The matter power spectrum from the Lyman-alpha for

arXiv:astro-ph/0509563v320Apr2006Mon.Not.R.Astron.Soc.000,000–000(0000)Printed5February2008(MNLATEXstylefilev2.2)ThematterpowerspectrumfromtheLyαforest:anopticaldepthestimateS.Zaroubi1,M.Viel2,A.Nusser3,4,M.Haehnelt2andT.-S.Kim21KapteynAstronomicalInstitute,UniversityofGroningen,P.O.Box800,9700AVGroningen,theNetherlands2InstituteofAstronomy,MadingleyRoad,CambridgeCB30HA3PhysicsDepartment,Technion–IsraelInstituteofTechnology,TechnionCity,Haifa32000,Israel4DivisionofTheoreticalAstrophysicsNationalAstronomicalObservatoryJapan,Mitaka181-8588,Japan5February2008ABSTRACTWemeasurethematterpowerspectrumfrom31Lyαspectraspanningtheredshiftrangeof1.6-3.6.Theopticaldepth,τ,forLyαabsorptionoftheintergalacticmediumisobtainedfromthefluxusingtheinversionmethodofNusser&Haehnelt(1999).Theopticaldepthisconvertedtodensitybyusingasimplepowerlawrelation,τ∝(1+δ)α.Thenon-linear1Dpowerspectrumofthegasdensityistheninferredwithamethodthatmakessimultaneoususeofthe1and2pointstatisticsofthefluxandcomparedagainsttheoreticalmodelswithalikelihoodanalysis.AColdDarkMatter(CDM)modelwithstandardcosmologicalparametersfitsthedatawell.Thepowerspectrumamplitudeismeasuredtobe(assumingaflatUniverse),σ8=(0.9±0.09)×(Ωm/0.3)−0.3,withαvaryingintherangeof1.56−1.8withredshift.Enforcingthesamecosmologicalparametersinallfourredshiftbins,thelikelihoodanalysissuggestssomeevolutioninthedensity-temperaturerelationandthethermalsmoothinglengthofthegas.TheinferredevolutionisconsistentwiththatexpectedifreionizationofHeiioccurredatz∼3.2.AjointanalysiswiththeWMAPresultstogetherwithapriorontheHubbleconstantassuggestedbytheHSTkeyprojectdata,yieldsvaluesofΩmandσ8thatareconsistentwiththecosmologicalconcordancemodel.Wealsoperformafurtherinversiontoobtainthelinear3Dpowerspectrumofthematterdensityfluctuations.Keywords:cosmology:theory–intergalacticmedium–hydrodynamics–large-scalestructureofUniverse–quasars:absorptionlines1INTRODUCTIONThenumerousLyαabsorptionfeaturesobservedinquasarspectrablue-wardsoftheirLyαemissionlineknownastheLyαforest,provideoneofthemainprobesoftheintergalac-ticmedium(hereafterIGM)(Bahcall&Salpeter1965;Gunn&Peterson1965).InrecentyearstwomainadvanceshaveshapedtheacceptedviewontheoriginoftheLyαabsorbingstructures.First,theadventof10-meterclasstelescopesequippedwithhigh-resolutionechellespectrographs(HIRESonKeckandUVESontheVeryLargeTelescope)haspro-videduswithdataofunprecedentedquality(seeRauch1998forareview).Second,theemergenceofatheoreticalparadigmwithinthecontextofthecolddarkmatter(CDM)cosmology(e.g.Bi,Boerner&Chu1992)supportedbynu-mericalhydrodynamicalsimulations(Cenetal.1994;Zhang,Anninos&Norman1995;Miralda-Escudeetal.1996;Hern-quistetal.1996;Wadsley&Bond1996;Zhangetal.1997;Theunsetal.1998;Machaceketal.2000;Viel,Haehnelt&Springel2004;Tytleretal.2004;Jenaetal.2005)andsemi-analyticalstudies(e.g.Pichonetal.2001;Matarrese&Mo-hayaee2002;Vieletal.2002).Accordingtothisparadigm,theabsorptionisproducedbyvolumefillingphotoionizedgasthatcontainsmostofthebaryonsatredshiftsz≈3(seee.g.Efstathiou,Schaye&Theuns(2000)forarecentreview),wheretheabsorbersarelocallyoverdenseextendedstruc-tures,closetolocalhydrostaticequilibrium(Schaye2001).TheparadigmalsopredictsthatmostofthegasprobedbytheLyαforest-absorptionfeatureswithcolumnden-sity∼1013.5cm−2-residesinmildlynon-lineardark-matteroverdensities.OnscalessmallerthantheJeansscalethebaryonicgasissmoothedbypressureforces,erasingthesmall-scalefluc-tuationsofthegasdensity,andsettingitsdistributionapartfromthedarkmattercomponent.OnthesesmallscalesthewidthoftheabsorptionfeaturesisdeterminedbythegasthermodynamicalpropertiesenablingthemeasurementoftheIGMtemperatureandtemperature-densityrelation(e.g.,Schayeetal.2000,Theuns&Zaroubi2000,McDon-c0000RAS2Zaroubietal.aldetal.2001,Theunsetal.2002aand2002b,Gleseretal.2005).OnscaleslargerthantheJeansscale,however,thegasdistributionfaithfullyfollowsthatoftheunderlyingdarkmatter.Thegasdistributiononthesescalesprovidesaprobeofthedarkmatterdistributionanditspowerspectrum(Croftetal.1998;Hui1999;Croftetal.2002,McDonaldetal.2000,Huietal.2001;Croftetal.2002;Vieletal.2003,2004,2005;McDonaldetal.2005;Seljaketal.2005;Des-jacques&Nusser2005;Lidzetal.2005,Viel&Haehnelt2005).The“standard”methodusedformeasuringthematterpowerspectrumfromtheLyαforestisbasedontheresultobtainedinnumericalsimulationsshowingthatthenormal-izedfluxpowerspectrumisproportionaltothatoftheun-derlyingmatter(Croftetal.1998).Thecalibrationoftherelationbetweenthetworeliesonnumericalsimulationsandonthevalueofthemeanflux.Bothofthesearesomewhatuncertain.Thecalibrationoftherelationdependsonthespecificcosmologicalparametersofthesimulation,andthemeanfluxonthespecificquasar(QSO)spectrumathand.Todate,almostallmatterpowerspectrainferredfromtheLyαforestarebasedonthisrelation.Thereis,however,somedebateonwhattoadoptforthemeanleveloftheflux.EarlypowerspectrummeasurementsfromtheLyαforest(e.g.,Croftetal.1998;2002;McDonaldetal.2000)adoptedaratherlowlevelofthemeanflux,andinferredarelativelylowamplitudeofthefluctuations.Thisresultisnotcom-pletelyconsistentwiththelargescale