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These perturbations around. the equilibrium seed. the parametric instabilitv: we would otherwise need to wait for the instability to grow [rom machine roundolf error. | These perturbations around the equilibrium seed the parametric instability; we would otherwise need to wait for the instability to grow from machine roundoff error. |
The vertical shearing motion e,—ὃς 15 the local manifestation of a large scale warping motion in a Ixeplerian disc. anc we shall loosely refer to it as “the warp. | The vertical shearing motion $v_x =
S z$ is the local manifestation of a large scale warping motion in a Keplerian disc, and we shall loosely refer to it as “the warp”. |
The boundary. conditions are as follows. | The boundary conditions are as follows. |
We integrate the basic equations (1)) ina rectangular box of length £, in the raclial direction. £, in the azimuthal direction. and των in the vertical direction. | We integrate the basic equations \ref{LOCMODEOM}) ) in a rectangular box of length $L_x$ in the radial direction, $L_y$ in the azimuthal direction, and $L_z$ in the vertical direction. |
The grid is centred on pr=y=20. | The grid is centred on $x = y = z = 0$. |
The radial boundaries (at.= +£4,/2) are subject tothe “shearing box” boundary conditions (e.g.. Llawley. Cammie. Balbus 1995). | The radial boundaries (at $x = \pm L_x/2$ ) are subject tothe “shearing box” boundary conditions (e.g., Hawley, Gammie, Balbus 1995). |
These require that [or f=veoosp. where or,—ory,|ελα. | These require that for $f = v_x, \delta v_y, v_z, \rho$, where $\delta v_y \equiv v_y +
q\Omega x$. |
The azimuthal boundaries (yo=#L,/2) are. periodic. | The azimuthal boundaries $y = \pm L_y/2$ ) are periodic. |
The vertical boundaries are reflecting. | The vertical boundaries are reflecting. |
The numerical model is integrated. using a version of the ZEUS algorithm. (Stone Norman 1992). | The numerical model is integrated using a version of the ZEUS algorithm (Stone Norman 1992). |
ZEUS is an explicit. finite-dilference. operator-split method. | ZEUS is an explicit, finite-difference, operator-split method. |
The variables lic on a staggered mesh. so that scalar quantities are zone-centred. while vector quantities are centred on zone faces. | The variables lie on a staggered mesh, so that scalar quantities are zone-centred, while vector quantities are centred on zone faces. |
It conserves mass and linear momentum to machine rouncolf error. | It conserves mass and linear momentum to machine roundoff error. |
The ZEUS algorithm has been extensively tested (Stone Norman 1992: see. e.g. Stone Llawley LOOT for a discussion of other applications). | The ZEUS algorithm has been extensively tested (Stone Norman 1992; see, e.g., Stone Hawley 1997 for a discussion of other applications). |
Our implementation has also been tested on a number of standard problems. | Our implementation has also been tested on a number of standard problems. |
It can. for example. reproduce standard linear results such as sound wave propagation. and standard. non-linear results such as the Sod shock tube. | It can, for example, reproduce standard linear results such as sound wave propagation, and standard non-linear results such as the Sod shock tube. |
One relevant test of our shearing box implementation is uniform epievclie motion. | One relevant test of our shearing box implementation is uniform epicyclic motion. |
This can be initiated by setting Ds=const. in the initial conditions. | This can be initiated by setting $v_x = {\rm
const.}$ in the initial conditions. |
Phe uid ought then to execute epievelie oscillations with period 2x/(O0(424)!>), | The fluid ought then to execute epicyclic oscillations with period $2\pi/(\Omega (4 - 2 q)^{1/2})$. |
This test. is non-trivial: for a naive implementation of the Coriolis and tidal forces the amplitude of the epievele will erow or decav. | This test is non-trivial: for a naive implementation of the Coriolis and tidal forces the amplitude of the epicycle will grow or decay. |
“Phis is because the time-step determined from the Courant. condition depends on epicyclie phase. | This is because the time-step determined from the Courant condition depends on epicyclic phase. |
Growth or decav of the oscillation can be prevented. by using “potential velocities” (y,=VE|405 and vy,=viU|02/4 rather than i.0, in the time-step condition. | Growth or decay of the oscillation can be prevented by using “potential velocities” $v_{p,x} \equiv
\sqrt{v_x^2 + 4 v_y^2}$ and $v_{p,y} \equiv \sqrt{v_y^2 + v_x^2/4}$ rather than $v_x,v_y$ in the time-step condition. |
AX second. relevant test is the evolution of a. linear amplitude bending wave. | A second, relevant test is the evolution of a linear amplitude bending wave. |
This test was. performed.in axisvmmoetrv. | This test was performedin axisymmetry. |
We set £,.£.=(10.10077. and the numerical resolution n.n.=64.64. | We set $L_x,L_z =
(10,10) H$, and the numerical resolution $n_x,n_z = 64,64$. |
We introduced a bending wave in the initial conditions with wavelength νε. | We introduced a bending wave in the initial conditions with wavelength $L_x$. |
Linear theory gives w=0.73400 (notice that this is significantly cülferent [rom ©. so pressure gradients play an important role in the mode dynamics: the mode is not a mere sloshing up and down of the [uid in a fixed potential). | Linear theory gives $\omega = 0.7340\Omega$ (notice that this is significantly different from $\Omega$, so pressure gradients play an important role in the mode dynamics; the mode is not a mere sloshing up and down of the fluid in a fixed potential). |
Phe measured mode frequeney (interval between successive zero crossings of the vertical velocity at a fixed point in the ΠΠ isa=0.73360. which cdillers from the true value by 1: part in 25107. indicating satisfactory performance on the test. | The measured mode frequency (interval between successive zero crossings of the vertical velocity at a fixed point in the fluid) is $\omega =
0.7336\Omega$, which differs from the true value by $1$ part in $2
\times 10^{3}$, indicating satisfactory performance on the test. |
The numerical model has seven important parameters: LoLg.Lionsny.ns. and 5. | The numerical model has seven important parameters: $L_x,L_y,L_z,n_x,n_y,n_z,$ and $S$. |
Before studying the elfect. of these parameters we will consider a single. fiducial run in detail. | Before studying the effect of these parameters we will consider a single, fiducial run in detail. |
The fiducial run has an initial amplitude S= ©. | The fiducial run has an initial amplitude $S = \Omega$ . |
The physical size of the box is LL,L.= (4.16.6)41. | The physical size of the box is $L_x,L_y,L_z = (4, 16, 6) H$ . |
The rellecting vertical boundaries. are therefore. 3. scale heights away from the mid-plane. | The reflecting vertical boundaries are therefore 3 scale heights away from the mid-plane. |
Phe numerical resolution | The numerical resolution |
determine the location of the snow line. | determine the location of the snow line. |
50 lar. the snow line location in an optically thick disk has been theoretically obtained by ID (radial) or I+1D (radial and vertical) disk structure caleulations (e.g.. Cassen 1994: Slepinski 1993). | So far, the snow line location in an optically thick disk has been theoretically obtained by 1D (radial) or 1+1D (radial and vertical) disk structure calculations (e.g., Cassen 1994; Stepinski 1998). |
The latest studies on the snow line location with a detailed disk structure caleulation were done by Davis (2005) ancl Garaud Lin (2007). | The latest studies on the snow line location with a detailed disk structure calculation were done by Davis (2005) and Garaud Lin (2007). |
Thev considered. the stellar radiation flux ancl (he viscous dissipation of gas as the main heating sources in a disk. ancl obtained disk temperature by solving the detailed radiative energy. transfer. | They considered the stellar radiation flux and the viscous dissipation of gas as the main heating sources in a disk, and obtained disk temperature by solving the detailed radiative energy transfer. |
They revealed that the snow line migrates inward as the disk evolves and the mass accretion rate decreases. because (he viscous dissipation of gas. which is the main heating source in the disk. reduces as the disk evolves. | They revealed that the snow line migrates inward as the disk evolves and the mass accretion rate decreases, because the viscous dissipation of gas, which is the main heating source in the disk, reduces as the disk evolves. |
Davis (2005) showed that the snow line reaches about 0.6 AU. which is the minimum radius in his ealeulations. | Davis (2005) showed that the snow line reaches about 0.6 AU, which is the minimum radius in his calculations. |
Similarly. Giraud Lin (2007) found (hat in the later phase. the snow line migrates outwardly since the stellar radiation penetrates deeper into the disk interior as the disk becomes optically thinner aud rises the (emperature. | Similarly, Garaud Lin (2007) found that in the later phase, the snow line migrates outwardly since the stellar radiation penetrates deeper into the disk interior as the disk becomes optically thinner and rises the temperature. |
One important point of their results is that the snow line comes inside the Earth orbit: ihe minimiun heliocentric distance of the snow line is about 0.6 AU (Davis 2005: Giraud Lin 2007). | One important point of their results is that the snow line comes inside the Earth orbit; the minimum heliocentric distance of the snow line is about 0.6 AU (Davis 2005; Garaud Lin 2007). |
If sufficiently large bodies like planetesimals were formed when the snow line was located at such a small heliocentric distance. Earth would have been lormec with icy planetesimals. | If sufficiently large bodies like planetesimals were formed when the snow line was located at such a small heliocentric distance, Earth would have been formed with icy planetesimals. |
Then. Earth should presently contain a comparable amount of water with silicate and iron. | Then, Earth should presently contain a comparable amount of water with silicate and iron. |
This conflicts with the eurrent. water content in Earth. | This conflicts with the current water content in Earth. |
In order to make clear the important inconsistency in planet formation. we investigate the detailed thermal evolution of protoplanetary disks using precise radiative (ransler calculations taking into account the frequency dependence on opacity. the scattering process of dust particles. and the ice opacity that previous studies did not consider. | In order to make clear the important inconsistency in planet formation, we investigate the detailed thermal evolution of protoplanetary disks using precise radiative transfer calculations taking into account the frequency dependence on opacity, the scattering process of dust particles, and the ice opacity that previous studies did not consider. |
According to Inoue. Oka. Nakamoto (2009) and Dullemonda£. ( | According to Inoue, Oka, Nakamoto (2009) and Dullemond. ( |
2002). disk midplane temperature | 2002), disk midplane temperature |
An estimate of the stellar mass component in galaxies is interesting for several different reasons. | An estimate of the stellar mass component in galaxies is interesting for several different reasons. |
In detail. by combining or comparing photometric stellar mass estimates. obtained by spectral energy distribution (SED) fitting methods. with dynamical or lensing measurements. it is possible to study the radial distribution of dark matter (e.g.. Ferreras et al. 2005: | In detail, by combining or comparing photometric stellar mass estimates, obtained by spectral energy distribution (SED) fitting methods, with dynamical or lensing measurements, it is possible to study the radial distribution of dark matter (e.g., Ferreras et al. \cite{fer05}; |
Napolitano et al. 200501). | Napolitano et al. \cite{nap05}) ), |
to investigate the relationship between stellar and total mass (e.g.. Lintott et al. 2006: | to investigate the relationship between stellar and total mass (e.g., Lintott et al. \cite{lin06}; |
Rettura et al. 2006)). | Rettura et al. \cite{ret06}) ), |
and to test hierarchical structure formation models (e.g.. Nagamine et al. 2004:; | and to test hierarchical structure formation models (e.g., Nagamine et al. \cite{nag04};; |
De Lucia et al. 2006)). | De Lucia et al. \cite{del06}) ). |
Interestingly. Treu Koopmans (2004)) have proved that the stellar mass fraction in elliptical lens galaxies can also be estimated with a joint lensing and dynamical analysis. | Interestingly, Treu Koopmans \cite{tre2}) ) have proved that the stellar mass fraction in elliptical lens galaxies can also be estimated with a joint lensing and dynamical analysis. |
Although it is common to measure stellar masses through these techniques. only a few studies have been performed to check the reliability of each method (e.g.. Drory et al. 20045). | Although it is common to measure stellar masses through these techniques, only a few studies have been performed to check the reliability of each method (e.g., Drory et al. \cite{dro04}) ). |
Further investigations are therefore important to probe the consistency of the different techniques. | Further investigations are therefore important to probe the consistency of the different techniques. |
Throughout this work we assume Hy=70kms!Mpe7!. Q,,=0.3. and Q4=0.7. | Throughout this work we assume $H_{0}=70 \mbox{ km s}^{-1} \mbox{ Mpc}^{-1}$, $\Omega_{m}= 0.3$, and $\Omega_{\Lambda} = 0.7$. |
In this Letter. we focus on a uniformly selected sample of 15 massive field early-type galaxies taken from the SLACS Survey (for more details on the selection procedure. see Bolton et al. 2006). | In this Letter, we focus on a uniformly selected sample of 15 massive field early-type galaxies taken from the SLACS Survey (for more details on the selection procedure, see Bolton et al. \cite{bol}) ). |
Table | summarizes the relevant photometric and spectroscopic properties of the galaxy sample. | Table \ref{Infotable} summarizes the relevant photometric and spectroscopic properties of the galaxy sample. |
The lens galaxies have a redshift between 0.06 and 0.33. F435W and F814W images. magnitudes and stellar velocity dispersions from theSDSS!. | The lens galaxies have a redshift between 0.06 and 0.33, F435W and F814W images, magnitudes and stellar velocity dispersions from the. |
. They are luminous red galaxies (LRG: Eisenstein et al. 2001)) | They are luminous red galaxies (LRG; Eisenstein et al. \cite{eis}) ) |
with properties similar to those of non-lensing early-type galaxies: redshifts. stellar velocity dispersions. stellar populations. and mass density profiles (see Treu et al. 2006:; | with properties similar to those of non-lensing early-type galaxies: redshifts, stellar velocity dispersions, stellar populations, and mass density profiles (see Treu et al. \cite{tre1}; |
Koopmans et al. 2006)). | Koopmans et al. \cite{koo3}) ). |
Here. we describe how the stellar mass of the galaxies of our sample is measured using two independent diagnostics. | Here, we describe how the stellar mass of the galaxies of our sample is measured using two independent diagnostics. |
Strong gravitational lensing provides the most accurate estimate of the total (stellar+dark) projected mass of a lens galaxy inside the Einstein radius. | Strong gravitational lensing provides the most accurate estimate of the total (stellar+dark) projected mass of a lens galaxy inside the Einstein radius. |
It has been shown by Treu Koopmans (2004)) that by combining lensing measurements with spatially resolved kinematic profiles in elliptical galaxies. the stellar and dark components can be separated precisely. | It has been shown by Treu Koopmans \cite{tre2}) ) that by combining lensing measurements with spatially resolved kinematic profiles in elliptical galaxies, the stellar and dark components can be separated precisely. |
If the velocity dispersion of stars is known only from a single (fiber) aperture. some information on the stellar mass fraction Cf.) inside Ruy, can still be obtained. | If the velocity dispersion of stars is known only from a single (fiber) aperture, some information on the stellar mass fraction $f_{*}$ ) inside $R_{\mathrm{Ein}}$ can still be obtained. |
This particular analysis has been performed on the SLACS sample by Koopmans et al. (2006)). | This particular analysis has been performed on the SLACS sample by Koopmans et al. \cite{koo3}) ). |
The results are shown in Table 2.. | The results are shown in Table \ref{Masstable}. |
We summarize here the main steps and assumptions: | .We summarize here the main steps and assumptions: |
Independent estimates of the harvon content of the Universe are provided by the theory of primordial. nucleosynthesis (c.g.2) and studies of the inhomogeneity of the cosmic microwave background (CAIB) (ee.2)... | Independent estimates of the baryon content of the Universe are provided by the theory of primordial nucleosynthesis \citep[e.g.][]{Pagel97} and studies of the inhomogeneity of the cosmic microwave background (CMB) \citep[e.g.][]{Spergel+07}. |
The resulting oxwvon density. proves to exceed by a factor LO tha accounted for by the stars ancl observed interstellar medium (ISAT) of galaxies (2).. | The resulting baryon density proves to exceed by a factor $\sim10$ that accounted for by the stars and observed interstellar medium (ISM) of galaxies \citep{ProchaskaTumlinson09}. |
This dissonance suggests that mos xwvons are in intergalactic space. | This dissonance suggests that most baryons are in intergalactic space. |
A fraction around. of these barvons may comprise ionisecl gas associated with he focal Lye forest. (?).. | A fraction around of these baryons may comprise ionised gas associated with the $local$ $\alpha$ forest \citep{Penton04}. |
The rest is still missing. anc srobably comprises the warm-hot. medium. (WIILM) tha is believed to permeate most of intergalactic space. | The rest is still missing, and probably comprises the warm-hot medium (WHIM) that is believed to permeate most of intergalactic space. |
In this rictuwe. spiral galaxies. like more massive structures such as ealaxy clusters. should be embedded in massive coronae of eas at the virial-temperature. | In this picture, spiral galaxies, like more massive structures such as galaxy clusters, should be embedded in massive coronae of gas at the virial-temperature. |
Phese coronae should typically extend to a few hundred kiloparsees from galaxy centres (?).. | These coronae should typically extend to a few hundred kiloparsecs from galaxy centres \citep{FukugitaPeebles06}. |
The observational quest for this medium is ongoing (?).. and there is some debate as to whether the observational constraints are compatible with the cosmological predictions or not (?7?).. | The observational quest for this medium is ongoing \citep{Bregman07}, and there is some debate as to whether the observational constraints are compatible with the cosmological predictions or not \citep{Rasmussen+09,
AndersonBregman10, AndersonBregman11}. |
Cosmological coronae. constitute α virtually infinite source of eas to feed star formation in galaxy clises. | Cosmological coronae constitute a virtually infinite source of gas to feed star formation in galaxy discs. |
In fact several lines of evidence indicate that eas accretion [rom the intergalactic medium. (LGAL) plays an important. role in galaxy evolution (2).. | In fact several lines of evidence indicate that gas accretion from the intergalactic medium (IGM) plays an important role in galaxy evolution \citep{Sancisi08}. |
Studies of the stellar content of the Milky Way's cise show that the Star Formation Rate (SER) in the solar neighborhood has declined by a factor of only 2.3 over the past 10 Civr (2227). | Studies of the stellar content of the Milky Way's disc show that the Star Formation Rate (SFR) in the solar neighborhood has declined by a factor of only $2-3$ over the past 10 Gyr \citep{Twarog80, Rocha-Pinto+00, Cignoni+08, AumerB09}. |
Phe slowness of the decline in the SER. suggests that the Galaxys meagre stock of cold gas is constantly. replenished. | The slowness of the decline in the SFR suggests that the Galaxy's meagre stock of cold gas is constantly replenished. |
This suggestion is reinforced by the scarcity of metal-poor €i dwarfs. which arises naturally if the Galaxy constantly accretes metal-poor eas (27). | This suggestion is reinforced by the scarcity of metal-poor G dwarfs, which arises naturally if the Galaxy constantly accretes metal-poor gas \citep{PagelPatchett,Chiappini+97}. |
. Finally. studies of the evolution of the cosmic SET and thus the rate of gas consumption across the Llubble time show that at any time galaxies must have accreted eas at a rate close to their SER (7?).. | Finally, studies of the evolution of the cosmic SFR and thus the rate of gas consumption across the Hubble time show that at any time galaxies must have accreted gas at a rate close to their SFR \citep{Hopkins+08, Bauermeister+10}. |
While it is widely agreed. that the. WIILM. contains the bull of the barvons. ancl that clise galaxies. sustain their star formation. by accreting from the WIILM. there | While it is widely agreed that the WHIM contains the bulk of the baryons, and that disc galaxies sustain their star formation by accreting from the WHIM, there |
for this result comes from the analysis of the fractions of IR supercluster members in different SED classes. | for this result comes from the analysis of the fractions of IR supercluster members in different SED classes. |
These fractions are displayed in Fig. | These fractions are displayed in Fig. |
15 for the different regions of the supercluster (results are displayed for the zUΖρ sample; very similar results are found for the z sample, and are not shown here). | \ref{f:sedregions} for the different regions of the supercluster (results are displayed for the $\rm{z} \cup \rm{z}_p$ sample; very similar results are found for the z sample, and are not shown here). |
They are clearly very similar, except perhaps for a very marginal excess of ETGs in the core region. | They are clearly very similar, except perhaps for a very marginal excess of ETGs in the core region. |
The fraction of AGNSs among IR-emitting galaxies is similar to that found in and in other galaxy clusters???). | The fraction of AGNs among IR-emitting galaxies is similar to that found in and in other galaxy clusters. |
. We compare the IR LF of A1763 with those of?,, ?,, and?,, for which the parameters of the best-fit Schechter function are available. | We compare the IR LF of A1763 with those of, , and, for which the parameters of the best-fit Schechter function are available. |
Ideally, one would like to compare IR LFs obtained within regions of similar galaxy number densities, to highlight differences due to different of IR-emitting galaxies. | Ideally, one would like to compare IR LFs obtained within regions of similar galaxy number densities, to highlight differences due to different of IR-emitting galaxies. |
Since previous determinations have been limited to the inner, virialized cluster regions, we consider in this comparison only the IR LF of the core region of A1763. | Since previous determinations have been limited to the inner, virialized cluster regions, we consider in this comparison only the IR LF of the core region of A1763. |
The areas where the LFs of ?,,?,,?,, and the A1763 core have been derived correspond to circular regions of effective limiting radii 0.90, 0.74, 0.82, and 0.65, in units of the respective cluster 12ρ0. | The areas where the LFs of , and the A1763 core have been derived correspond to circular regions of effective limiting radii 0.90, 0.74, 0.82, and 0.65, in units of the respective cluster $\rm{r}_{200}$. |
We derive the virial radii of the clusters from their velocity dispersions via the relation ofA. | We derive the virial radii of the clusters from their velocity dispersions via the relation of. |
. The effective limiting radii of the four clusters are similar, but not identical. | The effective limiting radii of the four clusters are similar, but not identical. |
We therefore apply scaling factors to the cluster IR LFs proportional to the estimated number densities of normal galaxies within these limiting radii. | We therefore apply scaling factors to the cluster IR LFs proportional to the estimated number densities of normal galaxies within these limiting radii. |
We compute these projected densities as in Appendix B.2 of?,, using the individual cluster virial radii and the model profile of with concentration c~3?).. | We compute these projected densities as in Appendix B.2 of, using the individual cluster virial radii and the model profile of with concentration $c \simeq 3$. |
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