Statistical characteristics of formation and evolu

arXiv:astro-ph/9901400v128Jan1999Mon.Not.R.Astron.Soc.000,000–000(0000)Printed1February2008(MNLATEXstylefilev1.4)Statisticalcharacteristicsofformationandevolutionofstructureintheuniverse.M.Demia´nski1,2&A.G.Doroshkevich3,41InstituteofTheoreticalPhysics,UniversityofWarsaw,00-681Warsaw,Poland2DepartmentofAstronomy,WilliamsCollege,Williamstown,MA01267,USA3TheoreticalAstrophysicsCenter,JulianeMariesVej30,DK-2100CopenhagenØ,Denmark4KeldyshInstituteofAppliedMathematics,RussianAcademyofSciences,125047Moscow,RussiaAccepted...,Received1998October...;inoriginalform1998October13ABSTRACTAnapproximatestatisticaldescriptionoftheformationandevolutionofstructureoftheuniversebasedontheZel’dovichtheoryofgravitationalinstabilityisproposed.ItisfoundthattheevolutionofDMstructureshowsfeaturesofself-similarityandthemainstructurecharacteristicscanbeexpressedthroughtheparametersofinitialpowerspectrumandcosmologicalmodel.FortheCDM-likepowerspectrumandsuitableparametersofthecosmologicalmodeltheeffectivemattercompressionreachestheobservedscalesRwall∼20–25h−1Mpcwiththetypicalmeanseparationofwall-likeelementsDSLSS∼50–70h−1Mpc.Thisdescriptioncanbedirectlyappliedtothedeeppencilbeamgalacticsurveysandabsorptionspectraofquasars.Forlarger3Dcatalogsandsimulationsitcanbeappliedtoresultsobtainedwiththecore-samplinganalysis.ItisshownthattheinteractionoflargeandsmallscaleperturbationsmodulatesthecreationrateofearlyZel’dovichpancakesandgeneratesbiasontheSLSSscale.Forsuitableparametersofthecosmologicalmodelandreheatingprocessthisbiascanessentiallyimprovethecharacteristicsofsimulatedstructureoftheuniverse.Themodelswith0.3≤Ωm≤0.5givethebestdescriptionoftheobservedstruc-tureparameters.Theinfluenceoflowmass”warm”darkmatterparticles,suchasamassiveneutrino,willextendtheacceptablerangeofΩmandh.Keywords:cosmology:large-scalestructureoftheUniverse—galaxies:clusters:general–theory.1INTRODUCTIONOverthepastdecadethelargemapsofthespatialgalaxydistributionhavebeenpreparedandtheunexpectedlycom-plicatedcharacterofthisdistributionwasestablished.ThestructurepredictedbytheZel’dovichtheoryofgravitationalinstability(Zel’dovich1970,1978)wasfoundalreadyinthefirstwedgediagrams(Gregory&Thompson1978)andnowtheLargeScaleStructure(LSS)isseeninmanyobser-vationalcatalogs,suchastheCfA(deLapparent,Geller&Huchra1987;Ramella,Geller&Huchra1992),theSRSS(daCostaetal.1988)andintheLasCampanasRedshiftSur-vey(Shectmanetal.1996,hereafterLCRS).Theobservedhighconcentrationofgalaxieswithinthewall-likestructureelementssuchastheGreatAttractor(Dressleretal.1987),andtheGreatWall(deLapparent,Geller&Huchra1988)andtheexistenceofextendedunderdenseregionssimilartotheGreatVoid(Kirshneretal.1983)putintheforefronttheinvestigationoftheSuperLargeScaleStructure(SLSS).NowtheSLSSisalsofoundinmanydeeppencilbeamred-shiftsurveys(Broadhurstetal.1990;Willmeretal.1994;Buryaketal.1994;Bellanger&deLapparent1995;Cohenetal.1996)asarichgalaxyclumpswiththetypicalsepa-rationsintherangeof(60–120)h−1Mpc.Hereh=H0/100km/s/MpcisthedimensionlessHubbleconstant.FurtherprogressinthestatisticaldescriptionoftheLSS&SLSShasbeenreachedwiththecore-samplingmethod(Buryaketal.1994)andtheMinimalSpanningTreetech-nique(Barrow,Bhavsar&Sonoda1985).Recentanaly-sisoftheLCRSperformedbyDoroshkevichetal.(1996&1997b,hereafterLCRS1&LCRS2,Doroshkevichetal.1998)revealedsomestatisticalparametersofthewall-likeSLSScomponentsuchastheirtypicalseparation,DSLSS≈50−60h−1Mpc,andthefractionofgalaxiesaccumulatedbytheSLSS,whichcanreach∼50%.Thesameanalysisindi-catesthatformationofricherwallscanberoughlydescribedasanasymmetric2DcollapseofregionswithatypicalsizeRwall∼20–25h−1Mpcthatisabouthalfoftheirtypicalc0000RAS2Demia´nski&Doroshkevichseparation.TheanalysisofDurham/UKSTredshiftsurveyconfirmstheseresults(Doroshkevichetal.,1999).Earliersimilarscales,intherangeof(50–100)h−1Mpc,werefoundonlyforspatialdistributionofclustersofgalaxies(see,e.g.,Bahcall1988;Einastoetal.1994)andforafewsuperclustersofgalaxies(see,e.g.,Oort1983a,b).Evolutionofstructurewasdiscussedandsimulatedmanytimes(see,e.g.,Sahnietal.1994;Doroshkevichetal.1997a,hereafterDFGMM;forreferences,Sahni&Coles1995).However,SLSSinthedarkmatter(DM)distributionsimilartothatseenintheLCRSwasfoundonlyrecentlyinafewsimulationswiththeCDM-likepowerspectrumandΩmh=0.2–0.3,(Cole,Weinberg,Frenk&Ratra1997;Doroshkevich,M¨uller,Retzalf&Turchaninov1999,here-afterDMRT).Hence,forsuitablecosmologicalmodelstheevolutionofsmallinitialperturbationsresultsintheSLSSformation.Inthispaperwepresentanapproximatestatisticalde-scriptionoftheprocessofDMstructureformationbasedonthenonlinearZel’dovichtheory.Thepotentialofthisap-proachislimitedasthesuccessiveconsiderationofmutualinteractionsofthesmallandlargescaleperturbationsbe-comesmoreandmorecumbersome.Inspiteofthisitallowsustoobtainsomeinterestingresults.Thus,itisshownthatformationofbothLSSandSLSSisajointprocesspossess-ingsomefeaturesofself-similarity.ThemainobservedcharacteristicsofLSSandSLSSareexpressedthroughthestructurefunctionsofpowerspectrumandthroughthetyp-icalscales,setbythepowerspectrum,thetime