Glimpsing through the high redshift neutral hydrogen fog

0.33 MB·English

by  S. Gallerani

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:[email protected] have tried to constrain xHI at high redshift by analyzing statisti-
† E-mail:[email protected] callytheopticaldepthinsideHIIregionsaroundhighredshiftQSO
‡ E-mail:[email protected] (Mesinger&Haiman2004;Mesinger&Haiman2006),orbymea-
§ E-mail:[email protected] 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-
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toaluminoussourceitwillhaveitsxHIdepressedwellbelowthat 2005,ApJ,634,L9
ofthesecondonelocatedawayfromit.Thus,opacityfluctuations MaiolinoR.,SchneiderR.,OlivaE.,BianchiS.,FerraraA.,MannucciF.,
naturallyarise.Ifso,peaksoflargerwidthcouldbeproducedifthe PedaniM.,RocaSogorbM.,OlivaE.,2004,Nature,431,533
density perturbation associated withithappens tobe locatedina MalhotraS.,RhoadsJ.E.,2005,astro-ph/0511196
MaselliA.,GalleraniS.,FerraraA.,ChoudhuryT.R.,2007,MNRAS,376,
regionwheretheUVBintensityishigherthanthemean.
34
MaselliA.,FerraraA.,2005,MNRAS,364,1429
McDonaldP.,Miralda-Escude’J.,2001,ApJ,549,L11
ACKNOWLEDGMENTS MesingerA.,HaimanZ.,2006,preprint(astro-ph/0610258).
MesingerA.,HaimanZ.,2004,ApJ,611,L69
We thank R. Cen, B. Ciardi, D. Eisenstein, J. P. Ostriker and S. Miralda-Escude’J.,HaehneltM.,ReesM.J.,2000,ApJ,530,1
Whitefor stimulatingdiscussions. Weare particularly grateful to MoH.J.,WhiteS.D.M.,2002,MNRAS,336,112
Z.Haiman,A.LidzandA.Maselliforenlighteningcommentson OhS.P.,FurlanettoS.R.,2005,ApJ,620,L9
the manuscript. XF acknowledges support from NSF grant AST PageL.etal.,2006,preprint(astro-ph/0603450)
PaschosP.,NormanM.L.,2005,ApJ,631,59
03-07384,aSloanResearchFellowship,aPackardFellowshipfor
SchirberM.,Miralda-Escude’J.,McDonaldP.,2004,AJ,610,105
ScienceandEngineering.
ShapiroP.R.,IlievI.T..,AlvarezM.A.,ScannapiecoE.,2006,ApJ,648,
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