The evolution of HI and CIV quasar absorption line systems at 1.9 < z < 3.2
Tae-Sun Kim, Adrian M. Partl, Robert F. Carswell, Volker Müller
aa r X i v : . [ a s t r o - ph . C O ] F e b Astronomy&Astrophysicsmanuscript no. dndz c (cid:13)
ESO 2018September 19, 2018
The evolution of H i and C iv quasar absorption line systems at . < z < . ⋆ T.-S. Kim , , Adrian M. Partl , R. F. Carswell , and Volker M¨uller Leibniz-Institut f¨ur Astrophysik Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany Department of Astronomy, University of Wisconsin-Madison, 475 N. Charter St., Madison, WI 53706, USA Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, UKReceived ; Accepted
ABSTRACT
We have investigated the distribution and evolution of ∼ i ) absorbers with H i column densitieslog N H i = [12 . , .
0] at 1 . < z < .
2, using 18 high resolution, high signal-to-noise quasar spectra obtained from the ESO VLT / UVESarchive. We used two sets of Voigt profile fitting analysis, one including all the available high-order Lyman lines to obtain reliable H i column densities of saturated lines, and another using only the Ly α transition. There is no significant di ff erence between the Ly α -onlyfit and the high-order Lyman fit results. Combining our Ly α -only fit results at 1 . < z < . mean number density at 0 < z < z ≤ . i absorbers at 1 . < z < . iv -enriched forest, depending on whether H i lines are associated with C iv at log N C iv ≥ . i column density distribution function (CDDF) can be described as the combination of thesetwo well-characterised populations which overlap at log N H i ∼
15. At log N H i ≤
15, the unenriched forest dominates, showing asimilar power-law distribution to the entire forest. The C iv -enriched forest dominates at log N H i ≥
15, with its distribution functionas ∝ N ∼− . i . However, it starts to flatten out at lower N H i , since the enriched forest fraction decreases with decreasing N H i . Thedeviation from the power law at log N H i = [14 ,
17] shown in the CDDF for the entire H i sample is a result of combining two di ff erentH i populations with a di ff erent CDDF shape. The total H i mass density relative to the critical density is Ω H i ∼ . × − h − , wherethe enriched forest accounts for ∼
40% of Ω H i . Key words.
Quasars: absorption lines – large-scale structure of Universe – cosmology: observations
1. Introduction
The resonant Ly α absorption by neutral hydrogen (H i ) in thewarm ( ∼ K) photoionised intergalactic medium (IGM) pro-duces rich absorption features blueward of the Ly α emission linein high-redshift quasar spectra known as the Ly α forest. The Ly α forest contains ∼
90% of the baryonic matter at z ∼ z ∼
6. Gas-dynamicalsimulations and semi-analytic models have been very successfulat explaining the observed properties of the Ly α forest mainlyat low H i column densities N H i ≤ cm − . These modelshave shown that the Ly α forest arises by mildly non-linear den-sity fluctuations in the low-density H i gas, which follows theunderlying dark matter distribution on large scales. This inter-pretation also predicts that the Ly α forest provides powerful ob-servational constraints on the distribution and evolution of thebaryonic matter in the Universe, hence the evolution of galax-ies and the large-scale structure (Cen et al. 1994; Rauch et al.1997; Theuns et al. 1998; Dav´e et al. 1999; Schaye et al. 2000b;Schaye 2001; Kim et al. 2002). In addition, the discovery oftriply ionised carbon (C iv ) associated with some of the forest ab-sorbers suggests that the forest metal abundances can be utilisedto probe early generations of star formation and the feedbackbetween high-redshift galaxies and the surrounding IGM fromwhich galaxies formed (Cowie et al. 1995; Dav´e et al. 1998; Send o ff print requests to : T.-S. Kim: [email protected] ⋆ The data used in this study are taken from the ESO archive for theUVES at the VLT, ESO, Paranal, Chile.
Aguirre et al. 2001; Schaye et al. 2003; Oppenheimer & Dav´e2006).The physics of the Ly α forest is mainly governed by threecompeting processes, the Hubble expansion, the gravitationalgrowth and the ionizing UV background radiation. The Hubbleexpansion which causes the gas to cool adiabatically and thegravitational growth are fairly well-constrained by the cosmo-logical parameters and the primordial power spectrum from thelatest WMAP observations (Jarosik et al. 2011). On the otherhand, the ionizing UV background radiation controls the pho-toionisation heating and the gas ionisation fraction, thus deter-mining the fraction of the observable H i gas compared to theunobservable H ii gas. The UV background is assumed to beprovided primarily by quasars and in some degree also by star-forming galaxies (Shapley et al. 2006; Siana et al. 2010) andLy α emitters (Iwata et al. 2009). However, the intensity / spectralshape of the UV background and the relative contribution fromquasars and galaxies as a function of redshift are not well con-strained (Bolton et al. 2005; Faucher-Gigu`ere et al. 2008). Oneof the common methods to measure the UV background and itsevolution is the quasar proximity e ff ect (Dall’Aglio et al. 2008).Unfortunately, measurements of the UV background through theproximity e ff ect are biased by the large scale density distributionaround the quasars which cannot be easily quantified observa-tionally (Partl et al. 2010, 2011).Two commonly explored quantities to constrain the proper-ties of the Ly α forest are the number of absorbers for a givenH i column density range per unit redshift, d n / d z , and the di ff er- i and C iv forest ential column density distribution function (CDDF, the numberof absorbers per unit absorption path length and per unit col-umn density, an analogue to the galaxy luminosity function).Compared with simulations, detailed structures seen in an over-all power-law-like CDDF ( ∝ N β H i ) such as a flattening or a steep-ening at di ff erent column density ranges constrain various for-est physical and galactic feedback processes (Altay et al. 2011;Dav´e et al. 2010). The CDDF is also one of the main observablesrequired in calculating the mass density relative to the criticaldensity contributed by the forest (Schaye 2001). The shape ofthe CDDF at lower N H i ≤ . − . cm s − (a typical detectionlimit for most available high-quality data) is of particular impor-tance, since the lower N H i absorbers are much more numerousthan higher N H i absorbers, thus they can trace a significant frac-tion of baryons, depending on the steepness of the CCDF at thelow N H i limit.On the other hand, d n / d z provides an additional way to studythe UV background radiation and its evolution. The gas den-sity decreases with decreasing redshift due to the Hubble ex-pansion. A lower gas density results in a strong reduction of therecombination rate, allowing the gas to settle in to a photoion-isation equilibrium with a higher ionisation fraction. With thenon-decreasing background radiation, this causes a steep numberdensity evolution. However, the decrease of the quasar numberdensity at z < . HST / FOS Quasar Absorption Line Keyproject shows such a slow change in the d n / d z evolution at z < . n / d z evolution shown at z > z (Kim et al.2002). Unfortunately, recent work based on better-quality HST data at z < . i Ly α at < n / d z results with a large scatter alongdi ff erent sightlines (Janknecht et al. 2006; Lehner et al. 2007;Williger et al. 2010). The only certain observational fact is thatall of these newer studies show a factor of ∼ − z < .
5. Consideringa lack of results from good-quality data at 1 < z < . n / d z can be considered as a singlepower law without any abrupt change in d n / d z at 0 < z < . R ∼
45 000), high signal-to-noise ( ∼ α for-est at 1 . < z forest < .
2. Our main scientific aims are to derivethe redshift evolution of the absorber number density and thecolumn density distribution function from a large and homoge-neous set of data available at z >
2, since most previous high-quality forest studies at z > N H i = − cm − (about 150 absorbers at z ∼ . α andLy β emission lines). However, for the stronger forest systemswith N H i ≥ cm − , more sightlines are required since thereare only about 10 absorbers per sightline at z ∼ .
5. Cosmic vari-ance also plays an important role at lower redshifts, especiallyfor stronger absorbers (Kim et al. 2002). Therefore, increasing the sample size at z ∼ N H i evolutionfor the Ly α forest.In addition to the increased sample size, we have improvedprevious results in two ways. First, most previous studies on theforest from ground-based observations at z > . α -only profile fitting analysis. This approachdoes not provide a reliable N H i for saturated lines, N H i ≥ . cm − for the present UVES data. To derive a more reliable N H i of saturated lines, we have included all the available high-orderLyman series in this study.Second, strong evidence have been accumulated in recentstudies that metals associated with the high-redshift Ly α for-est are within ∼
100 kpc of galaxies as in the circum-galacticmedium rather than in the intergalactic space far away fromgalaxies (Adelberger et al. 2005; Steidel et al. 2010; Rudie et al.2012). This implies that the H i absorbers containing metalsmight show di ff erent properties than the ones without detectablemetals. Taking C iv as a metal proxy, we have divided our datainto two samples, one with C iv (the C iv -enriched forest) andanother without C iv (the unenriched forest), in order to test thisscenario of the circum-galactic medium. Since our study lacksthe imaging survey around the quasar targets, we cannot claimthat the C iv -enriched forest is indeed located within ∼
100 kpcfrom a nearby galaxy. However, this study provides complemen-tary results to galaxy-absorber connection studies at high red-shifts (Steidel et al. 2010; Rudie et al. 2012).This study is also very timely since the Cosmic OriginsSpectrograph (COS), a high-sensitivity FUV spectrograph on-board
HST has started to produce many high-quality quasarspectra at z < z Ly α forest. Combined with results at high redshifts suchas our study, COS observations will make it possible to charac-terise the d n / d z evolution at 0 < z < . α -only fitare shown in Section 3. The analysis based on the high-orderLyman fit is presented in Section 4. Column density distributionand evolution of the Ly α forest containing C iv are presented inSection 5. Finally, we discuss and summarise the main results inSection 6. All the results on the number density and the di ff eren-tial column density distribution from our analysis are tabulatedin Appendix A. Throughout this study, the cosmological param-eters are assumed to be the matter density Ω m = .
3, the cos-mological constant Ω Λ = . H = h km s − Mpc − with h = .
7, which is in concordancewith latest WMAP measurements (Jarosik et al. 2011). The log-arithm N H i is defined as log N H i = log( N H i / − ).
2. Data and Voigt profile fitting
Table 1 lists the properties of the 18 high-redshift quasars anal-ysed in this study. The redshift quoted in Column 2 is mea-sured from the observed Ly α emission line of the quasars.Note that the redshift based on the emission lines is knownto be under-estimated compared to the one measured fromother quasar emission lines such as C iv (Tytler & Fan 1992;Vanden Berk et al. 2001). The spectrum of Q1101 −
264 is thesame one as analysed in Kim et al. (2002), while the rest ofspectra are from Kim et al. (2007). The raw spectra were ob-tained from the ESO VLT / UVES archive and were reduced withthe UVES pipeline. All of these spectra have a resolution of i and C iv forest Table 1.
Analysed quasars
Quasar z em z aLy α z bLy αβ z cLy , high − order Excluded z dC iv S / N per pixel e LL (Å) notesQ0055–269 3.655 f z = f z = ≤ f ≤ f f z = f ≤ ≤ ≤ f ≤ z = g ≤ ≤ z = a The redshift range of the Ly α forest region analysed for the number density evolution in the Ly α -only fit. For the di ff erential column densityevolution, we used the redshift range listed in Column 5. b The redshift range for which the high-order Lyman fit can be performed is listed only when it is di ff erent from the Ly α -only fit region. c The redshift range of the Ly α forest region analysed for the high-order Lyman fit is listed only when it is di ff erent from the Ly α -only fit region. d The redshift range excluded for the C iv -enriched H i forest analysis in Section 5 due to the lack of the coverage. Q0055 −
269 and J2233 − / N in the C iv region. No entries mean that the analyzed z C iv is the same as the one in Column 5. e The number outside the bracket is a S / N of the H i forest region. The first number inside the bracket is a typical S / N of the C iv region at1 . < z < .
4, while the second is for 2 . < z < .
2. The dotted entries indicate that no C iv forest region is available for a given redshift range.Two numbers inside the parentheses indicate the S / N of the C iv region at 1 . < z < . . < z < .
4, respectively, due to the dichroicsetting toward some sightlines. f Due to the absorption systems at the peak of the Ly α emission line or to the non-single-peak emission line, the measurement is uncertain. g Part of the continuum uncertainties toward shorter wavelengths is due to the local, non-smooth continuum shape, partly due to a lower S / N( ∼ R ∼
45 000 and heliocentric, vacuum-corrected wavelengths. Thespectrum is sampled at 0.05Å. A typical signal-to-noise ratio(S / N) in the Ly α forest region is 35–50 per pixel (hereafter all theS / N ratios are given as per pixel). Readers can refer to Kim et al.(2004) and Kim et al. (2007) for the details of the data reduc-tion. To avoid the proximity e ff ect, the region of 4,000 km s − blueward of the quasar’s Ly α emission was excluded.In order to obtain the absorption line parameters (the red-shift z , the column density N in cm − and the Doppler parameter b in km s − ), we have performed a Voigt profile fitting analysisusing VPFIT . Details can be found in the documentation pro-vided with the software, Carswell, Schaye & Kim (2002) andKim et al. (2007). Here, we only give a brief description of thefitting procedure.First, a localised initial continuum of each spectrum wasdefined using the CONTINUUM/ECHELLE command in
IRAF .Second, we searched for metal lines in the entire spectrum,starting from the longest wavelengths toward the shorter wave-lengths. We first fitted all the identified metal lines. When metallines were embedded in the H i forest regions, the H i absorptionlines blended with metals are also included in the fit. Sometimesthe simultaneous fitting of di ff erent transitions by the same ionreveals that the initial continuum needs to be adjusted to obtainacceptable ion ratios. In this case, we adjusted the initial con-tinuum accordingly. The rest of the absorption features were as-sumed to be H i .After fitting metal lines, we have fitted the entire spectrumincluding all the available higher-order Lyman series in theUVES spectra. This is absolutely necessary to obtain reliable Carswell et al.: http: // / ∼ rfc / vpfit.html N H i for saturated lines, as our study deals with saturated linesand relies on line counting. A typical z ∼ b ∼
30 km s − starts to saturate around N H i ≥ . cm − at the UVES resolution and S / N. Unfortunately, N H i and b values of saturated lines are not well constrained. In orderto derive reliable N H i and b values, higher-order Lyman series,such as Ly β and Ly γ , have to be included in the fit, as higher-order Lyman series have smaller oscillator strengths and start tosaturate at much larger N H i .During this process, another small amount of continuum re-adjustment was often required to achieve a satisfactory fit, i.e. areduced χ value of ∼ .
2. With this re-adjusted continuum, were-fitted the entire spectrum. This iteration process of continuumre-adjustments and re-fitting was then repeated several times un-til satisfactory fitting parameters were obtained. This producesthe final set of fitted parameters for each component of the high-order Lyman fit analysis.In addition to this high-order fit, we have also performed thesame analysis using only the Ly α transition region, i.e. the wave-length range above the rest-frame Ly β and below the proximitye ff ect zone. This additional fitting analysis was done, since mostprevious studies on the IGM N H i analysis based on Voigt pro-file fitting utilised only the Ly α region. For the Ly α -only fit, wekept the same continuum used in the high-order Lyman fittingprocess. In principle, the di ff erence between two sets of fittedparameters occurs only in the regions where saturated absorp-tion features are included. In both fitting analyses, we did not tiethe fitting parameters for di ff erent ions.Fig. 1 shows the numbers of absorption lines as a func-tion of N H i for both fitting analyses at the two redshift ranges,2 . < z < . . < z < .
2, in order to illustrate the di ff er- i and C iv forest Fig. 1.
Numbers of absorption lines as a function of N H i at 2 . < z < . . < z < .
2. The Ly α -only fits are shown as solid lines,while the high-order Lyman fits are marked as dashed lines. Solid errors indicate the 1 σ Poisson errors of the Ly α -only fits.ences at high and low redshifts. The di ff erences between the twosamples occurs mostly at N H i ≥ . cm − and at N H i ≤ cm − . This di ff erence in the line numbers at N H i ≥ . cm − seems to be stronger at 2 . < z < .
2, although it is still within2 σ Poisson errors. The line numbers at N H i ≤ cm − aremore susceptible to the incompleteness which depends on thelocal S / N than the di ff erence between the two fitting methods.The di ff erence at other column density ranges is smaller, whichin turn leads us to expect that there is no significant di ff erencebetween the Ly α -only fit and the high-order Lyman fit.We restrict our present analysis to log N H i = [12 . ,
17] at allredshifts. As clearly seen in Fig. 1, the incompleteness becomesquite severe for log N H i ≤ . z > N H i limit was chosen to belog N H i = .
75. We chose log N H i =
17 as the upper N H i limitsince we wanted to analyze only the Ly α forest whose traditionaldefinition is an absorber with log N H i < . N H i >
17 are very rare (Fig. 1).Note that the availability of the high-order Lyman series de-pends on the redshift of the quasar and whether the sightline con-tains a Lyman limit system. In addition, the amount of blendinga ff ects whether a reliable column density can be measured. Athigh redshifts z em >
3, line blending becomes severe. However,most UVES spectra also covers down to 3050 Å where Lymanlines higher than Ly δ are available. On the other hand, at z em < . β and Ly γ available. However, line blending is lessproblematic than at higher redshifts. We have generated tens ofsaturated artificial absorption lines and fitted them including andexcluding high-order Lyman lines. These simulations show that unblended absorption features at N H i ≤ cm − can be rea-sonably well constrained with Ly α and Ly β only. This indicates Fig. 2.
Total absorption distance X ( z ) covered with our sampleof 18 high-redshift quasars. The solid line is for the Ly α -only fit,while the dashed one is for the high-order fit.that our N H i can also be considered reliable even at z < . α and Ly β only.The absorption distance is obtained by integrating theFriedmann equation for a Ω m = . Ω Λ = . X ( z ) = Z H H ( z ) (1 + z ) d z (1)(Bahcall & Peebles 1969), where H is the Hubble constant at z =
0. The total absorption distance X ( z ) covered by the spectra i and C iv forest for both Ly α -only and high-order fits is shown in Fig. 2. The red-shift coverage of our sample steadily increases with decreasingredshift until it reaches its maximum at z ∼ .
1. For redshifts be-low z < . z = .
7. Note that the lowest redshift possible for the high-order Lyman line analysis is z ∼ .
97, while the Ly α -only fitanalysis is possible down to z ∼ .
7. Due to the reduced redshiftcoverage in the high-order Lyman range of individual sight linescaused by intervening Lyman limit systems, the sample coverageof the high-order fit analyses is reduced between 2 . < z < . z > .
22, the number of available for-est lines decreases and the sample consists of only one line ofsight. The low redshift limit for the high-order fit was set to bethe lowest redshift without any saturated lines when no Ly β isavailable for each quasar. This criterion restricts our high-orderLyman fit analysis to 1 . < z < .
2. Since the redshift coverage oflow-z quasars for the high-order fit is shorter than the one for theLy α -only fit and the high- N H i forest clusters stronger at lower z (Kim et al. 2002), the quasar-by-quasar d n / d z at z ∼ ff er from the low numberstatistics.In Table 1, Columns 3–6 summarise the redshift range usedfor the di ff erent analysis. Column 3 lists the redshift range ofthe Ly α forest region analysed for the number density evolu-tion in the Ly α -only fit. For the di ff erential column density evo-lution of the Ly α -only fit, we used the redshift range listed inColumn 5. Column 4 and Column 5 list the redshift range forwhich the high-order Lyman fit can be performed and the onefor which the high-order Lyman fit was done, respectively. Theregion is listed only when it is di ff erent from the Ly α -only fitregion in Column 3. Since there are no strongly saturated Ly α lines at 1 . < z < .
98 for some low- z quasar sightlines, weused a lower redshift range than the one listed in Column 4 forthe high-order Lyman fit analysis for these sightlines. Column 6shows the redshift range excluded for the C iv -enriched H i studyin Section 5. Due to the wavelength gaps caused by the UVESdichroic setup, the covered C iv redshift ranges are smaller thanthe Ly α forest coverage listed in Column 3. The region of ± − from the gap was excluded, and only the redshift rangecovering both C iv doublets was included in the analysis. Theblank entries mean that the analyzed z C iv is the same as the for-est z Ly , high − order . Q0055 −
269 and J2233 −
606 are excluded in theLy α –C iv forest study due to their lower S / N in the C iv region.In the HE2347 − α forest region, there are very strongO vi absorptions mixed with the two saturated Ly α absorptionsystems at 4012–4052 Å (Fechner et al. 2004). Since the fittedline parameters for these Ly α systems cannot be well constrained(their corresponding Ly β is below the partial Lyman limit pro-duced by the z ∼ .
738 systems), we excluded this forest regiontoward HE2347 − −
606 sightline, there are twopartial Lyman limit systems at 3489 Å ( z ∼ . z ∼ . N H i , we included the HST / STISechelle spectrum of J2233 − at 2280–3150 Å. The resolutionin this wavelength region is ∼
10 km s − and its S / N is ∼ / N of each quasar spectrum in Column7. The number outside the bracket is a S / N of the H i forestregion. The first number inside the bracket is a typical S / Nof the C iv region at 1 . < z < .
4, while the second is for The STIS spectrum is taken from (Savaglio et al. 1999).
Fig. 3.
Number of H i absorbers with log N H i = [12 . , α -only fit. The dashed lineis for the high-order fit, while the red heavy dot-dashed line isfor the Ly α -only fit for the redshift range used for the high-orderfit.2 . < z < .
2. The dotted entries inside the bracket indicate thatno C iv forest region is available for a given redshift range. Thelow redshift bin of the C iv forest covers the wavelength regionwhere the di ff erent CCDs from two dichroic settings were usedat ∼ z ∼ . / N at ≤ z < . / N region is larger than20% of the whole C iv forest range, two numbers were listed in-side the parentheses. The first number corresponds to the lowerS / N at 1 . < z < .
1, while the second number is for the higherS / N at 2 . < z < . ±
50 Å to the center of a sub-damped Ly α system ( N H i ≥ cm − ) are excluded, sincethey are associated directly with intervening high- z galacticdisks / halos and could have a possible influence on the appar-ent line densities in the forest. The sightline toward Q0453 − α red-shift range. All the calculations toward Q0453 −
423 account forthis redshift gap correctly. However, they are plotted as a sin-gle data point and their plotted redshift range is the whole Ly α redshift range without showing a gap. The sightlines towardPKS2126 −
158 and Q0420 −
388 also contain an intervening sub-DLA, which shortens the continuously available redshift cover-age for the high-order fit. Column 8 of Table 1 lists the observedwavelength of a Lyman limit (LL, 912 Å in the rest-frame wave-length) of each quasar, which is defined as the wavelength be-low which the observed flux becomes 0. The values are takenfrom Kim et al. (2004). When a Lyman limit is not detectedwithin available data, it is denoted to be less than the lowestavailable wavelength. Column 9 of Table 1 notes information onsub-DLAs along the sightline. When a sub-damped Ly α systemexists along the sightline, we discarded 50 Å centred at the sub-DLA each side to exclude its influence on the forest, such as ahigher frequency or lack of higher-column density forest. The to-tal number of H i lines for log N H i = [12 . ,
17] at 1 . < z < . α -only fitsample has 3778 H i lines at the total redshift range listed in the3rd column of Table 1. i and C iv forest In Fig. 3 the number of H i absorbers with log N H i = [12 . ,
17] from both fitting methods is shown as a functionof redshift. The number of absorbers obtained from each fit-ting analysis is roughly proportional to the absorption distancecoverage. Therefore, our sample shows the highest H i absorbernumbers around redshift z ∼ < z <
3. This isbecause what appear to be single saturated Ly α lines may havemore than one component present in the corresponding higherorder Lyman lines. At z ∼
2, the number of the Ly α -only-fit ab-sorbers (heavy dot-dashed line) is slightly larger than the high-order-fit absorbers. This is caused by the fact that some simplesaturated lines with log N H i <
17 in the Ly α -only fit analysis areactually absorbers with log N H i >
17 in the high-order fit analy-sis. Since the Ly α -only fit gives a lower N H i limit for a saturatedline, these lines are included in the Ly α -only fit sample, but ex-cluded in the high-order fit sample in Fig. 3.
3. Comparison with previous studies using Ly α only In Sect. 2 we have shown that including higher order transitionsin the fitting process slightly alters the column density statisticsat log N H i > .
0. In order to compare our quasar sample withprevious studies based only on the Ly α transition, we brieflypresent the column density distribution and evolution derivedfrom the Ly α -only fit in this section. A large redshift coverageis very important in the study of the absorber number density.Therefore we used all Ly α lines found in the whole availableLy α redshift ranges listed in Column 3 of Table 1 in this section.On the other hand, the di ff erential density distribution functionis not sensitive to a large redshift coverage. Thus, only the Ly α lines at 1 . < z < . d n / d z The absorber number density n ( z ) is measured by counting thenumber of H i absorption lines for a given column density rangefor each line of sight. The line count n is then divided by thecovered redshift range ∆ z to obtain d n / d z . If forest absorbershave a constant size and a constant comoving number density,its number density evolution due to the Hubble expansion canbe described asd n d z = π R N cH ( z ) − (1 + z ) , (2)where R is the size of an absorber, N is the local comovingnumber density and c is the speed of light (Bahcall & Peebles1969). For our assumed cosmology, Eq. 2 becomesd ndz ∝ (1 + z ) p . + z ) + . . (3)At 1 < z < .
5, Eq. 3 has an asymptotic behaviour of d n / d z ∝ (1 + z ) ∼ . , while at z < n / d z ∝ (1 + z ) ∼ . .For higher redshifts the asymptotic behaviour becomes d n / d z ∝ (1 + z ) . . Any di ff erences in the observed exponent from whatis expected from Eq. 3 indicate that the absorber size or / and thecomoving density are not constant. Fig. 4.
The number density evolution of the Ly α forest in the col-umn density range log N H i = [14 ,
17] of the Ly α -only fits. Blackfilled circles show results from our data set, which is tabulatedin Table A.1. Other data points indicate various results obtainedfrom the literature. The vertical error bars give the 1 σ Poissonerror, while the x-axis error bars show the redshift range coveredby each sightline. The solid line shows the fit to our data only.Dashed line is the result including the literature data for z > + z ) > . n / d z evolution based on a quasar-only UV background by Dav´e et al.(1999). The red dotted and the blue dot-dot-dot-dashed curves at z < n / d z based on momentum-drivenwind and no-wind models with a UV background by quasars andgalaxies, respectively (Dav´e et al. 2010).Empirically, d n / d z is described as d n / d z = A (1 + z ) γ . It hasbeen known that d n / d z evolves more rapidly at higher columndensities. At z > .
5, a γ ∼ . N H i = − cm − , and γ ∼ . N H i = . − cm − (Kim et al. 2002).At z < .
5, Weymann et al. (1998) found γ ∼ .
16 and A ∼
35 forabsorbers with a rest-frame equivalent width greater than 0.24 Åfrom
HST / FOS data. Later studies on d n / d z based on the pro-file fitting or curve of growth analysis using better-quality datafrom HST / STIS and
HST / GHRS show a factor of ∼ n / d z than the one found by Weymann et al. (1998). These stud-ies also show a larger scatter in d n / d z at z < . A ∼ z coverage at z < .
5, missing mostly at0 . < z < .
0. Keep in mind that the FOS result and most avail-able ground-based results at z > . α lines only, while most space-based results at z < . γ of d n / d z at0 < z < .
5. Strictly speaking, a fair comparison should be madeon the data with similar qualities and uniform analyses.The number density evolution is illustrated in Figs. 4, 5 and6 for two di ff erent column density ranges: log N H i = [14 , . , i and C iv forest Savaglio et al. (1999), Kim et al. (2001), Sembach et al. (2004),Williger et al. (2006), Aracil et al. (2006) , Janknecht et al.(2006) , Lehner et al. (2007) and Williger et al. (2010). To beconsistent with our definition of the proximity e ff ect zone, weapplied the same 4 000 km s − exclusion within the quasar’s Ly α emission line for all the literature data, whenever the line listsfrom the literature include all the Ly α lines below the Ly α emis-sion line of the quasar. When the published line lists are onlyfor the shorter wavelength region than the entire, available for-est region outside the 4 000 km s − proximity zone, such as theones by Hu et al. (1995), no such an exclusion is required. Weused all the reported H i lines in the literature mentioned above,without any pre-selection imposed on N H i or b parameters. Thelatest study on the low-redshift IGM by Williger et al. (2010)found that the number density from the HST / STIS results is afactor of 2–3 lower than the
HST / FOS results by Weymann et al.(1998). They applied the same selection criteria on H i absorbersused by Lehner et al. (2007), i.e. measurement errors less than40% and b <
40 km s − . As H i absorbers tend to have a larger b parameter at lower redshift (Lehner et al. 2007) and larger mea-surement errors in general, selecting H i absorbers at b >
40 kms − has a larger impact on d n / d z at lower redshift. In addition, asthe HST / FOS results are based on the H i sample without any im-posed selection criteria, using the full H i lines provides a morestraightforward comparison to the HST / FOS result.We have performed a linear regression to our data in log-arithmic space for the various column density bins, using themaximum likelihood method described in Ripley & Thompson(1987). This method accounts for the uncertainties in the num-ber density and incorporates the weighting using the uncertain-ties. Errors of the fit parameters were obtained using the maxi-mum likelihood method. Linear regressions were once obtainedfrom our data including the literature data and once withoutthem. Since for redshifts z . + z ) . .
3) thenumber density evolution could remain constant with redshift,cf. Weymann et al. (1998), only the literature data with redshift z > n / d z evolution for the column density in-terval of log N H i = [14 , z > . + z ) > . n / d z . Kim et al. (2002)notes that the scatter between di ff erent sightlines increases as z decreases down to z ∼
2. In fact, the data of Janknecht et al.(2006) at redshifts below z ∼ + z ) ∼ .
45) indicate that thescatter might well increase at lower z , although the errors are stillvery large to draw any firm conclusions. Considering that theFOS result is based on the equivalent width measurement, andthe conversion from the equivalent width to the column densityrequires the b parameters of individual absorbers, which are ill-constrained at the FOS resolution, the full HST / STIS H i sampletoward some sightlines is in good agreement with the HST / FOSresult (blue open triangles), although there still is a large sight-line variation. The full H i sample at z < . HST / FOS result, thatd n / d z flattens out at z ≤ . The revised line list was used. The fitted line parameters by Janknecht et al. (2006) show many H i lines with b <
20 km s − , about 25% of all lines. They attribute this totheir low signal-to-noise data of less than 10 per resolution element.Although there are 9 sightlines analysed, one sightline has a long wave-length coverage from VLT / UVES and
HST / STIS. This sightline wassplit into two data points in Figs. 4 and 5.
Table 2.
Linear regression results for d n / d z a) Using the Ly α -only fits and fits including literature data for z > ∆ log N H i log A γ log A γ . − . . ± .
14 2 . ± .
27 1 . ± .
06 1 . ± . . − . . ± .
20 3 . ± .
36 0 . ± .
08 2 . ± . . − . − . ± .
26 3 . ± .
48 0 . ± .
11 1 . ± . . − . . ± .
11 1 . ± .
21 1 . ± .
05 1 . ± . . − . . ± .
08 1 . ± . mean d n / d z using the Ly α -only fits at 0 < z < ∆ log N H i log A γ . − . . ± .
03 0 . ± . . − . . ± .
07 1 . ± . . < z < . ∆ log N H i log A γ log A γ . − . . ± .
12 1 . ± .
22 1 . ± .
13 1 . ± . . − . − . ± .
29 4 . ± . − . ± .
36 4 . ± . The linear regression to our results only (the solid line) with γ = . ± .
36 is di ff erent at 3 σ from the fit to all the availabledata at z > + z ) > .
3) which yields γ = . ± .
14 (thedashed line). This discrepancy is mainly due to the sparse data ofour sample at higher redshift z > . + z ) > .
65) and themissing constraints at z < .
0. The discrepancy is also in partcaused by how the power-law fit is performed. Our maximumlikelihood fit does the weighted fit. This gives a higher weighton higher- z data points where the 1 σ Poisson error is usuallysmaller. The non-weighted fit for our UVES data only results in asteeper power-law slope, ( − . ± . × (1 + z ) . ± . . The non-weighted fit for all the data at z > . ± . × (1 + z ) . ± . .Interestingly, some earlier numerical simulations and theo-ries with a quasar-only UV background have shown that thereshould be a break in the d n / d z evolution at z ∼ i ionis-ing photons (Theuns et al. 1998; Dav´e et al. 1999; Bianchi et al.2001). The green dot-dashed curve in Fig. 4 shows one ofsuch predicted d n / d z evolutions by Dav´e et al. (1999), whichoutlines the Weymann et al. d n / d z reasonably well. However,more recent simulations by Dav´e et al. (2010) predict di ff er-ent d n / d z evolutions. These simulations are based on the vari-ous galactic wind models and the UV background contributedboth by quasars and galaxies. The red dotted and the bluedot-dot-dot-dashed curves at z < n / d z based on momentum-driven wind and no-wind models,respectively. These newer simulations predict that d n / d z con-tinuously decreases with decreasing redshift. Their momentum-driven wind model agrees reasonably well with the observationsby HST / STIS with the H i absorber selection imposed (measure-ment errors less than 40% and b <
40 km s − ), but not with theWeymann et al. data. A better, uniform dataset from HST / COSobservations should resolve this discrepancy at z < . N H i = [14 . , . γ = . ± . ff erent sightlinesis large as stronger absorbers are rare at all redshifts (Dav´e et al.2010). There are more than 3 σ di ff erence between the lowestd n / d z sightline and the highest d n / d z sightline at z ∼
2. Kim et al. i and C iv forest Fig. 5.
The number density evolution of the Ly α forest in thecolumn density range log N H i = [13 . , . z < . + z ) < .
55) for this col-umn density interval. Even though more data points are availablein this study, this question cannot be conclusively answered andmore data covering lower redshifts are required.The line number density evolution for low column densitysystems in the range of log N H i = [13 . , .
0] is presented inFig. 5. Similar to Fig. 4, it suggests that the flattening of d n / d z at z < . z < . ff erent analysismethods and di ff erent S / N STIS data used by di ff erent studies.For example, the number density measured in the STIS spec-trum toward PKS0405 −
123 is di ff erent between the Williger etal. (2006) work (filled purple upside-down triangles) and theLehner et al. (2007) work (two of open red upside-down trian-gles). Again the results from our data agree well with previousresults found in the literature at z > .
5. The linear regressionto our data at z > . γ ≈ .
67, comparable to the fit in-cluding all available literature data points at z > .
0. However,these results do not compare well with the linear regression ob-tained by Kim et al. (2002) with γ = . ± .
14 (the dottedline), a shallower d n / d z evolution. This discrepancy arises dueto their rather small sample size at z < . ffi cult. This incompleteness e ff ect has beenshown to underestimate the line number density of low columndensity systems at log N H i = [13 . , .
6] by ∼
17% at z ∼ + z ) ∼ .
6) and by ∼
35% at z ∼ ff ects tend to flatten the evolution observationally fromits true value. In addition, the robust estimate of the exponent γ requires a large z leverage.Even though there are not many sightlines covering 0 . < z < .
5, we calculated the mean d n / d z from all the combinedH i fitted line lists including the literature data in Fig. 6. This mean d n / d z is not an averaged value of the individual sightlines.The literature data used in the combined line list include all the Fig. 6.
The mean number density evolution of the Ly α forest.The vertical error bars give the 1 σ Poisson error, while the x-axis error bars show the redshift range covered by each datapoint. The data point with the dotted error bar indicate theJanknecht et al. (2006) data. The dashed straight lines mark thefit to the mean data excluding the Janknecht et al. (2006) data.quasar sightlines shown in Figs. 4 and 5, except the
HST / FOSWeymann et al. (1998) data, the Williger et al. (2006) data andthe Savaglio et al. (1999) data. The
HST / FOS data was excludedsince they were based on the equivalent width measurements,while the Williger et al. (2006) data su ff ered from noise features.The Savaglio et al. (1999) result is from a single sightline andprovides the only data point besides the Janknecht et al. (2006)data at z ∼
1. Although the Janknecht et al. (2006) data alsosu ff er from noise, they were from 9 sightlines. We opted to use aresult based on the analysis of multiple sightlines from a singlestudy. This helps to reduce any systematics caused by combiningresults from di ff erent studies at z ∼
1. For z < .
4, the systematicuncertainty is larger since the line lists used are produced bydi ff erent studies.At log N H i = [13 . , . z ∼
1, if the Janknecht data were included. At log N H i = [14 , γ = . ± .
12 does not give a goodfit at 0 < z <
4, regardless of the inclusion of the Janknecht et al.data. It remains to be seen whether a single power law fits thed n / d z evolution for both high and low column density rangesat z = .
4. It should be noted that the d n / d z of Lyman limitsystems with a column density of log N H i = [17 . , .
0] doesnot fit to a single power law. It shows a slower evolution at z < z > n / d z of damped Ly α systems with log N H i = [20 . , .
0] showsa single power-law evolution with a slope γ = . ± .
11 at0 < z < . z < . might indicate the transition point where the evolv-ing number density changes into a non-evolving one, as is pre-dicted in earlier numerical simulations by Theuns et al. (1998)and Dav´e et al. (1999). i and C iv forest The di ff erential column density distribution function (CDDF) isdefined as the number of absorbers per unit absorption distance X ( z ) and per unit column density N H i . The absorption distance iscalculated using Eq. 1. Empirically, the di ff erential distributionfunction is reasonably well described by a single power law at z ∼ N H i = [13 ,
22] asd n d N H i d X = d n d N H i d X ! N β H i , (4)where (d n / (d N H i d X )) gives the normalisation point of the dis-tribution function and β denotes its slope. However, the detailedshape of the di ff erential column density distribution function isdependent on the N H i column density range (Prochaska et al.2010; Altay et al. 2011). It shows a flattening around the tran-sition from the forest to the Lyman limit systems at N H i atlog N H i ∼
17. Then it shows a steepening at log N H i ∼
20 wherea transition occurs from the sub-damped Ly α systems to thedamped Ly α systems.In Fig. 7 we present the results using the Ly α -only fits at1 . < z < .
2. Note that the redshift range used for the CDDFanalysis is di ff erent from the one used for the dn / dz analysis inSection 3.1. The total absorption distance X ( z ) at 1 . < z < . N H i = .
25 is used at log N H i = [12 . , . N H i = [15 . , . N H i >
19 at z ∼ . The topx-axis is in units of the gas overdensity δ which was computedaccording to Eq. 10 by Schaye (2001) N H i ∼ . × (1 + δ ) / ×× T − . Γ − + z ! / Ω b h . ! / f g . ! / cm − . (5)Here, the gas temperature T is assumed to be T = T × K,the photoionisation rate
Γ = Γ × − sec − . The parameter f g denotes the fraction of mass in gas. The IGM gas tempera-ture is assumed to be governed by the e ff ective equation of state T = T (1 + δ ) γ − , where T is the temperature at the cosmicdensity (Hui & Gnedin 1997). For Γ and γ , we interpolated re-sults obtained by Bolton et al. (2008). We assumed that T is2 × K, f g = .
16, and Ω b h = . ff erent N H i at di ff erent z ,the overdensity plotted in Fig. 7 is at the mean redshift, z = . N H i ∼ . N H i = [12 . , N H i < .
75, the CDDF starts to devi-ate from a power law due to the sample incompleteness forweak absorbers (Kim et al. 1997). From the linear regression,we find log (d n / (d N H i d X )) = . ± .
42 and a slope of β = − . ± .
03 for the log N H i = [12 . ,
14] range (the solid The plotted data points from the literature are the reported ones ineach study. Both O’Meara et al. (2007) and Noterdaeme et al. (2009)used the same cosmology as ours, while Petitjean et al. (1993) used the q = X ( z ) in our cosmology isabout 6% smaller than theirs. Since the CDDF uses the logarithm valueof X ( z ), the di ff erence in the CDDF is negligible even without convert-ing their CDDF to our cosmology. Fig. 7.
The di ff erential column density distribution at 1 . < z < . α -only fits. Both black (log N H i ≥ .
75) andgrey (log N H i < .
75) data points show the results from ourquasar sample. The grey data points mark the column densi-ties that are a ff ected by incompleteness. The stars are the datapoints obtained by Petitjean et al. (1993). The filled circles atlog N H i > . < log N H i < . < z > = .
02 by Noterdaeme et al. (2009) and fromO’Meara et al. (2007) at < z > = .
1, respectively. The solid linegives the power law fit to our data for log N H i = [12 . , z ∼ σ Poissonerrors, while the x-axis error bars show the N H i range coveredby each data point. Gas overdensities on the top x-axis are com-puted using Eq. 10 from Schaye (2001) at z = .
55 (see text fordetails).line). This result is slightly lower than β = − .
46 (no errorsgiven) by Hu et al. (1995) (the dotted line) or β = − . ± . N H i > N H i , as previously ob-served (Petitjean et al. 1993; Kim et al. 1997; Prochaska et al. i and C iv forest z ∼ N H i ≤ σ levelat log N H i = [16 ,
4. Analysis using higher-order Lyman lines
In the last section, we checked the Ly α absorber number den-sity evolution and the di ff erential column density distributionobtained from the Ly α -only fits for consistency with previousstudies. The analysis is now revisited with the results from theVoigt profile analysis including the higher order transitions at1 . < z < .
2, hence a sample with a more reliable N H i . Therefore,it can be established whether the dip seen in the di ff erential col-umn density distribution at log N H i between 14 . N H i . Allthe results from this section are tabulated in Appendix A. We now revisit the line number density evolution using the high-order Lyman sample, as described in the previous section. On aquasar by quasar analysis we determine d n / d z for a low columndensity range of log N H i = [12 . , .
0] and for high columndensities of log N H i = [14 , ff erential columndensity distribution function which follows a power-law is cov-ered, whereas the log N H i = [14 ,
17] interval covers those sys-tems responsible for the dip in the column density distributionfunction.The results are presented in Fig. 8. Linear regressions fromthe data are obtained and the resulting parameters are sum-marised in Table 2. Similar to the previous analysis, the linenumber density shows a decrease with decreasing redshift. Nosignificant di ff erences between the two di ff erent fits are present,even though the total redshift coverage used for the high-orderfit is about 20% smaller. In the case of the log N H i = [14 , α -onlyslope of γ = . ± .
36 to γ = . ± .
53 for the high-orderfit. This is in part caused by that the number of high column den-sity absorbers is larger in the high-order fit sample. However, theslopes of the two samples are still in the 2 σ uncertainty range,rendering the two results consistent to each other. Similar resultsare obtained for the log N H i = [12 . , .
0] range. The slope forthe high-order fit increases from γ = . ± .
16 for the Ly α -onlyfit to γ = . ± .
22. Again, the results from the two samplesagree within the 1 σ uncertainty range.In previous studies the number density evolution has beenusually derived on a quasar by quasar analysis. Previous studiesdid not have enough quasar sight lines available to sample thenumber density evolution at smaller redshift interval ∆ z , withoutsu ff ering from small number statistics. Our sample of 18 high-redshift quasars is characterised by a large redshift distance cov-erage in the redshift range of 1 . < z < . mean number density is derived in redshift bins of ∆ z = .
26, starting from z = . Fig. 8.
The line number density evolution derived on a quasarby quasar analysis using the high-order Lyman sample for col-umn density intervals of log N H i = [12 . , .
0] and log N H i = [14 , σ Poisson errors, whilethe x-axis error bars show the redshift range covered by eachsightline. The straight lines denote results from a linear regres-sion to the data with parameters given in Table 2. The data aretabulated in Table A.1.Results of the combined line number density evolution areshown in Fig. 9 for identical column density ranges as used inthe quasar by quasar analysis. Error bars have been determinedusing the bootstrap technique. For comparison, results using theLy α -only fits are overplotted as grey open circles for the highcolumn density bin.The high column density results are similar to the onesobtained from the Ly α -only fits. The number density itself ishigher in the high-order fits, since some strongly saturated sys-tems break up into multiple, strong components in the high-order Lyman transition. In addition, three absorbers (two towardHE0940 − − N H i >
17 in the Ly α -only fit.Therefore, these systems were not included in the Ly α -only re-sults. However, these Lyman limit systems break up into mul-tiple weaker components in the high-order fit and contribute tothe number count in the high order fit analysis. However, the dif-ferences between the two samples are smaller than the statisticaluncertainties.At low column densities, no noticeable di ff erences betweenthe two samples are observed, as expected.Again, linear regressions have been determined and their pa-rameters are given in Table 2. At log N H i = [12 . , . γ = . ± .
24, similar to γ = . ± .
22 from the quasar by quasar analysis. At log N H i = [14 , γ = . ± .
66 is alsosimilar to γ = . ± .
53 obtained from the quasar by quasaranalysis. The slopes from both analyses of our high-order fitsample at log N H i = [14 ,
17] are steeper than the ones obtainedfrom the Ly α -only fit sample. In particular, the ones from thecombined sample di ff er more than 3 σ . This di ff erence is mainlycaused by that the redshift range used for the combined sam-ple is di ff erent for two analyses. For the Ly α -only fit, the mean i and C iv forest Fig. 9.
The mean line number density evolution of the com-bined sample as a function of redshift using the high-orderLyman-series sample for column density intervals of log N H i = [12 . , .
0] and log N H i = [14 , ∆ z = .
26, starting from z = .
90. The vertical er-ror bars indicate 1 σ Poisson errors, while the x-axis error barsshow the redshift range covered by each data point. For compari-son, the results of the Ly α -only fits (grey open circles) are shownfor the log N H i = [14 ,
17] interval. The straight solid lines denoteresults from a linear regression to the binned data. Two dashedlines represent the mean number density evolution of the Ly α -only fit sample for log N H i = [14 ,
17] (log d n / d z = ( − . ± . + (4 . ± . × log(1 + z )) and for log N H i = [12 . , n / d z = (1 . ± . + (1 . ± . × log(1 + z )), respec-tively. Exactly same redshift range was used for both fit samples.The data are tabulated in Table A.2. The parameters of the fitsare given in Table 2.d n / d z is derived for 0 < z <
4, while for the high-order fit it isrestricted to 1 . < z < . Using the high-order fits, we have derived the di ff erential col-umn density distribution function (CDDF) for 1 . < z < .
2, anal-ogous to Section 3.2. In Fig. 10 we show the results for the entireredshift range. As in Fig. 7, the binsize of log N H i = .
25 is usedat log N H i = [12 . , . N H i = [15 . , . X ( z ) = . α -only fit CDDF analysis. As withthe Ly α -only fits, we included observations by Noterdaeme et al.(2009) and O’Meara et al. (2007).The high-order fit results show a power law relation which isalmost identical to the results of the Ly α -only fits. As with theLy α -only fits, the di ff erential column density distribution func-tion shows a deviation from the empirical power law at columndensities between 14 < log N H i <
19. Since the column densitydistribution deviates from a single power law at log N H i ∼ N H i = [12 . , . , , . , .
0] at 1 . < z < .
2, characterising the shape of the dis-tribution function. The resulting parameters are listed in Table 3.
Fig. 10.
The di ff erential column density distribution at 1 . < z < . N H i < .
75 mark thecolumn densities that are a ff ected by incompleteness. The greydata points above log N H i > .
75 represent the results from theLy α -only fit. The dashed line represents a theoretical predictionat z ∼ σ Poisson errors, while the x-axis error bars show the N H i rangecovered by each data point. The filled circles at log N H i > . . < log N H i < . < z > = .
02 by Noterdaeme et al. (2009) and from O’Meara et al.(2007) at < z > = .
1, respectively. The solid line gives the powerlaw fit to our data for log N H i = [12 . , . z = . N H i = [12 . , . N / (d N H i d X )) = . ± .
42 and aslope of β = − . ± .
03. This result is almost identical tothe Ly α -only fit, since di ff erences between the Ly α -only and thehigh-order fits start to be significant at log N H i >
15 (see Fig.10). The high-order fits show a larger number of absorbers at15 < log N H i <
17 than the Ly α -only fits. However, at highercolumn densities, the number of absorbers is lower for the high- i and C iv forest order fits than for the Ly α -only fits. This again indicates thebreaking up of high column density systems into multiple lower- N H i ones when including higher transitions than Ly α . For theentire redshift sample, the slope becomes steeper from ∼ − . ∼ − .
67 at log N H i = [14 , N H i = [15 , ∼ − .
55, a trend shown in the numerical simulation (the dashedline) by Altay et al. (2011) in Fig. 10.In order to determine the redshift evolution of the di ff erentialcolumn density distribution, we split the sample into two redshiftbins: z = [1 . , .
4] and [2 . , . ff erent redshift bins, where we overplot the power-law fitat log N H i = [12 . , .
0] for each redshift bin as the solid line.We also overplot the results of the power-law fit to the entireredshift range 1 . < z < . z = [1 . , . X ( z ) = N H i = [12 . , . γ = − . ± .
04 at high z to γ = − . ± .
04 at low z .However, the slopes are still consistent within 2 σ , i.e. no signif-icant CDDF evolution, cf. Williger et al. (2010). They are alsoconsistent with the result from the entire redshift range within1 σ .Let us now focus on column densities above log N H i > . ff erential column densitydistribution deviates from the power law form for column den-sities log N H i > .
0. The lower panels of Fig. 11 show the dif-ference between the observed CDDF and the power-law fit tothe CDDF for the entire redshift range (the dashed lines). Theentire redshift fit was used since the comparison requires an ab-solute reference. From the lower panels, it is clear that the de-viation from the power law is stronger for the low redshift bin.At the same time, the deviation column density above which thedeviation starts to be noticeable is lower at low redshift, fromlog N H i ∼ . . < z < . N H i ∼ . . < z < . N H i = [12 . ,
16] at z <
2, cf. Fig. 5 of Williger et al. (2010)at z ∼ .
08 and Fig. 9 of Ribaudo et al. (2011) at z <
2. Bothworks also found a steeper CDDF slope of ∼ ff erent fitting methods, the H i se-lection criterion discussed in Section 3.1 and the column densityrange over which the power law was performed. On the otherhand, Prochaska et al. (2010) found a more significant dip in thecolumn density distribution function at log N H I = [14 ,
19] at z ∼ . z ∼ z ∼ σ . These di ff erences couldbe simply due to our small sample size, or due to the di ff erentanalysis method or due to the strong CDDF evolution between z ∼ z ∼ N H i ≥ ff ect becomes evident at log N H i ≥
17 with a shal-lower slope than the extrapolated one at the lower log N H i (Altay et al. 2011). However, the dip in discussion occurs atlog N H i = [14 . , .
0] compared to the extrapolated power-law slope at log N H i = [12 . , . N H i from this single power law starts at log N H i ∼ .
5, where self-shielding has no e ff ect.
5. Characteristics of the metal enriched forest
The discovery of metal lines which are associated with H i ab-sorber in the Ly α forest, such as C iv or O vi (Cowie et al. 1995;Songaila 1998; Schaye et al. 2000a), have raised the questionof how the IGM has been metal enriched. As the forest hasa high temperature and a low gas density, it is not likely toform stars in-situ. Metals should be transferred from galax-ies by e.g. galactic outflows (Aguirre et al. 2001; Schaye et al.2003; Oppenheimer & Dav´e 2006). In recent years, studies ongalaxy-galaxy pairs at high redshift have revealed some evidencethat metals associated with the Ly α forest reside in the circum-galactic medium (Adelberger et al. 2005; Steidel et al. 2010;Rudie et al. 2012). In this interpretation, the metal-enriched for-est cannot be called the IGM in the conventional sense and islikely to show a di ff erent evolutionary behaviour compared tothe metal-free forest. In order to learn more about these enrichedhydrogen absorbers, we characterise C iv enriched H i absorbersin this section by determining their number density evolution anddi ff erential column density distribution. Note that we excludedQ0055 −
269 and J2233 −
606 for both the C iv enriched forest andthe unenriched forest samples in this section, as their C iv regionhas a much lower S / N of ∼
40 per pixel compared to the other 16quasar spectra whose S / N is greater than 100 per pixel in mostC iv regions. Due to the wavelength gap caused by the UVESdichroic setup, the C iv redshift coverage is shorter than the H i coverage for Q0420 − − − ±
200 km s − region from the wavelength gapand included the C iv region only when it covered both doublets.The excluded C iv redshift range for these three quasars is listedin Table 1. In this section, we used the column density and b pa-rameter of H i from the high-order Lyman fit, unless stated other-wise. All the results from this section are tabulated in AppendixA. Unfortunately there is no one-to-one relation between H i linesand C iv lines. Fig. 12 shows a velocity plot (the relative ve-locity centered at the redshift of an absorber vs normalisedflux) of a typical C iv -enriched H i absorber in the spectrum ofHE1122 − i components. Not all H i lines can be directlyassigned to one or only one C iv component. For example, theH i component at − .
02 km s − could be associated either withthe first C iv component at − .
72 km s − or with the secondone at − .
97 km s − , or with both. A general trend is that theassociated C iv features show an increased number of velocitycomponents as N H i increases. The absorption line centers of H i and C iv lines often show velocity di ff erences as well, indicatingthat the H i -absorbing gas might not be co-spatial with the C iv -producing gas. Therefore, we apply a simple assigning methodto our fitted absorber line lists, in order to determine if an H i absorption line is associated with C iv .We consider an H i absorber to be metal enriched if a C iv line with N C iv greater than a threshold value exists within thevelocity range ± ∆ v C iv centered at each identified H i line. Thethreshold N C iv should be large enough not to be a ff ected by theincompleteness of weak C iv detection, but not too large so thatthere are enough C iv enriched absorbers to have a meaningful i and C iv forest Table 3.
Linear regression results for the di ff erential column density distribution as a function of redshift and column density usingthe high-order fit. Here the normalisation point log (d n / (d N H i d X )) is denoted by B . log N H i = . − . N H i = . − . N H i = . − . N H i = . − . z B β B β B β B β . − . . ± . − . ± .
03 10 . ± . − . ± .
09 8 . ± . − . ± .
08 9 . ± . − . ± . . − . . ± . − . ± .
04 11 . ± . − . ± .
14 7 . ± . − . ± .
19 10 . ± . − . ± . . − . . ± . − . ± .
04 9 . ± . − . ± .
12 8 . ± . − . ± .
10 8 . ± . − . ± . Fig. 11.
Upper panels: The di ff erential column density distribution as a function of redshift. Both black and grey data points showthe results from the high-order Lyman sample. The grey data points at log N H i < .
75 mark the column densities that are a ff ectedby incompleteness. The vertical error bars indicate 1 σ Poisson errors, while the x-axis error bars show the N H i range covered byeach data point. The black solid line gives the power law fit for log N H i = [12 . , .
0] at each redshift bin, whereas the dashed lineis the fit to the z = [1 . , .
2] redshift range (see Fig. 10). The overdensity plotted on the top x-axis is calculated at the mean z foreach redshift bin. Lower panels: the residuals from the power law fit from the entire redshift range at log N H i = [12 . , . i component with mul-tiple C iv components and vice versa. As we are not concernedwith the one-to-one relation between N C iv and N H i of each H i component, but the existence of the C iv line for a given searchvelocity range, the multiple assigning of the same componentdoes not a ff ect the results.Two arbitrary choices of ∆ v C iv are considered: a conserva-tive narrow range of ±
10 km s − (a minimum b value of a singleLy α absorption line is roughly 20 km s − ) and a more generousinterval of ±
100 km s − . Fig. 13 shows the C iv column density distribution functionat 1 . < z < . . < z < . . < z < .
1, respectively, and greenopen squares from Songaila (2001) at 2 . < z < .
54. The turn-over seen in green open squares is due to the incompletenesse ff ect, i.e. not all weak C iv can be detected due to noise.Similar to the H i density distribution, the C iv CDDFdoes not fit with a single power law over a large N C iv range. The Pichon et al. result even suggests that the C iv i and C iv forest Fig. 12.
Example of a velocity plot (a relative velocity vsnormalised absorption profile plot) of H i and associated C iv detected in the z = . − iv component is set to be at thezero velocity. The observed spectra are plotted as a histogram,while Voigt-profile fits are as a smooth curve. Thick red curvesare the combined fit from individual components. The heavy tickmarks above the profiles indicate the velocity centroid of eachcomponent. Non-negligible blends by other ions are indicated ingray. The b value (in km s − ) and log N H i with the VPFIT fittingerrors are displayed next a tick mark indicating the center of thecomponent.density distribution might have a non-linear functional form.At log N C iv = [12 . , . N / (d N C iv d X ) = (6 . ± . + ( − . ± . × log N C iv (the solid line). At log C iv = [12 . , . N / (d N C iv d X ) = (11 . ± . + ( − . ± . × log N C iv (the dotted line). If the solid line is taken as a reasonable CDDFsince it fits the low- N C iv CDDF better, our C iv detection can beconsidered complete at log N C iv ≥ . N C iv completeness limitis reasonable is with the column density– b value diagram. Asseen in the 7th column of Table 1, the S / N di ff ers for di ff er- Fig. 13.
The C iv column density distribution. Filled circles areour results at the redshift range used for the high-order fit C iv -enriched H i sample at 1 . < z < .
2. The CCD gap in the C iv region was accounted for. Red filled triangles and blue filleddiamonds are from Pichon et al. (2003) at 1 . < z < . . < z < .
1, respectively. Green open squares are taken fromSongaila (2001) at 2 . < z < .
54. The vertical error bars indi-cate 1 σ Poisson errors, while the x-axis error bars show the N H i range covered by each data point. The black dotted line showsthe linear regression to filled circles at log N C iv = [12 . , .
5] :log d n C iv / (d N C iv d X ) = (11 . ± . + ( − . ± . × log N C iv .The solid line is the power law fit at log N C iv = [12 . , .
5] :log d n C iv / (d N C iv d X ) = (6 . ± . + ( − . ± . × log N C iv .The turn-over at log N C iv ∼ . iv . Similarly, the turn-overseen at log N C iv ∼ . ffi cult to quantify the correct 3 σ detectionlimit for a dataset containing spectra with di ff erent S / N.Fig. 14 shows the log N C iv – b C iv diagram at the two redshiftbins. The vertical heavy dot-dashed lines mark log N C iv = . σ detectionlimit for a spectrum with S / N =
120 (the left side) and 90 (theright side, an approximate lowest S / N) per pixel, respectively. Inthe lower panel, the heavy dashed line is a 3 σ detection limitfor S / N = / Ngreater than the given S / N. Overlaid as a histogram is the dis-tribution of the number of C iv lines with log N C iv ≥ . b C iv . For the distribution, the zero base is set to belog N C iv = .
2. Thick ticks above the distribution mark the me-dian b C iv . There is no correlation between N C iv and b C iv abovethe S / N detection limit at all of the reasonable expected b C iv values.At 2 . < z < . σ b C iv detectionlimit is 23.6 (13.4) km s − for S / N =
120 (90) at log N C iv ∼ . iv at the high redshift bin i and C iv forest CIV lines b C I V ( k m s - ) z < 3.2 S/N = 90S/N = 120 b med = 11.4 km s -1
11 12 13 14 15 16 17log N CIV b C I V ( k m s - ) z < 2.4 b med = 10.5 km s -1 Fig. 14.
Line width vs. column density for the C iv absorptionlines along 16 sightlines excluding Q0055 −
269 and J2233 − σ detection limit for a spectrum with S / N = / N =
90 per pixel. At 2 . < z < .
2, most spectra show S / Ngreater than 90. In the lower panel, the heavy dashed line showsa 3 σ detection limit for S / N = / N spectra. The vertical dotted line indicates the adopted low N C iv bound of log N C iv = . ff ect the C iv detection significantly. The histogramshown with the base at log N C iv = . iv lines as a function of b C iv with the b C iv binsize of 2 km s − .Thick ticks above the number distribution mark the median b C iv for log N C iv ≥ .
2. The total number of C iv lines is 194 and171 at 2 . < z < . . < z < .
4, respectively. Amongthem, 138 and 122 lines have log N C iv ≥ . ∼ ≤
10% of the C iv region.This contamination prevents isolated weak C iv lines from be-ing detected, however, can be treated as a lower-S / N region.Including the telluric-contaminated region, the wavelength cov-erage with S / N ≤
120 is about 1018 Å. In the C iv wavelengthregion with S / N ≥ iv lines withlog N C iv = [12 . , .
3] is 8. Out of those 8, none has b C iv ≥ . − . It is possible that a large fraction of C iv has a b C iv valuegreater than 23.6 km s − , and therefore, would be completelymissed even in the high-S / N spectra analysed here. However, asclearly seen in the upper panel of Fig. 14, the b C iv distributionat log N C iv ≥ . iv has b C iv ≥ . − . If a large fraction of C iv lines were broader regardlessof N C iv , the region around log N C iv ∼ . b C iv ∼
25 km s − in Fig. 14 should have been more crowded. Therefore, it is notlikely that many weak C iv lines with b C iv ≥ . − havebeen missed for S / N ≥ b C iv ≥ . − at log N C iv = [12 . , . iv lines would have beenmissed in the S / N ≤
120 region. One is a single isolated line,while the other is part of a multi-component C iv complex. Weassumed that the number of C iv lines with log N C iv ∼ . b C iv ≥ . − is 2 in the wavelength range of 2174 Å,i.e. the total wavelength range with S / N ≥ iv lines have a negligible clustering, about 1 (or2 × / (3192 − = .
9) C iv line with log N C iv ∼ . b C iv ≥ . − could have been missed in the C iv forestregion with S / N ≤ i lines with log N H i = [12 . , .
5] is foundwithin ±
100 km s − centered at these two C iv lines. The totalnumber of high-order-fit H i lines in the H i forest region corre-sponding to the S / N ≥
120 C iv forest region is [265, 363, 233,120, 50, 27, 5] for log N H i = [12.75–13.00, 13.0–13.5, 13.5–14.0, 14.0–14.5, 14.5–15.0, 15.0–16.0, 16.0–17.0], respectively.Among them, a negligible number of H i lines, [0, 0, 2, 0, 1, 0,1], is associated with these two C iv lines for the same N H i range,or less than 2%. The remaining one H i line has log N H i ≥ . iv line belongs to a C iv complex of a partialLyman limit system. Although the number of undetected weakand broad C iv lines in the S / N ≤
120 region is a very rough esti-mate, less than 2% of the H i lines would be mis-classified as theunenriched forest due to the incompleteness at log N C iv ∼ . / N limits of individual spectrais much higher than in the high redshift bin. If a similar logicwere applied to, the total C iv coverage is 5485 Å, and the onewith S / N ≤
120 is 2719 Å. In the S / N ≥
120 C iv region, thereis a total of 10 C iv lines with log N C iv = [12 . , . b C iv ≥ . − , the maximum b C iv valueto be detected for a line with log N C iv = [12 . , .
3] in a S / N =
90 spectrum. Among those 6 C iv lines, two C iv lines are partof a two-isolated-component complex, with the rest being partof a multi-component complex. Since stronger H i lines tend tobe associated with a C iv complex, using all these 6 C iv linesto calculate the associated H i fraction leads to a biased result.Therefore, we used 4 C iv lines which are part of a C iv com-plex with less than 3 components in order to estimate the missedenriched H i fraction.There is a total of 11 H i lines at log N H i = [12 . , . − centered at the 4 weak C iv lines. The ra-tio of the C iv enriched H i lines and the total H i lines in thewavelength regions corresponding to the S / N ≥
120 C iv forestis [2 / / / /
59, 1 /
28, 0 /
10] for log N H i = [12.75–13.00, 13.0–13.5, 13.5–14.0, 14.0–14.5, 14.5–15.0, 15.0–16.0],respectively, or ≤ iv is negli-gible even at the low redshift bin.Note that our estimate on the true undetected C iv frac-tion is uncertain. However, from Fig. 13, the incompleteness atlog N C iv = . σ Poisson error.While it is clear that the incompleteness does not play a sig-nificant role in the H i detection down to log N H i = .
75 and theC iv detection down to log N C iv = .
2, the combination of theH i and C iv detection could introduce a bias in the C iv assigningmethod. The pixel optical depth method which correlates the op-tical depth of H i ( τ H i ) and C iv ( τ C iv ) at the same redshift shows i and C iv forest z < 3.2 l og N C I V ∆ v = ±
100 km s -1 N HI l og N C I V ∆ v = ±
10 km s -1 Fig. 15.
The N H i – N C iv diagram for log N H i = [12 . , .
8] fromthe high-order fit sample at 1 . < z < .
2. The upper panel isfor the ∆ v C iv = ±
100 km s − sample, while the lower panel forthe ∆ v C iv = ±
10 km s − sample. Open circles represent H i ab-sorbers associated with all the possible C iv components, sincea single H i line could be assigned to several C iv lines. On theother hand, red filled circles indicate a H i absorber associatedwith only one closest C iv . The total number of open (filled) cir-cles is 1082 (451) and 184 (163) for the ∆ v C iv = ±
100 km s − and ∆ v C iv = ±
10 km s − sample, respectively.that at z ∼ median τ H i and the median τ C iv down to log τ H i ∼ .
15 orlog N H i ∼ .
73 for b H i =
28 km s − (a median b H i of the forestat z ∼ .
5) (Schaye et al. 2003). Below log τ H i ∼ .
15, the τ H i sig-nal is blended with noise at log τ C iv ∼ .
001 or log N C iv ≤ . b C iv = . − (a median b C iv of all the C iv lines in ourUVES sample).This result suggests that many low- N H i absorbers might bemis-assigned as unenriched H i absorber in our C iv assigningmethod. Unfortunately, the lower log N C iv ∼
11 limit that a typ-ical optical depth analysis explores is an order of magnitudelower than our adopted low N C iv limit of log N C iv = .
2. Thislog N C iv ∼
11 limit cannot be obtained even in the highest S / NC iv region with S / N ≥
220 in our UVES spectra. Therefore, ourC iv analysis can not confirm, nor refute the results from the op-tical depth method.Fig. 15 shows the N H i – N C iv diagram for the ∆ v C iv = ±
100 km s − sample (the upper panel) and for the ∆ v C iv = ±
10 km s − sample (the lower panel). Since one H i line can beassociated with several C iv lines, data points at the same N H i represent the same H i absorber. Open circles show all the H i absorbers associated with all the possible C iv lines. Red filledcircles indicate H i absorbers associated with only one closest C iv within the search velocity range. With a larger search veloc-ity range, the ∆ v C iv = ±
100 km s − sample has more lines. Thenumber of the red filled circles increases abruptly at log N H i ≤ . i absorbers is larger than stronger H i absorbers.If our C iv assigning method were biased due to our failureto detect C iv lines toward lower N H i values, there should be acorrelation in N H i and N C iv , such that a lower N H i line tends tobe associated with a lower N C iv line (cf. the relation betweenthe median τ H i and the median τ C iv ) or the number of the C iv -enriched H i lines at lower N H i is smaller. No such correlationsare seen in Fig. 15. Note that our method deals with the fittedindividual lines, while the optical depth analysis works with sta-tistical, median values. The optical depth analysis is not sensitiveto any minor C iv population, such as high-metallicity absorbers(Schaye et al. 2007).In reality, the detection of weak C iv is dependent on the lo-cal S / N as well as the combination of b C iv and N C iv . The S / Nof a spectrum does not change in a way to satisfy a higher S / Nat strong H i absorbers and a lower S / N at weaker H i absorbersor vice versa. Usually the S / N changes over a larger wavelengthinterval than the wavelength interval between typical strong H i lines. In addition, strong and weak H i lines do not occupy aportion of a spectrum separately, but exist mixed along the spec-trum. If a weak C iv were detected associated with a high- N H i line, a similar strength of C iv , if exists, should be detected forlow- N H i lines nearby or in a similar S / N region. Therefore, un-less a majority C iv fraction at lower N C iv and / or lower N H i has avery large b C iv value, i.e. high gas temperature, our C iv assign-ing method does not introduce a serious selection bias within theadopted N C iv limit. iv -enrichedabsorbers In a similar way to the analysis of all the H i absorbers, we cal-culate the absorber number density evolution d n H i + C iv / d z ona quasar by quasar analysis for all the C iv -enriched H i ab-sorbers. The resulting d n H i + C iv / d z evolution is shown in Fig.16 for the ∆ v C iv = ±
100 km s − and ∆ v C iv = ±
10 km s − in-terval from the high-order Lyman fit samples. For the ∆ v C iv = ±
100 km s − sample, the Q1101 −
264 sightline does not showany C iv in the redshift range of interest due to its short red-shift coverage. For the ∆ v C iv = ±
10 km s − sample, 7 sightlines(HE2347 − − − − − −
380 and Q1101 − iv -enriched H i absorbers at log N H i = [12 . , . − iv -enriched H i ab-sorber at log N H i = [14 , iv tends to be associated with strongH i absorbers and that the small search velocity is not adequatedue to the velocity di ff erence between H i and C iv observed inmany enriched absorbers. For these sightlines, d n H i + C iv / d z is 0.Therefore, their log n H i + C iv / d z is set to be 0 with a downwardarrow in Fig. 16.As for the entire Ly α forest analysis, the d n H i + C iv / d z evolu-tion resembles a power law. Therefore, linear regressions havebeen obtained from the data set and its results are summarised inTable 4. Sightlines showing no C iv -enriched H i absorbers werenot included in the regression. Similar to the entire high-order-fit H i sample, the ∆ v C iv = ±
100 km s − sample shows a de- i and C iv forest Fig. 16.
Quasar by quasar line number density evolution of C iv -enriched H i absorbers. The left panels are derived from the ∆ v C iv = ±
100 km s − sample, while the right panels represent the ∆ v C iv = ±
10 km s − one. The open circles in the upper panel representC iv -enriched absorbers having log N H i = [12 . , .
0] and the filled circles in the lower panel represent log N H i = [14 , σ Poisson errors, while the x-axis error bars show the redshift range covered by each sightline. Sightlineshaving no C iv -enriched H i absorbers for a given velocity range are plotted at log d dn C iv / d dz =
0. The solid lines represent linearregressions to the data, using the parameters summarised in Table 4. Sightlines with no C iv -enriched absorbers, log d n H i + C iv / d z isplotted to be 0 with a downward arrow.cline in the C iv -enriched absorber number density with decreas-ing redshift. This behaviour is present in both column densityranges. Comparing these results with the quasar-by-quasar d n / d z of the entire high-order fit sample at 1 . < z < . iv -enriched absorbers at log N H i = [14 ,
17] has a steeperslope (5 . ± . σ . Therobust result on the d n H i + C iv / d z evolution requires a large red-shift coverage and more sightlines per redshift coverage, espe-cially at high column density range. With a lack of more C iv forest data at z forest >
3, d n H i + C iv / d z derived in this study at thehigh column density range should be considered less robust com-pared to the entire H i d n / d z . Similarly, the d n H i + C iv / d z slope(0 . ± .
92) at log N H i = [12 . , .
0] is also consistent withthe one (1 . ± .
22) of the entire high-order-fit forest sample,given the rather large uncertainty. The actual number densitiesare lower at both column density ranges.This becomes apparent in the left panel of Fig. 17, wherethe ratios of the number densities of the C iv -enriched systemsd n H i + C iv / d z and the number density of the entire sample d n / d z are shown. The results for the ∆ v C iv = ±
100 km s − sample(filled circles) show that there is no significant evolution ofthe C iv enrichment fraction for log N H i = [12 . , . N H i = [14 , z ∼ z >
3. For the low column density log N H i = [12 . , .
0] sample we find that around 5% of all the H i ab-sorbers show C iv enrichment. The C iv enrichment fraction ishigher for larger column densities of log N H i = [14 , iv -enriched.This picture changes slightly for the ∆ v C iv = ±
10 km s − sample. For the high column densities, the d n H i + C iv / d z evolution Table 4.
Linear regression results for the number density evolu-tion d n H i + C iv / d z of the C iv -enriched H i forest absorbers in thequasar by quasar analysis. ∆ v C iv = ±
100 km s − ∆ v C iv = ±
10 km s − ∆ log N H i log A γ log A γ . − . . ± .
49 0 . ± .
92 2 . ± . − . ± . . − . − . ± .
53 5 . ± . − . ± .
64 4 . ± . is less strong compared to the one of the ∆ v C iv = ±
100 km s − sample. However, both are still consistent within 1 σ due to alarge uncertainty. Only the number density itself decreases bya factor of 1.7. The enrichment fractions in the right panel ofFig. 17 show that now around 20% to 30% of the high columndensity H i absorbers are C iv -enriched.On the other hand, d n H i + C iv / d z increases with decreasingredshift for the low column densities. Its negative slope of γ = − . ± .
94 shows an opposite behaviour from the one( γ = . ± .
92) of the ∆ v C iv = ±
100 km s − sample. Thisnegative slope is in part caused by the inadequacy in our C iv assigning method at the small search velocity, and in part by thefact that the number of high-metallicity absorbers increases atlow redshift (Schaye et al. 2007). However, due to several sight-lines containing no C iv -enriched weak H i absorbers which arenot included in the power-law fit, the negative slope should notbe taken literally. The fraction of enriched absorbers increasesfrom ∼ z ∼ ∼ z ∼ .
1, as expected fromd n H i + C iv / d z at the low H i column density. However, keep inmind that the cosmic variance is large as some sightlines showno enriched weak H i absorbers. i and C iv forest Fig. 17.
The fraction of the C iv -enriched H i absorber number density to the total absorber number density as a function of redshift.The left panels are derived from the ∆ v C iv = ±
100 km s − sample, while the right panels represent the ∆ v C iv = ±
10 km s − sample. The black open circles represent a column density interval of log N H i = [12 . , .
0] and the filled circles representlog N H i = [14 , σ Poisson errors, while the x-axis error bars show the redshift range coveredby each sightline. In the left panel for log N H i = [12 . , .
0] (gray open circles), two lowest data points at log(1 + z ) ∼ . z ∼
2) including an upper limit are from Q1101 −
264 and Q0122 − iv -enriched H i absorbers are plotted as upper limits with an arbitrary value of0.05 and 0.002 for log N H i = [14 ,
17] and log N H i = [12 . , . iv absorbers assigned tothe low H i column density. One group is associated with strong,saturated high column density H i absorbers. These absorbers aresometimes accompanied by lower N H i absorbers within a veloc-ity range of ∆ v <
200 km s − . In these systems, the C iv absorp-tion is usually found within 20 km s − to the strongest H i lines(Kim et al. 2013, in preparation ). Therefore, these accompaniedlow H i column density systems get associated with the C iv ab-sorbers if the velocity range ∆ v C iv is large. With a small veloc-ity search interval, however, only H i systems that have C iv intheir direct vicinity are flagged as C iv -enriched. This means thatthe aforementioned low column density systems around strongabsorbers are not considered C iv -enriched in a small velocitysearch interval.Another C iv -enriched group consists of usually isolated, lowcolumn density H i absorbers associated with strong C iv ab-sorption, i.e. the same high-metallicity forest population studiedby Schaye et al. (2007). An example of such a system towardHE1122 − i absorption feature is hardly recognisable, while strong C iv andN v doublets are present. The existence of both doublets makesthe identification of this absorber secure. Due to the low N H i and high N metals , these systems show a higher ionisation anda higher metallicity compared to a typical absorber with simi-lar N H i (Carswell et al. 2002; Schaye et al. 2007). Schaye et al.(2007) speculate that these systems could be responsible fortransporting metals from galaxies to the surrounding IGM. Asthe velocity di ff erence between H i and metal lines for thesesystems are usually very small, they dominate the weaker C iv -enriched forest at log N H i <
14 for the ∆ v C iv = ±
10 km s − . Inaddition, the high-metallicity absorbers are more common at lowredshift.The di ff erent characteristics of these two C iv groups ex-plains the di ff erent d n C iv / d z behaviour between the ∆ v C iv = ±
100 km s − and ∆ v C iv = ±
10 km s − samples at log N H i = [12 . , . Fig. 18.
A velocity plot of a highly enriched C iv absorber at z = . − z = . α absorption seenat the zero velocity, both C iv and N v doublets are present tosecure the existence of this absorber. Note that the y-axis rangefor each ion is di ff erent: from the normalised flux 0 to 1 for H i and from 0.5 to 1 for the rest of the ions. i and C iv forest Fig. 19.
The distribution function for C iv -enriched H i lines for ∆ v C iv = ±
100 km s − (red filled squares) and for ∆ v C iv = ±
10 km s − (blue stars) at 1 . < z < .
2. Also shown isthe di ff erential column density distribution function for all H i Ly α absorbers excluding Q0055 −
269 and J2233 −
606 (blackfilled circles) in the same redshift range analysed for the C iv -enriched forest. The solid line indicates the fit to filled circlesfor log N H i = [12 . , .
0] : log d N / (d N H i d X ) = (7 . ± . + ( − . ± . × log N H i . The vertical errors indicate 1 σ Poissonerrors, while the x-axis error bars show the N H i range coveredby each data point. All the grey data points indicate that the dataare incomplete at log N H i < . < z < ff erent fromthe typical, low-metallicity forest and resides in a di ff erent inter-galactic space. However, due to the low gas density and hightemperature, the Ly α forest does not have in-situ star forma-tion. Metals associated with the H i forest should have beentransported from nearby galaxies. In other words, all the C iv -enriched absorbers are close to galaxies. iv -enriched forest Fig. 19 shows the di ff erential column density distribution func-tion for C iv -enriched H i absorbers for 1 . < z < .
2. Red filledsquares and blue stars represent the search velocity ranges of
Table 5.
Linear regression results for the di ff erential columndensity distribution of the C iv -enriched forest at log N H i = [14 . , . n / (d N H i d X )) isdenoted by B . ∆ v C iv = ±
100 km s − ∆ v C iv = ±
10 km s − z B β B β . − . . ± . − . ± .
08 5 . ± . − . ± . . − . . ± . − . ± .
17 3 . ± . − . ± . . − . . ± . − . ± .
10 5 . ± . − . ± . ∆ v metal = ±
100 km s − and ∆ v metal = ±
10 km s − , respectively.Black filled circles are for all H i lines (excluding J2233 −
606 andQ0055 − N H i = .
25 is used at log N H i = [12 , N H i = [15 , N H i = [12 . , .
0] :log d N / (d N H i d X ) = (7 . ± . + ( − . ± . × log N H i .The total absorption distance is X ( z ) = . N H i >
15, the CDDF of the enriched forest is notsensitive to our choice of the search velocity and the ∆ v metal = ±
100 km s − CDDF becomes almost identical with the CDDFof the entire H i sample. For the column densities log N H i = [14 , i ab-sorbers at log N H i = [12 . , . N H i <
15, the distribution function of the C iv -enrichedforest starts to deviate significantly from the CDDF of theentire H i sample. The CDDF of the C iv -enriched H i foreststarts to flatten out toward lower N H i at both search velocityranges. Furthermore the flattening of the enriched forest dependsstrongly on the choice of ∆ v C iv . The large search velocity resultsin a steeper slope with a less fluctuation than the small one. Thisis due to the ∆ v C iv = ±
10 km s − sample being predominantlysensitive to highly enriched absorbers at log N H i <
14 and lesssensitive to mis-aligned broad C iv lines with b ≥
10 km s − .Note that our method to associate H i with C iv is only depen-dent on the relative velocity di ff erence between the line centers,but not the C iv profile shape. The large velocity range includesbroader C iv lines up to b ∼
100 km s − as well as narrow, highlyenriched absorbers. The ∆ v C iv = ±
100 km s − velocity range isa better filter to associate H i and C iv .The flattening of the distribution function seen at log N H i <
15 by C iv -enriched absorbers cannot be caused by the incom-pleteness of the H i sample. The H i incompleteness would resultin a similar flattening as is seen at log N H i < .
75 for the entiresample (as seen in Fig. 7). However, our sample of H i absorbersis complete for column densities larger than log N H i > . iv -enriched forest at log N H i <
15 could be in part caused by themissed weak, broad C iv lines. However, Fig. 13 shows that theC iv CDDF at log N C iv > . ff ected by the C iv incompleteness. The number ratio of the entire H i forest linesand the C iv -enriched forest lines at log N H i ∼
13 is ∼
25 forthe ∆ v C iv = ±
100 km s − sample. This ratio increases to ∼ ∆ v C iv = ±
10 km s − sample. Even if we took a max-imum correction for the C iv incompleteness of 50%, roughlyconsistent with the results by Giallongo et al. (1996) (see theirSection 2.3), the CDDF flattening of the enriched forest towardlower N H i is still present. Therefore, this flattening is real and i and C iv forest Fig. 20. Di ff erential column density distribution function for enriched and unenriched absorbers in our high-order fit sample us-ing ∆ v C iv = ±
100 km s − (upper panels) and ∆ v C iv = ±
10 km s − (lower panels) at the two di ff erent redshift ranges. Blackfilled circles and gray stars mark unenriched absorbers. Red filled squares and blue stars indicate the C iv -enriched forest for the ∆ v C iv = ±
100 km s − sample and the ∆ v C iv = ±
10 km s − sample, respectively. Both Q0055 −
269 and J2233 −
606 are excluded inthe analysis. The solid black line indicates the fit to the entire H i sample and the whole redshift range at log N H i = [12 . , .
0] asin Fig. 19. Red and blue dashed lines represent the fit to each C iv -enriched forest sample at log N H i = [14 . , σ Poisson errors, while the x-axis error bars show the N H i range covered by each data point. The lower parts of the panelsshow the di ff erence between the observed CDDF and the expected CDDF from the power-law fit obtained for the entire H i samples(black solid lines).physically related to the characteristics of the C iv -enriched ab-sorbers only with N C iv > . ff erential column density distribu-tion of the C iv -enriched forest flattens at low column densitiescan be easily explained by the fact that the enrichment fractionwith log N C iv > . N H i decreases. At log N H i = [13 . , . , . , . , . , . ∆ v C iv = ±
100 km s − sampleis roughly [4 , , , , , ff erence between theentire H i CDDF and C iv -enriched CDDF in Fig. 19. i and C iv forest The di ff erent CDDF shape between the C iv -enriched ab-sorbers and unenriched absorbers strongly supports that the C iv -enriched absorbers arise from the di ff erent physical environ-ment, i.e. the circum-galactic medium, while the unenriched for-est has its origin as the intergalactic medium. The fact that thenumber of C iv -enriched absorbers decreases with decreasing N H i is also consistent with the picture of IGM metal enrich-ment models by galactic winds (Aguirre et al. 2001). The lowerthe H i column density of absorbers is, the farther they are fromhigh-density gas concentrations where galaxies are formed. Asgalactic winds have a limited life time and outflow velocity totransport metals in to the low-density IGM, weaker absorberswill not be likely to be metal enriched.The redshift evolution of the distribution function of C iv -enriched and unenriched absorbers ( not the entire H i absorbers)is shown in the upper panels of Fig. 20 for the ∆ v C iv = ±
100 km s − sample and in the lower panels for the ∆ v C iv = ±
10 km s − sample at the redshift ranges z = [1 . , .
4] and[2.4, 3.2]. The total absorption distance is X ( z ) = . z = [1 . , .
4] and [2.4, 3.2], respectively, exclud-ing Q0055 −
269 and J2233 − N H i bin, the binsize of log N H i = . N H i = [12 . , . iv . Red filled squares and blue stars indi-cate the C iv -enriched forest for the ∆ v C iv = ±
100 km s − sam-ple and the ∆ v C iv = ±
10 km s − sample, respectively. The solidblack line indicates the power-law fit to the entire H i sample at1 . < z < . N H i = [12 . , .
0] as in Fig. 10. Redand blue dashed lines represent the power-law fit to each C iv -enriched forest sample at log N H i = [14 ,
17] (see Table 5).The upper panel of Fig. 20 suggests that the entire absorberpopulation can be considered as the combination of two pop-ulations of well-characterised absorbers, the enriched absorbersand the unenriched absorbers. The C iv -enriched absorbers dom-inate at log N H i >
15. Their CDDF is well-described as a powerlaw. The slope β ∼ − .
45 obtained at log N H i = [14 . ,
17] (reddashed lines) is similar to the slope β ∼ − .
44 for the entire H i sample at log N H i = [12 . , .
0] at both redshifts. The normali-sation value for the C iv -enriched forest is smaller, with about 10times lower absorber numbers. The enriched absorbers do notshow any strong redshift evolution at log N H i >
15, while theCDDF flattening at log N H i <
15 seems to be weaker at the lowredshift. The unenriched absorbers dominate at log N H i <
15 witha power-law CDDF. At higher N H i , the unenriched absorbersbecome significantly deviated from the extrapolated power lawobtained at lower N H i . There are no unenriched absorbers atlog N H i ≥ . ∆ v C iv = ±
10 km s − sample showsimilar results. There is no strong redshift evolution for the C iv -enriched absorbers at log N H i >
15. Again, there is a sugges-tion that the flattening at log N H i <
15 becomes less significantat lower redshifts. The unenriched forest starts to dominate atlog N H i <
15. However, the ∆ v C iv = ±
10 km s − sample shows aless-smooth CDDF. The highest- N H i data point at z = [2 . , . iv to H i when a small search velocity was used. Absorbers contributingthis data point are part of multi-component high column densitysystems. Their associated C iv shows a rather simple, broad, butmis-aligned profile from the H i center of saturated Ly α profiles.The H i line center of some components resolved at high-orderLyman lines is sometimes at ≥
10 km s − from the closest C iv component and thus they are flagged as the unenriched forest.In both samples, the two populations overlap at log N H i ∼ N H i ∼ . Table 6. H i density relative to the critical density at log N H i = [12 . , . i forest Ω H i , the enriched forest Ω H i + C iv and the unenriched forest Ω H i − C iv . Units are 10 − h − . ∆ v C iv = ±
100 km s − ∆ v C iv = ±
10 km s − z Ω H i Ω H i + C iv Ω H i − C iv Ω H i + C iv Ω H i − C iv shown in the CDDF for the entire H i sample in Fig. 10 is a resultof combining two di ff erent populations which show a di ff erentCDDF shape.To obtain a rough idea on the H i density relative to thecritical density of the entire forest ( Ω H i ), the enriched for-est ( Ω H i + C iv ) and the unenriched forest ( Ω H i − C iv ), we usedEq. (A12) from Schaye (2001) at log N H i = [12 . , . i to obtain the total hydrogen density Ω H was not corrected,since it is highly uncertain. The resulting mass fractions forlog N H i = [12 . , .
0] are given in Table 6. The derived CDDFis not well-constrained at log N H i ≥
16 due to the low numberstatistics. Therefore, the derived Ω values in Table 6 are onlyrough numbers. The ratio of Ω H i + C iv and Ω H i might decrease bya factor of 2 at low redshift for both ∆ v C iv samples. However, ahigh uncertainty in deriving Ω values does not allow to assurethis decrease. The C iv -enriched forest accounts for ∼
40% ofthe entire forest in mass at 1 . < z < . ∆ v C iv =
6. Conclusions
Based on an in-depth Voigt profile fitting analysis of 18 high-redshift quasars obtained from the ESO VLT / UVES archive, wehave studied ∼ i absorbers to investigate the numberdensity evolution and the di ff erential column density distribu-tion function at 1 . < z < . N H i = [12 . , . α transitionand another by including higher order Lyman transitions such asLy β and Ly γ . These higher order transitions provide a more re-liable column density measurement of saturated absorption sys-tems, since saturated and blended lines often become unsatu-rated at higher order transitions. This also enables us to resolvethe structure of absorbers more reliably. This study has increasedthe sample size by a factor of 3 from previous similar studies at z >
2. In addition, we have investigated whether there exist anydi ff erences in the N H i evolution between the C iv -enriched forestand the unenriched forest.We have found that the results based on the Ly α -only fit arein good agreement with previous results on a quasar by quasaranalysis. For our data only (values in parenthesis indicate re-sults including high-quality data from the literature at z > n / d z is d n / d z = (1 . ± . × (1 + z ) . ± . ((1 . ± . × (1 + z ) . ± . ) and d n / d z = (0 . ± . × (1 + z ) . ± . ((0 . ± . × (1 + z ) . ± . ) at log N H i = [13 . ff erence in theexponent between our sample and the sample including the datafrom the literature for stronger absorbers is caused by the factthat our sample does not cover a large redshift range and thatthe evolution of d n / d z is more significant for stronger absorbers.The scatter between di ff erent sightlines becomes larger at lower i and C iv forest redshifts and stronger absorbers due to the evolution of the large-scale structure.Combining our Ly α -only fit analysis at 1 . < z < . . < z <
4, the mean numberdensity evolution is not well described by a single power lawand strongly suggests that its evolution slows down at z ≤ . n / d z ∝ (1 + z ) . ± . and d n / d z ∝ (1 + z ) . ± . at log N H i = [13 . , .
0] and [14 , ff erential column density distribution function(CDDF) from the Ly α -only fit analysis is also consistent withprevious results. The single power-law exponent is − . ± . . < z < . N H i = [12 . N H i > . − . α -only fits. Thed n / d z evolution based on a quasar by quasar analysis yields avery similar result to the Ly α -only fit. The mean d n / d z basedon the combined sample from our quasars at 1 . < z < . n / d z = (1 . ± .
13) (1 + z ) . ± . and d n / d z = ( − . ± .
36) (1 + z ) . ± . at log N H i = [12 .
75, 14.0] and [14, 17], re-spectively.Using the high-order fits, we have derived the di ff erentialcolumn density distribution function at 1 . < z < . N H i = [14 ,
18] as seen in the Ly α -only-fit CDDF analysis. At 1 . < z < .
2, the power-law exponentof the di ff erential column density distribution function is − . ± . − . ± .
09 and − . ± .
08 at log N H i = [12 . , . ff erential column density distributionfunction for two redshift bins z = [1 . , . , and [2.4, 3.2],we observe that a deviation from the expected power-law atlog N H i = [14 . , .
0] is more prominent at lower redshifts. Inaddition, the power-law seems to be slightly steeper at the lowredshift for the column density range log N H i = [12 . , .
0] inwhich the distribution function follows a perfect single powerlaw. However, the CDDF at two redshift bins is consistent withno redshift evolution within 2 σ .Further, we have split the entire H i absorbers excluding 2quasars with a lower S / N C iv region into two samples: ab-sorbers associated with C iv tracing the metal enriched forest,and absorbers associated with no C iv tracing the unenrichedforest. A H i absorber is considered C iv -enriched, if a C iv linewith log N C iv greater than a threshold value is found within agiven search velocity interval centered at each H i absorptioncenter. The threshold log N C iv = . iv distribution function and the N C iv – b C iv diagram show that theC iv detection is reasonably complete down to log N C iv = . b C iv value found at log N C iv ≥ . ∆ v C iv = ±
100 km s − and ∆ v C iv = ±
10 km s − .At log N H i = [14 , n H i + C iv / d z of the C iv -enrichedH i absorbers show a similar evolution compared to the oneof the entire Ly α forest, with a power-law decrease in num-ber density with decreasing redshift. The power-law slope is[0 . ± . , . ± .
99] for log N H i = [12 . , .
0] and [14,17] at 1 . < z < . ∆ v C iv = ±
100 km s − sample.The enriched fraction is fairly constant with redshift at 1 . < z < .
2. About 5% of all absorbers show an association with C iv at log N H i = [12 . , N H i = [14 ,
17] for the ∆ v C iv = ±
100 km s − sample.For ∆ v C iv = ±
10 km s − sample, the low column densityenriched absorber suggests that d n H i + C iv / d z increases as red- shift decreases, i.e. a negative slope of − . ± .
94. Part of thisbehaviour is caused by the fact that high-metallicity absorberswhich are more sensitive to the small search velocity becomemore abundant at low redshift. However, this negative evolutionshould not be taken literally since about a half of sightlines doesnot show enriched absorbers at log N H i = [12 . , . ff erential column density distribution function for theenriched and unenriched systems show a significant di ff erence.However, each shows a well-characterised CDDF. At log N H i ≤ .
0, the unenriched forest dominates and its distribution showsa power law similar to the entire forest sample. On the otherhand, the C iv -enriched forest is found to flatten out at log N H i ≤
15. Depending on the search velocity interval, the number of en-riched systems is a factor of 25 ( ∆ v C iv = ±
100 km s − ) to 260( ∆ v C iv = ±
10 km s − ) lower than the one of the unenriched sys-tems at log N H i =
13. This flattening is mainly caused by the factthat the enriched fraction of the Ly α forest decreases as log N H i decreases.At the higher N H i range, the C iv -enriched forest domi-nates. Its distribution function can be described as a power lawwith its slope of − . ± .
08 similar to the power-law slope( − . ± .
03) of the entire H i forest at log N H i = [12 . , . ∼
10 times lower in the ab-sorber number. The unenriched forest disappears very rapidly aslog N H i increases.The distribution function of the entire H i forest can be de-scribed as the combination of these two well-characterised pop-ulations, overlapping at log N H i ∼
15. The deviation from thepower law at log N H i = [14 ,
17] seen in the CDDF for the en-tire H i sample is a result of combining two di ff erent H i popu-lations with a di ff erent CDDF shape. This result supports otherobservational evidence from absorber-galaxy studies at z ∼ α for-est are within ∼
100 kpc of galaxies (Adelberger et al. 2005;Steidel et al. 2010). Absorber-galaxy studies suggest that theC iv -enriched and unenriched forest would arise from the dif-ferent spatial and physical locations, therefore having a di ff er-ent physical / evolutionary behaviour suggested by the di ff erentCDDF shape. Therefore, our results combined with absorber-galaxy studies indicate that the C iv -enriched forest is thecircum-galactic medium, while the unenriched forest has its ori-gin as the intergalactic medium.At 1 . < z < .
2, the C iv -enriched forest contributes ∼ i density relative to the criticaldensity for the ∆ v C iv = ±
100 km s − sample. Acknowledgments
We are grateful to Drs. Martin Haehnelt, Jamie Bolton andGerry Williger for insightful discussions and comments. We arealso grateful to our anonymous referee for very constructivecomments. A.P. acknowledges support in parts by the GermanMinistry for Education and Research (BMBF) under grant FKZ05 AC7BAA.
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Appendix A: Data
In this appendix we present all the data for the quasar by quasarnumber density evolution (Table A.1), the mean number densityevolution (Table A.2), the di ff erential column density distribu-tion (CDDF) of the entire H i sample (Table A.3), the CDDF ofthe C iv -enriched forest (Table A.4) and of the unenriched for-est (Table A.5) for ∆ v metal = ±
100 km s − , and the CDDF ofthe C iv -enriched forest (Table A.6) and of the unenriched forest(Table A.7) for ∆ v metal = ±
10 km s − . i and C iv forest Table A.1.
Number density evolution data for each quasar Ly α -only fit high-order fitlog N H i = [12 . , .
0] log N H i = [14 ,
17] log N H i = [12 . , .
0] log N H i = [14 , < z > ∆ z log d n / d z log d n / d z < z > ∆ z log d n / d z log d n / d z Q0055 −
269 3.270 0.669 2.672 ± ± ± ± −
158 3.010 0.390 2.642 ± ± ± ± −
388 2.759 0.558 2.656 ± ± . ± .
022 2.160 ± − ± ± ± ± − ± ± ± ± −
422 2.457 0.496 2.651 ± ± ± ± −
255 2.395 0.513 2.483 ± ± ± ± − a ± ± ± ± − ± ± ± ± −
385 2.139 0.475 2.571 ± ± ± ± − ± ± ± ± − ± ± ± ± − ± ± ± ± −
606 1.978 0.445 2.533 ± ± ± ± −
23 1.972 0.415 2.519 ± ± ± ± −
232 1.947 0.456 2.514 ± ± ± ± −
380 1.921 0.442 2.434 ± ± ± ± −
264 1.989 0.216 2.493 ± ± ± ± a It includes a sub-DLA, which introduces a gap in the Ly α redshift range. The calculation of d n / d z and the listed ∆ z take into account theredshift gap. Table A.2.
Mean number density evolution data for ∆ z = . Ly α -only fit high-order fitlog N H i = [12 . , .
0] log N H i = [14 ,
17] log N H i = [12 . , .
0] log N H i = [14 , < z > a log d n / d z log d n / d z log d n / d z log d n / d z ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± a The exactly same redshift range was used for both fit samples.
Table A.3.
CDDF of the entire H i forest f = log (d N / (d N H i d X )) for the high-order fit sample z = . − . z = . − . z = . − . N H i f +∆ f − ∆ f f +∆ f − ∆ f f +∆ f − ∆ f i and C iv forest Table A.4.
CDDF f = log (d N / (d N H i d X )) of the C iv -enriched forest for ∆ v metal = ±
100 km s − z = . − . z = . − . z = . − . N H i f +∆ f − ∆ f f +∆ f − ∆ f f +∆ f − ∆ f ∞ ∞ ∞ -18.663 0.301 ∞ Table A.5.
CDDF f = log (d N / (d N H i d X )) of the unenriched forest for ∆ v metal = ±
100 km s − z = . − . z = . − . z = . − . N H i f +∆ f − ∆ f f +∆ f − ∆ f f +∆ f − ∆ f ∞ -16.663 0.301 ∞ Table A.6.
CDDF f = log (d N / (d N H i d X )) of the C iv -enriched forest for ∆ v metal = ±
10 km s − z = . − . z = . − . z = . − . N H i f +∆ f − ∆ f f +∆ f − ∆ f f +∆ f − ∆ f ∞ -18.263 0.301 ∞ i and C iv forest Table A.7.
CDDF f = log (d N / (d N H i d X )) of the unenriched forest for ∆ v metal = ±
10 km s − z = . − . z = . − . z = . − . N H i f +∆ f − ∆ f f +∆ f − ∆ f f +∆ f − ∆ f ∞ -17.863 0.301 ∞ ∞ -18.663 0.301 ∞∞