A New Empirical Model for the Structural Analysis

arXiv:astro-ph/0306023v12Jun2003ANewEmpiricalModelfortheStructuralAnalysisofEarly-typeGalaxiesandaCriticalReviewoftheNukerModel1AlisterW.GrahamDepartmentofAstronomy,UniversityofFlorida,Gainesville,FL,[e-mail],I.Trujillo,andA.AsensioRamosInstitutodeAstrof´ısicadeCanarias,LaLaguna,E-38200,Tenerife,SpainABSTRACTTheNukerlawwasdesignedtomatchtheinnerfew(∼3-10)arcsecondsofpredominantlynearby(.30Mpc)early-typegalaxylight-profiles;itwasneverintendedtodescribeanentireprofile.TheS´ersicmodel,ontheotherhand,wasdevelopedtofittheentireprofile;however,duetothepresenceofpartiallydepletedgalaxycorestheS´ersicmodelcannotalwaysdescribetheveryinnerregion.Wehavethereforedevelopedanewempiricalmodelconsistingofaninnerpower-law,atransitionregion,andanouterS´ersicmodeltoconnecttheinnerandouterstructureofellipticalgalaxies.WehaveadditionallyexploredthestabilityoftheNukermodelparameters.Surprisingly,nonearefoundtobestablequantities;allareshowntovarysystematicallywithaprofile’sfittedradialextent,andoftenbymorethan100%.Consideringellipticalgalaxiesspanningarangeof7.5magnitudes,werevealthatthecentralstellardensitiesoftheunderlyinghostgalaxiesincreasewithgalaxyluminosityuntiltheonsetofcoreformation,detectedonlyinthebrightestellipticalgalaxies.Wesuggestthattheso-called“power-law”galaxiesmayactuallybedescribedbytheS´ersicmodelovertheirentireradialrange.Subjectheadings:galaxies:ellipticalandlenticular,cD—galaxies:fundamentalparameters—galaxies:nuclei—galaxies:photometry—galaxies:structure1BasedonobservationsmadewiththeNASA/ESAHubbleSpaceTelescope,obtainedattheSpaceTelescopeScienceInstitute,whichisoperatedbytheAssociationofUniversitiesforResearchinAstronomy,Inc.,underNASAcontractNAS5-26555.–2–1.IntroductionEarlyHubbleSpaceTelescope(HST)observationsofellipticalgalaxiesandthebulgesofdiskgalaxies,hereaftercollectivelyreferredtoas‘bulges’(Craneetal.1993;Ferrareseetal.1994;Jaffeetal.1994;Forbes,Franx,&Illingworth1995),confirmedtheground-basedconclusionsofKormendy(1985)andLauer(1985):Galaxymodelswithflatcores(e.g.,King’s1966model)donotdescribethemajorityofellipticalgalaxies,oratleasttheresolvedpartoftheprofile.Inalmostallgalaxiessurveyed,thesurfacebrightnessprofilecontinuedtoriseinwarduntilresolutionwaslost.Subsequently,withtheenhancedimagequalityaffordedbytheHSThavecomenewmodelstodescribethecentersofnearbybulges.Ferrareseetal.(1994)introducedtwoclassesofgalaxiesaccordingtothebehavioroftheinnersurfacebrightnessprofile.Thosewitharesolvedcoreflatteningtowardsthecenterwerelabeledas“TypeI”,andthosethatroughlyfollowasteeppower-lawallthewayintothecenterweredesignatedas“TypeII”galaxies.Theseauthorsintroduceda4-parameterdoublepower-lawmodeltoquantifytheshapeofthegalaxyprofilewithintheinner∼10′′.Acoreradiusmarkedthetransitionbetweentheinnerandouterpower-lawshavingslopesβ1andβ2,respectively.Alloftheir“TypeI”galaxieshadaninnerslopeshallowerthan-0.31(noneofthemhadaslopeofzero);allbutoneoftheir“TypeII”galaxieshadaslopesteeperthan-0.47.Modelingalargergalaxysample,Laueretal.(1995;seealsoKormendyetal.1994)confirmedtheaboveresult2—thoughtheyinterpreteditdifferently—andintroducedamodelwithanadditionalparameter(α),whichbettercontrolledthetransitionbetweenthetwopower-laws.Thismodel3wasdesignatedthe‘Nukerlaw’bytheseauthors.ItcanbewrittenasI(r)=Ib2(β−γ)/αrrb−γ1+rrbα(γ−β)/α.(1)Theintensityatthecoreradius,alsoknownasthebreak-radiusrb,isdenotedbyIb.Theinnerpower-lawslopeisnowdenotedbyγandtheouterpower-lawslopeisdenotedbyβ.ThismodelreducestotheformproposedbyFerrareseetal.(1994)whenα=2(β2−β1).Laueretal.(1995)refertogalaxieswithγ0.3as“core”galaxiesandgalaxieswithγ0.5as“power-law”galaxies.2ItshouldbenotedthatRestetal.(2001)andRavindranathetal.(2001)havenowfoundseveralhigh-luminositygalaxieswithinnerprofileslope0.3γ0.5.3This5parameterdoublepower-lawmodelwasindependentlyintroducedbyZhao(1996)tomodelthespatial(i.e.notprojected)densityprofilesofellipticalgalaxies(seealsoZhao1997).–3–ApplicationoftheNukermodelhasprovedextremelypopular,andtherearephysicalgroundstointerpretthereductionincentralprofileslopeandtheimpliedcoredepletion.Manyauthorshavediscussedhowtheinnerregionofagalaxymayhavebeenpartiallyevacuatedbythecoalescenceofmergingsupermassiveblackholes(SMBHs;e.g.,Ebisuzaki,Makino,&Okumura1991;Makino&Ebisuzaki1996;Faberetal.1997;Makino1997;Quillen,Bower,&Stritzinger2000;Alexander&Livio2001;Milosavljevic&Merritt2001).Conversely,thepresenceof“power-law”cuspshasbeenusedtoargueforadiabaticgrowthofcentralblackholes,withthegrowingblackholereshapingthecentralregion(e.g.,vanderMarel1999),althoughRavindranath,Ho,&Filippenko(2002)haveusedthefittedpower-lawslopestoargueagainstthisscenario.Tobetterunderstandgalaxy“cores”,onewouldliketomeasurechangestoagalaxy’sinnerprofilerelativetoitsoriginalshape.Recently,theoverall“shape”ofabulge’slight-profile(asparameterizedbytheS´ersic1968r1/nshapeindexn)hasbeenshowntocorrelatestrongly(rs=0.92)withthemassofitscentralSMBH(Grahametal.2001a,2002;Erwin,Graham,&Caon2003).Thisimpliesastrongconnectionbetweentheformationandstructureoftheentirebulge