THE INCIDENCE OF COOL GAS IN ∼10¹³ M_☉ HALOS^*

A detailed description of how galaxies acquire their gas is essential in order to establish a comprehensive theory of galaxy evolution. Analytical calculations and hydrodynamical simulations have shown that the gas in M ≳ 10¹² M_☉ halos,⁴ is heated to high temperature by virial shocks (e.g., Birnboim & Dekel 2003; Kereš et al. 2005; Dekel & Birnboim 2006; Kereš et al. 2009). Within the hot gas halo, thermal instabilities can induce the formation of pressure-supported clouds of cool gas (e.g., Mo & Miralda-Escude 1996; Maller & Bullock 2004). Such clouds have been resolved in high-resolution hydrodynamic simulations of Milky Way type dark matter halos (e.g., Kaufmann et al. 2009; Kereš & Hernquist 2009). These clouds bring some baryonic material into the galaxy, but the overall cooling rate is reduced because the hot phase has lower density. Whether or not these clouds can form and survive in more massive halos is an open question.

Our empirical knowledge of the cool gas content of dark matter halos has been shaped primarily by H I 21 cm observations of local galaxies (e.g., Thilker et al. 2004; Doyle et al. 2005; Verdes-Montenegro et al. 2001, 2007). At z ≳ 0.1, we rely on intervening systems detected along the sight lines to background QSOs to describe the gas content of dark matter halos. (e.g., Lanzetta & Bowen 1990; Steidel et al. 1994; Chen et al. 2001; Chen & Tinker 2008). A number of studies have used the Mg ii λλ2796,2803 absorption doublets to trace cool, T ∼ 10⁴ K, gas and its physical association with foreground galaxies located near QSO sight lines (e.g., Tripp & Bowen 2005; Kacprzak et al. 2008; Chen & Tinker 2008). Insights into the cool gas content of dark matter halos can also be obtained by measuring the large-scale clustering amplitude of Mg ii systems (Bouché et al. 2006; Tinker & Chen 2008, 2010).

In Gauthier et al. (2009), we calculated the clustering amplitude of strong Mg ii absorbers (with rest-frame absorption equivalent width W_r(2796) ⩾ 1 Å) using luminous red galaxies (LRGs) at z ∼ 0.5. LRGs are old and passive galaxies (Eisenstein et al. 2001) residing in M ≳ 10¹³ h⁻¹ M_☉ halos. (e.g., Zheng et al. 2008; Blake et al. 2008; Padmanabhan et al. 2008; Gauthier et al. 2009). They are identified using photometric redshift techniques that offer a typical redshift accuracy of σ_z ≈ 0.045 at z_ph ∼ 0.5 (Collister et al. 2007).

An interesting result from Gauthier et al. (2009) is that the LRG–Mg ii cross-correlation signal is comparable to the LRG auto-correlation on small scales (≲300 comoving h⁻¹ kpc) that are well within the virial radii of the halos. The results suggest the presence of cool gas inside the dark matter halos of LRGs.

Here, we report the first results of an ongoing spectroscopic follow-up of the close LRG–Mg ii pairs found in Gauthier et al. (2009). In 5 of the 15 cases, the precise spectroscopic redshifts establish a physical connection between these LRG–Mg ii pairs. The spectroscopic study of LRGs is supplemented with a survey of Mg ii absorbers in the vicinity of photometrically identified LRGs in the Sloan Digital Sky Survey (SDSS) data archive. This survey allows us to utilize the vast survey data available in the SDSS archive to derive additional constraints on the covering fraction of cool gas in 10¹³ h⁻¹ M_☉ halos. We adopt a Λ cosmology with Ω_M = 0.3 and Ω_Λ = 0.7, and a dimensionless Hubble parameter h = H₀/(100 km s⁻¹ Mpc⁻¹) throughout the paper. All distances are in physical units unless otherwise stated.

To examine the cool gas content in massive halos, we have designed two experiments. The first one is a spectroscopic follow-up study of photometrically identified LRGs located near Mg ii absorbers (Sample A below). The spectroscopic observations allow us to identify physically associated LRG–Mg ii absorber pairs for interpreting the small-scale clustering signal seen in Gauthier et al. (2009). In addition, the optical spectra offer additional knowledge for the stellar and interstellar medium properties of the LRGs. The second experiment is a survey of Mg ii absorbers in the vicinity of photometrically identified LRGs (Sample B below). This study allows us to make use of the vast amount of galaxy and QSO survey data already available in the SDSS archive and derive statistically significant constraints for the covering fraction of cool gas around LRGs.

2.1. Sample A—LRGs in the Vicinity of Known Mg ii Absorbers

2.2. Sample B—Random LRGs Near QSO Sight Lines

In 2009 May, we obtained medium-resolution spectra of three LRGs in Sample A (all within ρ = 160 h⁻¹ kpc of a known Mg ii absorber) using the Double Imaging Spectrograph (DIS) on the 3.5 m telescope at Apache Point Observatory. The blue and red cameras have a pixel scale of 04 and 042 pixel⁻¹, respectively, on the 3.5 m telescope. We used the B400/R300 grating configuration with a 15 slit. The B400 grating in the blue channel has a dispersion of 1.83 Å pixel⁻¹ and the R300 grating in the red channel has a dispersion of 2.31 Å pixel⁻¹. The blue and red channels with the medium-resolution gratings together offer contiguous spectral coverage from λ = 3800 Å to λ = 9800 Å and a spectral resolution of FWHM ≈ 500 km s⁻¹ at λ = 4400 Å and FWHM ≈ 400 km s⁻¹ at λ = 7500 Å. The observations were carried out in a series of two exposures of between 1200 s and 1800 s each, and no dither was applied between individual exposures. Flat-field frames were taken at the end of the night for each night. Calibration frames for wavelength solutions were taken immediately after each science exposure using the truss lamps on the secondary cage. The DIS observations are characterized by a typical seeing of 13 (as measured with the slitviewer guide star). Note that we also retrieved the spectrum of one LRG in Sample A (SDSSJ113731.00+060748.6) from the SDSS archive and included it in our spectroscopic studies.

We pursued our spectroscopic observations of LRGs in 2009 September using the Boller & Chivens (B&C) spectrograph on the du Pont 2.5 m telescope at Las Campanas Observatory, Chile. We obtained long-slit medium-resolution spectra for seven additional LRGs in Sample A. In addition, we selected four LRGs from Sample B for the spectroscopic B&C observations. The B&C camera has a plate scale of 07 pixel⁻¹. We used the 300 ln/mm grating with a central wavelength of 6500 Å and a grating angle of 6°. Since most spectral features of early-type galaxies at z ∼ 0.5 are located at λ>5000 Å, we employed the blocking filter GG4495 to block the light blueward of ≈5000 Å, in order to avoid second-order contamination from the blue part of the spectrum. The slit width for all observations was 11. The adopted grating configuration had a dispersion of 3 Å pixel⁻¹ and a wavelength coverage of more than 6000 Å. For the calibration frames, we followed the methodology employed for the DIS observations. A series of dome and sky flats were taken each afternoon prior to the observations and calibration frames for wavelength solution were taken immediately after each science exposure. The typical seeing measured with the guide star was 1–14 during most observations.

All of the DIS and B&C spectroscopic data were reduced using standard long-slit spectral reduction procedures. The spectra were calibrated to vacuum wavelengths, corrected for the heliocentric motion, and flux-calibrated using a spectrophotometric standard. Redshifts of the LRGs were determined based on a cross-correlation analysis using known SDSS templates. The typical redshift uncertainty is Δz ∼ 0.0003.

In summary, the spectroscopic sample consists of 11 galaxies in Sample A and four in Sample B. A journal summarizing the observations of the 15 galaxies can be found in Table 1.

4.1. Optical Spectra of LRGs

The optical spectra described in Section 3 confirmed that five of the LRGs occur within 350 km s⁻¹ of an Mg ii absorber. Four of these LRGs belong to Sample A and one to Sample B. Figure 1 shows the optical spectra and SDSS images of these five LRGs. The close proximity of these LRGs and Mg ii absorber pairs (ρ≲ 300 h⁻¹ kpc and |Δv| ≲ 350 km s⁻¹) strongly argues for a physical association between the galaxy and the absorbing gas. We note that the volume spanned by |Δv| = ±350 km s⁻¹ and ρ = 350 h⁻¹ kpc is ∼5 comoving ( h⁻¹ Mpc)³ at z = 0.5. Within this small volume, we estimate based on the best-fit luminosity functions determined for red galaxies at z ∼ 0.5 (M_* − 5log h = −19.8; ϕ_* = 5.16 × 10⁻³ ( h⁻¹ Mpc)⁻³; see, e.g., Brown et al. 2007, 2008) that the probability of the LRG being a random galaxy is negligible.

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In Figure 2, we present absorption profiles of the Mg ii, Mg i, and Fe ii transitions from the SDSS QSO spectra for these five physical pairs. In each panel, zero velocity corresponds to the spectroscopic redshift of the LRG. All absorbers occur within |Δv| ≲ 350 km s⁻¹ of the spectroscopically identified LRGs. Although the spectral resolution of SDSS spectra does not allow us to resolve individual components, the panels show that three of the Mg ii absorbers have associated Fe ii and Mg i absorption features.

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All 15 LRG spectra exhibit spectral features dominated by absorption transitions, indicating an old underlying stellar population and little star formation in the recent past. A stellar population synthesis analysis done with the Bruzual & Charlot (2003) spectral library established that the most likely stellar population ages for these LRGs span 1–11.75 Gyr (J.-R. Gauthier et al. 2010, in preparation).

4.2. Incidence of Cool Gas in LRG Halos

We determined the covering fraction of cool gas in massive halos, based on the presence/absence of Mg ii absorbers in the spectrum of the background QSO near the redshifts of the LRGs in Sample B. For each LRG–QSO pair, we visually inspected the QSO spectrum in search of Mg ii absorbers in the redshift uncertainty range of the LRG, z_ph ± 3 σ_z. For σ_z ∼ 0.045 at z_ph = 0.5, this interval corresponds to approximately ±400Å centered at ∼4200 Å. We defined this interval as the search interval, which is large enough to identify all possible Mg ii absorbers that may be associated with the LRG. Despite the large redshift uncertainties, however, our search yielded a conservative maximum gas covering fraction κ_max of Mg ii absorbing gas in LRG halos. If no absorber was visually detected, we measured a 2σ upper limit per spectral resolution element, W_lim, for the equivalent width of the Mg ii λ2796 transition, using the noise spectrum. For each sight line with a detection, we measured the redshift and strength of the absorber based on a Gaussian profile analysis. For these sight lines, we also determined W_lim following the procedure described earlier. Because the signal-to-noise ratio (S/N) varies substantially between QSO spectra, W_lim represents the minimum absorption strength that can be recovered in each QSO spectrum. It serves to define a homogeneous sample of QSO spectra that can be adopted to determine the incidence of Mg ii absorbers.

To determine the incidence of Mg ii absorbers with W_r(2796) ⩾ W₀ Å around LRGs, we first identified from the parent LRG–QSO pair sample the QSO spectra that satisfy W_lim < W₀ Å to ensure that the QSO spectra have sufficient S/N for revealing an Mg ii absorber of minimum strength W₀. Next, we determined κ_max by evaluating the fraction of the QSO spectra that display an Mg ii absorber of W_r(2796)>W₀ in the vicinity of the LRGs. We calculate κ_max for different values of W₀ in different ρ intervals.

This search allowed us to estimate the maximum possible covering fraction of cool gas based on the incidence of Mg ii in LRG halos (see Section 5 for a discussion on the contamination rate due to correlated and random galaxies). We first considered the incidence of Mg ii absorbers at different absorption threshold W₀. All QSO spectra in the 620 close LRG–QSO pairs have sufficient S/N (W_lim < 1 Å) for uncovering an absorber of W_r(2796) ⩾ 1 Å. Our search showed that 45 of the 620 LRGs have a W_r(2796) ⩾ 1 Å absorber at ρ < 400 h⁻¹ kpc, indicating a mean covering fraction averaged over the entire LRG halos of κ_max(ρ < 400) = 0.07 for W_r(2796)>1 Å absorbers. Next, we calculated κ_max in different ρ intervals. Figure 3 shows that for W_r ≳ 1Å κ_max(ρ) ≈ 10% at ρ < 300 h⁻¹ kpc but declines to κ_max ≈ 5% at larger ρ (triangles).

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Similarly, 575 QSO spectra in the 620 close LRG–QSO pairs have sufficient S/N (W_lim < 0.5 Å) for uncovering an absorber of W_r(2796) ⩾ 0.5 Å, and 105 of the 575 LRG members have a W_r(2796) ⩾ 0.5 Å absorber at ρ < 400 h⁻¹ kpc. The search therefore yielded a mean covering fraction averaged over the entire LRG halos of κ_max(ρ < 400) = 0.18 for absorbers of W_r(2786)>0.5 Å. The estimated κ_max versus ρ for W_r(2796) ⩾ 0.5 Å absorbers are also presented in Figure 3 (squares).

The κ_max results at small separations (ρ ≲ 100 h⁻¹ kpc) are consistent with the covering fraction measurements from the spectroscopic Sample B. We found 1/4 LRGs physically associated with the Mg ii absorber and all four pairs are within ρ = 100 h⁻¹ kpc. We are currently increasing the number of spectroscopic pairs from Sample B to obtain a more accurate measurement of κ.

Our follow-up spectroscopic study of close LRG–Mg ii pairs has confirmed a physical association between the Mg ii absorber and the LRG in five of the 15 cases studied. The small velocity separations |Δ v| ≲ 350 km s⁻¹ and projected distances ρ < 160 h⁻¹ kpc demonstrate that at least some of the strong Mg ii absorbers [W_r(2796)>1 Å] that contributed to the small-scale [r_p = (1 + z) ×  ρ < 600 h⁻¹ kpc] clustering signal in Gauthier et al. (2009) do indeed originate in the hosting dark matter halos of LRGs. According to a stellar population analysis (using the stellar templates from Bruzual & Charlot 2003) done on the LRG spectra, we found that these galaxies are characterized by a stellar population at least 1 Gyr old with a most likely age between 1–11.75 Gyr. The optical spectra are characteristic of an evolved stellar population with little recent star formation.

In addition, our search of Mg ii absorption features in the vicinity of LRGs has yielded a conservative estimate of the maximum covering fraction of cool gas in LRG halos. Because of the redshift uncertainties of the LRGs, we cannot distinguish between whether the observed Mg ii absorbers are physically associated with the LRG halos or these absorbers occur due to chance coincidence, correlated galaxies, or surrounding satellite galaxies. Despite these various uncertainties, the observed incidence of Mg ii absorbers places a strong constraint on the maximum covering fraction of cool gas in massive LRG halos as probed by the Mg ii absorbers. We find that the cool gas covering fraction of absorbers with W_r(2796) ⩾ 0.5 Å in massive LRG halos is no more than 20% and no more than 7% for stronger absorbers W_r(2796) ⩾ 1 Å.

Although to establish a physical association between these close LRG–Mg ii absorber pairs requires spectroscopic data of the LRGs, we assess possible contaminations due to surrounding satellite galaxies and background random/correlated absorbers based on theoretical expectations of the satellite population and the mean number density of Mg ii absorbers per line of sight (LOS) observed along random QSO sight lines.

To estimate the incidence of Mg ii absorbers due to satellite galaxies in the LRG halos, we first adopt the mass function of subhalos (Equation (10) in Tinker & Wetzel 2009). The mass of subhalos is defined as the mass at the time of accretion—this mass will correlate with the gaseous halo that the subhalo initially had. Next, we adopt the gas radius at W_r(2796) ⩾ 1 Å and the covering fraction within the gas radius as a function of halo mass from Tinker & Chen (2010). The total cross section of subhalos within host halos of mass 10¹³ h⁻¹ M_☉ is then estimated according to

$$\begin{eqnarray} {\hat{\kappa }}_{\rm sub}(M_{\rm host}) &=& \frac{1}{\sigma (M_{\rm host})} \int dM_{\rm sub} n(M_{\rm sub}|M_{\rm host})\nonumber \\ &&\times \pi R^2(M_{\rm sub}, W_r=1) \kappa _g(M_{\rm sub}), \end{eqnarray} \tag{ 1 }$$

where M_host is the host halo mass (in this case, 10¹³ h⁻¹ M_☉), M_sub is subhalo mass at time of accretion, n(M_sub|M_host) is the subhalo mass function from Tinker & Wetzel (2009), R is the gas radius for W_r(2796) = 1 Å , and κ_g is the covering fraction within the gas radius. Both R and κ_g are adopted from Tinker & Chen (2010), which are calibrated on data to match the frequency function of absorbers and large-scale bias as a function of W_r(2796).

Under the assumption that the gaseous halos of satellite halos are the same as field halos of similar mass, Equation (1) yields a maximal covering fraction of 1.8% at ρ ≲ 350 h⁻¹ kpc. This is the maximum value because tidal stripping and ram pressure are not taken into account (e.g., Gunn & Gott 1972; Balogh et al. 2000). Equation (1) is also maximal because it assumes that the subhalos have a random distribution within the parent halo. If we further assume that the subhalos follow a Navarro–Frenk–White profile (Wetzel & White 2010), ${\hat{\kappa }}_{\rm sub}$ depends on impact parameter as shown in Figure 4. The satellite contribution is at most comparable to the κ_max measurements at ρ < 100 h⁻¹ kpc, but the satellite covering factor of cool gas is ≳1 dex below κ_max at ρ>200 h⁻¹ kpc.

To estimate the incidence of Mg ii absorbers due to structure along an LOS that intersects a large halo, we adopt the observed mean number density of W_r(2796) ⩾ 1 Å absorbers from Nestor et al. (2005) and Prochter et al. (2006). These authors report a number density of n ≈ 0.1 per unit redshift interval per LOS at z = 0.5 for Mg ii absorbers of W_r(2796) ⩾ 1 Å. Over a redshift interval of Δ z = 0.27, which corresponds to the redshift uncertainty of the LRGs, we therefore expect a background contamination of 0.027 absorbers per LOS. To estimate the incidence of Mg ii absorbers due to correlated large-scale galaxy distribution, we calculate the predicted incidence of correlated L_* halos around the LRGs. We select L_* halos because they are expected to be the dominant contaminant (Tinker & Chen 2008, 2010). First, we adopt Equation (11) in Tinker & Chen (2010) and modify this equation to take into account the correlated structures along the LOS. We integrate along the LOS distance from −300 to +300 h⁻¹ Mpc. We repeat the calculation for each projected distance to the LRG and determine the number of halos that could contribute to the signal based on their mass and size. Our calculation indicates roughly 10% enhancement in the background number density of Mg ii absorbers per LOS. We therefore conclude that background random and correlated galaxies would have contributed no more than 3% of the observed Mg ii absorbers around the massive LRGs.

Our exercise shows that contaminations due to surrounding satellite galaxies and background random/correlated galaxies are insufficient to account for the observed incidence of Mg ii absorbers in the vicinity of LRGs. The maximum covering fraction of strong absorbers is ∼7% averaged over the entire halo.

Bowen et al. (2006) reported 100% covering fraction of Mg ii absorbers within 100 kpc projected distance from four foreground QSO at z = 0.65–1.55. The observed large incidence of Mg ii absorbers in QSO halos appears to be inconsistent with the low gas covering fraction found in the LRG halos. This discrepancy can be understood by considering the mean mass scales of QSOs and LRGs. Ross et al. (2009) calculated the clustering of SDSS spectroscopic QSOs at z < 2.2. They found that, at z ∼ 0.5, the bias of the dark matter halos traced by QSOs is b ∼ 1.4 which is smaller than the bias estimate for the LRGs at the same redshift (b ∼ 2; Gauthier et al. 2009). This implies that the typical mass of the dark matter halos hosting QSOs is around log  M/h ∼ 12.3 (see Figure 12 in Ross et al. 2009), which is about 1 dex smaller than what is found for LRGs in Gauthier et al. (2009). The difference in the observed gas covering fraction therefore reflects the differences in the cold gas content of halos on different mass scales (see, e.g., Tinker & Chen 2008; Chen et al. 2010).

Recall that Mg ii absorbers trace high column density gas of neutral hydrogen column density $N({{\rm H}\,\mathsc{i}})> 10^{18}$ cm^-2 (Bergeron & Stasińska 1986; Rao et al. 2006). Furthermore, Rao et al. (2006) have shown that on average 42% of W_r(2796)>0.6 Å Mg ii absorbers with associated strong Fe ii and Mg i absorption transitions are likely to contain neutral gas of $N({{\rm H}\,\mathsc{i}})> 2\times 10^{20}$cm^-2. Two of the Mg ii absorbers presented in Figure 2 satisfy these criteria and are therefore likely damped Lyα absorbers. Our study therefore provide direct empirical evidence for the presence of high column density cool gas in 10¹³ h⁻¹ M_☉ halos. A large spectroscopic sample of LRGs will not only improve the constraints for κ_g in massive halos but also provide additional insights into the origin of the cool gas.

We thank the anonymous referee for helpful comments that improved the draft. We also thank Jennifer Helsby for assistance in obtaining and reducing some of the LRG spectra and Michael Rauch for helpful comments during the preparation of the draft. J.R.G. acknowledges support from the Sigma-Xi Grant-in-Aid of Research program and from the Brinson Foundation predoctoral fellowship. H.W.C. acknowledges partial support from NASA Long Term Space Astrophysics grant NNG06GC36G and an NSF grant AST-0607510.