---
abstract: |
    We investigate the relationship between galaxies and metal-line absorption systems in a large-scale cosmological simulation with galaxy formation. Our detailed treatment of metal enrichment and non-equilibrium calculation of oxygen species allow us, for the first time, to carry out quantitative calculations of the cross-correlations between galaxies and absorbers. We find the following: (1) The cross-correlation strength depends weakly on the absorption strength but strongly on the luminosity of the galaxy. (2) The correlation distance increases monotonically with luminosity from $\sim 0.5-1h^{-1}$Mpc for $0.1L_*$ galaxies to $\sim 3-5h^{-1}$Mpc for $L_*$ galaxies. (3) The correlation distance has a complicated dependence on absorber strength, with a luminosity-dependent peak. (4) Only 15% of absorbers lie near $\ge L_\mathrm{z,*}$ galaxies. The remaining 85%, then, must arise “near” lower-luminosity galaxies, though, the positions of those galaxies is not well-correlated with the absorbers. This may point to pollution of intergalactic gas predominantly by smaller galaxies. (5) There is a subtle trend that for $\gtrsim
    0.5L_\mathrm{z,*}$ galaxies, there is a positive correlation between absorber strength and galaxy luminosity in the sense that stronger absorbers have a slightly higher probability of finding such a large galaxy at a given projection distance. For less luminous galaxies, there seems to be a negative correlation between luminosity and absorber strength.
author:
- 'Rajib Ganguly, Renyue Cen, Taotao Fang and Kenneth Sembach'
title: Correlations between Absorbers and Galaxies at Low Redshift
---

Introduction
============

Cosmological hydrodynamic simulations have shown that most of the so-called missing baryons [@fhp98] may be in a filamentary network of Warm-Hot Intergalactic Medium [WHIM; @co99; @d01]. Visual inspection of simulations suggests that the WHIM is spatially correlated with galaxies. This is consistent with the observed large-scale structure of galaxies, as well as the physical expectation that both galaxies and intergalactic medium (IGM) are subject to the dominant gravitational force of dark matter which tends to lead to such large-scale structures [@z70].

Moreover, the WHIM may provide a primary conduit for matter and energy exchanges between galaxies and the IGM. Thus, a detailed understanding of the WHIM may shed useful light on galaxy formation [e.g., @cno05]. The $\lambda \lambda$1032, 1038 absorption line doublet in the spectra of low-redshift QSOs provides a valuable probe of the WHIM [e.g., @l07; @sd07; @t08]. In this [*Letter*]{} we use cosmological hydrodynamic simulations to make predictions of the correlations between absorbers and galaxies, which may be used for detailed comparisons with upcoming [*Hubble Space Telescope Cosmic Origins Spectrograph*]{} observations.

Simulation and Construction of Absorber and Galaxy Catalogs
===========================================================

We use the simulation from @co06 and @cf06, to make predictions of the relationship between WHIM absorption and the presence of galaxies. This cold dark matter simulation assumes: $\Omega_M = 0.31$, $\Omega_b = 0.048$, $\Omega_\Lambda=0.69$, $\sigma_8 = 0.89$, $H_0 = 100 h=69$[ [km s]{}$^{-1}$]{}Mpc$^{-1}$, $n_s = 0.97$, co-moving box size $85 h^{-1}$Mpc and $1024^3$ cells. The simulation follows star formation using a physically-motivated prescription and includes feedback processes from star formation to the IGM in the form of UV radiation and galactic superwinds carrying energy and metal-enriched gas [@co06]. In star-formation sites, “star particles” are produced at each time step, which typically have a mass of $10^6$M$_\odot$. Galaxies are identified post facto using the HOP grouping scheme [@Eisenstein98 see Nagamine et al. 2001 for details] on these particles. This grouping scheme provides a catalog of galaxies containing 3D positions, peculiar velocities, stellar masses and ages. The catalog consists of 33,887 galaxies. Stellar population synthesis models from @bc03 are used to compute luminosities in all SDSS bands. For the purposes of this paper, we focus on the Sloan z-band, which is centered at 9100Å, and has a width of 1200Å [@sdss]. For galaxies, the flux in this band is most tightly correlated (of all the Sloan bands) with the total stellar mass [e.g., @kauffmann03]. We find that the luminosities of field galaxies in this simulation follow a Schechter function down to $\sim10^{-3.5} L_\mathrm{z,*}$($L_\mathrm{z,*} = 3 \times 10^{11}\,L_\odot$, Ganguly et al. 2008, in preparation).

We extract a [$100 \times 100$]{} grid of sight-lines uniformly separated by $850 h^{-1}$kpc. For each sight-line, a synthetic spectrum of $\lambda$1032 absorption is generated, taking into account effects due to peculiar velocities and thermal broadening. For each sight-line, we decompose the spectrum into individual Gaussian-broadened components with an algorithm similar to [autovp]{} [@autovp]. Finally, we associate grouped components into systems; this is important since, physically, it does not serve our purpose to treat individual components separately when comparing to the locations of galaxies. \[A single physical system like a galactic disk/halo is often composed of multiple components. This is a result of complicated velocity structures and the clumpiness of gas. Historically, older surveys did not have the spectral dispersion needed to resolve individual components. Therefore, it is desirable to re-group these components back to physically independent systems.\] We accomplish this by computing the one-dimensional two-point correlation function of components and identify a characteristic velocity scale. We find that, on small scales, absorption-line components are correlated out to a velocity separation of $\sim\!\!\pm300$[ [km s]{}$^{-1}$]{}, which we adopt as the characteristic velocity interval to identify systems. For each system, we record the integrated flux-weighted centroid redshift, column density, and $\lambda$1032 rest-frame equivalent width. A total of $\sim$180,000 components were found to be grouped into $\sim$21,000 systems with $W_\lambda(\lambda1032) \ge 1$mÅ.

Analysis & Results
==================

We consider the probability that an absorber of a given equivalent width or column density lies within some distance of a galaxy with a certain luminosity. We take three approaches to address this question, but we must first tackle the problem of assigning galaxies to absorbers. Due to peculiar velocity effects, the exact 3D separation between an absorber and a galaxy cannot be precisely known, although the projected distance in the sky plane can be directly measured. Thus, we simply limit absorber-galaxy associations to within the physically motivated line-of-sight separation of $1000$[ [km s]{}$^{-1}$]{}, corresponding approximately to the velocity dispersion of clusters of galaxies.

Approach \#1: For each absorber, we find the most luminous galaxy within a projected distance of 1h$^{-1}$Mpc or 3h$^{-1}$Mpc (and within the aforementioned velocity separation). Figure \[fig:1\] shows the cumulative fraction of absorbers that have a galaxy of luminosity $>L_\mathrm{z}$ within this cylindrical volume. We show this distribution for absorbers of different integrated column density cuts (upper panel) or $\lambda$1032 equivalent width cuts (lower panel). For comparison, we also do the same exercise for a sample of galaxies placed randomly in the box, but with the same luminosity function and the same total number of galaxies.

Approach \#2: We relax the projected distance requirement, and find the closest galaxy with luminosity $\ge f L_\mathrm{z,*}$(with four different $f=0.03,0.1,0.3,1$). Figure \[fig:2\] shows the cumulative fraction of absorbers as a function of projected distance. As with Figure \[fig:1\], we show different column density (upper panel) and equivalent width cuts (lower panel). In addition, we show the different cuts in galaxy luminosity, and we repeat the exercise with a sample of randomly placed galaxies. Note that Figures \[fig:1\] and \[fig:2\] are complementary. A vertical cut in Figure \[fig:2\] at 1h$^{-1}$Mpc or 3h$^{-1}$Mpc, with the cumulative fraction of absorbers plotted against luminosity reproduces Figure \[fig:1\].

Approach \#3; For each absorber, we determine the number of galaxies that lie within the 3h$^{-1}$Mpc radius, 2000[ [km s]{}$^{-1}$]{} deep cylindrical volume. In Table \[tab:ngal\], we list the fraction of these absorbers that have more than n galaxies ($n=0,1,...$) in that volume. We do this for two subsamples of absorbers, those with $\lambda1032$ equivalent width larger than 30mÅ (typical detection limit for HST/STIS and FUSE spectra) and 10mÅ(expected limit for HST/COS observations). In addition to the equivalent width cuts in the absorber sample, we also make luminosity cuts in the galaxy sample. Current catalogs are typically able to reach galaxy luminosities of 0.1$L_*$ for statistically interesting volumes [e.g., @s06].

Taking Figures \[fig:1\] and \[fig:2\] together, we first address the question of which galaxies, and on what scales, are correlated (if any) with WHIM absorption. In Figure \[fig:1\], at luminosities fainter than $0.3-0.5
L_\mathrm{z,*}$, the curves lie below the equivalent curves for randomly-placed galaxies. That is, finding a lower luminosity galaxy near an absorber is less probable than if galaxies were uncorrelated with the absorbers for $D=1-3h^{-1}$Mpc. This merely implies that the correlation distance, defined to be the distance within which there is positive enhancement of pairs compared to random distributions, is smaller than $1h^{-1}$Mpc for these low luminosity galaxies, consistent with results summarized in Table 2 (see below). At higher luminosities, the curves are above the random galaxies. This implies that galaxies with $\gtrsim0.3
L_\mathrm{z,*}$ are correlated with WHIM absorption with the correlation distance larger than $3h^{-1}$Mpc, again consistent with results summarized in Table 2. This same information may be seen, in a different way, in Figure \[fig:2\], as the families of curves for fainter galaxies lie below equivalent ones for random galaxies, but the converse is true for higher luminosity galaxies. A perhaps somewhat counter-intuitive result in Figure 1 is that an absorber is more likely to find a faint galaxy within the $D=1h^{-1}$Mpc cylinder, if the galaxies were randomly distributed, and $\sim 30\%$ of absorbers do not find any galaxy to the faintest limit simulated. This is due to the fact that the galaxies themselves are more strongly clustered than absorbers among themselves or between galaxies and absorbers. Therefore, absorbers will have a lower probability of finding neighboring galaxies than when the latter are randomly distributed, beyond the cross-correlation distance.

An interesting feature immediately visible from Figures \[fig:1\] and \[fig:2\] is that the association between galaxies and absorbers depends weakly on either the column density or $\lambda$1032 equivalent width. This suggests that, while overall galaxies and absorbers are correlated on small scales, the physical properties of absorbers (e.g., strength, kinematics, number of components) themselves do not display any tight correspondence with nearby galaxies. It seems that the strengths of absorbers do not provide useful indicators for the properties of nearby galaxies. Physically, it suggests that absorbers may arise in the vicinities of galaxies in a wide variety of ways through complex feedback and thermodynamic processes. Complex interactions involving gravity-induced shocks, feedback and photoionization appear to have erased or smoothed out any potential trend with respect to column density or equivalent width. This finding is in accord with observations [e.g., @p06].

From Figure \[fig:2\], it appears that the distance out to which absorbers are correlated with galaxies is a function of both galaxy luminosity and absorber strength (even though the mere presence of a galaxy is not tightly correlated with absorber strength as from Figure \[fig:1\]). Comparison of the black curves in Figure \[fig:2\], showing the results of uncorrelated absorber and galaxy positions, with the equivalent families of the curves for the simulated galaxies and absorbers shows that there is typically a distance beyond which it is more probable to find an uncorrelated galaxy. This distance changes depending on the galaxy luminosity and the absorption strength. In the extreme case, there is no distance at which the strongest absorbers are correlated with the least luminous galaxies. In Table \[tab:distlum\], we list the correlation distances as a function of galaxy luminosity and absorption strength. We note two interesting features from the table: (1) For a given equivalent width limit, the correlation distance is a monotonic function of the limiting luminosity. (2) However, for a given limiting luminosity, the correlation distance is not a monotonic function of equivalent width limit. This may also point toward the eclectic nature of the absorbers as mentioned above.

It is interesting, however, to consider the number of galaxies that may be responsible for producing absorption. While the intragroup/intracluster medium (ICM) is typically too hot ($T\sim10^6$K) for to survive in appreciable quantities, the interfaces between warm, denser, photoionized clouds of temperature $T\sim 10^4$K and the ICM are potential locations for production. Examples of such interfaces include the boundaries between Milky Way high-velocity clouds and the hot Galactic corona [e.g., @fox05; @sem03]. From Table \[tab:ngal\], we find that 85% of , regardless of absorption equivalent width, do not lie near $L_\mathrm{z,*}$galaxies. Furthermore, the remaining 15% have at most 3 nearby $L_\mathrm{z,*}$, comparable the Local Group. This is not surprising given that $L_\mathrm{z,*}$ are not common. However, 99% of absorbers do lie near galaxies of lower luminosity, even if the presence of those galaxies is not correlated over what is expected from randomly placed galaxies.

Figure \[fig:2\] shows that $\le$20% of absorbers should find an $L_\mathrm{z,*}$ galaxy within a projected distance of $5 \mathrm{h}^{-1}$Mpc. Of course, one would not likely associate absorbers with $L_\mathrm{z,*}$ galaxies at such large projected separations, since, for example, one would have already found a nearby $\ge 0.03L_\mathrm{z,*}$ galaxy within 1h$^{-1}$Mpc, or $\ge 0.1L_\mathrm{z,*}$ galaxy at closer distance with comparable probability. In any case, it seems unlikely that $L_\mathrm{z,*}$ galaxies at such remote distances are responsible for creating the absorbers. The rapid rise of probability in Figure \[fig:2\] from $D_\mathrm{min}=0$ to $D_\mathrm{min}\sim 1 \mathrm{h}^{-1}$Mpc from galaxies $\ge
0.03-0.1L_\mathrm{z,*}$ may reflect a ubiquitous physical connection between absorbers and these relatively small galaxies, perhaps a result of galactic superwinds being able to transport metals to a distance of $\le 1 \mathrm{h}^{-1}$Mpc from these galaxies. This, however, does not necessarily exclude larger galaxies from being able to do the same. The slower rise of probability in Figure \[fig:2\] from $D_\mathrm{min}=0$ to $D_\mathrm{min}\sim 5 \mathrm{h}^{-1}$Mpc for galaxies $\ge
0.3-1L_\mathrm{z,*}$ may be a result of the intrinsic correlation of large galaxies and small galaxies on these scales. These more detailed issues will be examined subsequently elsewhere. Our results appear to be in broad agreement with observations [e.g., @s06; @s07; @t06].

We take a more detailed look at the dependencies of probability on the column density or equivalent width. Closer examination of the curves in Figure \[fig:1\] (lower-right corner of both panels) and in Figure \[fig:2\] (solid curves, lower-left corner of lower panel) reveals that the probability of finding a $\sim L_\mathrm{z,*}$ galaxy is higher for absorbers with a higher column density equivalent width. In particular, $N$()$\ge 10^{14}$cm$^{-2}$ or $W_\lambda\ge 100$ mÅ absorbers deviate noticeably from the weaker absorbers. This is a reversal of the trends from other parts of those figures. For smaller galaxies, e.g., $\ge 0.3L_\mathrm{z,*}$ galaxies (the set of dotted curves in the lower panel of Figure \[fig:2\]), the trend is considerably weaker although still visible. For still smaller galaxies, the trend is reversed, with weaker absorbers having a higher probability than stronger ones. These results seem to suggest that these very strong absorbers tend to be produced in richer, high density environments where the probability of finding massive galaxies is enhanced (we will examine this physical link elsewhere). The fact that weaker absorbers have a higher probability of finding a galaxy than stronger absorbers, for galaxies less luminous than $\sim 0.2-0.3L_\mathrm{z,*}$(Figure \[fig:1\]), once again suggests that these relatively weaker absorbers ($W_\lambda\le 50$mÅ) are probably produced by galaxies of $\sim 0.1L_\mathrm{z,*}$, not by more luminous galaxies. This is consistent with the trend in Figure \[fig:2\] above.

Conclusions
===========

We investigate the relationship between galaxies and metal-line absorption systems in a large-scale cosmological simulation with galaxy formation included. Our detailed treatment of metal enrichment and non-equilibrium calculation of oxygen species allow us, for the first time, to carry out quantitative calculations of the cross-correlations between galaxies and absorbers. We examine the the cross-correlations between absorbers and galaxies as a function of projection distance, with the line-of-sight velocity separation between an absorber and a galaxy constrained to within $\pm 1000$km/s. Here are some major findings: (1) The cross-correlation strength depends only weakly on the strength of the absorber but strongly on the luminosity of the galaxy. This result suggests that absorbers are produced ubiquitously and their physical/thermal properties and history vary widely, presumably due to the combined effects of gravitational shocks, feedback, photo-ionization and cooling processes. (2) The correlation length, however, does depend on both the galaxy luminosity and on the absorber strength from $\sim 0.5-1h^{-1}$Mpc for $0.1L_*$ galaxies to $\sim 3-5h^{-1}$Mpc for $L_*$ galaxies. While the dependence on luminosity is monotonic, the dependence on limiting equivalent width appears to peak at some luminosity-dependent value and then falls. (3) Only 15% of absorbers lie near $\ge L_\mathrm{z,*}$ galaxies. Thus the remaining 85% must be produced by gas ejected from fainter galaxies. The positions of lower-luminosity galaxies is not well correlated with absorbers (i.e. in comparison with randomly-placed galaxies). This may point toward pollution of intracluster gas by many galaxies, rather than a single high-luminosity galaxy. (4) For $\gtrsim 0.5L_\mathrm{z,*}$ galaxies, there is a positive correlation between absorber strength and galaxy luminosity (stronger absorbers have a slightly higher probability if finding such a large galaxy at a given projection distance). The reverse seems true for less luminous galaxies. On average, these results indicate that very strong absorbers tend to be produced in richer, high density environments where it is more likely to find massive galaxies.

The spatial resolution of our simulation is $\sim 80h^{-1}$kpc. While this is adequate for resolving large galaxies, it becomes marginal for galaxies in halos of total mass less than $\sim 10^{11}
M_\odot$. Therefore, some of the smaller galaxies of luminosities $0.01-0.03L_\mathrm{z,*}$ may be significantly affected and their abundances underestimated. In addition, systems that would have been produced from these under-resolved galaxies may be absent. As a result, one should treat the cross-correlation strength between absorbers and the low-luminosity galaxies as a lower bound. But we hope that the preliminary results presented here will provide a useful framework for comparison with upcoming imaging campaigns of galaxies in the field of quasars and spectroscopic observations with the [*Cosmic Origins Spectrograph*]{}.

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