On-the-Normalization-of-the-QSOs-Lyman-alpha-Fores

arXiv:astro-ph/0107185v110Jul2001OnthenormalizationoftheQSO’sLyαforestpowerspectrumPriyaJamkhedkar1,HongguangBi2andLi-ZhiFang3DepartmentofPhysics,UniversityofArizona,Tucson,AZ85721ABSTRACTThecalculationofthetransmissionpowerspectrumofQSO’sLyαabsorptionrequirestwoparametersforthenormalization:thecontinuumFcandmeantransmissione−τ.Traditionally,thecontinuumisobtainedbyapolynomialfittingtruncatingitatalowerorder,andthemeantransmissioniscalculatedovertheentirewavelengthrangeconsidered.ThefluxFisthennormalizedbyFce−τ.However,thefluctuationsinthetransmittedfluxaresignificantlycorrelatedwiththelocalbackgroundfluxonscalesforwhichthefieldisintermittent.Asaconsequence,thenormalizationoftheentirepowerspectrumbyanover-allmeantransmissione−τwilloverlooktheeffectofthefluctuation-backgroundcorrelationuponthepowers.Inthispaper,wedevelopaself-normalizationalgorithmofthetransmissionpowerspectrumbasedonamultiresolutionanalysis.Thisself-normalizedpowerspectrumestimatorneedsneitheracontinuumfitting,norpre-determiningthemeantransmission.Withsimulatedsamples,weshowthattheself-normalizationalgorithmcanperfectlyrecoverthetransmissionpowerspectrumfromthefluxregardlessofhowthecontinuumvarieswithwavelength.Wealsoshowthattheself-normalizedpowerspectrumisalsoproperlynormalizedbythemeantransmission.Moreover,thispowerspectrumestimatorissensitivetothenon-linearbehaviorofthefield.Thatis,theself-normalizedpowerspectrumestimatorcandistinguishbetweenfieldswithorwithoutthefluctuation-backgroundcorrelation.Thiscannotbeaccomplishedbythepowerspectrumwiththenormalizationbyanoverallmeantransmission.Applyingthisanalysistoarealdatasetofq1700+642Lyαforest,wedemonstratethattheproposedpowerspectrumestimatorcanperformcorrectnormalization,andeffectivelyrevealthecorrelationbetweenthefluctuationsandbackgroundofthetransmittedfluxonsmallscales.Therefore,theself-normalizedpowerspectrumwouldbeusefulforthediscriminationamongmodelswithouttheuncertaintiescausedbyfree(orfitting)[e-mail][e-mail][e-mail]–2–Subjectheadings:cosmology:theory-large-scalestructureoftheuniverse1.IntroductionLyαabsorption,shortwardofLyαemissioninQSOspectra,indicatesthepresenceofinterveningabsorberswithneutralhydrogencolumndensitiesrangingfromabout1013to1022cm−2.Theabsorberswithlowcolumndensities,e.g.from1013to1017cm−2,areusuallycalledLyαforest.Itisgenerallythoughtthatthelowcolumndensityabsorbersaresomekindofweaklyclusteredcloudsconsistingofphotoionizedintergalacticgas(e.g.Wolfe1991;Bajtlik1992).ThissuggeststhatLyαforestsarecausedbydiffuselydistributedIGMinpre-collapsedareasofthecosmicmassfield(Bi,1993;Fangetal.1993;Bi,Ge&Fang1995;Bi&Davidsen1997.)ObservationsofthesizeandvelocitydispersionoftheLyαcloudsathighredshiftalsoshowthattheabsorptionprobablyisnotcausedbyconfinedobjectsathighredshifts(Bechtoldetal.1994;Dinshawetal.1994;Fangetal1996;Crotts&Fang1998.)Withthispicture,thebaryonicmatterdistributionisalmostpoint-by-pointproportionaltothedarkmatterdistributiononallscaleslargerthantheIGM’sJeanslength,i.e.theLyαforestswouldbegoodtracersoftheunderlyingdarkmatterdistribution.Thus,thepowerspectrumofQSOLyαtransmittedfluxcanbeusedtoestimatethepowerspectrumoftheunderlyingmassfield,andthenbeusedtoconstraincosmologicalparameters(Croftetal1999;McDonaldetal1999;Hui1999;Feng&Fang2000.)Akeystepinthisapproachistocomparethepowerspectrumofobservedtransmittedfluxfluctuationswithmodel-predictedpowerspectrum.Oneuncertaintyinthepowerspectrumdeterminationoftherealdataisfromthenormalizationofthepowerspectrum.Therefore,inordertohaveaneffectiveconfrontationbetweentheobservedandtheoreticalpowerspectrumofLyαforests,itisnecessarytodevelopaproperalgorithmforthenormalizationofthepowerspectrum.Thisisthegoalofthispaper.TheobservedfluxofaQSOabsorptionspectrumisgivenbyF(λ)=Fc(λ)e−τ,whereFc(λ)isthecontinuum,e−τ(λ)thetransmission,andτtheopticaldepth.Thenormalizedpowerspectrumoftransmissionisthepowerspectrumofthetransmissionfluxfluctuationsδ(λ),definedasδ(λ)=F(λ)−F(λ)F(λ).(1)Thatis,thetransmissionpowerspectrumisnormalizedbythemeanfluxF(λ)=Fc(λ)eτ(λ).–3–Inotherwords,thenormalizationofthetransmissionpowerspectrumisdeterminedbytwofactors:thecontinuumFc(λ)andthemeantransmissioneτ(λ).Traditionally,thecontinuumisneededtobedeterminedbeforethepowerspectrumcalculation.Usuallythecontinuumisobtainedbyafittingofpolynomialoritsvariants.Assumingthatthecontinuumfluctuatesslowly,thepolynomialoritsvariantsaretruncatedatrelativelyloworders(e.g.Croftetal2000;Huietal2000).Thepre-assumedpolynomialorotherfunction,andthesubsequenttruncationmayleadtouncertaintyofthepowerspectrum.Anothersourceofuncertaintyofthetransmissionpowerspectrumisthemeantransmissione−τnormalization.Themeantransmissioniscalculatedbyaveragingthefluxovertheentirewavelengthrangeconsidered,andthepowerspectrumisnormalizedbythismeantransmissionforallscales.Thisimplicitlyassumesthatthereisnocorrelationbetweenthetransmittedfluxfluctuationsandthemeanflux.Thisassumptionistrueforagaussianfield,butmaynotbesoforanon-linearlyevolvedfield.Infact,thefluctuationsatposi