Mon.Not.R.Astron.Soc.000,000–000(0000) Printed1February2008 (MNLATEXstylefilev2.2) Glimpsing through the high redshift neutral hydrogen fog 1⋆ 1 2 3 S. Gallerani , A. Ferrara †, X. Fan ‡, T. Roy Choudhury § 1SISSA/InternationalSchoolforAdvancedStudies,viaBeirut2-4,34014Trieste,Italy 8 2StewardObservatory,TheUniversityofArizona,Tucson,AZ85721,USA 0 3InstituteofAstronomy,MadingleyRoad,CambridgeCB3OHA,UK 0 2 n 1February2008 a J 0 ABSTRACT 3 We analyze the transmitted flux in a sample of 17 QSOs spectra at 5.74 ≤ z ≤ 6.42 to em obtaintighter constraintson the volume-averagedneutralhydrogenfraction,xHI, at z ≈ 6. ] We study separately the narrow transmission windows (peaks) and the wide dark portions h p (gaps)in the observedabsorptionspectra. By comparingthe statistics of these spectralfea- - tureswithasemi-analyticalmodeloftheLyαforest,weconcludethatxHI evolvessmoothly o from10−4.4atz =5.3to10−4.2atz =5.6,witharobustupperlimitxHI <0.36atz =6.3. r t Thefrequencyandphysicalsizesofthepeaksimplyanoriginincosmicunderdenseregions s and/or in HII regions around faint quasars or galaxies. In one case (the interveningHII re- a [ gion of the faint quasar RD J1148+5253at z = 5.70 along the LOS of SDSS J1148+5251 atz = 6.42)the increaseofthepeakspectraldensityis explainedbythefirst-everdetected 2 transverseproximityeffectintheHILyαforest;thisindicatesthatatleastsomepeaksresult v fromalocallyenhancedradiationfield.Wethenobtainastronglowerlimitontheforeground 3 QSOlifetimeoft > 11Myr.Theobservedwidthsofthepeaksarefoundtobesystemati- 5 Q callylargerthanthesimulatedones.Reasonsforsuchdiscrepancymightresideeitherinthe 0 photoionizationequilibriumassumptionorinradiativetransfereffects. 1 . 6 Keywords: cosmology:large-scalestructureofUniverse-intergalacticmedium-quasars: 0 absorptionlines 7 0 : v i X 1 INTRODUCTION ofLAEsareroutinelyfoundatz > 6(e.g.Sternetal.2005; Iye etal.2006;Starketal.2007),possiblyrequiringasubstantialfree r Althoughobservationsofcosmicepochsclosertothepresenthave a electronfraction,resultinginanIGMrelativelytransparenttoLyα indisputablyshownthattheInterGalacticMedium(IGM)isinan photons. ionized state,itisyet unclear whenthephase transitionfromthe ConstraintsontheIGMionizationstatederivedbyusingLyα neutralstatetotheionizedonestarted.Thus,theredshiftofreion- forestspectroscopymusttakeintoaccounttheextremelyhighsen- ization,z ,isstillveryuncertain. rei sitivityofτ totinyneutralhydrogenamounts.Indeed,avolume AfterthefirstyearWMAPdataapossibletensionwasidenti- GP fiedbetweenCMBandSDSSresults.Thehighelectron-scattering averaged neutral hydrogen fraction as low as xHI ∼ 10−3 (Fan etal.2002)issufficienttocompletelydepressthetransmittedflux optical depth inferred from the TE-EE power spectra τ ≈ 0.17 e inQSOabsorptionspectra;thus,thedetectionofaGunn-Peterson (Kogutetal.2003;Spergeletal.2003)seemeddifficulttoberecon- ciledwiththestrongevolutionintheGunn-Petersonopticaldepth trough only translates into alower limitfor xHI. For this reason, recently,manystudieshavetriedtoclarifyiftheSDSSdataeffec- τ at z = 6 (Fan et al. 2001; Fan et al. 2003), accompanied GP tivelyrequirethattheIGMwasreionizedaslateasz ≈6(Gallerani bytheappearanceoflargedarkportionsinQSOabsorptionspec- et al. 2006, hereafter GCF06; Becker et al. 2006): in particular, tra (Becker et al. 2001; Djorgovski et al. 2001; Fan et al. 2006, GCF06 have shown that QSO observational data currently avail- hereafter F06). The 3-yr WMAP results have released the above ablearecompatiblewithahighlyionizedUniverseatthatredshift. tension by providing a smaller value for τ ≈ 0.1, which im- e pliesz ≈ 11foramodelwithinstantaneousreionization(Page Clearlythedeterminationofthereionizationepochisstrictly rei et al. 2006; Spergel et al. 2006). However, an increasing number related to the measurement of the neutral hydrogen fraction at z ≈ 6. To investigate this issue many different approaches can be used. To start with, it is worth mentioning that many authors ⋆ E-mail:galleran@sissa.it have tried to constrain xHI at high redshift by analyzing statisti- † E-mail:ferrara@sissa.it callytheopticaldepthinsideHIIregionsaroundhighredshiftQSO ‡ E-mail:fan@as.arizona.edu (Mesinger&Haiman2004;Mesinger&Haiman2006),orbymea- § E-mail:chou@ast.cam.ac.uk suringtheQSObubblesizes(Wyithe&Loeb2004; Wyitheetal. 2 S. Gallerani,A.Ferrara,X.Fan,T. RoyChoudhury Figure1.Leftpanel:Evolutionofthevolumefillingfactorofionizedregionsfortheearly(redsolidlines)andlate(bluedottedlines)reionizationmodels. Middlepanel:Volume-averaged photoionization rateΓ−12 = ΓHI/10−12s−1.Thefilledcircles,emptycircles,filledtrianglesandemptytrianglesshow resultsobtainedbyF06,MM01,B05andB07,respectively.Rightpanel:Evolutionoftheneutralhydrogenfraction.Thicklinesrepresentaverageresultsover 100LOS,whilethethinlinesdenotetheupperandlowerneutralhydrogenfractionextremesineachredshiftinterval.Solidcirclesrepresentneutralhydrogen fractionestimatesbyF06;emptysquaresdenotetheresultsobtainedinthiswork. 2005; Bolton & Haehnelt 2007b; Maselli et al. 2007, Lidz et al. comparison are given in Section 4; in Section 5 we evaluate the 2007).However,sufficientgroundforcontroversyremainsdueto robustness of our method against the specific line of sight to the intrinsicuncertaintiesofthevarioustechniques. highestredshiftQSO.TheconclusionsaresummarizedinSection By deriving sizesof HII bubbles surrounding observed z = 6. 6.5LAEs,Malhotra&Rhoads2005haveprovidedanupperlimit fortheneutralhydrogen fractionxHI . 0.2−0.5. Thisresultis inquitegoodagreementwiththeupperlimitxHI.0.45foundby 2 SIMULATIONS Kashikawaetal.2006, byinterpretingthedeficitmeasuredatthe brightendoftheLAELuminosityFunctionatz > 6asasudden The radiation emitted by QSOs could be absorbed through Lyα changeintheintergalacticneutralhydrogencontent.Nevertheless, transitionbytheneutralhydrogenintersectingthelineofsight,the theincreasingattenuationwithredshiftoftheLyαlinetransmission so-called Gunn-Peterson (GP) effect. The Lyα forest arises from could bepartiallyexplained asaconsequence of theevolution in absorption by low amplitude-fluctuations in the underlying bary- themassfunctionofdarkmatterhalos,thusimplyingamuchlower onicdensityfield(Bi,Bo¨rner&Chu1992),andisanaturalconse- upperlimit,xHI<0.05−0.2(Dijkstraetal.2007). quenceofthehierarchicalstructureformationexpectedinthecon- GRBspectroscopyhasalsotentativelyusedtoconstrainxHI; textofCDMcosmologies1. Totani et al. 2006 have observed a damping wing at wavelengths TosimulatetheGPopticaldepth(τ )distributionweusethe GP largerthantheLyαemissionline,findingthatthisfeaturecanbe methoddescribedbyGCF06,whosemainfeaturesarerecalledin explainedatbestbyassuminganinterveningdampedLyαsystem thefollowing.Thespatialdistributionofthebaryonicdensityfield immersed in a fully ionized IGM, and quoting an upper limit of anditscorrelationwiththepeculiarvelocityfieldaretakenintoac- xHI < 0.17 and 0.60 (68% and 95% confidence levels, respec- countadoptingtheformalismintroducedbyBi&Davidsen1997. tively). Toenterthemildlynon-linearregimewhichcharacterizestheLyα Finally,thewidthdistributionofdarkportions(gaps)seenin forestabsorbersweuseaLog-NormalmodelintroducedbyColes QSO absorption spectra has been recently introduced in order to &Jones 1991, widelyadopted later on (Bi 1993; Bi & Davidsen constraintheIGMionizationstate(Paschos&Norman2005;F06; 1997; Choudhury, Padmanabhan, & Srianand 2001; Choudhury, GCF06).F06hasusedthedarkgapdistribution,asobservedin19 Srianand,&Padmanabhan2001;Vieletal.2002;GCF06).Inpar- high-z QSOspectra,toputapreliminaryupper limitontheIGM ticular,GCF06have compared various Lyαstatistics,namely the neutral fraction xHI < 0.1−0.5. GCF06, by analyzing the sta- Probability Distribution Function (PDF) and the Gap Width dis- tisticallypropertiesofthetransmittedfluxinsimulatedabsorption tribution,computedusingtheLog-Normaldistributionwiththose spectra,haveshownthatthegapandpeak(i.e.transmissionwin- dows) widthstatisticsareverypromising toolsfor discriminating betweenanearly(z >6)andalate(z ≈6)reionizationsce- 1 Throughoutthispaperwewillassumeaflatuniversewithtotalmatter, rei rei nario.Herewecombinetheprevioustworesults:bycomparingthe vacuum, andbaryonic densities inunits ofthecritical densityofΩm = observed transmitted flux in high-z QSO spectra with theoretical 0.24,ΩΛ=0.76,andΩbh2=0.022,respectively,andaHubbleconstant predictions we obtain tighter constraints on the neutral hydrogen ofH0 = 100hkms−1Mpc−1,withh = 0.73.Theparametersdefining the linear dark matter power spectrum are n = 0.95, dn/dlnk = 0, fractionaroundz=6,acrucialepochinthereionizationhistory. σ8 =0.82.Notethatwehavechosenaσ8valuehigherthantheWMAP3 The plan of the paper is the following: in Section 2 we de- one(0.74).IndeedVieletal.2006,bycombiningWMAP3datawithSDSS scribethesemi-analyticalmodelingadopted;inSection3wecom- ones,foundσ8 ≈ 0.78(0.86)analyzinghigh(low)resolutionLyαforest pareobservational datawithsimulations.Theimplicationsofthis data.Mpcarephysicalunlessdifferentlystated. Glimpsingthroughthehighredshiftneutralhydrogenfog 3 Figure2.Leftpanel:EvolutionoftheGunn-Petersonopticaldepthforearly(ERM,solidredline)andlate(LRM,bluedotted).Thicklinesrepresentaverage resultson100LOSforeachemissionredshift,whilethethinlinesdenotetheupperandlowertransmissionextremesineachredshiftbin,weightedon100 LOS.FilledandemptycirclesareobservationaldatafromSongaila2004andF06,respectively.Middlepanel:ProbabilityDistributionFunction(PDF)ofthe fluxatz=6.0.FilledcirclesareobtainedbyFanetal.2002.Thicklinesrepresentsimulatedresultsaveragedover500LOS,whilethethinlinesdenotecosmic variance.Rightpanel:GapWidthdistributionintheredshiftrange5.0-5.5.SimulatedresultsarecomparedwithobservationsbySongaila&Cowie2002(filled circles).Theerrorsassociatedtobothsimulatedandobservedresultsdenotecosmicvariance. obtainedfromHYDROPMsimulations,findingagoodagreement forthetwomodelswiththerecentestimatebyF06,andtheones betweentheresults.ForagivenIGMtemperature,theHIfraction, by McDonald & Miralda-Escude’ 2001, Bolton et al. 2005, and xHI, can be computed from the photoionization equilibrium as a Bolton&Haehnelt2007a,hereafterMM01,B05andB07,respec- functionofthebaryonicdensityfieldandphotoionizationratedue tively.Finally,theevolutionofthevolume-averagedneutralhydro- totheultravioletbackgroundradiationfield.Forallthesequantities genfractionfor theERMand LRMispresented intherightmost we follow the approach of Choudhury & Ferrara 2006, hereafter panel. CF06. By assuming as ionizing sources QSOs, PopII and PopIII Thephotoionizationratepredictedbybothmodelsisinagree- stars (the latter neglected here, see below), their model provides mentwiththeresultsbyB05andB07atintherangez = 4.0 < excellent fitstoalargenumber of observational data,namely the z <6,whereasatz =5.5(6)theERMischaracterizedbyapho- redshift evolution of Lyman-limit systems, Lyα and Lyβ optical toionizationratewhichis≈2(6)timeslargerthantheestimatesby depths,electronscatteringopticaldepth,cosmicstarformationhis- F06.Inspiteofthesedifferences,ourpredictionsforxHIarecon- tory,andthenumbercountsofhighredshiftsources.IntheCF06 sistent with F06 measurements. This apparent contradiction does model, a reionization scenario is defined by the product of two not come as a surprise. In fact, the derivation of ΓHI requires an free parameters: (i) the star-formation efficiency f∗, and (ii) the assumption concerning the IGMdensity distribution. When mea- escapefractionfesc ofionizingphotonsofPopIIandPopIIIstars; suring ΓHI at 5 < z < 6, F06 assume the density Probability itisworth noting that theseparameters aredegenerate, since dif- DistributionFunctiongivenbyMiralda-Escude’etal.2000,here- ferentparametervaluescouldprovideequallygoodfitstoobserva- after MHR3. We instead adopt a Log-Normal (LN) model which tions.Inthiswork,byfittingalltheaboveobservationalconstraints, predictsahigher probabilitytofindoverdensities ∆ = ρ/ρ¯ & 1 weselecttwosetsoffreeparametersvaluesyieldingtwodifferent thanMHR.Forexample,atz = 6andfor∆ ≈ 1.5,P (∆) ≈ LN reionizationhistories:(i)anEarlyReionizationModel(ERM)for 2×P (∆)).Forthisreason,onceτ isfixedtotheobserved MHR GP (f∗,PopII = 0.1;fesc,PopII = 0.07),and(ii)aLateReionization value,theLNmodelrequiresahigherΓHI.AsxHI∝∆,thesetwo Model (LRM)for (f∗,PopII = 0.08;fesc,PopII = 0.04). Wedo effectscombinetogiveavaluesofxHIconsistentwiththedata. not consider contributions from PopIII stars, as PopII stars alone yield τ = 0.07 (0.06) for ERM (LRM), marginally consistent e withWMAP3results2. 3 COMPARISONWITHOBSERVATIONS Fig.1showstheglobalpropertiesofthetworeionizationmodels considered.IntheERMthevolumefillingfactorofionizedregions, 3.1 Controlstatistics Q =V /V =1atz≤7;intheLRMitevolvesfrom0.65 HII HII tot Wefirsttestthepredictionsofourmodelbyapplyingvarioussta- tounityintheredshiftrange7.0-6.0,implyingthattheUniverseis tisticalanalysistothesimulatedspectraandcomparingourresults stillinthepre-overlapstageatz ≥ 6,i.e.thereionizationprocess withobservations.Specifically,weusethefollowingcontrolstatis- isnotcompleteduptothisepoch.Inthemiddlepanelofthesame tics:(i)MeanTransmittedFluxevolutionintheredshiftrange2−6; Figurewecomparethevolume-averagedphotoionizationrateΓHI 3 F06require ΓHI tomatch the MM01measurement at z = 4.5. This 2 Small contributions from PopIII stars, i.e. f∗,PopIII = 0.013 estimateisbasedonameantransmittedflux(F¯ = 0.25)whichislower (f∗,PopIII = 0.08), in the ERM (LRM), would yield τe = 0.09 thanthemorerecent measurements F¯ ≈ 0.32bySongaila2004,which (τe=0.08),withoutaffectingsensitivelytheresultsbelow. impliesΓHI≈0.3. 4 S. Gallerani,A.Ferrara,X.Fan,T. RoyChoudhury Figure3.LargestGapWidthdistributionfortheLRandtheHRcases(leftandright,respectively).Filledcirclesrepresenttheresultoftheanalysisofthe17 QSOsobservedspectra.Solidred(dottedblue)linesshowtheresultsobtainedbythesemi-analyticalmodelingimplementedfortheERM(LRM).Vertical errorbarsmeasurepoissoniannoise,horizontalerrorsdefinethebinforthegapwidths. (ii)ProbabilityDistributionFunction(PDF)ofthetransmittedflux We divide the observed spectra into two redshift-selected sub- atthemeanredshiftsz = 5.5,5.7,6.0;(iii)GapWidth(GW)dis- samples: the “Low-Redshift” (LR) sample (8 emission redshifts tribution in 3.5 ≤ z ≤ 5.5. For what concerns the GW statis- 5.7 < z < 6),andthe“High-Redshift”(HR)one(9emission em ticswedefinegapsascontiguous regionsof thespectrum having redshifts6 < z < 6.4). Simulatedspectrahavethesamez em em aτ > 2.5overrest-framewavelength(λ )intervals> 1A˚. distributionoftheobservedsamples.FormostQSOsweconsider GP RF ThismethodwasfirstsuggestedbyCroft(1998)andthenadopted the(λ ) interval 1026-1200 A˚ andwenormalize eachwidthto RF by various authors (Songaila &Cowie 2002; Paschos & Norman thecorresponding redshiftpath.NotethattheLOSdonotextend 2005; F06; GCF06).The comparison of model and observational uptoz ;theupper(lower)limitoftheintervalchosenensuresthat em resultsintermsoftheabovethreestatisticsisplottedinFig.2.By weexcludefromtheanalysistheportionsofthespectrapenetrat- checking our models wefollow thesame approach of GCF06,to inginsidetheQSOHII(Lyβ)region.FortheQSOsSDSSJ1044- whichwereferforacompletedescriptionofthetechnicaldetails. 0125andSDSSJ1048+4637wechoosedifferentintervals,namely The outcome of the test is encouraging, as both ERM and 1050-1183 and 1050-1140, respectively. These two objects have LRMsuccessfully match the observational data at z ≤ 6 for the beenclassifiedasBALQSO(Goodrichetal.2001;Fanetal.2003; controlstatisticsconsidered.Thisallowsustoconfidentlyproceed Maiolino et al. 2004), since their spectra present Broad Absorp- thecomparisonwithmoreadvancedstatisticaltools. tionLinesassociatedwithhighlyionizedatomicspecies(e.g.SiIV, CIV).Byselectingtheaboveintervalsweexcludethoseportionsof thespectracharacterizedbyCIVabsorptionfeatureswhichextend 3.2 Advancedstatistics toz ≈5.56(z≈5.75)inSDSSJ1044-0125(SDSSJ1048+4637). ObserveddataweretakenwithaspectralresolutionR ≈ 3000− Since at z ≈ 6 regions with high transmission in the Lyαforest 6000; simulated spectra have been convolved with a gaussian of becomerare,anappropriatemethodtoanalyzethestatisticalprop- FWHM = 67 km/sec, providing R ∼ 4500. Moreover each ertiesofthetransmittedfluxisthedistributionof gaps.Inpartic- observed/simulatedspectrumhasbeenrebinnedtoaresolutionof ularGCF06suggestedthattheLargestGapWidth(LGW)andthe R=2600.Finally,weaddnoisetothesimulateddatasuchthatthe LargestPeakWidth(LPW)statisticsaresuitabletoolstostudythe fluxF ineachpixelisreplacedbyF +G(1)×σ ,whereG(1)is ionizationstateoftheIGMathighredshift4.TheLGW(LPW)dis- n aGaussianrandomdeviatewithzeromeanandunitvariance,and tributionquantifiesthefractionofLOSwhicharecharacterizedby σ istheobservednoiser.m.sdeviationofthecorrespondingpixel. thelargestgap(peak)ofagivenwidth.Asfarasthisworkiscon- n The results provided by the statistics adopted in this study cerned, we apply the LGW and the LPWstatistics both to simu- aresensitive to theS/N ratio, since spurious peaks could arisein latedandobservedspectrawiththeaimofmeasuringtheevolution spectral regions with noise higher than the F adopted. Indeed, ofxHIwithredshift. th theshapeoftheLGW/LPWdistributionsdependsontheF cho- We use observational data including 17 QSOs obtained by F06. th sen.Thus,weconsidertwodifferentvaluesforF ,namely0.03 th and0.08,respectively,and,forbothofthem,computepreliminary 4 Thedefinition of“peak”inthetransmitted fluxissimilartothe“gap” LGW/LPWdistributions.Finally,theLGW/LPWdistributionspre- one. A peak is a contiguous region of the spectrum over λRF intervals sentedareobtainedasthemeanofthepreliminaryones,weighted greaterthantheobservedpixelsize(≈0.5A˚)characterizedbyatransmis- on the corresponding errors (See Appendix A for a detailed dis- sionaboveagivenfluxthreshold(Fth=0.08inthiswork). cussion). In our analysis we do not consider 2 QSOs presented Glimpsingthroughthehighredshiftneutralhydrogenfog 5 Figure4.LargestPeakWidthdistributionfortheLRandtheHRcases(leftandright,respectively).Filledcirclesrepresentobservationaldataobtainedby analyzingtheobservedspectraofthe17QSOsconsidered.Solidred(dottedblue)linesshowtheresultsobtainedbythesemi-analyticalmodelingimplemented fortheERM(LRM).Verticalerrorbarsmeasurepoissoniannoise,horizontalerrorsdefinethebinforthepeakwidths. byF06,namelySDSSJ1436+5007 andSDSSJ1630+4012, since ByapplyingthesamemethodtotheHRsampleweconstrainthe thesespectrahavesignificantlylowerS/NtoapplyLGW/LPWtests neutralhydrogenfractiontobewithinlog10xHI = −4.2+−01..804 at (continuumS/N.7). z≈5.6. AlthoughthepredictedLGWdistributionsarequitesimilarforthe two models considered, yet some differences can be pointed out. 3.2.1 LGWdistribution BothfortheLRandHRcasestheearlyreionizationLGWdistribu- tionprovidesaverygoodmatchtotheobservedpoints,thussug- WenowdiscusstheLGWdistributionforobserved/simulatedspec- gestingz & 7.TheagreementissatisfactoryalsofortheLRM, tra;theresultsareshown inFig.3. TheQSOsemissionredshifts rei butitisimportanttonoticethatlatereionizationmodelspredicttoo usedandtheλ intervalchosenfortheLRsamplearesuchthat RF manylargestgaps≈60A˚ intheLRcaseandtoofewgaps≈20A˚ the mean redshift of the absorbers is hzi = 5.26, with a mini- intheHRone.Giventhelimitedquasarsampleavailable,thestatis- mum (maximum) redshift z = 4.69 (z = 5.86), and a min max ticalrelevanceoftheLRMdiscrepanciesisnotsufficienttofirmly r.m.s. deviation σ = 0.06. For the HR sample it is hzi = 5.55, ruleout thisscenario. However, sinceintheHRcase40% of the z = 4.90,z = 6.32,σ = 0.14.TheobservedLGWdis- min max linesofsightextendatz&6,wecanusetheLRMresultstoputan tributionevolves rapidly withredshift: inthe LR sample most of theLOSarecharacterizedbyalargestgap< 40A˚,whereasgaps upperlimitonxHIatthisepoch.IndeedintheHRcasewefindthat aslargeas100A˚ appearintheHRsample.ThismeansthatLOS aneutralhydrogenfractionatz≈6higherthanthatonepredicted bytheLRMwouldimplyanevenworstagreementwithobserva- toQSOsemittingatz . 6encounter “opticallythick”regions em tions, since a more abundant HI would produce a lower (higher) whosesizeis≤20Mpc,whileforz & 6blankregionsofsize em fractionof LOScharacterized by the largest gapsmaller (higher) upto46Mpcarepresent. than40A˚ withrespect toobservations. Thus,thisstudysuggests Superposed to the data in Fig. 3 are the predicted LGW distri- butionscorresponding toERMandLRM,obtainedbysimulating xHI < 0.36 atz = 6.32 (obtained fromthemaximum valuefor 800/900 LOS in the LR/HR case, corresponding to 100 LOS for xHIfoundintheLRMatthisepoch). eachemissionredshiftineachsample.InourERMsimulatedspec- tra, at z ≈ 6 gaps are produced by regions characterized by a 3.2.2 LPWdistribution mean overdensity ∆¯ ≈ 1 (∆ = 0.05, ∆ = 18) with a min max xHI ≈ 10−4, averaging on 100 LOS (xHI,min = 1.1 × 10−5, Next,weapplytheLargestPeakWidth(LPW)statistics(Fig4)to xHI,max=3.6×10−4). bothobservedandsimulatedspectra.FromtheobservedLPWdis- ItresultsthatboththepredictedLGWdistributionsprovideagood tribution we find that, in the LR (HR) sample, about 50% of the fittoobservationaldata.Weexploittheagreementbetweenthesim- linesofsight exhibit peaksofwidth< 12(8) A˚.Inmoredetails, ulated and observed LGW distributions to derive an estimate of thesizeP of thelargesttransmissionregions intheobserved max xHI,showninFig.1.Wefindlog10xHI=−4.4+−00..8940atz≈5.35. sampleare3 . Pmax . 10(1 . Pmax . 6)Mpcathzi = 5.3 (5.6).Thefrequencyandtheamplitudeofthetransmissionregions 5 ThexHIvaluequotedisthemeanbetweentheestimatespredictedbythe ERMandtheLRM.Moreover,weconsiderthemostconservativecasein providedbytheminimumxHIvaluefoundintheERMandthemaximum whichtheerrorsforthemeasurementoftheneutralhydrogenfractionare oneintheLRM. 6 S. Gallerani,A.Ferrara,X.Fan,T. RoyChoudhury rapidly decrease toward high redshift. This could be due both to isshiningonlyforafractionoftheHubbletimet /t ≈10−2at Q H theenhancementoftheneutralhydrogenabundanceatepochsap- z=5.5. proachingreionizationortoevolutionaryeffectsofthedensityfield In addition to the peak frequency, additional constraints on the (Songaila2004). Infactthegrowth factor D+ of densityfluctua- propertiesoftheionizingsourcescomefrombubblephysicalsizes. tionsdecreaseswithredshift(D+(z=6)=3/5×D+(z=3)for ΛCDM),thusimplyingalowdensitycontrastatz = 6withre- 4.1 QSOHIIregions specttolaterepochs.Stateddifferently,underdenseregionsthatare transparentatz=3,werelessunderdenseatz =6,thusblocking First,weconsiderthecaseinwhichthelargestpeaksareproduced transmission. As a consequence of the density field evolution to- byHIIregionsaround QSOs.Thebubble sizeR isrelatedto HII wardhigherz,onlyfew/smallpeakssurviveandwideGPtroughs theionizingphotonsemissionrateN˙ andQSOlifetimet as γ Q appear. SuperposedtothedatainFig.4arethepredictedLPWdistri- R = 3N˙γtQ 1/3, (2) butionscorresponding toERMandLRM,obtainedbysimulating HII „4πnHI« 800/900 LOSintheLR/HRcase. Inour ERMsimulatedspectra, wherenHI istheneutralhydrogennumberdensity.Eq.(2)applies at z ≈ 6, gaps are interrupted by narrow transparent windows for a homogeneous IGM and does not take into account both re- (i.e. peaks) originating from underdense regions with ∆¯ ≈ 0.1, combinationsandrelativisticeffects. averaging on 100 LOS (∆ = 0.03, ∆ = 0.26) and min max Therecombinationtimescalet isgivenby: xHI≈2×10−5,(xHI,min=7.8×10−6,xHI,max=3.6×10−5). rec Regions characterized by ∆ ∈ [0.05;0.26] and xHI ∈ [1.1 × trec =[CαBnH(1−xHI)]−1, (3) 10−5;3.6×10−5]couldcorrespondtobothgapsorpeaksdepend- whereC ≃26.2917exp[−0.1822z+0.003505z2]istheclumping ing on redshift and peculiar motions of the absorbers producing factor(Ilievetal.2007),α =2.6×10−13cm3s−1isthecaseB B them. hydrogenrecombinationcoefficientevaluatedatT = 104 K,and By comparing the simulatedLPWdistributions withthe ob- nH = 7×10−5[(1+z)/7]3cm−3 isthemeanhydrogennumber servedone, itisevident that simulationspredict peak widthsthat density.Thus,attheredshiftsofinterestz ≈6,eveninthelimiting aremuchsmallerthantheobservedonesbothforLRandHRcases. case xHI = 0, trec ≈ 2×108yr, thus being larger than typical In particular, in no LOS of our simulated samples we find peaks QSOslifetimet ≈ 107.Thisshowsthateq.(2)providesaplau- largerthan8A˚.Thedisagreementbetweentheobservedandsimu- Q sible value for the HII region extent. For instance, Maselli et al. latedLPWdistributionsdoesnotaffecttheestimateofxHIthrough (2007) haveshownthateq.(2)matchesquitewellthemeanvalue theLGWdistributions,sinceathighredshiftthepeaksarenarrow oftheHIIregionsizedeterminedthroughradiativetransfercalcu- (. 10A˚).Wediscussthepossiblereasonsforthisdiscrepancyin lations. thefinalSection. InthisSection,weneglect relativisticeffectswhichcouldsquash theionizationfrontalongthesight-line(Whiteetal.2003;Wyithe etal.2005b;Yu2005;Shapiroetal.2006),possiblyreducingthe 4 PHYSICALINTERPRETATIONOFTHEPEAKS lengthofthelinesofsight interestedbytheproximityeffect. We willdiscussthisissueindetailinSec.5,whenaddressingthefirst Themostnaturalinterpretationforthepeaksisthattheycorrespond observedcaseoftransverseproximityeffect. tounderdenseregions,wherethelowHIdensityofthegasallows Atz=5.5,assumingxHI=5.6×10−5(seeFig.1),RHII = ahightransmissivity.However,inprincipletheycouldalsoariseif 1 (10) Mpc could be produced by a QSO emitting a number of individualionizedbubblesproducedbyQSOsand/orgalaxiesare ionizing photons N = N˙ t = 7 × 1065 (7 × 1068). Thus, γ γ Q crossedbytheLOS.Inthelattercasethetypicalphysicalsizeand assumingaQSOlifetime≈ 107yr,theobservedpeaksintheLR frequencyofsuchsemi-transparentregionsmustberelatedtothe (HR)samplerequireN˙ = 2.2×1051 (2.2×1054)s−1,which γ emissionpropertiesandmassesofsuchobjects.Stateddifferently, wouldcorrespond tosources≈ 6(3) ordersof magnitudefainter thefractionofLOS,fLOS,havingthelargestpeakwidthequalto than QSOs observed at z ≈ 6, typically having N˙γ ≈ 1057s−1 Pmax can be interpreted as the probability ℘ to intersect an HII (Haiman&Cen2002)andblackholemassesMBH ≈109M⊙. regionofradiusRHII around adarkmatterhalohostingeithera SofarwehaveassumedthatthegasinsidetheHIIregionis QSOoragalaxyalongtheredshiftpath(zi−zf)spannedbythe fullyionizedor,stateddifferently,thatalongtheredshiftpathen- LOS. The comoving number density nh of dark matter halos of compassedbytheionizedbubblethefluxiscompletelytransmitted. massMhisrelatedto℘throughthefollowingequation: However, this is unlikely since a sufficiently high opacity due to n (M )= 3H0Ωm1/2(πR2 )−1 (1+z)3/2|zf −1℘, (1) rheysdornoagnetn(dinasmidpein(gouwtsinidge))otphteicaHlIdIerpetghioansscoacniatperdodwuictehtdhaerkneguatprasl. h h 2 c HII h zii Thus,therelationbetweenP andR is max HII WetakeR = 1(10)Mpc,consistentwiththesmaller(larger) HII H(z¯)λ (1+z¯) size Pmax of the observed largest peaks in the HR (LR) sample. Pmax = c Lyα(1+z )ftRHII =A(z)ftRHII, (4) As it is likely that statistically the LOS crosses the bubble with em non-zeroimpactparameter,adoptingR = P seemsarea- where f is the mean transmitted flux computed inside the prox- HII max t sonableassumption.Byfurtherimposing℘ = f wefindthat imityregion.Wewillderivef inSec.5fromanobservedcaseof LOS t n = 3.7×10−6 (2.2×10−8)Mpc−3 forP = 1(10)Mpc transverseproximityeffect, notethatvalues off < 1wouldre- h max t in the redshift range z = 5 to z = 6. Given our cosmology, sultinalargerluminosityoftheQSOproducingthetransmissivity i f such halo number density can be transformed at z = 5.5 into a window. typicalhalomassofMh & 1012 (1013)M⊙ (Mo&White2002). Finally,powerfulQSOs,asthoseobservedatz≈6,couldproduce Thus,thehaloshostingtheputativeluminoussourcesproducingthe transmissionwindowsconsistentwithobservationaldataiftheyare peaksmustbemassive.NotethatthisresultholdseveniftheQSO embeddedinoverdenseregionswherethehighdensitysustainsan Glimpsingthroughthehighredshiftneutralhydrogenfog 7 initialneutral fraction,xHI & 0.1, beforetheQSOturnson.The ThetwoQSOshaveaprojectedseparationof109”,whichcor- expansion of the HII region in such environment would result in respondstoR⊥ =0.66Mpc.ThelineofsighttoQSO2intersects considerablysmallersizes(Masellietal.2007).Inthiscase,both thebubbleproducedbyQSO1foraredshiftpath(∆z )whose prox thehostdarkmatterhalomassfoundabove(Mh ≈1012M⊙),and lengthdepends ontheradiusof theHII region(RHII) itself.We the sizeof theHII region would combine togive the correct fre- findR =39Mpc,bypluggingineq.(2)thefollowingvalues: HII quencyandspectralwidthoftheobservedpeaks. tQ =1.34×107yr,xHI =8.4×10−5,N˙γ =8.6×1055sec−1, wherexHIisprovidedbythemeanvaluebetweenthosepredicted byourmodelsatz =5.7(seerightmostpanelofFig.1),whileN˙ γ 4.2 GalaxyHIIregions iscompatiblewiththeluminosityofaQSO3.5magnitudesfainter thanQSO2(Mahabaletal.2005).InthisSection,wealsotakeinto InadditiontoQSOs,transmissivitywindowscouldbeproducedby accountrelativisticeffectswhichcouldsquashtheionizationfront HII regions around high-z galaxies. Adopting the canonical rela- alongtheLOS(Whiteetal.2003; Wyitheetal.2005b; Yu2005; tions Shapiroetal.2006).TheapparentsizeoftheHIIregion,computed M∗ =f∗ΩΩb Mh; Nγ =n¯γMm∗; fescNγ = 43πnHIRH3II, (5) followingthemethodoutlinedinYu2005,isshowninFig.5.By m p zoomingtheregionclosetoQSO1(smallboxinFig.(5))itisclear where M∗ is the stellar mass, n¯γ is the number of ionizing pho- that the apparent size of the HII region extends up to 2 Mpc in tonsperbaryonintostars,andm istheprotonmass,therelation thedirectiontowardQSO2.GivenR ,takingintoaccount rel- p HII betweenMhandRHII isgivenby: ativisticeffects, theregion ∆zprox extends fromz = 5.16 upto 3 z = 5.68. We re-compute xHI along the LOS to QSO2, adding 1+z Mh =3×108M⊙„ 6.5 « y−1RH3II, (6) rtoatethΓeQuSnOifo1rpmroUviVdeBdpbhyoQtoSioOn1iz,aotibotnainraetdesΓtaHrItinthgefrpohmotothioenfiozlaltoiwon- HI wherey−1=(xHIf∗−1fe−s1c)/0.1andweareassumingn¯γ =4000, ingequations: appropriateforaPopIIstellarpopulationwithastandardSalpeter ∞ J ν −3 fIMF;=we0a.s0s1u.mTehtehemfiadssucoifalavnalhuaelsoxhHoIst=ing5.a6s×tar1-f0o−r5m,ifn∗g=reg0i.o1n, ΓQHISO1=4πZνHI hννσ0„νHI« dν; (7) esc abletoproduceRHII ≈1(10)Mpcis2×108(2×1011)M⊙.At J = N˙νhν ; (8) z ≈ 5.5objectsofthesemassescorrespondstofluctuationsofthe ν 16π2R2 densityfield&1−σ(2−σ)(Barkana&Loeb2001). ∞ ∞ ν −α AsforQSOs,thebubblesize−peakfrequencytensioncouldbeal- N˙ = N˙ dν = N˙ dν, (9) leviated if the galaxies livein overdense environments where the γ ZνHI ν ZνHI νHI„νHI« photoionization rate only supports a xHI ≈ 0.1 (resulting in a whereνHIisthehydrogenphotoionizationfrequencythreshold,σ0 largervalueofy−1,andhenceofMh ineq.(6))priortotheonset is the Thompson scattering cross section, R is the distance from ofstarformationinthegalaxy.Obviously,thepreviousarguments QSO1totheLOS,N˙ istherateoftheemittedionizingphotons νHI neglect that because of clustering (Yu & Lu 2005; Kramer et al. atthehydrogenphotoionizationfrequencythresholdandα = 1.5 2006),asmultiplesourcescouldpowerasingleHIIregion;inor- isthespectralindexoftheQSOcontinuum.Integratingeq.(9)we dertogetfirmerresultsradiativetransfercosmologicalsimulations obtain: arerequired. (α−1)N˙ N˙ = γ. (10) νHI νHI Thus,itresults: 5 PEAKSFROMTHEPROXIMITYEFFECT InSec.4,wehavediscussedthepossibilitythattheobservedpeaks ΓQSO1= α−1 N˙γσ0, (11) HI „α+2«4πR2 areproducedbyionizingsourceswhosebubblesintersectthelines ofsighttothetargetQSO.Inthiscaseonecouldaskifthesource InFig.6wecomparetheobservedtransmittedfluxinthespec- responsible for the HII region would be detected in the observed trum of QSO2 with the simulated fluxes along 3 different LOS field. If the origin of transmissivity regions resides in bubbles with(bottomrow)orwithout(top)includingthecontributionfrom around high-z galaxies, these sources are too faint to be seen in QSO1tothetotalionizingflux.Forbrevity,werefertothesecase theSDSS;however,deepHSTimaging(Stiavellietal.2005)could as“withbubble”or“withoutbubble”.VisualinspectionofFig.6 detectsuchobjects.Onthecontrary,iftheHIIregionofaquasarin- showsthatthecase“withbubble”isinbetteragreementwithob- tervenesalongtheLOStoanhigherredshiftquasar,thefirstcould servations. Such statement can be made more quantitative by in- beobservedintheSDSSfield. troducingaquantitydenotedPeakSpectralDensity(PSD),i.e.the Mahabal et al. 2005 have discovered a faint quasar (RD number ofpeaksperunitλ interval. TocomputethePSDfor RF J1148+5253,hereafterQSO1)atz =5.70inthefieldofthehigh- thetwocases,wefixtwodifferentvaluesforthefluxthresholdin- estredshiftquasarcurrentlyknown(SDSSJ1148+5251, hereafter side(FIN =0.01)andoutside(FOUT =0.08)thebubble.While th th QSO2)atz = 6.42.InthisSectionwestudytheQSO2transmit- FOUT isthesameasthevalueusedinthisworksofar,FIN has th th tedflux,inorder toanalyze theproximityeffect ofQSO1onthe beenchosenaccordinglytothemaximumobservednoiser.m.s.de- QSO2spectrum.Forclarity,Fig.5presentsaschematicpictureof viation(forreasonsexplainedintheAppendix A)intheλ in- RF theconsideredgeometry.Astheredshiftz = 5.70quotedbyMa- terval∆λ = 1087−1092A˚,whereΓQHISO1 & ΓHI.Forboththe habaletal.2005isbasedonthepeakoftheLyαemissionline,and observed and simulated spectra, we compute the PSD inside and theestimatederrorfromsuchprocedureis∆z ≈ 0.05(Goodrich outsidethebubble,findingthefollowingresults: etal.2001),weassumezQSO1=5.65andwediscussthisissuein em furtherdetailsinAppendixB. (PSDOUT,PSDIN)=(0.11,0.40); obs obs 8 S. Gallerani,A.Ferrara,X.Fan,T. RoyChoudhury QSO2 J1148+5251 (a1) (a2) (a3) 0.8 0.6 0.4 0.2 0 QSO1 J1148+5251 (b1) (b2) (b3) 0.8 0.6 0.4 0.2 0 1050 1150 1050 1150 1050 1150 1050 1150 Figure 5. Schematic positions of quasars SDSS J1148+5251 (QSO2, Figure6.Leftmostpanels:Observedtransmittedflux(blackspectra)inthe zem = 6.42,redshiftpositionnotinscale)andRDJ1148+5252(QSO1, spectrum of QSO SDSS J1148+5251 (QSO2, zem = 6.42). The solid zem = 5.65).TheprojectedseparationisdenotedbyR⊥,thesizeofthe blacklineshowstheredshiftpath(∆zprox)inwhichthebubbleproduced HIIregion,RHII,intheQSO1restframeisrepresentedbythedottedcir- by QSO RD J1148+5252 (QSO1, zem = 5.65) intersects the LOS to cle;themagentasolidlineshowstheapparentshapeoftheionizationfront; QSO2.Toppanels(ai),withi=1,3:Simulatedfluxes(cyanspectra)along thedashedblacklineshowstheredshiftpath(∆zprox)inwhichthebubble 3differentrandomLOS(cases“withoutbubble”).Bottompanels(bi),with producedbyQSO1intersectstheLOStoQSO2. i=1,3:Simulatedfluxes(magentaspectra)alongthesameLOSsshownin thetoppanels,takingintoaccountthecontributionfromQSO1tothetotal ionizingflux(cases“withbubble”). (PSDOUT,PSDIN )=(0.04+0.06,0.24+0.35), sim sim −0.04 −0.24 theresultisshowninFig.7.Theagreementbetweenobservations whereerrorbarsprovidethemaximumandminimumPSDvalues andsimulations isat 1-σ confidence level for 86% of theplotted foundinthesimulatedLOS.Observationally,thePSDisfoundto points. ForR . 2 Mpc, themean optical depth 1.5 . τ¯ . 3.5 be≈ 4times6 largerinsidethatbubblethanoutsideit.Thisboost isquitewellreproducedbythesimulatedPSD,althoughtheirab- islowerthanthemeanvalueexpectedatz¯= 5.65(τ¯5.65 ≈ 4);it solutevaluesaresomewhatlowerthantheobservedones. approachesτ¯5.65atdistanceslargerthanRτ ∼2Mpc. tioniTshtheepfhoylsloicwailnign.teIrnptrheetaλtiono(frethdeshriefst)ulitnsterervpaolrt∆edλin=th1i0s8S7e−c- BonytthaekifnogretghreoudnifdfeQreSnOcelibfeettwimeeentQRτ>anRdτ−RcR⊥⊥,w+e(steτt−altoQwSeOr1li)m≈it 1092(∆zdet = 5.63−5.67)R,FwhereΓQHISO1 & ΓHI,mostofthe s1p1onMdyinr,gwtohethreetreτdashnidftstQzSO=1 r5e.p6r8esaenndt tzhQeScOo1sm=ic5t.i6m5e,srecsoprerec-- gapspresentinthecase“withoutbubble”disappear,makingroom τ em tively. forpeaks,asaconsequence ofthedecreasedopacityintheprox- Itisworthnotingthatourmodeldoesnottakeintoaccountneither imity of QSO1. Note that the ΓHI value adopted in our calcula- (i)theclusteringoftheionizingsources,nor(ii)theoverdenseenvi- tions(showninFig.1,middlepanel,redline)isclosetothemax- ronmentexpectedaroundtheQSO.Boththeseeffects,inprinciple, imum value suggested by previous studies. Moreover, ΓQSO1 ≈ HI could strongly affect the IGM ionization state, albeit in opposite 3.4×ΓHIat0.66MpcfromtheforegroundQSO.Thus,animplau- ways.Whileclusteringofsourceswouldenhancethetransmissiv- sibleΓHI value should beassumed toexplaintheobserved boost ityintheQSOnear-zones,theoverdenseenvironmentwouldtend inthePSDwithauniformUVB.Theenhancementinthetransmis- tosuppressit.Thefactthatwefoundagreementbetweenobserva- sivitydecreasesforλ smaller(larger)than1087(1092)A˚,since RF tionsandourmodelingcouldindicatethat,atleastalongthisLOS, atthecorrespondingredshiftΓQHISO1.ΓHI.Theseresults(i)con- thetwoeffectscompensate.Forwhatconcerns(ii),bycomparing firmthedetectionofaproximityeffect,(ii)showthattheredshift theopticaldepthevolutionobservedintheproximityregionsof45 stretchaffectedbytheproximityeffectis∆z <∆z . det prox QSOsatz & 4withtheoreticalexpectations, Guimaraesetal. Asafinaltestforour model, wecomputetheobserved evo- em 2007findevidenceforadensitybiascorrelatedwiththeQSOlu- lution of the optical depth as a function of the distance R from minosity. Since QSO1 is much fainter than the QSOs studied by QSO1andcompareitwiththepredictionsofmodel”withbubble”; Guimaraes et al. 2007 it seems likely that neglecting such effect does not introduce a significant error. However, the extension of 6 Thisfactordependsonthefluxthresholdused.Forexample,itisreduced theproposedapproachtoalargersamplecouldclarifytherelation to ≈ 2.7ifFIN = FOUT = 0.05. Nevertheless, for the purpose of between the clustering of sources and the overdensities in which th th ourtestwhatreallymattersistheboostofthisfactormovingfromoutside massiveobjectsarelikelytobeembedded. towardinsidethebubble. ItisimportanttonotethattheLOStowardSDSSJ1148+5251con- Glimpsingthroughthehighredshiftneutralhydrogenfog 9 We then apply the Largest Gap Width (LGW) and Largest Peak Width(LPW)statisticsintroduced by Gallerani et al. (2006) to a sampleof17QSOsintheredshiftrange5.74−6.42.BothERM andLRMprovidegoodfitstotheobservedLGWdistribution,fa- voringa scenario inwhich xHI smoothly evolves from10−4.4 at z≈5.3to10−4.2atz≈5.6. Discriminating among the two reionization scenarios would requireasampleofQSOatevenhigherredshifts.Infact,although accordingtoLRMatz & 6thereionizationprocessisstillinthe overlapphasewithamixtureofionizedandneutralregionschar- acterizingtheIGM,only≈ 10%ofthesimulatedLOSpiercethe overlapepoch, andfor a redshift depth ∆z . 0.2. Thisexplains whythepredictedLGWdistributionsarequitesimilarforthetwo modelsconsidered. Nonetheless, ERM provides a slightly better fit to observational datawithrespecttoLRM,favoringz &7.Withinthestatistical rei relevanceofoursample,wehaveshownthatLRMmodelscanbe usedtoputarobustupperlimitxHI<0.36atz =6.3. Wehavesuggestedthatpeakspreferentiallyarisefromunder- denseregionsofthecosmicdensityfieldandalsofromisolatedHII regionsproducedbyeitherfaintquasarsorgalaxies.Thefrequency Figure7.Evolutionoftheopticaldepthτ asafunctionofthedistanceR of the observed peaks implies that the dark matter halos hosting fromQSO1.Filledcirclesdenotetheobservedmeanvalueforτ,whileerror suchsourcesisrelativelylarge,≈ 1012 (1013)M⊙.BrightQSOs barsrepresentthemaximumandtheminimumobservedτ atagivendis- areunlikelytocontributesignificantlyintermsofpeaks, because tancefromtheforegroundQSO.Solid(dotted)magentalinesarethemean giventherequiredsizeoftheHIIregions, theyshould belocated (maximum/minimum)valuesfrom500simulatedLOS,computedadopting close enough to the LOS to the target QSO, that they should be thecase“withbubble”. Thedashedcyanhorizontal lineshowsthemean detectableinthefield. opticaldepthpredictedbytheERMincorrespondenceoftheemissionred- shiftoftheforegroundQSO.Thedottedcyanhorizontal linesdenotethe The previous conclusions are substantiated by the specific maximum/minimumopticaldepthatthesameredshift. caseofaninterveningHIIregionproducedbythefaintquasarRD J1148+5253(QSO1)atz = 5.70alongtheLOStowardthehigh- estredshiftquasarcurrentlyknown(SDSSJ1148+5251,QSO2)at tributestotheLPWdistributionwiththesmallestpeak(P ≈ max z = 6.42.Itisworthnotingthatsearchesforthetransverseprox- 2A˚)intheentiresample.Thus,evenifwesucceededinreproduc- imityeffect inthe HI Lyαforest at z ≈ 3 (Schirber et al. 2004) ingthefeaturesofthisLOSwithourmodel“withbubble”,westill havebeensofarunsuccessful.Sucheffecthasbeenisolatedonlyby havetoexplainthemysteriousoriginoftransmissivitywindowsas HeIIabsorptionstudies(Worseck&Wisotzki2006;Worsecketal. largeas10−15A˚. 2007).Thus,ourresultsrepresentthefirst-everdetectionintheHI InSec.4.1,weestimatetheQSO1luminosityrequiredtoexplain Lyαforest.WehaveanalyzedtheproximityeffectofQSO1onthe the observed P value, and we comment on the result depen- max QSO2 spectrum. Moreover, we have build up a simple model to dencefromf .Pluggingineq.(4)thevaluef ≈ 0.03 computed t t estimatethelocation/extension of theproximity zone. Withinthe insidetheproximityregion,weobtainaneffectivesizeforR ; HII proximityregionofQSO1wehavefoundanincreasednumberof byfurtherusingeq.(2),thistranslatesintoN˙ =9.2×1055s−1,a γ peaksperunitfrequencywithrespecttosegmentsoftheLOSlo- valueinquitegoodagreementwiththeQSO1ionizingratequoted catedoutsidethequasarHIIbubble.Thissupportstheideathatwe byMahabaletal.2005. are indeed sampling the proximity region of the QSO1 and that atleastsomepeaksoriginatewithinionizedregionsaround(faint) sources.WethenobtainastronglowerlimitontheforegroundQSO lifetime of t > 11 Myr. Proper inclusion of galaxy clustering, Q 6 DISCUSSION whichrequiresnumericalsimulations,mightaffectourconclusions (Faucher-Giguereetal.2007).Notethateveninthisclear-cutcase, Wehavestudiedseveralstatisticalpropertiesofthetransmittedflux thesizeof thelargest observed peak in thespectrum of QSO2is in high-z QSO spectra and compared them with those obtained onlyof2A˚. fromsimulatedLyαforestspectratoinferconstraintsontheioniza- tionstateoftheIGMatz ≈ 6.Wehaveconsideredtwodifferent Thus we are left withthe puzzling discrepancy between ob- reionization models: (i) an Early Reionization Model (ERM), in servedandsimulatedtransmissivitywindows(peaks)size,thefor- whichtheuniversereionizesatz =6,and(ii)aLateReioniza- merbeingsystematicallylarger.Verylikely,thisreflectsanunwar- rei tionModel(z ≈7). rantedassumptionmadebythemodel.Wedonotbelievethatthe rei Byfirstusingstandardcontrolstatistics(meantransmittedfluxevo- discrepancy could be impute to the assumption of a Log-Normal lution,probabilitydistributionfunctionofthetransmittedflux,gap model,testedagainst HYDROPMsimulationsbyGCF06.Never- width distribution) in the redshift range 3.5 < z < 6, we show theless,weplantocomparetheobservedLargestPeakWidthdis- that both ERM and LRM match the observational data. This im- tributionwithfullhydrodynamicalsimulationsinafutureworkto pliesthatcurrentobservationsdonotexcludethatreionizationcan study the correlation properties of the underdense regions, since havetakenplaceatredshiftwellbeyondsix. Coles et al. (1993) have shown that the Log-Normal model pro- 10 S. Gallerani,A. Ferrara,X. Fan,T. RoyChoudhury ducesatoo“clumpy”distributionofthedensityfield,whencom- ChoudhuryT.R.,PadmanabhanT.,SrianandR.,2001,MNRAS,322,561 paredwithN-bodysimulations. ChoudhuryT.R.,SrianandR.,PadmanabhanT.,2001,ApJ,559,29 Atleasttwophysicaleffects,neglectedhere,couldaffectthe ColesP.,JonesB.,1991,MNRAS,248,1 calculationofxHI:(i)non-equilibriumphotoionization,and(ii)UV ColesP.,MelottA.L.,ShandarinS.F.,1993,MNRAS,260,765 backgroundradiationfluctuations. CroftR.A.C.,1998,inOlintoA.V.,FriemanJ.A.,SchrammD.N.ed., EighteenthTexasSymposiumonRelativisticAstrophysics.WorldSci- Thefirstassumptionismadebythemajorityofstudiesdealingwith entific,RiverEdge,N.J.,p.664 the Lyα forest. However, if a fraction of the Lyα forest gas has Dijkstra M., Wyithe S., Haiman Z., 2007, MNRAS in press, astro- beenshock-heatedasitcondensesintothecosmicwebfilaments,it ph/0607331. mightcoolfasterthanitrecombines.Forexample,therecombina- DjorgovskiS.G.,CastroS.,SternD.,MahabalA.A.,2001,AJ,560,L5 tiontimetrbecomeslongerthantheHubbletimewhenthedensity FanX.etal.,2001,AJ,122,2833 contrastis∆<7.5[(1+z)/6.5]−3/2;hence,largedeviationsfrom FanX.,NarayananV.K.,StraussM.A.,WhiteR.L.,BeckerR.H.,Penter- photoionization equilibrium are expected where ∆ ≪ 1. Lower icciL.,RixH.,2002,AJ,123,1247 valuesofxHI withrespecttoequilibriumareexpectedinsuchre- FanX.etal.,2003,AJ,125,1649 gions,asaresultoftheexceedinglyslowrecombinationrates. FanX.etal.,2006,AJ,132,117 FangT.etal.,2005,astro-ph/0505182 Faucher-GiguereC.A,LidzA.,ZaldarriagaM,HernquistL.,2007,astro- Thesecondpossibleexplanationforthetoonarrowsimulated ph/0701042 peaksmightresideinradiativetransfereffects,alsoneglectedhere. GalleraniS.,ChoudhuryT.R.,FerraraA.,2006,MNRAS,370,1401 Atz≈6theincreaseinthemeanGPopticaldepthisaccompanied GoodrichR.W.etal,2001,ApJ,561,L23 byanevidentenhancement ofthedispersionofthismeasurement GuimaraesR.,PetitjeanP.,RollindeE.,deCarvalhoR.R.,DjorgovskiS.G., whichhasbeenascribedtospatialfluctuationsoftheUVBintensity SrianandR.,AghaeeA.,CastroS.,2007,astro-ph/0702369 neartheendofreionization.Aconsiderable(upto10%)scatterin HaimanZ.,CenR.,2002,ApJ,578,702 theUVBHIphotoionizationrateisexpectedalreadyatz ≈ 3,as IlievI.T.,MellemaG.,ShapiroP.R.,PenU.-L.,2007,MNRAS,376,534 shownbyMaselli&Ferrara2005throughdetailedradiativetrans- IyeM.,OtaK.,KashikawaN.,FurusawaH.,HashimotoT.,HattoriT.,Mat- fer calculations. 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