An improved measurement of the flux distribution of the Ly-alpha forest in QSO absorption spectra: the effect of continuum fitting, metal contamination and noise properties
T.-S. Kim, J. S. Bolton, M. Viel, M. G. Haehnelt, R. F. Carswell
aa r X i v : . [ a s t r o - ph ] N ov Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 16 November 2018 (MN L A TEX style file v2.2)
An improved measurement of the flux distribution of theLy α forest in QSO absorption spectra: the effect ofcontinuum fitting, metal contamination and noiseproperties ⋆ T.-S. Kim , , J. S. Bolton , , M. Viel , , M. G. Haehnelt , R. F. Carswell Astrophysikalisches Institut Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, UK Max-Planck-Institut f¨ur Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching bei M¨unchen, Germany INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, I-34131 Trieste, Italy
Received 2007 July 7; Accepted 2007 September 3
ABSTRACT
We have performed an extensive Voigt profile analysis of the neutral hydrogen (H i )and metal absorption present in a sample of 18 high resolution, high signal-to-noiseQSO spectra observed with VLT/UVES. We use this analysis to separate the metalcontribution from the H i absorption and present an improved measurement of the fluxprobability distribution function (PDF) due to H i absorption alone at < z > = 2.07,2.52, and 2.94. The flux PDF is sensitive to the continuum fit in the normalised fluxrange 0 . < F < . . < F < .
8. Our new measurementsof the flux PDF due to H i absorption alone are systematically lower at 0 . < F < . i effective optical depth τ effH i at 1 . < z < τ effH i = (0 . ± . z ) . ± . , in good agreement with previousmeasurements from comparable data. As also found previously, the effect of noise onthe flux distribution is not significant in high resolution, high signal-to-noise data. Key words: cosmology: observations – intergalactic medium – quasars: absorptionlines
The Ly α forest refers to the numerous, narrow absorp-tion features bluewards of the Ly α emission line in thespectra of high-redshift QSOs. Our understanding of theorigin of the Ly α forest has made major progress withthe advent of high resolution spectroscopy (Cowie et al.1995; Hu et al. 1995; Lu et al. 1996; Kirkman & Tytler1997; Rauch et al. 1997; Cristiani & D’Odorico 2000;Kim et al. 2001; Janknecht et al. 2006) and the availabilityof hydrodynamic cosmological simulations (Cen et al.1994; Miralda-Escud´e et al. 1996; Zhang et al. 1997;Weinberg et al. 1998; Croft et al. 1998; Theuns et al. 1998; ⋆ Based on data taken from ESO archive obtained with UVESat VLT, Paranal, Chile.
Bryan et al. 1999; Dav´e et al. 1999; Croft et al. 2002;Jena et al. 2005). Comparison of the predictions fromhydrodynamic cosmological simulations with observationshave established a picture where the Ly α forest is due to theneutral hydrogen (H i ) component of the warm ( ∼ K)photoionised intergalactic medium (IGM) which tracesmoderate-amplitude density fluctuations of the (dark)matter distribution in a simple manner. In this picturethe spectra of high- z QSOs provide a one-dimensionalprobe of the matter density along the line-of-sight to highredshift QSOs. The flux distribution in QSO absorptionspectra thus encodes information on the underlying matterdistribution and evolution and the Ly α forest has beenrecognised as a powerful cosmological tool, complementingother cosmological probes.So far it is mainly the power spectrum of the flux dis- c (cid:13) Kim et al. tribution which has been used to quantitatively probe theproperties of the large scale distribution of matter and its de-pendence on cosmological parameters. The flux power spec-trum is sensitive to the matter power spectrum over a wideredshift range (2 < z <
4) and on scales of 1–50 h − Mpc,significantly smaller than those probed by CMB fluctua-tions, galaxy surveys and gravitational lensing (Croft et al.2002; Seljak, McDonald & Makarov 2003; Viel, Haehnelt& Springer 2004b; McDonald et al. 2006; Viel, Haehnelt &Lewis 2006; Lesgourges et al. 2007).The probability distribution of the flux is alsosensitive to the spatial distribution of dark mat-ter and cosmological parameters, in particular, theamplitude of matter fluctuations (Rauch et al. 1997;Weinberg et al. 1998; Theuns, Schaye & Haehnelt 2000;Meiksin, Bryan & Machacek 2001). However, the effect ofthe thermal state of the IGM (Theuns et al. 2000) andother uncertainties make it more difficult to extract thisinformation from the flux PDF. First attempts at a jointanalysis of the flux PDF and the flux power spectrum havebeen made (Desjacques & Nusser 2005; Lidz et al. 2006;Desjacques, Nusser & Sheth 2007). The analysis of Des-jaques et al. gives a somewhat smaller amplitude for thematter power spectrum compared to studies based on theflux power spectrum alone. Note, however, that these re-sults were based on dark-matter-only numerical simulationsin which the gas distribution was modelled in an approxi-mate way rather than on full hydrodynamical simulations.The measured flux PDF is sensitive not only tothe H i absorption, but also, unfortunately, to continuumlevel uncertainties, contaminating heavy element absorp-tion, and noise. The effect of continuum fitting uncertain-ties on the H i effective optical depth has been discussedin detail (Press, Rybicki & Schneider 1993; Kim et al. 2002;Bernardi et al. 2003; Tytler et al. 2004; Kirkman et al.2005), but their impact on the flux PDF has not been con-sidered as extensively (see Rauch et al. 1997 and McDonaldet al. 2000 for notable exceptions). Very little, if anything,has been done to quantify the effect of metal absorptionand noise on the flux PDF. To remedy these omissions, weperform a detailed Voigt profile analysis of the metal andH i absorption in 18 high resolution, high signal-to-noise(S/N) VLT/UVES QSO absorption spectra to assess the im-pact of continuum fitting uncertainties, metal absorption,and noise properties on the H i flux probability distribu-tion at 1 . < z < . i effective optical depth at1 . < z < z than similar work based on 8Keck/HIRES spectra by McDonald et al. (2000). It also dif-fers significantly in the way we perform the continuum fittingand, more importantly, in the level of the characterisationof metal absorption. Most previous estimates of the effectiveoptical depth and the flux PDF due to H i absorption have ei-ther removed the metal lines statistically (Tytler et al. 2004;Kirkman et al. 2005), excluded the metal-contaminated re-gions from the study (McDonald et al. 2000; Lidz et al.2006) or included absorption due to metal lines (Songaila2004).We have carefully identified and fitted metal and H i ab-sorption lines with Voigt profiles for our sample of 18 spec-tra. The line fitting is essentially complete in the Ly α for- Figure 1.
The redshift range of the Ly α forest in the spectraused for this study. The sample is divided into redshift bins. Thethin dotted lines, thick solid lines and dashed lines represent the < z > = 2 . < z > = 2 .
52 and < z > = 2 .
94 sub-sample, respec-tively. est region and redwards of the Ly α emission lines, but lesscomplete in the higher-order Lyman forest where the corre-sponding spectral regions were not always available. Duringthe fitting process, we have adjusted the initially estimatedcontinuum level by a localised continuum fit in order to getan overall satisfactory fit to multiple-transition metal linesand higher-order Lyman series lines. This approach enablesus to remove the metal contribution in the forest directly andto recover one long continuous metal-free forest spectrum,and also to obtain an improved estimate of the continuumlevel.The paper is organised as follows. In Section 2, we de-scribe the data used for our analysis. In Section 3, we presentthe Voigt profile fitting analysis used to remove the metalcontribution in the forest. We investigate systematics of un-certainties affecting the flux PDF in Section 4. The observedflux PDF function and effective optical depth are presentedin Section 5. Our conclusions are given in Section 6. We have selected a sample of 18 spectra from the LUQASsample (Kim et al. 2004) of 27 spectra obtained withVLT/UVES (Dekker et al. 2000). The spectra in LUQAS(Large sample of UVES QSO Absorption Spectra) weretaken from the ESO archive and a large fraction of themwere observed as part of the Large Program 166.A-0106(Bergeron et al. 2004). The observations were performed inthe period 1999–2004. All spectra have high signal-to-noise(S/N > α forest region and a resolution of R ∼
45 000. The wavelengths are helio-centric and vacuum-corrected. The spectra were sampled with pixels of width0.05 ˚A.From the 27 spectra in the LUQAS sample, we have cho-sen those with a S/N in the forest region of at least 30–50, c (cid:13) , 000–000 he flux distribution of the Ly α forest a full coverage of the Ly α forest and at least some coverageof the Ly β forest. Most of the 18 spectra cover the wave-length range of the higher order Lyman forest down to theatmospheric cut-off at 3050 ˚A. Some, however, cover only apart of the Ly β forest due to their low emission redshift. ForLy α absorption at z .
99 the corresponding Ly β absorp-tion is not covered in these optical spectra. Note that wedid not include the spectrum of HE1341 − − bluewards of the Ly α emission line.Lyman limit absorption systems (LLSs) with column densi-ties 10 . cm − N H i < cm − are included in our fluxdistribution study, while 50 ˚A segments of the spectra havebeen excised to the left and right of the centre of sub-dampedLy α absorption systems (sub-DLAs, N H i = 10 − . cm − ).None of our spectra contain a damped Ly α system ( N H i > . cm − ) in the observed wavelength range down to ei-ther the atmospheric cutoff or at the Lyman limit disconti-nuity caused by LLSs or sub-DLAs along the spectra withnon-zero observed fluxes.The Ly α forest regions of the spectra were grouped into3 redshift bins with median redshifts < z > = 2.07, 2.52 and2.94, as shown in Fig. 1 and listed in Table A1 in AppendixA. We have chosen these redshift bins as a compromise be-tween minimising the Poisson fluctuations of the statisticalquantities we are interested in and being able to investigatetheir redshift evolution. As we will show in section 5.1, spa-tial fluctuations in the flux PDF are large and substantialredshift paths are necessary to reduce the the Poisson noise from individual absorption systems. If an object contains anabsorption profile which straddles a redshift bin boundarywe have assigned it to the redshift bin in which most of itlies, and adjusted the wavelength range contributed by thatQSO accordingly.The spectra used here are essentially the same as thoseused in Kim et al. (2004) in the analysis of the LUQAS sam-ple. There are, however, three differences between the spec-tra in the LUQAS sample and the spectra analysed here:First, additional data for HE1122 − − −
158 has been obtained since the LUQAS datareduction. The additional data has been reduced with MI-DAS/UVES as described in Kim et al. (2004), and addedusing the UVES popler (UVES POst PipeLine Echelle Re-duction) program , resulting in significantly larger S/N forthe spectra of these three QSOs.Second, we have re-reduced and performed a first-orderflux calibration for the spectra of four QSOs (Q0420 − − −
422 and HE2217 − http://astronomy.swin.edu.au/mmurphy/UVES popler.html,kindly provided by Dr. M. Murphy. resolution of the instrument . Consequently, most spectrain the LUQAS sample were not flux-calibrated. Even in thefew cases where flux calibrations were performed, such as forHE2217 − ∼
25 ˚A), and then the spectrumcannot be properly flux-calibrated in this way. A lack of aproper flux calibration and deficiencies in the flat-fieldingprocedure sometimes leave unwanted, oscillatory features inthe extracted spectrum, with periods corresponding to thescale of one echelle order. The flux is then higher at thecentral wavelength and lower at both ends of a given echelleorder compared to the flux at the same wavelengths from ad-jacent echelle orders. In addition, the non-calibrated spectrashow a different continuum shape for the same wavelengthregions covered by the different CCDs. These deficienciesaggravate the difficulties of continuum fitting the spectra,especially at high redshifts. Instead of an order-by-orderflux calibration, we performed a first-order flux calibrationas follows. We corrected each merged science spectrum us-ing the master response function provided by ESO for agiven observing period. When the master response functionswere not available for a particular period, we scaled the un-calibrated spectra to the flux-calibrated spectra from otherperiods. The flux-calibrated spectra were then combined asdescribed in Kim et al. (2004).Third, and most importantly, we performed new contin-uum fits to all spectra in the sample optimised for a Voigtprofile analysis. The normalised LUQAS spectra and thenormalised spectra analysed here therefore differ slightly.Details of the continuum fitting are described in the nextsection. The absorption due to intervening neutral hydrogen andmetals is imprinted on the QSO emission spectrum, whichhas several, normally broad, emission lines overlaid oncontinuum emission from thermal and non-thermal radia-tion processes. The spectral energy distribution (SED) ofthe emission therefore varies significantly between differentQSOs.Most statistical analysis of the absorption thus requirethe fitting of a continuum characterising the SED of the un-absorbed emission of the QSO (see Lidz et al. (2006) for arecent study that uses spectra that are not normalised inthis way). Careful continuum fitting is particularly impor-tant for a Voigt profile analysis of QSO absorption spectrasuch as the one performed here. Estimating the unabsorbedemission is particularly difficult at high redshifts where anincreasing fraction of the spectrum shows significant absorp-tion. The problem of continuum fitting has been extensivelydiscussed in the literature (Kim et al. 2002; Bernardi et al. The UVES pipeline reduction program determines the large-scale continuum shape from the ratio of the spectral shape of thetarget and the flat-field flux. For a fixed instrumental setting, theextracted spectra of the same object show a more or less similarshape of the large-scale continuum. (cid:13) , 000–000 Kim et al.
Table 1.
Analysed QSOsQSO z aem z Ly α λ Ly α (˚A) S/N Continuum (%) b Lyman limit c notes d Q0055–269 3.655 e − z =2.768 & 2.638Q0420–388 3.116 e z =3.087HE0940–1050 3.078 2.452–3.006 4197–4870 50–130 1 − f e − e − e − z =2.3052.091–2.217 3758–3911 60–100 1 − i opacityHE1347–2457 2.609 e − − − − e − z =1.673PKS1448–232 2.219 1.719–2.175 3306–3860 30–90 2 − − − z =1.8391.659–1.795 3233–3398 45–75 2 − i opacity a The redshift is measured from the observed Ly α emission line of the QSOs. The redshift based on the emission lines is known to beunder-estimated compared to the one measured from the absorption lines of the host galaxies (Tytler & Fan 1992; Vanden Berk et al.2001). b Rough estimate of the continuum fitting uncertainty. It varies across the spectrum. c The wavelength of the Lyman limit for each spectrum is defined here as the wavelength below which the observed flux is zero. This doesnot necessarily correspond to the Lyman limit of an identified Lyman limit system/sub-damped Ly α system. Whenever a FOS/HST orSTIS/HST spectrum is not available, the Lyman limit is assumed to occur at the shortest observed optical wavelength. FOS/STIS spectrafrom the HST archive are available for the following QSOs (any snap-shot survey or spectra with very low S/N are not used): Q0055 − − − − − − − − − − d In spectra with a sub-damped Ly α system, we discard at least 50 ˚A on each side of the centre of the sub-DLA system. e The emission redshift is uncertain due to absorption systems at the peak of the Ly α emission line or the occurrence of multiple peaks. f The spectrum shows very strong O vi absorption blended with two saturated Ly α absorption systems at 4012–4052 ˚A (Fechner et al.2004). Since the line parameters for these Ly α systems cannot be well constrained (their corresponding Ly β is below the partial Lymanlimit produced by the z ∼ .
738 systems), we discarded this wavelength region. α forest data and high resolution, high S/N data obtainedwith high resolution spectrographs such as VLT/UVESand Keck/HIRES. For low/intermediate resolution, low S/Ndata the unabsorbed continuum level is normally estimatedusing a simple extrapolation from the much less absorbedregion of the spectrum redward of the Ly α emission line atwavelengths λ rest − frame > locally connecting apparentlyabsorption-free regions (McDonald et al. 2000; Kim et al.2004; Kirkman et al. 2005). This detailed local fitting of a continuum is time consuming and ceases to work wellonce the redshift of the QSO becomes large ( z em > . < z em < .
5, however, this method still works well. Weused it to determine an initial guess for the continuum levelfor the 18 spectra in our sample. Due to the high resolution,high S/N of our data, emission lines both weak and strong(mainly near 1073 ˚A and 1123 ˚A in rest-frame; Bernardi etal. 2003; Tytler et al. 2004) are easily identified in the for-est, despite the lack of an appropriate flux calibration. Thestrong, broad ozone absorption bands at α forest at the lower end of the redshift range ofour sample (Schachter 1991). However, this is compensatedfor by the rather low density of absorption features at lowredshift which leaves more absorption-free regions to fit thecontinuum in our high resolution, high S/N spectra.Most of the spectra were not flux-calibrated, and theflat-fielding procedure was not always ideal, and as a conse- c (cid:13) , 000–000 he flux distribution of the Ly α forest quence there were some spurious broad features in a num-ber of the spectra. Rather than attempt to fit the entirespectrum using an impractically high order function, thespectrum was divided into chunks. The size of these wasdetermined interactively, and depended on the redshift andthe presence of strong absorption systems. Typically thesechunks were 150–300 ˚A long in the Ly α forest part of eachspectrum, and at longer wavelengths ranged from ∼
200 ˚Ain QSO emission lines up to ∼ ∼
20 in the Ly α forest, and up to ∼
200 at longer wavelengths, were fitted to each chunk, us-ing the IRAF CONTINUUM/ECHELLE procedure. Theselocal continua were then combined to produce a single con-tinuum for the entire spectrum, and any small discontinu-ities at the boundaries were adjusted manually to produce asmooth result. We will call the continuum obtained in thisway the initial continuum, C i .As we will describe in the next section we have per-formed a full joined Voigt profile analysis of the H i andmetal absorption in the spectra in order to obtain absorp-tion line parameters (the redshift z , the column density N in cm − and the Doppler parameter or b parameter in kms − ). The Voigt profile analysis is sensitive to the assumedcontinuum and the simultaneous fitting of different transi-tions caused by the same ion often reveals where the con-tinuum should lie in absorbed regions of the spectrum. Wehave therefore adjusted our initial continuum C i when wefitted absorption features with the Voigt profile fitting rou-tine VPFIT . The fitting procedure and the adjustment ofthe continuum level are very similar to the one describedin Carswell, Schaye & Kim (2002) and will be discussed inmore detail in Kim et al. (2007, in preparation).For each spectrum, we first searched for metal absorp-tion using the entire range of the available spectrum. Theidentified metal lines were the first to be fitted. During thisprocess, the continuum was adjusted to obtain acceptableion ratios. If the metal lines were blended with H i absorptionfeatures, the H i and metal lines were fitted simultaneously.Once all identified metal absorption was fitted we then fittedthe rest of the absorption features assuming they are due toH i absorption. For this we used higher-order Lyman serieslines whenever they were available to constrain saturatedlines. In doing so, we further adjusted the continuum levelto achieve a satisfactory fit for the available Lyman series.Using this second continuum estimated from the first profilefitting procedure, the profile fitting was repeated and thesecond continuum was checked manually again. This pro-cedure was repeated several times, until we were satisfiedwith the results. The fitting was performed both by R. F.Carswell and T.-S. Kim independently, and the final fittingwas carried out by T.-S. Kim. Note that we did not accountfor the possibility of an extended smoothly varying compo-nent of weak absorption often referred to as Gunn-Petersonabsorption. We further assumed that the response functionof UVES is smoothly varying for the non-calibrated spec-tra as seen in a smoothly varying master response functionprovided by ESO.The final adjusted continuum obtained from the fittingprocedure was then used to obtain the final normalised spec- ∼ rfc/vpfit.html tra used in this study. When we use the term “continuum”in the following, it always refers to this final continuum, C f . The difference between C f and C i is small and usu-ally restricted to some limited wavelength regions, except inthe regions around Lyman limit systems and sub-dampedLy α systems where the difference becomes rather large. Westress once again that these final continua are different fromthe continua used in Kim et al. (2004) which were estimatedusing the C i procedure only. Note also that these final con-tinua are not necessarily always completely smooth since insome regions of the spectrum continuum adjustments havebeen applied using a straight line to get reasonable columndensity ratios for different transitions. These small adjust-ments are required mainly because of the characteristics ofthe un-calibrated spectra, especially at shorter wavelengthsat i absorption in Section 4 and 5.The continuum uncertainty depends strongly on theS/N of the spectrum as listed in Table 1. The higher theS/N is, the smaller the continuum uncertainty is. In theupper panel of Fig. 2 we show the calibrated spectrumof Q0420 − − C − ) and increase ( C ) of the continuum levelby the dashed curves. It is obvious that C and C − dra-matically over/under-estimate the continuum level in thecase of Q0420 − − C and C − over/under-estimate the continuum in most parts. Unfortu-nately, a rigorous quantitative assessment of the continuumuncertainty is not possible given the complex nature of thecontinuum fitting process.In Table 1 we give rough estimates of the continuum un-certainty obtained from absorption-free regions of the spec-tra. For this we compared the highest and the lowest fluxlevels in absorption-free regions to the average flux level inthe same regions, disregarding localised excursions in onlyone pixel. Note that the continuum uncertainty is not con-stant across the spectrum. Note further that due to the pos-sible presence of extended featureless absorption, the Gunn-Peterson absorption, the continuum used in this study ismore likely to be an underestimate than an overestimate ofthe true continuum.The two lowest quality spectra in the sample are c (cid:13) , 000–000 Kim et al.
Figure 2.
One of the best (Q0420 −
388 with z em =3.166, upper panel) and one of the worst (PKS0329 −
255 with z em =2.704, lowerpanel) quality spectra in our sample. The solid curves show our final continuum fit, while the dashed curves show a continuum levelincreased/decreased by 5%. The dot-dash curves which are almost indistinguishable from the solid curves are the initial continuum fit, C i . The metal absorption has not been removed in both spectra. The spectrum of Q0420 −
388 is flux-calibrated and has one of thehighest signal-to-noise ratios. We estimate the uncertainty of its continuum fit to be less than 1%. The spectrum of PKS0329 −
255 isnot flux-calibrated and has low signal-to-noise (S/N ∼ PKS0329 −
255 (lower panel of Fig. 2) and J2233 − −
606 has a S/N of 30–35, and forPKS0329 −
255 the S/N is generally ∼ ∼ ∼ −
255 also has the largestzero flux-level offset (see the next subsection) in our sample.PKS1448 −
232 and Q0122 −
380 also have continuum uncer-tainties of ∼ ∼ As discussed in Kim et al. (2004), the UVES standardpipeline reduction program returns spectra where the sky c (cid:13) , 000–000 he flux distribution of the Ly α forest Figure 3.
Various examples of metal absorption in the Ly α forest region of the spectra in our sample. Thin and thick curves representobserved spectra and fitted line profiles, respectively. a) Region A in the upper panel shows an isolated metal absorption system, Si iv z = 2 .
221 towards HE0940 − ii z = 1 .
789 at 4485.4–4487.2 ˚A is not shown in order to make the figure simpler.The lower panel shows the spectrum after subtracting the metal absorption in region A and adding noise from nearby absorption-freeregions. b) The thick solid curve in the top panel shows Fe ii z = 1 .
919 (region B) and Fe ii z = 1 .
919 (region C) in thespectrum of HE0940 − ii transitions at other wavelengths. The fitted H i -only profile is shown in the middle and the difference between the observed profile andthe fitted H i profile is shown in the bottom panel. c) Regions D, E and F in the top panel mark absorption by C iv z = 1 . iv z = 1 .
735 and a mixture of C ii z = 2 .
175 and C iv z = 1 .
732 in the spectrum of HE0940 − i -only profile and the differencebetween the fitted H i -only and the observed profile are shown in the third and fourth panel, respectively. d) The absorption profile of ametal absorption system at z = 2 .
045 in the spectrum of Q0109 − iv and Si ii absorption suggest that two Si iii − and ∼
54 km s − (indicated by the arrows) which are blended with saturated H i absorption. e) The velocity profile forSi iii d) . The top panel shows the Si iii region at z = 2 . i Ly α profile at z = 2 . i Ly β profile at z = 2 . α and Ly β simultaneously, assuming no Si iii (at z = 2 . iii absorption profile with the two components at 0 and ∼
54 km s − , assumingthe same line strength ratio for these two components as estimated from the resolved Si ii and Si iii absorption. The fourth panel is thegenerated profile of the H i ( z = 2 . iii absorption ( z = 2 . i + Si iii profiles. f) The velocity profiles of a metal line system at z = 2 .
907 towards PKS2126 − iii profile assuming the contribution from the superimposed H i at z = 2 .
878 which was estimated from thecorresponding Ly β profile (top panel). The third panel shows the Si iii profile assuming no contribution from H i . The weak, broad Si ii ii transition in the optical spectra) in the fourth panel is assumed to be a non-detection.c (cid:13) , 000–000 Kim et al. level is somewhat under-subtracted. This problem becomesmore severe at shorter wavelengths ( −
255 witha typical offset, ∆ F zero = 0 .
015 in a spectrum normalisedto unit continuum. Note that this QSO also has one of theworst overall continuum uncertainty. Most spectra have anoffset of much less than ∆ F zero = 0 .
01. An offset from zeroflux can lead to significant problems for the Voigt profile fit-ting. Since the flux in saturated regions does not go to zero,VPFIT normally adds many narrow components whose fluxminima do not reach F ∼ I AND METAL ABSORPTION
Most simulations and models of the Ly α forest account onlyfor the distribution of H i . In reality, the Ly α forest con-tains significant absorption from intervening metals in theIGM. These metal absorption lines are obviously interest-ing in their own right and provide a wealth of informationon the spectrum of the metagalactic UV background andthe metal enrichment of the IGM by galaxies. For a statis-tical analysis of the H i absorption aimed at studying theunderlying matter distribution, they are, however, a sourceof contamination which leads to additional uncertainties. Inthis case it is therefore important to identify the metal linesin the forest and to remove them from further study, or atleast to quantify their effect on any statistic investigated.Most studies so far have dealt with this problem by exclud-ing spectral regions with strong metal contamination fromthe analysis, e.g. a strategy adopted by Rauch et al. (1997),McDonald et al. (2000) and Lidz et al. (2006).The metal contamination is, however, rather widespreadand varies strongly between different spectra. Excludingcontaminated regions is therefore problematic. If metallines are isolated, it is straightforward to excise the metal-contaminated regions. More often than not, metal absorp-tion is, however, blended with H i absorption at 2 < z < . . It is then difficult to decide which regions to exclude.Since there are only a few QSOs in each redshift bin in this The amount of the metal absorption blended with H i absorp-tion depends on redshift. At low redshift ( z < .
5) the H i ab-sorption is weaker and most metal absorption occurs in regionwith weak or no H i absorption. At higher redshift ( z > . i absorption features increases and the metalabsorption starts to blend in regularly with the H i absorption. Atvery high redshift ( z > . i absorption fea-tures becomes very high and many lines become saturated. In thiscase, many metal lines are blended with strongly saturated H i ab-sorption and their contribution to the total absorption diminishesor becomes negligible. and other similar studies, attempts to exclude metal contam-inated region are likely to lead to a selection bias, especiallyat z ∼ i and metal absorption per-formed by R. F. Carswell and T.-S. Kim which will be de-scribed in more detail elsewhere (Kim et al. 2007, in prepa-ration). In this Voigt profile analysis we have identified allmetal lines in the 18 spectra to the best of our knowledge.This allows us to remove their absorption contribution fromthe observed flux distribution. This method produces an es-timate of the continuous flux distribution without any ab-sorption due to identified metal lines.For the identification of metal lines, we made use ofknown properties of metal absorption:(i) Metal absorption features tend to be narrower thanH i lines.(ii) Metal absorption features are usually associated withstrong, often saturated H i absorption.(iii) In the redshift range considered here, it is unlikely forH i absorption to show corresponding Si ii without showingC iv , C ii , Si iv or Si iii . In short, H i absorption with nocorresponding C iv is unlikely to show other metal lines,especially for the weaker absorption systems with columndensity N H i cm − .We started by identifying metal absorption features red-ward of the Ly α emission where all absorption lines (apartfrom the telluric lines, which were omitted) are due to met-als. Most of these are C iv , Si iv , Si ii , Al ii , Al iii , Mg ii andFe ii . The rest-frame wavelengths and oscillator strengths fortransitions from these ions are given by Morton (2003). Us-ing these lines as a guide, we looked for other metal linesat the same redshift, such as C iii , O vi , C i . In a secondstep we searched for metal lines associated with H i absorp-tion with any column densities in the UVES spectra, i.e. at > i absorption orwith the Lyman discontinuity shown in the HST data listedin Table 1, i.e. at z < . all the metal linesin the forest. Severe line blending often makes the identifica-tion of metal lines difficult. Sometimes an absorption featurefirst thought to be due to H i did not show a correspondingLy β line of the expected strength when we attempted tofit higher-order Lyman series lines. Any excess absorptionat the Ly α wavelength was then considered as being due toyet to be identified metal lines.All other absorption not identified as being due to met-als we have assumed to be due to H i . There were a fewcomplexes of strong clustered rather narrow lines (Dopplerparameters less than 15 km s − ) which we suspect to beunidentified metal lines. We have flagged these as potentialmetal lines. These occasions, however, were rare. Note thatsome of the weak narrow lines which we considered as due toH i absorption could still be either weak, unidentified metallines or noise peaks, while stronger metal lines are almostcomplete in their identification. c (cid:13) , 000–000 he flux distribution of the Ly α forest The different metal lines and H i were all fitted inde-pendently. Only the transitions produced by the same ion of the same redshift systems were required to have the sameredshift and the Doppler parameters. Sometimes part of agiven metal line is blended with strong H i absorption whichmakes it difficult to separate the metal and H i lines. Only in such circumstances, the redshifts and the Doppler pa-rameters were tied with the ones measured from the otherclean metal lines within the same ionisation group (such asMg ii , Fe ii , C ii and Si ii for the low-ionisation group), sim-ilar to the method usually employed in the metal analysisof damped Ly α systems. Fortunately, most common metallines embedded in the forest, such as Mg ii , Fe ii , Si ii , C iv ,are multiplets. Identifying these lines is more reliable thansingle-transition lines, such as Si iii i .Fig. 3 shows some examples of the metal lines embeddedin the forest. It also illustrates how we have subtracted themetal contributions from the flux distribution. Thin linesare the observed profiles (H i +metal lines), while the thicklines are the fitted H i or metal lines. The upper panel ofFig. 3 a) shows a single isolated metal system and the lowerpanel shows the same region after removing the metal linesand adding the noise estimated from nearby, absorption-freeregions. About 40 −
50% of metals are isolated at z ∼
2, thefraction decreases to 20 −
30% at z ∼
3, due to increasedLyman line blending.The top panel of Fig. 3 b) shows a moderate-strengthmetal line blended with H i absorption. Such embeddedmetal lines have been identified by other transitions fallingoutside the forest region or in regions of the forest where theH i absorption is weak. The middle panel shows the H i -onlyabsorption profile generated from the parameters obtainedfrom the line fitting. The lower panel shows the differencebetween the flux in the top (H i +metal) and middle panels.The difference is of the same order as the pixel noise. If metalabsorption of weak to moderate strength is blended with sat-urated H i absorption, the metal absorption contributes verylittle to the combined absorption profile.Fig. 3 c) shows a very common configuration of metalabsorption. Approximately 45% of metal absorption systemsat z ∼ ∼
75% at z ∼ i ab-sorption. If we wanted to excise the metal absorption it isnot obvious if one should cut out the entire H i absorptioncomplex from 4226 ˚A to 4236 ˚A or only the region where themetals affect the H i profile from 4229.5 ˚A to 4231.2 ˚A asshown in the second panel. The third panel shows instead theH i -only absorption profile generated from the parametersobtained from our line fitting procedure. The bottom panelshows the difference between the H i and the H i +metal pro-files.The most difficult metal absorption features to obtaina reliable line fit for in the Ly α forest region of the spec-trum is the absorption due to the single transition of Si iii at 1206.5 ˚A (see McDonald et al. 2006). Sometimes we couldsuccessfully fit Si iii absorption profiles blended with H i ab- sorption using other metal lines, such as Ly α , Ly β , Si ii ,Si iv , Al iii , Al ii , C ii , C iv , and Mg ii . Sometimes, however,we could fit only part of a Si iii profile. In such cases somecontamination of the final H i profile is unavoidable, sincewe could not subtract all of the Si iii contribution from theH i +Si iii absorption feature. An example is shown in Fig. 3d) and e).Fig. 3 d) shows a typical metal line system at z = 2 . − iii is blended with H i ab-sorption at z = 2 . ii (Si iv ) suggest that there should be two components of Si iii at 0 km s − and ∼
54 km s − in the saturated H i profileat z = 2 . iii region of the system shown in paneld). Superimposed is the H i Ly α profile at z = 2 . β absorption(second panel), assuming no Si iii (at z = 2 . iii profile with the twocomponents at v = 0 and ∼
54 km s − (indicated by the ar-rows). These two components were generated assuming thesame relative line strengths between all successfully fittedSi ii and Si iii components. In the 4th panel the H i Ly α (at z = 2 . iii components (at z = 2 . i profile are thesame as in the first panel. The bottom panel shows the dif-ference between the observed and the fitted H i Ly α + Si iii profiles. The figure demonstrates that if the H i absorptionis saturated, then even strong metal lines do not contributesignificantly to the overall profile, unless the metal absorp-tion extends to the wings of the saturated H i absorptionprofiles.Fig. 3 f) shows a velocity plot of a metal line systemat z = 2 .
907 towards PKS2126 − iii iii i contribution at z = 2 .
878 constrained by the corresponding Ly β (the toppanel indicated by a thick tick mark) and assuming no H i contribution, respectively. In reality, its true column den-sity could range between the ones obtained with these twoassumptions. Similarly, the weak, broad feature at the ex-pected location for Si ii ii transitionavailable in the spectra) in the fourth panel could be a realdetection blended with weak H i (the upper limit for N Si ii can be estimated from non-detection of other Si ii transitionsabove the Ly α emission) or a weak broad H i . Since we donot want to over-identify metals and want to be conservative ,we adopted the lowest Si iii i ) and considered Si ii i from higher order Lyman series, we assumed thatthe absorption was due to metals only. Non-detection in Ly β in our spectra typically corresponds to N H i . cm − assuming b = 20 km s − (or F > . α ). Fortunatelythere are not many such cases in our sample. In Table A2in Appendix A we list uncertain line fits.In summary, for each QSO we have obtained a Ly α forest spectrum free of identified metal lines as follows: • for isolated metal lines the spectrum was replaced by c (cid:13) , 000–000 Kim et al. continuum with a noise level estimated from nearby contin-uum regions; • where metal lines and H i lines are blended, that partof the spectrum was replaced with the model H i lines de-termined from fitting Voigt profiles to the heavy elementand Lyman lines simultaneously, with noise using estimatesappropriate to the final flux levels determined from nearbyregions.In Fig. 4 we show the continuum fitted spectra of ourcomplete sample together with the metal contribution tothe total absorption to give a general impression of the metalcontamination. Note that the metal contribution to the totalabsorption differs significantly from the metal-only absorp-tion as metal absorption blended with strong H i has littleeffect on the total absorption profile. One of the main aims of the paper is to estimate the H i -only absorption flux PDF from the normalised spectra of oursample. The PDF of the flux is simply the number of pixelswhich have a flux between F and F + ∆ F for a given flux F divided by the total number of pixels (Jenkins & Ostriker1991; Rauch et al. 1997; Bryan et al. 1999; McDonald et al.2000; Kim et al. 2001).Before presenting our new measurement of the flux PDFfrom our full sample we will discuss the statistical errors ofthe measured flux PDF and investigate some of the system-atic uncertainties discussed in Section 2 on the flux. Follow-ing McDonald et al. (2000), we calculate the flux PDF forbins of width ∆ F = 0 .
05. Pixel with flux level smaller than F = 0 .
025 or greater than F = 0 .
975 have been allocated tothe F = 0 bin and the F = 1 . n c chunkswith a length of ∼
50 ˚A. If the PDF estimated from the fullsample at the flux bin F i is b P ( F i ) and the PDF estimatedwithout the k -th chunk at the flux bin F i is e P k ( F i ), then thecovariance matrix cov( i, j ) between the PDF in a flux bin F i and the PDF in a flux bin F j was calculated ascov( i, j ) = n c X k =1 [ b P ( F i ) − e P k ( F i )][ b P ( F j ) − e P k ( F j )] , (1)and the variance at a given flux level is given by the diagonalterms of the covariance matrix σ i = cov( i, i ) for a flux bin F i . We checked that this modified jackknife method is notsensitive to the length/number of chunks for a given samplesize. As expected, the errors are larger when the number ofpixels in the sample is smaller: ∼
15% for Q0420 −
388 with13561 pixels vs ∼
7% for the full < z > = 2 .
94 sample with34265 pixels at F = 0 .
5. We compared the errors obtainedwith the modified jackknife method with the errors obtainedby 500 bootstrap realisations of chunks of 100 pixels (or 5 ˚A) used by McDonald et al. (2000) and Schaye et al. (2003)(see Section 5.2 for more details for the bootstrap method).Both methods give comparable error estimates, while thePoisson errors (i.e. those based on the square root of thenumber of pixels) tend to be ∼
35% smaller.
We now move to a discussion of the effect of systematicuncertainties on the flux PDF. We start with the effect ofcontinuum fitting uncertainties. In Fig. 5 we show the fluxprobability distribution of the spectrum of Q0420 −
388 in-cluding the metal absorption (see also Fig. 6) with our finalcontinuum fit C f , our initial continuum fit C i and four fur-ther continua where we have applied a wavelength indepen-dent offset of the continuum level of ±
1% ( C and C − ) and ±
5% ( C and C − ). The dotted, dashed, solid, dot-dot-dot-dashed and dot-dashed curves show the PDF with C , C − , C f , C and C − , respectively. The flux PDF of the spectrawith the initial continuum fit C i is almost indistinguishablefrom the PDF of the spectra with the final continuum fit C f . As expected changing the continuum level affects thePDF most strongly at a flux level of F ∼
1, shifting thecorresponding peak in the PDF. Continuum fitting uncer-tainties also have a moderate effect on the slope of the PDFat flux levels 0 . < F < .
0. There is little effect at lowerflux levels as regions of saturated or very strong absorptionare not affected by an over-/under- estimated continuum asmuch as regions of weak absorption.Note again that a systematic change of the continuumlevel by 5% is a gross overestimate of the actual continuumfitting uncertainty for most of our spectra. We choose thisvalue here simply to demonstrate the effect more clearly.Most spectra in our sample have a continuum uncertaintyof ∼ As apparent from Fig. 4 the metal contribution to the ab-sorption varies significantly between different spectra. In Ta-ble A4 in Appendix A we quantify the metal contaminationof the H i +metals effective optical depth, i.e. observed val-ues before removal of the metal absorption, estimated usingthe effective optical depth after removal of the metal absorp-tion. The values vary from 0.5% to 28% (note that in thecase of Q0055 − − z , except thatspectra containing Lyman limit systems or sub-damped Ly α systems tend to show a larger absorption contribution bymetals. The mean metal contamination is ∼ statistical estimates ofthe metal contamination: ∼
19% at z = 1 . ∼
10% at z = 2 . .Fig. 6 illustrates the effect of absorption by metals on Both removed the metals in the forest statistically. Using pub-lished line parameters redwards of the Ly α emission of QSOs at1 . < z em < .
54, they estimated the amount of metals as afunction of rest-frame and observed wavelength.c (cid:13) , 000–000 he flux distribution of the Ly α forest Figure 4.
Normalised observed spectra and the additional metal contribution to the absorption for our sample of 18 VLT/UVES spectra(against rest-frame wavelength). The regions with no flux, such as at ∼ − i absorption and thus shows the additional absorption by metals which is significantly smaller than the absorption by metalswould be in the absence of H i absorption. The four vertical dotted lines indicate the rest-frame wavelength of Ly β , Ly α plus 1268 ˚Aand 1380 ˚A. Note that the weak metal absorption at 1268–1380 ˚A does not necessarily indicate a low metal contamination in the forest(see e.g. the spectra of HE0940 − − z QSO spectra is C iv . Thehigh column density absorption systems showing strong C iv (1548 ˚A and 1550 ˚A) and Si iv (1393 ˚A and 1402 ˚A) absorption featuresusually show other metal lines. These high column density absorption systems occur randomly along each sightline, i.e. at different z fordifferent sightlines. Therefore, stronger transitions e.g. Fe ii ii ii α forest region without there being any corresponding strongmetal lines in the 1268–1380 ˚A range. The metal contribution in the spectrum of Q0055 −
269 forest could be significantly underestimatedsince the wavelength coverage in the red is rather limited, only up to 6809 ˚A (observed).c (cid:13) , 000–000 Kim et al.
Figure 5.
The upper panel shows the flux PDF of Q0420 − . < z < . C f , while thecurve almost indistinguishable from the solid curve is the PDFfor the initial continuum C i . The dotted/dashed curve are thePDF for a continuum level increased/decreased by 5% ( C and C − ), while the dot-dot-dot-dashed/dot-dashed curve are for acontinuum level increased/decreased by 1% ( C and C − ) Theerrors were estimated using a modified jackknife method by Lidzet al. (2006) as described in the text. Different continuum fits alsoshift the peak of the PDF, as indicated by the arrow for C − . Thelower panel shows the following ratios PDF C − /PDF C f (dashedcurve) and PDF C − /PDF C f (dotted curve). The errors in thelower panel are similar for both curves but plotted only oncefor clarity. The errors correspond to the combined errors of bothPDF C − and PDF C f . the flux PDF. The upper panel shows the PDF of two arti-ficial spectra which were generated from the fitted line pa-rameters of PKS2126 − < F < . F ∼
1. Notethat the latter effect is likely to be underestimated as weakmetal absorption is difficult to identify. Since the numberof absorption features which we classified as suspected metallines are small and usually weak, these lines have a negligibleeffect on the PDF at 0 . < F < . Pixel noise will cause a slight smoothing of the flux PDF.For high-S/N spectra as in our sample the effect is smallbut noticeable. This is demonstrated in Fig. 7. The upperpanel shows the flux PDF of PKS0329 −
255 for the observedspectrum with metals (dot-dashed curve) and without met-als (solid curve with error bars). The observed spectrum hasS/N = 30–55. We generated 4 artificial spectra with differ-ent S/N using the fitted line parameters, assuming Gaussiannoise: the dashed curve is for S/N = 25, the dotted curveis for S/N = 50, and the two almost indistinguishable thin
Figure 6.
The upper panel shows the flux PDF of PKS2126 − F < . solid curves are for S/N = 100 and S/N = ∞ . Note thatthe generated spectra do not have a offset from the zeroflux level, i.e. the saturated lines go down to F = 0. Thebottom panel shows the ratio of the PDF for the artificialspectrum with S/N = ∞ (solid curve) and the PDF for thespectrum with metals (dot-dashed curve) to the PDF of themetal-removed spectrum.The effect of the signal-to-noise on the flux PDF ismost evident at flux levels of 0 < F < . F > .
9, where it can exceed that from the metal contami-nation. At intermediate flux levels, 0 . < F < .
9, the effectof the signal-to-noise is comparable or smaller than thatdue to metal absorption. It should, however, be noted herethat the contribution of metal absorption in the spectrum ofPKS0329 −
255 is rather small (2.8%) and that the spectrumhas the lowest S/N of our sample.In Fig. 8 we show the difference between the flux PDF ofartificial S/N = ∞ spectra (i.e. no zero-level offset) and theflux PDF of the observed spectra without metal absorptionfor our full sample at three different redshift bins. At fluxlevels of 0 . < F < . Note that the noise in the observed spectra is not exactly Gaus-sian. The noise at F ∼
0, i.e. the bottom of saturated lines, andat F ∼ F ∼ F ∼
1. However, for the purpose of illustrating theS/N effect on the PDF, the assumption of Gaussian noise is agood approximation. c (cid:13) , 000–000 he flux distribution of the Ly α forest Figure 7.
The upper panel shows the flux PDFs of the observedand artificial spectra of PKS0329-255 for different noise levels.The dot-dashed curve is for the observed spectrum including themetals, the solid curve with errors is for the observed spectrumafter the metals have been removed. The four other curves are theflux PDFs for artificial spectra generated from the line parameterswith different levels of Gaussian noise added. The dashed curve isfor S/N = 25, the dotted curve is for S/N = 50 and the two almostindistinguishable thin solid curves are for S/N = 100 and S/N= ∞ . The S/N = ∞ and S/N = 100 PDFs show a rather largedeviation at F < . F = 0 .
05. This isdue to the offset of the zero flux level of the observed spectrum (atypical offset from zero flux is ∼ . ∞ spectrum to the metal-removed spectrum (solid curve) and the PDF ratio of the metal-included spectrum to the metal-removed spectrum (dash-dottedcurve). The effect of low S/N on the flux PDF becomes noticeableat F < . F > .
9. At 0 . < F < .
9, the effect of the S/Nis comparable or smaller than that of the metal contamination.
Fig. 9 shows the main result of this paper, the flux PDF ofthe observed spectra in our full sample divided into threeredshift bins (Table A1 in Appendix A) after removal of allidentified metal lines. The thin, grey curves show the fluxPDFs of the individual spectra. As found previously there isconsiderable scatter between different lines-of-sight. This ismainly due to the occurrence of strong absorption systemswhich are rare in individual spectra (Viel et al. 2004a). Aconsiderable path length is therefore required to reach rea-sonable convergence to an average flux PDF. This is bestillustrated by the spectrum of Q0002 −
422 which shows themost deviant individual PDF compared with the mean PDFin its redshift bin. This is probably due to several factors.The spectrum falls at the upper end of its redshift bin. Ithas also the shortest usable path length (191 ˚A) and thelargest number of strong systems per unit redshift in thewavelength region used.In Fig. 10 we show the effect of the removal of theidentified metal absorption. The dashed and solid curvesin the upper panel show the flux PDF of the spectra with
Figure 8.
The difference between the flux PDFs for S/N = ∞ artificial spectra and metal-removed observed spectra for the fullsample divided into three redshift bins. The errors are those ofthe PDF of the metal-removed observed spectra. The combinederrors of both PDFs are larger. The effect of lower S/N and theoffset of the zero flux level on the PDF are negligible comparedto the statistical errors at flux levels 0 . < F < . and without the identified metal absorption, respectively.The lower panel shows the ratio of the two. Removing themetal absorption mainly affects the flux PDF at flux lev-els 0 . < F < .
8. Without metal absorption the fraction ofpixels in this flux range is 10 −
20% lower. The effect of metalabsorption, which appears to evolve little with redshift, ismore significant at lower redshift where the H i absorptionis smaller.In Fig. 11 we compare our new measurement of the fluxPDF with that of McDonald et al. (2000) at < z > = 2 . < z > = 3 .
0. The solid curves are the PDF when met-als are included. Unfortunately a comparison at higher red-shifts is not possible due to the lack of high-redshift spec-tra in our sample. At < z > = 2 .
41 our measurement isabout 10–20% lower at flux levels 0 . < F < . < z > = 3 . . < F < .
8. We can only speculate here where thisdiscrepancy comes from. Part of the difference is probablydue to the rather crude removal of metal absorption by Mc-Donald et al., which is likely to have led to more residualabsorption by unidentified metal lines in their spectra. Thedifference appears, however, to be larger than expected dueto this effect and increases rather than decreases with in-creasing redshift. Note that the McDonald et al. sample issignificantly smaller with a total of 8 spectra and some ofthe discrepancy can probably be explained as being due tovariations between different lines-of sight (see the grey thincurves in Fig. 9). Differences in the placement of the contin-uum level may also play a role. We list the mean flux PDFfor the five different redshift bins discussed in this section inTable A3 in Appendix A.The flux PDF is a statistical quantity which – at leastin principle – can be easily compared with that of simulatedspectra. Due to the expected tight correlation between H i c (cid:13) , 000–000 Kim et al.
Figure 9.
The flux PDF (filled circles with errors) of the full sample divided into three redshift bins after removal of the metal absorption.The thin grey curves show the PDFs of individual spectra. The 1 σ error bars are estimated using a modified jackknife method (Lidz etal. 2006). The dashed curve in the
07 bin is the PDF of the spectrum of Q0002 − Figure 10.
The flux PDF of the full sample divided into three redshift bins before (dashed curves) and after (solid curves) removalof the metal absorption. The lower panel shows the ratio of the PDFs before and after removal of the metal absorption. The effectiveoptical depth due to H i absorption is lower at lower redshift and the relative contribution of the metal absorption is therefore larger.c (cid:13) , 000–000 he flux distribution of the Ly α forest Figure 11.
Comparison of the flux PDF of our sample divided into two redshift bins with that of McDonald et al. (2000). The solidcurve and filled circles show the flux PDF of our sample before and after removal of the metal absorption, respectively. The lower panelshows the ratio of the flux PDF of McDonald et al. to that of our sample after removal of the metal absorption. optical depth, local gas density and temperature, the ob-served flux PDF can constrain astrophysical parameters ofthe IGM as well as cosmological parameters (Weinberg et al.1998; McDonald et al. 2000; Meiksin, Bryan & Machacek2001; Desjacques & Nusser 2005). The effect of the removalof metal absorption and the difference to the published fluxPDF by McDonald et al. is comparable or larger than theeffect of changing some of the model parameters within plau-sible ranges (e.g. Meiksin et al. 2001; Desjacques & Nusser2005). Our new improved measurement of the flux PDFshould therefore be relevant for attempts to use the fluxPDF to constrain astrophysical and cosmological parame-ters. i effective optical depth So far we have concentrated on the flux PDF of our sam-ple. The H i effective optical depth ( τ effH i ) is another intenselystudied quantity which is important for the comparison withmodels of the H i distribution. The H i effective optical depthis related to the mean flux as exp − τ effH i = < exp − τ H i > , where < > indicates the mean value averaged over wavelength.Note that the effective optical depth is not the average ofthe optical depth. The effective optical depth is the quan-tity which directly goes into measurements of the ampli-tude of the metagalactic UV background (Rauch et al. 1997;Bolton et al. 2005) and plays a crucial role in calibrating measurements of the matter power spectrum from Ly α for-est data based on the flux power spectrum (Croft et al.2002; Seljak et al. 2003; Tytler et al. 2004; Viel et al. 2004b;Lidz et al. 2006).As we have taken special care with the removal of themetal absorption in our spectra it is worthwhile to revisitthe effect the removal of the metal absorption has on the H i effective optical depth.In Fig. 12 we show the effective optical depth of our ob-served spectra before (open squares) and after (filled circles)removal of the metal absorption. The solid lines in both pan-els is the power-law fit of τ effH i to the optical depth of the high-resolution data from our sample and that compiled from theliterature, τ effH i = (0 . ± . z ) . ± . (the samepower-law fit as in Fig. 13). The errors of τ effH i were estimatedwith the same procedure adopted in McDonald et al. (2000)and Schaye et al. (2003) . Each spectrum was divided intochunks of 100 pixels (or 5 ˚A). We then performed 500 boot-strap realisations, treating each chunk as a one data point.The removal of the metal absorption leads to a typical reduc-tion in the observed effective optical depth (i.e. H i +metals)by 0.5% to 28% with the mean of ∼ Note that the modified jackknife method using a ∼
50 ˚A-longchunk generally gives error estimates of only ∼ ±
1% continuum un-certainty generally gives an error of ∼ (cid:13)000
1% continuum un-certainty generally gives an error of ∼ (cid:13)000 , 000–000 Kim et al.
Figure 12.
Left panel: Evolution of the effective optical depth of our full sample after removal of the metal absorption. The horizontaland vertical error bars show the redshift range used and the 1 σ errors. The 1 σ errors were estimated as in McDonald et al. (2000) andSchaye et al. (2003) using 500 bootstrap realisations of chunks of 100 pixels (5 ˚A). Right panel: Comparison of the evolution of theeffective optical depth of our full sample before (open squares) and after (filled circles) removal of the metal absorption. The solid linesin both panels represent a power-law fit to the effective optical depth τ effH i of our sample after removal of the metal absorption and othermeasurements from high-resolution data compiled from the literature at 1 . < z < τ effH i = (0 . ± . z ) . ± . . with a large scatter (see Table A4 in Appendix A). As men-tioned in Section 4.3, these numbers are estimated from theeffective optical depths of the observed spectra before and af-ter removal of the metal absorption. The H i effective opticaldepth is obviously also subject to the same systematic un-certainties as the flux probability distribution. The changeof continuum from C f to C ( C ) increases τ effH i by 0.049(0.010), which is identical for each QSO. The noise and theuncertainty in the zero-level flux have a negligible affect on τ effH i . The upper panel of Fig. 13 compares the τ effH i measure-ments of our 18 QSOs with those of Schaye et al. (2003).Both set of values are measured from spectra where metalabsorption has been removed. In the case of Schaye et al.(2003) this has been done by excising spectral regions con-taminated with strong metal absorption. The values are ingood agreement. Considering that half of the sample of spec-tra studied here is part of the sample of Schaye et al. (2003)this is not too surprising. For spectra common to both stud-ies the differences are, in most cases, less than 10% whenour wavelength ranges were adjusted to the ones used inthe Schaye et al. sample . Table A4 in Appendix A lists themeasurement of τ effH i as well as the mean flux, its varianceand the contribution of metal absorption in the forest. The There are several noticeable differences between the two τ effH i measurements. Since the two τ effH i values of the metal-includedspectra are very similar, the difference is mainly caused bythe incomplete metal removal in the Schaye et al. sample, i.e.their τ effH i is somewhat larger. QSOs with more than 10% dif-ference in τ effH i are: J2233 −
606 at 1 . < z < .
963 by ∼ − . < z < .
120 by ∼
11% and Q0002 −
422 at2 . < z < .
710 by ∼ − errors are estimated from the 500 bootstrap realisations ofa chunk of 5 ˚A.In the lower panel of Fig. 13 we have compiled a rangeof τ effH i measurements from the literature at 1 . < z < τ effH i from our sam-ple after removal of the metal absorption binned in red-shift bins with width ∆ z = 0 . τ effH i is estimated from the mean flux of all pixels ineach bin, instead of averaging the effective opacities of eachQSO (see Table A5 in Appendix A). The errors are esti-mated by the 500 bootstrap realisations of 5 ˚A using all pix-els in each bin. The open squares, filled squares and filledtriangles show the measurements of Schaye et al. (2003),Kirkman et al. (2005) and McDonald et al. (2000), respec-tively. The filled diamond at z = 1 .
86 and the open circle at z = 1 . . < z < .
3, although the latter did not includeany LLSs and removed the metal contribution statistically.The solid line in Fig. 13 is the best power-law fit to theoptical depth values of high-resolution data in the redshiftrange 1 . < z < τ effH i measurements are taken into account in the fit. Despitethe different method of measuring τ effH i , we also included theKirkman et al. measurement. Note that the point at z = 1 . τ effH i =(0 . ± . z ) . ± . . For our sample alone thepower law is τ effH i = (0 . ± . z ) . ± . . This fitis shallower than that of the combined τ effH i due to a smallnumber of QSOs and a lack of high- z QSOs in our sample c (cid:13) , 000–000 he flux distribution of the Ly α forest (cf. Kim et al. 2001; Kim et al. 2002). The dashed line isan extrapolated fit by Bernardi et al. (2003) to their lowresolution, low signal-to-noise SDSS data (their S/N > . < z <
4, while the dot-dot-dot-dashed line is a fit by Fan et al. (2006) to measurementsat 3 < z < . τ effH i ∝ (1 + z ) . ± . . The slope of the power law evolution measured byBernardi et al. is in good agreement within 1 σ . As discussedextensively in the literature (e.g. Seljak et al. 2003; Vielet al. 2004b) there is, however, a systematic offset of about ∼ τ effH i and our and othermeasurements from high-resolution, high S/N data. This ismost likely attributable to the difficulty of continuum fittingfor low resolution, low signal-to-noise data which appearsto lead to a systematic overestimate of the effective opticaldepth. The Fan et al. measurement (the dot-dot-dot-dashedline) has a somewhat steeper redshift evolution. This mightindicate that there is a deviation from a single power law at z >
4. Note that Becker, Rauch & Sargent (2007) have alsoargued that the redshift evolution at z > . < z <
4, we find no evidence for a deviation from apower law. Table A5 in Appendix A lists the measurementof τ effH i sampled at ∆ z = 0 . τ effH i of each QSObelonging to each redshift bin. We have obtained improved measurements of the flux prob-ability distribution at 1 . < z < . i absorption at 1 . < z < i andmetal absorption.The main results are as follows:(i) The normalised flux probability distribution (PDF) isaffected mainly by metals at the level of 10–20% at flux levelsof 0 . < F < . . < F <
1, depending on the signal-to-noise of the spectra.The effects of pixel noise and zero-level offset are very small,only noticeable at F ∼ F ∼
1. The metal contributionto the absorption varies from a few percent to up to 30percent between different lines of sight. A careful individualremoval of the metal absorption is therefore essential for anaccurate determination of the shape of the PDF.(ii) Our new measurements of the flux PDF due to H i alone are systematically lower at 0 . < F < . i absorption, compared to previous measurements where Figure 13.
Comparison of the evolution of the effective opticaldepth of our full sample after removal of the metal absorption(filled circles) with that measured in Schaye et al. (2003, greyopen squares). There is a large overlap in the two samples and asexpected the estimates from the two studies are in good agree-ment (for J2233 − σ errors. The er-rors were estimated using 500 bootstrap realisations of chunks ofspectra with 100 pixels. The lower panel shows a comparison ofthe evolution of the effective optical depth of our sample dividedinto redshift bins with width ∆ z = 0 . z = 1 .
86, and the open circle at z = 1 . . < z < τ H i = (0 . ± . z ) . ± . . The dashed curve is a fitfrom Bernardi et al. (2003) to their S/N > . < z < < z < . the metal absorption has been taken into account in sim-pler ways, is small. Our new measurements of τ effH i are ingood agreement with other measurements from high res-olution, high signal-to-noise spectra. In the redshift range1 . < z < τ effH i = (0 . ± . z ) . ± . . ACKNOWLEDGMENTS.
We would like to thank ESO, the ESO staff, the ESO scienceverification team and the UVES LP team of “The cosmicevolution of the intergalactic medium” for initiating, com-piling and making publicly available a superb set of QSO ab-sorption spectra. We also thank the UVES team for building c (cid:13) , 000–000 Kim et al. the spectrograph and our referee Michael Strauss for his use-ful suggestions. TSK would like to thank Michael Murphyfor providing his spectral combining program, UVES popler,and the IoA, Cambridge, UK, for hospitality during the finalstages of this work.
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Evolution of Large Scale Structure: From Recombinationto Garching , eds. A. J. Banday, R. K. Sheth & L. N. DaCosta (Twin Press: Vledder NL), p. 346Zhang Y., Anninos P., Norman M. L., Meiksin, A., 1997,ApJ, 485, 496 c (cid:13) , 000–000 he flux distribution of the Ly α forest Table A1.
The wavelength range of each spectrum in the threeredshift binsQSO
The wavelength range of each spectrum in the threeredshift binsQSO
Table A2.
Uncertain line fits for individual QSOs a QSO Uncertain line fitsQ0055–269 Si iii at z = 3 . ii z = 3 . ii z = 2 . iii at z = 2 . iii at z = 2 . iii z = 2 . iv z = 2 . iv z = 2 . ii z = 2 . ii z = 2 . i z = 2 . ii z = 2 . iii at z = 2 . ii z = 2 . ii z = 2 . iii at z = 2 . iii at z = 2 . iii at z = 2 . ii at z = 1 . iv z = 1 . iii at z = 1 . ii z = 1 . ii z = 2 . iii at z = 2 . iii at z = 2 . iii at z = 1 . iii at z = 1 . iii at z = 1 . ii z = 1 . iv . iii at z = 2 . ii z = 1 . ii z = 1 . ii z = 1 . iii at z = 1 . ii z = 1 . iii at z = 1 . iii at z = 1 . a The letters “m” and “l” indicate a “moderate” uncertainty and a “low” uncertainty, respectively. For the class “l” the H i profiles donot change significantly with and without the uncertain metal lines ( cf. Si ii iii absorption inFig. 3 f) is a typical uncertain line fit of class “m”. Table A3.
The mean PDF of the full sample divided into three and two redshift bins.
F < z > = 2 . < z > = 2 . < z > = 2 . < z > = 2 . a < z > = 3 . a ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± a The wavelength ranges for < z > = 2 .
41 and < z > = 3 .
00 are 3902–4325 ˚A (5 QSOs: HE2347 − − − −
423 and HE1347 − − − −
388 and and HE0940 − (cid:13) , 000–000 he flux distribution of the Ly α forest Table A4.
The H i effective optical depth a QSO wavelengths (˚A)
Table A5.
The evolution of the effective optical depth of the full sample divided into redshift bins with width ∆ z =0.2 a
606 3335–3525 0.203 ± − ± −
23 3361–3525 0.111 ± −
422 4012–4255 0.228 ± −
232 3306–3525 0.126 ± −
255 4012–4255 0.186 ± −
380 3282–3525 0.097 ± −
423 4084–4255 0.252 ± −
264 3282–3398 0.095 ± − ± ± ± −
385 3528–3769 0.128 ± −
388 4255–4498 0.266 ± − ± − ± − ± − ± − ± −
422 4255–4498 0.268 ± −
606 3525–3769 0.168 ± −
255 4255–4439 0.170 ± −
23 3525–3769 0.146 ± −
423 4255–4362 0.255 ± −
232 3525–3769 0.157 ± ± −
380 3525–3769 0.165 ± −
158 4638–4741 0.231 ± −
264 3525–3765 0.098 ± −
388 4498–4741 0.308 ± ± − ± −
422 3901–4012 0.269 ± − ± −
255 3815–4012 0.191 ± ± −
423 3769–3911 0.142 ± −
269 4785–4984 0.389 ± − ± −
158 4741–4984 0.310 ± −
385 3769–4012 0.138 ± −
388 4741–4914 0.380 ± − ± − ± − ± ± − ± −
269 4984–5227 0.362 ± −
606 3769–3886 0.096 ± −
158 4984–5112 0.203 ± b Q0055 −
269 5227–5577 0.462 ± a The errors were estimated using 500 bootstrap realisations of chunks of 100 pixels (5 ˚A). For each bin, τ effH i was estimated from themean flux of all pixels from the QSOs listed. b Q0055 −
269 is the only QSO in this z bin.c (cid:13)000