The Self-Similarity of the Circumgalactic
Galaxy Virial Mass: Implications for Cold-Mode Accretion
We apply halo abundance matching to obtain galaxy virial masses, , and radii, , for 183 “isolated” galaxies from the “Mgii Absorber-Galaxy Catalog” (MAGiiCAT). All galaxies have spectroscopic redshifts () and their circumgalactic medium (CGM) is probed in Mgii absorption within projected galactocentric distances kpc. We examine the behavior of equivalent width, , and covering fraction, , as a function of , , and . Bifurcating the sample at the median mass , we find:  systematic segregation of on the – plane (); high-mass halos are found at higher with larger compared to low-mass halos. On the – plane, mass segregation vanishes and we find ();  high-mass halos have larger at a given , whereas is independent of at all ;  is constant with over the range within a given or . The combined results suggest the Mgii absorbing CGM is self-similar with halo mass, even above , where cold mode accretion is predicted to be quenched. If theory is correct, either outflows or sub-halos must contribute to absorption in high-mass halos such that low- and high-mass halos are observationally indistinguishable using Mgii absorption strength once impact parameter is scaled by halo mass. Alternatively, the data may indicate predictions of a universal shut down of cold-mode accretion in high-mass halos may require revision.
Subject headings:galaxies: halos — quasars: absorption lines
Direct observation of the circumgalactic medium (CGM) is important for exposing the link between the intergalactic medium and galaxies, and the processes governing their star formation histories, stellar masses, luminosities, and morphologies. The CGM harbors a reservoir of chemically enriched gas with a mass that may rival the gas reservoir in galaxies (Tumlinson et al., 2011). The Mgii absorption doublet observed in quasar spectra is an ideal probe of the CGM (see Churchill, Kacprzak, & Steidel, 2005, for a review); it traces low-ionization gas over the broad range cm (Churchill et al., 1999, 2000; Rao & Turnshek, 2000; Rigby, Charlton, & Churchill, 2002) and is detected out to projected distances of proper kpc (Kacprzak et al., 2008; Chen et al., 2010a; Churchill et al., 2012a; Nielsen, Churchill, & Kacprzak, 2012).
In general, the CGM is a complex dynamical region affected by accretion, winds, and mergers. Two distinct modes of accretion are theorized to operate, “hot” or “cold”, where the mode depends on whether the halo mass, , is above or below a critical threshold , where (e.g., Birnboim & Dekel, 2003; Kereš et al., 2005; Dekel & Birnboim, 2006; Kereš et al., 2009; Stewart et al., 2011; van de Voort et al., 2011). Cold-mode accretion is predicted in halos, whereas hot-mode is predicted in halos. Though some observations provide plausible evidence for cold-mode accretion at (Kacprzak et al., 2011; Ribaudo et al., 2011; Thom et al., 2011; Kacprzak et al., 2012), the baryonic mass in the cold mode is expected to diminish with decreasing redshift.
If accretion dominates, the distribution of absorber equivalent widths, , and the absorption covering fraction, , are predicted to markedly decline in halos. If a large reservoir of cold gas (– K) is present in the CGM of halos, it could imply outflows (cf., Stewart et al., 2011). Indeed, winds are commonly observed in Mgii absorption (e.g., Tremonti et al., 2007; Martin & Bouché, 2009; Weiner et al., 2009; Rubin et al., 2010; Martin et al., 2012). Alternatively, the increased number of sub-halos associated with higher mass halos (Klypin et al., 2011) could counteract the predicted behavior of and .
To observationally examine the validity of the hot/cold accretion theoretical paradigm, we require the halo masses of galaxies associated with absorption systems. A robust method for determining these masses is the parameterless halo abundance matching technique (e.g., Conroy et al., 2006; Conroy & Wechsler, 2009; Behroozi, Conroy, & Wechsler, 2010; Trujillo-Gomez et al., 2011; Rodriguez-Puebla et al., 2012). The method has been extremely successful at reproducing the two-point correlation function with redshift, luminosity, and stellar mass (Conroy et al., 2006; Trujillo-Gomez et al., 2011), the galaxy velocity function, and the luminosity-velocity and baryonic Tully-Fisher relations (Trujillo-Gomez et al., 2011).
In this Letter, we explore the connection between and the Mgii absorbing CGM and show that the “cold” CGM is self-similar with halo mass over the mass range . For this work, we define halo mass as the galaxy virial mass, including dark matter and baryons. In § 2 we describe our galaxy sample and our method to estimate each galaxy’s halo mass. We present our findings in § 3. In § 4, we summarize and provide concluding remarks. Throughout, we adopt a , , flat cosmology.
2. The Sample, Viral Masses, and Virial Radii
Our sample comprises 183 “isolated” galaxies from the “Mgii Absorber-Galaxy Catalog” (MAGiiCAT, Nielsen, Churchill, & Kacprzak, 2013). Each galaxy has a spectroscopic redshift (). The impact parameter range is kpc. The ranges of the AB absolute - and - band magnitudes are and , with rest-frame colors . Including upper limits, the rest-frame Mgii equivalent widths have the range Å with one system at Å.
The for each galaxy was obtained by abundance matching halos in the Bolshoi -body cosmological simulation (Klypin et al., 2011) to the observed -band luminosity function (LF) from the COMBO-17 survey (Wolf et al., 2003). In short, the method links the luminosity of galaxies to halo properties in a monotonic fashion, reproducing the LF by construction. Following Trujillo-Gomez et al. (2011), we adopt the maximum circular velocity, , and solve for the unique relation , which properly accounts for the depth of the potential well and is unambiguously defined for both central halos and sub-halos.
The halos were matched in the five redshift bins centered at , , , , of the COMBO-17 -band LF. The galaxy -band absolute magnitudes, , were determined by -correcting (e.g., Kim, Goobar, & Perlmutter, 1996) the , SDSS , or HST/WFPC F702W observed magnitudes using the actual filter response curves. We employed Coleman et al. (1980) spectral energy distribution (SED) templates from Bolzonella et al. (2000). The adopted SED for each galaxy was obtained by matching its observed color to the redshifted SEDs. The resulting range of is .
Scatter between and originates from scatter in the – relation due to different formation times of halos with similar mass. After mapping to , we account for this scatter by computing the average in a bin centered on the of the galaxy. Thus, each derived is interpreted as the average halo mass of a galaxy with . Varying the bin size had virtually no systematic effect nor change in the scatter of each mass estimate.
The primary uncertainty in the derived is the observed LF. Tests bracketing reasonable extremes of possible systematic errors in the measured LF yield that are qualitatively unchanged. Full details of our methods and uncertainties are described in Churchill et al. (2013). The masses have the range with median . Including systematics and scatter, the uncertainties are at increasing quasi-linearly to at .
We obtain the virial radius, , for each galaxy using the formulae of Bryan & Norman (1998),
where . The resulting radii have the range proper kpc with uncertainty of , where the uncertainty in each accounts for the standard deviation in the average virial mass assigned to each galaxy.
3.1. versus and
The observed anti-correlation between and is firmly established (e.g., Nielsen, Churchill, & Kacprzak, 2012, and references therein). However, there is significant scatter in the relation. The source of the scatter has been investigated assuming a “second parameter”, i.e., galaxy luminosity (Kacprzak et al., 2008; Chen et al., 2010a), stellar mass or specific star formation rate (Chen et al., 2010b), morphology (Kacprzak et al., 2007), or geometry and orientation (Bouché et al., 2011; Kacprzak et al., 2011).
We divided the sample into halo mass quartiles. In Figure 1a, we plot versus with points colored by mass (see legend). The curve is a log-linear fit (Nielsen, Churchill, & Kacprzak, 2012). Generally, the highest-mass halos (yellow and red points) segregate above the fitted curve, whereas the lowest-mass halos (blue and green points) segregate below the fitted curve.
In Figure 1b, we plot the data split by the median mass: the high-mass subsample (red points) has , and the low-mass subsample (blue points) has . A 2D Kolomorov-Smirnov (KS) test yields a significance that the null hypothesis the two subsamples have identical – distributions is ruled out. Excluding galaxies with upper limits on [absorbers only], the significance is . Clearly, there is significant mass segregation in the – distribution, such that lower mass halos cluster toward smaller and , whereas higher mass halos cluster toward larger values.
Since halo mass is a correlated source of scatter on the – plane, we examine versus , since . We plot these data in Figure 1c. The solid line is the fit , using the Expectation Maximization-Likelihood method (Wolynetz, 1979; Isobe, Feigelson, & Nelson, 1986), which accounts for upper limits. The fit is normalized to the mean of absorbing galaxies at . We obtained and . The dashed lines are uncertainty curves.
A BHK- non-parametric rank correlation test (Brown, Hollander, & Korwar, 1974; Isobe, Feigelson, & Nelson, 1986), which accounts for upper limits, yielded an significance for the anti-correlation between and (Nielsen, Churchill, & Kacprzak, 2012). Using the BHK- test, we find that is anti-correlated with at a significance. Relative to the fits, the variance of the data on the – plane is reduced from 0.50 to 0.11 on the – plane (absorbers only). An -test comparing the individual variances, , in both planes yielded probability that their distributions are drawn from the same parent population; the scatter is significantly reduced in the – plane. Furthermore, the distribution of halo masses about the fit has been homogenized. A 2D KS test comparing the distributions of the low- and high-mass subsamples is consistent with their being drawn from the same parent distribution ().
In summary, there is significant systematic mass segregation on the – plane. However, on the – plane, the scatter about the fit is reduced with very high significance; the anti-correlation is highly significant and the segregation by mass vanishes. The data suggest that the Mgii absorbing CGM is strongly linked to halo mass such that . Interestingly, the CGM exhibits substantial “patchiness” for , where the relative number of sight lines with non detections begins to increase. To investigate if this may be connected to galaxy properties, we performed KS tests to compared the colors and luminosities of absorbing galaxies and non-absorbing galaxies with Å and ; we find no statistical differences.
3.2. Covering Fraction versus and
Further insight is provided by the behavior of the covering fraction of the Mgii absorbing CGM, which has been investigated in some detail (Kacprzak et al., 2008; Chen et al., 2010a; Nielsen, Churchill, & Kacprzak, 2012). Nielsen, Churchill, & Kacprzak (2012) showed a dependence on galaxy -band luminosity in that higher luminosity galaxies have higher covering fractions at a given impact parameter than lower luminosity galaxies. Since luminosity is a proxy for mass, their result motivates an examination of the covering fractions as a function of .
In the upper panels of Figure 2, we present , the CGM covering fraction in an impact parameter bin having . The uncertainties for all covering fractions presented in this work were computed using binomial statistics. We computed for the high-mass (red triangles) and low-mass (green squares) subsamples and for the full sample (dashed bars). Generally, high-mass halos have larger at kpc with increasing significance as is lowered. Note that, for kpc, low-mass halos have for all , whereas high-mass halos have –0.1.
In the lower panels of Figure 2, we plot , the CGM covering fraction in a bin with . We find that for high- and low-mass halos are statistically identical; has no mass dependence for all at all .
Using the median fit between and obtained by Ménard & Chelouche (2009), each converts to a mean minimum neutral hydrogen column density. However, we caution that we extrapolated below the minimum of their fit ( Å).
The combined behavior of and strongly suggests that the Mgii absorbing CGM is self-similar with halo mass over the range . If so, in a fixed bin, the higher values for higher mass halos is naturally explained by the fact that the CGM of higher mass halos is probed at smaller , whereas lower mass halos are probed at larger .
3.3. Covering Fraction versus
In Figure 3, we present versus , where is the CGM covering fraction within impact parameter with . We computed for both proper coordinates (black points) and for co-moving coordinates (open blue points). The behavior of is not sensitive to the choice of coordinates. We find that shows no definitive trend with , being consistent with a constant value within errors.
We also computed , the CGM covering fraction within with . We plot versus in Figure 4. Again, a suggestion of self-similarity of the Mgii absorbing CGM is apparent; is effectively constant with halo mass within errors, primarily depending on and the cut. Though a suggestion decreasing with increasing is visually apparent, non-parametric rank correlation tests indicate that no correlation with is consistent with the data (null hypothesis satisfied within –).
Most importantly, we point out that neither nor rapidly decline or vanish for . This behavior is in conflict with theoretical predictions in which cold-mode accretion diminishes for (cf., Birnboim & Dekel, 2003; Kereš et al., 2005; Dekel & Birnboim, 2006; Kereš et al., 2009; Stewart et al., 2011; van de Voort et al., 2011), either implying alternative origins for a ubiquitous Mgii absorbing CGM or that cold mode accretion persists above .
4. Discussion and Conclusions
We applied the halo abundance matching technique to determine the galaxy virial masses, , for 183 “isolated” galaxies from MAGiiCAT (Nielsen, Churchill, & Kacprzak, 2013). We report four main results:
1. To a significant degree, the substantial scatter about the – anti-correlation is explained by a systematic segregation of halo mass on the – plane. With significance, the high-mass halos exhibit larger at greater compared to the low-mass halos. The significance of the – anti-correlation is and the data indicate . On the – plane, systematic halo mass segregation vanishes and the scatter is reduced with very high significance. These results suggest that Mgii absorption strength is strongly linked to via halo mass.
2. For all and , there is no dependence of the covering fraction on , whereas for smaller and kpc, is higher for the high-mass halos. Since decreases with increasing , the dependence of can be explained by the fact that at a fixed , higher mass halos are probed at smaller and lower mass halos are probed at larger . The combined behavior of versus , , and strongly suggests that the Mgii absorbing CGM is self-similar with halo mass over the range .
3. The covering fraction is constant with . Similarly, the covering fraction is a constant with for all and cuts. The magnitude of the covering fraction depends only on and the and cuts, decreasing with increasing for fixed cut and with increasing cut for fixed . The lack of dependence of with further supports our conclusion of the self-similarity of the Mgii absorbing CGM with halo mass.
4. Neither nor precipitously drop for . This behavior is in direct conflict with theoretical expectations of cold-mode accretion. If the Mgii absorbing CGM is self-similar with halo mass, it would imply that Hi in cold gas is also self-similar with halo mass.
If cold-mode accretion substantially diminishes above some (Birnboim & Dekel, 2003; Kereš et al., 2005; Dekel & Birnboim, 2006; Kereš et al., 2009; Stewart et al., 2011; van de Voort et al., 2011), our results imply that the Mgii absorbing CGM must be sustained by other mechanisms in halos. A most obvious candidate is outflows, which are observed in starburst galaxies (e.g., Tremonti et al., 2007; Martin & Bouché, 2009; Weiner et al., 2009; Rubin et al., 2010; Martin et al., 2012). On average, this would imply that, in high-mass halos, the dynamical and cooling times of non-escaping wind material are balanced with the wind cycling time scale such that their cold gas reservoirs are more-or-less observationally indistinguishable from the cold accretion reservoirs of low-mass halos. Simulations indicate recycling time scales on the order of 0.5–1.0 Gyr that decrease with increasing (Oppenheimer et al., 2010; Stewart et al., 2011). Thus, galaxies in higher mass halos with quiescent star formation for longer than yr would not be expected to have detectable Mgii or strong Hi absorption (c.f., Churchill et al., 2012b).
On the other hand, since the number of sub-halos increases in proportion to halo mass (Klypin et al., 2011), it is plausible that absorption from sub-halos counteracts our ability to observe the cut off of cold-mode accretion in the central halos with . Alternatively, the theoretical prediction that cold-mode accretion universally diminishes in higher mass halos may not be correct.
Since and , we deduce that over the range . That is, for fixed and for fixed . This behavior is consistent with the halo mass segregation we observe on the – plane, and is corroborated by the -stellar mass correlation reported by Martin et al. (2012) for starburst galaxies and the stellar mass dependence on the halo cross section of Mgii absorbing gas (Chen et al., 2010b). However, it is contrary to the global – anti-correlation reported by Bouché et al. (2006) and Gauthier et al. (2009) based upon cross-correlation techniques. We explore implications of this discrepancy in Churchill et al. (2013).
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