Metal-Poor, Cool Gas in the Circumgalactic Medium of a $z=2.4$ Star-Forming Galaxy: Direct Evidence for Cold Accretion?

In our current galaxy formation paradigm, high-redshift galaxies are predominantly fuelled by accretion of cool, metal-poor gas from the intergalactic medium. Hydrodynamical simulations predict that this material should be observable in absorption against background sightlines within a galaxy's virial radius, as optically thick Lyman-limit systems (LLSs) with low metallicities. Here we report the discovery of exactly such a strong metal-poor absorber at an impact parameter $R_\perp=58$kpc from a star-forming galaxy at $z=2.44$. Besides strong neutral hydrogen (${\ensuremath{N_{\mathrm{H}^0}}}=10^{19.50\pm0.16}~{\rm cm\ensuremath{^{-2}}}$) we detect neutral deuterium and oxygen, allowing a precise measurement of the metallicity: $\log_{10}(Z/Z_\odot)=-2.0\pm0.17$, or $(7-15)\times10^{-3}$ solar. Furthermore, the narrow deuterium linewidth requires a cool temperature $<20,000$K. Given the striking similarities between this system and the predictions of simulations, we argue that it represents the direct detection of a high redshift cold-accretion stream. The low-metallicity gas cloud is a single component of an absorption system exhibiting a complex velocity, ionization, and enrichment structure. Two other components have metallicities $>0.1$ solar, ten times larger than the metal-poor component. We conclude that the photoionized circumgalactic medium (CGM) of this galaxy is highly inhomogeneous: the majority of the gas is in a cool, metal-poor and predominantly neutral phase, but the majority of the metals are in a highly-ionized phase exhibiting weak neutral hydrogen absorption but strong metal absorption. If such inhomogeneity is common, then high-resolution spectra and detailed ionization modelling are critical to accurately appraise the distribution of metals in the high-redshift CGM.

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

It is now recognized that the physical processes by which galaxies accrete, expel and recycle baryons are of central importance to galaxy evolution [e.g. @Dave12]. The current theoretical paradigm emphasizes a 'cold-mode' of accretion [@Birnboim03; @Keres05] that fuels the high star formation rates (SFRs) observed in the early universe. This cool ($T\sim 10^4$ K), accreting gas is predicted to produce observable signatures as high column density, low metallicity absorption systems [@Fumagalli11; @FaucherGiguere11; @Stewart11; @vandeVoort12_dla; @Kimm11; @Goerdt12; @Nelson13] in the spectra of background sightlines which pass through the circumgalactic medium (CGM) of high redshift galaxies. However, there is little direct observational evidence for the cold-accretion phenomenon. Instead, metal-enriched outflows are commonly observed from $z\sim2-3$ Lyman-break galaxies (LBGs) as blue-shifted absorption features in the galaxies' spectra [@Pettini01_LBG; @Steidel10]. Energetic 'feedback' in some form is required to regulate star formation in numerical simulations, which is necessary to match observables such as the stellar luminosity function [@Oppenheimer10] and galaxy rotation curves [@Stinson13_EarlyFeedback], but the distances to which these outflows travel and their energetics are poorly constrained. Precise measurements of the enrichment and physical conditions of the CGM are thus crucial both to test the cold accretion picture and to characterize how far outflowing material travels.

The best technique currently available to measure metallicities is by analyzing individual absorption line profiles from gas in the CGM. This technique has been used extensively to measure metallicities of high column density systems over a broad redshift range [e.g. @Steidel90_LLS; @Lehner13]. However, the relationship between the absorbing gas and galaxies in these studies is often unclear, making them difficult to interpret in the context of galaxy formation models. The cold accretion phenomenon may persist to lower redshifts in lower mass haloes, and several observational studies have discovered low metallicity ($Z/Z_\odot=0.01-0.1$) absorbers in the neighbourhood of $z<1$ galaxies [e.g. @Chen05_dla; @Tripp05; @Ribaudo11; @Kacprzak12; @Churchill12]. But measurements of CGM enrichment near vigorously star-forming galaxies at $z\sim2.5$, during the peak of the cosmic SFR and where cold accretion is predicted to occur over a wide range of halo masses, have proven to be much more challenging.

In this letter we analyze an echelle spectrum of a background QSO at an impact parameter of 58 kpc from a foreground star-forming galaxy discovered by @Rudie12[^1]. The high signal-to-noise ratio (${\rm
  S/N\sim 90}$), high-resolution (${\rm FWHM}\sim8.8~{\rm km~s\ensuremath{^{-1}\,}}$) spectrum combined with the rare detection of the deuterium isotope of hydrogen, enable us to effectively disentangle absorption produced by neutral, metal poor gas from that of more highly ionized, metal enriched gas. The deuterium detection allows us to precisely measure the metallicity of a metal-poor CGM absorber, and we show that it exhibits many of the characteristics expected for cold-mode accretion.

Observations and Analysis
=========================

The Background QSO and Foreground Galaxy
----------------------------------------

The bright background QSO J1444535$+$291905 ($g=16.4$) at redshift $z=2.660$ has been observed using the HIRES echelle spectrograph on Keck by several groups from 1995 to 2009. We obtained the spectra from the Keck archive and reduced them with <span style="font-variant:small-caps;">makee</span>[^2]. The final combined spectrum covers wavelength ranges $3100$ to $5950$ Å (resolution $8.8\,{\rm km~s\ensuremath{^{-1}\,}}$) and $7350$ to $9760$ Å (resolution $6.7\,{\rm km~s\ensuremath{^{-1}\,}}$).

The foreground galaxy's redshift ($z_{gal}=2.4391$) and impact parameter from the background QSO ($R_{\perp}=58$ kpc) are given by @Rudie12 [their figure 12]. The redshift uncertainty is $160-180$ <span>km s$^{-1}\,$</span>, which arises when rest-frame UV transitions such as <span>$\rm Ly\alpha$</span> emission and metal absorption are used to determine the intrinsic redshift [@Rakic11]. Rudie et al. do not publish further details on the galaxy, but such galaxies typically have a dust-extinction corrected SFR of 30 <span>$\rm M_{\odot}\;{\rm yr}^{-1}$</span> [@Erb06_sfr], a gas-phase ISM metallicity of $Z/Z_\odot\sim0.8$ [@Erb06_Z] and a dark matter halo mass $5\times10^{11}~{\ensuremath{\rm M_\odot}}$ [@Bielby13]. This halo mass implies a virial radius of 75 kpc [@Bryan98], and thus the projected separation from the background QSO sightline is comparable to the virial radius.

We note that @Rudie13 indicates a second star-forming galaxy is present at $R_\perp=50$ kpc within $250~{\rm km~s\ensuremath{^{-1}\,}}$ of the first galaxy, but does not publish the spectroscopic redshift. We adopt $R_\perp=58$kpc for our analysis, but our conclusions remain unchanged if a second galaxy exists at an even closer impact parameter.

The Absorption System at $z=2.44$
---------------------------------

The HIRES spectrum reveals a sub-damped absorption system, originally discovered by [@Simcoe02], that is coincident with the redshift of the foreground galaxy. Our Voigt profile fit to the damping wings implies a total neutral hydrogen column density ${\ensuremath{N_{\mathrm{H}^0}}}=10^{19.85\pm0.1}$ <span>cm$^{-2}$</span> (Figure \[f\_HI\], top). Absorption from low and high-ionization ionic metal line transitions is present in 16 distinct components spread across $320\,$<span>km s$^{-1}\,$</span> (Figure \[f\_metals\]). The total ${\ensuremath{N_{\mathrm{H}^0}}}$ is well-constrained, but as we will demonstrate, the metallicity varies by an order of magnitude among the components. Fortuitously, we can also constrain <span>$N_{\mathrm{H}^0}$</span> for several *individual* components.

We measured column densities in the system by fitting Voigt profiles with <span style="font-variant:small-caps;">vpfit</span>[^3], and by using the apparent optical depth [AOD, @Savage91] method. Voigt profile fits assess the degree to which a single kinematic model can explain all the observed absorption: low-ionization transitions were used to define the main velocity components, and we found that a single velocity structure matches all the low-ionization species well. The resulting models are shown in Figures \[f\_HI\] & \[f\_metals\]. The higher ionization transitions ,  and  do not follow the same velocity structure as the low-ions, indicating there is likely a contribution from a hotter or more highly-ionized phase. Similar offsets between low and high-ions have been observed in other high-$z$ absorbers [e.g. @Fox07]. Table \[t\_one\] gives Voigt profile parameters and our adopted column densities for each component. Our Voigt profile fits to both the high-ions and low-ions show no evidence for partial covering or unresolved saturated components.

\[p\] ![image](f1a.eps){width="0.6\columnwidth"}

\

  --------------------------------------------- ---------------------------------------------
   ![image](f1b.eps){width="0.95\columnwidth"}   ![image](f1c.eps){width="0.95\columnwidth"}
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![image](f2.eps){width="1.99\columnwidth"}

Components for which Abundances Can be Precisely Measured
---------------------------------------------------------

We identify three kinematic regions for which the neutral hydrogen column <span>$N_{\mathrm{H}^0}$</span>, and thus the metallicity, can be precisely measured. The first is at $-218$ <span>km s$^{-1}\,$</span> relative to the galaxy redshift, where absorption from neutral deuterium is detected at Ly-$\gamma$, Ly-$\delta$, Ly-$\epsilon$ and Ly-8. Deuterium detections in QSO absorbers are rare, as a measurement of the weak D absorption requires a narrow linewidth, high <span>$N_{\mathrm{H}^0}$</span>, and the absence of blending with weaker neighbouring <span>$\rm Ly\alpha$</span> forest lines [@Webb91]. Such detections are valuable however, because a precise D/H measurement constrains the cosmic baryon density according to big bang nucleosynthesis theory. For the D component we detect, ${\ensuremath{N_{\mathrm{D}^0}}}=10^{14.93\pm0.06}{\rm cm\ensuremath{^{-2}}}$ and $b({\ensuremath{\mathrm{D}^0}})=10.60\pm0.53~{\rm km~s\ensuremath{^{-1}\,}}$, which are consistent with the expected column density and width of the associated <span>$\mathrm{H}^0$</span>, estimated from the damping wings and the Lyman series, assuming thermal broadening and the cosmic D/H ratio inferred from the WMAP cosmic baryon density [@Keisler11]. This width is much narrower than is typical for a <span>$\rm Ly\alpha$</span> forest line with the ${\ensuremath{N_{\mathrm{H}^0}}}\approx10^{15}{\rm cm\ensuremath{^{-2}}}$ necessary to imitate , which demonstrates that this is not an interloping <span>$\rm Ly\alpha$</span> forest line.

We can use the D/H ratio implied by the cosmic baryon density to make a precise measurement of <span>$N_{\mathrm{H}^0}$</span> in this component. @Pettini12 find $\log_{10}({\rm D/H})=-4.585\pm0.02$ in QSO absorbers. The standard deviation in these QSO values (0.15) is larger than that expected from the measurement errors, and represents real scatter due to an unidentified astrophysical effect and/or underestimated systematic errors in the D/H analyses. We conservatively assume the scatter represents a physical variation and take $\log_{10}({\rm
  D/H})~=-4.585\pm0.15$. <span>$\mathrm{D}^0$</span>/<span>$\mathrm{H}^0$</span> is the same as D/H, and therefore $\log_{10}{\ensuremath{N_{\mathrm{H}^0}}}=19.50\pm0.16$ for this component.

Crucially, we also detect <span>O<span>i</span></span> in this component, which allows a direct measurement of the metallicity from O$^0/$H$^0$. For ${\ensuremath{N_{\mathrm{H}^0}}}\gtrsim 10^{19}~{\rm cm\ensuremath{^{-2}}}$, the ion ratio O$^0/$H$^0$ is a robust metallicity indicator, because the ionization potentials of <span>$\rm O^0$</span> and <span>$\mathrm{H}^0$</span> are very similar and the two species exchange electrons [@Field71], and O does not deplete strongly onto dust grains [@Jenkins09]. We find \[O/H\] $=-2.00\pm0.17$, which is comparable to the background metallicity of the IGM at this redshift [@Schaye03; @Simcoe04].

The remaining components for which we can accurately measure <span>$N_{\mathrm{H}^0}$</span> are partial Lyman limit systems at $\sim-20$ and $\sim+30$ <span>km s$^{-1}\,$</span>(Partial LLS 1 & 2, see Figure \[f\_metals\]). These show unsaturated  absorption at the Ly-10, Ly-11 and Ly-12 transitions, which imply ${\ensuremath{N_{\mathrm{H}^0}}}=10^{16.30\pm0.20}$ (Partial LLS 1) and $10^{16.43\pm0.30}~{\rm cm\ensuremath{^{-2}}}$ (Partial LLS 2). Since ionization corrections are significant at these <span>$N_{\mathrm{H}^0}$</span>, we estimate the metallicity of these components using the photoionization models described in the following section.

Photoionization Modelling {#s_cloudy}
-------------------------

We use <span style="font-variant:small-caps;">cloudy</span> photoionization models [version 8.01 @Ferland98] to predict the metal ion column densities for the D and partial LLS components given a metallicity and ionization parameter $U$ (defined as the ratio of the densities of ionizing photons to hydrogen atoms). All models assume solar abundance ratios, no dust, and an ionizing spectrum due to the ambient UV background [@Haardt12][^4]. We use a maximum likelihood technique to find the best-fitting metallicity and ionization parameter for each component (Crighton et al., in preparation) and their uncertainties. Column densities for low-ions together with upper limits on high-ions are used to constrain the models. Figure \[f\_cloudy2\] shows the models for the D component and partial LLS components, each at the best-fitting metallicity for that component.

For all three components we find that the UV background models provide a good match to the data. For the partial LLS components there is a minor discrepancy for $N_{\rm {\ensuremath{\rm Al^+}}}$, which is $0.3-0.4$ dex lower than predicted by the models. This could be due to uncertainties in the shape of the ionizing spectrum, although using a starburst-dominated ionizing spectrum makes the disagreement more severe. We believe this discrepancy is likely due to an Al underabundance relative to a solar abundance pattern [e.g. @Rolleston03]. The predicted N$^+$ column is close to the observed upper limit for Partial LLS 2, which may indicate that nitrogen is underabundant relative to solar. A nitrogen underabundance is often observed in damped systems at a similar redshift [e.g. @Prochaska02a]. For all other ionic species there is excellent agreement between the observed column densities and model predictions.

  ---------------------------
       ![image](f3a.eps)
   \[2mm\] ![image](f3b.eps)
   \[2mm\] ![image](f3c.eps)
  ---------------------------

Physical Conditions in the Absorption System {#s_phys}
--------------------------------------------

We have used two independent methods to show that the metallicity of the D component is $\sim1/100$ solar: $Z/Z_\odot=10^{-2.00\pm0.17}$ using O$^0/$H$^0$, and $Z/Z_\odot=10^{-1.92\pm0.18}$ from the <span style="font-variant:small-caps;">cloudy</span> models using all the metal transitions except <span>O<span>i</span></span>. The width of the  line requires a gas temperature $<20,000$ K, conservatively assuming thermal broadening such that $b=\sqrt{2kT/m_{\rm D}}$. From the models we find $\log_{10}U=-4.2\pm
0.95$, which implies that H is $\sim75\%$ neutral (${\ensuremath{N_\mathrm{H}}}\sim10^{19.6}~{\rm cm\ensuremath{^{-2}}}$) and has a temperature of $\sim10,000$ K, in agreement with $b$(). \[Fe/O\] $=-0.10\pm0.09$, therefore there is no evidence for strong dust depletion, as is expected from the low metallicity. The maximum $U$ permitted ($10^{-3.2}$) corresponds to a neutral fraction of $25\%$ and $n_\mathrm{H}=10^{-1.8}~{\rm cm\ensuremath{^{-3}}}\times
F_\nu^{\,912}/(3\times10^{-21}~{\ensuremath{{\rm erg~s}^{-1}~{\rm cm}^{-2}~{\rm Hz}^{-1}}})$, where $F_\nu^{\,912}$ is the magnitude of the ionizing spectrum at 912 Å. This implies a cloud thickness $\lesssim3$ kpc.

In contrast to the D component, Partial LLS 1 and 2 are metal enriched and highly ionized. Both LLS have similar conditions: the models yield $Z/Z_\odot=10^{-0.44\pm0.31}$ ($n_\mathrm{H}\approx10^{-2}~{\rm cm\ensuremath{^{-3}}}\times
F_\nu^{\,912}/(3\times10^{-21}~{\ensuremath{{\rm erg~s}^{-1}~{\rm cm}^{-2}~{\rm Hz}^{-1}}})$) and $\log_{10}U=-3.10\pm
0.15$, implying that less than $1\%$ of H is neutral (${\ensuremath{N_\mathrm{H}}}\sim10^{19}~{\rm cm\ensuremath{^{-2}}}$). Using a starburst-dominated ionizing spectrum allows a lower $Z/Z_\odot=10^{-0.8\pm0.32}$, but results in a 0.6-0.7 dex disagreement between the observed and predicted $N_{\rm{\ensuremath{\rm Al^+}}}$. Therefore we prefer the UVB-only models, but our main conclusions are unchanged if we were to instead use a starburst-dominated spectrum. A further difference between the D and partial LLS components is the presence of absorption from higher ionization gas (, , ) over the same velocity range as the low-ions. While some  components align with the low-ions, overall the high-ions have a different velocity structure, and are much stronger than expected from our photoionization modelling of the low-ions. Very broad components are also present in  (see Figure \[f\_metals\]). Thus these high-ions may trace another gas phase that is shock-heated and collisionally ionized [see e.g. @Simcoe02].

Finally, we calculate \[O/H\] for the entire system, including all low-ion components, assuming <span>$\rm O^0$</span> is associated with the bulk of the <span>$\mathrm{H}^0$</span> and that ionization corrections are negligible. This gives \[O/H\]$_{\rm total}=-1.89\pm0.11$. Therefore all the <span>O<span>i</span></span> components, spanning $\sim140~{\rm km~s\ensuremath{^{-1}\,}}$, must have a metallicity similar to the D component.

Discussion
==========

Figure \[f\_met\] shows the current state of gas-absorption metallicities measured around $z\sim2.5$ LBGs. Enriched gas with $Z/Z_{\odot}\gtrsim0.3$ is found in the partial LLS component in this paper at $R_\perp=58$ kpc, for the galaxy-absorber pair at $R_\perp=110$ kpc from @Simcoe06, and in the ISM of the gravitationally-lensed LBG cB58 [@Pettini02_cB58], shown at $R_{\perp}\sim4$ kpc. Systems at larger separations, also from Simcoe et al., approach the metallicity of the surrounding IGM, suggesting that enriched gas is common in the CGM up to $R_\perp\sim100$ kpc. Also shown are measurements from highly-neutral damped systems with nearby galaxies [@Krogager12; @Bouche13]. However, we caution that these systems were pre-selected based on their absorption properties, and so they may not be representative of the typical circumgalactic medium.

![\[f\_met\] Metallicity of gas associated with $z\sim2.5$ LBGs as a function of impact parameter. The ISM metallicity measured in the lensed LBG cB58 is shown at $R_{\perp}=4$ kpc. Other $R_\perp<30$ kpc measurements are for galaxies found by targeted searches around known neutral, damped systems. The D component and partial LLSs are shown by a red circle and red rectangle. Measurements at larger separations are from @Simcoe06.](f4.eps){width="0.9\columnwidth"}

The metallicity of the D component is more than an order of magnitude lower than the typical ISM metallicity of LBGs [@Pettini02_cB58], indicating that this gas has not been recently stripped or ejected in a wind from the galaxy. Could it be produced by a cold-mode accretion flow? It is close to the virial radius[^5], has a high column density ($10^{19.50\pm0.16}~{\rm cm\ensuremath{^{-2}}}$), low metallicity ($10^{-2.00\pm0.17}$), cool temperature ($20,000\mathrm{K}\ll T_{virial}\approx 10^6\,$K), and characteristic size $\lesssim 3$ kpc, which are all properties of inflowing streams expected from simulations [e.g. @Fumagalli11]. @Stewart11 predict that accreting streams have high angular momentum and often co-rotate with the galaxy's disk, producing offsets of up to $100$ <span>km s$^{-1}\,$</span> from the systemic galaxy redshift. The D component is at $-218\pm180$ <span>km s$^{-1}\,$</span> from the nearby galaxy, which is compatible with such an offset. All of the <span>O<span>i</span></span> components in the absorber, covering a velocity range of $\sim140$ <span>km s$^{-1}\,$</span>, also have low metallicities. Such velocity separations are seen by Stewart et al. when a sightline intersects multiple accreting streams. Therefore, in light of all the evidence above, we believe that this absorber represents the best existing candidate for a cold-mode accretion flow at high redshift.

The CGM around this galaxy is highly inhomogeneous: the D and partial LLS components have metallicities that differ by at least a factor of ten. These different metallicities are reminiscent of the bimodal metal distribution seen in $z<1$ Lyman limit systems [@Lehner13], which Lehner et al. argue results from physically distinct processes: metal-poor accreting gas, and metal-enriched gas stripped from galaxies or ejected in large-scale winds. Indeed, the two components in this system show further differences besides the metallicity: the D component is neutral and has very weak high-ion absorption, whereas the partial LLSs are highly ionized and have strong associated high-ions. These high-ions are not produced by the same ionizing spectrum that can reproduce the low-ions, and they may be caused by shock-heated, collisionally-ionized gas that is expected in a supernovae-driven outflowing wind [e.g. @Simcoe06]. This is also consistent with the hydrodynamical simulations of @Shen13, which indicate that enriched outflowing and metal-poor inflowing phases of the CGM are mixed kinematically.

If such a bimodality is common, as is implied by analyses of other $z\sim3$ sub-DLAs [e.g. @Prochter10], it has fundamental implications for interpreting observations of the CGM. Using the <span>$N_\mathrm{H}$</span> values inferred from photoionization modelling and the component metallicities, we conclude that the highly ionized partial LLSs contain <span>*most*</span> of the total metal mass in this system, significantly more than the low-metallicity component which dominates the total  absorption. Consider the case of this same system observed at a lower resolution, or of a composite spectrum which averages the absorption of many such systems [e.g. @Steidel10]. In this case, the metal absorption for individual components can no longer be matched to their respective , and we must measure the metallicity for the system as a whole. We showed in §\[s\_phys\] that doing this results in a low metallicity, \[O/H\]$\approx-1.9$. Thus the high metallicity partial LLSs would escape detection. An even more interesting case to consider is if the low-metallicity component had been more highly ionized, which would occur if it was illuminated by a stronger radiation field, or if it had a lower total <span>$N_\mathrm{H}$</span>, reducing its ability to self-shield. To explore this case we ran photoionization models for a range of $U$ values, using ${\ensuremath{N_{\mathrm{H}^0}}}=10^{17}{\rm cm\ensuremath{^{-2}}}$, and with other properties identical to the D component. These show that for a total ${\ensuremath{N_\mathrm{H}}}\le10^{20}{\rm cm\ensuremath{^{-2}}}$, characteristic of cold streams [@Fumagalli11], the strongest low-ion metal transition lying outside the <span>$\rm Ly\alpha$</span> forest[^6],  $\lambda1334$, always has a column density $<10^{13.1}{\rm cm\ensuremath{^{-2}}}$. Such a weak line approaches the detection limit even for echelle spectra. In low-resolution or composite spectra it would be easily swamped by stronger absorption from any kinematically nearby, metal-enriched gas, and the total metallicity inferred for the system would be dominated by metal-rich components. Therefore a large reservoir of metal-poor gas may be missed by existing studies of the $z\sim2.5$ CGM that use only low-resolution or composite spectra. Further studies employing high-resolution spectra of background QSOs near foreground galaxies are essential to accurately assess the metal content of the CGM.

By creating a large sample of similar absorption systems where metallicity measurements can be made at small impact parameters, we can realise the exciting possibility of mapping the enrichment distribution of the high-redshift CGM. Both our group and others [e.g. @Rudie12] are pursuing programs to assemble such a sample.

We thank J.O'Meara for a preliminary reduction of J1444535$+$291905, and the referee, whose comments improved the paper.

<span>48</span> natexlab\#1<span>\#1</span>

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<span>rcccccc</span> Ion & $z$ & $b$ & $\log_{10} N$ (VPFIT) & $\log_{10} N$ (AOD) & Adopted $\log_{10} N$ & AOD Transition\
& & (km s$^{-1}$)& (cm$^{-2}$) & (cm$^{-2}$) & (cm$^{-2}$) & ($\lambda_{\rm rest}$, Å)\
\
& 2.436599(01)& $<18$ & $19.50 \pm 0.16$ & – & $19.50 \pm 0.16$ &\
& & $10.60\pm 0.53$ & $14.93 \pm 0.02$ & $14.976^{+0.061}_{-0.064}$ & $14.93 \pm 0.06$ & 937\
& & 10.42& $11.96 \pm 0.02$ & $11.980^{+0.071}_{-0.075}$ & $11.980^{+0.071}_{-0.075}$ & 1670\
& & $11.4 \pm 0.2$ & $14.04 \pm 0.01$ & $14.014^{+0.018}_{-0.018}$ & $14.014^{+0.018}_{-0.018}$ & 1334\
& & & $<13.1$ & $13.863^{+0.018}_{-0.018}$ & $<13.1$ & 1335.7\
& & & $<12.15$ & $12.115^{+0.377}_{-0.862}$ & $<12.15$ & 1548\
& & 7.40& $12.98 \pm 0.04$ & $13.015^{+0.088}_{-0.082}$ & $13.015^{+0.088}_{-0.082}$ & 2600\
& & & – & $<13.9$ & $< 13.9$ & 1683\
& & $13.7 \pm 0.8$ & $13.20 \pm 0.02$ & $13.198^{+0.102}_{-0.094}$ & $13.198^{+0.102}_{-0.094}$ & 2803\
& & & $<13.3$ & $< 13.901$ & $<13.3$ & 1084\
& & & $<12.3$ & $< 12.558$ & $<12.3$ & 1242\
<span>O<span>i</span></span>& 2.436590(01)&$8.6 \pm 0.13$&$14.303\pm0.005$ & $14.261^{+0.014}_{-0.013}$ & $14.261^{+0.047}_{-0.013}$ & 1302\
& & & $<13.1$ & $< 13.323$ & $<13.1$ & 1031\
& &$10.43\pm0.17$& $13.36 \pm 0.006$ & $13.329^{+0.049}_{-0.051}$ & $13.329^{+0.049}_{-0.051}$ & 1526\
& & & $<12.30$ & $12.323^{+0.118}_{-0.146}$ & $<12.30$ & 1393\
\
& 2.438862(04)& $14.4\pm1.7$ &$16.30 \pm 0.20 $ & – & $16.30 \pm 0.20$ &\
& & 4.91&$11.63 \pm 0.03$ & $11.642^{+0.087}_{-0.107}$ & $11.642^{+0.087}_{-0.107}$ & 1670\
& & 7.35&$13.66 \pm 0.02$ & $13.674^{+0.015}_{-0.015}$ & $13.674^{+0.015}_{-0.015}$ & 1334\
& & &$<11.9$ & $< 12.021$ & $< 11.9$ & 1335.7\
& & &$>14.3$& $>14.29$& $>14.3$ & 1550\
& & &$<12.08$ & $12.067^{+0.335}_{-0.712}$ & $12.067^{+0.335}_{-0.712}$ & 2600\
& & & – & $<13.8$ & $< 13.8$ & 1683\
& & 5.17&$12.61 \pm 0.04$ & $12.681^{+0.084}_{-0.087}$ & $12.681^{+0.084}_{-0.087}$ & 2796\
& & &$<13.56$ & $<13.787$ & $<13.56$ & 1084\
& & &$<13.5$ & $<13.541$ & $<13.5$ & 1238\
<span>O<span>i</span></span>& & &$<12.18$ & $<12.349$ & $<12.18$ & 1302\
& & &$<14.5$ & $14.290^{+0.019}_{-0.018}$ & $<14.5$ & 1037\
& & $4.81\pm0.27$&$12.83\pm0.01$ & $12.811^{+0.096}_{-0.101}$ & $12.811^{+0.096}_{-0.101}$ & 1526\
& & &$<13.82$ & $13.480^{+0.019}_{-0.019}$ & $<13.82$ & 1402\
\
& & & $16.43 \pm 0.30$ & – & $16.43 \pm 0.30$ &\
& & & $11.859^{+0.032}_{-0.034}$& $11.851^{+0.087}_{-0.104}$ & $11.851^{+0.087}_{-0.104}$& 1670\
& & & $13.880^{+0.025}_{-0.026}$& $13.856^{+0.015}_{-0.015}$ & $13.856^{+0.015}_{-0.015}$& 1334\
& & & $<12.1$ & $< 12.114$ & $< 12.1$ & 1335.7\
& & & $>14.4$& $>14.4$& $>14.4$ & 1550\
& & & $<12.01$ & $< 12.307$ & $< 12.01$ & 2600\
& & & – & $<13.9$ & $< 13.9$ & 1683\
& & & $12.865^{+0.041}_{-0.046}$& $12.823^{+0.076}_{-0.076}$ & $12.823^{+0.076}_{-0.076}$& 2796\
& & & $<13.4$ & $13.316^{+0.072}_{-0.089}$ & $<13.4$ & 1084\
& & & $<13.45$ & $13.358^{+0.037}_{-0.041}$ & $<13.45$ & 1238\
<span>O<span>i</span></span>& & & $12.395^{+0.184}_{-0.327}$& $12.439^{+0.383}_{-0.698}$ & $12.439^{+0.383}_{-0.698}$& 1302\
& & & $<14.5$ & $14.311^{+0.020}_{-0.020}$ & $<14.5$ & 1037\
& & & $13.080^{+0.016}_{-0.017}$& $12.968^{+0.098}_{-0.114}$ & $12.968^{+0.098}_{-0.114}$& 1526\
& & & $<13.9$ & $13.609^{+0.019}_{-0.019}$ & $<13.9$ & 1402

[^1]: All distances given are proper, assuming $H_0=70\,{\rm km~s\ensuremath{^{-1}\,}}\,\mathrm{Mpc}^{-1}$, $\Omega_M=0.3$ and $\Omega_\Lambda=0.7$.

[^2]: <http://www.astro.caltech.edu/~tb/makee/>

[^3]: <http://www.ast.cam.ac.uk/~rfc/vpfit.html>

[^4]: we also consider a spectrum dominated by a starburst galaxy, but it does not significantly affect our results.

[^5]: We estimate the chance of a random sub-DLA falling within 250 <span>km s$^{-1}\,$</span> of the galaxy redshift at $<2.2\%$ based on the 12 QSO-galaxy pairs searched to find this system.

[^6]: Higher ionization states  and  cannot be used to detect this gas as they also arise in another co-spatial gas phase.

{'source': 'arXiv_out/1307'}