THE H i CONTENT OF THE UNIVERSE OVER THE PAST 10 GYR

Galaxy formation and evolution are critically dependent on the gas within and surrounding a galaxy. As galaxies evolve, gas is accreted onto the galaxy and expelled through various processes such as activity of an active galactic nucleus and stellar feedback. Providing observational constraints on this gas is therefore paramount in understanding how galaxies formed and evolved. At very low redshifts, neutral gas has been studied in detail using the H i 21 cm line. Unfortunately, such observations are limited with current facilities to very low redshifts, $z\lesssim 0.25$ (e.g., Zwaan et al. 2001; Catinella et al. 2008; Fernández et al. 2013; Catinella & Cortese 2015).

To study how the mass and distribution of neutral gas has evolved over cosmic time, we need to measure the cosmic density of this gas over a large redshift range. Such a study can be done by studying the gas through Lyα absorption in quasar spectra (Wolfe et al. 1986). Previous studies have shown that the highest column density absorbers, the damped Lyα systems (DLAs), which have neutral hydrogen column densities of ${N}_{{\rm{H}}{\rm{I}}}$ $\;\geqslant \;{10}^{20.3}$ cm⁻², contain the bulk of the neutral gas at both low and high redshifts (e.g., Prochaska et al. 2005; Wolfe et al. 2005; Zwaan et al. 2005; O'Meara et al. 2007). Observations of DLAs therefore provide an excellent opportunity to constrain the neutral hydrogen content of our universe over a large redshift range.

To quantify the overall H i content of our universe, we use a single quantity known as the neutral hydrogen column density distribution function, $f({N}_{{\rm{H}}{\rm{I}}},X)$, (e.g., Tytler 1987; Lanzetta et al. 1991; Prochaska et al. 2005). $f({N}_{{\rm{H}}{\rm{I}}},X)$ is a quantitative description of the large scale neutral hydrogen distribution of our universe, and its zeroth and first moment yield the line density of DLAs, ${{\ell }}_{{\rm{DLA}}}(X)$, and the total hydrogen mass density of the universe, ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$.

At high redshifts, $z\gtrsim 2$, $f({N}_{{\rm{H}}{\rm{I}}},X)$ for DLAs has been measured by many authors (e.g., Prochaska & Wolfe 2009; Noterdaeme et al. 2012; but see Crighton et al. 2015 and Sánchez-Ramírez et al. 2015), using large optical surveys such as the Sloan Digital Sky Survey (SDSS; Abazajian et al. 2009). These studies find that the shape of $f({N}_{{\rm{H}}{\rm{I}}},X)$ is invariant between $z\sim 2$ and $z\sim 3.5$, while the normalization is observed to evolve, decreasing by a factor of ≈1.3–2. This implies a concomitant decrease in ${{\ell }}_{{\rm{DLA}}}(X)$ and ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$. Such evolution may be explained by either gas conversion into stars over this redshift range or feedback processes that expel gas from galaxies (e.g., Prochaska & Wolfe 2009).

A key feature of $f({N}_{{\rm{H}}{\rm{I}}},X)$ and its moments is that they appear to converge by z ∼ 2 to the present-day values estimated using H i 21 cm studies (Zwaan et al. 2005; Braun 2012; Delhaize et al. 2013; Hoppmann et al. 2015). This suggests that these quantities have remained essentially unchanged over the last 10 billion years of galaxy evolution. Unfortunately, at $z\lesssim 2$, it is difficult to measure $f({N}_{{\rm{H}}{\rm{I}}},X)$ directly, because the effectiveness of optical surveys plummets due to the atmospheric absorption of ultraviolet (UV) radiation (Lanzetta et al. 1995). This problem can be circumvented by observing from space with the UV spectrographs on the Hubble Space Telescope (HST). However, due to the expense of these observations and the scarcity of DLAs in random lines of sight, large-scale blind surveys comparable to the SDSS have not been feasible within the limited time allocations of single observing programs.

To increase the rate of detection of high H i column density absorbers along quasar sightlines, previous studies at $z\lt 2$ have used several types of pre-selection methods, with the most common approach being the use of strong Mg ii absorption to pre-select DLA and H i 21 cm candidates (e.g., Briggs & Wolfe 1983; Rao & Turnshek 2000; Rao et al. 2006; Kanekar et al. 2009). At redshifts $z\gtrsim 0.1$, the Mg ii doublet is shifted into the optical regime. As the vast majority of DLAs show strong Mg ii absorption (rest equivalent width, ${W}_{0}^{\lambda 2796}\gt 0.5$ Å), pre-selecting quasars with strong Mg ii absorption will significantly increase the detection rate of DLAs in the sample. However, it has not so far been straightforward to understand the biases in such pre-selections, which are critical to obtain accurate estimates of $f({N}_{{\rm{H}}{\rm{I}}},X)$ for DLAs (e.g., Rao et al. 2006).

Fortunately, 20 years of HST observations with a variety of UV spectrographs have resulted in a large sample of observed quasars. As HST nears the end of its mission, the time has come to explore this large data set, and perform a study in the UV to evaluate $f({N}_{{\rm{H}}{\rm{I}}},X)$, ${{\ell }}_{{\rm{DLA}}}(X)$ and ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$ at $z\lt 1.6$, similar to earlier studies performed in the optical regime. In this paper, we use the HST spectroscopic archive to obtain a measurement of the above quantities between $z\sim 0.01$ and $z\sim 1.6$, covering the past 10 billion years of the universe. The sample for this study is described in Section 2, and the method is described in Section 3. Our results are presented in Section 4 and discussed in Section 5. Throughout this paper we adopt an $({{\rm{\Omega }}}_{M},{{\rm{\Omega }}}_{{\rm{\Lambda }}},h)=(0.3,0.7,0.7)$ cosmology.

To measure the amount of neutral hydrogen between $z\sim 0.01$ and $z\sim 1.6$, we have assembled a large sample of quasars observed with medium resolution spectrographs on the HST. Specifically, we performed a search of the HST archive for quasars observed with either the Space Telescope Imaging Spectrograph (STIS), the Faint Object Spectrograph (FOS) or the Cosmic Origins Spectrograph (COS). These instruments have gratings that provide enough spectral resolution for a high fidelity search for strong absorption line systems (see Table 2 and Section 3.1). We did not include the Goddard High Resolution Spectrograph (GHRS), as its spectral coverage is too small to provide a meaningful search path. In total, a sample of 878 quasars were observed with at least one of these instruments and gratings.

We will not outline the procedure here used to analyze the spectra. Instead, we refer the reader to the following papers that describe the reduction process in detail for each of the different instruments and gratings. The FOS G160L and STIS spectra reductions are described in Ribaudo et al. (2011). We note that the FOS G160L data were cut off at a wavelength of 1350 Å. This arbitrary cut-off does not affect the results in this paper (see Section 4). The reduction of the higher resolution FOS spectra is detailed in Bechtold et al. (2002). Finally, the analysis of the COS spectra is described in Thom et al. (2011) and Meiring et al. (2011).

The reduced spectra were compiled into a single list, and, for quasars with multiple observations with different instruments, the spectra were combined into a single spectrum. In cases of overlapping spectral coverage, the higher resolution spectrum was used. We visually confirmed the emission redshift, and the quality of the spectra for all the quasars. Several quasars are not included either due to too low signal-to-noise ratio (S/N) or bad spectra (99 quasars). We also exclude any quasars that exhibit strong broad absorption line (BAL) features (12 quasars). A total of 767 quasars satisfy the above criteria and form the sample of this paper, as tabulated in Table 1.

Table 1.  QSO Sample

QSO	${z}_{{\rm{em}}}$ a	Instrument	Grating	Search Path			Statistical Path			Proposal ID
				${F}_{{\rm{search}}}$ b	Min z	Max z	${F}_{{\rm{stat}}}$ c	Min z	Max z
J0000−1245	0.200	COS	G130M-G160M	1	0.010	0.299	1	0.010	0.188	12604
J0001+0709	3.234	STIS	G230L	1	⋯	⋯	0	⋯	⋯	8569
J0004−4157	2.760	FOS	G270H	1	1.501	1.695	0	⋯	⋯	6577
J0005+0524	1.900	FOS	G270H-G190H	1	0.829	1.695	1	0.829	1.695	4581, 6705
J0005−5006	0.033	COS	G130M-G160M	1	0.010	0.133	1	0.010	0.022	12936

Notes. (Omitted from this portion of the table for brevity are the columns for alternate QSO name, right ascension and declination.)

^aEmission redshift of quasar. ^bSearch flag: (0) Low S/N or bad spectrum; (1) Included; (2) BAL quasar. ^cStatistical flag: (0) Non-statistical; (1) Statistical; (2) Galaxy Sample.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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2.1. Statistical Sample

To search for absorption systems in the HST spectra, we apply a method similar to that described in Prochaska et al. (2005), but slightly adapted for our lower redshift sample. Specifically, we define the search path for each quasar sightline, with the lower limit of the search path set by the S/N of the spectrum. We determine the S/N by calculating a running median with a 20 pixel width for each wavelength. The lower limit to the search path is set to the wavelength for which this median S/N is greater than the minimum allowed S/N, which we take to be 4, or the wavelength of Lyα at z = 0 (${\lambda }_{\mathrm{Ly}\alpha }=1215.6701$ Å), whichever is greater. The choice of 4 for this minimum S/N is explained in Section 3.2. The upper limit to the search path is set to be either the end of the spectrum or the value $(1+{z}_{{\rm{em}}}+{\rm{offset}}){\lambda }_{\mathrm{Ly}\alpha }$, whichever is smaller. Here, ${z}_{{\rm{em}}}$ is the quasar redshift; the redshift offset is added to allow absorption systems to have slightly higher redshifts than that of the quasar. This offset redshift (chosen to be 0.1) also encompasses the uncertainty in the reported quasar emission redshifts. The complete search path is shown in the left panel of Figure 1.

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For those quasars that are part of the statistical sample, we also define a statistical search path, g(z). The lower limit to the statistical path is set again by the wavelength where the median S/N exceeds the minimum S/N value of 4, or a wavelength of $(1+{\rm{offset}}){\lambda }_{\mathrm{Ly}\alpha }$, whichever is greater. This time, we adopt a redshift offset of 0.01 which is ∼3000 km s⁻¹ from our Galaxy. This offset is introduced to prevent any biasing due to clustering in the Milky Way neighborhood. The upper limit is set to the end of the spectrum or the value $\sqrt{(c-{\rm{\Delta }}v)/(c+{\rm{\Delta }}v)}(1+{z}_{{\rm{em}}}){\lambda }_{\mathrm{Ly}\alpha }$, whichever is greater. Here, ${\rm{\Delta }}v$ is taken to be 3000 km s⁻¹ which prevents clustering around the quasar from affecting our measurements. The search path for the statistical sample (${f}_{{\rm{stat}}}$ = 1) is shown in the right panel of Figure 1.

After defining the search path, we run our search algorithm to find candidate absorption systems along the search path to each quasar. The algorithm searches regions of the spectrum that fall below a specified S/N cut, which occurs in the absorption trough of strong absorbers. Specifically, the algorithm assigns to each pixel a DLA score, which is a measure of how many pixels in a 3 Å window centered around this pixel fall below the assigned S/N cut per pixel. We take a 3 Å window because this is the core width of a ${N}_{{\rm{H}}{\rm{I}}}$ $=\;{10}^{20.3}$ cm⁻² absorber at z = 0.01, while the S/N threshold is taken to be 2. The central pixels for which greater than 60% of the surrounding pixels in the 3 Å window fall below the S/N threshold are flagged by the algorithm as candidate absorption systems. Altogether, we recorded 139 such candidates from the complete sample.

The final step in the search for absorption systems is the visual follow-up of these candidates. We fit individual absorption systems using a custom IDL Voigt-profile fitting program for DLAs, ${\mathtt{x}}\_{\mathtt{fitdla}}$, which is part of the the publicly available IDL library, XIDL.⁷ With this program, we are able to simultaneously fit both the Voigt profile and the continuum of the quasar as described in detail in Prochaska et al. (2003b). The largest source of uncertainty stems from the continuum placement.

As this process has inherently a human aspect to it, two of the authors (MN and JXP) independently carried out the fits to the candidate absorbers. The results were compared and, for most of the systems ($\gt 90\%$), the measured H i column density from both authors fell within the estimated 1σ uncertainty of the measurement. We therefore believe that our column density measurements are robust.

3.1. Resolution Considerations

Low resolution spectra could result in inaccurate H i column density measurements and/or non-detection of DLAs by the search algorithm. Our lowest resolution spectra are taken with the low resolution gratings of the STIS G230L and FOS G160L, which have resolutions as low as R $\approx \;250$. For such resolutions, only about half of a resolution element falls within the DLA trough of a low column density system, and therefore small deviations could result in a non-detection of such a DLA by the search algorithm.

To assess the impact of resolution on the recovery process, we created simulated spectra with similar S/N and resolution to the observational data. We added artificial DLAs to the spectra with a range of column densities. For this mock data set, the algorithm was successful in recovering greater than 99% of all of the absorbers with a column density above 10²⁰ cm⁻². We conclude that the resolution of the spectra is sufficient to accurately recover DLAs.

We also test our ability to recover correct H i column density measurements by adding DLAs to our lowest resolution spectra and fitting these DLAs with the fitting procedure described in Section 3. In particular, we added 50 DLAs with varying H i column densities to our lowest resolution spectra (i.e., both STIS and FOS-L) and measured their H i column densities via our fitting method. The results are shown in Figure 2. As can be seen from the figure, we are able to accurately recover the actual H i column density over the full range of input values, including the lowest column density systems. Furthermore, the lower resolution does not cause any systematic under- or over-estimate of the H i column density. The deviation around the actual value for this sample is 0.10 dex, which is comparable to the fit uncertainties (which have a mean of 0.15 dex) that we have assigned to the sample.

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As a final test, we have reanalyzed the results in this paper with the lowest resolution spectra omitted from the sample, and find no significant difference in any of the result presented.

3.2. S/N Considerations

4.1. The Full Sample of DLAs

Figure 3 shows the H i absorption profiles for all the absorbers with a measured H i column density greater than ${10}^{20.3}$ cm⁻². These absorbers are also listed in Table 3. Our sample contains a total of 47 DLAs with a mean redshift of z = 0.796. Of these 47 systems, 33 were selected due to the presence of strong Mg ii absorption, 6 due the presence of a galaxy close to the quasar sightline, 2 were known H i 21 cm absorbers, and 2 were known DLAs. Only 4 DLAs were discovered in sightlines not a priori selected to contain a strong absorber, and hence form the statistical sample of this paper.

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Table 3.  DLA Sample

QSO Name	Alternate QSO Name	${F}_{{\rm{stat}}}$ a	This Work		Literature		References
			${z}_{{\rm{abs}}}$	$\mathrm{log}{N}_{{\rm{H}}{\rm{I}}}$ (cm−2)	${z}_{{\rm{abs}}}$	$\mathrm{log}{N}_{{\rm{H}}{\rm{I}}}$ (cm−2)
J0021−0128	⋯	1	1.2420	20.55 ± 0.10	1.2412	20.50	(2)
J0051+0041	⋯	0	0.7420	20.60 ± 0.10	0.7400	20.40 ± 0.10	(3)
J0102−0853	⋯	0	0.8945	20.45 ± 0.10	⋯	⋯	(16)
J0106+0105	⋯	0	1.3020	20.85 ± 0.20	1.3002	20.95 ± 0.07	(1)
J0122−2843	B0120−28	1	0.1856	20.55 ± 0.10	0.1856	20.50 ± 0.10	(4)
J0126−0105	⋯	0	1.1930	20.65 ± 0.10	1.1916	20.60 ± 0.04	(1)
J0139−0023	⋯	0	0.6840	20.60 ± 0.15	0.6828	20.60 ± 0.07	(1)
J0153+0052	⋯	0	1.0610	20.35 ± 0.20	1.0599	20.43 ± 0.10	(1)
J0304−2212	B0302−2223	0	1.0094	20.30 ± 0.10	1.0140	20.00	(5), (6)
J0452−1640	⋯	0	1.0090	21.00 ± 0.10	1.0072	20.98 ± 0.06	(1)
J0456+0400	B0454+0356	0	0.8586	20.60 ± 0.10	0.8596	20.75 ± 0.02	(7)
J0741+3111	⋯	0	0.2220	20.60 ± 0.20	0.2213	20.90 ± 0.07	(1)
J0830+2410	B0827+2421	0	0.5191	20.40 ± 0.20	0.5247	20.30 ± 0.05	(1)
J0930+2848	SDSS-J093001.90+284858.4	2	0.0227	20.75 ± 0.10	⋯	⋯	(16)
J0938+4128	B0935+4141	1	1.3725	20.45 ± 0.15	1.3960	20.50	(15)
J0948+4323	⋯	0	1.2340	21.75 ± 0.15	⋯	⋯	(16)
J0953−0038	⋯	0	0.6390	20.30 ± 0.10	0.6381	19.90 ± 0.08	(1)
J0954+1743	⋯	0	0.2410	21.05 ± 0.20	0.2377	21.32 ± 0.05	(1)
J1001+5553	B0957+5608a	0	1.3913	20.30 ± 0.20	1.3911	20.28 ± 0.08	(8)
J1009+0713	SDSSJ100902.06+071343.8	2	0.1139	20.75 ± 0.10	0.1140	20.68 ± 0.10	(9)
J1009+0036	⋯	0	0.9730	20.30 ± 0.15	0.9714	20.00 ± 0.10	(1)
J1010+0003	⋯	0	1.2670	21.70 ± 0.10	1.2651	21.52 ± 0.06	(1)
J1017+5356	⋯	0	1.3070	20.70 ± 0.10	⋯	⋯	(16)
J1106−1821	B1104−1805b	0	1.6617	20.80 ± 0.10	1.6616	20.84	(10)
J1107+0048	⋯	0	0.7410	21.00 ± 0.15	0.7470	21.00 ± 0.04	(1)
J1124−1705	B1122−1648	1	0.6812	20.35 ± 0.15	0.6819	20.45 ± 0.15	(11)
J1130−1449	B1127−1432	0	0.3140	21.30 ± 0.15	0.3130	21.71 ± 0.07	(1)
J1224+0037	⋯	0	1.2350	20.75 ± 0.15	1.2346	20.88 ± 0.05	(1)
J1225+0035	⋯	0	0.7730	21.55 ± 0.10	0.7730	21.38 ± 0.12	(1)
J1232−0224	Q1232−022	0	0.3950	20.85 ± 0.15	0.3950	20.75 ± 0.07	(12)
J1251+4637	Q1251+463	0	0.3965	20.60 ± 0.15	⋯	⋯	(16)
J1331+3030	B1328+3045	0	0.6840	21.40 ± 0.15	0.6920	21.30	(13)
J1420−0054	⋯	0	1.3470	20.85 ± 0.15	1.3475	20.90 ± 0.05	(1)
J1431+3952	⋯	0	0.6040	21.30 ± 0.15	⋯	⋯	(16)
J1501+0019	⋯	0	1.4840	20.90 ± 0.10	1.4832	20.85 ± 0.14	(1)
J1512+0128	SDSS-J151237.05+012846.	2	0.0295	20.40 ± 0.10	⋯	⋯	(16)
J1527+2452	⋯	0	0.7345	20.40 ± 0.15	⋯	⋯	(16)
J1537+0021	⋯	0	1.1790	20.30 ± 0.10	1.1782	20.18 ± 0.10	(1)
J1616+4154	SDSSJ161649.42+415416.3	2	0.3210	20.65 ± 0.20	0.3211	20.60 ± 0.20	(9)
J1619+3342	SDSSJ161916.54+334238.4	2	0.0964	20.65 ± 0.10	0.0963	20.55 ± 0.10	(9)
J1624+2345	B1622+2352	0	0.6556	20.30 ± 0.10	0.6560	20.30	(14)
J1712+5559	⋯	0	1.2100	20.65 ± 0.15	1.2093	20.72 ± 0.05	(1)
J1727+5302	⋯	0	0.9480	21.25 ± 0.15	0.9448	21.16 ± 0.05	(1)
J1727+5302	⋯	0	1.0330	21.50 ± 0.15	1.0312	21.41 ± 0.03	(1)
J1733+5533	⋯	0	0.9990	20.80 ± 0.10	0.9981	20.70 ± 0.03	(1)
J2334+0052	⋯	0	0.4740	20.50 ± 0.15	0.4713	20.65 ± 0.15	(1)
J2339−0029	⋯	0	0.9680	20.60 ± 0.15	0.9664	20.48 ± 0.08	(1)
J2353−0028	⋯	0	0.6044	21.50 ± 0.10	0.6044	21.54 ± 0.15	(1)

Note.

^aDLA is found in the sightline of a quasar that is: (0) not in the statistical sample; (1) in the statistical sample; (2) in the galaxy sample (see Table 1 and Section 2.1).

References. Rao et al. (2006), (2) Aracil et al. (2002), (3) Lacy et al. (2003), (4) Oliveira et al. (2014), (5) Lanzetta et al. (1995), (6) Pettini & Bowen (1997), (7) Steidel et al. (1995), (8) Zuo et al. (1997), (9) Meiring et al. (2011), (10) Lopez et al. (1999), (11) De la Varga et al. (2000), (12) Boissé et al. (1998), (13) Cohen et al. (1994), (14) Steidel et al. (1997), (15) Jannuzi et al. (1998), (16) This Work.

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We can test our methodology and recovery rate of DLAs by comparing our list of DLAs to those found in Rao et al. (2006), as the latter is a subset of this larger sample. We find that our search algorithm recovers 28 of the 41 DLAs in the Rao et al. (2006) sample, with a mean dispersion of 0.10 dex between the H i column density estimates. Four of the DLAs were not covered by our spectra either due to the cut-off at 1350 Å in the FOS G160L or some other reduction issue. One of these is the serendipitously discovered DLA at z = 0.0912 toward B0738+313. However, we note that the omission of these DLAs do not affect the results in this paper, as these sightlines would not have been part of the statistical sample because of their pre-selection of Mg ii absorption.

Of the remaining 9 DLAs not recovered by our search algorithm, 8 fell in a portion of the spectrum with an S/N below our criterion (see Section 3.2). We note that these sightlines are also not included in our statistical search path and therefore do not affect the conclusions presented in this paper. The only DLA (in QSO J0153+0052 at ${z}_{\mathrm{abs}}=1.0599$) which did fall in the search algorithm's search path and was not detected was not found because the trough of this potential DLA showed significant flux. This could be either due to Lyα emission at the redshift of the DLA, or an issue with the zero point flux of the spectrum. We have visually checked all of the spectra and believe that this is a very rare occurrence.

4.2. The Column Density Distribution Function, $f({N}_{{\rm{H}}{\rm{I}}},X)$

We obtain the H i column density distribution function with the approach described in, e.g., Tytler (1987). $f({N}_{{\rm{H}}{\rm{I}}},X)$ ${{dN}}_{{\rm{H}}{\rm{I}}}\;{dX}$ is defined as the number of DLAs with H i column density between ${N}_{{\rm{H}}{\rm{I}}}$ and ${N}_{{\rm{H}}{\rm{II}}}+{{dN}}_{{\rm{H}}{\rm{I}}}$ and within the absorption distance dX. dX is defined as

$$\begin{eqnarray}&&{dX}\equiv \displaystyle \frac{{H}_{0}}{H(z)}{(1+z)}^{2}{dz},\end{eqnarray} \tag{ 1 }$$

where H₀ is the Hubble constant and H(z) is given by

$$\begin{eqnarray}&&H(z)={H}_{0}{[{(1+z)}^{2}(1+z{{\rm{\Omega }}}_{m})-z(z+2){{\rm{\Omega }}}_{{\rm{\Lambda }}}]}^{-1/2}.\end{eqnarray} \tag{ 2 }$$

The absorption distance is defined in this manner such that $f({N}_{{\rm{H}}{\rm{I}}},X)$ is constant for a non-evolving population of absorbers.

The statistical sample only contains 4 DLAs, and therefore we have poor constraints on the functional form of $f({N}_{{\rm{H}}{\rm{I}}},X)$. To increase the sample size, we include all sightlines selected to probe an intervening galaxy (i.e., those with ${f}_{{\rm{stat}}}$ = 2 in Table 1), resulting in a DLA sample of 9 DLAs. We note that the inclusion of these sight lines will likely bias the normalization of $f({N}_{{\rm{H}}{\rm{I}}},X)$ high. The resulting $f({N}_{{\rm{H}}{\rm{I}}},X)$ is shown in the left panel of Figure 4. Our results are consistent with the results of the local H i 21 cm study of Zwaan et al. (2005), and with those of DLA surveys at higher redshifts (e.g., Prochaska & Wolfe 2009; Noterdaeme et al. 2012). However, our sample size remains too small to constrain $f({N}_{{\rm{H}}{\rm{I}}},X)$ at the highest H i column densities.

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We also consider $f({N}_{{\rm{H}}{\rm{I}}},X)$ for the sample described in Rao et al. (2006). They note that their sample contains a large number of high H i column density systems, although this deviation is not statistically significant. We have broken up our sample into those DLAs that were found using the Mg ii selection criteria defined in Rao et al. (2006) and the remaining DLAs. The cumulative distribution plotted in the right panel of Figure 4 indeed shows that the Mg ii-selected DLA sample has a larger number of high H i column density systems than the rest of the low-z DLA sample (this work) or the high-z DLA sample of Noterdaeme et al. (2012). This corroborates the suggestion of Prochaska & Wolfe (2009) that selecting sightlines based on metal line absorption could bias the H i distribution toward high column densities. This result is also seen in recent work on metal-strong absorbers (Dessauges-Zavadsky et al. 2009; Kaplan et al. 2010; Berg et al. 2015).

4.3. Line Density of DLAs, ${{\ell }}_{{\rm{DLA}}}(X)$

The line density of DLAs, ${{\ell }}_{{\rm{DLA}}}(X)$, is defined as the zeroth moment of $f({N}_{{\rm{H}}{\rm{I}}},X)$, i.e.:

$$\begin{eqnarray}&&{{\ell }}_{{\rm{DLA}}}(X)={\displaystyle \int }_{{N}_{{\rm{DLA}}}}^{\infty }f({N}_{{\rm{H}}{\rm{I}}},X){dNdX},\end{eqnarray} \tag{ 3 }$$

where ${N}_{{\rm{DLA}}}$ is the threshold H i column density for DLAs. In practice, ${{\ell }}_{{\rm{DLA}}}(X)$ is estimated by measuring the number of DLAs in a given redshift bin and then dividing this value by the total absorption path length in this redshift bin. A correlated quantity is the redshift number density, ${n}_{{\rm{DLA}}}$, which is obtained by dividing the number of DLAs found in a redshift bin by the redshift path length. Both of these quantities describe the incidence rate of DLAs along a line of sight.

We have calculated ${{\ell }}_{{\rm{DLA}}}(X)$ and ${n}_{{\rm{DLA}}}$ for the complete statistical sample (those with ${f}_{{\rm{stat}}}=1)$, which covers the redshift range, $z=0.01\mbox{--}1.6$, with a median redshift of 0.623. The resultant ${{\ell }}_{{\rm{DLA}}}(X)$ is ${0.017}_{-0.008}^{+0.014}$, which equates to ${n}_{{\rm{DLA}}}$ = ${0.033}_{-0.015}^{+0.026}$. These values are put in context by plotting them with a compilation from the literature in Figure 5.

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Figure 5 shows that the line density obtained from this sample is lower than the locally measured values of Zwaan et al. (2005) and Braun (2012) (note that the latter estimate is based on an extrapolation from just three galaxies), although our estimate is consistent with these values within 2σ significance. Our ${{\ell }}_{{\rm{DLA}}}(X)$ estimate is also lower than the estimate of Rao et al. (2006), but the systematic uncertainties in their measurement are difficult to quantify.

Our new estimate of the line density of DLAs at $z\lt 1.6$ is lower than this value at $z\sim 2$ (Noterdaeme et al. 2012) at greater than 2σ significance. This result suggests that ${{\ell }}_{{\rm{DLA}}}(X)$ has evolved over this redshift range. This result is discussed further in Section 5.

We note that we have searched for evolution within our sample by dividing the sample into two subsamples at the median redshift of z = 0.623. However, the sample size is too small to discern any evolution within the sample, although the sample is consistent with an evolution of $\lt 0.05$ in ${{\ell }}_{{\rm{DLA}}}(X)$ per unit redshift, which agrees with the evolution at higher redshift (∼0.03 in ${{\ell }}_{{\rm{DLA}}}(X)$ per unit redshift, see, e.g., Sánchez-Ramírez et al. 2015).

4.4. Mass Density of ${\rm{H}}\;{\rm{I}}$, ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$

The final quantity we consider is the first moment of $f({N}_{{\rm{H}}{\rm{I}}},X)$, which is the mass density of H i contained in DLAs, ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$. This quantity is defined by

$$\begin{eqnarray}&&{\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}=\displaystyle \frac{{m}_{{\rm{H}}}{H}_{0}}{c}{\displaystyle \int }_{{N}_{{\rm{min}}}}^{{N}_{{\rm{max}}}}{N}_{{\rm{H}}{\rm{I}}}f({N}_{{\rm{H}}{\rm{I}}},X){dNdX},\end{eqnarray} \tag{ 4 }$$

where ${m}_{{\rm{H}}}$ is the mass of the hydrogen atom and c is the speed of light. The superscript clarifies that we are only measuring the fraction of H i in DLAs; of course, as noted earlier, these systems contain the bulk ($\gt 85\%$) of the H i at all redshifts (Zwaan et al. 2005; O'Meara et al. 2007; Noterdaeme et al. 2012). We also note that literature studies often provide estimates of the cosmological neutral gas mass density, ${{\rm{\Omega }}}_{g}^{{\rm{DLA}}}$. ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$ is related to ${{\rm{\Omega }}}_{g}^{{\rm{DLA}}}$ by the conversion factor $\mu /{\rho }_{c}$, where μ is the mean molecular mass of the gas and ${\rho }_{c}$ is the critical density of the universe.

As with $f({N}_{{\rm{H}}{\rm{I}}},X)$, ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$ cannot be accurately determined from our own study because the small sample size lacks the statistics to accurately determine the number of high H i column density (${N}_{{\rm{H}}{\rm{I}}}$ $\;\gtrsim \;{10}^{21}$ cm⁻²) systems (none are present in our survey). These systems are likely to contribute significantly to ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$ (Zwaan et al. 2005; O'Meara et al. 2007; Noterdaeme et al. 2012), and our results are hence likely to underestimate the underlying neutral gas density. To account for this, we assume that the mean column density of the low redshift absorber sample is unchanged from the mean column density at high redshifts, as measured by Noterdaeme et al. (2012; see Section 4.2).

Our data yield ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$ = (${0.10}_{-0.05}^{+0.08}\times {10}^{8}{M}_{\odot }\;{{\rm{Mpc}}}^{-3}$) over the redshift range $0.01\lesssim z\lesssim 1.6$, without any correction for the missing high H i column density absorbers. Using the mean H i column density estimate of Noterdaeme et al. (2012) to account for their absence, we obtain a corrected ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$ of ${0.25}_{-0.12}^{+0.20}\times {10}^{8}{M}_{\odot }\;{{\rm{Mpc}}}^{-3}$. Both the corrected (solid error bars) and uncorrected (dashed error bars) values are shown in Figure 6, along with other estimates of this quantity at different redshifts from the literature.

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Our corrected estimate of ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$ is lower than the earlier estimate over the same redshift range by Rao et al. (2006). The lower value compared to that of Rao et al. (2006) is due to both the decrease in ${{\ell }}_{{\rm{DLA}}}(X)$ and the lower adopted mean H i column density (see Section 4.2). Our H i mass density estimate is, however, in good agreement with the estimates from H i 21 cm studies at $z\approx 0\mbox{--}0.3$ (Zwaan et al. 2005; Lah et al. 2007; Delhaize et al. 2013; Rhee et al. 2013; Hoppmann et al. 2015). The results suggest a mild evolution in ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$, driven by the evolution in ${{\ell }}_{{\rm{DLA}}}(X)$, which was recently quantified by Crighton et al. (2015) and Sánchez-Ramírez et al. (2015) who measured ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$ at high redshifts.

Finally, we would like to point out the apparent discrepancy in the ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$ measurements of Prochaska & Wolfe (2009) and Noterdaeme et al. (2012) at $z\approx 3$. This discrepancy is due to two factors: (i) the sample analyzed by Prochaska & Wolfe (2009) led to an under-estimate in the break in $f({N}_{{\rm{H}}{\rm{I}}},X)$ by $\approx 0.2$ dex and therefore an under-estimate of ${\rho }_{{\rm{HI}}}$ by ≈20%; (ii) the results are now limited by systematic uncertainties that include the approach to measuring ${N}_{{\rm{H}}{\rm{I}}}$, dust obscuration, and color-selection bias in quasar surveys. These systematic errors must be addressed before further progress can be made in this field.

In this paper, we have used a large sample of quasars ($767$ systems) observed with the UV spectrographs on the HST to carry out a search for low-redshift DLAs. Of the 46 DLAs found in this study, only 4 are drawn from the statistical sample. The remainder were drawn from sightlines with foreknowledge of either an absorber or an intervening galaxy, or the lack of an absorber, close to or along the quasar line of sight.

Our statistical sample enables an unbiased determination of the line density of DLAs, ${{\ell }}_{{\rm{DLA}}}(X)$, over the redshift range $0.01\lesssim z\lesssim 1.6$. We obtain ${{\ell }}_{{\rm{DLA}}}(X)$ $=\;{0.017}_{-0.008}^{+0.014}$, significantly smaller than the previous estimate of Rao et al. (2006), which appears likely to be biased high. Unfortunately, current estimates of ${{\ell }}_{{\rm{DLA}}}(X)$ at these redshifts continue to suffer from the small sample size of quasar sightlines.

Previous studies, e.g., Prochaska et al. (2005), Rao et al. (2006), Prochaska & Wolfe (2009), and Noterdaeme et al. (2012), have claimed little evolution in the line density of DLAs in the past 10 Gyr. However, the results in this paper indicate that the line density at $z\approx 0.5$ is lower than estimates of this quantity at $z\approx 2$ at greater than 2σ significance. This suggests a mild evolution in ${{\ell }}_{{\rm{DLA}}}(X)$ from $z\approx 2$ to the present epoch, instead of the inferred constancy in the DLA line density. The decrease in ${{\ell }}_{{\rm{DLA}}}(X)$ at low redshifts can be explained if the majority of galactic-scale dark matter halos are fully assembled by $z\approx 2$, and, if the neutral hydrogen content of these halos slowly decreases, either by star formation or feedback processes.

One caveat to this result is the possibility of systematic errors that can bias our estimates low. Here we discuss three of these biases. One potential bias to our sample is the exclusion of sightlines that were targeted to pass close to foreground galaxies. A random sample of quasars would contain some sightlines that pass by intervening galaxies, and by removing all of these quasars from the sample, we could be biasing our result low. To estimate the effect of this potential bias, we include all sightlines that are specifically chosen to cross a foreground galaxy (i.e., the quasars with ${f}_{{\rm{stat}}}$ = 2). The resultant line density is ${{\ell }}_{{\rm{DLA}}}(X)$ $=\;{0.030}_{-0.010}^{+0.014}$, which is well within the 1σ statistical uncertainty of our original estimate, indicating that this bias is smaller than our uncertainties.

A second possible bias may arise due to the inclusion of sightlines at redshifts $z\gtrsim 0.3$. For these redshifts, metal lines (in particular Mg ii) would fall within the optical part of the quasar spectrum. The target selection criteria for the quasar sample may have included a lack of metal line systems in the optical part of the quasar spectrum. Similarly, by excluding all of the sightlines with known Mg ii systems, we might be biasing ourselves against quasars with metal lines in their sightlines. To test the bias in our sample against Mg ii systems, we have compared the line density of Mg ii systems in our quasar sample with the line density in the sample of Seyffert et al. (2013). We find that the line density of Mg ii systems is 0.119 over the full redshift range probed by the quasars in our statistical sample, which are also part of the sample of Seyffert et al. (2013) (n = 93 quasars). This value agrees well with the measured line density of 0.123 ± 0.001 over the slightly larger redshift range covered by the full sample of Seyffert et al. (2013), and hence we assert that this effect is unlikely to significantly bias our results.

Finally, the third possible source of bias is that against sightlines with a large amount of dust. This bias has been studied in detail using spectroscopy of radio-selected samples in high-z DLAs (e.g., Ellison et al. 2001; Akerman et al. 2005; Jorgenson et al. 2006) as well as dust reddening of quasars in SDSS (e.g., Murphy & Liske 2004; Frank et al. 2010; Fukugita & Ménard 2015; Murphy & Bernet 2016). This bias is correlated with the amount of metals in the gas (Vladilo & Péroux 2005), and therefore is amplified at low-z due to the higher metallicity of low-z DLAs (e.g., Prochaska et al. 2003a; Rafelski et al. 2012, 2014).

Following Vladilo & Péroux (2005), dust extinction becomes significant at zinc column densities greater than $\sim {10}^{13.5}$ cm⁻², an assertion corroborated by the few DLAs showing distinct dust signatures (Noterdaeme et al. 2009a; Kulkarni et al. 2011; Ma et al. 2015). For low column density DLAs (log ${N}_{{\rm{H}}{\rm{I}}}$ $\lt \;20.5$) these zinc column densities imply $[M/H]\gt 0.5$. Such systems are expected to be rare, both from metallicity measurements of lower column density systems, and metallicity measurements from star-forming galaxies (e.g., Tremonti et al. 2004). Since ${{\ell }}_{{\rm{DLA}}}(X)$ is dominated by low H i column density systems, we assert that the effect of dust on biasing this result is small. In passing, we note that the amount of dust reddening in quasars with DLAs is observed to be small at $z\approx 2$ (Murphy & Liske 2004), and evolves only slightly between redshifts 2.1 and 4.0 (Murphy & Bernet 2016) further suggesting that dust is not likely a large biasing factor.

We estimate the H i column density distribution function, $f({N}_{{\rm{H}}{\rm{I}}},X)$, and the H i gas density, ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$ from our statistical sample. However, the limited sample size means that the errors on the inferred quantities are large. We find that the H i column density distribution function in our low redshift sample is consistent with the $f({N}_{{\rm{H}}{\rm{I}}},X)$ measured at high redshift. The increase in the high H i column density systems found by Rao et al. (2006) could be due to their selection process, but we cannot establish this assertion with the current data set.

The H i mass density, ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$, is estimated to be ${0.25}_{-0.12}^{+0.20}\times {10}^{8}{M}_{\odot }\;{{\rm{Mpc}}}^{-3}$, after correcting for the lack of statistics at the high H i column density end due to our small sample size of DLAs. The correction makes the assumption that the mean H i column density of our low-z DLA sample is the same as that of the high-z DLA sample, as measured from the SDSS surveys (Noterdaeme et al. 2012). Our value of ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$ is markedly lower than that obtained in previous measurements at these redshifts, but is in agreement with estimates of the H i mass density at $z\lesssim 0.3$ using H i 21 cm studies (Zwaan et al. 2005; Lah et al. 2007; Delhaize et al. 2013; Rhee et al. 2013; Hoppmann et al. 2015). The apparent mild evolution seen in ${\rho }_{{\rm{H}}\;{\rm{I}}}^{{\rm{DLA}}}$ from $z\approx 2$ arises due to the evolution in ${{\ell }}_{{\rm{DLA}}}(X)$, since we have assumed a non-evolving mean H i column density.

In conclusion, this study has compiled the largest sample of quasars observed in the UV with spectral resolution sufficient to search for low-redshift DLAs. Even with a total of 767 quasars in our target sample, the final sample of DLAs in these spectra is small, containing only 46 DLAs. This is in part due to the smaller than expected incidence rate of DLAs compared to the measurements from Mg ii surveys (Rao et al. 2006). However, the lower incidence rate is in agreement with both the results at $z\approx 2$ and $z\approx 0$, if we assume a mild decrease in ${{\ell }}_{{\rm{DLA}}}(X)$ over this redshift range.

This research would not have been possible without the guidance and insights of the late A.M. Wolfe during the initial phases of the project. He will be sorely missed. We thank R. Sánchez-Ramírez for providing their results before publication, and the referee for helpful comments that improved the manuscript. This work was based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space Telescope Science Institute (STScI). The COS G130M/G160M data presented in this work were obtained from the COS-CGM Legacy database, which is funded by NASA through grant HST-AR-12854 from the STScI. Finally, support for this work was provided by NASA through grant HST-AR-12645 from the STScI. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. M.N. and J.X.P. further acknowledge support from NSF award AST-1109452. N.L. acknowledges support provided by NASA through grant HST-AR-12854. J.C.H. and N.L. acknowledge support from NSF award AST-1212012. M.R. acknowledges support from an appointment to the NASA Postdoctoral Program at Goddard Space Flight Center. N.K. acknowledges support from the Department of Science and Technology via a Swarnajayanti Fellowship (DST/SJF/PSA-01/2012–13).