1996AJ 112. . 105G -2 -1 THE ASTRONOMICALJOURNALVOLUME112,NUMBER1JULY1996 potential withadensityvaryingasp,whichtheyterm potential withacuspandbuildingself-consistentmodels Merritt &Fridman(1996)studiedtheinfluenceofacentral child 1992;Merritt&Fridman1995,1996).Inparticular, consequences forthephasespacestructureofgalaxy that is,theyconserveenergybut havenootherisolatingin- from theorbitlibrary.Theyhaveshownthatinatriaxial density cuspontheorbitalstructurebyfollowingorbitsina which theyterma“weakcusp,” afraction60%-80%(de- inner potentialspike.Theyalso showedthatifpr, tegrals. Thisbehavioriscaused byscatteringoffthesteep a “strongcusp,”fraction80%oftheorbitsareirregular, (Gerhard 1987;Hasan&Norman1990;LeesSchwarzs- 105 Astron.J.112 (1),July1996 0004-6256/96/112(l)/105/9/$6.00 r The massdensitydistributionforgalaxieshasimportant © American Astronomical Society • Provided by theNASA Astrophysics Data System nearly allthegalaxiesinoursample,logarithmicslopeofluminositydensity(S=dlogv/dlogr) We havenon-parametricallydeterminedtheluminositydensityprofilesandtheirlogarithmicslopesfor42 based ontheirsurfacebrightnessprofiles;i.e.,thosewithcuspycoresandwhosesteeppower-law from zero;i.e.,mostellipticalgalaxieshavecusps.Thereareonlytwoforwhichananalyticcore luminosity densityisuniquelydeterminedfromthesurfacebrightnessdatathroughAbelequation.For early-type galaxiesobservedwithHST.Assumingthattheisodensitycontoursarespheroidal,then profiles continueessentiallyunchangedintotheresolutionlimit.Thepeaksslopedistributionoccur the conclusionofLaueretal[AJ,110,2622(1995)]thatearly-typegalaxiescanbedividedintotwotypes measured at0.1"(theinnermostreliablemeasurementwiththeuncorrectedHST)issignificantlydifferent influence ofstochasticorbits.©1996AmericanAstronomicalSociety. elliptical galaxiesareeithernearlyaxisymmetricorsphericalnearthecenter,slowlyevolvedueto the recenttheoreticalworkofMerrittandFridman,theseresultssuggestthatmany(andmaybemost) 3i S=—0.8and-1.9.Morethanhalfofthegalaxieshaveslopessteeper-1.0.Takentogetherwith (S—>0) cannotbeexcluded.Thedistributionoflogarithmicslopesat0.1"appearstobimodal,confirming UCO/Lick Observatories,BoardofStudiesinAstronomyandAstrophysics,UniversityCalifornia,SantaCruz,California95064 THE CENTERSOFEARLY-TYPEGALAXIESWITHHST.III.NON-PARAMETRICRECOVERY Canadian InstituteforTheoreticalAstrophysics,UniversityofToronto,60St.GeorgeStreet,M5S3H8,Canada Kitt PeakNationalObservatory,OpticalAstronomyObservatories,P.O.Box26732,Tucson,Arizona85726 The ObservatoriesoftheCarnegieInstitutionWashington,813SantaBarbaraStreet,Pasadena,California91101 Department ofAstronomy,DennisonBuilding,UniversityMichigan,AnnArbor,Michigan48109 1. INTRODUCTION Institute forAstronomy,UniversityofHawaii,2680WoodlawnDrive,Honolulu,Hawaii96822 Electronic mail:[email protected],[email protected] OF STELLARLUMINOSITYDISTRIBUTIONS Karl GebhardtandDouglasRichstone Received 1995November3;revised1996March8 Edward A.AjharandTodR.Lauer Yong-Ik ByunandJohnKormendy S. M.FaberandCarlGrillmair Scott Tremaine Alan Dressler ABSTRACT pending onenergy)oftheorbitsareirregular.Thisisin box orbits)willbechaotic.Therefore,ifthedensitydistribu- they canbedescribedashaving“analytic”cores. of theorbitsareregular(reviewedindeZeeuw&Franx tion istriaxialandhasdlogp/dr1/2,orsteeper, eral, ifthedensitydistributionhasanonzerologarithmic portant intheaxisymmetriccase sinceorbitsdonotpassnear ritt &Fridman1995).Therole ofacentralcuspislessim- ture andevolutionofthecentral regionsofthegalaxy(Mer- then stochasticityislikelytoplayacriticalroleinthestruc- sharp contrastwithseparabletriaxialpotentials,inwhichall the centerbecausetheyconserve onecomponentofthean- (Taylor seriesexpandable)nearthecenterand,therefore, slope nearthecenter,orbitsthatpasscenter(i.e., 1991). Inallofthesepotentials,thedensityiswellbehaved Merritt andFridman’sworkstronglysuggeststhatingen- © 1996Am.Astron. Soc.105 1996AJ 112. . 105G profile. Theexistenceofacentralmassivedarkobject rected HST.Thesecanbedeprojectedtoobtaintheluminos- ness profilesforearly-typegalaxiesobservedwiththeuncor- important roleofhighresolutionsurfacebrightnessdistribu- practice anynoiseinthedataisamplifiedbyconstruction the massconcentration.Deprojectiontoobtainden- the luminositydensityprobablyprovidesalowerlimitfor ity densitywhichweassumealsorepresentsthemass tions inunderstandingthedynamicsofellipticalgalaxiesand guiar momentum.Merritt&Fridman’sworkemphasizesthe This equationisanAbelintegralwithsolution the surfacebrightnessasafunctionofprojectedradiusis spiral bulges. While thisapproachisreasonableandshouldyieldgood data beforedeprojecting.Themodelhadtheform time honoredprocedureoffittingaparametricmodeltothe construct S=dlogv(r)/d\ogr.InPaperI,wefollowedthe of v(r),andfurtheramplifiedbyaseconddifferentiationto given by symmetry. Ifthegalaxyhasaluminositydensityv(r),then sity isformallysimpleinthecaseofspherical(orspheroidal) (MDO) willonlyincreasethecentralmassconcentration,so The parametricmodelcanthenbeinvertednumericallyus- maximum-likelihood technique(Byunetal.1996,PaperII). This parametricmodelwasfittedtotheobserveddatabya Fig. 3andEq.28ofTremaineetal(1994)(seealsoDehnen is somecauseforconcerninitsapplication. estimates ofviftheparametricmodelfitsdatawell,there ing Eq.2toestimatethestellardensityrunnearcenter. 106 GEBHARDTETAL:EARLY-TYPEGALAXIES.III. projected radius.Analternative andmorefrighteningwayto put thisisthatthe useofEq.3asaparametric model creates havior ofv(r)nearthebreak radius(r~linthe d log/(/?)/*/logÆ=0),despitethefactthatcentralden- The figureandEq.28showthatfor2
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