COMPOSITION OF LOW-REDSHIFT HALO GAS

We perform cosmological simulations with the adaptive mesh refinement Eulerian hydrocode, Enzo (Bryan 1999; Bryan & Norman 1999; O'Shea et al. 2005). The version we use is a "branch" version (Joung et al. 2009), which includes a multi-tiered refinement method that allows for spatially varying maximum refinement levels, when desired. This Enzo version also includes metallicity-dependent radiative cooling extended down to 10 K, molecular formation on dust grains, photoelectric heating, and other features that are different from or not in the public version of the Enzo code. We use the following cosmological parameters that are consistent with the WMAP7-normalized (Komatsu et al. 2011) LCDM model: Ω_M = 0.28, Ω_b = 0.046, Ω_Λ = 0.72, σ₈ = 0.82, H₀ = 100 h km s⁻¹ Mpc⁻¹ = 70 km s⁻¹ Mpc⁻¹, and n = 0.96. These parameters are also consistent with the latest Planck results (Planck Collaboration et al. 2013) if one adopts the Hubble constant, which is the average of the Planck value and the values derived from the Type Ia supernovae and HST key program (Riess et al. 2011; Freedman et al. 2012). We use the power spectrum transfer functions for cold DM particles and baryons using fitting formulae from Eisenstein & Hut (1998). We use the Enzo inits program to generate the initial conditions.

First, we ran a low-resolution simulation with a periodic box of 120 h⁻¹ Mpc on the side. We identified two regions separately, one centered on a cluster of mass the size of ∼2 × 10¹⁴ M_☉ and the other centered on a void region at z = 0. We then resimulate each of the two regions separately with a high resolution, but embedded in the outer 120 h⁻¹ Mpc box to properly take into account the large-scale tidal field and appropriate boundary conditions at the surface of the refined region. We name the simulation centered on the cluster the "C" run and that centered on the void the "V" run. The refined region for the "C" run has a size of 21 × 24 × 20 h⁻³ Mpc³ and the size of the "V" run is 31 × 31 × 35 h⁻³ Mpc³. At their respective volumes, they represent 1.8σ and −1.0σ fluctuations. The root grid has a size of 128³ with 128³ DM particles. The initial static grids in the two refined boxes correspond to a 1024³ grid on the outer box. The initial number of DM particles in the two refined boxes corresponds to 1024³ particles on the outer box. This translates into an initial condition in the refined region with a mean interparticle separation of 117 h⁻¹ kpc comoving and a DM particle mass of 1.07 × 10⁸ h⁻¹ M_☉. The refined region is surrounded by two layers (each of ∼1 h⁻¹ Mpc) of buffer zones with particle masses successively larger by a factor of eight for each layer, which then connects with the outer root grid that has a DM particle mass 8³ times that of the refined region. The initial density fluctuations are included up to the Nyquist frequency in the refined region. The surrounding volume outside the refined region is also followed hydrodynamically, which is important in order to properly capture matter and energy exchanges at the boundaries of the refined region. Because we still cannot run a very large volume simulation with adequate resolution and physics, we choose these two runs of moderate volumes to represent two opposite environments that possibly bracket the universal average.

We choose a varying mesh refinement criterion scheme where the resolution is always better than 460 h⁻¹ proper parsecs within the refined region and corresponds to a maximum mesh refinement level of 9 above z = 3, of 10 at z = 1–3, and 11 at z = 0–1. The simulations include a metagalactic UV background (Haardt & Madau 2012) and a model for shielding UV radiation with atoms (Cen et al. 2005). The simulations also include metallicity-dependent radiative cooling and heating (Cen et al. 1995). We clarify that our group has included metal cooling and metal heating (due to photoionization of metals) in all our studies since Cen et al. (1995) to avoid all doubt (e.g., Wiersma et al. 2009; Tepper-García et al. 2011). Star particles are created in cells that satisfy a set of criteria for star formation proposed by Cen & Ostriker (1992). Each star particle is tagged with its initial mass, creation time, and metallicity; star particles typically have masses of ∼10^5–6 M_☉.

Supernova feedback from star formation is modeled following Cen et al. (2005). Feedback energy and ejected metal-enriched mass are distributed into 27 local gas cells centered at the star particle in question, weighted by the specific volume of each cell (i.e., weighting is equal to the inverse of density), which is to mimic the physical process of supernova blast wave propagation, which tends to channel energy, momentum, and mass into the least dense regions (with the least resistance and cooling). We allow the whole feedback processes to be hydrodynamically coupled to surroundings and subject to relevant physical processes, such as cooling and heating, as in nature. The extremely inhomogeneous metal enrichment process demands that both metals and energy (and momentum) are correctly modeled so that they are transported in the right direction in a physically sound (albeit still approximate at the current resolution) way, at least in a statistical sense. In our simulations, metals are followed hydrodynamically by solving the metal density continuity equation with sources (from star formation feedback) and sinks (due to subsequent star formation). Thus, metal mixing and diffusion through advection, turbulence, and other hydrodynamic processes are properly treated in our simulations.

The primary advantages of this supernova energy-based feedback mechanism are three-fold. First, nature does drive winds in this way and the energy input is realistic. Second, it has only one free parameter, e_SN, namely, the fraction of the rest mass energy of stars formed that is deposited as thermal energy on the cell scale at the location of supernovae. Third, the processes are treated physically, obeying their respective conservation laws (where they apply), allowing the transport of metals, mass, energy, and momentum to be treated self-consistently, and taking into account relevant heating/cooling processes at all times. We use e_SN = 1 × 10⁻⁵ in these simulations. The total amount of explosion kinetic energy from Type II supernovae with a Chabrier initial mass function (IMF) translates into e_SN = 6.6 × 10⁻⁶. Observations of local starburst galaxies indicate that nearly all of the star formation-produced kinetic energy (due to Type II supernovae) is used to power galactic superwinds (e.g., Heckman 2001). Given the uncertainties on the evolution of IMF with redshift (i.e., possibly more top heavy at higher redshift) and the fact that newly discovered prompt Type I supernovae contribute a comparable amount of energy compared to Type II supernovae, it seems that our adopted value for e_SN is consistent with observations and physically realistic. The validity of this thermal energy-based feedback approach comes empirically. In Cen (2012b), the metal distribution in and around galaxies over a wide range of redshift (z = 0–5) is shown to be in excellent agreement with respect to the properties of observed damped Lyα systems (Rafelski et al. 2012), whereas in Cen (2012a) we further show that the properties of O vi absorption lines at low redshift, including their abundance, Doppler-column density distribution, temperature range, metallicity, and coincidence between O vii and O vi lines, are all in good agreement with observations (Danforth & Shull 2008; Tripp et al. 2008; Yao et al. 2009). This is not trivial by any means because they require that the transport of metals and energy from galaxy star formation sites to megaparsec scale be correctly modeled as a function of distance over the entire cosmic timeline, at least in a statistical sense.

We identify galaxies in our high-resolution simulations using the HOP algorithm (Eisenstein & Hu 1999) operated on stellar particles, which was tested and found to be robust and insensitive to specific choices of concerned parameters within reasonable ranges. Satellites within a galaxy are clearly identified separately. The luminosity of each stellar particle at each of the five Sloan Digital Sky Survey (SDSS) bands is computed using the GISSEL (Galaxy Isochrone Synthesis Spectral Evolution Library) stellar synthesis code (Bruzual & Charlot 2003) by supplying the formation time, metallicity, and stellar mass. Collecting luminosity and other quantities of member stellar particles, gas cells, and DM particles yields the following physical parameters for each galaxy: position, velocity, total mass, stellar mass, gas mass, mean formation time, mean stellar metallicity, mean gas metallicity, star formation rate (SFR), luminosities in five SDSS bands (ugriz), and others. At a spatial resolution of proper 460 pc h⁻¹ with more than 2000 well-resolved galaxies at z = 0, this simulated galaxy catalog presents an excellent (by far the best available) tool to study CGM around galaxies at low redshift.

In some of the analysis we perform here, we divide our simulated galaxy sample into two sets according to the galaxy color. We shall call galaxies with g − r < 0.6 blue and those with g − r > 0.6 red. We found that g − r = 0.6 is at the trough of the galaxy bimodal color distribution of our simulated galaxies (Cen 2011; Tonnesen & Cen 2012), which agrees well with that of observed low-z galaxies (e.g., Blanton et al. 2003).

The photoionization code CLOUDY (Ferland et al. 1998) is used post-simulation to compute the abundance of O vi. We adopt the shape of the UV background calculated by Haardt & Madau (2012) normalized by the intensity at 1 Ryd determined by Shull et al. (1999) and assume ionization equilibrium. We generate synthetic absorption spectra given the density, temperature, metallicity, and velocity fields in simulations. Each absorption line is identified by the velocity (or wavelength) interval between one downward-crossing and the next upward-crossing points at a flux equal to 0.99 (a flux equal to unity corresponds to an unabsorbed continuum flux) in the spectra. We do not add instrumental and other noises to the synthetic spectra. Since the absorption lines in question are sparsely distributed in the velocity space, their identifications have no significant ambiguity. Column density, equivalent width, Doppler width, mean column density-weighted velocity and physical space locations, mean column density-weighted temperature, density, and metallicity are computed for each line. We sample the C and V runs, respectively, with 72, 000 and 168, 000 random lines of sight at z = 0, with a total path length of Δz ∼ 2000. A total of ∼30, 000  ⩾  50 mA O vi absorbers are identified in the two volumes. While a detailed Voigt profile fitting of the flux spectrum would have enabled a closer comparison with observations, simulations suggest that such an exercise does not necessarily provide a better physical understanding of the absorber properties, because bulk velocities are very important and velocity substructures within an absorber do not necessarily correspond to separate physical entities (Cen 2012a).

The C and V runs at z = 0 are used to obtain an "average" of the universe. This cannot be done precisely without much larger simulation volumes, which is presently not feasible. Nevertheless, we make the following attempt to obtain an approximate average. The number density of galaxies with luminosity greater than 0.1 L_* in the SDSS r band in the two runs is found to be 3.95 × 10⁻² h³ Mpc⁻³ and 1.52 × 10⁻² h³ Mpc⁻³, respectively, in the C and V boxes. We fix the weighting for the C and V runs in order to average the statistics of the C and V runs by requiring that the average density of galaxies with luminosity greater than 0.1 L_* in the SDSS r band in the simulations are equal to the observed global value of 2.87 × 10⁻² h³ Mpc⁻³ by SDSS (Blanton et al. 2003). In the results shown below, we use this method to obtain averages of the statistics, where doing so allows for some more quantitative comparisons with observed data.

Figure 1 shows the cumulative probability distribution functions of ⩾50 mA O vi absorbers for finding ⩾0.1 L_* galaxies at z = 0–0.2 from simulations as well as observations. We find good agreement between simulations and observations, quantified by the χ square per degree of freedom of 1.2. In comparison, if we use only the low-temperature (T < 3 × 10⁴ K) O vi absorbers in the simulations, the cumulative probability is no longer in reasonable agreement with observations, with the χ square per degree of freedom being equal to 7.6; this exercise, however, only serves as an illustration of what a photoionization-dominated model may produce. It will be very interesting to make a similar calculation directly using smoothed particle hydrodynamic (SPH) simulations that have predicted the dominance of photoionized O vi absorbers even for strong O vi absorbers as shown here (e.g., Oppenheimer et al. 2012).

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The significant difference found with respect to the strong O vi absorber–galaxy cross-correlations between the photoionization and collisional ionization-dominated models stems from the relative difference in the locations of strong O vi absorbers in the two models. In the collisional ionization-dominated model (Cen 2012a; Shull et al. 2012), the strong O vi absorbers are spatially closer to galaxies in order to have a high enough temperature (hence high O vi abundance) and a high enough density to make strong O vi absorbers, whereas in the photoionization-dominated model (Oppenheimer et al. 2012), they have to be sufficiently far from galaxies to have low enough densities to be photoionized to O vi. An additional requirement in the latter for the production of strong O vi absorbers is high metallicity (⩾0.1 Z_☉) to yield high enough O vi columns, as found in SPH simulations (Oppenheimer et al. 2012).

Observations have shown an interesting dichotomy between the O vi incidence rates of blue and red galaxies. Figure 2 shows the cumulative probability distribution functions of $N_{{\rm O\,\scriptsize{VI}}}>10^{14}$ cm⁻² O vi absorbers for finding a (red, blue) galaxy of luminosity of ⩾0.1 L_* at z = 0.2 from simulations. In Figure 3, we show the ratio of the cumulative radial distribution per red galaxy to that per blue galaxy of ⩾0.1 L_* at z = 0.2, compared to observations. Figure 3 shows that in the r = 50–300 kpc range, the ratio of the incidence rate of strong O vi absorbers around red galaxies to that around blue galaxies is about 1:5, which is in quantitative agreement with observations. In the case with photoionized O vi absorbers only, the fraction of O vi absorbers around red galaxies is much lower and lies significantly below the observational estimates, although the current small observational sample prevents us from reaching strong statistical conclusions based on this ratio alone.

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We see in Figure 2 that statistical uncertainties for the radial probability distribution of simulated O vi absorbers are already very small due to a significant number of simulated galaxies and a still larger number of simulated absorbers used. What limits us from making firm statistical statements is the sample size of observational data. Hypothetically, if the mean remains the same, a factor of two smaller error bars would render the photoionization-dominated model inconsistent with observations at ⩾2σ confidence level, whereas our collisionally dominated model would be consistent with observations within 1σ.

We now turn to analysis to give a physical description for the origin of O vi absorbers in the CGM in the context of the cold dark matter model. While this section is interesting on its own for physically understanding halo gas, the next section on halo gas mass decomposition is not predicated on it.

First, we ask whether the warm gas traced by O vi absorbers requires significant energy input to be sustained over the Hubble time. Figure 4 shows the metal mass in the warm gas (T = 10⁵–10⁶ K) distributed in the density–metallicity phase space. We see that most of the warm metals are concentrated in a small phase space region centered at (n, Z) = (10⁻⁵ cm⁻³, 0.15 Z_☉). We note that the amount of gas mass in the WHIM is 40% of the total gas averaged over the simulation, which is in agreement with previous simulations (e.g., Cen & Ostriker 1999, 2006; Davé et al. 2001) and other recent simulations (Smith et al. 2011; Davé et al. 2010; Shen & Kelly 2010; Tornatore et al. 2010). For this gas we find that the cooling time is t_cool = 6 × 10⁸ yr (assuming a temperature of 10^5.5 K), shorter than the Hubble time by a factor of ⩾20. For the strong O vi absorbers considered here, the cooling time is still shorter. In other words, either (1) energy is supplied to sustain existing O vi gas, (2) new warm gas is accreted, or (3) some hotter gas needs to continuously cool through the warm phase. Since O vi gas by itself does not define a set of stable systems and is spatially well mixed or in close proximity to other phases of gas, this suggests that the O vi gas in halos is "transient" in nature.

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We consider three sources of warm halo gas: mechanical feedback energy from stellar evolution, gravitational binding energy released from halo formation and interactions, and direct accretion from the IGM. This simplification sets a framework to make a quantitative assessment of these three sources for warm gas that we now describe. We denote by F_b and F_r the O vi incident rate (in some convenient units) per blue and red ⩾0.1 L_* galaxy due to star formation feedback energy heating, by G_b and G_r those due to gravitational heating, and by A_b and A_r those due to accreted gas from the IGM. It is useful to stress the distinction between G and A. A is gas directly accreted from IGM that is either already warm or heated up to be warm by compression upon accretion onto the halo. On the other hand, G is gas that is shock heated to the warm phase or to a hotter phase that cools back down to become warm. Restricting our analysis to within a galactocentric radius of 150 kpc and reading off numbers from the red curve in Figure 3, we obtain two relations:

$$\begin{eqnarray} F_{b} + G_{b} + A_{b} &=& 5, \nonumber \\ F_{r} + G_{r} + A_{r} &=& 1. \end{eqnarray} \tag{ 1 }$$

An additional reasonable assumption is now made: feedback heating rate S_r (S_b) is proportional to the average SFR_r (SFR_b), which in turn is proportional to their respective gas accretion rate A_r (A_b). This assumption allows us to lump F_r and A_r (F_b and A_b):

$$\begin{eqnarray} S_{b} = F_{b} + A_{b} &=& C\times {\rm SFR_{b}} \nonumber \\ S_{r} = F_{r} + A_{r} &=& C\times {\rm SFR_{r}}, \end{eqnarray} \tag{ 2 }$$

where C is a constant. We will return to determine F_r and A_r (F_b and A_b) separately later. Equation (1) is now simplified to

$$\begin{eqnarray} S_{b} + G_{b} &=& 5, \nonumber \\ S_{r} + G_{r} &=& 1. \end{eqnarray} \tag{ 3 }$$

The ratio of SFR_b to SFR_r can be computed directly in the simulations and was found to be 8.4. Rounding it down to 8 and combining it with Equation (2) gives us:

$$\begin{eqnarray} &&S_{b}/S_{r}=8. \end{eqnarray} \tag{ 4 }$$

Finally, a direct assessment of the relative strength of gravitational heating of warm gas in blue and red galaxies is obtained by making the following ansatz: the amount of hot T ⩾ 10⁶ K gas is proportional to the overall heating rate, to which the gravitational heating rate of warm gas is proportional. Figure 5 shows the gas mass of the three halo gas components interior to the radius shown in the x-axis. Within the galactocentric radius of 150 kpc, we found that the amount of hot halo gas per red ⩾0.1 L_* galaxy is twice that per blue ⩾0.1 L_* galaxy:

$$\begin{eqnarray} &&G_{r}/G_{b}=2. \end{eqnarray} \tag{ 5 }$$

Solving Equations (3), (4), and (5) yields

$$\begin{eqnarray} S_{b}&=24/5, G_{b} = 1/5; \nonumber \\ S_{r}&=3/5, G_{r}=2/5. \end{eqnarray} \tag{ 6 }$$

The estimate given in Equation (5) is admittedly uncertain. Therefore, an estimate of how much conclusions depend on it is instructive. We find that if we had used G_r/G_b = 1 (instead of 2), we would have obtained S_b = 32/7, G_b = 3/7, S_r = 4/7, G_r = 3/7; had we used G_r/G_b = 1/2, we would have obtained S_b = 4, G_b = 1, S_r = 1/2, G_r = 1/2. Thus, a relatively robust conclusion for the sources of warm halo gas emerges: (1) for red ⩾0.1 L_* galaxies, (F_r + A_r) and G_r have the same magnitude, and (2) for blue ⩾0.1 L_* galaxies, (F_b + A_b) overwhelmingly dominates over G_b.

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It is prudent to test the conclusion that star formation feedback may dominate the heating of warm gas that produces the observed O vi absorbers in blue galaxies. In Figure 5, the horizontal blue dot-dashed line is obtained by assuming a Chabrier-like IMF that is used in the simulations, which translates into 2/3 × 10⁻⁵ SFR × t_cool × c²/(k10^5.5 K), where c is the speed of light and k is the Boltzmann constant; also assumed is that 2/3 of the initial supernova energy is converted into gas thermal energy, which is the asymptotic value for Sedov explosions, SFR is the respective average SFR per ⩾0.1 L_* blue galaxy, and t_cool = 6 × 10⁸ yr is the estimated cooling time for warm halo gas. From this illustration, we see that with about 20% efficiency of heating warm gas, star formation feedback energy is already adequate for accounting for all the observed warm gas around blue galaxies. We therefore conclude that the required energy from star formation feedback to heat up the warm gas is available and our conclusions are self-consistent, even if the direct accretion contribution is zero, which we will show is not. Our results on warm gas mass are also in reasonable agreement with observations by Tumlinson et al. (2011a), as is the oxygen mass contained in the warm component, as shown in Figure 6.

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We now determine F_r and A_r (F_b and A_b) individually in the following way. We compute the warm metal mass that has inward and outward radial velocities within a radial shell at r = [50, 150] kpc separately for all red >0.1 L_* galaxies and all blue >0.1 L_* galaxies, denoting inflow warm metal mass as M_Z(v_r < 0) and outflow warm metal mass as M_Z(v_r > 0), where v_r is the radial velocity of a gas element with positive being outflowing and negative being inflowing. We define the inflow warm metal fraction as f_in ≡ M_Z(v_r < 0)/(M_Z(v_r < 0) + M_Z(v_r > 0)), which is listed as the first of the three elements in each entry in Table 1 under column |v_r| > 0 km s⁻¹. We also compute the mean metallicities (in solar units) for the inflow and outflow warm gas, which are the second and third of the three elements in each entry in Table 1. Four separated cases are given: (1) red galaxies in the C run (C red), (2) red galaxies in the V run (V red), (3) blue galaxies in the C run (C blue), and (4) blue galaxies in the V run (V blue). In order to make sure that inflow and outflow are not confused with random motions of gas in a Maxwellian-like distribution, we separately limit the magnitude of infall and outflow radial velocities to greater than 100 km s⁻¹ and 250 km s⁻¹ and list the computed quantities under the third column |v_r| > 100 km s⁻¹ and the fourth column |v_r| > 250 km s⁻¹, respectively.

It is interesting to first take a closer look at the difference in metallicities between inflow and outflow gas. The warm inflow gas in red galaxies in the C run has consistently higher metallicity than warm outflow gas, Z_in = (0.27–0.31)Z_☉ versus Z_out = 0.17 Z_☉. The opposite holds for red galaxies in the V run: Z_in = (0.11–0.21) Z_☉ versus Z_out = (0.26–0.33) Z_☉. The warm inflow gas in blue galaxies in the C run has almost the same metallicity as warm outflow gas at Z = (0.09–0.1) Z_☉. The warm inflow gas in blue galaxies in the V run, on the other hand, has a substantially lower metallicity than the warm outflow gas, Z_in = (0.08–0.10) Z_☉ versus Z_out = (0.14–0.24) Z_☉. Except in the case of C blue, we note that the inflow and outflow gas has different metallicities, with the difference being larger when a higher flow velocity is imposed in the selection. This difference in metallicity demonstrates that the warm inflows and outflows are distinct dynamical entities, not random motions in a well-mixed gas, making our distinction of inflows and outflows physically meaningful. A physical explanation for these metallicity trends can be made as follows. In a low-density environment (i.e., in the V run) CGM has not been enriched to a high level and hot gas is not prevalent. As a result, warm (and possibly cold) inflows of relatively low metallicities still exist at low redshift. The progression from blue to red galaxies in the V run reflects a progression from very low density regions (i.e., true voids) to dense filaments and group environments, with higher metallicities for both inflows and outflows in the denser environments in the V run, but the difference between inflow and outflow metallicities remains. For red galaxies in high-density environments (C run) the CGM has been enriched to higher metallicities. Higher cooling rates of higher-metallicity gas in relatively hot environments preferentially produce higher-metallicity warm gas that originates from hot gas and has now cooled to become warm gas. The blue galaxies in the C run are primarily in cosmic filaments and the metallicity of the inflow gas is about 0.1 Z_☉, which happens to coincide with the metallicity of the outflow gas. One needs to realize that at the radial shell r = [50–150] kpc over which the tabulated quantities are computed, the outflow gas originated in star-forming regions has loaded a substantial amount of interstellar and CGM in the propagation process.

Let us now turn to the warm inflow and outflow metal mass. It appears that the fraction of inflow warm metals (out of all warm metals) lies in a relatively narrow range of f_in = 45%–65%. For our present purpose we will just say F_r = A_r and F_b = A_b. Armed with these two relations our best estimates for various contributions to the observed warm halo metals, as a good proxy for the O vi absorption, can be summarized as follows.

• 1.  
  For red ⩾0.1 L_* galaxies at z = 0.2, contributions to warm metals in the halo gas from star formation feedback (F_r), accretion of intergalactic medium (A_r), and gravitational shock heating (G_r) are (F_r, A_r, G_r) = (30%, 30%, 40}).
• 2.  
  For blue ⩾0.1 L_* galaxies at z = 0.2 contributions to warm metals in the halo gas from the three sources are (F_b, A_b, G_b) = (48%, 48%, 4}).
• 3.  
  Dependencies of warm halo gas metallicities on galaxy type and environment are complex but physically understandable. For red galaxies, the metallicity of inflowing warm gas increases with increasing environmental overdensity, whereas that of outflowing warm gas decreases with increasing environmental overdensity. For blue galaxies, the metallicity of inflowing warm gas depends very weakly on environmental overdensity, whereas that of outflowing warm gas decreases with increasing environmental overdensity. As a whole, the mean metallicity of warm halo gas in red galaxies is ∼0.25 Z_☉, while that of blue galaxies is ∼0.11 Z_☉.

We suggest that these estimates of source fractions are not seriously in error on average, if one is satisfied with an accuracy of a factor of two. The relative metallicity estimates should be quite robust with errors much smaller than a factor of two. We stress that these estimates are averaged over many red and blue galaxies and correlations (such as between warm gas mass and SFR) do not hold strictly for individual galaxies. Rather, we expect large variations from galaxy to galaxy, even at a fixed SFR. Figure 7 makes this important point clear and shows that, while there is a positive correlation between warm metal mass within a 150 kpc radius and SFR for galaxies with non-negligible SFR (i.e., appearing in the SFR range shown), a dispersion of ∼1 dex in warm metal mass at a fixed SFR in the range of 0.1–100 M_☉ yr⁻¹ exists. The goodness of the fit can be used as a way to rephrase this significant dispersion. If one assumes that the error bar size of each log mass determination for each shown galaxy is 1, one finds that the χ square per degree of the fitting line (green) is 0.80, indicating that the correlation between log M_Z(T = 10^5–6 K) and log SFR is only good to about 1 dex in warm metal gas mass.

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In Cen (2012a), we show that the properties of O vi absorption lines at low redshift, including their abundance, Doppler-width-column density distribution, temperature range, metallicity, and coincidence between O vii and O vi lines, are all in good agreement with observations (Danforth & Shull 2008; Tripp et al. 2008; Yao et al. 2009). In the above we have shown that O vi–galaxy relations as well as oxygen mass in galaxies in the simulations are also in excellent agreement with observations. These tests together are non-trivial and lend us significant confidence to now examine the overall composition of halo gas at low-z.

Figure 8 shows the differential (left panel) and cumulative (right panel) mass fractions of each gas component as a function of galactocentric distance for red (red curves) and blue (blue curves) galaxies. We note that the fluctuating behaviors (mostly in the differential functions on the left panel) are due to occasional dense cold clumps in neighboring galaxies. Overall, we see that, within about (10, 30) kpc for (red, blue) galaxies, the cold (T < 10⁵ K) gas component completely dominates, making up about (80%, >95%) of all gas at these radii. For both >0.1 L_* (red, blue) galaxies, cold gas remains the major component up to r = (30, 150) kpc, within which its mass comprises 50% of all gas. At r > (30, 200) kpc for (red, blue) galaxies the hot (T > 10⁶ K) gas component dominates. The warm gas component, while having been extensively probed observationally, appears to be a minority in both red and blue galaxies at all radii. The warm component's contribution to the overall gas content reaches its peak value of ∼30% at r = 100–300 kpc for blue galaxies, whereas in red galaxies it is negligible at r < 10 kpc and hovers around the 5% level at r = 30–1000 kpc. The prevalence of cold gas at small radii in red (i.e., low star formation activities) galaxies is intriguing and perhaps surprising to some extent. Some recent observations indicate that early-type galaxies in the real universe do appear to contain a substantial amount of cold gas, consistent with our findings. For example, Thom et al. (2012) infer a mean mass of 10⁹–10¹¹ M_☉ of gas with T < 10⁵ K at r < 150 kpc based on a sample of 15 early-type galaxies at low redshift from COS observations, which is shown as the red square (its horizontal position is slightly shifted to the right for display clarity) in Figure 5. Their inferred range is in fact consistent with our computed value of ∼6 × 10¹⁰ M_☉ of cold T < 10⁵ K gas for red >0.1 L_* galaxies, shown as the red dashed line in Figure 5.

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Figure 9, which is analogous to Figure 8, shows the corresponding distributions for metal mass fractions in the three components for red and blue galaxies. The overall trends are similar to those for total warm gas mass. We note one significant difference here. The overall dominance of metal mass in cold gas extends further out radially for both red and blue galaxies, whereas the contributions to metal mass from the other two components are compensatorily reduced. For example, we find that the radius within which the cold mass component makes up 50% of total gas in (red, blue) galaxies is (40,150) kpc, whereas the radius within which the cold mass component makes up 50% of total gas metals in (red, blue) galaxies becomes (200, 500) kpc. This is largely due to a significantly higher metallicity of the cold component in both red and blue galaxies compared to the other two components, as shown in Figure 10. We also note from Figure 10 that the warm gas in red galaxies has a higher metallicity than in blue galaxies, as found earlier, with the mean metallicity (∼0.25 Z_☉, ∼0.11 Z_☉) in (red, blue) galaxies within a radius of 150 kpc.

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