An Ultraviolet Survey of Low-Redshift Partial Lyman-Limit Systems with the HST Cosmic Origins Spectrograph
J. Michael Shull, Charles W. Danforth, Evan M. Tilton, Joshua Moloney, Matthew L. Stevans
DDraft version August 9, 2018
Preprint typeset using L A TEX style emulateapj v. 12/16/11
AN ULTRAVIOLET SURVEY OF LOW-REDSHIFT PARTIAL LYMAN-LIMIT SYSTEMSWITH THE HST COSMIC ORIGINS SPECTROGRAPH
J. Michael Shull, Charles W. Danforth, Evan M. Tilton, Joshua Moloney
CASA, Department of Astrophysical & Planetary Sciences,University of Colorado, Boulder, CO 80309 and Matthew L. Stevans
Dept. of Astronomy, University of Texas at Austin, Austin, TX 78712
Draft version August 9, 2018
ABSTRACTWe present an ultraviolet spectroscopic survey of strong H I absorbers in the intergalactic medium,probing their evolution over the last 6-7 Gyr at redshifts 0 . ≤ z ≤ .
84. We measure column densities N HI (cm − ) from the pattern of Lyman-series absorption lines and flux decrement at the Lyman limit(LL) when available. We analyzed 220 H I absorbers in ultraviolet spectra of 102 active galacticnuclei (AGN) taken by the Cosmic Origins Spectrograph aboard the Hubble Space Telescope withG130M/G160M gratings (1134-1795 ˚A). For 158 absorbers with log N HI ≥
15, the mean frequency is d N /dz = 4 . ± .
39 over pathlength ∆ z = 31 .
94 (0 . ≤ z ≤ . N HI ≥ .
2) and 54 partial systems (pLLS) with 16 . ≤ log N HI < .
2. Toward159 AGN between 0 . < z abs < .
84 with ∆ z ≈
48, we find four damped Ly α absorbers (DLA)with ( d N /dz ) DLA = 0 . +0 . − . at (cid:104) z (cid:105) = 0 .
18. The mean LLS frequency between z = 0 . − .
48 is( d N /dz ) LLS = 0 . +0 . − . fitted to N ( z ) = (0 . +0 . − . )(1 + z ) . . For 54 pLLS we find ( d N /dz ) pLLS =1 . ± .
23 at (cid:104) z (cid:105) = 0 .
39, a frequency consistent with gaseous halo sizes R ≈ h − kpc for (0 . − L ∗ )galaxies. A maximum-likelihood analysis yields a distribution f ( N, z ) = C N − β (1 + z ) γ with β =1 . ± .
05 and γ = 1 . +0 . − . for 15 ≤ log N HI ≤ .
5. The far-UV opacity gradient is dτ eff /dz ≈ (0 . z ) . over the range 15 ≤ log N HI ≤
17, implying mean LyC optical depth τ eff ≈ . − . z = 1 − Subject headings: cosmological parameters — ultraviolet: galaxies — observations — intergalacticmedium — quasars: absorption lines INTRODUCTION
Over the past decade, astronomers have uncoveredlarge reservoirs of gas in the outer portions of galaxyhalos (Tumlinson et al. 2011a, 2013; Stocke et al. 2013,2014) and in the intergalactic medium or IGM (Pentonet al. 2004; Shull et al. 2012a), far from the gravita-tional influence of individual galaxies. These gaseousstructures are detected by absorption-line spectra ofquasars and other active galactic nuclei (AGN) usingresonance lines of neutral hydrogen (H I ) and metalions (e.g., C IV , O VI , Si III , C II ) in the rest-framefar-ultraviolet. Shortward of the Ly α emission line at1215.67 ˚A, numerous weak H I absorption lines blan-ket the AGN continuum in the “Lyman-alpha forest”with column densities that we have been able to mea-sure reliably through HST /COS absorption-line spectraover the range 12 . ≤ log N HI (cm − ) ≤ . < log N HI < ∼
17, theLyman lines are highly saturated, and column densitiesare difficult to measure from Lyman series absorptionalone. When log N HI ≥ .
2, photoelectric absorptionin the Lyman continuum (LyC) produces optical depth τ LL ≥ λ LL = 911 .
753 ˚A.These redshifted absorbers are called Lyman-limit sys-tems (LLS), while those with slightly lower column den- [email protected], [email protected] sities are termed “partial Lyman-limit systems” (pLLS).In this paper, we use the term Lyman Limit (LL) in ref-erence to the redshifted wavelength (912 ˚A rest frame)and the types of absorbers (pLLS or LLS). The term Ly-man decrement refers to the drop in transmitted flux atthe LL, which is used to define continuum optical depth( τ LL ).Spanning a loosely defined range (16 < log N HI < . HST surveys (Storrie-Lombardi et al. 1994; Stengler-Larreaet al. 1995; Ribaudo et al. 2011a) focused primarily ontrue LLS, we note that two recent surveys of “Lymanlimit systems” (Ribaudo et al. 2011a; Lehner et al. 2013)also included many partial LLS in their tables. TheLLS and pLLS dominate the continuum opacity of theIGM (Shull et al. 1999; Haardt & Madau 2012; O’Mearaet al. 2013) and probe the metallicities in the environ-ment around galaxies (Ribaudo et al. 2011b; Tripp et al.2011; Lehner et al. 2013; Fox et al. 2013). Even rarerare the Damped Lyman-alpha (DLA) absorbers (Wolfeet al. 2005; Meiring et al. 2011; Turnshek et al. 2015)whose column densities, N HI ≥ × cm − , are suf-ficient to produce strong Lorentzian wings in their ab-sorption profiles. These H I lines provide the dominant a r X i v : . [ a s t r o - ph . GA ] O c t technique for measuring the baryon content of the IGM(Shull et al. 2012a), and the LLS/pLLS are a benchmarkfor determining the metallicity of the CGM (Tripp et al.2011). Strong H I absorbers have been linked (Simcoeet al. 2006; Lehner et al. 2009; Ribaudo et al. 2011b)to the extended regions of galaxies. The semantic ques-tion of “where galaxies end” (Shull 2014) depends ontheir gravitational influence as well as dynamical effectsof gaseous outflow and infall from the cosmic web (Trippet al. 2011).In our recent survey (Danforth et al. 2016) of low-redshift Ly α absorbers with the Cosmic Origins Spec-trograph (COS) on the Hubble Space Telescope ( HST ),we fitted the column densities to a power-law differentialdistribution, f ( N HI ) ∝ N − β HI , with β = 1 . ± .
02 overthe range 12 . ≤ log N HI ≤ .
0. Column densities de-termined from strong Ly α lines are uncertain owing toline saturation at log N HI ≥
14 for typical Doppler pa-rameters b ≈ −
35 km s − . The distribution is alsopoorly constrained at log N HI >
15 because strong Ly α absorbers are rare. Some progress in defining their col-umn densities has been made with access to higher Ly-man lines (Ly β , Ly γ , Ly δ ) from the FUSE satellite (Shullet al. 2000) and
HST (Danforth & Shull 2008; Danforthet al. 2016). The higher Lyman lines become available toCOS at modest redshifts ( z ≥ .
107 for Ly β , z ≥ . γ ) and they yield more accurate measurementsof the curve of growth (CoG). The LL shifts into theCOS/G130M window at z abs ≥ .
24. At log N HI > ∼ . > ∼
10) we can usethe flux decrement at the Lyman edge to confirm andsupplement the CoG solutions.In this paper, we explore the pLLS/LLS distribution in N HI and redshift, employing a “Lyman-comb” techniqueto find strong H I absorbers between z abs = 0 . − . λ obs = (911 .
753 ˚A)(1 + z abs ). We use high-S/N spectraof 102 AGN at z AGN ≥ .
24 with the COS G130M/160Mgratings. Figure 1 shows the redshift coverage of oursurvey, plotting the number of AGN sight lines sensi-tive to the LL (at 912 ˚A rest-frame). Our survey hasmuch higher spectral resolution ( R ≈ , R ≈ − HST /FOS and
HST /STIS. In well-exposedspectra with S/N > ∼
10, we are able to resolve veloc-ity components ∆ v = 40 −
400 km s − within absorbersand construct multi-component CoGs when needed. Forabsorbers with log N HI > .
2, the continuum opticaldepth at the LL is usually detectable by HST/COS withoptical depth τ LL = (6 . × − cm ) N HI > .
1. Bycombining the Lyman decrement with CoG fitting, wecan confirm the H I column density and its range of un-certainty.The continuum can be influenced by AGN emissionlines in the UV and EUV, many of which are broad andblended features that produce bumps and undulationsin the underlying power-law continuum. Fortunately, wehave a good template for the location of these emissionfeatures (Figure 2) obtained from the composite rest-frame UV/EUV spectrum of AGN (Shull et al. 2012b; Fig. 1.—
Distribution in redshift, g ( z ), showing the numberof AGN that contribute pathlength capable of detecting theredshifted LL of H I between z = 0 . − .
96. We consideronly absorbers at z ≥ .
24 (dashed line) whose LL is red-shifted into the COS/G130M band ( λ > I column densities and assess systematic errors. Stevans et al. 2014). We refer the reader to our paperson AGN composite spectra (Shull et al. 2012; Stevanset al. 2014) which describe our choice of line-free win-dows. Typical errors in continuum choice typically re-sult in ± .
02 errors in log N HI . In the rest-frame far-UV,the most prominent emission lines are the O VI doublet(1032 and 1038 ˚A), C III (977 ˚A), and a blend of O I features (930-950 ˚A). The dominant emission lines in therest-frame EUV (550 ˚A to 912 ˚A) are lines of O II andO III (833 ˚A and 834 ˚A), a broad complex (760-800 ˚A)consisting of the Ne
VIII doublet (770 ˚A and 780 ˚A) andO IV
788 ˚A, the 700 ˚A blend of O
III (702 ˚A) and N
III (686 ˚A), and strong emission lines of O IV (608 ˚A, 554 ˚A)and O V (630 ˚A). A full list of EUV lines in the AGNcomposite spectrum is provided in Table 4 of Shull et al.(2012b).The sample used in this survey began with 159 AGNtargets chosen because their UV brightness allowed themto be observed by HST /COS with both G130M andG160M gratings. Of these 159 AGN, 102 had red-shifts z AGN ≥ .
24, sufficient to shift the LL and higherLyman-series lines into the G130M window. This sam-ple includes many AGN previously observed by the
In-ternational Ultraviolet Explorer (IUE) and
HST spectro-graphs. Many were used by the COS-GTO team (Dan-forth et al. 2016) and COS-Halos project (Tumlinsonet al. 2013) for the purpose of studying the low-redshiftIGM and galactic halo gas. Stevans et al. (2014) used 159AGN with redshifts 0 . < z AGN ≤ .
476 to produce aCOS composite spectrum of AGN in their rest-frame UVand EUV. The AGN in the COS-Halos program were se-lected to avoid strong Mg II absorbers at z > .
4, whichwould bias the survey against LLS. Because our surveyof LLS and pLLS used only AGN with z abs ≥ .
24, it ex-cludes nearby Seyfert galaxies whose sight lines might bebiased against LLS. Further discussion of potential sam-ple biases for LLS and DLA is given in Section 3.3 and
Fig. 2.—
AGN composite spectrum based on Stevans et al. (2014) and annotated with prominent EUV broad emission linesof metal ions (O, N, Ne). Red spectrum shows spline fit to AGN flux passing above Ly α absorption lines (black). The AGNemission lines must be identified and fitted before placing the underlying EUV continuum (blue dotted line). Measuring theLL optical depth of absorbers requires careful attention to the the continuum on either side of the LL. The true continuumcan be contaminated by broad emission lines such as the Ne VIII λ ,
780 doublet, O IV λ III and O
III . Shorter wavelength EUV lines of O IV , O V , and Ne V can affect the continuum around absorbers at z LLS = 0 . − . in Ribaudo et al. (2011a) and Neeleman et al. (2016).Spectra taken with the COS G130M/G160M gratings(Green et al. 2012) provide moderate spectral resolu-tion ( R = λ/ ∆ λ ≈ , − − z abs ≈ .
95, using a template of Lyman-series absorp-tion lines at the same redshift. Even at log N HI < . τ LL < . N HI ≈ . S/N > ∼ I absorbersbetween log N HI = 15 . − .
25, found through higherLyman-series absorption lines (Ly γ through Ly8). InFigure 4, we demonstrate the effectiveness of using theLyman-line pattern, compared to the injection of weak“mock absorbers” 300 km s − to the red of the actual ab-sorber. This confirms our our ability to detect systemsbelow 50 m˚A equivalent width in data with S/N > ∼ I absorbers in our full sam-ple, 0 . ≤ z abs ≤ . z eff = 31 .
94 and identified 211 absorbers:8 were LLS with log N HI ≥ .
2, 54 were pLLS between16 . < log N HI < .
2, and the remainder lay between14 . < log HI < .
0. Our COS survey contains thelargest number of low- z LLS and pLLS to date, a dis-tribution that we compare to absorbers in the HST/FOSKey-Project surveys of LLS at 0 . < z < . z < . f ( N, z ), in column density and redshift. Wefind a line frequency d N /dz = 4 . ± .
39 for 15 . < log N HI < . . < z < .
84. Wequantify the pLLS distribution in H I column densityand redshift through maximum-likelihood fitting to theform, f ( N, z ) = C N − β (1 + z ) γ , with best-fit parame-ters β = 1 . ± .
05 and γ = 1 . +0 . − . . Although theevolutionary index γ ≈ . f ( N HI , z ), over column density, we com-pute the redshift gradient in LyC opacity, dτ eff /dz , forabsorbers between 12 . ≤ log N HI ≤ .
2. We estimate afar-UV (1130 ˚A) continuum opacity, τ eff ≈ . − .
5, to-ward AGN at z ≈ . − . I absorbers, 23 of whichwere studied in previous surveys. Appendix B describesour statistical analysis and the maximum-likelihood ap-proach to obtaining distribution parameters. SURVEY TECHNIQUES
Our survey of strong H I absorbers comes as a naturalby-product of the UV composite spectra of AGN con-structed from moderate-resolution HST/COS data (Ste-vans et al. 2014). To find the underlying AGN contin-uum, we used G130M/G160M spectra to identify the nu-merous Ly α forest lines, as well as the less frequent butstronger (LLS and pLLS) absorbers. We did not consider Fig. 3.—
Three examples of COS/G130M detections of H I absorbers with log N HI = 15 . ± .
02 (at z = 0 . N HI = 15 . ± .
02 (at z = 0 . N HI = 15 . ± .
02 (at z = 0 . β in allthree systems and in Ly α for the bottom two systems; Ly α shifts beyond the G160M window at z > .
47. The panelsshow detections in the higher Lyman-series lines (Ly γ , Ly δ ,Ly (cid:15) , etc). Middle panel includes a strong DLA at z a = 0 . N HI = 20 . ± .
10) toward J1009+0713. absorbers associated with the host galaxy of the AGN.Owing to the high resolution of COS, we are able to dis-tinguish individual absorption lines and resolve the truecontinuum level between them (Figures 3 and 4). Asdiscussed in our AGN composite paper (Stevans et al.2014), we corrected the AGN continuum for H I photo-electric absorption by pLLS and LLS absorbers. Thesecorrections are important for establishing the underlyingcontinuum longward and shortward of the H I absorptionfeatures. The LyC optical depth is related to H I columndensity by τ λ ≈ (6 . × − cm )( λ/λ LL ) N HI for λ ≤ λ LL . After determining N HI from the flux decre-ment, we multiply the observed flux shortward of the LLby exp( τ λ ) to restore the true AGN continuum.The LLS and pLLS absorption systems are identifiedby a “Lyman comb” technique (Stevans et al. 2014) inwhich we search for a pattern of lines in the H I Ly-man series together with the corresponding Lyman decre-ment when detectable. Table 1 lists the wavelengths,redshift bands, and column densities for which the first
Fig. 4.—
Six Lyman-series absorption lines towardHS 1102+3441 detected at the same redshift ( z abs = 0 . β ) to 39 m˚A (Ly7) and are fit-ted (red-dashed lines) to a CoG with log N HI = 15 . ± . b = 25 km s − . Mock absorbers with observed-frameEWs of 50 m˚A (blue-dashed lines) are inserted 300 km s − redward of each Lyman line. This simple example illustratesour ability to find such absorbers in data with S/N > ∼ eight Lyman lines and decrement are easily detectable(greater than 50 m˚A equivalent width). To implementthe method, we inspect the spectra for flux decrementsat the LL, employing a computer script that scans forcorrelated down-pixels at the locations of higher-orderLyman lines of strong absorbers. When a system is con-firmed, we measure the equivalent widths of up to thefirst 12 Lyman lines and fit them to a CoG to deter-mine the column density and Doppler parameter ( b inkm s − ). Our technique depends primarily on identify-ing the pattern of Lyman lines and less on detecting theLyman decrement. For the standard wavelength cover-age in the COS/G130M grating (1134–1459 ˚A), the LLbecomes detectable at z LL > .
244 and shifts out of theG130M band at z LL > .
60. By including wavelengthcoverage with the G160M grating (1400–1795 ˚A) we canobserve the far-UV range with access to the LL out to z LL ≈ .
95 and to various Lyman lines (Ly α - Ly ζ ) overthe redshift ranges shown in Table 1.Figure 3 illustrates our method for the higher Lymanlines of three H I absorbers with log N HI = 15 . − . z abs = 0 . β , and two of themhave Ly α (for the absorber at z = 0 . α has shiftedbeyond the G160M window). From the expected detec-tion limits (Table 1) in COS spectra like those shownin Figure 3, our survey is able to identify strong ab-sorbers down to log N HI ≈
15. In some AGN sightlines with low S/N ( ∼ z > .
75) where we lose Ly β , we may miss some ab-sorbers at log N HI = 15 . − . z ≥ .
24, we only searched for strong absorbers towardthose 102 quasars with redshifts z AGN ≥ .
24. For ourstatistical sample, we dropped a weak absorber at lowcolumn density (log N HI = 13 . z = 0 . z = 0 .
24. Wecarefully re-analyzed all systems with log N HI ≥ . τ LL weexamined the AGN spectrum for broad emission-line con-tamination of the continuum on either side of the LL. Inour re-analysis, we found an additional strong absorberomitted in Stevans et al. (2014), a DLA at z abs = 0 . . ≤ z abs ≤ .
928 we found eight trueLLS (log N HI ≥ . N HI = 20 . ± . . ≤ log N HI < . z < .
24) wefound a total of four DLAs towards all 159 surveyedAGN, at redshifts z DLA = 0 . N HI ≥ .
75, many of which ex-hibit multiple velocity components separated by ∆ v ≈ −
400 km s − . In some cases, the G130M spectra extend down to 1130 ˚A,allowing detection of the LL at z ≥ .
24. Because our Lyman-combmethod relies on finding pLLS through a pattern of Lyman lines,we could also detect Lyman lines from pLLS at lower redshifts: z > .
107 for Ly β , z > .
167 for Ly γ , and z > .
195 for Ly δ . Inthis survey we only report on systems at z ≥ . Measuring N HI from Lyman Lines andLyman-Edge In a HST/COS survey of H I column densities in thelow-redshift IGM along 82 AGN sight lines, Danforthet al. (2016) found 2577 distinct H I absorption systems,some of them single-line (Ly α ) systems. For statisticalanalysis, they defined a “uniform sample” of 2256systems in which N HI was found by multi-line CoGanalysis, using either (Ly α + Ly β ) or (Ly β + Ly γ )at a minimum for log N HI ≥ .
5, and Ly α alone forwell-measured weaker lines. Of these 2256 absorbers, 65had column densities N HI ≥ cm − . These columndensities were determined by a traditional CoG, whichworks best for absorption lines that are unsaturated ormildly saturated. At N HI < . cm − , IGM surveystypically rely on Ly α absorbers, since Ly β is too weak todetect at typical COS sensitivity (15-20 m˚A equivalentwidths). When higher Lyman lines become availableat higher z and greater N HI , the CoG yields reliableparameters ( N, b ).Once the Lyman lines become strongly saturated, withequivalent widths on the “flat portion” of the CoG, theinferred column densities are more uncertain. The onsetof saturation is gauged by the line-center optical depth, τ = ( πe /m e c )( N f λ/π / b ), where b = (25 km s − ) b is a typical doppler parameter. For the first four Lymanlines, these optical depths are τ (Ly α ) = (30 . N b − τ (Ly β ) = (4 . N b − τ (Ly γ ) = (1 . N b − τ (Ly δ ) = (0 . N b − , (1)for N HI scaled to (10 cm − ) N . As long as someLyman lines remain near the linear portion of the CoG,this method works well. For b ≈
25 km s − , the Ly α linebegins to saturate ( τ > N HI > .
5) producinglarge uncertainties at 14 . < log N HI < . I absorbers,using their Lyman decrements to derive accurate columndensities over the range 16 . ≤ log N HI ≤ .
85. Withour Lyman-comb technique and
S/N ≥
10, we candetect the Lyman decrement at optical depths τ LL ≥ . N HI ≥ .
2. Once log N HI ≥ . τ LL > .
46) it becomes difficult to detect transmittedflux in the Lyman continuum. In a few cases with highS/N ( > ∼
20) we detected or limited the residual fluxtransmission equivalent to τ LL ≥ . N HI ≥ . N HI from damping wings in the Ly α line, when present (Ly α shifts out of the COS/G160M band at z > ∼ . N HI > . .Widely separated velocity components are identifiedsemi-automatically (see Danforth et al. 2016), butclosely blended components require interactive iden- tification and fitting. We compare the models tothe observed spectrum in normalized flux space viaa χ minimization package mpfit (Markwardt 2009)with equivalent widths fitted to line profiles of eachcomponent (not to the observed flux). Moderatelysaturated lines with simple component structure are wellconstrained by this method, and the CoG gives muchbetter ( N, b ) solutions for H I than a single-line profile fit.Figures 5–8 illustrate our technique for Lyman-seriesand Lyman decrement absorption for two LLS withlog N = 17 . ± .
02 and log N = 17 . ± .
10 andtwo pLLS absorbers with log N HI = 16 . ± .
03 and17 . ± .
05. The presence of a Lyman decrement typ-ically yields log N HI accurate to ± .
05 or better. Fig-ure 9 shows spectra of the other eight strong H I ab-sorbers with log N HI > .
0. Strong H I absorbers areoften composed of multiple, blended components. Lower-order Lyman lines are typically too strong to see blendedcomponents, but higher-order lines can reveal their pres-ence. Absorbers where the minimized χ solution failsto match the data may harbor unresolved componentstructure. For example, in the strong absorber towardSBS 1108+560 (Figure 5), a weaker component is seenin the blue wing of Ly (cid:15) and higher lines. When blendedcomponents are present, we fit a CoG to each component,using only lines in which they are unambiguously sepa-rable, eliminating lines contaminated with airglow emis-sion or unrelated absorption. Line profiles and total col-umn densities for the combined solution (e.g., N , b , z and N , b , z ) are then calculated and compared qual-itatively to the stronger, lower-order Lyman lines. Inseveral cases, the CoG solution does not reproduce theobserved line profiles, or it differs from the Lyman decre-ment. The CoG is determined from the measured equiv-alent widths of the lines. Sometimes a solution with asmaller b and larger N (or vice versa) is required to matchthe observed line profiles or decrement. Lyman line overlap and velocity components
The CoG techniques generally give accurate resultswith the availability of higher Lyman lines. However,line overlap sets in at Ly15 ( λ = 915 .
329 ˚A) or Ly16( λ = 914 .
919 ˚A) as the higher Lyman series convergeson the Lyman limit at λ LL = 911 .
753 ˚A. Line crowd-ing and uncertain continuum placement makemeasure-ments of equivalent widths difficult when the wavelengthseparation, ∆ λ n,n +1 , between sequential Lyman linesis comparable to their line width. Table 2 shows lineseparations and line-center optical depths for Ly12 -Ly24, scaled to the ratio, N /b , for column densi-ties N HI = (10 cm − ) N . The lines are distinguish-able up to Ly15, where ∆ λ n,n +1 ≈ . λ FWHM = 2(ln 2) / (∆ λ D ) ≈ (0 .
127 ˚A) b λ , where λ is a typical (L15 - Ly20) wavelength in units of 914 ˚Aand ∆ λ D = λ ( b/c ) is the doppler width. Severe over-lap sets in above Ly20, where separations become lessthan 0.2 ˚A. At this point, higher Lyman lines overlap intheir wings, 10% below the continuum, defined by width∆ λ = 2(ln 10) / (∆ λ D ) ≈ (0 .
231 ˚A) b λ . A fewabsorbers have b = 40 −
50 km s − , with wing overlap affecting Ly 14 - Ly17 at line separations of 0.4 - 0.5 ˚A.Overlap creates difficulties in measuring equivalentwidths, with offsetting effects of shared line absorptionand continuum placement. Multiple velocity compo-nents complicate the problem further., and a propertreatment requires multi-line radiative transfer. There-fore, we do not include lines above Ly15 in our analy-sis, as illustrated in Figure 10 for the absorber towardPKS 0552-640. The standard CoG up to Ly15 giveslog N HI = 17 . ± .
05, whereas including additional(overlapping) lines from Ly16 to Ly24 gives an erroneousfit with log N HI = 16 . ± .
02. In this case, the observedLyman decrement provides an accurate column density,log N HI = 17 . ± .
03, verifying the CoG solution up toLy15.Appendix A provides narrative discussion for our anal-ysis of 73 strong H I absorbers with log N HI > . N HI > .
25, our combi-nation of CoG fits and Ly decrement measurements un-covered a few discrepancies with previous values in theliterature (Lehner et al. 2013; Fox et al. 2013; Stevanset al. 2014). For four systems with well-resolved velocitycomponents separated by 150-200 km s − or greater, wetreated the components as separate absorbers: Systems RESULTS
To analyze the bivariate distribution, f ( N, z ), of H I absorbers, we group them into a binned array, F ( i, j ),shown in Table 3, with redshift indices ( i = 1 −
15) andcolumn density indices ( j = 1 − z = 0 .
04 from z = 0 . − .
84. Thefirst 12 column-density bins have width ∆(log N HI ) =0 .
25 spanning 14 < log N HI ≤
17. The last three bins( j = 13 , ,
15) are wider and cover the 10 strongest ab-sorbers with log N HI = 17 . − .
5. As shown in Ta-ble 1 (column 4), the higher Lyman lines (Ly γ , Ly δ ,Ly (cid:15) ) are easily detectable, at 50 m˚A equivalent width,for column densities log N HI ≥ . − .
9. Because thebest COS data have S/N >
20, we have regularly de-tected the first three Lyman lines (Ly α , Ly β , Ly δ ) andoften even higher Lyman lines (Figure 3). This allowsus to identify absorbers with log N HI = 14 −
15, eventhough the Lyman edge is undetectable at these columndensities. The LLS and stronger pLLS absorbers withlog N HI > . I column densities via CoG.At higher redshifts, the two strongest Lyman lines moveout of the G160M window (Ly α at z > .
47 and Ly β at z > . I detectionsrely on Ly γ and higher lines, we could miss a few ab-sorbers with log N HI = 15 . − .
5. Column densities forstrong absorbers can sometimes be influenced by veloc-ity components. In well-exposed COS spectra, we canidentify components with ∆ v = 40 −
400 km s − , all ofwhich contribute to the Lyman decrement. We derive in-dividual column densities with multi-component CoGs,which could affect absorber counts for the bins betweenlog N HI = 14 . − .
00. We have taken a conservativeapproach, only splitting the velocity components in fourwell-separated systems with ∆ v ≥ −
200 km s − .The observed distribution in column density (Table 3)exhibits the expected falloff in numbers at high column Fig. 5.— (Top) Normalized COS/G130M spectrum of SBS 1108+560 showing lines of System z abs = 0 . N HI = 17 . ± .
02 and doppler parameter b = 18 ± − , not fits to individual lines. (Middlepanels) Line profiles of Lyman lines (Ly α - Ly10). (Bottom) Higher Lyman lines (Ly11 - Ly20) and transmitted flux in LyC.Note C II λ .
53 interstellar absorption in the LyC (bottom left panel).
Fig. 6.—
Same as Figure 5 for pLLS toward PKS 0552-640 (System z abs = 0 . α absorption extends from 1216-1226 ˚A. Red dashed lines in spectrum show profiles of Lyman lines (Ly α -Ly10) for model with log N HI = 17 . ± .
05 and b = 16 ± − . (Bottom) Higher Lyman-series lines (Ly11 - Ly20) andtransmitted flux in LyC above the Galactic DLA. Fig. 7.—
Same as Figure 5 for pLLS toward PG 1216+069 (System z abs = 0 . (cid:15) - Ly10) show strongest component fitted to CoG with log N HI = 16 . ± .
03 and b = 25 ± − . Lyman decrement gives τ LL = 0 . ± .
02 or log N HI = 16 . ± .
06. (Bottom) Higher Lyman lines (Ly11 - Ly20) andtransmitted flux in LyC. Fig. 8.—
Same as Figure 5 for LLS toward SDSS J154553.48+093620.5 (System z abs = 0 . β - Ly10) show strongest component fitted to CoG withlog N HI = 17 . ± .
15 and b = 35 ± − . This column density would give τ LL = 2 .
95 and transmitted flux of 5.25%,inconsistent with observations of flux below the LL (bottom panels) which imply log N HI ≥ . Fig. 9.—
COS Spectra of eight strong H I absorbers (log N HI > . N HI = 17 .
15 and 17.04). Other strong absorbers wereshown in Figures 4, 5, and 7. Spectra for Systems densities owing to their scarcity. We believe the decreasein absorber numbers in bins j = 1 − N HI = 14 − N HI < .
2, we rely on finding a pat-tern of higher Lyman lines (Ly γ , Ly δ , Ly (cid:15) ) whose detec-tion in the G160M window requires log N HI ≥ . − . z > . N HI ≥ .
0. Our statistical analysisin Appendix B restricts the H I absorber sample to therange 0 . ≤ z abs ≤ .
84 and 15 ≤ log N HI ≤
20, wherewe feel confident in detecting most systems in AGN sightlines with well-exposed COS spectra (S/N > . ≤ z ≤ .
48, as describedin Section 3.3. This technique differs from that in our re- cent IGM survey (Danforth et al. 2016), which detectedprimarily weak H I absorbers through Ly α lines. Redshift Coverage per Bin
The total (effective) redshift pathlength, ∆ z (tot)eff , isfound from the spectral coverage of the AGN in our sur-vey. We chose redshift bins of width ∆ z = 0 .
04, startingat bin 1 (0 . < z < .
28) where the Lyman edge atwavelength λ LL = (911 .
753 ˚A)(1+ z ) first falls within therange of most COS/G130M data (1134–1459 ˚A). Table 4shows the number of AGN with sensitivity to detect-ing a LL in each redshift bin. Each AGN with redshiftabove the bin contributes pathlength ∆ z = 0 .
04, pluspartial redshift coverage for a few AGN whose redshiftsfall within the bin. The redshift-bin pathlengths, ∆ z ( i )eff ,are shown in column 5 of Table 4. To determine this red-shift path, we subtracted a few spectral regions blockedby strong absorbers (log N HI >
17) along ten AGN sight2
Fig. 10.— (Top) Curve of growth of the Lyman series(Ly β through Ly15) for pLLS toward PKS 0552-640 at z abs =0 . W λ in m˚A), areplotted vs. line strengths, fλ , with oscillator strengths f andwavelengths λ (˚A) from Morton (2003). The best fit giveslog N HI = 17 . ± .
05 with b = 16 . ± . − (reduced χ noted in header.) (Bottom) CoG including lines of Ly16 -Ly24. Line overlap and crowding result in reduced equivalentwidths and an erroneous fit with log N HI = 16 . ± .
02 and b = 17 . ± . − . lines shown in Table 5. In practice, only a few of thestrongest LLS absorbers, with log N HI > .
5, producesignificant blockage. Strong foreground absorption bythe Galactic interstellar H I (Ly α ) does not impact ∆ z eff or the Lyman comb, since it usually blocks only one ofthe Lyman lines.With the far-UV spectral coverage between 1134 ˚A and1795 ˚A and availability of many lines in the Lyman series,we were able to detect strong H I systems between z abs =0 . − . z = 0 . − .
84. Sensitivity tohigher Lyman lines declines at z > .
846 as Ly γ shiftsout of the COS/G160M band. The total pathlength inthis sample (Table 4) is ∆ z (tot)eff = 31 .
94. For individualbins, the pathlength decreases from ∆ z ( i )eff = 3 .
83 for bin 1(¯ z = 0 .
26 and λ LL = 1149 ˚A) to ∆ z ( i )eff = 2 .
80 for bin 5 (¯ z = 0 .
42 and λ LL = 1295 ˚A). Although bin 5 covers theredshift ( z = 0 . β shifts out of G130M,spectral overlap with G160M (1400–1459 ˚A) allows Ly β to be continuously observed to z = 0 .
75. The Lymanedge shifts out of G130M beyond bin 9 (0 . < z < . z ( i )eff ≈ . − . z = 0 . α absorbers at z = 0 . − . β absorbers at z = 0 . − .
42, and Ly γ absorbers at z = 0 . − .
50. However, this effect is minor. BecausepLLS identification requires finding a pattern of severalLyman lines, our survey is most sensitive between z ≈ . − . z AGN thatare less likely to contain strong LLSs and DLAs (see Sec-tions 3.3 and 3.4). Our sample of 159 AGN (Stevanset al. 2014) contains 29 targets at z > .
70 and 43 at z > .
60, many of them observed previously by
IUE , HST , and
FUSE . To be detected in the G130M/G160Mgratings, these AGN were “UV-qualified” for sufficientfar-UV flux, usually by
GALEX or IUE . A number ofthese AGN came from the COS-Halos project (Tumlin-son et al. 2013) whose QSOs were selected to have highfluxes in the
GALEX far-UV band and avoid strong Mg II absorbers at z abs > . Bivariate Distribution in log N and z Table 6 lists 41 strong H I absorbers with log N HI ≥ .
0, classified as LLS or pLLS (systems N HI ≥ .
0) the absorber frequency per redshift is d N /dz ≈ . ± .
39 averaged over 0 . < z < .
84. Wesee some indication of an increase in frequency with red-shift. Figure 11 shows the distribution in column densityfor our pLLS data, together with the Ly α forest distribu-tion from Danforth et al. (2016). Some offset is expected,as the COS Ly α forest survey covers z < .
47 with me-dian redshift z abs = 0 .
14, whereas our pLLS survey spans0 . < z < .
93 with median z abs = 0 .
43. The eight de-tected LLS range from z = 0 .
237 to 0.474, with medianredshift z abs = 0 .
39. The absence of LLS at z > .
48 issurprising statistically, as we expected to detect 3 . +3 . − . LLS between 0 . < z < .
84 based on the derived red-shift evolution (Section 3.3). This may be evidence for abias toward AGN with high far-UV fluxes, unblocked byLLS at z > .
5. We do not see this effect for the strongerpLLS with log N HI = 16 . − .
0. For pLLS statistics, weuse the full redshift range (0 . ≤ z ≤ .
84) but restrictthe LLS sample to bins 1–6 (0 . ≤ z ≤ . α forest and pLLS distributions match fairlywell at log N HI ≥
16. A possible turnover in the pLLSdistribution appears at log N HI < .
5, which could markthe onset of survey incompleteness. Because of the smallnumber of absorbers, one expects fluctuations in the3
Fig. 11.—
Distribution of H I absorbers in column density(per log N HI ) over total redshift pathlength ∆ z eff = 31 . . ≤ z ≤ .
84. Solid diamonds (green) are fromthe HST/COS survey (Danforth et al. 2016) of Ly α forest at0 < z < .
47, and filled circles (black) show the current surveyof pLLS and LLS at 0 . < z < .
84. Green dotted line isa least-squares fit to the differential distribution, f ( N, z ) ∝ N − β , with β = 1 . ± . range log N HI = 15 . − . j = 5 − z = 0 .
04, ∆(log N HI ) = 0 . . < log N HI < . z > .
47, when Ly α shifts outof the G160M window. The absorber numbers in bins6–9 could also be affected by velocity components withinstrong systems, which separate into distinct absorbers.The distinction between “systems” and “components”is a subtle one that we have not pursued beyond theobvious cases in Systems I column density and frequency, we haveapplied a maximum-likelihood analysis (Appendix B)to the parameterized form f ( N, z ) ≡ d N /dz dN HI = C N − β HI (1 + z ) γ . We fitted all absorbers in the ranges0 . ≤ z ≤ .
84 and 15 ≤ log N HI ≤
20, using Monte-Carlo Markov-Chain (MCMC) simulations to derive val-ues β = 1 . ± .
05 and γ = 1 . +0 . − . . Figure 12 showsthe 2 D joint probability distributions in power-law pa-rameters and their 1 σ error bars. Both distributions areclose to Gaussian, although the column-density distribu-tion is much better constrained (3.4% error in β ) thanthe redshift evolution index, γ . The uncertainty in γ isillustrated in Figure 13 with a histogram of the redshiftdistribution from z = 0 . − .
84. This evolution indexis similar to those determined in our Ly α survey (Dan-forth et al. 2016). Over redshifts 0 < z < .
47, we found γ all = 1 . ± .
04 for all absorbers with log N HI >
13. Re-fitting the distribution of 65 absorbers at log N HI ≥ . γ = 1 . ± . Fig. 12.—
Parameterized evolution of the distribution ofH I absorbers in column density and redshift, f ( N, z ) = C N − β (1 + z ) γ , from Monte-Carlo Markov Chain (MCMC)samples for power-law parameters. Lower-left panel plotsthe 2 D joint-probability of γ and β , and other panels showthe marginalized distributions with median and 1 σ boundsmarked by dashed lines. The normalization ( C ) of our (MCMC) distributionfollows from integrating over observed (and fitted) rangesin redshift ( z < z < z ) and column density ( N 48 togive 1 . × − . The redshift integral gives 0.983, for z = 0 . z = 0 . γ = 1 . 14, and assuming ∆ z eff ( z )to be constant across the full redshift range with path-length ∆ z (tot)eff = 31 . 94. Thus, we find C = 3 . × for N tot = 159 absorbers. If we weight f ( N, z ) by the effec-tive pathlengths, ∆ z eff ( z i ), of the 15 individual redshiftbins (Table 4), we find a slightly larger normalization, C = 4 . × . We adopt C = 4 × for N (cm − ). True Lyman-Limit Systems By convention, true LLS are defined as absorbers with τ LL ≥ N HI ≥ . 2. Although most surveys fol-low this definition, several recent papers included pLLSabsorbers with lower column densities in their lists. Be-cause of the scarcity of low-redshift LLS, extending thedefinition of LLS into the pLLS range creates sampleswith better statistics. In our survey, we retain standarddefinitions of LLS and pLLS (16 . < log N HI < . 2) andanalyze a total of 158 H I absorbers with log N HI ≥ . z = 0 . − . N HI = 20 . ± . 12) and 54 are4 Fig. 13.— Parameterized evolution of the number of H I absorbers per unit redshift, d N /dz , for z = 0 . − . 84, in-tegrating f ( N, z ) = C N − β (1 + z ) γ over 15 ≤ log N HI ≤ γ = 1 . +0 . − . . Horizontal (yellow) band showsthe average line frequency, (cid:104) d N /dz (cid:105) = 4 . ± . 39, and red-dashed line is the MCMC fit with γ = 1 . 14. Histogram showsmeasured number of absorbers per unit redshift in 20 equalbins with error bars determined according to Poisson statis-tics. A non-integer number of absorbers may contribute to binvalues because uncertainty in N HI measurements can place aportion of an absorber’s probability density outside the rangeused in fit. pLLS. This HST /COS survey is one of the largest sam-ples of strong H I absorbers at low redshift (full rangefrom 0 . ≤ z ≤ . R ≈ , z abs = 0 . − . z abs = 0 . 39. Extrapolating the pLLS distribution (Sec-tion 3.2) into the LLS regime, we expect a frequency, (cid:18) d N dz (cid:19) LLS = C (1 + z ) γ (cid:90) N N N − β dN ≈ . 44 (1 + z ) γ , (3)for C = 4 × and β = 1 . 48. For γ = 1 . 14, the pre-dicted number of LLS over the full survey, with ∆ z eff =31 . 94 for 0 . ≤ z ≤ . 84, would be N LLS = 13 . +4 . − . ,larger than the observed 7 (or 8) LLS. We found no LLSin redshift bins 7–15 (0 . ≤ z ≤ . N LLS = 3 . +3 . − . . For therestricted LLS range (0 . ≤ z ≤ . 64) in which the Ly-man edge falls at λ < z eff = 26 . 82 over bins 1-10. We would then expect toobserve N LLS = 7 . +3 . − . , in agreement with our surveynumbers. This deficit suggests that some of the “high-redshift” ( z > . 5) AGN sight lines in our sample arebiased against finding strong LLS and DLAs that block their far-UV flux in the most sensitive portion (1420–1650 ˚A) of the GALEX far-UV band often used in QSOtarget selection. Many of these AGN have been stud-ied with previous UV spectrographs ( IUE , FUSE , HST )based on their far-UV brightness. Although we found noLLS between 0 . ≤ z ≤ . 84, these AGN sight lines docontain strong pLLS absorbers (16 . ≤ log N HI ≤ . τ LL > z > . 5, we re-strict our LLS sample to z ≤ . 48 and analyze the sevenLLS in bins 1-6 over surveyed pathlength ∆ z eff = 19 . d N /dz = 0 . +0 . − . , atthe median z LLS = 0 . 39. Translating to standard form, d N /dz = N (1 + z ) γ , this frequency corresponds to N = 0 . +0 . − . , after dividing by (1 + z ) γ ≈ . 46 atthe median redshift with γ = 1 . 14. This LLS frequencyis in agreement with previous studies (see Table 7 for asummary). We begin with the HST /FOS Key Projectsurvey of QSO absorption lines at 0 . < z < . d N /dz =(0 . +0 . − . )(1 + z ) . ± . based on seven LLS observedby FOS at 0 . < z < . 036 with median redshift z abs = 0 . d N /dz = (0 . +0 . − . )(1 + z ) . ± . .In a recent survey of strong absorbers at z < . 6, Rib-audo et al. (2011a) analyzed 206 LLS and pLLS ab-sorbers with low-resolution gratings ( R ≈ I absorbers in that survey were at z > 1; Table 4 intheir paper lists five absorbers at z < . z < . 84 (17 LLS). From theirLLS sample with τ LLS ≥ 1, they fitted the evolution to d N /dz = (0 . z ) . ± . over 0 . < z < . z < 1) LLS re-ported in the literature is small, with just seven LLS inthe HST /FOS Key Project and eight in our HST /COSsurvey (these 8 are distinct from those seen with FOS).We are also aware of three LLS at z < . 24, found by the FUSE satellite in the far-UV:PHL 1811 ( z abs = 0 . N HI = 17 . ± . z abs = 0 . N HI = 17 . ± . z abs = 0 . N HI = 18 . +0 . − . (Lehner et al. 2009)We return to the observed deficit of LLS at z > . GALEX far-UV magni-tudes < . 5) with median redshift z AGN = 0 . > II absorbers at z > . z > . z AGN ≥ . 24 includes 37 targets from the COS-Halossample: 20 at z AGN > . 5, 14 at z AGN > . 6, and 9 with z AGN = 0 . − . IUE (Tripp et al.1994): PG 1407+265 ( z = 0 . z =50 . z = 1 . z = 1 . z = 1 . z = 1 . z = 1 . z = 0 . z = 0 . HST GTO Program and Guest Investigator Programs11248, 11264, 11585, 11598, 11741, with diverse scientificgoals including intergalactic absorbers (Danforth et al.2016), high-redshift absorbers (Tripp et al. 2011; Rib-audo et al. 2011b), galaxy-quasar pairs (Keeney et al.2006; Crighton et al. 2010; Meiring et al. 2011; Tumlin-son et al. 2013; Stocke et al. 2013; Bordoloi et al. 2014),and interstellar high-velocity clouds (Shull et al. 2009).Several of these high- z AGN were selected to study inter-vening Ne VIII absorbers and the hot phase of the IGM(Narayanan et al. 2011; Tripp et al. 2011; Savage et al.2011; Meiring et al. 2013; Hussain et al. 2015).Our derived LLS coefficient, N = 0 . +0 . − . , is consis-tent with previous values (Table 7) from low-resolution HST surveys with FOS and STIS. Our fit to pLLS red-shift evolution over 0 . < z < . 84 gives γ pLLS =1 . +0 . − . , consistent with estimates noted above (Storrie-Lombardi et al. 1994; Stengler-Larrea et al. 1995; Rib-audo et al. 2011a). However, the HST surveys are allbased on small numbers of LLS with different redshiftcoverages. The median LLS redshifts are z = 0 . 65 for theseven FOS Key Project absorbers and z = 0 . 39 for theeight LLS studied by COS. The Ribaudo et al. (2011a)survey was dominated by systems at z > 1, with onlythree LLS at z ≤ . 5. Thus, the redshift evolution of LLSand pLLS remains uncertain. Our best fit, γ pLLS = 1 . γ LF = 1 . ± . 06 (Danforth et al.2016) for weak Ly α forest absorbers and also to that, γ LLS = 1 . ± . 56 (Ribaudo et al. 2011a) fitted to theLLS ( τ LLS ≥ 1) absorbers at z < . N inferred fromextrapolating f ( N, z ) could be used to detect a turnoverin the power-law slope ( β ) at log N > 17. However, thenumber of low- z LLS absorbers is currently too small toprovide reliable statistics. Obviously, larger UV surveysof LLS and pLLS that cover a wider range of redshiftswould have greater leverage for determining the evolu-tion index γ .Accurate values of pLLS/LLS evolution out to z ≈ N HI > . 5) resultsin large fluctuations about these mean optical depths.However, the accumulated far-UV absorption from pLLScould decrease F λ and flatten the spectral energy distri-bution in the far-UV. There may also be bias in the se-lection of the intermediate-redshift quasars (1 . < z < . 2) used to construct rest-frame LyC composite spectra(Telfer et al. 2002; Shull et al. 2012b; Stevans et al. 2014;Tilton et al. 2016). To be selected, these AGN neededto have detectable fluxes in the GALEX far-UV chan-nel covering 1344–1786 ˚A (Morrissey et al. 2005). Thus,the observed AGN sight lines generally avoided encoun-tering LLS at z LLS ≈ . − . N HI > . Damped Ly α Absorbers Although we have focused primarily on pLLS andLLS absorbers, we also include a discussion of the fourDLAs detected along the sight lines to all 159 AGN inour sample We provide these low-redshift statistics withonly moderate astronomical interpretation, because ofthe small numbers and the accompanying uncertaintiesin deriving effective pathlengths We compare our valueswith several previous DLA surveys that used UV dataat z < . 65 (Rao et al. 2006; Meiring et al. 2011; Bat-tisti et al. 2012; Turnshek et al. 2015; Neeleman et al.2016). Table 8 lists these four DLAs, together with sixsub-DLAs (log N HI = 19 . − . 3) and two strong ab-sorbers (log N HI ≈ . ± . 5) whose large error barsplace them near the sub-DLA range. As with our LLSstatistics, we only consider redshifts z abs < . 48. In-deed, all four DLAs in our sample are at low redshifts( z < . II absorbers at z > . 4. The fourthDLA ( z abs = 0 . z ≥ . 24, we hadan effective pathlength ∆ z = 19 . 24 sensitive to detect-ing LLS and DLA between 0 . < z < . 48. We in-clude the extra pathlength (∆ z = 29 . 26) at the red-shifts between 0 . < z < . 24 available to all 159AGN, and subtract a small amount (∆ z = 0 . z ≈ 48 sensitive to DLAs. Our statistics for DLA fre-quency are therefore based on four low-redshift DLAs:J1619+3342 ( z a = 0 . N HI = 20 . ± . z a = 0 . N HI = 20 . ± . z a = 0 . N HI = 20 . ± . 10; andJ1616+4153 ( z a = 0 . N HI = 20 . ± . z = 48, these four DLAs correspondto a line frequency, (cid:18) d N dz (cid:19) DLA = 0 . +0 . − . , (4)at mean redshift (cid:104) z (cid:105) = 0 . 18. We now compare thisDLA frequency to those inferred from other surveys at z < . 65. Owing to the small numbers of low- z DLAs,these surveys also have large uncertainties, ranging from d N /dz = 0 . +0 . − . (Neeleman et al. 2016) to 0 . +0 . − . (Meiring et al. 2011). Most of the DLAs in those surveysare at higher redshifts ( z > 1) compared to the 4 DLAsin our COS survey ( z = 0 . HST /STIS, identifying DLAs from a Mg II and Fe II selected sample. They found d N /dz = 0 . ± . z < . 65 based on 18 DLAs found in 108Mg II systems at (0 . < z < . 9) with median red-shift z = 0 . n ( z ) = n (1 + z ) γ with n = 0 . ± . γ = 1 . ± . 11. Meiring et al. (2011) found d N /dz = 0 . +0 . − . from three DLAs along a COS-6surveyed path with ∆ z = 11 . 94. These three DLAs werealso identified in our survey: J1616+4153 ( z a = 0 . z a = 0 . z a = 0 . z < . z = 123 . d N /dz = 0 . +0 . − . at median redshift z = 0 . II targeting or because of a galaxy close to the QSOsightline.In the most recent survey, Rao et al. (2017) exam-ined the statistical properties of DLAs at 0 . < z < . 65 using UV measurements ( HST /ACS, GALEX and HST /COS). Over a wide range of redshifts ( z = 0 − d N /dz = (0 . ± . z ) . ± . . Thisfit corresponds to d N /dz = 0 . 036 at the mean redshift( z = 0 . 18) of our survey. They find no bias with Mg II -selected samples of DLAs. Their COS sample turned upno true DLAs (all had log N HI ≤ . 0) but two of themwere sub-DLAs, also found in our survey (Systems Opacity of the Low- z IGM After the epoch of reionization of neutral hydrogenat z ≈ 7, the IGM becomes mostly ionized. How-ever, the UV continuum of intermediate-redshift AGNis still blanketed by Ly α absorbers that produce pho-toelectric opacity in their Lyman continua. This LyCopacity determines the mean-free-path of ionizing pho-tons in the IGM, attenuates the ionizing photons fromgalaxies and quasars, and determines the metagalacticEUV background radiation (Fardal et al. 1998; Miralda-Escud´e 2003; Haardt & Madau 2012; O’Meara et al.2013). This continuum opacity is also relevant to measur-ing the composite spectrum of quasars in their rest-frameLyC. Our recent studies of AGN at intermediate redshifts( z ≈ . − . 2) exhibit frequent pLLS absorption (Shullet al. 2012b; Stevans et al. 2014; Tilton et al. 2016) whoseLyC optical depth and recovery at shorter wavelengthsis used to restore the underlying AGN continuum.The primary observable of our survey is the bivariatedistribution of H I absorbers in redshift and column den-sity. For a Poisson-distributed ensemble of H I absorbers(Paresce et al. 1980), one can compute the average pho-toelectric continuum opacity in the low-redshift IGM byintegrating over the relevant range of column densities.We find the gradient of optical depth with redshift, dτ eff dz = (cid:90) (cid:18) d N abs dz dN (cid:19) [1 − exp {− N σ ( z ) } ] dN . (5)Here, N denotes N HI and we define the H I photo-electric optical depth as τ ( λ o ) = N σ ( λ ) at a typ-ical observed far-UV wavelength, λ o ≡ λ LL (1 + z o ).The Lyman continuum cross section is approximated as σ ( λ o ) ≈ σ ( λ o /λ LL ) where σ = 6 . × − cm .We adopt a fiducial far-UV wavelength λ o = 1130 ˚Awhere the COS/G130M coverage begins. By construc-tion, λ o < λ LL (1 + z ) and z o < z in order for λ o to lie in the LyC of the absorber.We now compute the cumulative optical depth, τ eff ( z o , z ), due to a population of H I absorbers at red-shift z . For absorbers with τ LL < N < . × cm − ) we approximate [1 − exp( − τ )] ≈ τ . We expressthe H I column density distribution as separable powerlaws in column density and redshift, f ( N, z ) ≡ d N abs dz dN = C N − β (1 + z ) γ , (6)for column densities N measured in cm − . In ourpLLS survey, a maximum-likelihood fit finds β pLLS =1 . ± . γ pLLS = 1 . +0 . − . , and C = 4 × over thehigher range in column density (15 ≤ log N ≤ λ o depends on an integral over the column-densitydistribution, dτ eff ( z o , z ) dz = C σ (cid:20) z z (cid:21) (1 + z ) γ (cid:90) N N N ( − β +1) dN = C σ (1 + z ) γ (2 − β ) (cid:20) z z (cid:21) (cid:104) N (2 − β )2 − N (2 − β )1 (cid:105) . (7)For β pLLS = 1 . ± . 05, the H I opacity is weaklydominated by the higher-column density absorbers with τ eff ∝ N . . Here, σ ( λ o ) ≈ σ [(1 + z ) / (1 + z )] isthe cross section at wavelength λ o . From the observeddistribution parameters we derive an opacity gradient, dτ eff /dz = (0 . z ) γ pLLS [(1 + z ) / (1 + z )] for thestrong absorbers, 15 ≤ log N HI ≤ . 2. We then inte-grate τ eff ( z o , z ) from redshift z o out to higher redshifts, τ (pLLS)eff ( z o , z ) = (0 . (cid:90) zz o (cid:20) z o z (cid:21) (1 + z ) γ dz = (0 . z o ) γ +1 (2 − γ ) (cid:34) − (cid:18) z o z (cid:19) (2 − γ ) (cid:35) . (8)For our best-fitting index, γ pLLS = 1 . 14, the opticaldepths at λ o = 1130 ˚A ( z o = 0 . 24) are τ eff ( z o , z ) =(0 . , . , . 39) for sources at z = (1 . , . , . γ pLLS . For γ pLLS = 2, the integral has a logarithmic dependence, τ (pLLS)eff ( z o , z ) = (0 . z o ) ln (cid:20) z z o (cid:21) . (9)At z = (1 . , . , . τ eff ( z o , z ) = (0 . , . , . γ pLLS could be higher than our assumed valueof γ = 1 . 14. However, this best-fit index is similar toprevious studies. For example, Ribaudo et al. (2011a)found γ = 1 . ± . 56 for LLS with τ LL ≥ . < z < . 59. However, their survey only had3 LLS at z ≤ . z ≤ . α forest, with log N < 15, con-tribute less optical depth, dτ eff /dz = (0 . z ) γ LF ,7from which we find τ (LF)eff ( z o , z ) = (0 . z o ) γ +1 (2 − γ ) (cid:34) − (cid:18) z o z (cid:19) (2 − γ ) (cid:35) . (10)For the index, γ LF = 1 . ± . 06, that fits all absorbersat log N HI > . α -forest optical depths at λ o = 1130 ˚A ( z o = 0 . 24) are τ eff ( z o , z ) = 0 . z = 1 . 0, 1.5, and 2.0. Combining the pLLS and Ly α for-est, we find average optical depths of τ eff ( z o , z ) = 0 . z o = 0 . 24 and sources at z = 1 . 0, 1.5, 2.0. SUMMARY AND DISCUSSION This HST /COS survey is one of the largest sets of 220strong H I absorbers at low redshift. Our survey spanscolumn densities (14 . ≤ log N HI ≤ . 4) and redshifts(0 . ≤ z ≤ . z = 0 . z = 0 . − . 84 and ∆(log N HI ) = 0 . 25. With sen-sitivity to multiple lines in the H I Lyman series, ourpLLS survey should be nearly complete for the 158 ab-sorbers with log N HI > 15. The column densities of a fewabsorbers in two bins (log N HI = 15 . − . 5) may haveshifted to adjoining bins owing to CoG effects of velocitycomponents. We may also have missed some weak ab-sorbers at z > . 5, detected only in higher Lyman-serieslines, since Ly α and Ly β shift out of the COS/G160Mwindow at z > . 47 and z > . 75 respectively. Oursurvey includes 8 true LLS (log N HI ≥ . N HI = 20 . ± . . ≤ log N HI < . R ≈ , 000 or∆ v ≈ 18 km s − ) sufficient to measure multiple linesin the H I Lyman series, along with the Lyman decre-ment at log N HI ≥ . 2. Our Lyman-comb technique issuperior for column-density determination compared tomethods based on low resolution ( R ≈ N HI and its bivariatedistribution, f ( N HI , z ).The COS distribution is in good agreement withprevious HST surveys of LLS at 0 . < z < . d N /dz = N (1 + z ) γ and summarized in Ta-ble 7. Storrie-Lombardi et al. (1994) found d N /dz =(0 . z ) . ± . and Stengler-Larrea et al. (1995)found d N /dz = (0 . z ) . ± . . Each of theseFOS studies analyzed the same seven LLS. From FOSand STIS data, Ribaudo et al. (2011a) fitted an index γ = 1 . ± . 56 for LLS absorbers between 0 . < z < . 59. The eight LLS systems in our COS survey are dis-tinct from those in the FOS study and range from z abs =0 . z = 0 . z abs = 0 . z = 19 . 24 between 0 . < z < . 48, we find a mean frequency, (cid:104) d N /dz (cid:105) LLS = 0 . +0 . − . .With median redshift z LLS = 0 . 39, this translates to N ( z ) = N (1 + z ) γ where N = 0 . +0 . − . at z = 0. Anindex γ ≈ . z < 1. For a ΛCDM cosmology withstandard (Planck-2016) parameters, the expected red- shift evolution for absorbers with constant space density φ and cross section σ is: d N dz = φ σ cH (1 + z ) [Ω m (1 + z ) + Ω Λ ] / ≡ (cid:18) φ σ cH (cid:19) S ( z ) . (11)Over our sampled range in redshift, 0 . ≤ z ≤ . 84, withΩ m ≈ . Λ ≈ . 7, the cosmological factor is well-fitted by S ( z ) = (1 . z ) . to 3% accuracy. Thus,our derived maximum-likelihood value γ = 1 . +0 . − . , isconsistent with non-evolving absorbers, although the al-lowed range in γ provides poor constraint on their low- z evolution. Ultraviolet spectroscopic surveys of pLLS at z = 0 . − . 5, with better statistics and redshift leverage,would narrow the range of γ pLLS and help to characterizetheir redshift evolution.In the Introduction, we alluded to the relationship be-tween LLS absorbers and the extended regions of galax-ies. Using our statistical sample of pLLS, with ob-served frequency d N /dz = 1 . ± . 33, equation (11)implies a cross section, σ = πR , with effective radius R if we associate the pLLS with an appropriate spacedensity of galaxies. We use the luminosity function oflow-redshift ( z = 0 . 1) galaxies from the Sloan DigitalSky Survey (Blanton et al. 2003), with normalization φ ∗ = (1 . ± . × − h Mpc − and faint-end slope α = − . ± . 01, to find: R = (cid:20) d N dzπ ( c/H ) φ ∗ S ( z )(∆ L/L ∗ ) (cid:21) / ≈ (110 ± 10 kpc) h − [ S ( z )(∆ L/L ∗ )] − / . (12)The cosmological factor S ( z ) ≈ . 57 at the median ab-sorber redshift ( z = 0 . L/L ∗ ) depends on the minimum luminos-ity and ranges from 0.56 (integrating down to 0 . L ∗ ) to1.83 (integrating down to 0 . L ∗ ). Both scaling factorsenter as the square root. Taking h ≈ . d N /dz , to be associated with extended halos of lu-minous (0 . − . L ∗ ) galaxies. In the COS-Halos Survey,the CGM of star-forming galaxies has been detected inO VI absorption (Tumlinson et al. 2011) out to distancesof 100-150 kpc. Tumlinson et al. (2013) detected strongH I absorption averaging ∼ α equivalent widthout to 150 kpc, with 100% covering fraction for star-forming galaxies. Radial extents of 100-200 kpc are alsoconsistent with the region of gravitational influence of10 M (cid:12) galaxies, estimated from a proper treatment ofthe virial radius (Shull 2014), R vir ( M h , z a ) = (206 kpc) h − / M / (1 + z a ) − × (cid:20) Ω m ( z a ) ∆ vir ( z a )200 (cid:21) − / . (13)This expression differs from often-used formulae by thescaling with overdensity ∆ vir and by the factor (1+ z a ) − .This factor reflects the fact that most galaxies under-went virialization in the past, when the IGM backgrounddensity was higher by a factor of (1 + z a ) . Typical“half-mass assembly” redshifts are z a ≈ . − . 2. Af-ter initial assembly, their proper size changes gradually8because of continued mass infall into the halo. Fromthe statistics of current pLLS survey, we are unable toascertain the H I column density at which “strong H I absorbers” are less directly associated with galaxy halos.Based on the steep fall-off of the observed differentialdistribution, f ( N HI , z ) ∝ N − . , it likely occurs below N HI = 10 cm − . This prediction is consistent with ob-servations (Figure 5 in Stocke et al. 2013) which find thatvirtually no absorbers with log N HI ≤ . I “covering factor” is difficult to constrain in our sam-ple, since we have not undertaken a program to identifythe associated galaxies. Many of them are at z > . z ≈ N HI > . 5) results in large fluctuationsabout these mean optical depths. Far-UV absorptionfrom pLLS could decrease F λ and flatten the spectral en-ergy distribution in the far-UV. Selection bias may affectthe intermediate-redshift quasars (1 . < z < . 2) used toconstruct rest-frame LyC composite spectra (Telfer et al.2002; Shull et al. 2012b; Stevans et al. 2014; Tilton et al.2016). These AGN need to have detectable fluxes in the GALEX far-UV channel covering 1344–1786 ˚A (Morris-sey et al. 2005). Thus, the observed AGN sight linesgenerally avoided encountering LLS at z LLS ≈ . − . N HI > . z AGN = 1 − f ( N, z ), tohigher redshifts, and targeting via the presence or ab-sence of strong Mg II absorbers will bias the LLS survey.The current COS survey provides reliable data at lowredshift ( z < . d N /dz ,continuously to values at z > . . ≤ z ≤ . 84, the average fre-quency for strong H I absorbers (log N HI ≥ . (cid:104) d N /dz (cid:105) ≈ . ± . 39. We parameterize the bi-variate distribution of H I absorbers as f ( N, z ) = C N − β HI (1 + z ) γ , where a maximum likelihood fitover the ranges 0 . ≤ z ≤ . 84 and 15 ≤ log N HI ≤ 20 gives β ≈ . ± . γ ≈ . +0 . − . , and C =4 × for column densities N HI in cm − . This dis-tribution is poorly determined at log N HI > . γ ≈ . 1) is consistent withabsorbers of constant space density and cross sec-tion.2. Based on seven true LLS with log N HI ≥ . . < z < . 48, we derive a LLS frequencyof ( d N /dz ) LLS = (0 . +0 . − . )(1 + z ) γ , assuming thebest-fitting index γ = 1 . 14 derived from MCMCsimulations of all strong absorbers. The frequency for pLLS is ( d N /dz ) pLLS = (1 . ± . z ) γ .If these absorbers are associated with halos ofluminous (0 . − . L ∗ ) galaxies, the pLLS fre-quency implies circumgalactic gas cross sections of100 − 150 kpc radial extent.3. Over the range (0 . < z < . 48) of the COS sur-vey of 159 AGN sensitive to DLAs, we found 4DLAs over pathlength ∆ z ≈ 48. From this, weestimate an absorber frequency, ( d N /dz ) DLA =0 . +0 . − . . Although uncertain, this frequencyis lower than the previous (COS-studied) value,0 . +0 . − . (Meiring et al. 2011), which was basedon 3 DLAs over ∆ z = 11 . 94, but larger than thevalues d N /dz ≈ . − . 036 (Neeleman et al.2016; Rao et al. 2017). All of these surveys sufferfrom small-number statistics.4. Combining the data from low-redshift COS surveysof pLLS and Ly α forest absorbers, we estimatethe H I photoelectric opacity gradient, dτ eff /dz ,for mean optical depth in the far-UV continuum(1130 ˚A). For indices γ pLLS = 1 . 14 and γ LF = 1 . τ eff ( z o , z ) = 0 . 29, 0.39, and0.46 for sources at z = 1 . 0, 1.5, and 2.0.5. The observed distributions of strong H I absorbersare expected to have considerable variations amongsight lines. Above N HI = (10 cm − ) N ,the fitted cumulative frequency is small, d N ( >N HI ) /dz = (0 . N − . (1 + z ) γ . Our estimatesof far-UV continuum opacity suggest that surveysof intermediate-redshift AGN may have a selectionbias toward sight lines with low optical depths,lacking strong LLS absorbers.This survey was based on observations made with theNASA/ESA Hubble Space Telescope, obtained from thedata archive at the Space Telescope Science Institute.STScI is operated by the Association of Universitiesfor Research in Astronomy, Inc. under NASA contractNAS5-26555. The project originated from individual andsurvey observations of AGN taken with the Cosmic Ori-gins Spectrograph on the Hubble Space Telescope . Weappreciate helpful discussions with John Stocke, ToddTripp, and David Turnshek. In early stages, this re-search was supported by grant HST-GO-13302.01.A fromthe Space Telescope Science Institute to the Universityof Colorado Boulder. More recent work was carried outthrough academic support from the University of Col-orado.9 REFERENCES Bahcall, J. N., Bergeron, J., Boksenberg, A., et al. 1993, ApJS, 87,1Battisti, A. J., Meiring, J. D., Tripp, T. M., et al. 2012, ApJ, 744,93Blanton, M. R., Hogg, D. W., Bahcall, N. A., et al. 2003, ApJ, 592,819Bordoloi, R., Tumlinson, J., Werk, J. K., et al. 2014, ApJ, 796, 136Clauset, A., Shalizi, C. R., & Newman, M. E. J. 2009, SIAMReview, 51, 661Cooksey, K. L., Prochaska, J. X., Chen, H.-W., et al. 2008, ApJ,676, 262Crighton, N. H. M., Morris, S. L., Bechtold, J., et al. 2010, MNRAS,402, 1273Danforth, C. W., & Shull, J. M. 2008, ApJ, 679, 194Danforth, C. W., Keeney, B. A., Tilton, E. M., et al. 2016, ApJ,817, 111Fardal, M. A., Giroux, M. L., & Shull, J. M. 1998, AJ, 115, 2206Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013,PASP, 125, 306Fox, A. J., Lehner, N., Tumlinson, J., et al. 2013, ApJ, 778, 187Gehrels, N. 1986, ApJ, 303, 336Goldstein, M. L., Morris, S. A., & Yen, G. G. 2004, EuropeanPhysical Journal B, 41, 255Goodman, J., & Weare, J. 2010, Commun Appl Math Comput Sci.,5, 65Green, J. C., Froning, C. S., Osterman, S., et al. 2012, ApJ, 744,60Haardt, F., & Madau, P. 2012, ApJ, 746, 125Hussain, T., Muzahid, S., Narayanan, A., et al. 2015, MNRAS, 446,2444Janknecht, E., Reimers, D., Lopez, S., & Tytler, D. 2006, A&A,458, 427Jenkins, E. B., Bowen, D. V., Tripp, T. M., & Sembach, K. R.2005, ApJ, 623, 767Keeney, B. A., Stocke, J. T., Rosenberg, J. L., Tumlinson, J., &York, D. G. 2006, AJ, 132, 2496Kim, T.-S., Carswell, R. F., Cristiani, S., D’Odorico, S., &Giallongo, E. 2002, MNRAS, 335, 555Lehner, N., Prochaska, J. X., Kobulnicky, H. A., et al. 2009 ApJ,694, 734Lehner, N., Howk, J. C., Tripp, T. M. et al. 2013 ApJ, 770, 138Markwardt, C. B. 2009, Astronomical Data Analysis Software andSystems XVIII, ASP Conference Series, Vol. 411, 251Meiring, J. D., Tripp, T. M., Prochaska, J. X., et al. 2011, ApJ,732, 35Meiring, J. D., Tripp, T. M., Werk, J. K., et al. 2013, ApJ, 767, 49Miralda-Escud´e, J. 2003, ApJ, 596, 66Morrissey, P., Schiminovich, D., Barlow, T., et al. 2005, ApJ, 619,L7Morton, D. C. 2003, ApJS, 149, 205Muzahid, S., Srianand, R., & Charlton, J. 2015, MNRAS, 448, 2840Narayanan, A., Savage, B. D., Wakker, B. P., et al. 2011, ApJ, 730,15Neeleman, M., Prochaska, J. X., Ribaudo, J., et al. 2016, ApJ, 818,113Newman, M. E. C. 2005, Contemporary Physics, 46, 323O’Meara, J. M., Prochaska, J. X., Worseck, G., Chen, H.-W., &Madau, P. 2013, ApJ, 765, 137Paresce, F., McKee, C. F., & Bowyer, S. 1984, ApJ, 240, 387 Penton, S. V., Stocke, J. T., & Shull, J. M. 2004, ApJS, 152, 29Prochaska, J. X., Werk, J. K., Worseck, G., et al. 2017, ApJ, 837,169Rao, S. M., Turnshek, D. A., & Nestor, D. B. 2006, ApJ, 636, 610Rao, S. M., Turnshek, D. A., Sardane, G. M., & Monier, E. M.2017, MNRAS, 471, 3428Ribaudo, J., Lehner, N., & Howk, J. C. 2011a, ApJ, 736, 42Ribaudo, J., Lehner, N., Howk, J. C., et al. 2011b, ApJ, 743, 207Rudie, G. C., Steidel, C. C., Shapley, A. E., & Pettini, M. 2013,ApJ, 769, 146Sargent, W. L. W., Steidel, C. C., & Boksenberg, A. 1989, ApJS,69, 703Savage, B. D., Lehner, N., Narayanan, A., et al. 2011, ApJ, 743,180Shull, J. M. 2014, ApJ, 784, 142Shull, J. M., Roberts, D., Giroux, M. L., et al. 1999, AJ, 118, 1450Shull, J. M., Giroux, M. L., Penton, S. V., et al. 2000, ApJ, 538,L13Shull, J. M., Jones, J. R., Danforth, C. W., & Collins, J. A. 2009,ApJ, 699, 754Shull, J. M., Smith, B. D., & Danforth, C. W. 2012a, ApJ, 759, 23Shull, J. M., Stevans, M. L., & Danforth, C. W. 2012b, ApJ, 752,162Shull, J. M., Danforth, C. W., & Tilton, E. M. 2014, ApJ, 796, 49Simcoe, R. A., Sargent, W.L. W., Rauch, M., & Becker, G. 2006,ApJ, 637, 648Songaila, A., & Cowie, L. 2010, ApJ, 721, 1448Steidel, C. C. 1990, ApJS, 74, 37Stengler-Larrea, E. A., Boksenberg, A., Steidel, C. C., et al. 1995,ApJ, 444, 64Stevans, M. L., Shull, J. M., Danforth, C. W., & Tilton, E. M.2014, ApJ, 794, 75Stocke, J. T., Keeney, B. A., Danforth, C. W. et al. 2013, ApJ,763, 148Stocke, J. T., Keeney, B. A., Danforth, C. W. et al. 2014, ApJ,791, 128Storrie-Lombardi, L. J., McMahon, R. G., Irwin, M. J., & Hazard,C. 1994, ApJ, 427, L13.Tejos, N., Morris, S. L., Finn, C. W., et al. 2014, MNRAS, 437,2017Telfer, R., Zheng, W., Kriss, G. A., & Davidsen, A. F. 2002, ApJ,656, 773Tilton, E. M., Stevans, M. L., Shull, J. M., & Danforth, C. W.2016, ApJ, 817, 56Tripp, T., Bechtold, J., & Green, R. F. 1994, ApJ, 433, 533Tripp, T., Meiring, J. D., Prochaska, J. X. et al. 2011, Science, 334,952Tumlinson, J., Thom, C., Werk, J. K., et al. 2011a, Science, 334,948Tumlinson, J., Werk, J. K., Thom, C., et al. 2011b, ApJ, 733, 111Tumlinson, J., Thom, C., Werk, J. K., et al. 2013, ApJ, 777, 59Turnshek, D. A., Monier, E. M., Rao, S. M., et al. 2015, MNRAS,449, 1536Tytler, D. 1987a, ApJ, 321, 49Tytler, D. 1987b, ApJ, 321, 69Weymann, R. J., Jannuzi, B. T., Lu, L., et al. 1998, ApJ, 506, 1Wolfe, A. M., Gawiser, E., & Prochaska, J. X. 2005, ARA&A, 43,861 APPENDIX APPENDIX A: NOTES ON LLS AND PLLS ABSORBERS In this Appendix, we discuss the column-density determinations for 73 strong H I absorbers (log N HI > . 75) at z abs ≥ . 24. In an approximate analysis used in our construction of an AGN composite spectrum (Stevans et al.2014), the H I column densities of these systems were estimated and used to correct the underlying continuum. Theseestimates were based on automated CoG fitting, which becomes uncertain when the Lyman lines reach saturation(Table 2) and in the presence of multiple velocity components. In the current survey, we carefully examined each ofthese systems, combining multi-component CoG fits with an analysis of the flux decrement at the Lyman limit. Infitting the continuum above and below the LL, we looked for contamination by broad AGN emission lines using thetemplate shown in Figure 1. The underlying continuum lies below these emission lines. Systems labeled N HI ≥ . 5, for which we expect a clear Lyman limit with optical depth τ LL ≥ . 2. Systems . ≤ log N HI ≤ . 49. System N HI = 20 . ± . 12 at z abs = 0 . − , we combined them into a single system. In a few instances with clearly separatedcomponents (∆ v > − 200 km s − ) we kept separate track of the individual column densities and split them intoseparate absorbers, denoted Systems τ LL , typically arise from all components within 100-400 km s − . With good S/Nin the higher-order Lyman lines, we are able to identify absorption systems with ∆ v ≥ 100 km s − . In comparing ourcolumn densities with prior work, we usually found good agreement (∆ log N HI ≤ . + z AGN = 0 . , z abs = 0 . . — See Figure 9. Because the COS observations forthis sight line only covered wavelengths λ > (cid:15) ) and the Lyman edge arenot accessible. However, Ly α shows a sub-DLA with damping wings that we fit with log N HI = 19 . ± . 05, a valueslightly smaller than that (log N = 19 . ± . 15) quoted by Battisti et al. (2012), Meiring et al. (2013), and Lehneret al. (2013). Although our CoG solution for Ly α - Ly (cid:15) gives a lower value (log N = 19 . ± . b = 37 ± − ),we adopt log N HI = 19 . ± . 10 and b = 35 ± − because the lower column density from the CoG does notreproduce the observed Ly α damping wings. − z AGN = 1 . , z abs = 0 . . — See Figure 9. The flux at λ < < τ LL > . N HI > . α - Ly12 constrains log N HI tothe range 18.1-18.9 with b = 45 ± − , in agreement with the observed line profiles. In their Appendix A, Tejoset al. (2014) quoted log N HI = 18 . ± . 03 with b = 34 ± − . However, this error bar seems far too small, andwe adopt log N HI = 18 . ± . + z AGN = 0 . , z abs = 0 . . — See Figure 9. Low-quality data ( S/N ∼ VIII and O IV . From transmission shortward of the Ly edge, we find log N HI =17 . ± . 06. The Lyman lines show a single component, with a CoG fit to Ly α - Ly12 giving log N HI = 18 . ± . b = 43 ± − . Two absorption components are seen in Si III in this system, not apparent in the H I lines. Weadopt the decrement measurement, log N HI = 17 . ± . 06, and find that b = 45 ± − reproduces the observedline profiles. + z AGN = 0 . , z abs = 0 . . — See Figure 9. The initial redshift measurement ofthis system at z = 0 . z abs = 0 . − . n > 11) lie blueward of the edge of the COS spectra, and no Ly decrement measurement is possible. Amore careful examination of the data shows two absorbers at redshifts slightly below z = 0 . 24, and thus outside bin 1.Our CoG fits to the red and blue components are inconsistent with the higher-order Lyman line profiles, suggestingthe presence of additional components. We find qualitative agreement with the line profiles for Ly α - Ly10 using athree-component model: Component 1 ( z = 0 . N = 17 . ± . b = 35 ± − ; Component 2( z = 0 . N = 15 . ± . b = 25 ± − ; Component 3 ( z = 0 . N = 16 . ± . b = 25 ± − . The velocity separations are ∆ v = 97 km s − and ∆ v = 121 km s − . We adopt the summedtotal column density log N HI = 17 . ± . + z AGN = 0 . , z abs = 0 . . — See Figure 9. The initial estimate of this system,log N = 17 . ± . 04 (Stevans et al. 2014) underpredicts the Ly decrement significantly. The continuum at λ < τ LL > 5, log N > . α - Ly6) are contaminatedwith other absorption. We adopt a CoG fit to Ly7 - Ly12 with log N HI = 18 . ± . b = 37 ± − , consistentwith the decrement and providing a good match to the line profiles. This column is similar to the range (18 . − . N HI = 18 . ± . 2) in Lehner et al. (2013). This sight line alsocontains a DLA (Meiring et al. 2011) at z abs = 0 . N HI = 20 . ± . 10 (see Table 8). + + z AGN = 0 . , z abs = 0 . . — See Figure 9. The Stevans et al.(2014) CoG measurement of this system (log N HI = 17 . ± . 04) significantly underpredicts the observed Lymandecrement. The continuum at λ < τ LL > 5, log N HI > . α profile imply an even higher column density. Battisti et al. (2012) found log N HI =19 . ± . 10 by fitting the Ly α profile wings. We use a CoG fit to Ly α - Ly11, constrained by the requirement thatlog N HI > 18, to find log N HI = 19 . ± . 12 and b = 45 ± − , consistent with both the line profiles and the Lydecrement. + z AGN = 0 . , z abs = 0 . . — See Figure 8. This absorber exhibits a strong Lymandecrement ( τ LL > 5) implying log N HI > . 9. The transmitted flux shows no recovery from the LL ( λ obs = 1344 ˚A)shortward to the end of the COS/G130M data ( λ obs ≈ N HI ≥ . 1. A CoG fit to Ly β -Ly12 is gives log N = 17 . ± . 15, inconsistent with the Ly decrement. The Ly α absorption line lies redward of the endof the COS/FUV data, and we cannot use its damping wings as a measurement of column density. The redward wingof Ly β limits log N < . 0, but the CoG suggests log N HI < . 5. The dominant absorption in metal lines (C II , Si II ,and O VI ) occurs at z = 0 . − redward ( z = 0 . II and O VI .However, this second component cannot explain the redward wing of Ly β . We adopt a range 18 . < log N HI ≤ . N HI = 18 . ± . 2, and find that b = 25 − 35 km s − matches the line profiles. + z AGN = 0 . , z abs = 0 . . — This AGN sight line also contains system I (1355-1370 ˚A observed), C III λ 977 (1430–1450 ˚A observed), and O VI λ τ LL = 0 . +0 . − . (log N = 16 . +0 . − . ). A CoG fit gives log N HI = 16 . ± . 09 with b = 38 ± − , inconsistent with the Ly decrement. We adopt the decrement value, with its asymmetric errorbars, log N HI = 16 . +0 . − . . + z AGN = 0 . , z abs = 0 . . — See Figure 5. The CoG solution to this system (log N ∼ . above the interstellarabsorption line of C II λ . 53; we also see Si II absorption lines at 1190 ˚A and 1193 ˚A. The transmitted flux in theLyman continuum is 1 . ± . τ LL = 4 . ± . 15 and our adopted value, log N HI = 17 . ± . b = 18 ± − provides a good match to the relatively narrow Lymanline profiles. A second, blue component visible in Ly (cid:15) - Ly13 is fitted with a CoG having log N HI = 15 . ± . 05 and b = 20 ± − . The combination of these two components, the weaker of which makes little contribution to theLy decrement, fits the line profiles well. + z AGN = 1 . , z abs = 0 . . — See Figure 9. This high-redshift absorption system is observableby COS only in the higher Lyman lines (Ly6 and above). However, the high-quality of the data and the Ly decrementallow accurate measurements for this pLLS (Tripp et al. 2011). Two components appear in the n ≥ τ LL = 0 . ± . 02, implies a total column density log N tot = 17 . ± . 05, but the allocation tothe two components remains uncertain. Two components fit the profiles well (∆ v = 156 km s − ): Component 1 (at z = 0 . N = 16 . ± . b = 28 ± − ; Component 2 (at z = 0 . N = 16 . ± . b = 25 ± − . Their column densities sum to log N tot = 17 . ± . 06 and account for the Ly decrement: Intheir study of this absorber, Tripp et al. (2011) fitted three clusters of 9 velocity components, which they labeledGroup A (log N A = 15 . N B = 16 . N A = 15 . N tot = 17 . ± . 11) is 0.05 dex less than our adopted value, log N HI = 17 . ± . 10, which is intermediate betweenour CoG and LL measurements. + z AGN = 1 . , z abs = 0 . . — See Figure 9. Our measurement of the Lyman decrement( τ LL = 0 . ± . 04) requires total column density log N = 17 . ± . 05, comparable to previously reported valuesof 17 . ± . 05 (Ribaudo etal 2011b), 16 . ± . 05 (Lehner et al. 2013), and 16 . ± . 04 (Stevans et al. 2014).Higher-order lines (Ly7 - Ly13) show two components (∆ v = 75 km s − ): a strong, blue component ( z = 0 . N = 16 . ± . b = 28 ± − ) and a weaker, red component ( z = 0 . N = 16 . ± . b = 25 ± − ). We adopt log N tot = 17 . ± . + z AGN = 1 . , z abs = 0 . . — The Ly decrement from this absorber is determinedby N HI of both system z = 0 . − to the red. The LL optical depth was fittedto τ LL = 0 . ± . 03 (log N tot = 16 . ± . v = 77 km s − )velocity components. CoG fits to the Lyman lines, where separable in Ly7 - Ly13, give: Component 1 ( z = 0 . N = 16 . ± . b = 25 ± − ; and Component 2 ( z = 0 . N = 16 . ± . b = 20 ± − summing to our adopted value log N tot = 16 . ± . 10 for system N HI = 16 . ± . 05 for system N tot = 16 . ± . 10, consistent with the Ly decrement.Although system v ≈ 390 km s − ) in their Lyman line absorption. + z AGN = 0 . , z abs = 0 . . — The AGN continuum appears to have broad O I emission features (1310–1335 ˚A observed frame). The observed decrement ( τ LL = 0 . ± . 05) implies log N HI ≈ . ± . 05. The CoG solution to Ly α - Ly13, omitting Ly γ , Ly δ , and Ly11 which are blended, gives a consistent(adopted) solution, log N HI = 16 . ± . b = 19 ± − . This sight line also contains a sub-DLA at z abs = 0 . N HI = 19 . ± . 10 (see Table 7). + z AGN = 0 . , z abs = 0 . . — See also system S/N ∼ 2) and an undulating AGN continuum in the region of the Lyman limit make decrement measurementsunreliable. However, the uncertain values, log N HI = 16 . ± . . +0 . − . (Prochaska et al.2017) are not supported, as we detect no Ly decrement ( τ LL < . β , Ly γ , Ly (cid:15) ,and Ly6 - Ly10 gives log N HI = 16 . ± . b = 21 ± − , consistent with the lack of a measurable Ly decrement + z AGN = 0 . , z abs = 0 . . — This absorber is offset by just 146 km s − bluewardof the AGN systemic velocity. The LL lies on the red wing of a damped Ly α absorber profile at 1332.7 ˚A ( z DLA =0 . N HI = 20 . ± . 10 (see Table 7). However, there is sufficiently recovered continuum in the blue wingof the DLA (1310–1320 ˚A) to measure a LL decrement with τ LL = 0 . ± . 05 and log N HI = 16 . ± . 05. Thissolution fits the stronger Lyman lines (Ly α - Ly8) but increasingly overpredicts the higher-order absorption profiles( n ≥ N HI = 16 . ± . 10 and b = 32 ± − , noting unresolved structure in the system. + z AGN = 0 . , z abs = 0 . . — This sight line has two strong absorbers ( − I and H I emission lines. The AGN continuum may be contaminated by broad O IV λ τ LL = 0 . ± . N HI = 16 . ± . 10, a factor of 2 lower than that (16 . ± . 06) found by Stevans et al. (2014) from aCoG fit. Additional absorption is present in some of the higher-order Lyman lines ( n > 8) which is not accountedfor by this lower- N solution. This may have driven the previous CoG solution to a higher column density. We adoptlog N HI = 16 . ± . b = 40 ± − . + z AGN = 0 . , z abs = 0 . . — The Lyman decrement ( τ LL = 0 . ± . N HI = 16 . ± . 05) is consistent with the Stevans et al. (2014) value, log N HI = 16 . ± . 05. We adoptlog N HI = 16 . ± . 05 with b = 25 ± − . − z AGN = 0 . , z abs = 0 . . — See Figure 6. This system lies on the red edge of a damped Ly α profile (the Galactic DLA). However, the Lyman edge lies ∼ 10 ˚A redward of the line center where the continuum hasrecovered from DLA absorption. The decrement ( τ LL = 0 . ± . 04) requires log N HI = 17 . ± . 03. The data are ofvery high quality ( S/N ∼ α to Ly ω ). Thehighest-order lines ( n ≥ 16) are blended and not useful in CoG analysis as noted in Table 2. A fit to Ly β - Ly15 giveslog N HI = 17 . ± . b = 16 ± − . This column density is above previous values, 16 . ± . 08 (Lehner et al.2013) and 16 . ± . 03 (Stevans et al. 2014). + z AGN = 0 . , z abs = 0 . . — This AGN sight line has three strong absorbers(systems τ LL = 0 . ± . 02, although the local continua may be contaminated by AGN emission lines. The LL-inferred columndensity, log N HI = 16 . ± . 07, is much smaller than the CoG fit, log N HI = 16 . ± . 09, but additional absorptionappears in the higher ( n > 8) Lyman lines. We adopt log N HI = 16 . ± . 10 based on the Ly decrement, with anincreased error. + z AGN = 0 . , z abs = 0 . . — As noted for system τ LL = 0 . ± . 03) implies log N HI = 16 . ± . . ± . 2) from Stevans et al. (2014). The local continua may be contaminatedby AGN emission lines. A two-component profile is seen in the n > z = 75 km s − ) individual components in Ly6 - Ly11 gives: Component 1 ( z = 0 . N = 16 . ± . b = 22 ± − , and Component 2 ( z = 0 . N = 16 . ± . b = 35 ± − , summing to ouradopted column density, log N tot = 16 . ± . 11, similar to the observed decrement.3 + + z AGN = 0 . , z abs = 0 . . — The AGN continuum is contami-nated by the prominent emission lines of Ne VIII ( λ , IV ( λ III and N III (1220–1250 ˚A observedframe). The Ly decrement is somewhat uncertain because of this line emission and continuum placement. Choosingcontinua redward and blueward of the LL to avoid these emission lines, our best fit gives τ LL = 0 . ± . 04 andlog N HI = 16 . ± . 06. Two closely separated (∆ v = 95 km s − ) components are apparent in Ly δ - Ly12 (geocoronalairglow is blended with Ly8 - Ly10). The redder component is the stronger and dominates the LL decrement. We adopt z = 0 . N = 15 . ± . b = 24 ± − , and z = 0 . N = 16 . ± . b = 35 ± − ,summing to log N tot = 16 . ± . 05. Because of CoG uncertainties, we adopt the Ly decrement value with an increasederror, log N HI = 16 . ± . − z AGN = 0 . , z abs = 0 . . — The continuum is well defined above the edge, despitea few AGN emission features (the 700 ˚A feature from O III and N III observed near 1370 ˚A). Our fit to the Lymandecrement ( τ LL = 0 . ± . 02) implies log N HI = 16 . ± . 03. A CoG fit to the system (Ly γ - Ly15) gives log N HI =16 . ± . 06 and b = 25 ± − . We adopt the Ly decrement solution with a wider the error range, log N HI =16 . ± . + z AGN = 0 . , z abs = 0 . . — The LL optical depth, τ LL = 0 . ± . 02, implieslog N HI = 16 . ± . 02. However, the decrement is determined by column densities of both system z = 0 . − to the red. A 2-component CoG to system N HI ≈ . ± . 08. Including log N HI = 16 . ± . 05 for system N tot = 16 . ± . 07. We adopt the Ly decrement value, but widen the error range to log N HI = 16 . ± . + z AGN = 1 . , z abs = 0 . . — Three velocity components (denoted τ LL = 0 . ± . 04 (log N HI = 16 . ± . v = 216 km s − and ∆ v = 243 km s − , we treat these as distinct absorbers,where we adopt: Component 1 ( z = 0 . N = 14 . ± . b = 25 ± − ; Component 2( z = 0 . N = 16 . ± . b = 30 ± − ; Component 3 ( z = 0 . N = 15 . ± . b = 22 ± − , summing to log N tot = 16 . ± . 05. The LL optical depth is reasonably consistent with this3-component CoG sum. + z AGN = 1 . , z abs = 0 . . — The decrement ( τ LL = 0 . ± . 03) implies log N HI = 16 . ± . . ± . 05 and 16 . ± . 04) reported by Lehner et al. (2013) and Stevans et al. (2014). Combinedwith our CoG fit to the higher Lyman lines, we adopt log N HI = 16 . ± . 05 and b = 29 ± − . − z AGN = 1 . , z abs = 0 . . — Our fit to the Ly decrement implies log N HI = 16 . ± . 02, slightlystronger than the Stevans et al. (2014) CoG solution of 16 . ± . 08 and the value 16 . ± . 03 from Lehner et al.(2013). Including our CoG fit to the higher Lyman lines, we adopt log N HI = 16 . ± . 05 and b = 30 ± − . + z AGN = 1 . , z abs = 0 . . — Also known as PHL 1377. The AGN continuum appearscontaminated by broad emission lines (O IV λ 608 and O V λ N HI = 16 . − . v = 99 km s − ): Component 1 ( z = 0 . N = 15 . ± . b = 15 ± − ) and Component 2( z = 0 . N = 16 . ± . b = 17 ± − ) summing to log N tot = 16 . ± . 05. This column densityis somewhat larger than that (16 . ± . 02) quoted by Lehner et al. (2013) but comparable to that (16 . ± . 2) inStevans et al. (2014). We adopt our summed 2-component CoG solution, log N tot = 16 . ± . 05, with the error basedon combining the CoG with the Ly decrement constraint. + z AGN = 1 . , z abs = 0 . . — This AGN sight line has three strong absorbers in our survey( III and N III near700 ˚A (observed near 1550 ˚A). The fitted Ly decrement ( τ LL = 0 . ± . N HI = 16 . ± . 07 with theerror bar arising from the uncertain placement of the continuum shortward of the LL. From CoG fitting, we adoptlog N HI = 16 . ± . 05 with b = 20 ± − , comparable to previous values of 16 . ± . 05 (Lehner et al. 2013),16 . ± . 04 (Stevans et al. 2014), and 16 . ± . 04 (Tilton et al. 2016). + z AGN = 1 . , z abs = 0 . . — As noted for system IV λ 554 and Ne V λ 570 observed between 1240-1260 ˚A. TheLy decrement ( τ LL = 0 . ± . N HI = 16 . ± . 19. The higher error arises from uncertain placement ofthe continuum shortward of the LL. We performed CoG fits to two components separated by ∆ v = 76 km s − : Compo-nent 1 ( z = 0 . N = 16 . ± . b = 32 ± − ) and Component 2 ( z = 0 . N = 15 . ± . b = 18 ± − ) summing to log N tot = 16 . ± . 05. We adopt log N HI = 16 . ± . 10, comparable to previousvalues of 16 . ± . 13 (Lehner et al. 2013) and 16 . ± . 06 (Stevans et al. 2014).4 − z AGN = 0 . , z abs = 0 . . — The fit to the Ly decrement implies log N HI = 16 . ± . 02, butthe placement of the continuum shortward of the LL is somewhat uncertain. Using CoG fitting of Ly β - Ly17, wefind log N HI = 16 . ± . 05 and b = 18 ± − , a column density similar to the value of 16 . ± . 04 (Lehneret al. 2013) but higher than 16 . ± . 03 (Stevans et al. 2014). We adopt the Ly decrement value with a wider error,log N HI = 16 . ± . + z AGN = 0 . , z abs = 0 . . — This AGN sight line has four strong absorbers inour survey ( III andN III ) observed between 1300-1320 ˚A. The Ly decrement is below the detectable level ( τ HI < . 1, log N HI < . N HI = 16 . ± . 05 with b = 25 ± − . This column is the same as quotedby Stevans et al. (2014) but below that (16 . ± . 07) quoted in Lehner et al. (2013), which would produce a largerLyman decrement than observed. + z AGN = 0 . , z abs = 0 . . — The continuum near the LL (1300 ˚A observedframe) is not flat, with no obvious decrement ( τ LL < . 15 and log N HI < . III and N III (observed between 1300-1315 ˚A). Using CoG fitting, we adoptlog N HI = 16 . ± . 10 and b = 23 ± − . This column density is slightly above previous values of 16 . ± . . ± . 02 (Stevans et al. 2014). + z AGN = 0 . , z abs = 0 . . — The continuum is contaminated by AGN emissionlines of Ne VIII and O IV observed between 1445-1475 ˚A. We see no obvious Ly decrement ( τ LL < . 1, log N HI < . N HI = 16 . ± . 10 and b = 16 ± − , a column intermediate between values of16 . . , − . 12) (Lehner et al. 2013) and 16 . ± . 07 (Stevans et al. 2014). + z AGN = 0 . , z abs = 0 . . — We see a Ly decrement ( τ LL = 0 . ± . N HI = 16 . ± . 12) based on a small flux decrement between 1258-1265 ˚A). Prochaska et al. (2017) quote log N HI < . 65 from low-resolution (COS/G140L) data. Using CoG fitting, we adopt log N HI = 16 . ± . 05 and b = 32 ± − . This column density is similar to values of 16 . ± . 05 (Lehner et al. 2013) and 16 . ± . 02 (Stevans et al.2014). + z AGN = 0 . , z abs = 0 . . — Because of continuum undulations (1220-1240 ˚A),we cannot measure a reliable Ly decrement. CoG fitting gives values identical to those of Lehner et al. (2013) andStevans et al. (2014). We adopt log N HI = 16 . ± . 05 with b = 25 ± − from CoG fitting. + z AGN = 0 . , z abs = 0 . . — Based on high quality data, we measure a Ly decrement, τ LL =0 . ± . N HI = 16 . ± . 03, comparable to previous values of 16 . ± . 02 (Lehner et al. 2013) and16 . ± . 03 (Stevans et al. 2014). Including CoG fitting, we adopt log N HI = 16 . ± . 05 with b = 32 ± − . + z AGN = 0 . , z abs = 0 . . — See Figure 7. Based on high quality data, we measure a Lydecrement, τ LL = 0 . ± . 02, implying log N HI = 16 . ± . 06. CoG fitting to Lye - Ly14 gives log N HI = 16 . ± . b = 25 ± − , comparable to 16 . ± . 05 (Lehner et al. 2013). + z AGN = 0 . , z abs = 0 . . — We see no obvious Ly decrement, but the wave-length calibration near the Lyman edge (1150-1165 ˚A) is uncertain. Using CoG fitting, we adopt log N HI = 16 . ± . b = 29 ± − . This column density is similar to previous values 16 . ± . 05 (Lehner et al. 2013) and 16 . ± . + z AGN = 0 . , z abs = 0 . . — The AGN continuum near the Ly edge is uncertain, owing tobroad emission lines of Ne VIII and O IV observed between 1440-1470 ˚A. Fitting a continuum below those emissionfeatures, we estimate a Ly decrement of τ LL = 0 . ± . 04 and log N HI = 16 . ± . 08. We also fit a CoG with threevelocity components separated by ∆ v = 129 km s − and ∆ v = 58 km s − : Component 1 ( z = 0 . N = 15 . ± . b = 27 ± − ; Component 2 ( z = 0 . N = 16 . ± . b = 21 ± − ;Component 3 ( z = 0 . N = 15 . ± . b = 21 ± − , summing to our adopted value,log N tot = 16 . ± . 06 with b = 29 ± − . This column density is comparable to the value of 16 . ± . . ± . 02 of Lehner et al. (2013). The Ly decrement is consistent withour higher value. − z AGN = 1 . , z abs = 0 . . — The AGN continuum below the LL is contaminated by the broad700 ˚A emission lines of O III and N III observed between 1445-1455 ˚A. The continuum below the Ly edge ( λ < τ LL = 0 . ± . 03, implying log N HI = 16 . ± . v = 46 km s − and ∆ v = 89 km s − : Component 1( z = 0 . N = 16 . ± . b = 18 ± − ; Component 2 ( z = 0 . N = 15 . ± . b = 60 ± 10 km s − ; Component 3 ( z = 0 . N = 15 . ± . b = 16 ± − . Our adoptedsummed total, log N tot = 16 . ± . 10, is higher than previous values of 16 . ± . 04 (Lehner et al. 2013) and 16 . ± . − z AGN = 0 . , z abs = 0 . . — The AGN continuum is contaminated by broad emissionfeatures of O I (observed at 1265-1275 ˚A) and C III (observed at 1310-1320 ˚A) and by an absorption dip (1290-1300 ˚A). The flux shortward of the LL is complicated by the redward damping wing of Galactic Ly α absorption(1227-1232 ˚A). The Ly decrement is uncertain, τ LL = 0 . − . 20 or log N HI = 16 . − . 50, and we place more weighton CoG fitting. We fit two closely separated (∆ v = 73 km s − ) absorbers at z = 0 . N = 15 . ± . 03) and z = 0 . N = 16 . ± . N tot = 16 . ± . 04, well below the estimated Ly decrement.Because of the continuum uncertainty with the Ly decrement, we adopt the summed CoG value, log N tot = 16 . ± . + z AGN = 0 . , z abs = 0 . . — This AGN has a well-defined continuumlongward of the LL ( λ > . α absorption. Our fit to the redward wing of the Galactic DLA suggests τ LL = 0 . ± . 03 (log N HI = 16 . ± . N HI = 16 . ± . 08. The CoGfrom Stevans et al. (2014) gave 16 . ± . 02. Our new two-component (∆ v = 69 km s − ) CoG fit to Ly δ - Ly9 givesvalues: z = 0 . N = 15 . ± . 09 and z = 0 . N = 15 . ± . 06, summing to log N tot = 16 . ± . N HI = 16 . ± . 12, reflecting the Ly decrement. + z AGN = 0 . , z abs = 0 . . — The continuum is not well defined, owing to likelycontamination by O I emission (1560-1570 ˚A observed frame). A weak Ly decrement suggests τ LL = 0 . ± . 015 orlog N HI = 16 . ± . 07. However, the continuum below the LL is uncertain. We adopt the value from CoG-fitting,log N HI = 16 . ± . 07 with b = 36 ± − . z AGN = 0 . , z abs = 0 . . — Three velocity components are evident a4 z = 0 . z = 0 . z = 0 . v = 104 km s − and ∆ v = 88 km s − . The Ly decrement falls in theGalactic DLA and is unobservable. Our new 3-component CoG fit finds log N = 15 . ± . 03, log N = 15 . ± . N = 16 . ± . 09, summing to log N tot = 16 . ± . 12 and similar to the value 16 . ± . 01 (Stevans et al.2014). We adopt a column density, log N HI = 16 . ± . 05, consistent with both CoG and Ly decrement. + z AGN = 0 . , z abs = 0 . . — A new CoG fit gives log N HI = 16 . ± . . ± . 03. The continuum is fairly well defined, but portions may becontaminated by broad emission lines of Ne VIII and O IV observed at 1320–1350 ˚A. The Ly decrement implies τ LL = 0 . ± . 020 and log N HI = 16 . ± . 05. With the CoG information, we adopt log N HI = 16 . ± . + z AGN = 0 . , z abs = 0 . . — There are three strong absorbers in this sight line,including systems z = 0 . z = 0 . N HI = 16 . ± . + z AGN = 0 . , z abs = 0 . . — The data quality is poor, and the continuumhas likely contamination from AGN emission lines of O I observed at 1670-1690 ˚A and C III λ 977 observed at1740 ˚A. No Ly decrement is evident to a limit log N HI < . 6. Because the component splittings are easily separable,∆ v = 390 km s − and ∆ v = 230 km s − , we treat these as distinct absorbers, denoted z = 0 . N = 16 . ± . z = 0 . N = 15 . ± . z = 0 . N = 16 . ± . γ , Ly δ , and Ly (cid:15) . The summed CoG fit giveslog N tot = 16 . ± . 11 with b = 40 ± − . − z AGN = 0 . , z abs = 0 . . — Because no data were taken at λ < N =15 . ± . 10 and b = 25 ± − (blue component with Ly (cid:15) and Ly ζ ) and log N = 15 . ± . b = 41 ± 12 km s − (red component with Ly β to Ly ζ ). These column densities sum to log N tot = 16 . ± . + z AGN = 0 . , z abs = 0 . . — No clear Ly decrement is seen (log N HI < . β to Ly10 to findlog N HI = 16 . ± . 09 with b = 19 ± − . + z AGN = 0 . , z abs = 0 . . — A weak Ly decrement may be present withlog N HI = 16 . ± . 15, with an uncertain continuum redward of the edge owing to O I emission lines observed at1770-1790 ˚A. We fit a CoG to Ly δ up to Ly10, with our adopted value log N HI = 16 . ± . 05 and b = 29 ± − . + z AGN = 0 . , z abs = 0 . . — The source has a well-defined continuum, with aLy decrement suggesting τ LL = 0 . ± . 02 or log N HI = 16 . ± . 02 for a flat continuum. This decrement includes bothsystems z = 0 . − blueward. These absorbers are visible in blended Lyman lines (Ly γ , Ly δ , Ly (cid:15) ) at redshifts z = 0 . N = 16 . ± . 05) and z = 0 . N = 16 . ± . N HI = 16 . ± . 05, consistent with the decrement. In our statistics, we treat systems + z AGN = 1 . , z abs = 0 . . — The source has a well-defined continuum, with LLoptical depth τ LL = 0 . ± . 03 (log N tot = 16 . ± . 04) produced by absorption from system z = 0 . z = 0 . v ≈ 390 km s − in theLyman lines (Ly γ , Ly δ , Ly (cid:15) ) Our CoG gives log N HI = 16 . ± . 05 for system + z AGN = 1 . , z abs = 0 . . — This AGN sight line has three absorbers with Lyman edgesnear 1537 ˚A (system II and O III (rest-frame 833-834 ˚A). For this system, the weak Ly decrementat 1478 ˚A is poorly determined. CoG fitting gives log N HI = 16 . ± . 06 for − z AGN = 1 . , z abs = 0 . . — This AGN is also known as PHL 1377 (see also system N HI = 16 . ± . 04 with b = 34 ± − . + z AGN = 0 . , z abs = 0 . . — The data have high S/N, and a Lyman series is evident up to Ly 12with higher lines intruding on the red wing of the Galactic DLA. We use the excellent CoG fit with log N HI = 16 . ± . b = 17 ± − , consistent with a weak LL flux decrement. + z AGN = 0 . , z abs = 0 . . — This AGN also contains system z abs = 0 . α to Ly6 plus Ly10 and Ly11 yields log N HI = 15 . ± . 06 with b = 26 ± − . − z AGN = 0 . , z abs = 0 . . — The LL at 1133.5 ˚A falls just below the COS/G130M data range,and blueward continuum is not visible. However, a CoG fit to Ly γ , Ly (cid:15) Ly8, and Ly10 gives log N HI = 15 . ± . b = 22 ± − . − z AGN = 0 . , z abs = 0 . . — A CoG fit to Ly β through Ly14 gives a very good fit with log N HI =15 . ± . 02 and b = 28 ± − . This column density is consistent with a weak LL decrement visible in very gooddata. + z AGN = 0 . , z abs = 0 . . — The data quality is poor, with no obvious Ly decre-ment. A double-component structure is seen in Ly β through Ly8, easily separable as components denoted z = 0 . N = 15 . ± . b = 17 ± − ) and z = 0 . N = 15 . ± . b = 36 ± − ) summing to log N HI = 16 . ± . + z AGN = 0 . , z abs = 0 . . — This sight line has a very strong LLS (system v = 233 km s − ) in Ly α through Ly9, with considerable blending from other absorption. Because the componentsare easily separable, we treat these as distinct absorbers, denoted z = 0 . N = 16 . ± . b = 34 ± − ) and z = 0 . N = 16 . ± . b = 57 ± − )summing to log N HI = 16 . ± . 08. The implied τ LL = 0 . 17 is difficult to confirm, given the poor data at 1173 ˚A andthe likely presence of AGN broad emission lines of O III and N III (1150-1170 ˚A observed frame). + z AGN = 0 . , z abs = 0 . . — The LL at 1140 ˚A is barely within theCOS/G130M data range. The data are quite noisy, and several Lyman lines are blocked (Ly γ ) or contaminatedby other absorption (Ly7). A CoG fit with log N HI = 16 . ± . 08 and b = 24 ± − implies a Ly decrement with τ LL = 0 . 12 that is hard to confirm. However, this column density over-predicts the line profiles of Ly8, Ly9, and Ly10.We widen the error and adopt log N HI = 16 . ± . − z AGN = 0 . , z abs = 0 . . — The data quality is quite good, with no LLdecrement visible at 1411.6 ˚A. We see hints of two velocity components (∆ v ≈ 40 km s − ) with extra absorption inasymmetric red wings of Ly (cid:15) through Ly10. A two-component CoG gives log N = 15 . ± , 07 and log N = 16 . ± . 17, summing to 16 . 23. We adopt a single-component CoG to Ly β through Ly12 which gives log N HI = 16 . ± . b = 26 ± − . + z AGN = 0 . , z abs = 0 . . — This sight line includes system z abs = 0 . II and O III at833-834 ˚A rest-frame). A CoG fit to Ly β through Ly9 gives log N HI = 15 . ± . 03 with b = 28 ± − . + z AGN = 0 . , z abs = 0 . . — This sight line also includes system z abs = 0 . N HI = 16 . ± . 04 and b = 19 ± − . The observedweak Ly decrement is consistent with this column density.7 + z AGN = 0 . , z abs = 0 . . — This sight line also includes systems z = 0 . z = 0 . v = 2440 km s − ).The data quality is not good, and no Ly decrement is apparent. A CoG fit to Ly β , Ly γ , Ly δ , Ly (cid:15) , and Ly7 giveslog N HI = 15 . ± . 07 with b = 37 ± − . + z AGN = 0 . , z abs = 0 . . — This sight line also includes systems z = 0 . γ lineis strong, and lines of Ly δ to Ly ζ show two velocity components (∆ v = 66 km s − ) which we fit with CoGs to find: z = 0 . N = 15 . ± . b = 16 ± − ) and z = 0 . N = 15 . ± . b = 19 ± − )summing to log N HI = 16 . ± . + z AGN = 0 . , z abs = 0 . . — The data are of very high quality data with a weak Lydecrement. A CoG fit to Ly δ through Ly12 gives log N HI = 16 . ± . 02 with b = 34 ± − . + z AGN = 0 . , z abs = 0 . . — The data are of very high quality data, but no Ly decrement isvisible. A CoG fit to Ly γ through Ly12 gives log N HI = 16 . ± . 04 with b = 14 ± − . − z AGN = 0 . , z abs = 0 . . — The data are of very high quality data, but no Ly decrement isvisible. Two broad, well-separated absorption components (∆ v = 142 km s − ) are seen in Ly β through Ly (cid:15) , with thestronger (redder) component visible up to Ly10. A two-component CoG fit finds: z = 0 . N = 15 . ± . b = 40 ± − ) and z = 0 . N = 15 . ± . b = 40 ± − ) summing to log N HI = 15 . ± . − z AGN = 0 . , z abs = 0 . . — A very weak Ly decrement may be present, consistent withlog N HI < . 1. A CoG fit to Ly δ through Ly12 gives log N HI = 15 . ± . 04 with b = 30 ± − . + z AGN = 1 . , z abs = 0 . . — This sight line also includes systems z = 0 . z = 0 . v ≈ 72 km s − , which we fit with: z = 0 . N = 15 . ± . b = 27 ± − ) and z = 0 . N = 15 . ± . b = 42 ± − ) summing to log N HI = 15 . ± . + z AGN = 1 . , z abs = 0 . . — Owing to its high redshift (for this survey), the COS spectrashow absorption in Ly (cid:15) through Ly10, but no Ly decrement is visible. There appear to be two velocity components(∆ v = 66 km s − ) with a stronger blue component ( z = 0 . N HI = 15 . ± . 04, but a poorly constraineddoppler parameter, b = 99 ± 49 km s − ). A weaker red component at z = 0 . (cid:15) throughLy7, with a poorly constrained column density, log N HI = 15 . ± . 2. The total system has log N HI = 15 . ± . + z AGN = 0 . , z abs = 0 . . — This DLA did not appear in the Stevans et al. (2014)list, but we found it in our new examination through its Lyman edge at 1204.5 ˚A. Meiring et al. (2011) and Battistiet al. (2012) quote log N HI = 20 . ± . 20 from fitting the Ly α damping wings. Our CoG fit to Ly β and Ly δ - Ly8yields a somewhat smaller column density, log N HI = 20 . ± . 12 with b = 49 ± − . Stevans et al. (2014) listedno other strong H I absorbers in this sightline with log N HI > . APPENDIX B: MAXIMUM-LIKELIHOOD FITTING OF THE PLLS DISTRIBUTION Following the convention in studies of quasar absorption lines (Weymann et al. 1998; Kim et al. 2002, among manyothers), we express the column density distribution as separable power laws in column density, N , and redshift, z , f ( N, z ) ≡ d N abs dz dN = C N − β (1 + z ) γ . (B1)As presented in Tables 3-4, the pLLS and LLS absorbers are allocated to bins in z and log N , with the survey sensitivityexpressed through the effective redshift, ∆ z eff , covered by QSOs in our sample. Many studies (e.g., Janknecht et al.2006; O’Meara et al. 2013) including our previous work (e.g., Danforth et al. 2016, and references therein) haveemployed variants of least-squares fitting of f ( N, z ) to binned histograms in order to determine β and γ . Thisapproach has several benefits, most notably its illustrative value in plots or tables and its computational simplicity inthe presence of measurement errors and search pathlengths that may vary as functions of N and z . In the limit of smallbins of zero uncertainty, it tends toward the maximum-likelihood results. However, in the presence of finite binneddata, this least-squares approach does not generally yield the maximum-likelihood estimates of the parameters forpower-law distributions (Newman 2005; Clauset et al. 2009) and it introduces systematic biases in the fit parametersand their confidence intervals . Because of the prevalence of binned fits in the literature, it is worth explaining indetail the maximum-likelihood approach to obtaining these parameters, as implemented in the present study.From Equation B1, the likelihood function for a dataset of N absorbers given the parameters β and γ is L (cid:16) (cid:126)P ( N, z ) | β, γ (cid:17) = N (cid:89) i =1 (cid:18)(cid:90) out P i ( N, z ) dN dz + C (cid:90) z max z min (cid:90) N max N min P i ( N, z ) N − β (1 + z ) γ w ( N, z ) dN dz (cid:33) . (B2)Here, P i ( N, z ) is the normalized probability density distribution for measurements of N and z for absorber i , and w ( N, z ) is a weight function that accounts for the surveyed pathlength in z . The first term in Equation B2 representsthe total probability that absorber i is outside the range in z or N over which we wish to fit the free parameters.The normalized distribution P i ( N, z ) characterizes the data-derived uncertainties and correlations in the measure-ments, which will depend on factors such as data quality and line-fitting techniques, and it introduces the need toevaluate the double-integral in Equation B2. In moderate resolution spectra, such as the COS G130M and G160Mdata used in this study, the uncertainty in redshift determination is quite small, and we neglect it. We assume that P i ( N, z ) ≈ P i ( N ) δ ( z − z i ) where z i is the measured redshift of the absorber, although this assumption is not validfor all datasets used in IGM studies. The column density measurements, on the other hand, can be subject to sub-stantial and widely varying uncertainty that can potentially affect the derived parameters. Following Stevans et al.(2014), we assume that P ( N ) is a log-normal distribution defined by the measured column density parameters fromTable 2 in Stevans et al. (2014) with modifications listed in Table 6 of the present paper. The one exception is theabsorber at z = 0 . . < log N < . 0) and treat as a uniform distribution over that interval.The function w ( N, z ) gives the number of observed targets over which an absorber of column density N and redshift z could have been observed. Put another way, the integral of this function is the aforementioned effective pathlengthover a given redshift and column density interval, ∆ z eff = (cid:82) (cid:82) w ( N, z ) dN dz . In general, such a function depends onproperties of the observations, including but not limited to the observed wavelengths, the redshifts of the backgroundAGNs, and the wavelength-dependent signal-to-noise ratios of the spectra. Often, this function must be evaluatednumerically, but in some cases simplifying assumptions can be made. Because the present study is concerned onlywith relatively strong H I absorbers in high signal-to-noise, well-resolved data, we assume that w is a function only of z and can be expressed as w ( N, z ) ≈ w ( z ) ≈ N AGN (cid:88) j =1 [ H ( z − z min , j ) − H ( z − z max , j )] , (B3)where H ( x ) is the Heaviside step function and z min , j and z max , j are the minimum and maximum redshifts at which anabsorber could be detected in sightline j , respectively.Note that if all of the measured column densities and redshifts had no measurement errors and the pathlengthwas independent of N and z , the likelihood function would remain a pure power law. If upper integration limits arefurther allowed to go to infinity, it becomes straightforward to derive analytical formulae for a maximum-likelihoodpower-law exponent and its uncertainty, as shown in Newman (2005), Clauset et al. (2009), and references therein.Several authors have used these formulae to calculate β and/or γ (e.g., Tytler 1987a,b; Storrie-Lombardi et al. 1994;Stengler-Larrea et al. 1995; Songalia & Cowie 2010; Ribaudo et al. 2011a; Rudie et al. 2013). However, typical IGM Discussion of these effects are given in published papers (Gold-stein et al. 2004; Newman 2005; Clauset et al. 2009 and sub- sequent on-line revisions, found in https://arxiv.org/abs/cond-mat/0412004 and http://arxiv.org/abs/0706.1062. N and z , as well as large uncertainties in N that spana wide range of magnitudes depending on z and their location on the CoG. Thus, these surveys may not sufficientlyapproximate the assumptions of such analytical formulae. In general, the approach of using these formulae introduces asystematic bias in the derived power-law exponents. Although the simplifications chosen for the present study maintainthe separability of the likelihood function and thus the independence of the two fit parameters, this is not necessarilytrue for all possible forms of w ( N, z ) and P ( N, z ), which could introduce correlations between β and γ . In such a case,each term in Equation B2 must be explicitly evaluated as a two-dimensional integral at each step in the optimizationprocess. These calculations are not computationally prohibitive, even if they must be performed numerically in theabsence of an analytical solution.The normalization C is fixed by β and γ under the requirement that each observed absorber’s existence has unityprobability within the dataset. It can be evaluated as C = N (cid:48) (cid:34)(cid:90) z max z min (cid:90) N max N min N − β (1 + z ) γ w ( N, z ) dN dz (cid:35) − , (B4)where the limits of integration are the search ranges of the survey and the single power-law approximation remainsvalid. In our standard fits, we set ( N min , N max ) = (10 cm − , cm − ) and ( z min , z max ) = (0 . , . N (cid:48) (in contrast to the unprimed N ). This distinction isnecessary to maintain definitional consistency of C while accounting for the effects of the finite limits of integrationin the second term of Equation B2, which may allow a fraction of P ( N, z ) to fall outside the region of integration, intothe first term of Equation B2. Therefore, N (cid:48) is the non-integer number of (fractional) absorbers contributing to thelikelihood function, N (cid:48) = N (cid:88) i =1 N (cid:48) i = N (cid:88) i =1 (cid:90) z max z min (cid:90) N max N min P i ( N, z ) dN dz , (B5)where N (cid:48) i is the individual fractional contribution of an absorber i .Using each of our assumptions with Equation B2 and taking the logarithm for computational convenience, we obtainthe log-likelihood function that we use for optimization of β and γ in the present study:ln L (cid:16) (cid:126)P ( N ) , (cid:126)z | β, γ (cid:17) = N (cid:88) i =1 ln (cid:32)(cid:90) N min −∞ P i ( N ) dN + (cid:90) ∞ N max P i ( N ) dN + C (1 + z i ) γ w ( z i ) (cid:90) N max N min P i ( N ) N − β dN (cid:33) . (B6)For our dataset, the second term within the logarithm in Equation B6 is negligibly small and therefore not evaluated.Because this likelihood function contains multiple numerical integrals that must be evaluated for each absorber, it canbe computationally expensive to evaluate for some choices of P ( N ) and ( N min , N max ). For this reason, we optimizethe likelihood function and determine β and γ by sampling the posterior probability distribution with version 2.1.0of emcee (Foreman-Mackey et al. 2013), which implements the affine-invariant Markov-chain Monte Carlo (MCMC)ensemble sampler from Goodman & Weare (2010). We adopt uniform priors over − < γ < 10 and 0 < β < 10. Weinitialize 250 walkers randomly over the domain, allowing each to take 250 steps, the first 75 of which are discardedas a burn-in period.This MCMC procedure yields median values of β = 1 . ± . 05 and γ = 1 . +0 . − . , and C = 2 . × (for N incm − ). The error bars indicate the 1 σ quantiles around the median in the highly-Gaussian, marginalized posteriorprobability distributions. Figures 12 and 13 show the fits and differential distributions.0 TABLE 1 Detectability Ranges for H I Lyman Absorption a Feature λ f log N HI ( z min − z max ) ( z min − z max )(˚A) N HI (cm − ) (G130M) (G160M)Ly α β γ δ (cid:15) ζ η θ a Detectability ranges in redshift ( z min and z max ) for the first eight Lyman lines (and Lyman limit) of H I. Columns 2 and 3 show theabsorption oscillator strengths ( f ) and wavelengths ( λ ). Column 3 gives the H I column density detectable in Lyman-series absorption at50 m˚A equivalent width, N HI = (5 . × cm − )[ f λ (˚A)] − , or in a 10% flux decrement at the Lyman edge. Last two columns showredshift coverage for HST/COS observations in gratings G130M (1134–1459 ˚A) and G160M (1400–1795 ˚A). Because we usually detectan absorber pattern from Ly α through Ly (cid:15) our survey should be complete for log N HI ≥ 15. However, most LL decrements would beundetected at log N HI < . TABLE 2 Line Overlap Parameters (Higher Lyman Lines) a Lyman ( n ) λ (˚A) ∆ λ n,n +1 f n τ ( n )0 (in 10 − ) ( × N /b )Ly12 917.1805 0.949 ˚A 7.231 3.97Ly13 916.4291 0.751 ˚A 5.777 3.17Ly14 915.8238 0.605 ˚A 4.689 2.57Ly15 915.3289 0.495 ˚A 3.858 2.12Ly16 914.9192 0.410 ˚A 3.212 1.76Ly17 914.5762 0.343 ˚A 2.703 1.48Ly18 914.2861 0.290 ˚A 2.297 1.26Ly19 914.0385 0.248 ˚A 1.968 1.08Ly20 913.8256 0.213 ˚A 1.699 0.930Ly21 913.6411 0.185 ˚A 1.477 0.808Ly22 913.4803 0.161 ˚A 1.293 0.707Ly23 913.3391 0.141 ˚A 1.137 0.622Ly24 913.2146 0.125 ˚A 1.006 0.550 a Wavelength separations (∆ λ n,n +1 ) between Lyman transitions, λ n and λ n +1 , and optical depths, τ ( n )0 . Here, Ly n denotes transitionfrom ( n + 1) p → s , and line-center optical depth τ ( n )0 = (0 . N b − f − λ , with N HI = (10 cm − ) N and doppler parameterscaled to b = 25 km s − . Oscillator strengths f n (in units of 10 − ) and wavelengths ( λ scaled to 914 ˚A) are from Morton (2003). TABLE 3 Absorber Distribution in Redshift and Column Density a z -bin 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 N tot Redshifts( i = 1) 2 0 4 5 5 3 2 1 2 2 0 0 1 0 1 [28] 0 . − . i = 2) 0 5 1 5 2 4 1 0 3 2 0 0 0 0 1 [24] 0 . − . i = 3) 1 1 1 1 2 4 3 0 5 2 0 0 1 0 2 [23] 0 . − . i = 4) 0 1 3 5 5 0 1 0 1 0 0 2 0 0 1 [19] 0 . − . i = 5) 0 0 3 8 3 1 6 1 1 1 2 1 0 1 0 [28] 0 . − . i = 6) 0 1 1 0 1 4 2 2 0 1 0 1 0 1 1 [15] 0 . − . i = 7) 0 0 1 0 3 0 3 0 0 2 1 0 0 0 0 [10] 0 . − . i = 8) 1 0 0 0 2 1 2 2 3 2 0 1 0 0 0 [14] 0 . − . i = 9) 0 0 1 0 3 2 3 0 1 0 0 0 0 0 0 [11] 0 . − . i = 10) 0 0 1 1 1 2 3 2 1 1 1 0 0 0 0 [12] 0 . − . i = 11) 0 0 0 0 2 0 1 2 1 0 0 0 0 0 0 [6] 0 . − . i = 12) 0 0 0 0 0 2 3 0 0 2 2 0 0 0 0 [9] 0 . − . i = 13) 0 0 0 0 0 2 0 0 1 0 1 1 0 0 0 [5] 0 . − . i = 14) 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 [2] 0 . − . i = 15) 0 0 0 0 2 0 3 0 3 0 1 0 0 0 0 [9] 0 . − . . − . a Array F ( i, j ) shows the number of H I absorbers per bin, with total numbers summed across rows and columns. In total, this table lists 211absorbers: 158 (log N HI ≥ . N HI ≥ . N HI ≥ . i, j ) denote redshift bins ( i = 1 − 15) of width ∆ z = 0 . . ≤ z ≤ . 84 and column-density bins ( j = 1 − 15) of width ∆ log N HI = 0 . 25 except for bins 13, 14, 15. Column density ranges of bins are:(1) log N HI = 14.00-14.25, (2) 14.25-14.50, (3) 14.50-14.75, (4) 14.75-15.00, (5) 15.00-15.25, (6) 15.25-15.50, (7) 15.50-15.75, (8) 15.75-16.00, (9)16.00-16.25, (10) 16.25-16.50, (11) 16.50-16.75, (12) 16.75-17.00, (13) 17.00-17.50, (14) 17.50-18.00, (15) log N HI ≥ . 00. Five absorbers (Systems TABLE 4 Redshift Distribution of H I Absorbers Bin ( i ) Redshift Range ( N AGN ) a ( N abs ) b (∆ z eff ) ( i )a ( d N /dz ) b . . , − . . . , − . . . , − . . . , − . . . , − . . . , − . . . , − . . . , − . . . , − . . . , − . . . , − . . . , − . . . , − . . . , − . . . , − . a Number ( N AGN ) of AGN sight lines providing full or partial spectral coverage of the H I Lyman edge (912 ˚A) over redshift bins ( i = 1 − z eff , is based on N AGN subtracting partial coverage of bins and portions of spectrum blocked by strong absorbers. b Distribution ( N abs ) of 158 H I absorbers with log N HI ≥ 15 for the 15 redshift bins (from 0 . ≤ z ≤ . N HI ≥ 14 (211 in all). Last column shows the frequency of absorbers per unit redshift, d N /dz ≡ N abs / ∆ z eff , for log N HI ≥ σ ) error bars for one-sided Poisson statistics (Gehrels 1986) on N abs . Over total pathlength ∆ z eff = 31 . 94, the average absorberfrequency is d N /dz ≈ . ± . 39. Full statistical analysis (MCMC) of the bivariate distribution, f ( N, z ) ≡ ( d N abs /dz dN ), is given in AppendixB. TABLE 5 Strong Absorbers and Wavelength Blockage a QSO b z abs log N HI z QSO Affected Wavelength Blockage1 0.24770 19 . ± . 10 0.47114 Bin 1 opaque below 1137.6 ˚A2 0.39043 18 . ± . . ± . 05 0.694596 Bins 1-5 opaque below 1286.2 ˚A4 0.23740 17 . ± . 11 0.5251 . . . opaque below 1128.2 ˚A5 0.35586 18 . ± . . ± . 12 0.7462 Bins 1-2 opaque below 1188.6 ˚A7 0.47379 18 . ± . . ± . 05 0.4632 Bins 1-5 minor influence below 1294.0 ˚A9 0.46334 17 . ± . 02 0.7666 Bins 1-6 opaque below 1334.2 ˚A10 0.92772 17 . ± . 05 1.1625 Bins 1-14 minor influence below 1757.6 ˚A a Potential spectrum blockage by 10 strong absorbers listed with redshifts z abs and fitted column densities, log N HI . Absorber column densities andredshifts are revised from values in Stevans et al. (2014), based on analysis of the Lyman limit flux decrement and new fits to CoG for high-orderLyman lines. See Appendix B for details. In 8 cases, strong LyC absorption produces flux decrements at wavelengths λ ≤ (911 . 753 ˚A)(1 + z abs )listed in comments. Potentially affected bins are noted. However, our survey can still find pLLS by detecting higher Lyman lines longward of theLyman edge. b QSO targets: (1) SDSS J092554.70+400414.1; (2) FIRST J020930.7-043826; (3) SDSS J151428.64+361957.9; (4) SDSS J113327.78+032719.1; (5)SDSS J100902.06+071343.8; (6) SDSS J100102.55+594414.3; (7) SDSS J154553.48+093620.5; (8) SDSS J091029.75+101413.6; (9) SBS 1108+560;(10) PG 1206+459. TABLE 6 Strong Absorbers (LLS and pLLS) a No. QSO Name z abs z AGN log N HI log N HI log N HI Lehner + 13 Stevans + 14 This Paper1 J092554.70+400414.1 0.2477 0.471139 19 . ± . 15 19 . ± . 06 19 . ± . 102 J020930.7-043826 0.39035 1.131 18 . ± . . ± . 43 J151428.64+361957.9 0.41065 0.694596 17 . ± . . ± . 064 J113327.78+032719.1 0.23756 0.525073 17 . ± . 10 17 . ± . 115 J100902.06+071343.8 0.35586 0.455631 18 . ± . 20 17 . ± . 04 18 . ± . 26 J100102.55+594414.3 0.30360 0.746236 17 . ± . 04 19 . ± . 127 J154553.48+093620.5 0.47379 0.665 17 . ± . . ± . 28 J091029.75+101413.6 0.41924 0.463194 17 . ± . . +0 . − . . ± . . ± . . ± . 10 17 . ± . 08 17 . ± . . ± . 05 16 . ± . 04 17 . ± . . ± . 02 16 . ± . . ± . 07 16 . ± . 06 16 . ± . . ± . . ± . . ± . . ± . . ± . 06 16 . ± . 117 J155048.29+400144.9 0.4919 0.496843 16 . ± . 02 16 . ± . . ± . 08 16 . ± . 03 17 . ± . . ± . . ± . . ± . . ± . . ± . 02 16 . ± . − − 25 0.39913 0.956 16 . ± . 02 16 . ± . . ± . 05 16 . ± . . ± . 01 16 . ± . . ± . 05 16 . ± . 09 16 . ± . . ± . 03 16 . ± . 08 16 . ± . . ± . 02 16 . ± . . ± . . ± . 05 16 . ± . 04 16 . ± . . ± . 13 16 . ± . 06 16 . ± . . ± . 04 16 . ± . 03 16 . ± . . ± . 07 16 . ± . 03 16 . ± . . ± . 06 16 . ± . 02 16 . ± . . ± . 17 16 . ± . 07 16 . ± . . ± . 05 16 . ± . 02 16 . ± . . ± . 09 16 . ± . 09 16 . ± . . ± . 02 16 . ± . 03 16 . ± . . ± . 05 16 . ± . 01 16 . ± . . ± . 05 16 . ± . 03 16 . ± . . ± . 03 16 . ± . 02 16 . ± . . ± . 04 16 . ± . 04 16 . ± . . . . . . . . ± . a Strong absorbers estimated (Stevans et al. 2014) with log N HI ≥ . N HI = 16 . − . z abs ) and AGN ( z AGN ). Our column densities (this paper) are from new CoG fits to Lyman-series approaching LL. Appendix A discusses CoGsand Ly decrements. TABLE 7 Summary of LLS Frequency fitting a Survey Instrument Redshift Range N γ N LLS This Paper COS 0.24 – 0.48 0 . +0 . − . . ± . 89 8Storrie-Lombardi et al. 1994 FOS 0.40 – 4.69 0 . +0 . − . . ± . 45 7Stengler-Larrea et al. 1995 FOS 0.40 – 4.69 0 . +0 . − . . ± . 39 7Ribaudo et al. 2011a FOS/STIS 0.25–2.59 0 . ± . 05 1 . ± . 56 17 a Redshift evolution of low-redshift LLS (log N HI ≥ . 2) studied with UV spectra and fitted to ( d N /dz ) = N (1 + z ) γ . We include the currentCOS survey, two HST low-resolution surveys with FOS/G140L (Storrie-Lombardi et al. 1994; Stengler-Larrea et al. 1995) and a low-resolutionsurvey with FOS/G140L and STIS/G140L/G230L (Ribaudo et al. 2011a). The last column gives the number N LLS of low redshift ( z < . 84 LLSin the COS survey, z < . 04 in the FOS Key Project, and z < . 84 in Ribaudo et al. (2011a). These surveys contain many more pLLS, which areused in the fits. TABLE 8 List of Strong (DLA and sub-DLA) Absorbers a AGN z abs z AGN log N HI (cm − ) b CommentsPG 1216+069 0.00635 0.331 19 . ± . 03 Sightline to System . ± . 15 Two other strong absorbers (log N = 15 . , . . ± . 10 Sightline to Systems . ± . 10 Sightline to System . ± . 15 No other strong absorbers with log N > . . ± . 10 No other strong absorbers with log N > . . ± . 10 Sightline to System . ± . . ± . 15 System . ± . 12 System . ± . 12 System . ± . a Four low-redshift Damped Ly α (DLA) and six sub-DLA systems identified in our survey, ordered by absorber redshift ( z abs ). The first eightabsorbers lie below the minimum redshift ( z abs = 0 . 24) of our survey and are not included in our statistical analysis. DLA systems have log N HI > . . < log N HI < . 3. Two other absorbers have column densities log N HI = 18 . ± . 5) near the sub-DLA range. b Column densities for several systems in this list were listed in other papers (Meiring et al. 2011; Muzahid et al. 2015; Tejos et al. 2014) withcolumn densities determined by fitting damping wings of Ly α profile. For other absorbers (systems αα