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1、Supplementsto“ACriticalSupermassiveBlackHoleMassRegulatingGalaxyEvolution”1GalaxyFormationModellingThemainstrategybehindthemodellingapproachwefollowistofirstcalculatethecollapseandmerginghistoryofindividualdarkmatterhalos,whichisgovernedpurelybygravitationalinterac-tions,
2、andsecondlytocalculatethemorecomplexphysicsofthebaryonsinsidethesedarkmatterhalos,includinge.g.radiativecoolingofthegas,starformationandfeedbackfromsupernovaebysimplifiedprescriptionsontopofthedarkmatterevolution.Eachofthedarkmatterhalosconsistofthreemaincomponentswhichar
3、edistributedamongindividualgalaxiesinsidethem.Astel-lar,coldandhotgascomponent,wherethelatterisonlyattributedtocentralgalaxies,themostmassivegalaxiesinsideindividualhalos.Inthefollowingsections,wewilldescribebrieflytherecipesusedtocalculatethesedifferentcomponentswhichare
4、mainlybasedonrecipespresentedinKauffmannetal.1(hereafter,K99)andSpringeletal.2(hereafter,S01),andwereferreadersformoredetailsonmodelimplementationstotheirworkandreferencestherein.Throughoutthispaperweusethefollowingsetofcosmologicalparameters:Ω0=0.3,ΩΛ=0.7,Ωb/Ω0=0.15,σ8=
5、0.9andh=0.65.DarkMatterEvolutionWecalculatethemerginghistoryofdarkmatterhalosaccordingtotheprescriptionpresentedinSomervilleetal.3.ThisapproachhasbeenshowntoproducemerginghistoriesandprogenitordistributionsinreasonableagreementwithresultfromN-bodysimulations1ofcolddarkma
6、tterstructureformationinacosmologicalcontext4.ThemerginghistoryofdarkmatterhalosisreconstructedbybreakingeachhaloupintoprogenitorsabovealimitingminimumprogenitormassMmin.Thismasscutneedstobechosencarefullyasitensuresthattherightgalaxypopulationandmerginghistoriesareprodu
7、cedwithinthemodel.ProgenitorhaloswithmassesbelowMminaredeclaredasaccretioneventsandtheirhistoriesarenotfollowedfurtherbackintime.Progenitorslabelledasaccretioneventsshouldideallynothostanysignificantgalaxiesinthemandbecomposedmainlyofprimordialhotgasattheprogenitorhalo'sv
8、irialtemperature.Toachieveagoodcompromisebetweenaccuracyandcomputationaltime,weuseM=1010M,min⊙whichensu