directly comparable. and erroneous results are derived if morphological evolution is ignored.," The two samples are therefore not directly comparable, and erroneous results are derived if morphological evolution is ignored."567 As a result. the evolution in the mean M/L ratio of the early-type galaxies is very slow (panel d).," As a result, the evolution in the mean $M/L$ ratio of the early-type galaxies is very slow (panel d)."568 The slope of the M/L — z relation is comparable to the slope for a single stellar population which formed at z2x. (indicated by the dashed line). even though the mean formation redshift of the stars in all early-type galaxies at z2O 1s low at (z.;c2.," The slope of the $M/L$ – $z$ relation is comparable to the slope for a single stellar population which formed at $z=\infty$ (indicated by the dashed line), even though the mean formation redshift of the stars in all early-type galaxies at $z=0$ is low at $\langle z_* \rangle \approx 2$."569 Even more remarkable ts the fact that the scatter in M/L ratios is virtually constant., Even more remarkable is the fact that the scatter in $M/L$ ratios is virtually constant.570 These effects are caused by the fact that the youngest galaxies continuously drop out of the sample going to higher redshifts., These effects are caused by the fact that the youngest galaxies continuously drop out of the sample going to higher redshifts.571 In the subsections below we specify a broader range of models. and explore the consequences.," In the subsections below we specify a broader range of models, and explore the consequences."572 The full models are quantified by three parameters: fan. the time when star formation starts. r5. the time scale which characterizes the distribution of times when star formation stops. and 7... which describes the star formation rate between the start and end of star formation.," The full models are quantified by three parameters: $\tstart$, the time when star formation starts, $\taustop$, the time scale which characterizes the distribution of times when star formation stops, and $\fstar$, which describes the star formation rate between the start and end of star formation."573 The last two parameters are defined in the following way., The last two parameters are defined in the following way.574 The parameter Το determines the probability distribution Of A. the tme when star formation stops for an individual galaxy: We show later that this expression can provide a satisfactory fit to the data.," The parameter $\taustop$ determines the probability distribution of $\tstop$, the time when star formation stops for an individual galaxy: We show later that this expression can provide a satisfactory fit to the data."575 If. rp»<fo. with f the present age of the Universe. star formation in the progenitors terminated at very high redshift.," If $\taustop \ll \t0$, with $\t0$ the present age of the Universe, star formation in the progenitors terminated at very high redshift."576" At the other extreme. r4,=x corresponds to a constant transformation rate."," At the other extreme, $\taustop=\infty$ corresponds to a constant transformation rate."577 For each individual galaxy. the morphological transformation to early-type galaxy occurs at Kop+0.1o. Le. ~1.5 Gyr after truncation of star formation.," For each individual galaxy, the morphological transformation to early-type galaxy occurs at $\tstop + 0.1 \t0$, i.e., $\sim 1.5$ Gyr after truncation of star formation."578 The parameter f. characterizes the variation of the star formation rate., The parameter $\fstar$ characterizes the variation of the star formation rate.579 The star formation history of the galaxies can include bursts. and increasing or decreasing continuous formation rates as a function of time.," The star formation history of the galaxies can include bursts, and increasing or decreasing continuous formation rates as a function of time."580 After star formation ceases. the lummosity and color evolution of such a complex population is well approximated by a single age population of stars with the same luminosity weighted mean age (e.g.. van," After star formation ceases, the luminosity and color evolution of such a complex population is well approximated by a single age population of stars with the same luminosity weighted mean age (e.g., van"581This interpretation should account for the main selection ellects associated. with based GW observations and properly constrain models of radio pulsar and BCO populations.,This interpretation should account for the main selection effects associated with ground-based GW observations and properly constrain models of radio pulsar and BCO populations.582 As a result of our caleulations we also make realistic estimates for the extrapolation of Galactic inspiral detection rates based on the known spatial distribution of galaxies in (he nearby universe and the expected mass distributions of binary compact objects., As a result of our calculations we also make realistic estimates for the extrapolation of Galactic inspiral detection rates based on the known spatial distribution of galaxies in the nearby universe and the expected mass distributions of binary compact objects.583 Our results are summarized as follows:, Our results are summarized as follows:584into the bubble.,into the bubble.585 This topic will be explored in a forthcoming publication., This topic will be explored in a forthcoming publication.586 In reftig:vaporl the evolution of the magnetic field in the field quickly evolves into a simple torus equilibrium. via a figure-of-eight shaped configuration consisting of a twisted flux tube twisted around itself.," In \\ref{fig:vapor1} the evolution of the magnetic field in the field quickly evolves into a simple torus equilibrium, via a figure-of-eight shaped configuration consisting of a twisted flux tube twisted around itself."587 In fig., In fig.588 5 the evolution of the magnetie field in An intermediate state is reached which consists of two torus-shaped fields connected by two flux tubes: however the two tori are pulled together again by the tension in the tubes which join them. and a current sheet forms at the interface.," \ref{fig:merger} the evolution of the magnetic field in An intermediate state is reached which consists of two torus-shaped fields connected by two flux tubes; however the two tori are pulled together again by the tension in the tubes which join them, and a current sheet forms at the interface."589 Eventually the two tori become one. significantly weaker torus.," Eventually the two tori become one, significantly weaker torus."590 It appears that the most basic equilibrium is a “ball of string twisted torus shape., It appears that the most basic equilibrium is a `ball of string' twisted torus shape.591 All equilibria consist of twisted flux tubes arranged in some pattern. the simple torus being a special case where the flux tube makes a circle.," All equilibria consist of twisted flux tubes arranged in some pattern, the simple torus being a special case where the flux tube makes a circle."592 Tubes may be twisted in either sense. corresponding to positive and negative magnetic helicity.," Tubes may be twisted in either sense, corresponding to positive and negative magnetic helicity."593 Magnetic fields with greater helicity tend to evolve directly into simpler equilibria: conversely when the helicity is very small the energy drops by a large factor. reducing the Alfvénn speed to such an extent that continued simulation of the evolution becomes impossible.," Magnetic fields with greater helicity tend to evolve directly into simpler equilibria; conversely when the helicity is very small the energy drops by a large factor, reducing the Alfvénn speed to such an extent that continued simulation of the evolution becomes impossible."594 It seems plausible that all fields eventually evolve into a simple torus configuration. the important question being whether this happens on a sufficiently short timescale.," It seems plausible that all fields eventually evolve into a simple torus configuration, the important question being whether this happens on a sufficiently short timescale."595 We now explore the effect of the bubble density., We now explore the effect of the bubble density.596 To do this. simulations were run with the following values of the density ratio fs/po parameter: 0.1 Cas above). Land 10.," To do this, simulations were run with the following values of the density ratio $\rho_{\rm i}/\rho_{\rm o}$ parameter: $0.1$ (as above), $1$ and $10$."597 Of course. the former (0.1) is the only ratio consistent with the observations but it is informative to look at other values.," Of course, the former $0.1$ ) is the only ratio consistent with the observations but it is informative to look at other values."598 In fig., In fig.599 6. three simulations are compared which have identical initial conditions except for pi/p»: their behaviour is quite different.," \ref{fig:vapor2}600 three simulations are compared which have identical initial conditions except for $\rho_{\rm i}/\rho_{\rm o}$; their behaviour is quite different."601 The main difference between the simulations is that the denser bubbles move into the surroundings more easily. become more spherical and are more prone to breaking up. even though the field strength is the same and the Alfvénn speed is lower.," The main difference between the simulations is that the denser bubbles move into the surroundings more easily, become more non-spherical and are more prone to breaking up, even though the field strength is the same and the Alfvénn speed is lower."602 In the figure we see that in the low-density case (left column) the bubble becomes somewhat distorted but then returns to a more spherical shape. forming a simple torus.," In the figure we see that in the low-density case (left column) the bubble becomes somewhat distorted but then returns to a more spherical shape, forming a simple torus."603" In the run with pif,=1 (middle column) different parts of the bubble move away from each other and several small torus shapes are formed. connected by weak flux tubes."," In the run with $\rho_{\rm i}/\rho_{\rm o}=1$ (middle column) different parts of the bubble move away from each other and several small torus shapes are formed, connected by weak flux tubes."604" To illustrate how a bubble can break up. field lines of a run with pi/p,=1 are plotted in fig. 7.."," To illustrate how a bubble can break up, field lines of a run with $\rho_{\rm i}/\rho_{\rm o}=1$ are plotted in fig. \ref{fig:break_up}."605 This run has very low helicity Ay=0.00025.section.," This run has very low helicity $\lambda_{\rm i}=0.00025$,."606 The bubbles with higher helicity always form a simple torus-shaped equilibrium regardless of the density., The bubbles with higher helicity always form a simple torus-shaped equilibrium regardless of the density.607 This dependence on the bubble density can be understood in the following way., This dependence on the bubble density can be understood in the following way.608" During reconnection, material inside the bubble is moving around with velocity comparable to the Alfvénn speed. so that the bubble will not stay spherical for very long."," During reconnection, material inside the bubble is moving around with velocity comparable to the Alfvénn speed, so that the bubble will not stay spherical for very long."609 The Kinetic energy density of the plasma is comparable to the magnetic energy density 2?/87 and its momentum per unit volume is 2Vραπ., The kinetic energy density of the plasma is comparable to the magnetic energy density $B^2/8\pi$ and its momentum per unit volume is $B\sqrt{ \rho/ 4\pi }$.610 A denser (and colder) bubble has more momentum and can penetrate the surrounding medium more easily., A denser (and colder) bubble has more momentum and can penetrate the surrounding medium more easily.611 Alternatively. one can think of the distance over which a projectile slows down via aerodynamic drag: it is comparable to the distance over which it has to push its own mass out of the way. which is obviously further if it is more dense.," Alternatively, one can think of the distance over which a projectile slows down via aerodynamic drag: it is comparable to the distance over which it has to push its own mass out of the way, which is obviously further if it is more dense."612" Since in reality we know that bubbles have a low density. Le. mp,«1/3 and probably even lower. we should expect only a modest deformation of the bubble from the Alfvénnic motions inside them."," Since in reality we know that bubbles have a low density, i.e. $\rho_{\rm i}/\rho_{\rm o}<1/3$ and probably even lower, we should expect only a modest deformation of the bubble from the Alfvénnic motions inside them."613Note that here itis assumed,We will explain why the above policy is nevertheless advantageous.614 that Y4 0 and Dp pp +38D, One may set e.g. $U_2(r)=U_1(r)$ by a redefinition of the $r$ -coordinate.615 asp pp! +3Dyusp'ptp' + Diaptptp! 20. (52) = = = = = = (ii," This choice of “gauge” may result in a trivial equation of motion for $U_1(r)$, leaving us with only one independent equation of motion."616i) -i.For thecasepl Diyosp? nDio Di DiDos Do Dy Doe Das, The missing equation of motion has to be obtained from the requirement that the action is invariant under the choice of gauge.617" 1. Di py 20g 0 —El ZiHE! —= ""2!j (53)mi", I.e. the variation of the non-gauged-fixed action with respect to $U_2(r)$ must vanish.618 Field Equations, This is also known as a Hamiltonian constraint.619 DB Derivation of the Metric," However, this is just the original equation of motion for $U_2(r)$ that we threw away by the gauge fixing."620 orderto simplifythe derivation of theequations ofmotion.," Thus we will simply retain all three degrees of freedom in the metric, which will give two independent equations of motion after gauge fixing."621 write the Lagrangian in form whichis accounted for in the computation.," One may now be concerned about other gauge fixings implicit in the choice of coordinates of \ref{u1u2u3metric}) ), e.g. vanishing off-diagonal components or $g_{\theta\theta}=g_{\phi\phi}/sin^2\theta$."622 equation: OL.Cy In our case. the action contains curvature tenso," However, our metric is the “maximally general” metric preserving the assumed isometries of the solution, namely staticity and spherical symmetry \cite{barakol}."623rs whicharebuilt from secondorderderivatives. Thus we needto take thefull secon," For such a solution, the equations of motion corresponding to the trivial metric components would be automatically satisfied and would not yield new constraints."624dorder variation. Alternativelv.one may in," In order to be consistent with the notation of our solution \ref{r2nesol}) ), we will actually use the metric: where $f(r)$ is given."625tegrate theaction bv parts., The solution to the equations of motion is given by where $U(r)$ is given.626and take (he usual [ist order," When deriving the equations of motion, we must retain the separate degrees of freedom of the metric."627 variation. We assumea static and spherica," The fields $F_{ab}^{-I},T_{ab}^-$ in our solution, are given as the anti-selfdual parts written with tangent space indices."628lly sviumetrie metric.," In this form, these fields contain metric components, while the metric-independent fields are $F_{\mu\nu}^{I},T_{\mu\nu}$."629A general formof sucha metric is only(wo independent i-Iunction degrees of freedom.," Let us denote by $F_{01}^{-I}(r),T_{01}^{-I}(r)$ the $(0,1)$ components of these fields as given in our solution \ref{fsol}) ), \ref{r2nesol}) ), before we explicitly introduced the separate metric degrees of freedom."630 Thus one ofthethree equations ofmotion willbe redundant.," When these fields appear in the Lagrangian explicitly (including via the hatted fields \ref{hatted}) )), they should be rewritten as Alternatively, one may work with the $F_{\mu\nu}^{I},T_{\mu\nu}$ form and put appropriate projection operators in the Lagrangian."631star formation rate. surface deusitv and magnetic field streneth.,"star formation rate, surface density and magnetic field strength."632 Consequently the escape radius depeuds on time.," Consequently, the escape radius depends on time."633 If the disk was contracted from ~SO to 30 kpc in radius. it could be even more natural to construct a model in which the stellar surface density decays with 7? slowly enough. with no stellar truncation radius.," If the disk was contracted from $\sim 80$ to $30$ kpc in radius, it could be even more natural to construct a model in which the stellar surface density decays with $R$ slowly enough, with no stellar truncation radius."634 Even asstuning that stars in the outer disk were nof formed until the eas disk stopped its contraction. which is in contrast with observations that show old stars in the outer disk (e.g. Ferguson Johusou 2001). the planar velocity dispersious of the stars should iucrease dramatically with A&R aud this is not observed (e.g. Ptenniger et al.," Even assuming that stars in the outer disk were not formed until the gas disk stopped its contraction, which is in contrast with observations that show old stars in the outer disk (e.g., Ferguson Johnson 2001), the planar velocity dispersions of the stars should increase dramatically with $R$ and this is not observed (e.g., Pfenniger et al."635 1991: Valléce 1991)., 1994; Valléee 1994).636 Iu the past vears. much of the challenge involved iu making the magnetic alternative viable concerned the excessive faring of the disk. which is caused by the vertical magnetic pressure (Cuddeford&Binney1993).," In the past years, much of the challenge involved in making the magnetic alternative viable concerned the excessive flaring of the disk, which is caused by the vertical magnetic pressure \citep{cud93}."637. Tn a two- analysis. Dattaner&Florido(1995) predict a scale height of 3 3.5 kpe at a radius of 15 spc aud of 7 kpe at 30 kpe for the disk of ND31.," In a two-dimensional analysis, \citet{bat95} predict a scale height of $3$ $3.5$ kpc at a radius of $15$ kpc and of $7$ kpc at $30$ kpc for the disk of M31."638 These values are still too large by a factor of 3.5 if comparing with the observed scale height observed in the Galaxy by Diplas1991) and Burton(1992)., These values are still too large by a factor of $3$ $5$ if comparing with the observed scale height observed in the Galaxy by \citet{dip91} and \citet{bur92}.639. This discrepancy in the scale height is the least of our worries., This discrepancy in the scale height is the least of our worries.640 Au inspection ofthe radial profile of the magnetic y.reneth (fe., An inspection of the radial profile of the magnetic strength (fig.641 3 of Dattaner Florido 1995) reveals that rere is something deeply wrong iu their calculations., 3 of Battaner Florido 1995) reveals that there is something deeply wrong in their calculations.642 As shown ius refsec:oned.. the magnetic field cannot decrease faster ian L/R in order to have a disk with a faster rotation.," As shown in \\ref{sec:oned}, the magnetic field cannot decrease faster than $1/R$ in order to have a disk with a faster rotation."643 Therefore. a magnetic field of 5G at 15 kpe implies a field strength larger than 2.5 μι at 30 kpe.," Therefore, a magnetic field of $5\,\mu$ G at $15$ kpc implies a field strength larger than $2.5\,\mu$ G at $30$ kpc."644 The magnetic ficld estimated by Battauer&Florido(1995.2000) decays aster than 1/7.," The magnetic field estimated by \citet{bat95,bat00} decays faster than $1/R$ ."645 If the dark matter contribution to the rotation curve is null. the required magnetic fields iu the outer parts of typical spiral galaxies are so intense (5 10404) that the problem of excessive faring is uuresolved.," If the dark matter contribution to the rotation curve is null, the required magnetic fields in the outer parts of typical spiral galaxies are so intense $\sim 5$ $10\,\mu$ G) that the problem of excessive flaring is unresolved."646 The faring problem is exacerbated when the magnetic pressure of the simalbscale maenetic field is iucluded because it also contributes to the vertical expansion of the disk., The flaring problem is exacerbated when the magnetic pressure of the small-scale magnetic field is included because it also contributes to the vertical expansion of the disk.647" This pressure is observed to be comparable to the magnetic pressure of the regular field at least in the optical disk of the Calas,", This pressure is observed to be comparable to the magnetic pressure of the regular field at least in the optical disk of the Galaxy.648 Ou the other haud. the excessive flaring is also ageravated if the magnetic pitch angle is not zero.," On the other hand, the excessive flaring is also aggravated if the magnetic pitch angle is not zero."649 Iu this Section. we will discuss the role of mmaeguetic fields as a remedy for the cuspy problem of dark halos.," In this Section, we will discuss the role of magnetic fields as a remedy for the cuspy problem of dark halos."650 It is interesting to see whether the magnetic pressure of the randoni component. as well as certain configurations of a global-scale maguctic field (not necessarily. azimuthal) could help to explain the discrepancy between the profiles of dark halos obtained iu cold dark matter (CDAD siuulations. which becomes very cuspy towards the center (e.g. Navarro. Freunk White 1996. 1997). aud observations of the halos of dwarf galaxies aud LSB. which are better fitted with a core-douunated halo (see de Blok. Bostua MeCGanel 2003. aud. references. therein).," It is interesting to see whether the magnetic pressure of the random component, as well as certain configurations of a global-scale magnetic field (not necessarily azimuthal) could help to explain the discrepancy between the profiles of dark halos obtained in cold dark matter (CDM) simulations, which becomes very cuspy towards the center (e.g., Navarro, Frenk White 1996, 1997), and observations of the halos of dwarf galaxies and LSB, which are better fitted with a core-dominated halo (see de Blok, Bosma McGaugh 2003, and references therein)."651 One possibility is that galaxies are indeed eubedded iu cuspy halos following the profile fouud by Navarre. Freuk and White (1096: hereafter NEW) but the combination of asyvuuuetre drifts and magnetic effects wipe out completely the iuuer cusp. leading to rotation curves that ninic a halo with a core.," One possibility is that galaxies are indeed embedded in cuspy halos following the profile found by Navarro, Frenk and White (1996; hereafter NFW) but the combination of asymmetric drifts and magnetic effects wipe out completely the inner cusp, leading to rotation curves that mimic a halo with a core."652 The magnetic pressure of the random component gives sole support to the disk. reducing the rotation speed.," The magnetic pressure of the random component gives some support to the disk, reducing the rotation speed."653 Since it is expected to be in equipartition with the eas turbulent pressure. corrections due to the magnetic oessure should be of the order of the asviunetrie dift. —-235hmns! (c.g.. de Blok Dosma 2002). which are stnaller or conrparable to observational uncertaimties. ypically | Glas +.," Since it is expected to be in equipartition with the gas turbulent pressure, corrections due to the magnetic pressure should be of the order of the asymmetric drift, $\sim 2$ $3$ km $^{-1}$ (e.g., de Blok Bosma 2002), which are smaller or comparable to observational uncertainties, typically $4$ $6$ km $^{-1}$."654 This contribution. however. could be arecry Ina certain radial portion of the disk if the magnetic xessiire decavs fasterthan e.," This contribution, however, could be larger in a certain radial portion of the disk if the magnetic pressure decays fasterthan $v_{\rm t}$."655" Writting the Alfveéun speed associated to the random field as e$= g(R)c2. with he turbulent velocity dispersion ον constant with A. aud dgfdR<0, the rotation curve changes according to the relation: Following deBlok&Bosima(2002).. we define Ai, as the radius of the imuermost sampled poiut of the rotation curve. and assume that at Ro>Ri. g(R)=(RyRY"" for simplicity."," Writting the Alfvènn speed associated to the random field as $v_{\rm A}^{2}=g(R) v_{\rm t}^{2}$, with the turbulent velocity dispersion $v_{\rm t}$ constant with $R$, and $dg/dR<0$ , the rotation curve changes according to the relation: Following \citet{deb02}, we define $R_{\rm in}$ as the radius of the innermost sampled point of the rotation curve, and assume that at $R>R_{\rm in}$, $g(R)=(R_{\rm in}/R)^{n}$ for simplicity."656 Doing so. we are imposing that at HW. CA&ον.," Doing so, we are imposing that at $R_{\rm in}$, $v_{\rm A}\approx v_{\rm t}$."657 The second term of the RIS of Eq. (12)), The second term of the RHS of Eq. \ref{eq:drift}) )658" is of the order of the asvnuuetric dift (comparable to observational uncertainties). whereas the last term is nezRE2R""."," is of the order of the asymmetric drift (comparable to observational uncertainties), whereas the last term is $-nv_{\rm t}^{2}R_{\rm in}^{n}/2R^{n}$."659 As the observed roteion curve differs from the NEW profile along a significant range of ealactocentric radius.sav at RomRinmSOO pe. then O—0zxl. implvine that ezREARx¢2/2—50 kms] ? (for ow=d0 km s +).," As the observed rotation curve differs from the NFW profile along a significant range of galactocentric radius,say at $R\gg R_{\rm in}\approx 500$ pc, then $0<n\leq 1$, implying that $nv_{\rm t}^{2}R_{\rm in}^{n}/2R^{n}<v_{\rm t}^{2}/2\sim 50$ $^{2}$ $^{-2}$ (for $v_{\rm t}=10$ km $^{-1}$ )."660 Consequently. this effect would be ouly siguificaut very close to the eulactie center where ex10 kins |. aregion with large observational wucertaiutics.," Consequently, this effect would be only significant very close to the galactic center where $v_{\rm c}\leq 10$ km $^{-1}$, a region with large observational uncertainties."661 Sunimniug up. the contribution from the total pressure to the circular velocity is less than 5 Glans +.," Summing up, the contribution from the total pressure to the circular velocity is less than $5$ $6$ km $^{-1}$."662 This result agrees with the act that CO. Πα and rotation curves reveal the same οποιαος for the ceutral regions of some galaxies (6.8... Bolatto et al.," This result agrees with the fact that CO, ${\alpha}$ and rotation curves reveal the same kinematics for the central regions of some galaxies (e.g., Bolatto et al."663 2002). which suggests that magnetic folds do not contribute sienificautlv to the support of the gas disks.," 2002), which suggests that magnetic fields do not contribute significantly to the support of the gas disks."664 In particular. the CO rotation curves are expected to race the motion of the highest density regious. imcludiug uolecular clouds. which are thought to be hardly affected w the ealactic magnetic fields.," In particular, the CO rotation curves are expected to trace the motion of the highest density regions, including molecular clouds, which are thought to be hardly affected by the galactic magnetic fields."665 Iu conchision. maguetic effects are not sufficient to solve he cuspy halo problem satisfactorily.," In conclusion, magnetic effects are not sufficient to solve the cuspy halo problem satisfactorily."666 It has been recognized for decades that the ealactic magnetic field provides siguificant vertical support to the iuterstellar medium, It has been recognized for decades that the galactic magnetic field provides significant vertical support to the interstellar medium.667 The role of the maguetic tensionin the vertical hydrostatic configuration was considered bv Cox(1988). aud Boulares&Cox (1990).. whereas the role ofthe tension iu the plane of the disk was studied by Nelson (1988).. Battaneretal.(1992). aud Benjamin [sce also Piddington 1961].," The role of the magnetic tensionin the vertical hydrostatic configuration was considered by \citet{cox88} and \citet{bou90}, , whereas the role ofthe tension in the plane of the disk was studied by \citet{nel88}, \citet{bat92} and \citet{ben00} [see also Piddington 1964]."668 The idea that large- magnetic flelds can explain the rotation curves of, The idea that large-scale magnetic fields can explain the rotation curves of669"All the contributions to Hea,in (14)) ave included for the orbit caleulation.",All the contributions to $\H_\star$in \ref{Hstar}) ) are included for the orbit calculation.670" The photon trajectories include all contributions to WH""! in (17)) except for Hl"",", The photon trajectories include all contributions to $\H^\photon$ in \ref{Hphoton}) ) except for $\H^\torq$.671 Naturally we would like to compute the redshift contributions of the various relativistic terms. and verify that thev follow the expected scalings (31)).," Naturally we would like to compute the redshift contributions of the various relativistic terms, and verify that they follow the expected scalings \ref{scalings}) )."672 In order to do (his. we examine the dillerences between redshifts computed [rom clilferent post-Newtonian and post-Minkowskian cases.," In order to do this, we examine the differences between redshifts computed from different post-Newtonian and post-Minkowskian cases."673 This allows us to isolate (he effects of Jas. Hip. 2090 and Hoste+ HEP. as follows.," This allows us to isolate the effects of $\H_\schw,$ $\H_\fd,$ $\H^\slo$ and $\H^\snlo+\H^\fd$ , as follows."674"where c, is the sound speed.",where $c_s$ is the sound speed.675" We can then write the mixing time as where torp is the local orbital period and we have used the fact that h/cs~tos /27. Using Prmg=1 (Guan&Gammie2009;r/veLesurLongarettiFro-mang&Stone2009) and ay=0.005 suggests that the memory of the initial conditions will be lost on a timescale of f£,~200t;,5."," We can then write the mixing time as where $t_{\rm orb}$ is the local orbital period and we have used the fact that $h/c_s\sim r/v_\phi\sim t_{\rm orb}/2\pi$ Using $Pr_{\rm676 m,eff}=1$ \citep{guan09b,lesur09,fromang09} and $\alpha_M=0.005$ suggests that the memory of the initial conditions will be lost on a timescale of $t_{\rm mix}\sim 200t_{\rm orb}$."677 This crude estimate is in reasonable agreement with the timescale on which we see the flux-stress relationship achieve a stationary state., This crude estimate is in reasonable agreement with the timescale on which we see the flux-stress relationship achieve a stationary state.678" It has been a long-held ansatz that one can extract and model the dynamics of a local patch of an accretion disk and obtain results (for the angular momentum transport, for that have meaning for the disk as a whole."," It has been a long-held ansatz that one can extract and model the dynamics of a local patch of an accretion disk and obtain results (for the angular momentum transport, for example) that have meaning for the disk as a whole."679" By example)examining local patches of a high resolution global disk simulation, we have provided a direct test of this notion."," By examining local patches of a high resolution global disk simulation, we have provided a direct test of this notion."680 We have shown that MRI-driven turbulence in global geometrically thin accretion disks behaves in a way consistent with scaling laws derived for local simulations., We have shown that MRI-driven turbulence in global geometrically thin accretion disks behaves in a way consistent with scaling laws derived for local simulations.681" In particular, we find that global disks display a local flux-stress relation qualitatively similar to that found in local simulations (Hawleyetal.1995;Pessah2007).."," In particular, we find that global disks display a local flux-stress relation qualitatively similar to that found in local simulations \citep{hawley95,boxscaling}."682" However, other aspects of the global models are distinctly different: We would like to thank Cole Miller, Sean O'Neill, Aaron Skinner, Eve Ostriker, and Jim Stone for valuable discussions and comments, and the Isaac Newton Institute for Mathematical Sciences for their hospitality during the completion of this work."," However, other aspects of the global models are distinctly different: We would like to thank Cole Miller, Sean O'Neill, Aaron Skinner, Eve Ostriker, and Jim Stone for valuable discussions and comments, and the Isaac Newton Institute for Mathematical Sciences for their hospitality during the completion of this work."683 K.A.S. thanks the Maryland-Goddard Joint Space Science Institute (JSI) for support under their JSI graduate fellowship program., K.A.S. thanks the Maryland-Goddard Joint Space Science Institute (JSI) for support under their JSI graduate fellowship program.684 K.A.S.and C.S.R. gratefully acknowledge, K.A.S.and C.S.R. gratefully acknowledge685The outline of this article is as follows.,The outline of this article is as follows.686 Section 2 briefly describes the numerical techniques., Section \ref{sc:numerics} briefly describes the numerical techniques.687 The parameters. for which we run simulations. are specified inSect. 3..," The parameters, for which we run simulations, are specified inSect. \ref{sec:simulations}."688 The phenomenology of turbulence in thermally bistable gas is described for a representative parameter set in Sect. 4.., The phenomenology of turbulence in thermally bistable gas is described for a representative parameter set in Sect. \ref{sec:results}.689 For this parameter set. the grid resolution was varied from 128? to 512? to check for the resolution dependency of the results.," For this parameter set, the grid resolution was varied from $128^3$ to $512^3$ to check for the resolution dependency of the results."690 Next. we analyse the variation of statistical properties for different simulation parameters.," Next, we analyse the variation of statistical properties for different simulation parameters."691 In Sect. 5..," In Sect. \ref{sec:discussion},"692 the results are discussed in the context of other numerical studies and observations. followed by a summary of the main results and an outlook in Sect. 6..," the results are discussed in the context of other numerical studies and observations, followed by a summary of the main results and an outlook in Sect. \ref{sec:conclusion}."693 The simulation presented in. this article are.performed with the open source code Enzo (O'Sheaetal.2005)., The simulation presented in this article areperformed with the open source code Enzo \citep{OShea05}.694. We solve the compressible Euler equations using the precewise-parabolie method (PPM) of Colella&Woodward(1984)., We solve the compressible Euler equations using the piecewise-parabolic method (PPM) of \citet{Colella84}.695. Besides an external driving forcef.. which is responsible for generating turbulent motions. we include different heating and cooling terms. combined into a net cooling rate per unit mass £.," Besides an external driving force, which is responsible for generating turbulent motions, we include different heating and cooling terms, combined into a net cooling rate per unit mass ${\fam=2 L}$."696" The resulting equations for the mass density p. the velocity s. and the specific total energy e of the fluid can be written as where the total time derivative is defined by The Otspecific- total energy e is mEgiven by where y(y=5/3 lp1s the adiabatic exponent of monatomic gas. and the gas pressure P is related to the mass density and the temperature 7 via the ideal gas law: The constants Kg. 4. and ay, denote the Boltzmann constant. the mean molecular weight. and the mass of a hydrogen atom. respectively."," The resulting equations for the mass density $\rho$, the velocity $\vec{u}$, and the specific total energy $e$ of the fluid can be written as where the total time derivative is defined by The specific total energy $e$ is given by where $\gamma = 5/3$ is the adiabatic exponent of monatomic gas, and the gas pressure $P$ is related to the mass density and the temperature $\mathcal{T}$ via the ideal gas law: The constants $k_B$, $\mu$, and $m_H$ denote the Boltzmann constant, the mean molecular weight, and the mass of a hydrogen atom, respectively."697 The cooling function p£ was defined by Audit&Hen-nebelle (2005)., The cooling function $\rho{\fam=2 L}$ was defined by \citet{Audit05}.698. It includes the fine-structure cooling of andOr. as well as the cooling by H (Lye-line) and by electron. recombination. onto. charged grams.," It includes the fine-structure cooling of and, as well as the cooling by H $\alpha$ –line) and by electron recombination onto charged grains."699 The only heating process considered is the photoelectric effect on small grains and polveyelie aromatic hydrocarbons (PAH) caused by far-ultraviolet galactic background radiation., The only heating process considered is the photoelectric effect on small grains and polycyclic aromatic hydrocarbons (PAH) caused by far-ultraviolet galactic background radiation.700 For detailed information about the different processes see Wolfireetal.(1995.2003);Spitzer(1978) and Bakes&Tielens(1994).," For detailed information about the different processes see \citet{Wolfire95, Wolfire03, Spitzer78} and \citet{Bakes94}."701 The cooling is implemented in the form of an explicit scheme into Enzo (Niklausetal.2009)., The cooling is implemented in the form of an explicit scheme into Enzo \citep{Niklaus09}.702. After each time step. the state variables are updatedin several subcycles by adding the resulting total energy increment.," After each time step, the state variables are updatedin several subcycles by adding the resulting total energy increment."703 As the considered cooling and heating processes are only well defined in the diffuse ISM. the calculation of £(o.7 ) is constrained to temperatures 7. € [10 K. 100000 ΚΙ.," As the considered cooling and heating processes are only well defined in the diffuse ISM, the calculation of ${\fam=2 L}$ $\rho$ $\mathcal{T}$ ) is constrained to temperatures $\mathcal{T}$ $\in$ [10 K, 000 K]."704 For gas with temperatures aboveK.. we use 4(p.10 0000 K). which leads to an underestimate of the emitted energy. hence to warmer gas than expected.," For gas with temperatures above, we use ${\fam=2 L}$ $\rho$ 000 K), which leads to an underestimate of the emitted energy, hence to warmer gas than expected."705 In strongly driven simulations we apply a temperature cutoff atK.. assuming that the gas would cool down very fast beyond this limit.," In strongly driven simulations we apply a temperature cutoff at, assuming that the gas would cool down very fast beyond this limit."706 Since the speed of sound increases with the temperature. the cutoff allows us to avoid very small time steps arising from unphysical values of the temperature outside the range of the cooling function.," Since the speed of sound increases with the temperature, the cutoff allows us to avoid very small time steps arising from unphysical values of the temperature outside the range of the cooling function."707 The concerned simulation runs are mentioned in Sect. 4.., The concerned simulation runs are mentioned in Sect. \ref{sec:results}.708 The specific force f in Eqs. (2)), The specific force $\vec{f}$ in Eqs. \ref{equ:momentum}) )709 and (3)). which generates large-scale motions of the gas. iscomposed in Fourier space.," and \ref{equ:energy}) ), which generates large-scale motions of the gas, iscomposed in Fourier space."710 Each mode of the force field is given by a stochastic process that is based on the Ornstein-Uhlenbeck process (Eswaran&Pope1988;Schmidtetal. 2006).," Each mode of the force field is given by a stochastic process that is based on the Ornstein-Uhlenbeck process \citep{Eswaran88,Schmidt06}."711. For the details of this method. see Schmidtetal.(2009).," For the details of this method, see \citet{Schmidt09}."712. The forcing varies on the autocorrelation timescale 7. which ts given by the ratio of the integral length L to the characteristic velocity V. of the large-scale motions.," The forcing varies on the autocorrelation timescale $T$, which is given by the ratio of the integral length $L$ to the characteristic velocity $V$ of the large-scale motions."713 We set the integral length to half of the box size., We set the integral length to half of the box size.714 Thus. the wavelengths of the forcing modes range from L/2 to 2L.," Thus, the wavelengths of the forcing modes range from $L/2$ to $2L$."715 The free parameter V specifies the magnitude of the forcing. i. e.. the specific force is ~V7/L.," The free parameter $V$ specifies the magnitude of the forcing, i. e., the specific force is $\sim V^{2}/L$."716 By applying a Helmholtz decomposition in Fourier space. the ratio of solenoidal (divergence-free) to compressive (rotation-free) modes can be arbitrarily adjusted.," By applying a Helmholtz decomposition in Fourier space, the ratio of solenoidal (divergence-free) to compressive (rotation-free) modes can be arbitrarily adjusted."717 We use the decomposition parameter Z such that €=| corresponds to purely solenoidal forcing. and the force becomes increasingly compressive as Z decreases from | to 0.," We use the decomposition parameter $\zeta$ such that $\zeta=1$ corresponds to purely solenoidal forcing, and the force becomes increasingly compressive as $\zeta$ decreases from $1$ to $0$."718 Since we are interested in the local structure of the diffuse ISM. we treat the simulation domain as a part of a larger region with — in the statistical sense - homogeneous properties.," Since we are interested in the local structure of the diffuse ISM, we treat the simulation domain as a part of a larger region with – in the statistical sense – homogeneous properties."719 Numerically. this is done by using a cubic simulation domain with periodic boundaries and a linear size of At the simulation start. the box ts filled with atomic hydrogen of uniform density po and temperature Τη.," Numerically, this is done by using a cubic simulation domain with periodic boundaries and a linear size of At the simulation start, the box is filled with atomic hydrogen of uniform density $\rho_{0}$ and temperature $\mathcal{T}_{0}$."720 For the mean particle densities 2/5 (which remains constant because of the periodic boundaries). we choseLl.0cm.. and-.. which are comparable to the mean density of the diffuse ISM.," For the mean particle densities $n_0$ (which remains constant because of the periodic boundaries), we chose, and, which are comparable to the mean density of the diffuse ISM."721 In the initial phase. the nearly homogeneous gas will adjustvery fast to the equilibrium temperature that is given by the condition £=0. regardless of the choice of 7.," In the initial phase, the nearly homogeneous gas will adjustvery fast to the equilibrium temperature that is given by the condition ${\fam=2 L}=0$, regardless of the choice of $\mathcal{T}_{0}$ ."722 For this reason. we set Τρ equal to the equilibrium temperature correspondingσι to no.," For this reason, we set $\mathcal{T}_{0}$ equal to the equilibrium temperature corresponding to $n_0$."723 The pressure equilibrium curve P400). following from and the ideal gas equation (see Sect. 2)).," The pressure equilibrium curve $P_{\mathrm{eq}}(n)$ following from and the ideal gas equation (see Sect. \ref{sc:numerics}) ),"724 is plotted in Fig. |. , is plotted in Fig. \ref{fig:1}. .725Via the isobaric instability criterion of Hunter (1970). one can determine the regions of the thermal instability (TI) in the phase diagram that is shown in Fig. 1..," Via the isobaric instability criterion of \citet{Hunter70}, , one can determine the regions of the thermal instability (TI) in the phase diagram that is shown in Fig. \ref{fig:1}. ."726 We define three different phases. a cold phase withK.. an unstable phase with K.. and a warm phase with K..," We define three different phases, a cold phase with, an unstable phase with , and a warm phase with ."727"The WKB results above are not exact, especially when the modes of interest are global and the disk mass is significant relative to Mau (both of which are typically the case!).","The WKB results above are not exact, especially when the modes of interest are global and the disk mass is significant relative to $M_{\rm BH}$ (both of which are typically the case!)."728" To show that our conclusions are robust, we also demonstrate the same points regarding the propagation of modes using exact linear solutions for particular global normal modes."," To show that our conclusions are robust, we also demonstrate the same points regarding the propagation of modes using exact linear solutions for particular global normal modes."729" Our methodology is described in detail in ?,, which we briefly summarize here."," Our methodology is described in detail in \citet{hopkins:slow.modes}, which we briefly summarize here."730 We define Ro for the power-law disk model (eq. 7)), We define $R_{0}$ for the power-law disk model (eq. \ref{powerlaw}) )731 so that Μις.Ro)=Msu/[oQ—7)] — No=Msu/oR5).," so that $M_{d}(<R_{0})=M_{\rm BH}/[\alpha\,(2-\eta)]$ – $\Sigma_{0}=M_{\rm BH}/(2\pi\,\alpha\,R_{0}^{2})$."732 Unlike in the WBK analysis we do not expand the equationsQ7 to linear order in Ma/Mpu but keep the full linear perturbation equations., Unlike in the WBK analysis we do not expand the equations to linear order in $M_d/M_{\rm BH}$ but keep the full linear perturbation equations.733" We consider a stellar-dominated (collisionless) disk since in our numerical results, the dominant torques in the gas are due to the stellar modes."," We consider a stellar-dominated (collisionless) disk since in our numerical results, the dominant torques in the gas are due to the stellar modes."734" The resulting equations of motion for linear perturbationsare where ®,=So”dr!r'P(r,r')Xa(r’) follows from Poisson’s vy= OInX/OInR, and A=κ)-(Q-wy."," The resulting equations of motion for linear perturbationsare where $\Phi_{a} = \int_{0}^{\infty}\,{dr^{\prime}}\,{r^{\prime}}\,P(r,\,r^{\prime})\,\Sigma_{a}(r^{\prime})$ follows from Poisson's $\nu_{X}\equiv \partial \ln X/\partial \ln R$ , and $\Delta \equiv \kappa^{2}-(\Omega-\omega)^{2}$."735 It is straightforward to solve eq., It is straightforward to solve eq.736 13 for the eigenfunctions (normal modes) of the system., \ref{eqn:mode.eom} for the eigenfunctions (normal modes) of the system.737 For convenience and realism we modify the disk mass profiles with a steep outer power-law cutoff (SaR1+[R/a])6-»/ 3) so that they have finite total mass Ma=Mag; ? shows that the exact choice of M; and/or the cutoff radius has no affect on any of our conclusions.," For convenience and realism we modify the disk mass profiles with a steep outer power-law cutoff $\Sigma\propto R^{-\eta}\,(1+[R/a]^{2})^{-(3-\eta)/2}$ ) so that they have finite total mass $M_{d} = M_{\rm BH}$; \citet{hopkins:slow.modes} shows that the exact choice of $M_{d}$ and/or the cutoff radius has no affect on any of our conclusions."738 Figure 2. shows some of the resulting normal modes for astellar disk., Figure \ref{fig:m1.3} shows some of the resulting normal modes for astellar disk.739" The growth rates y and pattern speeds Ωρ are indicated on each panel, in units of Q(Ro)."," The growth rates $\gamma$ and pattern speeds $\Omega_p$ are indicated on each panel, in units of $\Omega(R_0)$."740" For any choice of disk parameters, there is a large variety of normal modes; here, we focus on the most rapidly growing ""global"" modes in each model."," For any choice of disk parameters, there is a large variety of normal modes; here, we focus on the most rapidly growing ""global"" modes in each model."741" The results are qualitatively similar for all global modes (local modes, potentially supported at all radii but localized in radius, are not of interest here)."," The results are qualitatively similar for all global modes (local modes, potentially supported at all radii but localized in radius, are not of interest here)."742" We take 6=0.1 for the softening, but our conclusions are essentially identical for a wide range of 6; in ? we show that this extends to 6=0.3, nnearly-spherical configurations."," We take $\beta=0.1$ for the softening, but our conclusions are essentially identical for a wide range of $\beta$; in \citet{hopkins:slow.modes} we show that this extends to $\beta\gtrsim0.3$, nearly-spherical configurations."743" This is because the manner in which X(R) enters the equations means that the important dimensional parameter is really Menc(<R) at a given radius, so puffier systems and even multiple overlapping disks making a quasi-spherical configuration give a qualitatively identical result."," This is because the manner in which $\Sigma(R)$ enters the equations means that the important dimensional parameter is really $M_{\rm enc}(<R)$ at a given radius, so puffier systems and even multiple overlapping disks making a quasi-spherical configuration give a qualitatively identical result."744" The important parameter we focus on here is the power-law index of the disk mass profile 7, for which we show various choices in Figure2:: 7=0.05,0.50,0.80,1.10, 1.85."," The important parameter we focus on here is the power-law index of the disk mass profile $\eta$, for which we show various choices in Figure\ref{fig:m1.3}: $\eta=0.05,\,0.50,\,0.80,\,1.10,\,1.85$ ."745" For each value of η, Figure 2 shows the absolute value and real component of the surface density perturbation a(R)=Σ/Σ and the induced eccentricity R;/R, where R, is the magnitude of the radial perturbation from the linear equations of motion."," For each value of $\eta$, Figure \ref{fig:m1.3} shows the absolute value and real component of the surface density perturbation $a(R)=\Sigma_{a}/\Sigma$ and the induced eccentricity $R_{a}/R$, where $R_{a}$ is the magnitude of the radial perturbation from the linear equations of motion."746 The modes are normalized so that MAX(|a(R)|)=1., The modes are normalized so that ${\rm MAX}(|a(R)|)=1$.747" Where the eccentricities are significant, there can be orbit crossings and shocks in the gas."," Where the eccentricities are significant, there can be orbit crossings and shocks in the gas."748 This dissipation helps drive rapid inflow; see ? for a detailed discussion of this physics., This dissipation helps drive rapid inflow; see \citet{hopkins:inflow.analytics} for a detailed discussion of this physics.749 The key result in Figure 2 is how the structure of the global modes changes with 7; this confirms our intuition derived from the WKB approximation., The key result in Figure \ref{fig:m1.3} is how the structure of the global modes changes with $\eta$; this confirms our intuition derived from the WKB approximation.750" When the disk surface density profile is shallow (7< 1/2), the modes cannot propagate inwards efficiently - they are confined to a moderate range of radii."," When the disk surface density profile is shallow $\eta\lesssim1/2$ ), the modes cannot propagate inwards efficiently – they are confined to a moderate range of radii."751" At η=1/2, the modes are suddenly able propagate to arbitrarily small R."," At $\eta=1/2$, the modes are suddenly able propagate to arbitrarily small $R$ ."752" Going to somewhat larger η=0.7— 0.8, the structure of the modes is quite similar."," Going to somewhat larger $\eta=0.7-0.8$ , the structure of the modes is quite similar."753" For 7> 1, the induced eccentricity is strongly suppressed at small radii(see 2.1)) even though the mode formally has"," For $\eta > 1$ , the induced eccentricity is strongly suppressed at small radii(see \ref{sec:wkb}) ) even though the mode formally has"754For the first four samples the mean stellar ages of ERGs at all 1«2<2.5 are spread over the range between z~5 and shortly (a few; 107 vr) before the epoch of observation.,For the first four samples the mean stellar ages of ERGs at all $1<z<2.5$ are spread over the range between $z\sim 5$ and shortly (a few $\times 10^8$ yr) before the epoch of observation.755 They seem to divide into two groups with νο2 and μις d., They seem to divide into two groups with $z_{msf}\sim2$ and $z_{msf}\sim 3$ –4.756 The Longhetti ct al. (, The Longhetti et al. (7572005) sample of very luminous ERGs dilers from the others in that it seems {ο he concentrated. towards higher formation redshifts it contains 5 galaxies with ος5.,2005) sample of very luminous ERGs differs from the others in that it seems to be concentrated towards higher formation redshifts – it contains 5 galaxies with $z_{msf}>5$.758 These have stellar masses OO.I0ll7M... more than twice. the mass ofB any ERG4 ain our sample.," These have stellar masses $9.4\times 10^{11}M_{\odot}$, more than twice the mass of any ERG in our sample."759 Llence their ages may be evidence that the very most massive spheroicals formed significantly earlier and/or Formed their stars most quickly. as in the model of Granato et al. (," Hence their ages may be evidence that the very most massive spheroidals formed significantly earlier and/or formed their stars most quickly, as in the model of Granato et al. ("7602004).,2004).761 Lt is also notable that the formation redshifts appear to trace the plotted ος loci., It is also notable that the formation redshifts appear to trace the plotted $z_{msf}$ loci.762 Phe ages of the oldest galaxies at each redshift. as a function of redshift. is an important tracer of the expansion of the universe and hence the cosmological mocel (e.g. Jimenez and Loeb 2002).," The ages of the oldest galaxies at each redshift, as a function of redshift, is an important tracer of the expansion of the universe and hence the cosmological model (e.g. Jimenez and Loeb 2002)."763 We would expect z;r for the oldest galaxies to be constant with observed redshift. and the agreementwith the plotted loci would support a AXc0.75 cosmological constant (w= 1) model.," We would expect $z_{msf}$ for the oldest galaxies to be constant with observed redshift, and the agreementwith the plotted loci would support a $\Lambda\simeq 0.75$ cosmological constant $w=-1$ ) model."764 As Pie. represents a Blux-weighted: mean stellar age. 1ο true age of a galaxy since formation must always |be ereater. to a degree dependent on the detailed form of the star-formation history.," As $T_{pas}$ represents a flux-weighted mean stellar age, the true age of a galaxy since formation must always be greater, to a degree dependent on the detailed form of the star-formation history."765 One interpretation may therefore be iu most or all of the red. galaxies observed as ERCs at 2] 2 ave galaxies. or mergers of galaxies. which formed ab zz4 5. and that the spread in their stellar ages up to js maximunm. redshift can be attributed to differences in iir individual evolution. i.c. the mergers ancl starbursts jov have experienced.," One interpretation may therefore be that most or all of the red galaxies observed as ERGs at $z=1$ –2 are galaxies, or mergers of galaxies, which formed at $z\geq 4$ –5, and that the spread in their stellar ages up to this maximum redshift can be attributed to differences in their individual evolution, i.e. the mergers and starbursts they have experienced."766 Caputi et al. (, Caputi et al. (7672004. 2005) using photometric redshift estimates derived from seven-band photometry of ERGs and other A«22 galaxies in this field. found. the comoving number density of massive (2510/7M.) galaxies in a full A-selected: sample to fall only slowly from τς=1.55 to 2=3.5. where a significant traction. 2025 per cent. of today’s massive galaxies were already in place.,"2004, 2005), using photometric redshift estimates derived from seven-band photometry of ERGs and other $K<22$ galaxies in this field, found the comoving number density of massive $>5\times 10^{10}\rm768M_{\odot}$ ) galaxies in a full $K$ -selected sample to fall only slowly from $z=1.75$ to $z=3.5$, where a significant fraction, 20–25 per cent, of today's massive galaxies were already in place."769 However. the comoving number density of the reddest subse of these galaxies. the ERGs. evolves much more rapicly. steadily increasing with time from z=3.5 to z=1. anc following a trend whieh extrapolates to the present-cay I5/8O population at z—0.," However, the comoving number density of the reddest subset of these galaxies, the ERGs, evolves much more rapidly, steadily increasing with time from $z=3.5$ to $z=1$, and following a trend which extrapolates to the present-day E/SO population at $z=0$."770 At 2=1 1.5. the rising comoving number density of ERGs approached that of all A-selectec ealaxies at the higher recshilt of 2~3.5.," At $z=1$ –1.5, the rising comoving number density of ERGs approached that of all $K$ -selected galaxies at the higher redshift of $z\sim 3.5$."771 llence. this suggests that a substantial population of massive galaxies formed at zο4 and were initially. starbursting and relatively blue. but with increasing age many became red enough to be classed as ERGs.," Hence, this suggests that a substantial population of massive galaxies formed at $z\geq 4$ and were initially starbursting and relatively blue, but with increasing age many became red enough to be classed as ERGs."772 Interestinely. for the brightest. (4.<24.5) Lyman break ealaxics at 4. Allen et al. (," Interestingly, for the brightest $I<24.5$ ) Lyman break galaxies at $z\sim 4$, Allen et al. ("773"2005) measure strong clustering of ry=114c2h54, Alpe comoving. consistent with these evolving into the ERGs at z—1 2.","2005) measure strong clustering of $r_0=11.4\pm774 2 \rm h_{100}^{-1}$ Mpc comoving, consistent with these evolving into the ERGs at $z=1$ –2."775 To produce the evolution in ERC number density these galaxies must have entered the ERC class over a wide redshift range κ2<d. again implying much variation in their star-formation histories.," To produce the evolution in ERG number density these galaxies must have entered the ERG class over a wide redshift range $1<z<4$, again implying much variation in their star-formation histories."776 The formation of so many massive galaxies at 24 places significant constraints on models of galaxy formation (c.g. Fontana οἱ al., The formation of so many massive galaxies at $z\geq 4$ places significant constraints on models of galaxy formation (e.g. Fontana et al.777 2004) and may favour mocels with feedback between the star-formation in formative spheroidals and the growth of supermassive black holes within them (Ciranato et al., 2004) and may favour models with feedback between the star-formation in formative spheroidals and the growth of supermassive black holes within them (Granato et al.778 2004: Silva et al., 2004; Silva et al.779 2005)., 2005).780 Yan et al. (, Yan et al. (7812004a) and Doherty et al. (,2004a) and Doherty et al. (7822005). found. that 275 per cent of ERC spectra have prominent absorption features anc 4000. breaks. while >50 per cent also show some OLI] emission.,"2005), found that $\geq 75$ per cent of ERG spectra have prominent absorption features and $4000\rm \AA$ breaks, while $>50$ per cent also show some [OII] emission."783 We find the same for our slightly deeper sample., We find the same for our slightly deeper sample.784 For only 3 ERGs do we find neither OL] emission nor any indication of a voung stellar population from a blue excess in the SED., For only 3 ERGs do we find neither [OII] emission nor any indication of a young stellar population from a blue excess in the SED.785 This is consistent with the Doherty et al. (, This is consistent with the Doherty et al. (7862005) estimate that 28 per cent of ERGs show no evidence of recent star-formation.,2005) estimate that 28 per cent of ERGs show no evidence of recent star-formation.787 For a clear majority of ERGs. 10/13 at 2<1.5. we detect a OL]37217A emission linc.," For a clear majority of ERGs, 10/13 at $z<1.5$, we detect a $\rm [OII]3727 \AA$ emission line."788 Vhis includes two galaxies where the line only just detected with an equivalent width  5X. while at the other extreme we have 3 ERGs with OL) equivalent widths zz30.," This includes two galaxies where the line only just detected with an equivalent width $\sim 5\rm \AA$ , while at the other extreme we have 3 ERGs with [OII] equivalent widths $\geq \rm 30\AA$."789 For the 10 emission-line galaxies. the OLL]3727A Iluxes - uncorreeted. for dust - correspond t0 à mean SER of 1.63 Above1. intermediate between the 28 M.vr. 1amean ΟΕΠο of Yan et al. (," For the 10 emission-line galaxies, the $\rm[OII]3727 \AA$ fluxes - uncorrected for dust - correspond to a mean SFR of 1.63 $\rm M_{\odot} yr^{-1}$, intermediate between the 2.8 $\rm M_{\odot} yr^{-1}$ mean $\rm SFR_{OII}$ of Yan et al. ("7902004a) and the 1.1 Myr fof the Doherty et al. (,2004a) and the 1.1 $\rm M_{\odot} yr^{-1}$ of the Doherty et al. (7912005) ERGs.,2005) ERGs.792 Of course the true SLRs of the emission-line ELCs will be higher., Of course the true SFRs of the emission-line ERGs will be higher.793 On the basis of the dust. extinction. estimated from our moclel fits. we estimate the real mean SER. will be about 1224 M.vr +t.," On the basis of the dust extinction estimated from our model fits, we estimate the real mean SFR will be about 12–24 $\rm M_{\odot} yr^{-1}$ ."794 This may still be an underestimate as emission line regions of current SE may. suller more extinction than the continuum produced by SE over a longer period., This may still be an underestimate as emission line regions of current SF may suffer more extinction than the continuum produced by SF over a longer period.795 Spitzer mid-I1t. observations(Yan et al., Spitzer mid-IR observations(Yan et al.796 2004b) of, 2004b) of797numbers (e.g.. plane Couette and. Couette-Tavlor flows with appropriate parameters).,"numbers (e.g., plane Couette and Couette-Taylor flows with appropriate parameters)."798" A larger minimal Ievnolds number is à sign of a greater difficulty to trigger turbulence. i.e. an increased difficulty. for turbulent. transport to dominate over the viscous one. aud therefore is a slgn of a smaller scale turbulence. due to the physical picture underlving the turbulent viscosity prescription (ie.. the (transport occurs over a smaller. ""mean [free path 7/4. and correlatively with a smaller ""random velocity ey, due to the assumption of identical shear rale between the two different. flows)."," A larger minimal Reynolds number is a sign of a greater difficulty to trigger turbulence, i.e. an increased difficulty for turbulent transport to dominate over the viscous one, and therefore is a sign of a smaller scale turbulence, due to the physical picture underlying the turbulent viscosity prescription (i.e., the transport occurs over a smaller “mean free path"" $l_M$, and correlatively with a smaller “random velocity"" $v_M$ due to the assumption of identical shear rate between the two different flows)."799 From these relations. one can easily check that. at the minimum Revnolds number. the advection term. which dominates scale coupling and is (he primary cause of (he inertial turbulent spectrum. is comparable to the dissipation term. at the turbulent (ransport scale.," From these relations, one can easily check that, at the minimum Reynolds number, the advection term, which dominates scale coupling and is the primary cause of the inertial turbulent spectrum, is comparable to the dissipation term, at the turbulent transport scale."800 As a consequence. the turbulence possesses litile or no inertial domain at its threshold.," As a consequence, the turbulence possesses little or no inertial domain at its threshold."801 Furthermore. as long as there is no change in the turbulence generating process. increasing the Revnolds number can only result in lowering the dissipation scale with respect to 7/3. and therefore in the progressive build up of an inertial spectrum (e.g.. imagine one does this by reducing the viscosity while maintaining the large scale structure of the flow unchanged).," Furthermore, as long as there is no change in the turbulence generating process, increasing the Reynolds number can only result in lowering the dissipation scale with respect to $l_M$, and therefore in the progressive build up of an inertial spectrum (e.g., imagine one does this by reducing the viscosity while maintaining the large scale structure of the flow unchanged)."802 It is important to notice that the estimates of Eqs. (17)), It is important to notice that the estimates of Eqs. \ref{lm}) )803 and (13)) remain valid. [or Revnolds numbers larger5 than the turbulence thireshold. as long5 as the turbulence 5generating process is unchanged.," and \ref{vm}) ) remain valid for Reynolds numbers larger than the turbulence threshold, as long as the turbulence generating process is unchanged."804 The predictions of the scaling proposed here are well supported by the available empirical and numerical evidence. as shown in Appendix A. Eqs. (17))," The predictions of the scaling proposed here are well supported by the available empirical and numerical evidence, as shown in Appendix A. Eqs. \ref{lm}) )"805 and (18)) have particularly interesting consequences for the understanding ol turbulence in Couette-Tavlor flows., and \ref{vm}) ) have particularly interesting consequences for the understanding of turbulence in Couette-Taylor flows.806 For definiteness. I will first [ocus on flows where the inner evlinder is at rest.," For definiteness, I will first focus on flows where the inner cylinder is at rest."807 As argued at the end of section ??.. [or r9Ar. the Navier-Stokes equation for Couette-Tavlor flows [Eq. (8))]," As argued at the end of section \ref{CTF}, for $r\gg\Delta r$, the Navier-Stokes equation for Couette-Taylor flows [Eq. \ref{NSCT}) )]"808 then reduces to the Navier-Stokes equation for planar Couette flows [Eq. (1))], then reduces to the Navier-Stokes equation for planar Couette flows [Eq. \ref{NSC}) )]809 and the minimal Revnolds number is constant., and the minimal Reynolds number is constant.810 However. when Avr r. the geometric terms O(u?/r)e(GNO)?/r become comparable (o the advection one on scale Ar.," However, when $\Delta811r\rightarrow r$ the geometric terms $O(w^2/r)\sim812(r\Delta\Omega)^2/r$ become comparable to the advection one on scale $\Delta r$."813" Furthermore. if at some radial location r in the flow. /e,,, remained constant when Ar>>r. Eq. (17))"," Furthermore, if, at some radial location $r$ in the flow, $Re_m$ remained constant when $\Delta r\gg r$, Eq. \ref{lm}) )"814" would imply that /y, could become arbitrarily larger than r. which makes little sense."," would imply that $l_M$ could become arbitrarily larger than $r$, which makes little sense."815 In fact. one expects that /3;xr once Ar/r exceecls some critical ratio A. (which for the time being is expected to be of order unitv). for two reasons: first.the geometric terms introduce a limiting scale (the radius r). which must be accounted for by," In fact, one expects that $l_M\propto r$ once $\Delta r/r$ exceeds some critical ratio $\Delta_c$ (which for the time being is expected to be of order unity), for two reasons: first,the geometric terms introduce a limiting scale (the radius $r$ ), which must be accounted for by"816In order to resolve the surface of the observed star during a microlensing event. the magnification pattern created by the lens needs to supply a large magnification gradient.,"In order to resolve the surface of the observed star during a microlensing event, the magnification pattern created by the lens needs to supply a large magnification gradient."817 Two such configurations meeting this requirement have been discussed extensively in the literature: a point-caustic at the angular position of a single point-like lens (2222222222) and a line-shaped fold caustic produced by a binarylens (2222222).," Two such configurations meeting this requirement have been discussed extensively in the literature: a point-caustic at the angular position of a single point-like lens \citep{WM94,NemWick94,Gould94:extsrc,BC95,BC96,Witt95,GW96,GG:detld,Heyetal2000,Hey2003} and a line-shaped fold caustic produced by a binarylens \citep{SchneiWei:QSO,SchneiWag, GG:detld,Rhie:ld,Do:SecondLD,Do:Fold,Do:FoldLD}."818 It has been pointed out by ? that fold-caustic events are more common and their observation is easier to plan. whereas close-impact events where the source transits a point caustic can provide more information.," It has been pointed out by \citet{GG:detld} that fold-caustic events are more common and their observation is easier to plan, whereas close-impact events where the source transits a point caustic can provide more information."819 However. I will argue that this apparent gain of information can usually not be realized due to potential lens binarity.," However, I will argue that this apparent gain of information can usually not be realized due to potential lens binarity."820 In contrast to fold caustics which form a generically stable singularity. point caustics are not stable and do not exist in reality.," In contrast to fold caustics which form a generically stable singularity, point caustics are not stable and do not exist in reality."821 Instead. there is always a small diamond-shaped caustic containing four cusps.," Instead, there is always a small diamond-shaped caustic containing four cusps."822 In this paper. the influence of lens binarity on the measurement of stellar. limb-darkening coefficients. and. proper motion is investigated and the arising limitations of the power of close-impact events where the source passes over a single closed caustic are discussed.," In this paper, the influence of lens binarity on the measurement of stellar limb-darkening coefficients and proper motion is investigated and the arising limitations of the power of close-impact events where the source passes over a single closed caustic are discussed."823 Sect., Sect.824 2. discusses the basics of close-impact microlensing events with the effect of source size. the potential of measuring stellar proper motion and limb darkening. and the effect of lens binarity.," \ref{sec:cie} discusses the basics of close-impact microlensing events with the effect of source size, the potential of measuring stellar proper motion and limb darkening, and the effect of lens binarity."825 Sect., Sect.826 3. shows the influence of lens binarity on the extraction of information from such events., \ref{sec:binvsld} shows the influence of lens binarity on the extraction of information from such events.827 First. the effect of lens binarity on the light curves is demonstrated by means of two illustrative examples involving K and M Bulge giants.," First, the effect of lens binarity on the light curves is demonstrated by means of two illustrative examples involving K and M Bulge giants."828 Subsequently. a simulation of data corresponding to these configurations is used to investigate the potential misestimates of parameters if lens binarity is neglected.," Subsequently, a simulation of data corresponding to these configurations is used to investigate the potential misestimates of parameters if lens binarity is neglected."829 Sect., Sect.830 4. presents the final conclusions and a summary of the results., \ref{sec:conclusions} presents the final conclusions and a summary of the results.831" As pointed out by ?.. a point-like source star at a distance 2s from the observer exhibits a magnification due to the gravitational field of a lens star with mass AZ at 24, by a factor where source and lens are separated by the angle 56p and denotes the angular Einstein radius."," As pointed out by \citet{Pac86}, a point-like source star at a distance $D_\rmn{S}$ from the observer exhibits a magnification due to the gravitational field of a lens star with mass $M$ at $D_\rmn{L}$ by a factor where source and lens are separated by the angle $u\,\theta_\rmn{E}$ and denotes the angular Einstein radius."832 The proper motion ;; of the source relative to the lens constitutes a microlensing event with the time-scale /p.= θε. for which the lens-source separation becomes," The proper motion $\mu$ of the source relative to the lens constitutes a microlensing event with the time-scale $t_\rmn{E} = \theta_\rmn{E}/\mu$ , for which the lens-source separation becomes"833"where /,,.= AR/o,.,.N is the number of stars, /! is the radius and σι, is the velocity dispersion.","where $t_{cross}= R/\sigma_v$ , $N$ is the number of stars, $R$ is the radius and $\sigma_v$ is the velocity dispersion."834 We have used the value σι 3 km ! (?).., We have used the value $\sigma_v$ = 3 km $^{-1}$ \citep{binmer}.835 The clusters were divided into regions so as to obtain a significant number of stars in each region., The clusters were divided into regions so as to obtain a significant number of stars in each region.836" For King 16, we obtained a core radius 0.59€0.24."," For King 16, we obtained a core radius $0.89 \pm 0.24$."837 We divided the cluster into three regions: core (0'—0.907). halol (0.39'—3’) and halo2 (ο)—7).," We divided the cluster into three regions: core $0'-0.89'$ ), halo1 $0.89'-3'$ ) and halo2 $3'-7')$."838" In the case of NGC 1931, we divided the cluster into three regions: halol (0!— 4), halo2 (4'— *') and halo3 (s'—12’)."," In the case of NGC 1931, we divided the cluster into three regions: halo1 $0'-4'$ ), halo2 $4'-8'$ ) and halo3 $8'-12'$ )."839" Due to the central obscuring nebula, we have no stars in the core region, and hence we excluded the same."," Due to the central obscuring nebula, we have no stars in the core region, and hence we excluded the same."840" In the case of NGC 637, we divided the cluster into three regions: core (0'—0.4). halol (0.4— 3) and halo2 (3'— 6’)."," In the case of NGC 637, we divided the cluster into three regions: core $0'-0.4'$ ), halo1 $0.4-3$ ) and halo2 $3'- 6'$ )."841 As there were no stars in the core of NGC 189 and the cluster is very small. we divided the cluster into only two regions: halol (0— 2.5') and halo2 (2.5'— 5’).," As there were no stars in the core of NGC 189 and the cluster is very small, we divided the cluster into only two regions: halo1 $0-2.5'$ ) and halo2 $2.5'-5'$ )."842 The values of 4 for different regions of the clusters are also indicative of mass seggregation and are shown in Table 5 with the mass estimatesfor each region., The values of $\chi$ for different regions of the clusters are also indicative of mass seggregation and are shown in Table \ref{dypar} with the mass estimatesfor each region.843" The mass estimates for the clusters King 16, NGC 1931, NGC 637 and NGC 189 are 1332E44. 8,,"," The mass estimates for the clusters King 16, NGC 1931, NGC 637 and NGC 189 are $1382 \pm 44 M_{\odot}$ \ref{mfk16},"844Short Waveleught (SW) camera was used. with a projected pixel size of (71118 and a field of view of 1524152 arcsec.,"Short Wavelenght (SW) camera was used, with a projected pixel size of 148 and a field of view of $\times$ 152 arcsec."845 Observations were performed through the J (A= 12h AA=0.291). H(X=1.6549: AX= 0.304) and Wy (A=2.169: AX= 0.2759) band filters.," Observations were performed through the $J$ $\lambda= 1.25 \mu$ ; $\Delta \lambda= 0.29 \mu$), $H$ $\lambda= 1.65 \mu$; $\Delta \lambda= 0.30 \mu$ ) and $K_s$ $\lambda= 2.16 \mu$; $\Delta \lambda= 0.27 \mu$ ) band filters."846" To allow for the subtraction of the variable IR sky backeround. observations 1 cach filter were split iu sequences of shorther dithered exposures with integration times of 50 sin the 7/7 aud A, baus and of 120 s in the J baud ione cach point of the dithering pattern."," To allow for the subtraction of the variable IR sky background, observations in each filter were split in sequences of shorther dithered exposures with integration times of 50 s in the $H$ and $K_s$ bands and of 120 s in the $J$ band along each point of the dithering pattern."847 The journal of 6servations is reported in Table 1., The journal of observations is reported in Table 1.848 The total integration times over all nights were 2154) s (J). 6250 s (If). and 1500s (I).," The total integration times over all nights were 3480 s $J$ ), 6250 s $H$ ), and 4500s $K_s$ )."849 For each baud. observation were taken under photomoetric conditions with a secing often better than 1700 and aimmass below 1.5.," For each band, observation were taken under photometric conditions with a seeing often better than 0 and airmass below 1.5."850 Atinospheric conditions were average with ouly the nights of February Lith. 16th. and 19th affected by a Blunidity up to1054.," Atmospheric conditions were average with only the nights of February 11th, 16th, and 19th affected by a humidity up to."851. Twilight fat fields. dark frames. as well as nuages of standard stars from the Persson e al. (," Twilight flat fields, dark frames, as well as images of standard stars from the Persson et al. ("8521998) fields. were taken daily as part of the calibration plan.,"1998) fields, were taken daily as part of the calibration plan."853 We downloaded the data from the ESO publie Science Data and we reduced/calibrated them using the updated version of the ESOppipeline*., We downloaded the data from the ESO public Science Data and we reduced/calibrated them using the updated version of the ESO.854. For each exposure sequence. single frames were registered and coadded to produce a background subtracted and cosmic-ray free image.," For each exposure sequence, single frames were registered and coadded to produce a background subtracted and cosmic-ray free image."855 We used the SLUW nuage as a relative reference frame to register the ppositiou ou the luuages., We used the 814W image as a relative reference frame to register the position on the images.856 Photometry was performed using the v2.[. which implements the “first monent? algovitlin(7).," Photometry was performed using the v2.4, which implements the “first moment” algorithm."857". In view of the nou-optimal sky couditious. we performed a photometric calibration of cach image using a set of 25 2ALASS stars as a reference,"," In view of the non-optimal sky conditions, we performed a photometric calibration of each image using a set of 25 2MASS stars as a reference."858 Our solutions turned out to be very good. with a ruis.," Our solutions turned out to be very good, with a r.m.s."859 of ~0.1 mae in the J. II aud Iss bands. respectively.," of $\sim0.1$ mag in the J, H and Ks bands, respectively."860 The resulting fluxes of source Z are J=21.53+0.07. W=20.63+0.11. Ks=20.53+0.18.," The resulting fluxes of source Z are $21.53\pm0.07$, $20.63\pm0.11$, $20.53\pm0.18$ ."861 Such results are in broad agreemoeut with and with?., Such results are in broad agreement with and with.862. The upper limits to the ciission of aare J~23.9. II22.7 and Ks21.7.," The upper limits to the emission of are $\sim23.9$, $\sim22.7$ and $\sim21.7$."863 Ou test withHST.. based ou both absolute and relative astrometry on iuultiiepoch images. firmly rules out aux physical association of Source Z with5209.," Our test with, based on both absolute and relative astrometry on multi-epoch images, firmly rules out any physical association of Source Z with."864. What is source Z?, What is source Z?865 Multicolor photometry. based. on the aand ddatasets. poiuts to an unrelated background red dwarf.," Multicolor photometry, based on the and datasets, points to an unrelated background red dwarf."866 Flux aud colors are consistent with (although slightlv redder than) au AIS star located at ~5 προ reddened by ECD-V)—0.1.," Flux and colors are consistent with (although slightly redder than) an M5 star located at $\sim5$ kpc, reddened by $\sim$ 0.1."867 We note that the uupper lits based on our 2002 observations in the R band ive not cousisteut with the source flux as measured with im 2005., We note that the upper limits based on our 2002 observations in the R band are not consistent with the source flux as measured with in 2005.868 This could be due to some intrinsic variability of the dwarf star. and/or to coufusion effects in the images. due to the PSF wines of the two much brighter stars ling a few aresec away to the South-West.," This could be due to some intrinsic variability of the dwarf star, and/or to confusion effects in the images, due to the PSF wings of the two much brighter stars lying a few arcsec away to the South-West."869 Of course. in both cases the conclusion about the non-association of source Z with wwould not change.," Of course, in both cases the conclusion about the non-association of source Z with would not change."870 Thus. iecluains. as vet. unidentified in the optical/IR. as all the other CCOs observed so fax(22777). with the ouly possible exception of the source in the Vela Jv. SNR(?).," Thus, remains, as yet, unidentified in the optical/IR, as all the other CCOs observed so far, with the only possible exception of the source in the Vela Jr. SNR."871. The upper limits to the optical/IR flux prescuted here are the deepest available so far for a member of the CCO class and corresponc to an (unabsorbed) optical to. X-rav flux ratio PA4qweΈναsear~5<LO9.," The upper limits to the optical/IR flux presented here are the deepest available so far for a member of the CCO class and correspond to an (unabsorbed) optical – to – X-ray flux ratio $F_{814W}/F_{0.3-3872keV}\, \sim 5\times10^{-6}$."873 The spectral energv distribution or lis shown in Figure 2.., The spectral energy distribution for is shown in Figure \ref{sed}.874 Such upper limits virtually rule out the possibility of any stellar companion tied to the NS in a binary At the distance of5209.. taking reddening iuto account. oulv a very low-mass star (AM~0.1 ML.) would beallowed.," Such upper limits virtually rule out the possibility of any stellar companion tied to the NS in a binary At the distance of, taking reddening into account, only a very low-mass star $M\sim0.1$ $_{\odot}$ ) would beallowed."875 It is very unlikely that a binary svstei, It is very unlikely that a binary system876 It is very unlikely that a binary svsteii, It is very unlikely that a binary system877Receutly it. has becone echuicallv feasible to observe the full 2D velocity fied (VF) of local galaxies iu optical wavebands using 1iutegral field units (IFUs) such as SAURON (e.g. Cancι ο al.,Recently it has become technically feasible to observe the full 2D velocity field (VF) of local galaxies in optical wavebands using integral field units (IFUs) such as SAURON (e.g. Ganda et al.878 2006) Fabry-Perot iuterferoimmetry (e.g. Cheniu et al., 2006) or Fabry-Perot interferometry (e.g. Chemin et al.879 2006. Carrido et al. 2002)).," 2006, Garrido et al. \cite{Garrido}) )."880 For intermedivue and lieh redshift galaxies. however. there aro bv oidrow hardly anv observational studies of 2D velocity fields available.," For intermediate and high redshift galaxies, however, there are by now hardly any observational studies of 2D velocity fields available."881 Flores et al. (, Flores et al. (8822006) ---observed the 2D velocity field of 35 ealaxies at redshift (hl cz 0.75) using FLA\ES/CIRAFFE at VLT.,2006) observed the 2D velocity field of 35 galaxies at intermediate redshift (0.4 $<$ z $<$ 0.75) using FLAMES/GIRAFFE at VLT.883 One aspect was ο Investigate the redshift evolution of the Tullv-Fisher relation., One aspect was to investigate the redshift evolution of the Tully-Fisher relation.884 A different approach. used by our eroup. was oeseuted by Ziegler et a]l. (," A different approach, used by our group, was presented by Ziegler et al. ("8852006) and I&utdenüir et al. (,2006) and Kutdemir et al. (8862007) who utilize uultiple-object spectroscopy from the VLT with differcut slit positions on cach galaxy in order ο construct he full velocitv field for each galaxy.,2007) who utilize multiple-object spectroscopy from the VLT with different slit positions on each galaxy in order to construct the full velocity field for each galaxy.887 Most of he other sticies of cistaut. faint. and stall galaxies are still based oi xit spectro scopy(e.g. Vogt 2001. Bohlin et al.," Most of the other studies of distant, faint, and small galaxies are still based on slit spectroscopy (e.g. Vogt 2001, Böhhm et al."888 2001)., 2004).889 To account fx distortions and reguaritics in the velociv fields is in oth cases critical. especially when amans at a distalit Tully-Fisher study.," To account for distortions and irregularities in the velocity fields is in both cases critical, especially when aiming at a distant Tully-Fisher study."890 Iu two receut yapers we showed that observational constraints and galaxy interacto scan severelv influence the determination of the rotation curve of observed disc ealaxies (IXapferer ct al., In two recent papers we showed that observational constraints and galaxy–galaxy interactions can severely influence the determination of the rotation curve of observed disc galaxies (Kapferer et al.891 2006. τομοσο et al.," 2006, Kronberger et al."892 2006)., 2006).893 Iu this paper we investiga eto what excut the full 2D velocity field of a galaxy cal be used o gain iuformalon on its internal kincunatic ‘sand cal LOTICC Huprove the quality of c.g. Tully-Fishe Yosudies., In this paper we investigate to what extent the full 2D velocity field of a galaxy can be used to gain information on its internal kinematics and can hence improve the quality of e.g. Tully-Fisher studies.894 TUs question 1s also nmuportaut to possibly disentanele different interaclon processes by lapping 2D velocity flelds aud to study t1011) Παρα ou galaxy evolution., This question is also important to possibly disentangle different interaction processes by mapping 2D velocity fields and to study their impact on galaxy evolution.895 We foas on the question how fje visibility of distortions depends onu the redshift of the observed. galaxy. the actual spatial resolution of the galaxy.," We focus on the question how the visibility of distortions depends on the redshift of the observed galaxy, i.e. the actual spatial resolution of the galaxy."896 For that àivestieation we place a galaxy at different redshifts aud bin the velocity according to the spatial resolution at this redshift., For that investigation we place a galaxy at different redshifts and bin the velocity according to the spatial resolution at this redshift.897 A similar study. for observed galaxies was presented by Epiuat et al. (, A similar study for observed galaxies was presented by Epinat et al. (8982006).,2006).899 Additionally to he exanunation of 2D velocity fields of intermediate redshift ealaxies frou optical spectroscopy we investigate the performance of ucar-infrarced inteeral fied spectrograplis hat are used together with adaptive optics., Additionally to the examination of 2D velocity fields of intermediate redshift galaxies from optical spectroscopy we investigate the performance of near-infrared integral field spectrographs that are used together with adaptive optics.900 As a prototype we taτο the characteristics of SINFONI at the Verv Large Telescope of the European Southern Observatory to study the velocity fields of galaxiesoO at z—2., As a prototype we take the characteristics of SINFONI at the Very Large Telescope of the European Southern Observatory to study the velocity fields of galaxies at $\sim$ 2.901 For example. CGenzel et al. (," For example, Genzel et al. ("9022006) observed the velocity field of a massive protodisc at z=2.38 deecting an ordered rotation without aux hint for a major merecr event m the svsteni.,2006) observed the velocity field of a massive protodisc at z=2.38 detecting an ordered rotation without any hint for a major merger event in the system.903 Very recently also Jesseit et al. (, Very recently also Jesseit et al. (9042007) analvsed 2D velocity fields of simulated galaxies.,2007) analysed 2D velocity fields of simulated galaxies.905 They focused on siuulated disc merger remnants and found that maux different kinematical phenomena can be observed iu the stellar velocity maps. such as kinematic musaligued discs Or couiter-rotating-cores.," They focused on simulated disc merger remnants and found that many different kinematical phenomena can be observed in the stellar velocity maps, such as kinematic misaligned discs or counter-rotating-cores."906 Fort1e analysis they also used the sleetric method of Ίντα]novi ot al. (, For the analysis they also used the kinemetric method of Krajnović et al. (90720066) as we do iu his paper.,2006) as we do in this paper.908 They did. however. uot investigate the redshift dependence of the 2D velocity fields.," They did, however, not investigate the redshift dependence of the 2D velocity fields."909 The paper is organised as follows., The paper is organised as follows.910 Iu Sect., In Sect.911 2 and 3. we describe the simulations. the interaction ecometrics. aud the wav we extract realistic 2D velocity fields from the miucrical data.," 2 and 3, we describe the simulations, the interaction geometries, and the way we extract realistic 2D velocity fields from the numerical data."912 Iu Sect., In Sect.913 the results for cdlifferent iuteraction scenarios and thencependence on the augular resolution are presented., 4 the results for different interaction scenarios and their dependence on the angular resolution are presented.914 We cud with a παν of the main conclusions iu Sect., We end with a summary of the main conclusions in Sect.915 5., 5.916 In this work we use some of the simulated svstenis presented in Kapferer et al (, In this work we use some of the simulated systems presented in Kapferer et al. (9172005). which Were subsequently used bv Ivapterer ct al. (,"2005), which were subsequently used by Kapferer et al. ("9182006) and Iroubereer et (,2006) and Kronberger et al. (9192006).,2006).920 The simmlations were carried out with theal.N-bodv/SPII code GADGET-2 developed by V. Springel(sce Spriugel 2005 for details)., The simulations were carried out with the N-body/SPH code GADGET-2 developed by V. Springel (see Springel 2005 for details).921 Iu this code the gas of the galaxies is treated bydrodvuamically andl prescriptions for cooling. star formation. stellar feedback. and ealactic winds are iuclhuded (Spriugel IIeruquist. 2003).," In this code the gas of the galaxies is treated hydrodynamically and prescriptions for cooling, star formation, stellar feedback, and galactic winds are included (Springel Hernquist, 2003)."922 The collisionless dvanizaudces of the dark iatter, The collisionless dynamics of the dark matter923from the X-ray studies of SN 1006: IXovamaetal.(1995). discovered svuchrotvon X-rays from the shells of this SNR. indicating the existence of extremely high energy electrons up to the knee energy produced by Che first order Fermi acceleration.,"from the X-ray studies of SN 1006; \citet{koyama1995} discovered synchrotron X-rays from the shells of this SNR, indicating the existence of extremely high energy electrons up to the knee energy produced by the first order Fermi acceleration."924 Further. Tanimorietal.(1998) confirmed (he presence of high energy electrons with the detection of the TeV 5-ravs. which are cosnic microwave photons up-scattered by high energy. electrons (the inverse Compton process) in the north east shell (the NE shell) of SN 1006.," Further, \citet{tanimori1998} confirmed the presence of high energy electrons with the detection of the TeV $\gamma$ -rays, which are cosmic microwave photons up-scattered by high energy electrons (the inverse Compton process) in the north east shell (the NE shell) of SN 1006."925 The combined analvsis of the svuchrotron A-ravs and inverse Compton TeV 5-ravs nicely reproduces (he observed fIux and spectra. and predicts a rather weak magnetic field of 46 μα (Tanimori )..," The combined analysis of the synchrotron X-rays and inverse Compton TeV $\gamma$ -rays nicely reproduces the observed flux and spectra, and predicts a rather weak magnetic field of 4–6 $\mu$ G \citep{tanimori1998,tanimori2001}."926 since (hese discoveries. detection of svnchrotvon N-ravs and/or TeV 5-ravs. from other shell-like SNRs has been aceumulating: G347.3-0.5 (IxovamaAluraishietal.2000:Enomoto 2002).. ROW 86 (Dambaetal.2000:Borkowski 2001b).. and G266.6—1.2 (Slaneetal.2001).," Since these discoveries, detection of synchrotron X-rays and/or TeV $\gamma$ -rays, from other shell-like SNRs has been accumulating: $-$ 0.5 \citep{koyama1997,slane1999,muraishi,enomoto}, RCW 86 \citep{bamba,borkowski2001b}, and $-$ 1.2 \citep{slane2001}."927. These discoveries provide good evidence Lor (he cosmic ray acceleration al the shocked shell of SNRs., These discoveries provide good evidence for the cosmic ray acceleration at the shocked shell of SNRs.928 The mechanism of the cosmic rav acceleration has also been studied for a long time and the most plausible process is a diffusive shock acceleration (DSA) (Bell1978:Dlandford&Ostriker1975:Eichler1987:Jones&Ellison1991:MalkovDrury 2001).," The mechanism of the cosmic ray acceleration has also been studied for a long time and the most plausible process is a diffusive shock acceleration (DSA) \citep{bell, blandford1978, drury1983,blandford1987,jones,malkov}."929. Apart from the globally successful picture of DSA. detailed but important. processes. such as the injection. magnetic field configuration. and the reflection of accelerated particles. have not vet been well understood.," Apart from the globally successful picture of DSA, detailed but important processes, such as the injection, magnetic field configuration, and the reflection of accelerated particles, have not yet been well understood."930 The spatial distribution of accelerated particles responsible for the non-thermal X-rays. max. provide Κον information on these unclear subjects.," The spatial distribution of accelerated particles responsible for the non-thermal X-rays, may provide key information on these unclear subjects."931 Previous observations. however. are limited in spatial resolution for a detailed study on Che structure of shock acceleration process and injection elliciency.," Previous observations, however, are limited in spatial resolution for a detailed study on the structure of shock acceleration process and injection efficiency."932 Although many observations aad theoretical models are made for SN 1006. these problems are still open issue Gotthelf2001:Berezhkoetal. 2002)..," Although many observations and theoretical models are made for SN 1006, these problems are still open issue \citep{reynolds1998,aharonian,vink,ellison,dyer,allen,berezhko}."933 In (his paper. we report on the first resulis of the spectral and spatial studies on the thermal and non-thermal shock structure in the NE shell of SN 1006 with 3)).," In this paper, we report on the first results of the spectral and spatial studies on the thermal and non-thermal shock structure in the NE shell of SN 1006 with \ref{analyses}) )."934 In 4.1 and$& 42. we discuss the spectral analvses and determine (he scale widths of the structures for thermal and non-thermal electrons on the base of a simple DSA with shock parallel magnetic field.," In \ref{discuss1} and \ref{discuss2}, we discuss the spectral analyses and determine the scale widths of the structures for thermal and non-thermal electrons on the base of a simple DSA with shock parallel magnetic field."935 We also derive the injection efficiency (7) of non-thermal electrons from the thermal plasma near the shock front., We also derive the injection efficiency $\eta$ ) of non-thermal electrons from the thermal plasma near the shock front.936 Based on these results. we cliscuss possible implications on the DSA process in the NE shell of SN 1006.," Based on these results, we discuss possible implications on the DSA process in the NE shell of SN 1006."937 In this paper. we assume the distance of SN 1006 to be 1.8 kpe (Green 2001)..," In this paper, we assume the distance of SN 1006 to be 1.8 kpc \citep{green}. ."938HCO* does not show an obvious trend with increasing CR rates in the high density case.,$^+$ does not show an obvious trend with increasing CR rates in the high density case.939 The HCO* abundance anti-correlates with CR rate in the low density case., The $^+$ abundance anti-correlates with CR rate in the low density case.940" It does not seem to be a tracer that can be easily used as a CR tracer, but it does provide information when used in combination with e.g. the water chemistry."," It does not seem to be a tracer that can be easily used as a CR tracer, but it does provide information when used in combination with e.g. the water chemistry."941" CO* is very irresponsive to the CR rates at high density except for very high CR rates (Z>5-107 s!),"," $^+$ is very irresponsive to the CR rates at high density except for very high CR rates $\zeta942> 5\cdot 10^{-14}$ $^{-1}$ )."943" In the low density case, N(CO*) does not show a very obvious trend."," In the low density case, $N({\rm944 CO}^+)$ does not show a very obvious trend."945pattern of variability very simular to that of (Nicdziclski1995... 199Ga. b: Wessolowski /Niedzielskà 1996: Niedzielski 19985)).,"pattern of variability very similar to that of \cite{Niedzielski95}, 1996a, b; Wessolowski Niedzielski 1996; \cite{Niedzielski99}) )."946 Stroug line-profile variability was observed. as well as apparently cvclical (according to P zx 2.667 davs) variations iu the EWs of À 1686 and À5112 (Niedzieldki 1996a)).," Strong line-profile variability was observed, as well as apparently cyclical (according to $\cal P$ $\approx$ 2.667 days) variations in the EWs of $\lambda$ 4686 and $\lambda$ 5412 \cite{Niedzielski96a}) )."947 The first claim of periodic variabiltvin with Pom 7.7 days was made by Lamontagne(1983) from an analysis of the radial velocity variations of A 1686., The first claim of periodic variabilityin with $\cal P$ $\approx$ 7.7 days was made by \cite{Lamontagnep} from an analysis of the radial velocity variations of $\lambda$ 4686.948 The first photometric ionitoriug of this object has shown to be variable. with au indication of a 6.1 day period (Aloffat Shara 1986).," The first photometric monitoring of this object has shown to be variable, with an indication of a 6.1 day period (Moffat Shara 1986)."949 Receutly Marcheuko«al.(1998a}) discussed broadband. plotometric data which revealed that also displays relatively long-term photometric variations. with a mareial evidence for à P = 1ll.6s + 0.11 dav periodicity.," Recently, \cite{Marchenko98a} discussed broadband photometric data which revealed that also displays relatively long-term photometric variations, with a marginal evidence for a $\cal P$ = 11.68 $\pm$ 0.14 day periodicity."950 As can be seen. controversy persits in the literature concerning the possible evclical nature of the variations i1.," As can be seen, controversy persits in the literature concerning the possible cyclical nature of the variations in."951 We present in this paper the results of spectroscopic aud. photometric monitoring of carried out in 1995 and 1996 aiming at shedding some elt ou this issue., We present in this paper the results of spectroscopic and photometric monitoring of carried out in 1995 and 1996 aiming at shedding some light on this issue.952 The photometric variability of has been investigated diving the interval 1996 September LSOctober 5 by use of the sinele chanucl photometer ou the 0.81 ii telescope of the Observatorio Astrouónmico Nacional at San Pedro Marrtir (Mexico)., The photometric variability of has been investigated during the interval 1996 September 18–October 5 by use of the single channel photometer on the 0.84 m telescope of the Observatorio Astronómmico Nacional at San Pedro Márrtir (Mexico).953 Two additional objects were nonitored during this observing rum. namely. and155.," Two additional objects were monitored during this observing run, namely, and."954. The nights were generally clear., The nights were generally clear.955 was observed through a narrowband ο filter centered ou 5110 ((FWIIM = 90 Aj)., was observed through a narrowband $v$ filter centered on 5140 (FWHM = 90 ).956 This filter samples a continmiuu-cdominated region of the WR spectrum., This filter samples a continuum-dominated region of the WR spectrum.957 We applied the following sequence of 60 s integration through a ddiaplvagim: sky. C3. CI. WR. CL. WR. CI. C2. «e.," We applied the following sequence of 60 s integration through a diaphragm: sky, C2, C1, WR, C1, WR, C1, C2, sky."958 The sae nearby comparison stars as used by Moffat&Shara(19586) have heen chosen., The same nearby comparison stars as used by \cite{Moffatp} have been chosen.959 These conrparison stars are simular in terms of their magnitude and colour to1: AB AVR Cl) - 0.17. ALB V|OWR Cl) = 0.17. AB (WR ο) - 0.26. ALB VP) AVR C2) = 0.9.," These comparison stars are similar in terms of their magnitude and colour to: $\Delta B$ (WR – C1) = – 0.17, $\Delta$ $B$ – $V$ ] (WR – C1) = – 0.17, $\Delta B$ (WR – C2) = – 0.26, $\Delta$ $B$ – $V$ ] (WR – C2) = – 0.19."960 An extinction coefficieut hk. = 0.20 was used throughout the data reduction., An extinction coefficient $k_v$ = 0.20 was used throughout the data reduction.961" The scatter in the (C2 C1) data for the whole dataset amounts to c = L7 µας,", The scatter in the (C2 $-$ C1) data for the whole dataset amounts to $\sigma$ = 4.7 mmag.962 The differential magnitudes quoted iu Table 1l are averaged over two consecutive cycles typically separated by about 20 minutes., The differential magnitudes quoted in Table 1 are averaged over two consecutive cycles typically separated by about 20 minutes.963 Lone-slt spectra of have been obtained during various campaigns at the Observatoire du Mount Méeeauticao and Doiinion Astroplivsical Observatory (Canada) iu 1995 October aud 1996 September., Long-slit spectra of have been obtained during various campaigns at the Observatoire du Mont Méggantic and Dominion Astrophysical Observatory (Canada) in 1995 October and 1996 September.964 Reticon spectra were also obtained at DAO iu 1996 November., Reticon spectra were also obtained at DAO in 1996 November.965 The 1996 campaign at the Observatoire di Mout Móeeauticao was coordinated to support the photometric campaign described above., The 1996 campaign at the Observatoire du Mont Méggantic was coordinated to support the photometric campaign described above.966 Table 2 lists the mode of observation. he dates of the spectroscopic observations. the interval of the observations du lehoceutric Julian dates. the observatory name. the mmmber of CCD spectra obtained. he selected spectral domain. the reciprocal dispersion of he spectra. and the typical signal-to-noise ratio (S/N) iu he contimmuu.," Table 2 lists the mode of observation, the dates of the spectroscopic observations, the interval of the observations in heliocentric Julian dates, the observatory name, the number of CCD spectra obtained, the selected spectral domain, the reciprocal dispersion of the spectra, and the typical signal-to-noise ratio (S/N) in the continuum."967 The spectra were reduced using the data reduction packages., The spectra were reduced using the data reduction packages.968 The bias and sky subtraction. flat-field clivision. removal of cosmic rav eveuts. extraction of je spectra. and waveleneth calibration were carried out in the usual wax.," The bias and sky subtraction, flat-field division, removal of cosmic ray events, extraction of the spectra, and wavelength calibration were carried out in the usual way."969 Spectra of calibration laps were taken iuuediatelv before aud after the stella: exposure., Spectra of calibration lamps were taken immediately before and after the stellar exposure.970 The stellar spectra were subsequently continui normalized by fitting a low-order Legeudre polvuomial to carefully selected. line-free regions., The stellar spectra were subsequently continuum normalized by fitting a low-order Legendre polynomial to carefully selected line-free regions.971 Iu order to minimize the spurious velocity shifts induced by an inevitably iuperfec wavelength calibration. the spectra were coaligued iu velocity space by using the interstellar doublet AADSOU. 5896 as fiducial marks.," In order to minimize the spurious velocity shifts induced by an inevitably imperfect wavelength calibration, the spectra were coaligned in velocity space by using the interstellar doublet $\lambda$$\lambda$ 5890, 5896 as fiducial marks."972 When not available. the doublet AA3931. 3968 or the diffuse interstellar baie at 1501 wwere used.," When not available, the doublet $\lambda$$\lambda$ 3934, 3968 or the diffuse interstellar band at 4501 were used."973 A treud for a svstematic shift of the zero point of the wavelength scale has been correcte by redshifting most of the spectra by an average value of 35 aus i, A trend for a systematic shift of the zero point of the wavelength scale has been corrected by redshifting most of the spectra by an average value of 35 km $^{-1}$.974 Echelle spectra have been obtained diving the period 1996 September 1619 with the Echelle spectrograph (Levine&Chakrabarty 1995)) on the 2.1 1m telescope of theSan Pedro Márrtir Observatory., Echelle spectra have been obtained during the period 1996 September 16–19 with the Echelle spectrograph \cite{Levine}) ) on the 2.1 m telescope of theSan Pedro Márrtir Observatory.975 The UCL camera aud a 1021 « 102 coater CCD-Tek chip have been used., The UCL camera and a 1024 $\times$ 1024 coated CCD-Tek chip have been used.976" The selected erating (300 lines 1) vields a reciprocal dispersion of 0.16 and 0.23 | at Πς and Πα, respectively,"," The selected grating (300 lines $^{-1}$ ) yields a reciprocal dispersion of 0.16 and 0.23 $^{-1}$ at $\gamma$ and $\alpha$, respectively."977 The spectra cover 27 orders aud span the spectral range 3720-6900Α., The spectra cover 27 orders and span the spectral range 3720-6900.978. The reduction procedure. (bias subtraction. division by a normalized flat field. removing of scattered light. extraction of the orders) was carried out using the reduction tasks iu the packageechelle.," The reduction procedure (bias subtraction, division by a normalized flat field, removing of scattered light, extraction of the orders) was carried out using the reduction tasks in the package."979 Comparison spectra of ThAx lamps have been used for thewavelength calibration., Comparison spectra of Th–Ar lamps have been used for thewavelength calibration.980 The typical accuracy of the waveleneth calibration can be judged by the dispersion iu the heliocentric radial velocities of the interstellar line AbBSOU: στ 2laus +., The typical accuracy of the wavelength calibration can be judged by the dispersion in the heliocentric radial velocities of the interstellar line $\lambda$5890: $\sigma$ $\approx$ 2 km $^{-1}$ .981 The iustrmuental respouse has bee-, The instrumental response has been982the hyvdrodynamie calculations is concerted.,the hydrodynamic calculations is concerted.983 Phe smoothing lengths in VINE are initially set to a constant value of fron.0.8 kpe at the time of the magnetic field inclusion., The smoothing lengths in $\textsc{Vine}$ are initially set to a constant value of $h_\mathrm{gas}\approx 0.3$ kpc at the time of the magnetic field inclusion.984 Figs., Figs.985 7 and S show simulations starting [rom the same initial conditions as before., \ref{eulerVINE} and \ref{eulerGAD} show simulations starting from the same initial conditions as before.986 However. this time the evolution of the magnetic field was Followed using the Euler potentials.," However, this time the evolution of the magnetic field was followed using the Euler potentials."987 Again. we show magnetic field energies ancl gas densities.," Again, we show magnetic field energies and gas densities."988 This time the amplification of the magnetic field energy. in 10 spiral arms is only three orders of magnitude for both Lgimulations with VINE and CAbGET. with both showing a remarkably similar evolution.," This time the amplification of the magnetic field energy in the spiral arms is only three orders of magnitude for both simulations with $\textsc{Vine}$ and $\textsc{Gadget}$, with both showing a remarkably similar evolution."989 Phe most notable cüfference to 1e simulations with direct magnetic field treatment shown in Fig., The most notable difference to the simulations with direct magnetic field treatment shown in Fig.990 5. and 6 is at the centre of the galaxies. where in 10 direct. simulations the field amplification was strongest.," \ref{indVINE} and \ref{indGAD} is at the centre of the galaxies, where in the direct simulations the field amplification was strongest."991 With Euler potentials the magnetic field grows mostly in the Esoral arms of the galaxy. (see also Fig. 13))., With Euler potentials the magnetic field grows mostly in the spiral arms of the galaxy (see also Fig. \ref{Bwithr}) ).992 Since the magnetic fields in our simulations are passive. re density. profiles (Figs.," Since the magnetic fields in our simulations are passive, the density profiles (Figs."993 2 and 3)) of the disc are the same for all runs., \ref{sigma_gas} and \ref{sigma_disc}) ) of the disc are the same for all runs.994 Ehus. the dillerent profiles of the magnetic field energy cannot be traced back to the density. profiles.," Thus, the different profiles of the magnetic field energy cannot be traced back to the density profiles."995 In fact. it is the numerical V-B which presumably causes the high amplification of the magnetic field at the centre in simulations with the direct. magnetic field treatment.," In fact, it is the numerical $\nabla\cdot \textbf{B}$ which presumably causes the high amplification of the magnetic field at the centre in simulations with the direct magnetic field treatment."996 Fig., Fig.997 10 shows the radial profile of the numerical -[VB|/|B]| at time /zz1.5 Gye for simulations using direct magnetic Ποιά treatment (blue for simulations without applying the viscosity limiter and orange where the limiter was applied) and Euler potentials (black) performed using GADGET (solid lines) and. VINE (dotted line)., \ref{divergence_radius} shows the radial profile of the numerical $h\cdot|\nabla\cdot \textbf{B}|/|\textbf{B}|$ at time $t\approx 1.5$ Gyr for simulations using direct magnetic field treatment (blue for simulations without applying the viscosity limiter and orange where the limiter was applied) and Euler potentials (black) performed using $\textsc{Gadget}$ (solid lines) and $\textsc{Vine}$ (dotted line).998 Utilising the direct magnetic field description. the numerical V: is highest at small raclii. and much larger than for the EulerDB potential formalism.," Utilising the direct magnetic field description, the numerical $\nabla\cdot \textbf{B}$ is highest at small radii, and much larger than for the Euler potential formalism."999 As will be discussed in the following section. high V:B corresponds to high amplification of the magnetic field.," As will be discussed in the following section, high $\nabla\cdot \textbf{B}$ corresponds to high amplification of the magnetic field."1000 Fig., Fig.1001 11. shows the magnetic field vectors for the normal resolution VINE simulation utilising Euler potentials at the ime fz0.9 Civr., \ref{vectors} shows the magnetic field vectors for the normal resolution $\textsc{Vine}$ simulation utilising Euler potentials at the time $t\approx 0.9$ Gyr.1002 This time the colours correspond to the gas density on a logarithmic scale from 0.3:10.5 to 2:3107AJ. . overplotted with the field. vectors.," This time the colours correspond to the gas density on a logarithmic scale from $0.3\cdot 10^{-3}$ to $2.3\cdot 10^3 M_\odot$ $^{-3}$ , overplotted with the field vectors."1003" The length. / of he vectors is normalised to the initial value ancl clisplaved ogarithmically as f=3:log(CD/Du). ic. /=0 corresponds o DzzDy or smaller. /2110 D22-Du. 1—210 De5D, and ἐξ310 D—10:By."," The length $l$ of the vectors is normalised to the initial value and displayed logarithmically as $l=3\cdot \log(B/B_0)$, i.e. $l=0$ corresponds to $ B\approx B_0$ or smaller, $l=1$ to $B\approx 2\cdot B_0$, $l=2$ to $B\approx 5\cdot B_0$ and $l=3$ to $B=10\cdot B_0$."1004 The magnetic field. lines follow he spiral structure of the gas., The magnetic field lines follow the spiral structure of the gas.1005 They. have been. amplified »v contraction in regions of higher density and restructured w dillerential rotation of the galaxy., They have been amplified by contraction in regions of higher density and restructured by differential rotation of the galaxy.1006 Their orientation is caused by the motion of the gas., Their orientation is caused by the motion of the gas.1007 These characteristics are very similar to typical observations of magnetic fields. in ealactic discs (e.g. Fig. 1))., These characteristics are very similar to typical observations of magnetic fields in galactic discs (e.g. Fig. \ref{M51}) ).1008 Qualitatively. this behaviour is the same for all simulations using both codes.," Qualitatively, this behaviour is the same for all simulations using both codes."1009 Only the central region in simulations using direct magnetic eld treatment shows chaotic orientation of the magnetic field. lines. indicating artificial amplification of the magnetic field. due to high numerical V-D.," Only the central region in simulations using direct magnetic field treatment shows chaotic orientation of the magnetic field lines, indicating artificial amplification of the magnetic field due to high numerical $\nabla\cdot \textbf{B}$."1010 ., Figs.10115 (6)) and 7 (8)). respectively. reveal the dilferences in the magnetic field amplification for the direct. magnetic field. treatment ancl the Euler potentials formalism: Using the direct description. the amplification of themagnetic field energy in the spiral arms is higher by at least two orders of magnitude. and at the centre even more than six orders of magnitude compared to the Euler potentials method.," \ref{indVINE} \ref{indGAD}) ) and \ref{eulerVINE} \ref{eulerGAD}) ), respectively, reveal the differences in the magnetic field amplification for the direct magnetic field treatment and the Euler potentials formalism: Using the direct description, the amplification of themagnetic field energy in the spiral arms is higher by at least two orders of magnitude, and at the centre even more than six orders of magnitude compared to the Euler potentials method."1012 This difference is probably caused by the numerical V:B in these simulations (Fig. 10)).," This difference is probably caused by the numerical $\nabla\cdot \textbf{B}$ in these simulations (Fig. \ref{divergence_radius}) ),"1013 but possibly also by the fact that field winding is not traced bevond a certain evolutionary state in the Euler potentials formulation. (see section 3.1.6))., but possibly also by the fact that field winding is not traced beyond a certain evolutionary state in the Euler potentials formulation (see section \ref{EULER}) ).1014 Since the Euler potentials are free from physical divergence by construction (Le. the divergence is zero to measurements errors). the numerical divergence in simulations using the Euler potentials is due to the SPL derivative approximation when calculating the magnetic field. from the potentials (Eq. 18)).," Since the Euler potentials are free from physical divergence by construction (i.e. the divergence is zero to measurements errors), the numerical divergence in simulations using the Euler potentials is due to the SPH derivative approximation when calculating the magnetic field from the potentials (Eq. \ref{euler}) )."1015 In this sense. the numerical divergence. found in simulations using Euler potentials reflects the ability. of SPLL operators to measure the &radient of a curl to zero.," In this sense, the numerical divergence found in simulations using Euler potentials reflects the ability of SPH operators to measure the gradient of a curl to zero."1016 Thus. the fact that V:B is higher bv approximately one order of magnitude in the disc (i.e. within z5 to 15 kpe) and. by several orders of magnitude at the centre (Fig. 10)).," Thus, the fact that $\nabla\cdot \textbf{B}$ is higher by approximately one order of magnitude in the disc (i.e. within $\approx 5$ to 15 kpc) and by several orders of magnitude at the centre (Fig. \ref{divergence_radius}) ),"1017 oesumably causes the dilferent magnetic field amplification in these simulations., presumably causes the different magnetic field amplification in these simulations.1018 This is the case at least in the disc region. where the winding of the field is not strong chough o constrain the Euler potentials formulation.," This is the case at least in the disc region, where the winding of the field is not strong enough to constrain the Euler potentials formulation."1019 To get a better idea of the influence of numerical VD on the amplification of the magnetic filed. we have »erformed simulations applying magnetic field smoothing. a echnique allowing for reduction of small scale Iuctuations and therefore. also the numerical divergence (2)).," To get a better idea of the influence of numerical $\nabla\cdot \textbf{B}$ on the amplification of the magnetic filed, we have performed simulations applying magnetic field smoothing, a technique allowing for reduction of small scale fluctuations and therefore also the numerical divergence \citealp{GadgetMHD}) )."1020 Within his method. the magnetic fieldis smoothed periodically as suggested by 7..," Within this method, the magnetic fieldis smoothed periodically as suggested by \citet{Borve2001}. ."1021 Fig., Fig.1022 12. shows again the magnetic field energies and gas densities for a GADGET simulation starting rom the same initial conditions as before anc without, \ref{smoothGAD} shows again the magnetic field energies and gas densities for a $\textsc{Gadget}$ simulation starting from the same initial conditions as before and without1023the visual extinction of the stellar light if standard gas-to-dust mass ratios are assumed.,the visual extinction of the stellar light if standard gas-to-dust mass ratios are assumed.1024" This has been interpreted as being due to dust-depleted accretion streams falling from the disk to the star, thus absorbing X-rays from the underlying corona (Güdeletal.,2007b)."," This has been interpreted as being due to dust-depleted accretion streams falling from the disk to the star, thus absorbing X-rays from the underlying corona \citep{guedel07b}."1025". It is possible that in these cases the soft jet component is discernible simply because the stellar component is absorbed at low X-ray energies, while in less strongly accreting (and therefore less absorbed) objects the jet component is outshone by the coronal spectrum."," It is possible that in these cases the soft jet component is discernible simply because the stellar component is absorbed at low X-ray energies, while in less strongly accreting (and therefore less absorbed) objects the jet component is outshone by the coronal spectrum."1026" Four objects in our sample have been interpreted as showing soft X-ray jets: DG Tau, DP Tau, HN Tau, and also Sz 102, the latter revealing only a soft component, the hard component possibly being completely absorbed by a near-edge-on disk al., 2009b)."," Four objects in our sample have been interpreted as showing soft X-ray jets: DG Tau, DP Tau, HN Tau, and also Sz 102, the latter revealing only a soft component, the hard component possibly being completely absorbed by a near-edge-on disk \citep{guedel09b}."1027. Three of these objects show very high Liwem while for DP Tau an upper limit is available.," Three of these objects show very high $L_{\rm [Ne\,II]}$, while for DP Tau an upper limit is available."1028" We find no specific trend for the four objects tighter than what is shown in Figs. 2,, 3,"," We find no specific trend for the four objects tighter than what is shown in Figs. \ref{fig2}, \ref{fig3},"1029 or 4.., or \ref{fig4}.1030" However, except for Sz 102 where only a soft component is present, we have adopted the hard component as representing the stellar radiation."," However, except for Sz 102 where only a soft component is present, we have adopted the hard component as representing the stellar radiation."1031" The luminosities in the components are, 9.6x1075 erg s!, 1.5x10?? erg s, 4.0x10? erg sl, and 8.9x1025 erg s! for DG Tau, HN Tau, DP Tau, and Sz 102, respectively (see Güdeletal. 2009b,, and this paper for Sz 102)."," The luminosities in the components are, $9.6\times 10^{28}$ erg $^{-1}$, $1.5\times 10^{29}$ erg $^{-1}$, $4.0\times 10^{27}$ erg $^{-1}$, and $8.9\times 10^{28}$ erg $^{-1}$ for DG Tau, HN Tau, DP Tau, and Sz 102, respectively (see \citealt{guedel09b}, , and this paper for Sz 102)."1032" The corresponding Liner values are, respectively, 6.1x103 erg s!, 5.6x1078 erg s!, <2.6x10°8 erg s, and 1.7x10? erg s!, not suggesting any correlation."," The corresponding $L_{\rm [Ne\,II]}$ values are, respectively, $6.1\times 10^{29}$ erg $^{-1}$, $5.6\times 10^{28}$ erg $^{-1}$, $<2.6\times 10^{28}$ erg $^{-1}$, and $1.7\times 10^{29}$ erg $^{-1}$, not suggesting any correlation."1033" However, it may be interesting to note that MossLxsoft=(30,1.2,<0.15)x10?!Mo yr! erg s! for DG Tau, HN Tau, and DP Tau, respectively, which roughly correlates with Ίο=(24,0.6,0.06)x10?? erg s! and with Lien]=(61,5.6,<2.6)x10?5 erg s! although the statistics are too small for significant conclusions."," However, it may be interesting to note that $\dot{M}_{\rm loss}L_{\rm X, soft} = (30, 1.2, <0.15)\times 10^{21}~M_{\odot}$ $^{-1}$ erg $^{-1}$ for DG Tau, HN Tau, and DP Tau, respectively, which roughly correlates with $L_{{\rm [O\,I],}f} = (24, 0.6, 0.06)\times 10^{30}$ erg $^{-1}$ and with $L_{\rm [Ne\,II]} = (61, 5.6, <2.6)\times 10^{28}$ erg $^{-1}$ although the statistics are too small for significant conclusions."1034" Although jets may produce both [Νεπ]] emission and very soft X-rays independently by shock heating, the latter may also contribute to ionization and heating of the predominantly cool jet gas locally, thus adding to π]] emission."," Although jets may produce both ] emission and very soft X-rays independently by shock heating, the latter may also contribute to ionization and heating of the predominantly cool jet gas locally, thus adding to ] emission."1035" Our finding that π]] emission is enhanced in ΟΤΤΟ with jets, supported by spatially resolved π]] emission from the T Tau jet system (vanBoekeletal.,2009),, finds a parallel in observations of infrared rovibrational H» emission from similar targets."," Our finding that ] emission is enhanced in CTTS with jets, supported by spatially resolved ] emission from the T Tau jet system \citep{boekel09}, finds a parallel in observations of infrared rovibrational $_2$ emission from similar targets."1036" The Hz v=1-0S(1) line at 2.12 um shares excitation conditions with ΠΠ], i.e., excitation in warm gas heated by UV, X-rays, or shocks, where emission from the disk gas is expected to be confined within 30-50 AU (Becketal.2008 and references therein)."," The $_2$ $v = 1-0~S(1)$ line at 2.12 $\mu$ m shares excitation conditions with ], i.e., excitation in warm gas heated by UV, X-rays, or shocks, where emission from the disk gas is expected to be confined within 30–50 AU \citealt{beck08} and references therein)."1037" Hy rovibrational emission has been detected from many CTTS, but again, the emission source is often resolved."," $_2$ rovibrational emission has been detected from many CTTS, but again, the emission source is often resolved."1038" In the Becketal.(2008) high-resolution study of six CTTS (including DG Tau, T Tau, and RW Aur from our sample), the Hz emission morphologies, its detection beyond 50 AU from the star, excitation temperatures exceeding 1800 K, kinematics measureed in the features, and the consistency with calculated shock models suggest that the bulk of the H» emission is shock-excited emission from jets and outflows rather than emission from disk gas excited by short-wavelength flux from the central star."," In the \citet{beck08} high-resolution study of six CTTS (including DG Tau, T Tau, and RW Aur from our sample), the $_2$ emission morphologies, its detection beyond 50 AU from the star, excitation temperatures exceeding 1800 K, kinematics measureed in the features, and the consistency with calculated shock models suggest that the bulk of the $_2$ emission is shock-excited emission from jets and outflows rather than emission from disk gas excited by short-wavelength flux from the central star."1039 A comparison of their Hy map of the T Tau system with the spatial distribution of π]] emission reported by vanBoekeletal.(2009) indeed suggests some common emission sources., A comparison of their $_2$ map of the T Tau system with the spatial distribution of ] emission reported by \citet{boekel09} indeed suggests some common emission sources.1040" On the other hand, our finding of a correlation between uJ] luminosity and stellar X-ray luminosity specifically for objects with jets suggests an important role of the stellar short-wavelength radiation in exciting [Νεπ]] in the jet gas, at least relatively close to the star (see also estimates in vanBoekelal.2009 for the jet system in T Tau detected in π]] out to about 2 arcsec)."," On the other hand, our finding of a correlation between ] luminosity and stellar X-ray luminosity specifically for objects with jets suggests an important role of the stellar short-wavelength radiation in exciting ] in the jet gas, at least relatively close to the star (see also estimates in \citealt{boekel09} for the jet system in T Tau detected in ] out to about 2 arcsec)."1041 Explicit theoretical calculations by Shang(2010) for the X-wind model of a YSO jet irradiated by X-rays supports this conclusion further.," Explicit theoretical calculations by \citet{shang10}1042 for the X-wind model of a YSO jet irradiated by X-rays supports this conclusion further."1043" Our correlations show systematic scatter of typically an order of magnitude in Liner, regardless of the parameter against which the latter is plotted."," Our correlations show systematic scatter of typically an order of magnitude in $L_{\rm [Ne\,II]}$, regardless of the parameter against which the latter is plotted."1044" Although some stellar or disk parameters, such as Lx or Macc are themselves subject to considerable measurement error, the scatter in Liner clearly requires further systematic effects."," Although some stellar or disk parameters, such as $L_{\rm X}$ or $\dot{M}_{\rm acc}$ are themselves subject to considerable measurement error, the scatter in $L_{\rm [Ne\,II]}$ clearly requires further systematic effects."1045 One possibility is that several parameters considered here matter in concert., One possibility is that several parameters considered here matter in concert.1046 We have specifically investigated the correlations with theproduct of some parameters with Lx in an attempt to show that X- irradiation is one important factor to produce [Νοπ]] emission., We have specifically investigated the correlations with theproduct of some parameters with $L_{\rm X}$ in an attempt to show that X-ray irradiation is one important factor to produce ] emission.1047" No decisive improvement of the correlations was found, however."," No decisive improvement of the correlations was found, however."1048" On the other hand, we have ignored a number of parameters thatmay influence π]] emission."," On the other hand, we have ignored a number of parameters thatmay influence ] emission."1049" In particular, we have not"," In particular, we have not"1050that both GWB-eencrated residuals and the intrinsic timing noise are stochastic Gaussian processes. then we can represent them by the (nn) coherence matrices: with the total coherence matrix given by The timine-residuals are then distributed as a multidimensional Gaussian: where P denotes the probability. distribution of the timing-residuals.,"that both GWB-generated residuals and the intrinsic timing noise are stochastic Gaussian processes, then we can represent them by the $(n \times n)$ coherence matrices: with the total coherence matrix given by The timing-residuals are then distributed as a multidimensional Gaussian: where $P$ denotes the probability distribution of the timing-residuals."1051 To be able to use Eq. € 2))), To be able to use Eq. \ref{eq:gaussian}) )1052 we (1) be able to evaluate the GWD-induced: coherence matrix from the theory. as a function. of variables that parametrise the CWD spectrum. and (2) introduce wellkmotivatecl parametrization of the pulsar timing noise.," we (1) be able to evaluate the GWB-induced coherence matrix from the theory, as a function of variables that parametrise the GWB spectrum, and (2) introduce well-motivated parametrization of the pulsar timing noise."1053 In this work. the spectral density of the stochastic GA background is taken to be a power law (222?) where ον represents the spectral density. zd is the CAV amplitude. f is the CAV frequency. ancl 5 is an exponent characterising the GWB spectrum.," In this work, the spectral density of the stochastic GW background is taken to be a power law \citep{Phinney, Jaffe, Wyithe, Maggiore}1054 where $S_h$ represents the spectral density, $A$ is the GW amplitude, $f$ is the GW frequency, and $\gamma$ is an exponent characterising the GWB spectrum."1055 I£ the GW3B is dominated by the supermassive black hole binaries. then ~=7/3 (Phinney 2001).," If the GWB is dominated by the supermassive black hole binaries, then $\gamma=7/3$ (Phinney 2001)."1056 This definition is equivalent to the use of the characteristic strain as defined in ?:: with=12a., This definition is equivalent to the use of the characteristic strain as defined in \citet{Jenet-2006}: with $\gamma = 1 - 2\alpha$.1057" The CWD-induced coherence matrix is then given by Llere ay, is the gcometric factor given by where 6,5 is the angle between pulsar e and pulsar ο (?).. τςΌπίϊω Wü) Uis the gamma function. and. fj is the low eut-olf frequency. chosen so that ή is much greater than the duration of the PPA operation."," The GWB-induced coherence matrix is then given by Here $\alpha_{ab}$ is the geometric factor given by where $\theta_{ab}$ is the angle between pulsar $a$ and pulsar $b$ \citep{Hellings}, $\tau=2\pi\left(t_{ai}-t_{bj}\right)$ , $\Gamma$ is the gamma function, and $f_L$ is the low cut-off frequency, chosen so that $1/f_L$ is much greater than the duration of the PTA operation."1058 Introducing f; is a mathematical necessity. since otherwise the GWDB-induced correlation function would diverge.," Introducing $f_L$ is a mathematical necessity, since otherwise the GWB-induced correlation function would diverge."1059 However. we show below that the low-frequeney part of the GAB is indistinguishable from an extra spin-down of all pulsars which we alreacly correct for. and that our results do not depend on the choice of fj provided that fir«x1.," However, we show below that the low-frequency part of the GWB is indistinguishable from an extra spin-down of all pulsars which we already correct for, and that our results do not depend on the choice of $f_L$ provided that $f_L\tau\ll 1$."1060 The pulsar timing noise is assumed to be Gaussian. with a certain functional form of the power spectrum.," The pulsar timing noise is assumed to be Gaussian, with a certain functional form of the power spectrum."1061 The true profile of the millisecond pulsar timing noise spectrum. is not well-known at present time., The true profile of the millisecond pulsar timing noise spectrum is not well-known at present time.1062 The timing residuals of the most precisely observed: pulsars indicate that pulsar timing noise has a white and. poorly-constrained red. component (J. Verbiest and €i. Hobbs. private communications).," The timing residuals of the most precisely observed pulsars indicate that pulsar timing noise has a white and poorly-constrained red component (J. Verbiest and G. Hobbs, private communications)."1063 For the purposes of this paper we will always choose the spectra to be of the same functional form for all pulsars. but this is not an inherent limitation of the algorithm.," For the purposes of this paper we will always choose the spectra to be of the same functional form for all pulsars, but this is not an inherent limitation of the algorithm."1064 We consider 3 cases of pulsar timing noise (1) White (lat) (2) Lorentzian (3) Power-law Obviously. one could also consicer a timing noise which is a superposition of these components: we do not do this at this exploratory stage.," We consider 3 cases of pulsar timing noise (1) White (flat) (2) Lorentzian (3) Power-law Obviously, one could also consider a timing noise which is a superposition of these components; we do not do this at this exploratory stage."1065" LE we choose the pulsar timing noise spectrum to be white. with an amplitude AY. the resulting correlation matrix becomes: The Lorentzian spectrum is a red spectrum with a typical frequeney that determines the redness of the timing nolse: which vields the following correlation matrix: where fo isa typical freequeney and iN, is theamplitude."," If we choose the pulsar timing noise spectrum to be white, with an amplitude $N_a$, the resulting correlation matrix becomes: The Lorentzian spectrum is a red spectrum with a typical frequency that determines the redness of the timing noise: which yields the following correlation matrix: where $f_0$ is a typical frequency and $N_a$ is theamplitude."1066" ὃν using a power law spectral density with amplitude AN, and spectral index σαν one gets a timine-noise coherence matrix analogous to the one in Iq. (8)):"," By using a power law spectral density with amplitude $N_a$ and spectral index $\gamma_a$, one gets a timing-noise coherence matrix analogous to the one in Eq. \ref{eq:CGW}) ):"1067 The method: described. in this report is based. upon a Bayesian approach to the parameter inference., The method described in this report is based upon a Bayesian approach to the parameter inference.1068 The general idea of the method is to (a) assume that the physical processes which produce the timing-residuals can be characterised by several parameters. and (b). use. the Daves theorem to derive. from. the measured. cata the probability distribution of the parameters of our interest.," The general idea of the method is to (a) assume that the physical processes which produce the timing-residuals can be characterised by several parameters, and (b) use the Bayes theorem to derive from the measured data the probability distribution of the parameters of our interest."1069 In our case. we assume that the timing residuals are created by (1) the GAB: we parametrise it by its amplitude 24 and slope 5. às in equation (6))," In our case, we assume that the timing residuals are created by (1) the GWB; we parametrise it by its amplitude $A$ and slope $\gamma$ , as in equation \ref{eq:spectraldensity})"1070 In our case. we assume that the timing residuals are created by (1) the GAB: we parametrise it by its amplitude 24 and slope 5. às in equation (6)).," In our case, we assume that the timing residuals are created by (1) the GWB; we parametrise it by its amplitude $A$ and slope $\gamma$ , as in equation \ref{eq:spectraldensity})"1071ttelescope images in two passhands. far-UV (FUV)) aud near-UV (NEV) (Martinetal.2005).,"telescope images in two passbands, far-UV ) and near-UV ) \citep{mar05}."1072. The ppasshands are aand the photometric system is described in Hewettal.(2006)., The passbands are and the photometric system is described in \citet{hew06}.1073. The description of the ssurvev is eiven idu Lawrenceetal.(2007)., The description of the survey is given in \citet{law07}.1074 Alodel magnitudes. as defined bySDSS.. are not computed by audUlIDSS.," Model magnitudes, as defined by, are not computed by and."1075. Therefore. we use Petrosian maguitudes (Petrosiau1976). for aand Wrou-like elliptical aperture magnitudes (INrou1980) for suce Petrosian mnasuitudes are not available in the ccatalogue.," Therefore, we use Petrosian magnitudes \citep{pet76} for and Kron-like elliptical aperture magnitudes \citep{kro80} for since Petrosian magnitudes are not available in the catalogue."1076 The majority of galaxies iu our sample are not large iu angular size. aud so the differeuce between these magnitudes should not be siguiicaut.," The majority of galaxies in our sample are not large in angular size, and so the difference between these magnitudes should not be significant."1077 We exclude oohjects which have been debleuded because of a known error in the pipeline that results in erroneous Petrosian uaenitudes for these objects(Smithetal.2009)., We exclude objects which have been deblended because of a known error in the pipeline that results in erroneous Petrosian magnitudes for these objects \citep{smi09}.1078 Photometric data were obtained from online catalogue:μα via SOL (Structured. Query Lanenage) queries throug[um he CCatalogue Archive Server the ABDNDultinission Archive at STScI (MAST)CAS!°.. and he WWECAAL Science Archive.," Photometric data were obtained from online catalogues via SQL (Structured Query Language) queries through the Catalogue Archive Server, the Multimission Archive at STScI (MAST), and the WFCAM Science Archive."1079"(WSA)9., The UV. and jezr-IR. data were obtained by cerossauatchiug the thost galaxy coordinates with the aand ccatalogues using ah” ssearch radius.", The UV and near-IR data were obtained by cross-matching the host galaxy coordinates with the and catalogues using a search radius.1080 Of the 305 thost galaxies. 198 (65%)) have inuatehes and 178 (58%)) have inatclies within. while 127 )) lave matches in th. aandUIKIDSS.," Of the 305 host galaxies, 198 ) have matches and 178 ) have matches within, while 127 ) have matches in both and."1081. We do not require every galaxy to have photometry iu all 11 bands(FOTW.NUV.. vjhk)).," We do not require every galaxy to have photometry in all 11 bands, )."1082 The addition of UV data helps to coustrain age. metallicity. aud receut star formation. while near-IR data probe the older stellar populations that compose a large portion of the mass.," The addition of UV data helps to constrain age, metallicity, and recent star formation, while near-IR data probe the older stellar populations that compose a large portion of the mass."1083 For example. adding ddata to ddata has been shown to ereatlv improve estimates of dust optical depth aud star formation rate 2005).," For example, adding data to data has been shown to greatly improve estimates of dust optical depth and star formation rate \citep{sal05}."1084 The distance modulus for a particular iiu the nunodelis given by where wy (stretch parameter). e (color). and imp (apparent B-baud magnitude at peak) are obtained from ffor cach bby fitting its light curve: a and 2 are cocficicuts which we asstuue to be coustaut: aud AL is the absolute magnitude.," The distance modulus for a particular in the model is given by where $x_1$ (stretch parameter), $c$ (color), and $m_B$ (apparent $B$ -band magnitude at peak) are obtained from for each by fitting its light curve; $\alpha$ and $\beta$ are coefficients which we assume to be constant; and $M$ is the absolute magnitude."1085 The distance modulus along with à aud > are determined from the output of musing the program ApJ}). which is part of the ppackage.," The distance modulus along with $\alpha$ and $\beta$ are determined from the output of using the program ), which is part of the package."1086 ls able to caleulate a and .} independent of cosmology bv nüuiuizmg the scatter im the IIubble relation in sanall redshift bins., is able to calculate $\alpha$ and $\beta$ independent of cosmology by minimizing the scatter in the Hubble relation in small redshift bins.1087 Values of à and . in this work are computed from the sample of tthat pass the lieht-curve cuts iu Section 2.1 and which are cither spectroscopicall-confunnied or photometrically-typed— and lave lost redshifts., Values of $\alpha$ and $\beta$ in this work are computed from the sample of that pass the light-curve cuts in Section \ref{LCcuts} and which are either spectroscopically-confirmed or photometrically-typed and have host redshifts.1088 —We find the best-fit values to be a=0.121 and |j=2.82. and use these to obtain the distance modulus.jpx.," We find the best-fit values to be $\alpha = 0.121$ and $\beta = 2.82$, and use these to obtain the distance modulus,."1089. The IIubble Constant Gvhich is degenerate with AL) is effectively a coustaut offset to aand is an input toSALT2mu: we choose fy=70 km Ἐ t., The Hubble Constant (which is degenerate with $M$ ) is effectively a constant offset to and is an input to; we choose $H_0 = 70$ km $^{-1}$ $^{-1}$.1090 We define IIubble residuals as UR = pigx-pre.. where Hs the distance modulus obtained from elt curves via aand Hs the distance modulus calculated from the redshift of he and the best-fit cosmologv.," We define Hubble residuals as HR $\equiv$ $-$, where is the distance modulus obtained from light curves via and is the distance modulus calculated from the redshift of the and the best-fit cosmology."1091 The best-fit cosmology rere is determined by phased on the first-vear ssanaple (I&essloeretal.200923)... 7 0.735.," The best-fit cosmology here is determined by based on the first-year sample \citep{kes09a}, i.e. $\Omega_\mathrm{M} = 0.274,\ \Omega_\Lambda = 0.735$ ."1092 A wwith a UR >0 siguifies that it is fainter than expected for the best-fit cosmology even after correcting for lelt-curve shape., A with a HR $> 0$ signifies that it is fainter than expected for the best-fit cosmology even after correcting for light-curve shape.1093" Tere it is useful to define ""underluuiuous? to refer to wwith IIR. >0 and voverlunineus” to refer to wwith UR <0."," Here it is useful to define “underluminous"" to refer to with HR $> 0$ and “overluminous” to refer to with HR $< 0$."1094 Exrors in IIR. are derived by adding the OYTOYS Ol aand im quadrature. where the errors on aare caleulated as [Ce|το)plzmrl2.," Errors in HR are derived by adding the errors on and in quadrature, where the errors on are calculated as $[\mu(z+z_{err})-\mu(z-z_{err})]/2$."1095 Stellar population svuthesis (SPS) codes are commonly used to create model templates of galaxies based ou stellar evolution calculations with the goal of inferring ealaxv properties such as mass. age. metallicity. aud star formation.," Stellar population synthesis (SPS) codes are commonly used to create model templates of galaxies based on stellar evolution calculations with the goal of inferring galaxy properties such as mass, age, metallicity, and star formation."1096 We use the Flexible Stellar Population Svuthesis code vv2.1) developed by Conroyctal.(2009). and updated in Conrov&πια(2010) to generate spectral energv distributions (SEDs) of composite stellar populations (CSPs)., We use the Flexible Stellar Population Synthesis code v2.1) developed by \citet{con09} and updated in \citet{con10} to generate spectral energy distributions (SEDs) of composite stellar populations (CSPs).1097 lis simular to codes such as Bruzual&Charlot(2003) , is similar to codes such as \citet{bc03} 1098"with matter density parameter in the range €,€ [0.2,0.4], M€[10!!,105]Μο A, and z€[0,10], themaximal error is ~1.8% with a mean error of ~0.4%..","with matter density parameter in the range $\Omega_\mm\in[0.2,0.4]$ , $M\in[10^{11},10^{15}]\ M_\odot\ h^{-1}$ and $z\in[0,10]$, themaximal error is $\sim$ with a mean error of $\sim$."1099" A similar functional dependence can be found for A,(M,z)."," A similar functional dependence can be found for $\Delta_\vv(M,z)$."1100 Only a small correction term has to be added to arrive at a satisfactory accuracy., Only a small correction term has to be added to arrive at a satisfactory accuracy.1101" We find with a=0.3819, b=0.5379, c=0.7589, and d= 107."," We find with $a=0.3819$, $b=0.5379$, $c=0.7589$, and $d=3.456\times10^{-4}$ ."1102" In the same range as above, the maximal error is~5% with a mean error of ~1%..In Fig."," In the same range as above, the maximal error is$\sim$ with a mean error of $\sim$.In Fig."1103" [// we plot both 6, and A, as a function of the initial ellipticity e andprolaticity p centered around their expectation values given by Eq.", \ref{fig:influenceEP} we plot both $\delta_\cc$ and $\Delta_\vv$ as a function of the initial ellipticity $e$ andprolaticity $p$ centered around their expectation values given by Eq.1104 for three different cosmologies., for three different cosmologies.1105" For increasing e and decreasing p, both parameters grow qualitatively in the same way as already reported by ? (cf."," For increasing $e$ and decreasing $p$, both parameters grow qualitatively in the same way as already reported by \citet{Sheth2001} (cf."1106 their Fig., their Fig.1107 1)., 1).1108 Quantitative deviations arise from the differences in the applied algorithm as discussed in Sect. .2]., Quantitative deviations arise from the differences in the applied algorithm as discussed in Sect. \ref{subsec:parameters}.1109" For a given mass and virialisation redshift, the initial overdensity for the EdS universe is larger compared to both ACDM and OCDM due to a shorter physical time interval that corresponds to the same redshift interval, resulting in a larger (e) andc, but also in larger curvatures of 6, and A, with respect to e and p."," For a given mass and virialisation redshift, the initial overdensity for the EdS universe is larger compared to both $\Lambda$ CDM and OCDM due to a shorter physical time interval that corresponds to the same redshift interval, resulting in a larger $\langle e \rangle$ and$\sigma_e$, but also in larger curvatures of $\delta_\cc$ and $\Delta_\vv$ with respect to $e$ and $p$."1110" These are the sources of the larger error in the approximation (€)=E((e),(p)) discussed in Sect. 2.3}."," These are the sources of the larger error in the approximation $\langle\xi\rangle\approx\xi(\langle e \rangle,\langle p\rangle)$ discussed in Sect. \ref{subsec:epIni}."1111" Since the redshift-time relation is not very different between ACDM and OCDM, the dependences of ὃς and A, on e and p are comparable."," Since the redshift-time relation is not very different between $\Lambda$ CDM and OCDM, the dependences of $\delta_\cc$ and $\Delta_\vv$ on $e$ and $p$ are comparable."1112" Using Eq.(29).,"," Using Eq.,"1113" we are able to construct the mass function of dark-matter haloes using the extended Press-Schechter formalism developed by ? and ?,, which is based on the first- distribution of the densitycontrast 6 as a function of the “time variable"" S=a?(M)."," we are able to construct the mass function of dark-matter haloes using the extended Press-Schechter formalism developed by \citet{Bond1991} and \citet{Lacey1993}, which is based on the first-upcrossing distribution of the densitycontrast $\delta$ as a function of the “time variable” $S\equiv\sigma^2(M)$ ."1114 We shall proceed similarly as ?? and define the scaled variable v=DNIS to derive the mass function for our standard ACDM cosmology.," We shall proceed similarly as \citet{Sheth1999,Sheth2002} and define the scaled variable $\nu\equiv\delta_\mathrm{c,sph}^2/S$ to derive the mass function for our standard $\Lambda$ CDM cosmology."1115" As ? pointed out, expressing the first-upcrossing distribution f as a function of v has the advantage that it is only necessary to calculate f(v) for a barrier of height B(v,z) at one arbitrary redshift to infer the mass function n(M) atany other redshift by a simple rescaling."," As \citet{Sheth2002} pointed out, expressing the first-upcrossing distribution $f$ as a function of $\nu$ has the advantage that it is only necessary to calculate $f(\nu)$ for a barrier of height $B(\nu,z)$ at one arbitrary redshift to infer the mass function $n(M)$ atany other redshift by a simple rescaling."1116" For a given first-upcrossing distribution f(v), the differential mass function can be calculated using the relation where py is the background density of the Universe."," For a given first-upcrossing distribution $f(\nu)$, the differential mass function can be calculated using the relation where $\rho_\mathrm{b}$ is the background density of the Universe."1117" First, we want to find an accurate fit to the first-upcrossing distribution of a moving barrier which is given by the mass-dependent linear overdensity parameter of the ellipsoidal collapse, (see Eq. 9p."," First, we want to find an accurate fit to the first-upcrossing distribution of a moving barrier which is given by the mass-dependent linear overdensity parameter of the ellipsoidal collapse, (see Eq. \ref{eq:fitDeltaC}) )."1118" The parameter 6¢,sph is evaluated at z,=0."," The parameter $\delta_\mathrm{c,sph}$ is evaluated at $z_\vv=0$."1119" We ran one million random walks and recorded the first-upcrossing values for v€[0.01,20] in 100 equidistant bins in logarithmic space."," We ran one million random walks and recorded the first-upcrossing values for $\nu\in[0.01,20]$ in 100 equidistant bins in logarithmic space."1120" The resulting distribution ν/(ν) is nicely expressed by the function Thus, our suggested fitting formula is a mixture of the functional forms proposed by ? and ?.."," The resulting distribution $\nu f(\nu)$ is nicely expressed by the function Thus, our suggested fitting formula is a mixture of the functional forms proposed by \citet{Sheth1999} and \citet{Sheth2002}."1121" The remaining best-fit parameters are A=0.357, p=0.212 and a=1.171.The result is shown in Fig.[8]. "," The remaining best-fit parameters are $A=0.357$, $p=0.212$ and $a=1.171$.The result is shown in Fig. \ref{fig:firstUpDist}. ."1122"Second, to find a viable mass function from the first-upcrossing distribution, we proceed as ? and ?,, normalise f(v) to unity and rescale the variable a such that we are in agreement with the standard ? massfunction and a mass function based on N-body simulations proposed by ?.."," Second, to find a viable mass function from the first-upcrossing distribution, we proceed as \citet{Sheth1999} and \citet{Sheth2001}, normalise $f(\nu)$ to unity and rescale the variable $a$ such that we are in agreement with the standard \citeauthor{Sheth1999} massfunction and a mass function based on $N$ -body simulations proposed by \citet{Courtin2010}."1123" The latter is based on a first-upcrossing distribution that has the same functional form as that proposed by?,, but slightly different best-fit parameters, withA= 0.348, à= 0.695, and p= 0.1."," The latter is based on a first-upcrossing distribution that has the same functional form as that proposed by\citet{Sheth1999},, but slightly different best-fit parameters, with$\tilde{A}=0.348$ , $\tilde{a}=0.695$ , and $\tilde{p}=0.1$ ."1124" Note that in their definition of v, the linear density contrast ó;,p, has to be taken at collapse."," Note that in their definition of $\nu$ , the linear density contrast $\delta_\mathrm{c,sph}$ has to be taken at ."1125. Normalisingthe first-upcrossing distribution based on the moving barrier of our ellipsoidal-collapse model to unity yieldsa rescaled parameter A—A’= 1.364A.," Normalisingthe first-upcrossing distribution based on the moving barrier of our ellipsoidal-collapse model to unity yieldsa rescaled parameter $A\rightarrow A'=1.364\,A$ ."1126 We compare the resulting mass function with those by ? and ? for three different redshifts in Fig.[J]., We compare the resulting mass function with those by \citet{Sheth1999} and \citet{Courtin2010} for three different redshifts in Fig. \ref{fig:massFunctions}.1127 The parameter a was rescaled by a>a’=0.625 a.," The parameter $a$ was rescaled by $a\rightarrow a'=0.625\,a$ ."1128 Deviations from the ? mass function at, Deviations from the \citeauthor{Sheth1999} mass function at1129"CCD stellar photometry in two voung open star clusters Basel 4 and NGC 7067 aiming to investigate the cluster's oie parameters (c.g. reddening. distance and age). mass ""unction and mass segregation etc.","CCD stellar photometry in two young open star clusters Basel 4 and NGC 7067 aiming to investigate the cluster's basic parameters (e.g. reddening, distance and age), mass function and mass segregation etc."1130 The existing basic informations on both the clusters are given in Table 1., The existing basic informations on both the clusters are given in Table 1.1131 The an of the paper is as follows., The plan of the paper is as follows.1132 In Sec., In Sec.1133 2 we summarize he previous studies of Basel 4 anc NGC 7067. while Sec.," 2 we summarize the previous studies of Basel 4 and NGC 7067, while Sec."1134 3 is dedicated on the observation and. data recluction strategies., 3 is dedicated on the observation and data reduction strategies.1135 Sec., Sec.1136 4 deals with the determination of clusters oic parameters as well as detail study of interstellar extinction. mass function and mass segregation in the clusters under study.," 4 deals with the determination of clusters basic parameters as well as detail study of interstellar extinction, mass function and mass segregation in the clusters under study."1137 Finally. Sec.," Finally, Sec."1138 5 summarizes our findings.4:, 5 summarizes our findings.:1139 This cluster was studied by Svolopoulos (1965) whotographically first in IU system., This cluster was studied by Svolopoulos (1965) photographically first in RGU system.1140 According to him the ocation of this cluster coincides with spiral arm. |ELE which could be expected. — if existing at all at a similar distance., According to him the location of this cluster coincides with spiral arm +III which could be expected $-$ if existing at all $-$ at a similar distance.1141 In any case. it dis remarkable that tvpical representatives of he galactic disk population are located: so far out in the direction of the galactic anticenter.," In any case, it is remarkable that typical representatives of the galactic disk population are located so far out in the direction of the galactic anticenter."1142" Ee classified this cluster as a Lil 2m. In addition to this. he also concluded: that Basel dis 10° ves old. and has total apparent ciamoeter of , .4 at a distance. of⋅ 5.9."," He classified this cluster as a III 2m. In addition to this, he also concluded that Basel 4 is $\times$ $^{7}$ yrs old, and has total apparent diameter of $^{\prime}$ .4 at a distance of 5.9."1143 ⊳∖To our knowledge no other studies. ave been carried out. so7067:: Vhis cluster was first studied by Becker (1963)., To our knowledge no other studies have been carried out so: This cluster was first studied by Becker (1963).1144 lt is à poor voung open cluster lving in Cygnus. spiral arm., It is a poor young open cluster lying in Cygnus spiral arm.1145 Lt was again revisited by Becker (1965) and indicated hat the earliest. spectral type of the cluster member. is 90.5., It was again revisited by Becker (1965) and indicated that the earliest spectral type of the cluster member is b0.5.1146 11ο also estimated the cluster angular diameter οἱ 2']. which corresponds to a linear diameter of 2.6. pe.," He also estimated the cluster angular diameter of $^\prime$ .1, which corresponds to a linear diameter of 2.6 pc."1147 Hassan (1973) also studied this cluster photoelectricallv and derived. a distance of about 44 Ixpe having E((D1)=0.83 mag and age less than 10 vears.," Hassan (1973) also studied this cluster photoelectrically and derived a distance of about 4.4 Kpc having $E(B-V) =11480.83$ mag and age less than $10^{7}$ years."1149 Dias et. al. (, Dias et al. (11502002) mentioned a distance of 1.3 Ixpe for this cluster.,2002) mentioned a distance of 1.3 Kpc for this cluster.1151 The distance determination to the cluster is thus quite uncertain., The distance determination to the cluster is thus quite uncertain.1152 We used CCD imaging to obtain CBV. Johnson and Ri Cousins photometry of the stars in the region of the open clusters Basel 4 and NGC 7067 on 02/03 Jan 2000 and 11/12 Oct 2001 respectively., We used CCD imaging to obtain $UBV$ Johnson and $RI$ Cousins photometry of the stars in the region of the open clusters Basel 4 and NGC 7067 on 02/03 Jan 2000 and 11/12 Oct 2001 respectively.1153 The cata were obtained using 2A CCD system at the [7/13 C'assegrain focus of the I04-cm Sampurnanand telescope of the State Observatory. Naini Tal.," The data were obtained using $\times$ 2K CCD system at the f/13 Cassegrain focus of the 104-cm Sampurnanand telescope of the State Observatory, Naini Tal."1154 Log of CCD observations is given in Table 2., Log of CCD observations is given in Table 2.1155" ""Phe 07.36/pixel. plate scale. resulted in a [eld of view of 125.3. 127.3.", The $^{\prime\prime}$ .36/pixel plate scale resulted in a field of view of $^{\prime}$ $\times$ $^{\prime}.3$.1156" ""Phe read-out noise and gain of the CCD are 5.3 6. and 10 6. /ADU respectively.", The read-out noise and gain of the CCD are 5.3 $^{-}$ and 10 $^{-}$ /ADU respectively.1157 For the accurate photometric measurements of fainter stars. 2 to 3 deep exposures were taken in cach passband.," For the accurate photometric measurements of fainter stars, 2 to 3 deep exposures were taken in each passband."1158 Furthermore. observations were taken in 2.2 pixel binning mode to improve the S/N ratio.," Furthermore, observations were taken in $\times$ 2 pixel binning mode to improve the S/N ratio."1159 An identification map of cluster aud ield regions for both the clusters are shown in Fig 1., An identification map of cluster and field regions for both the clusters are shown in Fig 1.1160 Besides hem. a number of standard star field: were also observed or calibration purposes.," Besides them, a number of standard star field were also observed for calibration purposes."1161 We observed. M67 (open cluster) and eld | 051 of Landolt’ (1992) for. calibrating Basel 4 and NGC 7067 respectively., We observed M67 (open cluster) and field $+$ 051 of Landolt (1992) for calibrating Basel 4 and NGC 7067 respectively.1162 The V. mag range of stars used for calibration is 19 mag in M67 and 16 mag in | 051 while the (V.1) colour range is Ld mag in M67 and 2.0 in |051., The $V$ mag range of stars used for calibration is $-$ 13 mag in M67 and $-$ 16 mag in $+$ 051 while the $(V-I)$ colour range is $-$ 1.1 mag in M67 and $-$ $-$ 2.0 in $+$ 051.1163 Thus. he standard stars in these fields provide a good magnitude and colour coverage. essential to obtain reliable photometric ransformations.," Thus, the standard stars in these fields provide a good magnitude and colour coverage, essential to obtain reliable photometric transformations."1164 The standard field are also observed. in UDVRE at dillerent airmasses to obtain a reliable estimate of the atmospheric extinction coelIicients., The standard field are also observed in $UBVRI$ at different airmasses to obtain a reliable estimate of the atmospheric extinction coefficients.1165 For correcting the nas level to the image. a number of bias frame were taken during the observations while for the flat Geld correction. a number of [at frames were taken on the twilight skv in cach ilter.," For correcting the bias level to the image, a number of bias frame were taken during the observations while for the flat field correction, a number of flat frames were taken on the twilight sky in each filter."1166 The CCD images were processed using IRAP data reduction package., The CCD images were processed using IRAF data reduction package.1167 Then. for a given filter. frame of the same exposure time were combined into one. to improve the statistics of the faintest) stars.," Then, for a given filter, frame of the same exposure time were combined into one, to improve the statistics of the faintest stars."1168 Instrumental magnitucles were derived through Point Spread. Function (PSL) fitting using DAOPLIOT (Stetson 1987) within MIDAS., Instrumental magnitudes were derived through Point Spread Function (PSF) fitting using DAOPHOT (Stetson 1987) within MIDAS.1169 During the process of determining. PSE. we used. several well isolated stars to construct a single PSP for the entire [rame on cach exposure.," During the process of determining PSF, we used several well isolated stars to construct a single PSF for the entire frame on each exposure."1170 The bright stars were measured on the frames with short exposure times. as they were saturated in the longer exposure frames.," The bright stars were measured on the frames with short exposure times, as they were saturated in the longer exposure frames."1171 For transforming the instrumental magnitude to the standard magnitude. the photometric calibration equations are as n=l|O404001L(0.053:0.022(€.—DO.5ON b=B|4A39+001(00240.01)(2V)0:36X r=]408£0.01(001EO.0DCD.V)|O2BN r=|4000.01.(0.0220.01)(V—A)OTS ," For transforming the instrumental magnitude to the standard magnitude, the photometric calibration equations are as $u=U+6.40\pm0.01-(0.03\pm0.02)(U-B)+0.59X$ $b=B+4.39\pm0.01-(0.02\pm0.01)(B-V)+0.36X$ $v=V+4.08\pm0.01-(0.01\pm0.01)(B-V)+0.23X$ $r=R+4.00\pm0.01-(0.02\pm0.01)(V-R)+0.18X$ "1172the standard model is a 20 maimain sequence star that has gone through a wind mass loss of 2A... left a neutron star of 1.4A... thus ejecting about 16 wwith a progenitor racius of 3x10 om.,"the standard model is a 20 main sequence star that has gone through a wind mass loss of 2, left a neutron star of 1.4, thus ejecting about 16 with a progenitor radius of $\times10^{13}$ cm."1173 The energetics of the simulation has a total energv of 1x10°! eres or 1 [oe (ten to the fiftv one eres) and ejects 0.07 79Ni mixed throughout the 6 IIIe core., The energetics of the simulation has a total energy of $\times10^{51}$ ergs or 1 foe (ten to the fifty one ergs) and ejects 0.07 $^{56}$ Ni mixed throughout the 6 He core.1174 The standard model is similar to SN 1987À except for the larger radius ancl less extensive mixing., The standard model is similar to SN 1987A except for the larger radius and less extensive mixing.1175 ln this paper the parameter space around this model is In (his paper I show the results of how varving each parameter can inlluence (he shape and absolute magnitude of Type 11 light curves out to 400 days., In this paper the parameter space around this model is In this paper I show the results of how varying each parameter can influence the shape and absolute magnitude of Type II light curves out to 400 days.1176" The five parameters explored in this study are: the progenitor radius. envelope mass. explosion energy. ""Ni mass. ancl? Ni mixing."," The five parameters explored in this study are; the progenitor radius, envelope mass, explosion energy, $^{56}$ Ni mass, and $^{56}$ Ni mixing."1177 All light curves calculated in this paper use the numerically evolved 20 AZ. mmain sequence model with a 6 helium. core from Wooslev aud. Weaver (19380)., All light curves calculated in this paper use the numerically evolved 20 $M{_\odot}$ main sequence model with a 6 helium core from Woosley and Weaver (1980).1178 The envelope parameters. mass and racius. are varied using homology transformations (section 2).," The envelope parameters, mass and radius, are varied using homology transformations (section 2)."1179 The models are (hen exploded ina one dimensional. [Inx-Iimited hyedrocdynamical eode with a simple prescription for deposition (section 3).," The models are then exploded in a one dimensional, flux-limited hydrodynamical code with a simple prescription for gamma-ray deposition (section 3)."1180""" The bolometric light. curves are calculated and. plotted on an absolute magnitude scale (section 4).", The bolometric light curves are calculated and plotted on an absolute magnitude scale (section 4).1181 The results are discussed in section For the initial models of all explosions I use the 6 M... helium core from Woosley. aud Weaver (L980) .. originally a 20 A. main sequence star.," The results are discussed in section For the initial models of all explosions I use the 6 $M{_\odot}$ helium core from Woosley and Weaver (1980) \nocite{ww80}, originally a 20 $M{_\odot}$ main sequence star."1182 The envelope mass and radius are subsequently modilied in a svstematie wav., The envelope mass and radius are subsequently modified in a systematic way.1183 A total of 8 models were constructed that are identified by a specific mass and radius (Table D)., A total of 8 models were constructed that are identified by a specific mass and radius (Table I).1184 In this study three different envelope Inasses were used producing total masses of 8. 12. and 16 M...," In this study three different envelope masses were used producing total masses of 8, 12, and 16 $M{_\odot}$."1185 For each envelope mass. three different radii where used 43 R. (3x107 em). 430 R. (3.x10/7 em). and 4300 R. (3xLol cm).," For each envelope mass, three different radii where used 43 $_\odot$ $3\times10^{12}$ cm), 430 $_\odot$ $3\times10^{13}$ cm), and 4300 $_\odot$ $3\times10^{14}$ cm)."1186 The original Il rich envelope was modified by homologous transformations to give the various masses and radii (Schwarzschild1958:Chandrasekhar1939).," The original H rich envelope was modified by homologous transformations to give the various masses and radii \citep{s58,c39}."1187. For a homologous transformation in radius: where Ris the old radius. R is the new radius. and .r is the percent changed.," For a homologous transformation in radius: where R is the old radius, $'$ is the new radius, and $x$ is the percent changed."1188 For a homologous transformation in mass :, For a homologous transformation in mass :1189density. Z plasma temperature. £j heat flux. & plasma hermal conductivity and 5=5/3.,"density, $T$ plasma temperature, $F_c$ heat flux, $\kappa$ plasma thermal conductivity and $\gamma = 5/3$."1190 The flare is assumed ο occur on a solar-like star. with solar surface eravity aud radius.," The flare is assumed to occur on a solar-like star, with solar surface gravity and radius."1191 Plasma thermal conduction is isotropic., Plasma thermal conduction is isotropic.1192 Radiative osses are those of Ravimoud and Suuith (1977) but are set o zero for Tz:2«10! K. ie. for chromospherie plasma.," Radiative losses are those of Raymond and Smith (1977) but are set to zero for $T \approx 2\times119310^4$ K, i.e. for chromospheric plasma."1194" The heating term generally consists of a steady heating erui which iuaintaius the προς, atinosphere im hermal equilibrium and of a transient term. which rigecrs the flare."," The heating term generally consists of a steady heating term which maintains the unperturbed atmosphere in thermal equilibrium and of a transient term, which triggers the flare."1195 In our simulations. the steady heating das been set to zero both in the chromosphere aud elsewhere. since the transicut heating is switched on. in order to describe the free plasa cooling with no interference from any heating source.," In our simulations, the steady heating has been set to zero both in the chromosphere and elsewhere, since the transient heating is switched on, in order to describe the free plasma cooling with no interference from any heating source."1196 The trausicut heating term has been assumed as a separable function of space aud time: The spatial distribution of the heating is a 2-D circular Caussian: As for the temporal evolution ο) the impulsive beating has been asstmed to be switched ou at t=0 (0)= 0). kept constant (g(t)= 1) for aeiven time lapse O<fxty and then switched off g(f>ty)= 0.," The transient heating term has been assumed as a separable function of space and time: The spatial distribution of the heating is a 2-D circular Gaussian: As for the temporal evolution g(t) the impulsive heating has been assumed to be switched on at t=0 $g(0)=0$ ), kept constant $g(t)=1$ ) for agiven time lapse $0 \leq t \leq t_H$ and then switched off $g(t >1197t_H ) = 0$ ."1198"bv the color correction factor of 1.09 to place the data on a constant wf, scale. which is also the appropriate color correction (within 254)) for a wide range of possible ealaxy SEDs (see SSC web pages for calibration and color-correction details).","by the color correction factor of 1.09 to place the data on a constant $\nu f_\nu$ scale, which is also the appropriate color correction (within ) for a wide range of possible galaxy SEDs (see SSC web pages for calibration and color-correction details)."1199 Tn comparison. the calibration correction adopted here is lavecr than the calibration adopted for the xFLS analysis (Fraver ct al.," In comparison, the calibration correction adopted here is larger than the calibration adopted for the xFLS analysis (Frayer et al."1200 2006)., 2006).

Showing the first 1,200 of 10429 lines. Download the file for the rest.