THE COS-HALOS SURVEY: AN EMPIRICAL DESCRIPTION OF METAL-LINE ABSORPTION IN THE LOW-REDSHIFT CIRCUMGALACTIC MEDIUM

The COS-Halos program targeted 38 galaxies with photometric redshifts z_phot ≈ 0.15–0.4 having a range of galaxy color (u − r) and stellar mass M_* = 10^9.5–10^11.5 M_☉, and distributed at impact parameters R ≈ 15–160 kpc from a background, UV-bright quasar (see J. Tumlinson et al., in preparation for a complete description of the sample definition). The survey selection criteria implied no explicit biases regarding the galaxy inclination or local environment. Previous studies of Lyα absorption in galaxy halos have indicated that the CGM of L ≈ L* galaxies extends to at least 300 kpc (Rudie et al. 2012; Prochaska et al. 2011b). We emphasize that our survey probes the inner 160 kpc, and therefore may not probe the entire, metal-bearing CGM of L* galaxies. Because of the occasional semi-catastrophic error in the photometric redshift, a small fraction of the galaxies have z ≲ 0.1 and correspondingly lower stellar mass and luminosity than expected. In the following, we restrict the study to galaxies with L > 0.1L* to isolate L ≈ L* galaxies, where we use the R-band absolute magnitude of −21.2 for an L* galaxy (Blanton et al. 2003). Future works will study the CGM of the fainter, dwarf galaxy population.

In the course of acquiring spectra for these targeted galaxies, we discovered an additional 21 galaxies at close impact parameters to the quasar and also with z < z_qso and L > 0.1L*. Although not our primary targets, these galaxies were selected without bias to CGM absorption and therefore are included in the following analyses, in identical fashion as the targeted sample. A full description of the galaxy spectra, photometry, and the inferred galaxy properties (e.g., SFR, stellar mass) is given in Werk et al. (2012). For convenience, Table 1 provides a summary of the galaxies studied here and Figure 1 shows histograms of a few key properties. Throughout the paper, we identify each galaxy according to the quasar field and its angular offset from the quasar, e.g., galaxy J0042−1037_358_9 is located 9'' from the quasar J004222.29−103743.8 oriented 358° east of north. Figure 2 shows the SDSS imaging and our Keck/LRIS spectrum of the representative galaxy J1233+4758 94_38. Once we trim the sample to exclude galaxies with L < 0.1L* and duplicate absorbers, defined as galaxies meeting all criteria outlined above with a more massive companion L* galaxy at the same redshift (see discussion below), we are left with 44 galaxy absorbers in total.

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Galaxies, owing to the processes of hierarchical structure formation, are known to cluster, form groups, and even merge with one another. For these reasons, "random" L* galaxies often reside within a virialized galaxy cluster or group, and a smaller subset are currently experiencing a merger with another galaxy. In the former cases, standard treatment is to refer to the cluster (group) member as a satellite of the far more massive, underlying dark matter halo. At z ∼ 0, models predict that tidal stripping significantly diminishes the size of the individual satellites' halos (Okamoto & Habe 1999). By extension, we infer that a large fraction of the gas at R < 160 kpc (pertaining to a galaxy's CGM) would likely be distributed throughout the intracluster or intragroup medium. In clusters, then, the localized intracluster or intragroup medium may dominate any observed absorption. This may be especially true for highly ionized species like O⁺⁵.

For the COS-Halos sample, Werk et al. (2012) carefully considered the environments of our target and bonus samples, as assessed from previous analyses of SDSS spectroscopy and photometry (maxBCG cluster catalog; Koester et al. 2007), and reported that only five of the galaxies (within three QSO fields) are probable members of a massive group or galaxy cluster: J0928+6025: 110_35 (0.766 Mpc projected from cluster center; 620 km s⁻¹ velocity offset), 129_19 (0.731 Mpc projected from cluster center; 570 km s⁻¹ velocity offset), and 187_15 (0.701 Mpc projected from cluster center; 700 km s⁻¹ velocity offset); J1016+4706: 359_16 (0.573 Mpc projected from cluster center; 985 km s⁻¹ velocity offset); and J1514+3620: 287_14 (19.3 Mpc from the cluster center; 1550 km s⁻¹ velocity offset). For reference, Koester et al. (2007) consider a galaxy to be a cluster member if the velocity offset is less than 2000 km s⁻¹. In addition to those galaxies that match a maxBCG cluster, we find three galaxies in the QSO field J2257+1340 (270_40, 238_31, and 230_25) that have confirmed spectroscopic redshifts z ∼ 0.177, all of which are probable members of a previously unidentified group of galaxies. In our analysis, we treat these systems in identical fashion to the others.

While the complications related to group/cluster environments are predicted (and observed) to be a rare concern for our program, projected pairs of L ≈ L* galaxies are more common. Deep sky surveys reveal that the fraction of ∼L* galaxies at z ∼ 0.2 that lie in close projected pairs is 2%–3% for R ⩽ 30 kpc (e.g., Zepf & Koo 1989; Kartaltepe et al. 2007) and ∼20% for R ⩽ 100 kpc (Lin et al. 2004). From our follow-up spectroscopy on the fields, there are seven cases where two or more L > 0.1L* galaxies with a very similar spectroscopic redshift (Δz < 0.004) lie within R = 160 kpc of the same quasar sightline. This number includes two cases of galaxy cluster/groups identified in the previous paragraph (QSO sightlines J2257+1340 and J0928+6025). Based on SDSS galaxy catalogs and less-accurate photometric redshifts, at least 10 additional galaxies included in our study could have an L > 0.1L* galaxy (in two cases, multiple galaxies) within a 300 kpc projected radius. In these cases, it is possible if not probable that the CGM of each galaxy contributes to the observed absorption. For example, the very high incidence of Lyα absorption from the CGM (e.g., Prochaska et al. 2011a; J. Tumlinson et al., in preparation) implies that any galaxy close to a quasar sightline will contribute H i absorption. In the case of galaxy pairs, assigning all of the observed absorption to a single galaxy would overestimate the CGM of that galaxy. It will be difficult if not impossible, however, to separate the contributions from each galaxy: the gas need not have identical velocity and line-blending further complicates the analysis.

For these reasons, we have taken the following approach to CGM analysis in fields where multiple galaxies lie close to the sightline and have velocity offset |δv| < 500 km s⁻¹ based on spectroscopic redshifts. We associate all observed absorption with the CGM of the most massive galaxy (gauged by the stellar mass) with virial radius r_vir ⩾ R (see J. Tumlinson et al., in preparation). This approach is partly justified by the expectation that lower mass galaxies near the sightline will lie within the dark matter halo of the most massive galaxy. In this case, lower mass galaxies are considered satellites. In short, our procedure yields constraints on the CGM for a population of 44 ≈L* galaxies with a diverse set of environments. Future analysis will focus on the importance of environment for the nature of the CGM from such galaxies.

There are several systematic errors associated with this procedure. First, projection effects can occur; on occasion, placing the smaller galaxy within the halo of the larger will be incorrect because the two are truly well separated. Second, stellar mass is not a perfect proxy for dark matter halo mass. Third, interactions amongst galaxies and their satellites may be a crucial aspect of the formation and evolution of the CGM. It may inappropriate or at least non-representative, to focus on the CGM of individual, isolated galaxies. Nevertheless, a proper treatment of modeling the CGM must take into account projection effects, the matching of stellar mass to dark matter halos, etc. Such analysis will be presented in a future paper of our own on this topic. This paper provides an empirical assessment of the CGM subject to the uncertainties described above.

J. Tumlinson et al. (in preparation) fully describe the acquisition, reduction, and calibration of the data from the Large Cycle 17 HST program (PID: 11598) known as COS-Halos whose COS spectroscopy provides all of the far-UV spectra analyzed here. For every sightline, these observations yielded a continuous spectrum spanning λ ≈ 1150–1800 Å. The exposure times were chosen to achieve a signal-to-noise ratio (S/N) of 7–10 per resolution element (FWHM ≈ 15 km s⁻¹) at λ ≈ 1300 Å. The analysis that follows was performed on the data binned by three native spectral "pixels" to a dispersion of Δλ ≈ 0.0367 Å.

Because the COS optics do not correct for the mid-frequency wave front errors arising from zonal irregularities in the HST primary, the true COS line-spread function (LSF) is not characterized by a single Gaussian. Instead, it is well described by a Gaussian convolved with a power law that extends to many tens of pixels beyond the line center (Ghavamian et al. 2009). These broad wings affect both the precision of our equivalent width measurements and complicate assessments of line saturation. We mediate these effects when we fit absorption lines (described in Section 3.3) by using the nearest wavelength grid point and convolving with the real LSF.

Although our coadding procedures properly preserve the Poisson counting statistics of the data, we find that we usually have enough counts in each pixel such that we can use standard propagation of error in the Gaussian regime. All of the spectra were continuum normalized with automated routines in ≈20 Å chunks centered on transitions of interest. These continuum models were visually inspected and manually adjusted as necessary. Figure 2 shows a representative slice of the COS spectra centered at the Lyα transition associated with the galaxy J1233+4758 94_38. One also notes strong Si iii λ1206 absorption consistent with this redshift.

To supplement the far-UV spectra from HST/COS, we obtained Keck/HIRES echelle spectra for 35 quasars (Table 2). For galaxies at z > 0.1, these data provide coverage of the Mg ii λλ2796, 2803 doublet, an excellent diagnostic of cool (T ⩽ 10⁴ K), metal-enriched gas. Because these data were taken at substantially higher spectral resolution and (generally) higher S/N than the COS data, they also offer additional constraints on line saturation and the kinematics of the CGM.

The HIRES spectra were obtained over four runs spanning the nights of UT 2008 October 6, 2010 March 26, 2010 September 2, and 2012 April 12–13. On each night, the instrument was configured with the blue cross-disperser and collimator, i.e., HIRESb. We employed an echelle angle ECH = 0° and a cross-disperser angle XDANGL ≈1.0 to give nearly continuous wavelength coverage from λ = 3050 to 5880 Å with ≈20 Å gaps at λ ≈ 3970 and 4965 Å, owing to the CCD mosaic configuration. We used the C1 decker for all observations giving a FWHM ≈ 6 km s⁻¹ spectral resolution.⁶ The data were reduced and calibrated using standard techniques with the HIRedux⁷ software package. The optimally coadded exposures (generally two per target) were continuum normalized with custom software, and a single combined spectrum sampled at Δv = 1.3 km s⁻¹ per pixel was generated for the absorption-line analysis. A portion of the Keck/HIRES spectrum for J1233+4758, centered at the Mg ii doublet of the z = 0.2221 94_38 galaxy, is shown in Figure 2.

For all important transitions not severely compromised by a line-blend or sky emission, we measured the rest equivalent width W_r and estimated its uncertainty with a simple boxcar summation over the analysis interval. These intervals and the W_r measurements are given in Table 3. The errors reported are statistical only; one may adopt an additional ≈20 mÅ systematic error owing to uncertainty in continuum placement (of order 5%). We estimate this typical error by considering an absorption-line profile that spans 100 km s⁻¹, corresponding to 430 mÅ at 1300 Å (observed), where 5% continuum placement error leaves us with an uncertainty of ≈20 mÅ . While 20 mÅ is a characteristic value for this uncertainty based on our data, one must bear in mind that the continuum placement uncertainty will more adversely affect the weakest, broadest, and shallowest absorption lines with a low central optical depth.

In cases where a line is significantly blended with another feature, we report the W_r measurement as an upper limit. We also provide upper limits (2σ statistical) for key transitions where the line is not detected at 3σ statistical significance. For the majority of the COS spectra, this corresponds to a detection threshold of ≈60 mÅ. The important exceptions are the Si iv and C iv doublets, which lie at observed wavelengths λ > 1500 Å, where the sensitivity of COS is degraded.

At a spectral resolution of R ≈ 20, 000, the COS spectra will generally not resolve individual components of the metal-line profiles with characteristic line-widths b ⩽ 10 km s⁻¹. Nevertheless, for weak absorption lines (W_r ≲ 200 mÅ), the effects of line saturation should be modest.

Our primary evaluation of the column densities was derived using the apparent optical depth method (Savage & Sembach 1996), over the same interval used to measure the equivalent width. Additionally, we have derived column densities using the curve-of-growth technique, but they rarely give converged values because of the significant component structure of the observed absorption lines. While the curve-of-growth technique can be more accurate for a single component or profiles that are dominated by a single strong component, that condition does not often hold in these strong absorbers. These measurements and associated error estimates (statistical only) are presented in Table 3.

If the normalized flux of a given transition goes below 0.1 at any of the binned pixels, we have automatically set the column density to be a lower limit (saturated). Non-detections are listed as 2σ (statistical) upper limits. The values for ions with multiple transitions were carefully inspected for consistency and signatures of line saturation. The measurements for many transitions are reported as lower limits due to line-saturation concerns. In cases with multiple measurements, we report the weighted mean in Table 3.

In addition to the AODM measurements of column densities, we fit Voigt profiles, where possible, to the detected absorption features in order to assess kinematic component structure and improve column density estimates of severely saturated lines. Additionally, profile fitting is essential for estimating the column densities of severely blended absorption lines, such as N iii λ989, which is often badly blended with Si ii λ989. The procedure used to perform the fits and derive the column density N, Doppler b, and velocity offset v for each component is described in greater detail in J. Tumlinson et al. (in preparation). In short, it is an iterative fitting program that makes use of the MPFIT software⁸ to optimize the fit and to generate errors near the best-fit point. The initial parameters, including the number of components, are set based on a by-eye examination of the data. Different transitions of the same ionic species are required to have the same component structure,⁹ and are therefore fit simultaneously to give a single solution. However, we do not impose such requirements on the different ionization states of the same element.

We tabulate the results of this analysis in Table 4, and include the AODM-derived column density in the final column for comparison. The profiles that are fit to the data are shown along with the data in Figure 3. In the subsequent analysis, we use the AODM-derived total column densities in figures and throughout most of the analysis. As a conservative measure, we exclude badly blended lines from the analysis and treat saturated lines as lower limits. The total fit column densities are predominantly consistent with the AODM-derived columns, even in cases of complete blending (Si ii λ989 affects the total column density of N iii λ989 at the 1%–2% level), so this choice has no impact on the results and trends that follow. The primary utility of the fits for this work is in a component analysis, which we touch on in Sections 4 and 5.

As discussed in Thom et al. (2012) and J. Tumlinson et al. (in preparation), the COS-Halos sample almost uniformly exhibits strong H i absorption (W_Lyα ≳ 1 Å, N_H i ⩾ 10¹⁴ cm⁻²). This indicates a substantial, cool gas phase for the CGM at R < 160 kpc from L* galaxies, independent of galaxy properties. If this medium is significantly enriched in heavy elements, then we may expect to detect at least a trace amount of dominant low ions (e.g., Si⁺, O⁰, Mg⁺). For the purposes of this work, we define "low ions" to be the first ion of each heavy element that has an ionization potential exceeding 1 Ryd. These should be the dominant ions in an optically thick gas where photons with hν > 1 Ryd are preferentially absorbed by the surrounding hydrogen.

In Figure 4, we show the equivalent width and column density measurements for the three low ions with a sensitive and large sample of measurements: Mg⁺, Si⁺, and C⁺. These quantities are plotted against the physical impact parameter R from the quasar sightline to the galaxy. The SF and non-SF galaxies are denoted by color (blue and red, respectively) and the symbol size is proportional to the measured H i column density (scaled linearly from log N_H i = 13 to 17).

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Focusing first on the SF galaxies, which dominate the sample, each ion shows weaker absorption at larger R (i.e., lower equivalent widths and column densities). Similarly, the fraction of sightlines with non-detections increases with R (Tables 5 and 6). For example, the median equivalent width of C ii λ1036 (Mg ii λ2796) $\tilde{W}_{1036}$ ($\tilde{W}_{2796}$) drops from 204(314) mÅ for R < 75 kpc to 59(85) mÅ for R > 75 kpc, while the median low ion column density drops from $\tilde{N}({\rm C^+}) = 10^{14.4}$ to 10^14.0 cm⁻² for C and $\tilde{N}({\rm Mg^{+}}) = 10^{13.3}$ to 10^12.3 cm⁻² for Mg. One draws similar results from estimates of the average values, although such analysis is complicated by the presence of both upper and lower limits. A two-sample log-rank test using the ASURV package on the W₂₇₉₆ or N(Mg⁺) values¹⁰ rules out the null hypothesis that the R < 75 kpc and R > 75 kpc subsets being drawn from the same population at 98% confidence.

One concludes, at high confidence, that the average surface density of low ions decreases with increasing impact parameter. This must reflect a decreasing total surface density, a decreasing metallicity, and/or an increasing ionization state with increasing R. Since it is likely that the H i column density also decreases with increasing impact parameter (J. Tumlinson et al., in preparation), an outwardly decreasing CGM metallicity gradient is the least likely to drive the main effect. Despite the decreasing column of low ion gas with increasing R, we report positive detections to at least 130 kpc and lack sufficient sample size to conclude that there is negligible low ion absorption at larger radii.¹¹ Future work should assess the covering fraction of low ion gas to the virial radius (and beyond) for L ≈ L* galaxies.

One cannot draw strong conclusions on the behavior of the low ions for the smaller, non-SF sample. There is a low detection rate at R < 75 kpc (1/4 sightlines), but a comparable or even higher rate of detection than the SF sample at R > 75 kpc. The dominant factor in a positive detection appears to be the N_H i value, which is uncorrelated with R for this small set of galaxies.

We now consider how the low ion absorption relates to other absorption properties of the system and characteristics of the associated galaxies. We derive the quantity N_Low for each system, defined as follows: (1) N_Low = N(Si⁺), if the Si⁺ measurement is a value or lower limit; (2) N_Low = N(Mg⁺), if the Si⁺ measurement is an upper limit (or there is none recorded) and a Mg⁺ measurement exists. We choose Si⁺ as the primary ion because it has multiple transitions in the far-UV bandpass with a range of oscillator strengths yielding more reliable column density estimates. The Mg ii doublet, meanwhile, offers more sensitive upper limits. Because we measure N(Si⁺) ≈ N(Mg⁺) in cases where both are measured, we apply no offset when adopting one versus the other. In all, there are roughly half of the systems in each category.

In Figure 5, we plot N_Low against N_H i for the full sample. Despite the preponderance of limits, there are several results to glean from the measurements (illustrated, in part, by the dashed and dotted lines in the figure). First, there is a complete absence of systems with N_H i ⩾ 10¹⁶ cm⁻² and N_Low < 10^12.3 cm⁻². In fact, only 2 of the 12 systems with these N_H i values have N_Low < 10^13.3 cm⁻². This suggests a low incidence of metal-poor gas in the CGM of L* galaxies (e.g., Ribaudo et al. 2011). Second, with only one exception, sightlines definitively exhibiting N_H i ⩽ 10¹⁶ cm⁻² (ignoring lower limits) are all consistent with having N_Low < 10^12.3 cm⁻². (One notable counterexample from the literature is the sightline studied by Tripp et al. 2011, which has many components with N_H i ⩽ 10¹⁶ cm⁻² and very extensive low ion absorption.) While in principle this could result from lower metallicity at lower N_H i, we suspect this result follows from the ionization state of the gas possibly combined with a lower surface density of total hydrogen. Third, all systems with N_Low ⩾ 10¹³ cm⁻² are consistent with N_H i > 10¹⁶ cm⁻² and all systems with N_Low < 10^13.3 cm⁻² have N_H i < 10¹⁶ cm⁻². In at least rough terms, therefore, N_H i = 10¹⁶ cm⁻² demarcates a relatively rapid transition from significant to nearly negligible low ion absorption. By the same token, the presence of significant low ion absorption (e.g., a Mg ii doublet) implies gas with a non-negligible opacity at the Lyman limit, at least for sightlines intercepting the CGM of an L* galaxy.

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Turning to the relation of low ion absorption with galaxy properties, the top two panels of Figure 6 plot N_Low against (a) SFR and (b) stellar mass, with the symbol size inversely proportional to the impact parameter. In terms of SFR, there may be a general trend of lower N_Low values (average or median) with decreasing SFR, but there is substantial scatter at all values. This scatter appears well correlated with R for the SF galaxies, but possibly anti-correlated with R for the non-SF galaxies. In any case, we conclude that it is unlikely that SFR is a dominant factor driving the strength of low ion absorption, which runs contrary to the inferences drawn by Ménard & Chelouche (2009).

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In contrast, the N_Low values appear well correlated with stellar mass, indicating that there is more circumgalactic gas in more massive galaxy halos. For example, the galaxies with M_* > 10¹¹ M_☉ show the highest N_Low values and a high incidence of positive detections (6/7) even though the sample is almost exclusively red, non-SF galaxies. Meanwhile, the non-SF galaxies with M_* < 10¹¹ M_☉ are dominated by non-detections. In fact, restricting the evaluation to the non-SF galaxies, there is a significant trend with M_*. Even with the small sample size, the non-SF galaxies with M_* < 10¹¹ M_☉ have a distribution of N_Low values that differs from the M_* > 10¹¹ M_☉ at 95% confidence. This cannot be simply attributed to differences in impact parameter between the two subsamples. Despite an apparent trend of decreasing N_Low with decreasing M_* for the SF galaxies with M_* < 10¹¹ M_☉, the null hypothesis of no correlation is not ruled out at very high confidence (94%) by a generalized Kendall-tau test. If such a trend exists, it will require a larger sample of galaxies, possibly controlled for impact parameter.

For the purposes of this work, we define an "intermediate ion" as the first species of an element which requires an excess of 1 Ryd in energy to produce it. For example, the intermediate ions of C and Si are C⁺⁺ and Si⁺⁺, which require 24.4 and 16.3 eV of energy, respectively, to ionize the previous (low ion) stage. Owing to their higher ionization potential, one predicts that these ions trace more highly ionized gas, e.g., the inner portions of an H ii region.

In the far-UV, there are two particularly strong transitions from these intermediate ions, Si iii λ1206 and C iii λ977. Measurements of their equivalent widths and column densities for the COS-Halos sample are presented in Figure 7. It is immediately evident that the sightlines show a high covering fraction, even exceeding the observed values for the low ions. For C iii 977, the SF galaxies exhibit a nearly 100% C_f (Tables 5 and 6) with the only non-detection in 14 cases having R ≈ 160 kpc. Within R = 50 kpc, the results are especially striking. The SF galaxies uniformly exhibit equivalent widths W₉₇₇ > 400 mÅ corresponding to lower limits on N(C⁺⁺) of 10^14.2 cm⁻² and higher. Some of the values may even exceed the observed H i column densities.

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The results for Si⁺⁺ are similar, albeit with a greater dynamic range of equivalent widths and column densities, and somewhat lower C_f values. Si⁺⁺ (f_{λ, 1206} = 1.660) has a larger oscillator strength than Si⁺ (f_{λ, 1260} = 1.007), which may play a role in this difference. Nonetheless, the greater dynamic range reveals a key result: the absorption strength of intermediate ions is highly correlated with impact parameter. Restricting to the positive detections of the SF galaxies and treating all of these as values,¹² we measure a Spearman's rank correlation of −0.65 and −0.69 for W₁₂₀₆ and N(Si⁺⁺) versus R implying an anti-correlation at 99.95% and 99.99% confidence. Motivated by the strong anti-correlation, we modeled the radial variation in W₁₂₀₆ and N(Si⁺⁺) with single power-law expressions:

$$\begin{equation} W_{1206} = W_{(10\,\rm kpc)} \left(\,\frac{R}{10\,{\rm kpc}} \,\right) ^{\alpha _W}, \end{equation} \tag{ 1 }$$

$$\begin{equation} N({\rm Si^{++}}) = N_{\rm (10\,kpc)} \left(\,\frac{R}{10\,\rm kpc} \,\right) ^{\alpha _N}. \end{equation} \tag{ 2 }$$

In each case, we have restricted the analysis to the positive detections and have taken lower limits at their measured value. Minimizing χ² with equal weighting for each measurement, we derive log W_(10 kpc) = 0.13 ± 0.44, α_W = −0.84 ± 0.24 and log N_(10 kpc) = 14.1 ± 0.2, α_N = −1.11 ± 0.29. This simple model is overplotted on the data in Figure 8. The preponderance of lower limits to N(Si⁺⁺) at R < 50 kpc implies a even higher log N_(10 kpc) and steeper α_N values than reported by this simple analysis. We discuss the implications and possible origins of this central result in Section 5.

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Regarding the non-SF galaxies, the incidence of positive detections for the intermediate ions is lower than that observed for the SF galaxies, with C_f ≈ 50% for Si⁺⁺ and C⁺⁺. On the other hand, the equivalent widths and column densities of the positive detections are comparable or even higher than those for the SF galaxies. This gives a bimodal distribution in the non-SF galaxy subset which is not evident in the SF galaxy sample (Figure 9). The implication is that the gas is either less smoothly distributed within individual halos of non-SF galaxies and/or that there is a bimodal separation in the CGM amongst the galaxies themselves. A similar result holds for C⁺⁺ as well. A less likely option to explain this result would be that all of the non-SF galaxies for which we have detected low and intermediate ion absorption have a fainter, SF galaxy in their vicinity that is associated with the gas. We have not completed a redshift survey of all faint sources in the COS-Halos quasar fields, and the SDSS images are not sensitive to galaxies fainter than 0.1L* at z ∼ 0.2, so it is impossible to comment in detail about this option. However, we do note that a visual inspection of the SDSS images of the non-SF galaxy QSO fields yields very few additional blue L > 0.1L* candidates within 2'. Even if there are other SF galaxies in their vicinity, the CGM gas is nonetheless physically associated with the elliptical and very likely bound to its dark matter halo. Establishing the origin of the CGM is beyond the scope of this empirically focused paper.

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To explore further the characteristics of the intermediate ions, we plot in the lower two panels of Figure 6 N(Si⁺⁺) against the (c) SFR and (d) stellar mass of the associated galaxies. Similar to the low ion absorption, there is no obvious correlation with intermediate ion column density and SFR. Regarding M_*, however, one identifies notable trends. Restricting first to the SF population, the N(Si⁺⁺) values appear correlated with M_*; the null hypothesis is ruled out at 99% confidence by a generalized Kendall-tau correlation test. Similarly, the median column density for M_* > 10^10.5 M_☉ is $\tilde{N}({\rm Si^{++}})= 10^{13.4} \,{{\rm cm}^{-2}}$ and $\tilde{N}({\rm Si^{++}})= 10^{12.9} \,{{\rm cm}^{-2}}$ for M_* < 10^10.5 M_☉. Within the non-SF population, there is a preponderance of low N(Si⁺⁺) values for M_* < 10¹¹ M_☉ (6/8). Indeed, this stands in stark contrast to the SF population. The notion of a correlation, however, is tempered by several positive detections at these masses. Another notable result revealed by Figure 6 is that the quiescent galaxies are well separated from the SF galaxies within the M_* panels, both low and intermediate ions.

In concluding this section, we compare the column densities and component structure of the low and intermediate ions. We supplement this analysis by comparing these profile fits with those of O⁺⁵ (Tumlinson et al. 2011). Figure 10 plots the N(Si⁺)/N(Si⁺⁺) and N(C⁺)/N(C⁺⁺) ratios against two quantities that may be expected to correlate with the ionization state of the gas: H i column density and the SFR scaled inversely by the impact parameter squared. For the former, one expects stronger low ion absorption as N_H i increases and the gas becomes optically thick to ionizing radiation. The quantity SFR/R², meanwhile, represents an estimate of the ionizing flux from massive stars. This assertion is subject, of course, to uncertainties in the escape fractions of galaxies, to error in using R as the distance from source to gas, and to the relative flux of the galaxy to the extragalactic UV background.

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The main point to emphasize from Figure 10 is that the N(Si⁺)/N(Si⁺⁺) ratios are uniformly low; nearly every system¹³ is consistent with N(Si⁺)/N(Si⁺⁺) < 1. If the gas arises in a single phase, this requires that the majority of CGM gas is significantly ionized. One draws the same conclusion from the observed N(C⁺)/N(C⁺⁺) ratios. Inspection of Figure 10 also reveals there are no obvious trends with SFR/R² or N_H i. Perhaps the only noteworthy observation in this regard is that the two systems with N(Si⁺)/N(Si⁺⁺) exceeding unity have amongst the lowest SFR/R² values in the SF population.

If the low and intermediate ions arise from a single phase, then one would expect the kinematic component structure of their absorption profiles to be similar. We may test this prediction through an analysis of the profile fits generated from the absorption lines (Table 4). As we impose no restrictions on the component structure between different ionization states of the same element, any qualitative and quantitative similarities between the fits arise naturally. Indeed, a visual inspection of the fitted absorption features indicates strong similarities between low and intermediate ionization states of Si, C, and N (Figures 3 and 11). Errors in the COS wavelength solution should only weaken such correlations. Generally, the intermediate ion absorption tends to be stronger than the low ion absorption in the CGM of L* galaxies, but there is no evidence that the low and intermediate ionic absorption arise from different gas phases based on their component structure alone.

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We have also shown in Figure 11 the profile fits to the O⁺⁵ absorption line, which were derived from our COS data set and analyzed previously by Tumlinson et al. (2011). Unlike the clear correspondence between the black (low ion) and red (intermediate ion) lines, a qualitative assessment of the overall agreement and component structure of the blue (high ion: O⁺⁵) lines is complex. In nearly all cases, the individual fitted components of the O⁺⁵ absorption lines are broader than those of the lower ionization states, but there is generally good correspondence between the shape and number of components. There are impressive alignments (e.g., J1419+4207 132_30; J1009+0713 204_17), but just as many, if not more, complete misalignments (e.g., J1330+2813 289_13; J1435+3604 68_12). This comparison suggests that the relationship between low and high ionization states of gas along the same sightlines is not straightforward, and commenting further here is beyond the scope of this paper. Future work will perform a quantitative comparison of these profiles and examine the implications for the origins and overlap of this broad range of circumgalactic gas ionization states.

A valuable measure of assessing the distribution of absorption by the CGM is through estimations of the covering fraction C_f. Strictly speaking, the C_f value describes the fraction of random sightlines that pass within a given impact parameter to a galaxy (or population of galaxies) that exhibit a specified absorption strength for a given transition or ion. For example, one can measure the fraction of sightlines exhibiting W_{r, 2796} > 0.3 Å when passing within¹⁴ 50 kpc of a SF L* galaxy at z = 0. The covering fraction assesses how gas in the CGM is distributed (as projected on the sky), gives a rough assessment of the strength of absorption, and reduces complex distributions to a single number. Furthermore, it presents a simplified target for theoretical models to consider.

Despite its apparent simplicity, estimating the C_f values for the equivalent width of a specific transition or the column density of a given ion is non-trivial. This is due to several factors. First, we have a limited sample of galaxies under study and cannot claim to have a complete sample, nor (necessarily) even a fully representative sample of any given population. Second, we have limited sampling of the CGM on scales of R < 30 kpc. Third, the projected area scales with radius whereas we designed the COS-Halos project to uniformly sample impact parameter from R ≈ 30 to 160 kpc. A strict comparison of models to our data set must account for these issues. Lastly, both the equivalent width and column density measurements include a mix of measurements and upper/lower limits. Given these limitations, we proceed conservatively.

For the covering factors relating to the equivalent width measured for a specific transition (e.g., W_{r, 2796}, W_{r, 1334}), we chose thresholds that exceeded nearly all of the observed upper limits. These values are listed in Column 4 of Table 5. In cases where an upper limit exceeds this threshold, we included that measurement as if it exceeds the threshold, thereby increasing C_f. The error reported in C_f, which follows a standard binomial Wilson score, accounts for this uncertainty by calculating the 68% confidence interval assuming that upper limits above the threshold do not satisfy it.

The evaluation of C_f for column density measurements are more challenging because they often include a mix of upper and lower limits (Table 6). Again, we aimed for a column density threshold that exceeded the upper limits while not exceeding the lower limit values. Similar to the C_f for W_r values, we treated upper limits above the threshold as detections. We also considered lower limits below the line as satisfying the threshold. In this respect the resultant C_f values may be considered maximal, aside from the uncertainty of Poisson statistics.

In Figure 12, we present a comparison of the C_f values for transitions spanning a wide range of ionization state. The results for H i and O⁺⁵ are drawn from the J. Tumlinson et al. (in preparation) and Tumlinson et al. (2011) papers, respectively. It is evident that the H i gas exhibits the highest covering fraction, not only for the SF galaxies; L* galaxies of all spectral type exhibit a CGM of cool, hydrogen gas (Thom et al. 2012). Examining the metal-line transitions, which are arranged from lowest to highest ionization potential, one observes a significant covering (C_f > 0.5) for all ions and populations except O⁺⁵ for the non-SF galaxies (Tumlinson et al. 2011). This demonstrates significant metal enrichment throughout the CGM of L* galaxies. It further suggests a multi-phase medium because it is nearly physically impossible to find strong low ion and O⁺⁵ absorption in the same gas. One also observes a trend of increasing C_f with increasing ionization state. For the SF galaxies, there is a monotonic increase in C_f from 60% in the low ion species to nearly 90% for the highly ionized O⁺⁵ gas. This implies that the gas is significantly ionized. The non-SF galaxies also show increasing C_f until O⁺⁵ where one finds much less gas (Tumlinson et al. 2011). The CGM of quiescent L* galaxies is also enriched, but that there is a qualitative difference between the two populations at the highest ionization states.

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We explore variations in C_f with impact parameter in the lower panel of Figure 12. Within the SF population (blue), there is a clear difference between the two radial cuts for metals such that the metal covering fraction is lower for higher impact parameters. While a declining metallicity gradient could be responsible, this trend is more likely the result of the decreasing total gas surface density with radius (J. K. Werk et al., in preparation). Oddly, the opposite trend is noted for the quiescent galaxies (red). We are concerned, however, that this may be masked by the small number statistics of this sub-population.

As a check on our analysis, we may wish to compare our results against similar measurements from the literature. Such comparisons may reveal systematics in our line measurements or anomalies in the sample definition. Unfortunately, very few analyses have been performed on the low and intermediate ionization states of metal-line absorption in the CGM of L* galaxies. The obvious exception is Mg⁺, which has been extensively surveyed over the past several years (e.g., Barton & Cooke 2009; Chen et al. 2010), and to a lesser extent C⁺³ (not covered by this work), which is found to extend out to 150 kpc (Chen et al. 2001).

In Figure 13, we present a comparison of our W_{r, 2796} measurements against impact parameter with those reported by Chen et al. (2010). We also plot their favored model for the variation of W_{r, 2796} with impact parameter, adopting L = L* in the calculation. Qualitatively, we find that the two data sets are in good agreement. The positive detections occupy similar regions of the W_{r, 2796}, R parameter space and the upper limits occur primarily at R > 50 kpc. Both data sets show a very large dispersion with respect to the W_{r, 2796}(R) model; in fact, the line appears to best describe the division between detections and non-detections at R > 70 kpc. We conclude that our sample, which extends to many ions beyond Mg⁺, has no especially anomalous characteristics.

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