Draftversion January3,2013 PreprinttypesetusingLATEXstyleemulateapjv.03/07/07 THE (BLACK HOLE MASS)–(HOST SPHEROID LUMINOSITY) RELATION AT HIGH AND LOW MASSES, THEQUADRATIC GROWTHOFBLACKHOLES,AND INTERMEDIATE-MASSBLACKHOLECANDIDATES Alister W. Graham1 and Nicholas Scott CentreforAstrophysicsandSupercomputing, SwinburneUniversityofTechnology, Hawthorn,Victoria3122,Australia. Draft version January 3, 2013 3 1 ABSTRACT 0 2 Fromasampleof72galaxieswithreliablesupermassiveblackholemassesMbh,wederivetheMbh– (host spheroid luminosity, L) relation for i) the subsample of 24 core-S´ersic galaxies with partially n depleted cores, and ii) the remaining subsample of 48 S´ersic galaxies. Using K -band Two Micron a All Sky Survey data, we find the near-linear relation M L1.10±0.20 for the csore-S´ersic spheroids J bh ∝ Ks 2 thoughttobebuiltinadditivedrymergerevents,whileMbh ∝LK2.s73±0.55fortheS´ersicspheroidsbuilt from gas-rich processes. After converting literature B-band disk galaxy magnitudes into inclination- ] and dust-corrected bulge magnitudes, via a useful new equation presented herein, we obtain a similar O result. Unlike withthe M –(velocitydispersion)diagram,whichis alsoupdated hereusingthe same bh C galaxy sample, it remains unknown whether barred and non-barred S´ersic galaxies are offset from . each other in the Mbh–L diagram. h While black hole feedback has typically been invoked to explain what was previously thought to p be a nearly constant M /M mass ratio of 0.2%, we advocate that the near-linear M – - bh Spheroid ∼ bh o L and Mbh–MSpheroid relations observed at high masses may have instead largely arisen from the r additive dry merging of galaxies. We argue that feedback results in a dramatically different scaling t s relation, such that black hole mass scales roughly quadratically with the spheroid mass in S´ersic a galaxies. Wethereforeintroducearevisedcold-gas’quasar’modefeedingequationforsemi-analytical [ models to reflect what we dub the quadratic growth of black holes in S´ersic galaxies built amidst gas-richprocesses. Finally,weuseournewS´ersicM –Lequationstopredictthemassesofcandidate 3 bh v intermediate mass blackholes in almost50 low luminosity spheroidscontainingactive galacticnuclei, 9 finding many masses between that of stellar mass black holes and supermassive black holes. 9 Subject headings: black hole physics — galaxies: evolution — galaxies: nuclei 1 3 . 1. INTRODUCTION & Richstone (1995, their figure 14) revealed an appar- 1 ently linear correlationbetween black hole mass and the 1 The(blackholemass)–(hostspheroiddynamicalmass) brightness / mass of the host spheroid. As the sample 2 M –M relation (e.g. Marconi & Hunt 2003; bh Sph,dyn size grew, researchers began to apply a single log-linear, 1 Ha¨ring & Rix 2004) has recently been revised such : that core-S´ersic galaxies (whose spheroidal components i.e. power-law, relation to the data (e.g. Richstone et v al. 1998;Kormendy & Gebhardt 2001; McClure & Dun- are thought to be built in simple additive dry merger i X events) define a near-linear relation while S´ersic galax- lop 2002). However the samples remained dominated by fairlyluminousspheroidsandtheapplicabilityofthenew r ies (whose spheroidalcomponentsare likelybuilt amidst a gas-richprocesses)defineanear-quadraticrelation(Gra- Mbh–L relations (e.g. McClure & Dunlop 2004;Marconi & Hunt 2003;Graham2007a)to low-luminositysystems ham 2012a). Graham (2012a,b) additionally predicted was not securely established. Indeed, Graham (2007a) that the previously established log-linear, i.e. single noted that the M –L and M –σ relations (Ferrarese power-law, relation between black hole mass and host bh bh & Merritt 2000; Gebhardt et al. 2000) cannot both be spheroid luminosity, L, must also require a significant modification such that M L1.0 for the spheroidal described by a power-law because the relationship be- bh ∝ tweenluminosityandvelocitydispersion,σ,forelliptical component of luminous (M . 20.5 mag) core-S´ersic B galaxieswhileM L2.5forthe−fainterS´ersicspheroids galaxies is not described by a single power-law. bh ∝ As reviewed in Graham (2012c), the elliptical galaxy —iftheirdynamicalmass-to-lightratioscaleswithL1/4. L–σ relation has long been known to be ‘broken’, such If (M/L) L1/3 then one expects M L8/3. Here,fordthyneamfiricsatlt∝ime,weshowthattheMbh–bLh r∝elation SthcahtecLhte∝r 1σ9580a;t Mthaelulummutinhou&s-eKnidrsh(MneBr 1.98−1;20V.o5nmDaegr: is indeed bent, and we provide new expressions to pre- Linden et al. 2007; Liu et al. 2008) and possibly even dict black hole masses in core-S´ersic galaxies and S´ersic as steep as L σ6 (Lauer et al. 2007), while L σ2 galaxies using the luminosity of their spheroidal compo- ∝ ∝ at intermediate and faint luminosities (e.g. Davies et al. nent.2 1983; Held et al. 1992; de Rijcke et al. 2005; Matkovi´c From a literature sample of eight galaxies, Kormendy & Guzma´n 2005; Kourkchi et al. 2012). Galaxy sam- ples containing both bright and intermediate luminosity 1CorrespondingAuthor: [email protected] 2 Readersunfamiliarwiththecore-S´ersicmodel(Grahametal. elliptical galaxies will therefore naturally yield L–σ re- 2003; Trujilloetal.2004)ortheS´ersic(1963) model,fortheclas- lationships with exponents around 3 to 4 (e.g., Faber sification of galaxies, may like to refer to the review article by & Jackson 1976; Tonry 1981; de Vaucouleurs & Olson Graham&Driver(2005). 2 Graham & Scott 1982;Desrochesetal.2007). Itshouldbenotedthatthis permassive black holes, and has ramifications for semi- change in slope of the L–σ relation at M 20.5 mag analytic computer codes which try to mimic this coevo- B ≈− (S´ersicn 3–4)isnotrelatedto(i)theonsetofthecoex- lution. Moreover,as noted in Graham (2012a), the real- ≈ istenceofclassicalbulgesandpseudobulgesatn .2, izationofabrokenM –Lrelationwillinfluence,among bulge bh nor (ii) the alleged divide at M = 18 mag (n . other things: evolutionary studies of the (black hole)- B galaxy − 1–2)betweendwarfandordinaryellipticalgalaxies(Kor- (host spheroid) connection over different cosmic epochs mendy1985;Kormendyetal.2009). Instead,thechange (e.g. Cisternas et al. 2011; Li, Ho & Wang 2011; Hiner in slope at M 20.5 mag coincides with the division etal.2012;Zhang,Lu&Yu2012);predictionsforspace- B ≈− betweencore-S´ersicgalaxies(whichhaveacentraldeficit basedgravitationalwavedetectionswhichusetheM –L bh oflightrelativetotheinwardextrapolationoftheirouter relationtoestimateblackholemasses(e.g.Mapellietal. S´ersic light profile) and S´ersic galaxies3 which do not 2012,andreferences therein); andestimates of the black (Graham & Guzma´n 2003; Graham et al. 2003; Trujillo hole mass function and mass density based on spheroid et al. 2004; Matkovi´c & Guzma´n 2005). If (non-barred) luminosity functions (e.g. Vika et al. 2009; Li, Wang, & S´ersicandcore-S´ersicgalaxiesfollowthesameM σ5 Ho 2012). bh ∝ relation (see section 3.1), they therefore obviously can- Recent studies of the M –L relation have contin- bh not follow the same M –L relation because they do ued to be largelydominated by luminous spheroidswith bh not follow the same L–σ relation. Simple consistency Mbh & 107–108M⊙, and have continued to fit a straight arguments dictate that the core-S´ersic galaxies should line to the data (e.g. Sani et al. 2011; Vika et al. 2011; follow the relation M L1.0 while the (non-barred) McConnelletal.2011a;Beifiorietal.2012). However,an bh S´ersicgalaxiesshould foll∝ow the relationM L2.5 (or inspection of their M –L diagrams reveals the onset of bh bh M L3 if M σ6). ∝ a steepening relation in their lower luminosity spheroids bh bh Wh∝ilethecore-S∝´ersicmodelhasprovidedanewmeans which have Mbh . 107–108M⊙, as also seen in the dia- to identify and quantify the stellar deficits, i.e. the flat- gramsfromGraham(2007a)andGu¨ltekinetal.(2009b). tened cores, which have long been observed in giant In addition, a number of models are actually generating galaxies (e.g. King 1978, and references therein), the ra- ‘bent’ M –M relations which show a steepening bh Spheroid tionale for a physical divide between core-S´ersic galax- at low masses (e.g. Cirasuolo et al. 2005, their figure 5; ies and S´ersic galaxies also existed long ago. Early-type Khandaietal.2012,theirfigure7;Bonoli,Mayer&Cal- galaxies brighter than M = 20.5 mag tend to be legari 2012, their figure 7). Here we build on this (ten- B − anisotropic, pressure supported elliptical galaxies with tativeobservational)evidence ofasteepening relationat boxyisophotes,whilethelessluminousearly-typegalax- low masses by using a sample of 72 galaxies with di- ies tend to have disky isophotes and often contain a ro- rectly measured black hole masses that are tabulated in tating disk of stars (e.g. Carter 1978,1987; Davies et al. Section 2 and span 106–1010M⊙. For the first time we 1983; Bender et al. 1988; Peletier et al. 1990; Jaffe et both identify and quantify the bend in the M –L rela- bh al. 1994; Faber et al. 1997; Emsellem et al. 2011). In tion (Section 3). addition,andasnotedalready,the L–σ relationchanges Rather than fitting a single quadratic relation to the slope at M 20.5 mag (Davies et al. 1983; Matkovi´c (M ,L)distributionofpoints—whichwouldbe inline B bh ≈− & Guzma´n 2005): the core-S´ersicgalaxies(M . 20.5 withthe use ofa log-quadraticrelationinthe M –ndi- B bh mag) define the relation L σ5 while the S´ersic g−alax- agram by Graham & Driver (2007a) — we embrace the ies (M & 20.5 mag) fo∝llow the relation L σ2, large body of data which shows that S´ersic and core- B − ∝ with no discontinuity at M = 18 mag. Similarly, S´ersic galaxies have distinguishing characteristics sug- B − the elliptical galaxy L–µ relation, where µ is the cen- gestive of a different formation history (e.g. Davies et 0 0 tral surface brightness, also breaks at M 20.5 mag al. 1983; Faber et al. 1997; Graham & Guzma´n 2003; B ≈− and remains linear at M = 18 mag (e.g. Graham & Gavazzi et al. 2005; Ferrarese et al. 2006) and therefore B Guzma´n 2003)4. While gas-ri−ch processes and mergers fit two M –L relations, one for each type of galaxy. bh are thought to build the S´ersic galaxies, relatively gas- In Section 4 we provide a discussion of some of the free galaxy mergers are thought to build the core-S´ersic moresalientpoints arisingfromthe new M –Lrelation bh galaxies. The coalescenceof massiveblackholes — from for S´ersic and core-S´ersic galaxies. In particular, Sec- thepre-merged,gas-poorgalaxies—scouroutthecoreof tion 4.1 provides updated black hole mass estimates for thenewlymerged‘core-S´ersic’galaxy(Begelman,Bland- nearly50low-luminosityspheroids,andrevealsthatthey ford,&Rees1980;Ebisuzaki,Makino,&Okumura1991; occupy the holy grail mass range for intermediate mass Merritt, Mikkola, & Szell 2007). blackholes, rangingfrom the stellar mass black hole up- The above expectation for the ‘bent’ Mbh–L relation per limit of 102M⊙ to the lower-bound of 105–106M⊙ ∼ impactsdramaticallyuponourpredictionsforblackhole for supermassive black holes. In Section 4.2 we intro- masses at the centers of other galaxies, has implications duce a significantly modified expression for use in semi- for the competing formation scenarios proposed to ex- analytical models which try to mimic the coevolution plain the coevolution of galactic spheroids and their su- of supermassive black holes and galaxies. We provide a new quadratic cold-gas ‘quasar’ mode feeding equation 3S´ersicgalaxieswerepreviouslyreferredtoas‘power-law’galax- to match the quadratic (black hole)-to-(host spheroid) ies before it was realized that their spheroidal component’s inner growth observed in S´ersic galaxies built from gas-rich lightprofilesarebetterdescribedbythecurvedS´ersicmodelthan processes. Finally, Section 4.3 discusses the observation byapower-law(e.g.Trujilloetal.2004). 4 As shown, and explained, in Graham 2012c, it is only from that barred and non-barred disk galaxies currently ap- the use of ‘effective’ radii and ‘effective’ surface brightnesses that pear to occupy the same region of the M –L diagram. bh apparent breaks are seen at MB =−18 maginwhat areactually continuous, curvedrelations. 2. DATA The M –L relation 3 bh spheroid We have continued to build on past catalogs of reli- the rare ‘compact elliptical’ galaxy class and is thus not able supermassive black hole masses obtained from di- representative of the majority of galaxies. Such galaxies rect maser, stellar or gas kinematic measurements (e.g. are thought to be heavily stripped of an unknown frac- Ferrarese & Ford (2005); Hu (2008); Graham (2008b); tion of their stars (e.g. Bekki et al. 2001), and as such Graham et al. 2011) by adding 16 galaxies from the lit- this galaxy may bias our analysis. We do however note erature. This gives us an initial sample of 80 galaxies that M32, and the Milky Way, have been included in withdirectly measuredblackhole masses. Since the cat- a preliminary M –σ diagram (Figure 1). We therefore bh alogin Grahamet al. (2011)was prepared,we note that mentionherethatwehaveusedahostbulgevelocitydis- several updates over the last two years have resulted in persion of 55 km s−1 from M32’s bulge stars outside of the doubling of black hole masses at the high-mass end M32’scoreregion;thisvalueislowerthanthecommonly of the M –σ diagram (e.g. van den Bosch & de Zeeuw used central aperture values of 72–75 km s−1 which are bh 2010; Walsh et al. 2010, 2012) and two ten-billion solar biased high by the dynamics around the central black mass black holes have been reported (e.g. McConnell et hole (Igor Chilingarian, priv. comm.). This leaves us, al. 2012). thus far, with a sample of (80 5 =) 75 galaxies. For − reasonsdiscussed atthe startof Section3, anadditional 2.1. Galaxy exclusions three galaxies (NGC 1316, NGC 3842 and NGC 4889) are excluded from some of the analyses. Separatefromtheabovesampleof80galaxies,wehave maintainedourexclusionofNGC7457,becauseitsblack 2.2. Galaxy distances and magnitudes holemasswasderivedassumingthatthisgalaxy’sexcess nuclear light was due to an AGN rather than a massive For the bulk of the sample, we have used the dis- nuclear disk and dense star cluster (Balcells et al. 2007; tance moduli from Tonry et al. (2001) after first de- Graham & Spitler 2009), and the exclusion of the Sc creasing these values by 0.06 mag and thereby reducing galaxy NGC 2748 due to potential dust complications both the galaxy distances and the black hole masses by withitsestimatedblackholemass(Atkinsonetal.2005; 3%. This small adjustment arises from Blakeslee et ∼ Hu 2008). al.’s (2002, their Section 4.6) recalibration of the sur- For the following reasons, our sample of 80 galaxies is face brightness fluctuation method based on the final reduced here by five. The best-fitting parameter set in Cepheid distances given by Freedman et al. (2001, with the massmodeling ofNGC 5252byCapettietal.(2005) the metallicity correction). In addition to listing each had resulted in a reduced χ2 value of 16.5, indicative of galaxy’sdistanceandvelocitydispersion,primarilytaken a poor fit to the data and resulting in its exclusion by from HyperLeda6 (Paturel et al. 2003),Table 1 presents Gu¨ltekinetal.(2009b). We toonowexcludethis galaxy, theirobserved(i.e.uncorrected)B-bandmagnitude,B , T whichwouldotherwise appear to have a black hole mass from the Third Reference Catalogue of Bright Galaxies that is an order of magnitude too high in the M –σ (deVaucouleursetal.1991,hereafterRC3)andtheirto- bh diagram. The inclined, starburst spiral galaxy Circinus tal K -band magnitude as provided by the Two Micron s is also excluded due to its complex kinematics (e.g. For, All Sky Survey (2MASS)7 (Jarrett et al. 2000). Due to Koribalski & Jarrett 2012, and references therein) and thebrightstarnearthecenterofNGC2974,weusedthe location on the other side of the Galactic plane. With a K-band magnitude from Cappellari et al. (2006) rather Galacticlatitudeoflessthan5degrees,thesuggestedB- than the 2MASS value for this galaxy. band extinction correctionfor Circinus is 5 mag or more Both the observed B- and K -band magnitudes need s (Schlafly&Finkbeiner 2011)andisconsideredtobe un- to be corrected for Galactic extinction, which we have reliable. Theabovetwogalaxiescannotbeusedreliably taken from Schlegel et al. (1998), as provided by the ineithertheM –LdiagramortheM –σ diagram,and NASA/IPAC Extragalactic Database (NED)8 and in- bh bh they are therefore not listed in our Table 1. cluded in Table 1 as A and A for ease of reference. B K Following Gu¨ltekin et al. (2009b), we exclude the We additionally provide K-corrections for the 2MASS barredgalaxyNGC3079. AlthoughNGC3079hasawell K -band magnitudes, derived from each galaxy’s helio- s determinedblack hole mass (Kondratkoetal. 2005),the centric redshift z (taken from NED) and total J K − observed stellar velocity dispersion drops rapidly from a color(takenfrom2MASS)coupledwiththe prescription centralvalueof 150kms−1 to60kms−1 orlesswithin from Chilingarian, Melchior & Zolotukhin (2010) which just 1 kpc (Shaw∼, Wilkinson, & Carter 1993). The dy- is available online9. In passing, we note that for the low namicsin this Sc galaxy’sboxy peanut-shapedbulge are redshifts associated with our galaxy sample, this K Ks known to be affected by bar streaming motions (Merri- correctionis approximately 2.1z, 2.2z,and 2.5z for − − − field & Kuijken (1999; Veilleux, Bland-Hawthorn,& Ce- the elliptical, S0 and Sa, and later spiral galaxy types, cil 1999)which were not modeled by Shaw et al. (1993). respectively. WithoutreliableB R orB I colors,the − − Such additional motions are a general concern in barred B-bandK-correctionstabulatedinTable1aresuchthat galaxies, as detailed in Graham et al. (2011), and it is K equals 4z, 3.5z, 3z, and 2.5z for the elliptical, S0, B notclearwhatvelocitydispersionshouldbe usedfor the Sa, and later spiral galaxy types, respectively. As can bulge component of this galaxy5. The bulge luminosity be seen in Table 1, these corrections are minor and they oftheMilkyWayisuncertainduetodustinourGalaxy’s have had no significant impact on the final results. Fi- disc, and is therefore not included in our M –L nally,in ouranalysiswe correctedallgalaxymagnitudes bh spheroid diagram. Finally, we also exclude M32 which belongs to 6 http://leda.univ-lyon1.fr 5WhilethisgalaxycouldbeusedintheMbh–Lspheroiddiagram, 7 www.ipac.caltech.edu/2mass wedonotsoastobeconsistentwithourgalaxysampleinthefinal 8 http://nedwww.ipac.caltech.edu Mbh–σ diagram. 9 http://kcor.sai.msu.ru 4 Graham & Scott for cosmologicalredshift dimming. and 2.3. Bulge magnitudes ∆Mdisk =Mdisc,obs Mdisc,intrin=d1+d2[1 cos(i)]d3, − − (7) In addition to the above three corrections that were where the coefficients in the above equations depend applied in the analysis rather than in Table 1, the tabu- on the passband used and are provided in Driver et al. lateddiskgalaxymagnitudeswereadjustedfortwoother (2008). The cosine of the disk inclination angle i, such factors: their observed, total magnitudes were converted that i = 0 degrees for a face-on disk, is roughly equal into dust-corrected, bulge magnitudes. Rather than do to the minor-to-major axis ratio, b/a, at large radii. For this galaxy by galaxy (e.g. Grootes et al. 2012), which our galaxy sample, these values have been provided in wouldrequirecarefulbulge/disk decompositions,we can the final column of Table 1. take advantage of our large sample size and employ a Wehaveusedaconservative(small)uncertaintyof5% mean statistical correction. While this will result in in- for the velocity dispersions, and assigned a typical un- dividualbulgemagnitudesnotbeingexactlycorrect,the certaintyof0.25magtotheellipticalgalaxymagnitudes. ensemble average correction will be correct. Given that Regardingthediskgalaxies,theobservedrangeofbulge- dust has an order of magnitude less impact in the K - s to-disk flux ratios (Graham & Worley 2008) has a 1σ band thanin the B-band, we canexpect there to be less scatter equal to a factor of 2 for any given disk galaxy scatter in our Ks-band Mbh–L relation, at least for the morphologicaltype. Wethe∼reforeassignanotablylarger S´ersic sample which contains the bulk of the bulges. uncertaintyof 0.75mag to our bulge magnitudes. While Using the relation M = 2.5log(L), the observedand − this may at first sound worryingly high, we again note the intrinsic (i.e. dust-corrected) bulge and disk lumi- that the sample average shift from a disk galaxy magni- nosities are related as follows. tudetoabulgemagnitudewillbemoreaccurate,thereby Lbulge,obs/Lbulge,int=10−∆Mbulge/2.5, (1) much less affecting the recovery of the Mbh–L relation. L /L =10−∆Mdisk/2.5, (2) It is only now that the disk galaxy sample size N = 44 disk,obs disk,int is sufficiently large (coupled with 9 elliptical galaxies in L +L =10−Mgalaxy,obs/2.5, (3) the S´ersicsample) that we canuse this methodology be- bulge,obs disk,obs cause the uncertainty in the disk-galaxy sample average L /L =B/D, (4) bulge,int disk,int correctionscales with 1/√N. where ∆M and ∆M are the differences between bulge disk the observed and intrinsic magnitudes (given below). 2.4. Galaxy core type The above equations can be combined to give the use- ful expression As described in the Introduction, several global prop- erties and scaling relations of galaxies depend on their M =M bulge,int galaxy,obs core type. We have therefore identified galaxies with or +2.5log 10−∆Mbulge/2.5+ 10−∆Mdisk/2.5(5.) wshiathlloouwtlaigphatrptiraolfilyledse,palreetetdhostueglhlatrtcoorhea.vSeufochrmcoerdesd,uwriinthg (cid:20) (B/D) (cid:21) ‘dry’ galaxy merger events in which a binary supermas- The average dust-corrected bulge-to-disk (B/D) flux sive black hole’s orbit decays by gravitationally ejecting ratio is well known to be a function of both galaxy mor- stars from the center of the newly merged galaxy (e.g. phologicaltypeandpassband,varyingmainlyduetothe Begelman et al. 1980; Ebisuzaki et al. 1991; Graham bulge luminosity (e.g. Yoshizawa & Wakamatsu 1975; 2004; Merritt et al. 2007). However S´ersic galaxies that Trujilloetal.2001). Graham&Worley(2008)presented have n . 2–3 may also have a resolved inner, negative over 400 K-band, B/D flux ratios as a function of disk logarithmic light-profile slope (for the spheroid) which galaxy morphological type. Given that extinction due is less steep than 0.3, although they have no depleted to dust is still an issue at near-infrared wavelengths, al- core relative to their outer profile. Graham et al. (2003) beit notably less in the K-band than the H-band, these warnedthat some of these galaxiesmay be misidentified flux ratios were corrected by Graham & Worley (2008) as‘core’galaxiesandDullo&Graham(2012)haveshown for dust following the prescription given by Driver et al. thatthis hasoccurred 20%ofthe time inthe past. We (2008). Most studies have not made this important cor- ∼ thereforehaveapreferenceforcoresidentifiedasadeficit rectionwhicheffectivelyincreasestheobservedB/Dflux relative to the inward extrapolation of the spheroid’s ratio after accounting for the light from the far-side of outer S´ersic profile (e.g. Trujillo et al. 2004; Ferrarese thebulgewhichisobscuredbythecentrally-concentrated et al. 2006; Dullo & Graham 2012). Such galaxies are dustinthe disk. HerewehaveslightlyadjustedGraham referred to as ‘core-S´ersic’ galaxies, while those with no & Worley’s (2008)B/D values by combining the S0 and deficit or instead additional nuclear components are re- S0/aclassesasoneinourTable2andensuringthatthey ferred to as ‘S´ersic’ galaxies (e.g. Graham et al. 2003; do not have a smaller B/D ratio than the Sa galaxies. Graham&Guzma´n2003;Balcellsetal.2003;Trujillo et By combining these ratios with the average,inclination- al. 2004). dependent ∆M and ∆M values below, one can bulge disk For most of the luminous galaxies we have been able derive the expected ‘intrinsic’ bulge magnitude from the to identify from suitably high-resolutionimages whether observed(dust-dimmed)galaxymagnitudeandtheincli- or not they possess a partially-depleted core, although nation of the disk. Specifically, for ∆M and ∆M bulge disk some are at too great a distance to know. At the low- we have used the expressions from Driver et al. (2008) luminosityendoftherelation,dustynucleicanmakethis such that task more challenging. When no core designation was ∆M =M M =b +b [1 cos(i)]b3, available or possible from the literature (see column 4 bulge bulge,obs bulge,intrin 1 2 − − (6) of Table 1) we used the velocity dispersion to help us The M –L relation 5 bh spheroid TABLE 1 Blackhole / Galaxydata. Galaxy Type Dist core σ Mbh BT Ks AB AK KB KKs R25 MB MKs [Mpc] kms−1 [108M⊙] [mag] [mag] [mag][mag][mag] [mag] [mag] [mag] (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) 30Ellipticals A1836,BCGE1 158.0[3a] y? 309[5a] 39+4 [6a] 14.56 9.993 0.277 0.024 0.15 −0.07 ... −21.72−26.25 −5 A3565,BCGE1 40.7[3a] y? 335[5b]11+2 [6a] 11.61 7.502 0.265 0.023 0.05 −0.03 ... −21.71−25.65 −2 IC1459 E3 28.4 y? 306 24+10 [6b] 11.61 7.502 0.265 0.023 0.02 −0.01 ... −21.37−25.50 −10 NGC821 E6 23.4 n[4a] 200 0.39+0.26 [6c] 11.67 7.900 0.474 0.040 0.02 −0.01 ... −20.65−24.02 −0.09 NGC1399 E1 19.4 y[4b] 329 4.7+0.6 [6d] 10.55 6.306 0.056 0.005 0.02 −0.01 ... −20.95−25.17 −0.6 NGC2974 E4 20.9 n[4c] 227 1.7+0.2 [6e] 11.87 8.00[8a] 0.235 0.020 0.03 −0.01 ... −19.97−23.66 −0.2 NGC3377 E5 10.9 n[4d] 139 0.77+0.04 [6f] 11.24 7.441 0.147 0.013 0.01 −0.01 ... −19.09−22.78 −0.06 NGC3379 E1 10.3 y[4b] 209 4.0+1.0 [6g] 10.24 6.270 0.105 0.009 0.01 −0.01 ... −19.93−23.83 −1.0 NGC3608 E2 22.3 y[4b] 192 2.0+1.1 [6c] 11.70 8.096 0.090 0.008 0.02 −0.01 ... −20.13−23.68 −0.6 NGC3842 E3 98.4[6h] y[4b] 270[6h]97+30 [6h] 12.78 9.082 0.093 0.008 0.08 −0.04 ... −22.28−26.02 −26 NGC4261 E2 30.8 y[4e] 309 5.0+1.0 [6i] 11.41 7.263 0.078 0.007 0.03 −0.02 ... −21.11−25.24 −1.0 NGC4291 E3 25.5 y[4b] 285 3.3+0.9 [6c] 12.43 8.417 0.158 0.013 0.02 −0.01 ... −19.76−23.66 −2.5 NGC4374 E1 17.9 y[4f] 296[6j] 9.0+0.9 [6j] 10.09 6.222 0.174 0.015 0.01 −0.01 ... −21.35−25.08 −0.8 NGC4473 E5 15.3 n[4b] 179 1.2+0.4 [6c] 11.16 7.157 0.123 0.010 0.03 −0.02 ... −19.89−23.83 −0.9 NGC4486 E1 15.6 y[4f] 334 58+3.5 [6k] 09.59 5.812 0.096 0.008 0.02 −0.01 ... −21.47−25.19 −3.5 NGC4486a E2 17.0[3b] n[4f] 110[5c] 0.13+0.08 [6l] 13.20[7a] 9.012 0.102 0.009 0.00 −0.00 ... −18.05−22.15 −0.08 NGC4552 E0 14.9 y[4b] 252 4.7+0.5 [6e] 10.73 6.728 0.177 0.015 0.00 −0.00 ... −20.31−24.16 −0.5 NGC4621 E5 17.8 n[4f] 225 3.9+0.4 [6e] 10.57 6.746 0.143 0.012 0.01 −0.00 ... −20.83−24.52 −0.4 NGC4649 E2 16.4 y[4b] 335 47+10 [6m] 9.81 5.739 0.114 0.010 0.01 −0.01 ... −21.38−25.37 −10 NGC4697 E6 11.4 n[4g] 171 1.8+0.2 [6c] 10.14 6.367 0.131 0.011 0.02 −0.01 ... −20.28−23.96 −0.1 NGC4889 E4 103.2[6h]y[4g] 347[6h]210+160 [6h] 12.53 8.407 0.041 0.004 0.09 −0.04 ... −22.59−26.80 −160 NGC5077 E3 41.2[3a] y[4h] 255 7.4+4.7 [6n] 12.38 8.216 0.210 0.018 0.04 −0.02 ... −20.91−24.94 −3.0 NGC5576 E3 24.8 n[4b] 171 1.6+0.3 [6o] 11.85 7.827 0.136 0.012 0.02 −0.01 ... −20.26−24.19 −0.4 NGC5813 E1 31.3 y[4b] 239 6.8+0.7 [6e] 11.45 7.413 0.246 0.021 0.03 −0.01 ... −21.28−25.12 −0.7 NGC5845 E4 25.2 n[4h] 238 2.6+0.4 [6c] 13.50 9.112 0.230 0.020 0.02 −0.01 ... −18.74−22.95 −1.5 NGC5846 E0 24.2 y[4i] 237 11+1 [6e] 11.05 6.949 0.237 0.020 0.02 −0.01 ... −21.11−25.02 −1 NGC6086 E3 138.0[3a] y[4j] 318[6p]37+18 [6p] 13.79 9.973 0.162 0.014 0.13 −0.05 ... −22.08−25.93 −11 NGC6251 E2 104.6[3a] y? [6q] 311 5.9+2.0 [6q] 13.64[7b]9.026 0.377 0.032 0.10 −0.04 ... −21.84−26.25 −2.0 NGC7052 E4 66.4[3a] y[4k] 277 3.7+2.6 [6r] 13.40[7b]8.574 0.522 0.044 0.06 −0.03 ... −21.24−25.68 −1.5 NGC7768 E2 112.8[6h]y[4l] 257[6h]13+5 [6h] 13.24 9.335 0.167 0.014 0.11 −0.05 ... −22.20−26.11 −4 45Bulges CygnusA Sa? 232.0[3a] y? 270 25+7 [6s] 17.04 10.276 1.644 0.140 0.17 −0.070.13−20.80−25.81 −7 IC2560 SBb 40.7[3a] n? [4m]144[5d]0.044+0.044 [6t] 12.53[7b]8.694 0.410 0.035 0.02 −0.020.20−19.02−22.78 −0.022 NGC224 Sb 0.74 n[4n] 170 1.4+0.9 [6u] 4.36 0.984 0.268 0.023 0.00 −0.000.49−18.67−21.82 −0.3 NGC253 SBc 3.5[3c] n[4o] 109[5e] 0.10+0.10 [6v] 8.04 3.772 0.081 0.007 0.00 −0.000.61−17.33−21.42 −0.05 NGC524 S0 23.3 y[4e] 253 8.3+2.7 [6w] 11.30 7.163 0.356 0.030 0.03 −0.020.01−20.15−23.61 −1.3 NGC1023 SB0 11.1 n[4g] 204 0.42+0.04 [6x] 10.35 6.238 0.262 0.022 0.01 −0.000.47−19.82−23.01 −0.04 NGC1068 SBb 15.2[3a] n[4p] 165[5f] 0.084+0.003 [6y] 9.61 5.788 0.145 0.012 0.01 −0.010.07−19.45−23.47 −0.003 NGC1194 S0 53.9[3a] n? 148[5g] 0.66+0.03 [6z] 13.83 9.758 0.330 0.028 0.05 −0.030.25−19.58−22.91 −0.03 NGC1300 SBbc 20.7[3a] n[4q] 229 0.73+0.69 [6aa] 11.11 7.564 0.130 0.011 0.01 −0.010.18−18.05−21.91 −0.35 NGC1316 SB0 18.6[3d] ? 226 1.5+0.75 [6ab] 9.42 5.587 0.090 0.008 0.02 −0.020.15−21.33−24.68 −0.8 NGC1332 S0 22.3 y? 320 14.5+2 [6ac] 11.25 7.052 0.141 0.012 0.02 −0.010.51−20.37−23.74 −2 NGC2273 SBa 28.5[3a] n[4r] 145[5g] 0.083+0.004 [6z] 12.55 8.480 0.305 0.026 0.02 −0.010.12−19.33−22.66 −0.004 NGC2549 SB0[2a] 12.3 n[4q] 144 0.14+0.02 [6w] 12.19 8.046 0.282 0.024 0.01 −0.010.48−18.24−21.44 −0.13 NGC2778 SB0[2b]22.3 n[4d] 162 0.15+0.09 [6c] 13.35 9.514 0.090 0.008 0.02 −0.020.14−17.79−21.15 −0.1 NGC2787 SB0 7.3 n[4s] 210 0.40+0.04 [6ad] 11.82 7.263 0.565 0.048 0.01 −0.000.19−17.41−20.98 −0.05 NGC2960 Sa? 81.0[3e] n? 166[5g] 0.117+0.005 [6z] 13.29[7b]9.783 0.193 0.016 0.05 −0.030.16−20.79−23.69 −0.005 NGC3031 Sab 3.8 n[4t] 162 0.74+0.21 [6ae] 7.89 3.831 0.346 0.029 0.00 −0.000.28−19.59−22.56 −0.11 NGC3115 S0 9.4 n[4a] 252 8.8+10.0 [6af] 9.87 5.883 0.205 0.017 0.01 −0.010.47−19.88−23.00 −2.7 NGC3227 SBa 20.3[3a] n[4e] 133 0.14+0.10 [6ag] 11.10 7.639 0.098 0.008 0.01 −0.010.17−19.87−22.75 −0.06 NGC3245 S0 20.3 n[4e] 210 2.0+0.5 [6ah] 11.70 7.862 0.108 0.009 0.02 −0.010.26−19.37−22.61 −0.5 NGC3368 SBab 10.1 n[4u] 128 0.073+0.015 [6ai]10.11 6.320 0.109 0.009 0.01 −0.010.16−19.14−22.17 −0.015 NGC3384 SB0 11.3 n[4a] 148 0.17+0.01 [6c] 10.85 6.750 0.115 0.010 0.01 −0.010.34−19.05−22.47 −0.02 NGC3393 SBa 55.2[3a] n[4m] 197 0.34+0.02 [6aj] 13.09[7b]9.059 0.325 0.028 0.04 −0.020.04−20.21−23.56 −0.02 NGC3414 S0 24.5 n[4e] 237 2.4+0.3 [6e] 11.96 7.981 0.106 0.009 0.02 −0.010.14−19.40−22.87 −0.3 6 Graham & Scott TABLE 1 cont. Galaxy Type [MDipsct] core kmσs−1 [10M8Mbh⊙] [mBaTg] [mKasg] [mAaBg][mAaKg][mKaBg] [KmKags] R25 [mMaBg] [MmKags] (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) NGC3489 SB0 11.7 n[4q] 105 0.058+0.008 [6ai] 11.12 7.370 0.072 0.006 0.01 −0.010.24−18.69−21.88 −0.008 NGC3585 S0 19.5 n[4q] 206 3.1+1.4 [6o] 10.88 6.703 0.276 0.023 0.02 −0.010.26−20.27−23.69 −0.6 NGC3607 S0 22.2 n[4e] 224 1.3+0.5 [6o] 10.82 6.994 0.090 0.008 0.01 −0.010.30−20.47−23.68 −0.5 NGC3998 S0 13.7 y? [4v] 305 8.1+2.0 [6ak] 11.61 7.365 0.069 0.006 0.01 −0.010.08−18.41−22.21 −1.9 NGC4026 S0 13.2 n[4q] 178 1.8+0.6 [6o] 11.67 7.584 0.095 0.008 0.01 −0.010.61−18.88−22.11 −0.3 NGC4151 SBab 20.0[3a] n[4e] 156 0.65+0.07 [6al] 11.50 7.381 0.119 0.010 0.01 −0.010.15−19.24−22.60 −0.07 NGC4258 SBbc 7.2[3f] n[4w] 134 0.39+0.01 [6am] 9.10 5.464 0.069 0.006 0.00 −0.000.41−17.95−21.76 −0.01 NGC4342 S0 23.0[3g] n[4x] 253 4.5+2.3 [6an] 13.41 9.023 0.088 0.008 0.01 −0.010.33−17.99−21.73 −1.5 NGC4388 Sb 17.0[3b] n? [4y] 107[5g] 0.075+0.002 [6z] 11.76 8.004 0.143 0.012 0.02 −0.020.64−20.07−23.65 −0.002 NGC4459 S0 15.7 n[4f] 178 0.68+0.13 [6ad] 11.32 7.152 0.199 0.017 0.01 −0.010.12−19.15−22.73 −0.13 NGC4564 S0[2c] 14.6 n[4f] 157 0.60+0.03 [6c] 12.05 7.937 0.151 0.013 0.01 −0.010.38−18.49−21.87 −0.09 NGC4594 Sa 9.5 y[6ao] 297[6ao] 6.4+0.4 [6ao] 8.98 4.962 0.221 0.019 0.01 −0.010.39−20.71−23.86 −0.4 NGC4596 SB0 17.0[3b] n[4z] 149 0.79+0.38 [6ad] 11.35 7.463 0.096 0.008 0.02 −0.010.13−19.20−22.60 −0.33 NGC4736 Sab 4.4[3i] n? 104 0.060+0.014 [6ap]8.99 5.106 0.076 0.007 0.00 −0.000.09−18.37−21.55 −0.014 NGC4826 Sab 7.3 n? 91 0.016+0.004 [6ap]9.36 5.330 0.178 0.015 0.00 −0.000.27−19.36−22.47 −0.004 NGC4945 SBcd 3.8[3i] n? [4aa] 100 0.014+0.014 [6aq] 9.30 4.483 0.762 0.065 0.00 −0.000.72−16.39−20.60 −0.007 NGC5128 S0 3.8[3i] n? [4ab]120 0.45+0.17 [6ar] 7.84 3.942 0.496 0.042 0.01 −0.000.11−19.84−22.87 −0.10 NGC6264 Sa? 146.3[3a] n? 159[5g] 0.305+0.004 [6z] 15.42[7b]11.407 0.280 0.024 0.10 −0.070.15−20.04−23.47 −0.004 NGC6323 SBab[2d]112.4[3a] n? 159[5g] 0.10+0.001 [6z] 14.85[7b]10.530 0.074 0.006 0.06 −0.050.48−20.01−23.44 −0.001 NGC7582 SBab 22.0[3a] n[4ac] 156 0.55+0.26 [6as] 11.37 7.316 0.061 0.005 0.01 −0.010.38−19.77−22.94 −0.19 UGC3789 SBab 48.4[3a] n? 107[5g] 0.108+0.005 [6z] 13.30[7b]9.510 0.280 0.024 0.03 −0.040.06−19.48−22.46 −0.005 3extra NGC3079 SBc 20.7[3a] n? [4ad]60-150[5h]0.024+0.024 [6at] 11.54 7.262 0.049 0.004 0.01 −0.000.74−17.80−21.86 −0.012 MilkyWaySBbc 0.008[6au]n[4ae] 100[5i] 0.043+0.004 [6au]... ... ... ... ... ... ... ... ... −0.004 M32 E?[2e] 0.79 n[4ae] 55[5j] 0.024+0.005 [6av] 9.03 5.095 0.268 0.023 0.00 −0.000.13−15.73−19.42 −0.005 Note. — Column1: Galaxyname. Column2: Basicmorphologicaltype,primarilyfromNEDa.Column3: Distance,primarilyfrom Tonryetal.(2001)andcorrectedaccordingtoBlakesleeetal.(2002). Column4: Presenceofapartiallydepletedcore. Theadditionofa questionmarkisusedtoindicatethatthisclassificationhascomefromthevelocitydispersioncriteriamentionedinthetext. Column5: VelocitydispersionprimarilyfromHyperLedab (Patureletal.2003). Column6: Blackholemass,adjustedtothedistancesincolumn3. Column 7: BT is the total (observed) magnitude in the B system from the RC3, unless otherwise noted. Column 8: Ks is the total 2MASSKs-band magnitude. Columns 9& 10: TheB and K-bandGalactic extinction fromSchlegel et al. (1998). Columns 11 & 12: TheBandK-bandK-correction. Column13: R25,takenfromtheRC3,isthe(base10)logarithmofthemajor-to-minor(a/b)isophotal axis ratio at µB=25 mag arcsec−2. Columns 14 & 15: Corrected, absolute, B- and K-band spheroid magnitude. References: 2a = Krajnovi´c et al. (2009); 2b = Rix et al. (1999); 2c = Trujillo et al. (2004); 2d = Jarrett et al. (2000) 2MASS image; 2e = Graham (2002); 3a = NED (Virgo + GA + Shapley)-corrected Hubble flow distance; 3b = Jerjen et al. (2004); 3c = Rekola et al. (2005); 3d = Madore et al. (1999); 3e = Violette Impellizzeri et al. (2012); 3f = Herrnstein et al. (1999); 3g = Mei et al. (2007), Blakeslee et al. (2009),Blometal.(2012), Bogd´anetal. (2012b); 3h=Herrmannetal.(2008);3i=Karachentsevetal.(2007); 4a=Ravindranathet al.(2001); 4b=Dullo&Graham(2012); 4c=Lauer etal.(2005); 4d=Restetal.(2001); 4e=Richingsetal.(2011); 4f=Ferrarese etal.(2006);4g=Faberetal.(1997); 4h=Trujilloetal.(2004);4i=Forbes,Brodie,&Huchra(1997);4j=Laineetal.(2003); 4k= Quillenetal.(2000); 4l=Grillmairetal.(1994); 4m=Mun˜ozMar´ınetal.(2007); 4n=Corbin,O’Neil,&Rieke(2001); 4o=Kornei &McCrady(2009);4p=Macchettoetal.(1994);4q=Graham(2012b);4r=Malkan,Gorjian&Tam(1998);4s=Erwinetal.(2003); 4t=Fisher&Drory(2008);4u=Nowaketal.(2010);4v=Gonz´alezDelgadoetal.(2008);4w=Pastorinietal.(2007);4x=vanden Bosch, Jaffe, &vander Marel(1998); 4y=Pogge&Martini(2002); 4z=Gerssen, Kuijken,&Merrifield(2002); 4aa=Marconietal. (2000); 4ab=Radomskietal.(2008); 4ac=Wold&Galliano(2006); 4ad=Ceciletal.(2001); 4ae=Graham&Spitler(2009); 5a= DallaBonta` et al. (2009); 5b = Smith et al. (2000); 5c = DeFrancesco et al. (2006); 5d = CidFernandes et al. (2004); 5e = Olivaet al.(1995); 5f=Nelson&Whittle(1995); 5g=Greeneetal.(2010); 5h=Shaw,Wilkinson,&Carter(1993); 5i=Merritt&Ferrarese (2001a); 5j = Lucey et al. (1997), Chilingarian (2012, in prep.); 6a = Dalla Bonta` et al. (2009); 6b = Cappellari et al. (2002), stellar dynamicalmeasurement; 6c=Gebhardtetal.(2003), Gu¨ltekinetal.(2009b); 6d=Houghton etal.(2006), Gebhardt etal.(2007); 6e =Preliminaryvalues determinedbyHu(2008) fromConf.Proc.figures ofCappellarietal.(2008); 6f= Copinetal.(2004); 6g=van denBosch&deZeeuw(2010);6h=McConnelletal.(2012);6i=Ferrareseetal.(1996);6j=Walshetal.(2010);6k=Gebhardtetal. (2011); 6l =Nowaketal.(2007); 6m= Shen&Gebhardt (2009); 6n=DeFrancescoetal.(2008); 6o= Gu¨ltekinetal.(2009a); 6p= McConnelletal.(2011b); 6q=Ferrarese&Ford(1999); 6r=vanderMarel&vandenBosch(1998); 6s=Tadhunter etal.(2003); 6t =Ishiharaetal.(2001),Nakaietal.(1998);6u=Baconetal.(2001), Benderetal.(2005); 6v=Rodr´ıguez-Ricoetal.(2006), afactor of 2 uncertainty has been assigned here; 6w = Krajnovi´c et al. (2009); 6x = Bower et al. (2001); 6y = Lodato & Bertin (2003); 6z = Kuoetal.(2011); 6aa=Atkinsonetal.(2005); 6ab=Nowaketal.(2008); 6ac=Ruslietal.(2011); 6ad=Sarzietal.(2001); 6ae= Devereuxetal.(2003);6af=Emsellemetal.(1999); 6ag=Daviesetal.(2006), Hicks&Malkan(2008); 6ah=Barthetal.(2001); 6ai = Nowak et al. (2010); 6aj = Kondratko et al. (2008); 6ak = Walsh et al. (2012); 6al = Onken et al. (2007), Hicks & Malkan (2008); 6am =Herrnsteinetal.(1999); 6an= Cretton &vanden Bosch(1999), Vallurietal.(2004); 6ao= Jardelet al.(2011), NGC 4594 is a core-S´ersic galaxy with an AGN; 6ap = Kormendy et al. (2011), priv. value from K.Gebhardt; 6aq = Greenhill et al. (1997); 6ar = Neumayer(2010);6as=Woldetal.(2006);6at=Trotteretal.(1998),Yamauchietal.(2004),Kondratkoetal.(2005);6au=Gillessen et al. (2009); 6av = Verolmeet al.(2002); 7a = BT (Johnson), Gavazzi et al. (2005); 7b= The RC3’s mB value (which they reduced totheBT system);8a=Cappellarietal.(2006). ahttp://nedwww.ipac.caltech.edu bhttp://leda.univ-lyon1.fr The M –L relation 7 bh spheroid lation. Toavoidissuesofinconsistentsamples,thesetwo TABLE 2 galaxies are also excluded from the ensuing M –L dia- Averagedust-corrected (intrinsic) bulge-to-disk flux bh ratios gram, although doing so has no significant effect on our M –L relation. Galaxy<log(B/D)> <log(B/D)> bh Although NGC 1316 is not an outlier fromthe M –σ Type B-band K-band bh diagram (Figure 1), we do additionally exclude it from S0/S0a -0.29 -0.31 whatfollowsduetothepreviouslymentioneduncertainty Sa -0.29 -0.34 Sab -0.39 -0.54 associated with its core type. If NGC 1316 is confirmed Sb -0.87 -0.60 topossessapartially-depletedcore,somethingassociated Sbc -1.13 -0.82 with dry mergerevents, then it will be the only suchex- Sc -1.28 -1.06 ample in a barredgalaxy(with bars ofcourseassociated Scd -1.55 -1.23 with secular evolutionrather than dry mergers). Until a AdaptedfromGraham&Worley(2008). three-component S´ersic-bulge plus exponential-disk plus bar model has been fit to this galaxy, it is premature to assign the core type. This meant that for seven galax- claim from a fitted single-component, core-S´ersic model ies with σ > 270 km s−1, all but one of which actu- that this galaxy has a depleted core. ally have σ > 300 km s−1, we classified them as core- Our cautious exclusion of these three galaxies S´ersic galaxies. For 12 galaxies with σ 166 km s−1 we (NGC 1316, NGC 3842 and NGC 4889), leaves us with ≤ have classified them as S´ersic galaxies. This approach our final sample of (75-3=) 72 galaxies, comprised of 24 relates to the trend in which low-luminosity spheroids, core-S´ersicgalaxies and 48 S´ersic galaxies. often found in disk galaxies, do not possess partially de- pleted cores while luminous spheroids do (e.g. Nieto et 3.1. The Mbh–σ diagram al. 1991; Ferrarese et al. 1994; Faber et al. 1997). For In Figure 2a we have performed a symmetrical linear the remaining galaxies, their core type was determined regression for the 24 core-S´ersic galaxies in the M –σ bh from high-resolution images (see column 4 of Table 1). diagram. Thiswasachievedusingthebisectorregression While Faber et al. (1997) reported that the peculiar analysis in the BCES routine from Akritas & Bershady galaxy NGC 1316 (Fornax A) has a partially-depleted (1996). The results are provided in Table 3. Of note core, we feel that a proper bulge/disk/bar decomposi- is that the symmetrical M –σ relation has a slope con- bh tion—whichis beyondthe scopeofthis paper—might sistent with a value of 5 (Ferrarese & Merritt 2000; Hu be required for this barred S0 galaxy. This may reveal 2008;Graham et al. 2011). a bulge with a small S´ersic index and a shallow inner Wehaveadditionallyperformedthesamesymmetrical profile slope, rather than an actual depleted core. Al- regression for the S´ersic sample (see Table 3). However, thoughNGC1316isamergerremnant(Deshmukhetal. due to each supermassive black hole’s limited sphere-of- 2012, and references therein) — which may support the influence, r GM /σ2 (Merritt & Ferrarese 2001b), infl bh presence of a depleted core if it had been a dry merger there is an asso∼ciated galaxy distance limit to which we event—the presenceofmuchdust andgas,plus the ex- canspatiallyresolvetheblackhole’sdynamicalinfluence istenceofabar,isindicativeofaminor,wetmerger. We on its surrounding gas and stars. Shown in Figure 2a is notethatnootherbarredgalaxyinoursamplehasacore the limit to which one can detect black holes at a dis- whichispartiallydepletedofstars,andtobesafewefelt tance of 1.3 Mpc when the spatial resolutionis 0′′.1 (i.e. itbesttoexcludethisgalaxyfromourfinalanalysisuntil roughlythatachievablewiththeHubbleSpaceTelescope a more detailed investigationof its stellar distribution is andground-basedadaptive-optics-assistedobservations). performed. For galaxies further away, this limit moves vertically in the diagram to higher black hole masses. Attempts to 3. ANALYSISANDRESULTS occupy the lower right of Figure 2a may need to wait Our initial investigation of the M –σ diagram uses for the next generation of telescopes with greater spa- bh all 75 galaxies (including NGC 1316) plus M32 and the tialresolution,and as suchwe currentlyhave a selection Milky Way’s bulge to give a total sample of 77 galaxies. limit, a kind of floor, in this diagram (Batcheldor 2010; It is apparent that there is something unusual with the Schulze & Wisotzki 2011). Galaxies canexist below this twoultramassiveblackholesreportedforNGC3842and floor, but they are at distances such that we can not re- NGC 4889by McConnelletal.(2011a). Figure1reveals solvetheirblackhole’ssphere-of-influence. Toavoidthis thattheymaybeareoutliersbiasingtheM –σ relation sample selection bias on the samples which extend into bh defined by the remaining data. Performing a symmetri- the lower portion of the diagram, we have additionally callinearregressiononthecore-S´ersicgalaxies,including performed an ordinary least squares (OLS) regressionof NGC3842andNGC4889,yieldsaslopeofroughly7.0 1 theabscissa(i.e.,thehorizontalX value)ontheordinate ± (see Table 3). Uncertain as to whether there is an error (i.e., the vertical Y value) for the reasons expounded in in the black hole masses for NGC 3842 and NGC 4889, Lynden-Bell et al. (1988, their Figure 10). or perhaps with their velocity dispersion measurements, Giventhat the 27 non-barredS´ersic galaxiesdefine an or if instead these values are fine and these galaxies are M –σ relation which is consistent with that defined by bh representative(ofapossiblynew class)ofgalaxieswhich the 24 core-S´ersicgalaxies (see Table 3), they have been deviate from the M –σ relation as we know it, in the combinedtoproduceasinglenon-barredM –σrelation. bh bh following section we have elected to repeat the M –σ These 51 galaxies yield a slope of 5.53 0.34, consistent bh ± regression analysis without these two galaxies. If these with the value of 5.32 0.49 reported by Graham et al. ± galaxies are outliers, then this additional approach pro- (2011) using a sample of 44 non-barred galaxies. Barth, vides a more robuststatistical analysisof the M –σ re- Greene,&Ho(2005,theirfigure2)offersfurthersupport bh 8 Graham & Scott Fig. 1.— Black hole mass versus central velocity dispersion. The faint dot-dashed gray line corresponds to a black hole’s sphere-of- influence of 0′′.1 at a distance of 1.3 Mpc. With such a limiting spatial resolution of 0′′.1, black holes residing below this line cannot be reliablydetected. Panel a) Red dots represent the core-S´ersic galaxies, open blue circles represent the S´ersic galaxies, while the open crossesdesignatethosewhicharebarred. All77galaxiesshownherehavebeenincludedintheanalysisofthisFigure. Theuppersolidred linecorrespondstothesymmetricalregressionforthe27core-S´ersicgalaxies,while(duetothesampleselectionlimit)thedottedandsolid blue lines correspond to the ‘ordinary least squares’ OLS(σ|Mbh) regression for the barred and non-barred S´ersic galaxies (see Table 3). Panel b)Reddots represent thenon-barredgalaxies whilethe openbluecrosses designate those whicharebarred. Thesolidredlineisa fittothenon-barredgalaxies,whilethedashedblacklineisafittoallgalaxies. M32,theMilkyWayandFornaxA(NGC1316)havebeen markedwithagreensquare,theyarenotincludedinFigure2forthereasonsmentionedinSection 2. TheS´ersicgalaxywiththehighest blackholemassisNGC3115(seesection2.4). forthislinearrelationafterreducingtheiractivegalactic For those who may not know if their galaxy of in- nuclei (AGN) black hole mass estimates by a factor of terest is barred or not, using the full 72 galaxies and 2 due to a revision in the virial f-factor used to deter- an OLS(M σ), bisector, and OLS(σ M ) regression bh bh ∼ | | mineblackholemassesinAGN(Onkenetal.2004;Gra- to construct the classical (all galaxy type) M –σ rela- bh ham et al. 2011). While Graham et al. (2011) discussed tion gives slopes of 5.21 0.27,5.61 0.27 and 6.08 ± ± ± why a 5% uncertainty on the velocity dispersion may be 0.31, respectively. The associated intercepts are 8.14 ± optimistic, we note that using a 10% uncertainty on σ, 0.04,8.14 0.05and 8.15 0.05. These steeper relations ± ± rather than 5%, results in the same slope to the M –σ are expected giventhe offset nature of the barredgalax- bh relation when using the OLS(σ M ) regression. Cou- ies. bh plingtheknowledgethatL σ2|fortheS´ersicspheroids, with the relation Mbh σ5∝.5, one would expect to find 3.2. The M –L diagram M L2.75 for the S´er∝sic spheroids. bh bh For∝a value of σ =400 km s−1, the non-barredM –σ In Figures 2b and 2c we have performed a symmet- bh relationyields ablack holemass of7.7 109M⊙. This is rical linear regression for the 24 core-S´ersic galaxies in b3ytitmheesegllripeatitcearltghaalnaxtyheMvbahl–uσe orefl2a.t6io×n×1fr0o9mM⊙Gu¨plrteedkiicnteedt ttuhdeeMs absh–luLmdiniaogsritaimes., wEexpfirnedsstihnagttMhebihr ∝sphLeK1r.1so0i±d0m.20agannid- al. (2009b), and better, although not fully, matches the M L1.35±0.30, in reasonable agreement with the re- bh ∝ B expectations from Hlavacek-Larrondo et al. (2012) for lation M L1.0 and with past analyses of predomi- bh black holes in brightest cluster galaxies if they reside on nantlybrigh∝tgalaxies10. We note thatdepending onthe the “fundamental plane of black hole activity” (Merloni progenitor galaxy mass ratios — among the individual et al. 2003; Falcke et al. 2004). dry merger events which built one’s core-S´ersic sample As reported by Graham (2007b, 2008a,b) and Hu — the slope of the M –L relation can be expected to bh (2008),thebarredgalaxiesare,onaverage,offsettolower deviateslightly froma value of1. Although, for galaxies black hole masses or higher velocity dispersions than builtfromasufficientnumberofdrymergers,thisshould the non-barred galaxies, with the latter scenario possi- become a secondorder effect in terms of the overallevo- bly expected from barredgalaxy dynamics (e.g. Gadotti lutionary scenarioin the M –L diagram,for the reason bh & Kauffmann 2009; Graham et al. 2011; DeBuhr, Ma described by Peng (2007) and Jahnke & Maccio (2011). & White 2012). Consistent with Graham et al. (2011), The effective sample selection boundary shownin Fig- we find a mean vertical offset of 0.30 dex between the ure 2a has been mapped into Figures 2b and 2c by con- barred and non-barred galaxies in the Mbh–σ diagram, verting this line’s velocity dispersion into the expected which corresponds to a factor of 2 in black hole mass, when σ =200 km s−1. ∼ 10 The inclusion of NGC 3842 and NGC 4889 does not signifi- cantlychange theseresults. The M –L relation 9 bh spheroid TABLE 3 Blackhole scaling relations #andType Regression α β ∆dex Figure1(includessomequestionabledatapoints) log[Mbh/M⊙]=α+βlog[σ/200kms−1] 27Core-S´ersic Bisector 8.02±0.17 6.95±1.17 0.45 28Non-barredS´ersicBisector 8.21±0.06 4.39±0.53 0.32 23Barred Bisector 7.78±0.10 4.14±0.55 0.34 54Non-barredAll Bisector 8.29±0.05 5.09±0.44 0.39 28Non-barredS´ersicOLS(σ|Mbh) 8.25±0.06 4.82±0.64 0.34 23Barred OLS(σ|Mbh) 7.89±0.16 4.98±1.00 0.37 54Non-barredAll OLS(σ|Mbh) 8.28±0.06 5.57±0.52 0.41 77All OLS(σ|Mbh) 8.20±0.05 6.08±0.41 0.46 Figure2,panela),Mbh–σ log[Mbh/M⊙]=α+βlog[σ/200kms−1] 24Core-S´ersic Bisector 8.20±0.13 5.35±0.92 0.35 27Non-barredS´ersicBisector 8.23±0.06 5.02±0.41 0.31 21BarredS´ersic Bisector 7.75±0.12 4.03±0.69 0.34 51Non-barredAll Bisector 8.23±0.05 5.14±0.31 0.33 28Elliptical Bisector 8.23±0.05 4.86±0.50 0.34 27Non-barredS´ersicOLS(σ|Mbh) 8.27±0.06 5.53±0.51 0.33 21Barred S´ersic OLS(σ|Mbh)7.92±0.23 5.29±1.47 0.40 51Non-barred All OLS(σ|Mbh)8.22±0.05 5.53±0.34 0.34 28Elliptical OLS(σ|Mbh) 8.21±0.10 5.54±0.71 0.37 72All OLS(σ|Mbh) 8.15±0.05 6.08±0.31 0.41 Figure2,panelb),Mbh–LKs,sph log[Mbh/M⊙]=α+β[MKs,sph+25] 24Core-S´ersic Bisector 9.05±0.09−0.44±0.08 0.44 log[Mbh/M⊙]=α+β[MKs,sph+22.5] 48S´ersic Bisector 7.39±0.14−1.09±0.22 0.95 Figure2,panelc),Mbh–LB,sph log[Mbh/M⊙]=α+β[MB,sph+21] 24Core-S´ersic Bisector 9.03±0.09−0.54±0.12 0.44 log[Mbh/M⊙]=α+β[MB,sph+19] 48S´ersic Bisector 7.37±0.15−0.94±0.16 0.93 Mbh =blackholemass,σ =hostgalaxyvelocitydispersion,MKs,sph =dust-corrected,2MASSKs-bandspheroidmagnitude,MB,sph = dust-corrected, RC3B-bandspheroidmagnitude. Asymmetrical“bisector”regressionwasused,inadditiontoanon-symmetrical ‘ordinaryleastsquares’OLS(X|Mbh)regressiontocompensateforthesampleselectionlimit,orfloorinthedata,atthelow-massend (seeFigure2). Thetotal rmsscatter inthelogMbh directionisgivenby∆,androughlyscaleslinearlywiththeslope(withineach panel). Thelineshighlightedinboldshowthepreferredfits,seethetextfordetails,whileTable4providesrevisedMbh–LKs relations accordingtoSchombert&Smith’s(2012) correctionofthe2MASSphotometry. magnitude according to the L–σ relations defined by tometry error in the 2MASS Extended Source Catalog the S´ersic galaxies in these diagrams. The need for (Jarrett et al. 2000), such that the total 2MASS magni- an OLS(LM ) regression on the S´ersic galaxies in the tudes are, on average,0.33 mag too faint in the J-band. bh | M –L diagrams, rather than a symmetrical regression, ThereisasimilaroffsetintheK -banddata(Schombert bh s isnolongerasapparentbecausethe‘floor’tothesample 2012, priv. comm.) such that the V K colors are too s − selection has significantly shifted/rotated. blue by this amount. Therefore, for those using K or It is not clear if the barred S´ersic galaxies are offset K -band data not from the 2MASS catalog for the pre- s from the non-barred S´ersic galaxies in Figures 2b and diction of black hole masses, the normalizing values of 2c and so we have therefore grouped them together in 25 and 22.5 used in the M –L equations shown in bh Ks our analysis. The results of which, given in Table 3, are Table 3 should be increased by 0.33 to 25.33 and 22.83. suchthatM L2.73±0.55 andM L2.35±0.40 forthe Onecanactuallygoalittlefurtherthanthis. Assigninga bh ∝ Ks bh ∝ B S´ersicspheroids11. Wenoteinpassingthatitisexpected 1-sigmauncertaintyof0.33/2=0.165magtothiscorrec- that the color-magnitude relation for S´ersic spheroids tion,thatis,assumingthatthescatterseeninSchombert (e.g., Tremonti et al. 2004; Jim´enez et al. 2011), as op- & Smith’s figure 12 has a 1-sigma value of 0.33/2 mag, posedtothe flatcolor-magnituderelationforcore-S´ersic wecanestimatethe impactofthis correctiononourKs- galaxies (as discussed in Graham 2012c), will result in band Mbh–L relations. Because they were constructed thesetwoexponentsnotbeingequaltoeachother. How- using N = 24 core-S´ersic galaxies and N = 48 S´ersic everthecurrentuncertaintyonthesetwoexponentsdoes galaxies,our‘normalizing’valuesof25and22.5maghave not allow us to detect this difference. an additional uncertainty of 0.165/√24 and 0.165/√48 Finally, Schombert (2011) and Schombert & Smith mag associated with them, which is a small but non- (2012,see their Appendix) have recently detailed a pho- zero0.034and0.024mag, respectively. Giventhe slopes of our two M –L relations, this is equivalent to in- bh Ks 11 TheinclusionofNGC3079does notchangetheseresults. creasing the uncertainty on their intercept from 0.09 to 10 Graham & Scott Precise knowledge of the intrinsic scatter in the above TABLE 4 equations is a difficult task because it requires an accu- Corrected Mbh–LKs scaling relations rate knowledge of the measurement errors, which we do #andType Regression α β ∆dex not claim to have. As such, the scatter in our current log[Mbh/M⊙]=α+β[MKs,sph+25.33] Mbh–L diagram probably cannot be used to help dis- 24Core-S´ersicBisector 9.05±0.12−0.44±0.08 0.44 tinguish between competing formation scenarios, as has log[Mbh/M⊙]=α+β[MKs,sph+22.83] beencleverlyproposed(e.g.Lahavetal.2011;Shankaret 48S´ersic Bisector 7.39±0.16−1.09±0.22 0.95 al.2012). Themeasurementerrorsshouldaddinquadra- Ks-bandMbh–Lrelationsaftercorrectingforthe2MASS turewiththeintrinsicscattertogivethetotalrmsscatter magnitudeerrorsnotedbySchombert&Smith(2012). ∆. We can thus quickly proceed with a rough estimate 0.12 and from 0.14 to 0.16, respectively. The result of of the intrinsic scatter. In terms of the vertical scatter applying these corrections is shown in Table 4). While aboutthe M –σ relation,wehaveseenfromGrahamet bh this is a rather minor adjustment to our equations, it al. (2011, their Table 2) that ǫ 3∆/4. Here we shall remainstrue thatthose using the 2MASScatalogofKs- use a rough value of 0.3 dex, w≈hich is consistent with band magnitudes for individual galaxies may have the the results in Gu¨ltekin et al. (2009b). For the M –L bh true galaxy magnitude wrong by the extent shown by relation,Graham(2007a,his Table 4)reporteda similar Schombert & Smith (2012), which will thus affect their value of around 0.3 dex for his predominantly luminous predicted black hole mass. galaxysample. Obviously studies which have attempted It may be worth providing one additional comment tomeasurethis(seealsoGu¨ltekinetal.2009b)butfailed in regard to photometric errors. If the 2MASS mag- toaccountforthebentnatureoftheM –Lrelationwill bh nitudes are shown to contain a systematic error such beinerroratsomelevel. Weshallhoweverusethisvalue that a greater fraction of galaxy light at large radii is here for the core-S´ersic galaxies. For the fainter S´ersic increasingly missed in the intrinsically brighter galaxies, galaxies, which follow an M –L relation that may be bh i.e. those with extended light profiles, this will not ex- some 2.5 times steeper, we use a value of 0.75 dex. This plain the bend in the Mbh–L relation. Bulges in (often increase to the intrinsic scatter in the vertical direction truncated)exponentialdiskarenotsignificantlyaffected isexpectediftheintrinsicscatterinthehorizontaldirec- bythis potentialproblem. The affectis greateringalax- tion, i.e. for the magnitudes, is equal for both types of ies with higher S´ersic indices, specifically the core-S´ersic galaxy, i.e. core-S´ersic and S´ersic galaxies. elliptical galaxies. Such a correction would therefore act The above equations are used in Section 4.1 where we to slightly reduce the slope of the core-S´ersic Mbh–L re- predictanumberofblackholemasseswhicharelessthan lation,thusincreasingtheapparent‘bend’intheMbh–L one million solar masses. diagrambetweentheS´ersicandthecore-S´ersicspheroids. 3.4. Method of regression 3.3. Propagation of errors Park et al. (2012) explored how the BCES linear re- It is important to appreciate the uncertainties on the gression code from Akritas & Bershady (1996) can pro- slopeandinterceptoftherelationsgiveninTables3and duceabiasedM –σrelationifone’svelocitydispersions bh 4,plustheassociatedintrinsicscatterǫ. Forexample,the havelargemeasurementerrors. Theyrevealedthatthere maximum 1-sigma uncertainty on the predicted value of is not a bias when these errors are less than 15%, the MbhusingtheMbh–LKs relationisacquiredbyassuming uppermostvalueusedintheliterature. Parket∼al.(2012) uncorrelatederrorsonthemagnitudeMKs andtheslope additionally showed that the ‘forward’ and ‘inverse’ lin- andinterceptoftherelation. Gaussianerrorpropagation ear regression from the BCES code yield M –σ rela- bh for the linear equation y = (b δb)(x δx)+(a δa), tions which are consistent with those derived using the ± ± ± gives an error on y equal to ‘forward’and‘inverse’versionsofthemodifiedFITEXY expression from Tremaine et al. (2002). That there is δy= (dy/db)2(δb)2+(dy/da)2(δa)2+(dy/dx)2(δx)2 agreementbetweenthese codes in the M –σ diagramis bh p = x2(δb)2+(δa)2+b2(δx)2. not a new result (e.g. Novak et al. 2006; Graham & Li p 2009;Grahametal.2011),butitmaybeapoorlyappre- In the presence of intrinsic scatter (ǫ) in the y-direction, ciatedpointworthyofsomeexplanationbeforeusingthe the uncertainty on y is modified FITEXY code to check on our BCES-derived δy = x2(δb)2+(δa)2+b2(δx)2+ǫ2. Mbh–L relations. p It is known that a linear regression which minimizes For the S´ersic M –L relation in Table 4, x = bh Ks the offset of data from a fitted line will typically yield [M +22.83], and thus Ks,sph a different result if one minimizes the offset in either (δlogMbh/M⊙)2=[MKs,sph+22.83]2(0.22)2+(0.16)2 the vertical or the horizontal direction (e.g. Feigelson & Babu 1992). It is also known that minimization of the +( 1.09)2[δM ]2+ǫ2, − Ks,sph vertical offsets (the so-called ‘forward’ regression) yields where δM is the uncertainty associated with the a shallower slope than obtained through minimization Ks,sph spheroid’s magnitude. of the horizontal offsets (the ‘inverse’ regression). Ob- For the preferred non-barred M –σ relation in Ta- viously neither of these are symmetrical regressions be- bh ble 3, x = log(σ/200kms−1), so dx/dσ = 1/[ln(10)σ], cause there is a preferred variable, that is, they do not and therefore treat the x and y data equally and therefore they gen- erate different fitted lines. The two lines from each of (δlogMbh/M⊙)2=[log(σ/200kms−1)]2(0.34)2+(0.05)2 these non-symmetrical regressions can however be com- +[5.53/ln(10)]2[δσ/σ]2+(ǫ)2. binedtoproduceasymmetricalregression. Forexample,