THE SUPERMASSIVE BLACK HOLE MASS–SPHEROID STELLAR MASS RELATION FOR SÉRSIC AND CORE-SÉRSIC GALAXIES

Supermassive black hole masses, M_BH, are well known to scale with a number of properties of their host galaxy. This was first reported by Kormendy & Richstone (1995), who found a linear correlation between supermassive black hole mass and host spheroid luminosity. Later studies found log-linear correlations between supermassive black hole mass and: stellar velocity dispersion, σ (Ferrarese & Merritt 2000; Gebhardt et al. 2000), stellar concentration (Graham et al. 2001), and dynamical mass, M_dyn∝σ² R (Magorrian et al. 1998; Marconi & Hunt 2003; Häring & Rix 2004). These initial studies reported strong log-linear correlations.

Recent work using larger galaxy samples, with accurate measurements of their black hole masses and host galaxy properties, has indicated that these simple log-linear scaling relations are not always sufficient descriptions of the observed distribution. In particular, Graham & Driver (2007) showed that the black hole mass–Sérsic index (n) relation was not log-linear, and Graham (2012a) showed that the M_BH–M_{sph, dyn} relation requires two separate log-linear relations: with a slope of ∼2 for Sérsic galaxies (whose bulge surface brightness profiles are well-represented by a single Sérsic 1968, model ³ ) and with a slope ∼1 for core-Sérsic galaxies (whose bulge surface brightness profiles deviate from a single Sérsic function by having a partially depleted core: Graham et al. 2003; Graham & Guzmán 2003; Trujillo et al. 2004; Ferrarese et al. 2006b). In addition Graham & Scott (2013, hereafter GS13) demonstrated that the M_BH–L_sph relation is also better described by two log-linear relations, with K_s-band slopes ∼2.73  ±  0.55 and ∼1.10  ±  0.20 for the Sérsic and core-Sérsic galaxies, respectively. In contrast the M_BH–σ relation is well described by a single log-linear relation with slope ∼5 (Ferrarese & Merritt 2000; Graham et al. 2011; McConnell & Ma 2013; Park et al. 2012, GS13) over this same black hole mass range, once the offset barred and pseudobulge galaxies are properly taken into account (Graham 2008a; Hu 2008; Graham & Li 2009).

These revisions to the supermassive black hole scaling relations are in fact expected, given other observed galaxy scaling relations. As observational samples have explored a broader range in galaxy luminosity, the L–σ relation has been revised from L∝σ⁴ (Faber & Jackson 1976) to exhibit two different slopes at high and low luminosity. The relation for luminous galaxies is given by L∝σ⁵ (Schechter 1980; Liu et al. 2008) but for M_B > −20.5 mag L∝σ² (Davies et al. 1983; Matković & Guzmán 2005). Cappellari et al. (2012) have recently reported a bent M–σ relation, with a break at 5 × 10¹⁰  M_☉. Given this form of the L–σ relation, and the log-linear M_BH–σ relation, the M_BH–L relation cannot be log-linear—it must exhibit the same bend as the L–σ relation. From these correlations, the expected form of the M_BH–L_sph relation is M_BH∝ $L_\mathrm{sph}^{1.0}$ for luminous core-Sérsic galaxies and M_BH∝ $L_\mathrm{sph}^{2.5}$ for the typically less-luminous Sérsic galaxies, consistent with the findings of GS13.

The steep M_BH–L_sph relation for Sérsic galaxies implies that their black hole must grow much more rapidly than their host spheroid. In these intermediate-mass galaxies, the accretion of gas plays a significant role in the growth of the spheroid and in fueling the central supermassive black hole. This is seen at high redshift through the coexistence of active galactic nuclei (AGNs) with rapidly star-forming submillimeter galaxies (e.g., Blain et al. 1999; Page et al. 2001; Alexander et al. 2005; Pope et al. 2008; Page et al. 2012; Simpson et al. 2012) and ultra-luminous far-IR-detected galaxies (e.g., Norman & Scoville 1988; Alonso-Herrero et al. 2006; Daddi et al. 2007; Murphy et al. 2009), and through large spectroscopic surveys of AGN hosts (e.g., Silverman et al. 2009; Chen et al. 2013). At low redshift this is evident from the coincidence of ongoing star formation or young stellar populations and AGN activity (e.g., Kauffmann et al. 2003a; Netzer 2009; Rosario et al. 2013). These observations are all consistent with a model in which there is a strong physical link between star formation and AGN activity (Hopkins et al. 2006). In a large sample of low-redshift AGNs, LaMassa et al. (2013) find that the star formation rate is related to the black hole accretion rate by: $\dot{M} \propto {\rm SFR}^{2.78}$, indicating that gas accretion contributes much more significantly to black hole growth than to star formation.

An accurate determination of the true form of the supermassive black hole scaling relations is critical in a number of areas of extragalactic astrophysics. Supermassive black holes play a critical role in semi-analytic models of galaxy formation, through their ability to regulate star formation via AGN feedback (Silk & Rees 1998; Kauffmann & Haehnelt 2000). This feedback is vital in matching the predicted galaxy/bulge luminosity functions of such models to observations. Modern semi-analytic models use the observed local supermassive black hole scaling relations as a key constraint on the rate of black hole growth (e.g., Springel et al. 2005; Bower et al. 2006; Croton et al. 2006; Di Matteo et al. 2008; Booth & Schaye 2009; Dubois et al. 2012). Using an incorrect form of the local scaling relations can significantly alter the degree of AGN feedback in these simulations, resulting in an inaccurate determination of the efficacy of that feedback, or in incorrect rates of star formation and build-up of stellar mass.

Another important application of the local supermassive black hole scaling relations is to the study of the evolution of the black hole–host spheroid connection with redshift. The M_BH–L_sph and M_BH–M_{sph, *} relations have been determined over a range of redshifts, including at z ≲ 0.5 (Woo et al. 2006; Salviander et al. 2007; Shen et al. 2008; Canalizo et al. 2012; Hiner et al. 2012), z ∼ 1 (Peng et al. 2006; Salviander et al. 2007; Merloni et al. 2010; Bennert et al. 2011; Bluck et al. 2011; Zhang et al. 2012) and z > 2 (Borys et al. 2005; Kuhlbrodt et al. 2005; Peng et al. 2006; Shields et al. 2006). These studies typically search for changes in the high-redshift scaling relations with respect to the local scaling relations in an effort to identify evolution in the relationship between supermassive black holes and their host spheroids. From any apparent evolution, they then attempt to determine whether the onset of spheroid or black hole growth occurred first, and therefore which is the driving mechanism for the local correlations. Correctly determining the local scaling relations is therefore critical in identifying any evolution with redshift—as the local scaling relations are much more accurately known than those at high redshift much of the constraint on evolution comes from the local scaling relations. Using an incorrect local scaling relation can hide (or incorrectly identify) evolution with redshift in the black hole–host spheroid connection.

In this work we extend the investigation of the bent supermassive black hole scaling relations to include the stellar mass of the host spheroid; the M_BH–M_{sph, *} relation. In Section 2 we present our sample of galaxies containing supermassive black holes and describe the derivation of their associated spheroid's stellar luminosity and mass. The luminosities used here differ slightly from those in GS13 due to our use of updated photometry, which we describe below. In Section 3 we use a linear regression to examine the bent nature of the M_BH–M_{sph, *} relation. In Section 4 we discuss the implications of bent supermassive black hole scaling relations on the intrinsic scatter of supermassive black hole scaling relations, the coevolution of supermassive black holes and their host spheroids, and the alleged common origins of nuclear star clusters and supermassive black holes. We present our conclusions in Section 5.

We make use of the sample of 78 supermassive black hole masses and host spheroid magnitudes presented in GS13. Following GS13, we continue to exclude M32 (due to an unknown amount of stellar stripping), the Milky Way (due to its uncertain bulge magnitude due to dust extinction) and NGC 1316 (due to its uncertain core type), giving a final sample of 75 galaxies. All galaxies in the sample have directly measured supermassive black hole masses, with typical uncertainties ∼50% (for detailed references see GS13, their Section 2). GS13 provide apparent B- and K_s -band magnitude data and a prescription to determine absolute spheroid magnitudes. Although we make use of their B-band magnitudes, we use different initial K_s -band apparent total galaxy magnitudes as described below.

GS13 used K_s -band magnitudes from the Two Micron All Sky Survey (2MASS) Extended Source Catalogue (Jarrett et al. 2000); however, they noted that some errors have recently been reported for the 2MASS catalogue photometry (Schombert & Smith 2012). Given these concerns we derive new total galaxy magnitudes from the same 2MASS K_s -band images using the archangel photometry pipeline (Schombert & Smith 2012). The pipeline takes a galaxy's name as input, parsing the name through the NASA Extragalactic Database (NED) to resolve its position on the sky. The pipeline then extracts the four sky strip images surrounding the galaxy's coordinates from the 2MASS Atlas Image Server, stitching the images together to form a single raw image. The 2MASS project provides calibrated, flattened, kernel-smoothed, sky-subtracted images so these steps are not duplicated by the pipeline. An accurate sky determination is then made using user-defined sky boxes clear of obvious stellar or galaxy sources, which are then summed and averaged. The final step is the extraction of isophotal values as a function of radius using an ellipse fitting routine. Elliptical apertures are used to determine curves of growth for determination of photometric values.

Our new K_s magnitudes improve on the 2MASS Extended Source Catalogue values in three ways. First, as described in Schombert & Smith (2012), the sky background is over-subtracted by the 2MASS data reduction pipeline, resulting in an underestimation of the total galaxy magnitude. This over-subtraction truncates the surface brightness profile of luminous elliptical galaxies at large radii, causing the 2MASS pipeline to underestimate the physical size of each object. This results in the total magnitude being measured from an aperture that significantly underestimates the true physical size of an object, thus resulting in a total magnitude that is 10%–40% lower than the total magnitudes derived by archangel. Finally, our archangel derived magnitudes are determined from pipeline fits to the surface brightness profiles, extending out to radii where the uncertainty in the surface brightness of the object exceeds 1 mag arcsec⁻², which is typically further than the four-half-light-radii apertures used for 2MASS total magnitudes. For low Sérsic index profiles there is little difference in the total magnitudes derived from these two apertures; however, as shown in Figure 1, for Sérsic n ≳ 3 the flux missed by the 2MASS aperture can be significant.

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In Figure 2 we show a comparison between the 2MASS catalogue magnitudes and our new archangel magnitudes for 67 galaxies. Eight galaxies of our 75 were too large on the sky to model readily with archangel. For these eight remaining galaxies we derived a correction to their 2MASS magnitudes using the following procedure. We divided the sample of 67 galaxies into three morphological types (ellipticals, lenticulars and spirals) and fit linear relations to the 2MASS versus archangel magnitudes for each subset (indicated by the lines in Figure 2). Based on these relations and the 2MASS catalog magnitude we derived corrected magnitudes for the 2/8 remaining elliptical galaxies and used the 2MASS magnitudes for the 6/8 S0 and Sa disk galaxies. The relation between the 2MASS and archangel K_s -band magnitudes for elliptical galaxies in our sample is:

$$\begin{equation} K_{s,\mathrm{ARCH}} = (1.070 \pm 0.030) K_{s,\mathrm{2MASS}} + (1.527 \pm 0.061). \end{equation} \tag{ 1 }$$

The two galaxies for which this procedure was used are indicated with a † in Table 1, along with the six disk galaxies for which we used 2MASS photometry. As tabulated in GS13, total apparent B-band magnitudes were drawn from the Third Reference Catalogue of Bright Galaxies (de Vaucouleurs et al. 1991).

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Table 1. Properties of Our Sample of 75 Nearby Galaxies Hosting a Supermassive Black Hole

Galaxy	Type	Core	MBH	Ks, sph	B − Ks	Msph, *
			(108  M☉)	(mag)	(mag)	(1010  M☉)
Abel1836	BCG	y?	39$^{+ 4}_{- 5}$	−26.29	4.57	69$^{+59}_{-32}$
Abel3565	BCG	y?	11$^{+ 2}_{- 2}$	−25.84	4.13	37$^{+32}_{-17}$
CenA†	S0	n?	0.45$^{+ 0.17}_{- 0.10}$	−22.87	3.03	1.4$^{+2.0}_{-0.8}$
CygnusA†	S?	y?	25$^{+ 7}_{- 7}$	−25.81	5.01	55$^{+80}_{-33}$
IC1459	E3	y?	24$^{+ 10}_{- 10}$	−25.50	4.13	27$^{+23}_{-12}$
IC2560	SBb	n?	0.044$^{+0.044}_{-0.022}$	−22.97	3.95	2.4$^{+3.5}_{-1.4}$
M31†	Sb	n	1.4$^{+ 0.9}_{- 0.3}$	−21.69	3.02	0.46$^{+0.68}_{-0.28}$
M81†	Sab	n	0.73$^{+?}_{-?}$	−22.56	2.97	1.0$^{+1.5}_{-0.6}$
M84	E1	y	9.0$^{+ 0.9}_{- 0.8}$	−25.25	3.90	19$^{+16}_{-9}$
M87†	E0	y	58$^{+ 3.5}_{- 3.5}$	−25.43	3.96	23$^{+ 19}_{- 10}$
NGC 253†	SBc	n	0.10$^{+ 0.10}_{- 0.05}$	−21.42	4.09	0.61$^{+0.89}_{-0.36}$
NGC 524	S0	y	8.3$^{+ 2.7}_{- 1.3}$	−23.82	3.67	4.6$^{+6.6}_{-2.7}$
NGC 821	E	n	0.39$^{+ 0.26}_{- 0.09}$	−24.60	3.95	11$^{+9}_{-5}$
NGC 1023	SB0	n	0.42$^{+ 0.04}_{- 0.04}$	−23.07	3.25	1.9$^{+2.7}_{-1.1}$
NGC 1068	SBb	n	0.084$^{+0.003}_{-0.003}$	−23.57	4.12	4.5$^{+6.6}_{-2.7}$
NGC 1194	S0	n?	0.66$^{+ 0.03}_{- 0.03}$	−22.80	3.22	1.4$^{+2.1}_{-0.8}$
NGC 1300	SBbc	n	0.73$^{+ 0.69}_{- 0.35}$	−21.73	3.69	0.66$^{+0.97}_{-0.40}$
NGC 1332	S0	y?	15$^{+ 2}_{- 2}$	−23.92	3.55	4.7$^{+6.9}_{-2.8}$
NGC 1399	E	y	4.7$^{+ 0.6}_{- 0.6}$	−25.32	4.37	26$^{+22}_{-12}$
NGC 2273	SBa	n	0.083$^{+0.004}_{-0.004}$	−22.94	3.61	2.0$^{+2.9}_{-1.2}$
NGC 2549	SB0	n	0.14$^{+ 0.02}_{- 0.13}$	−21.42	3.18	0.39$^{+0.57}_{-0.23}$
NGC 2778	SB0	n	0.15$^{+ 0.09}_{- 0.1}$	−21.19	3.40	0.35$^{+0.52}_{-0.21}$
NGC 2787	SB0	n	0.40$^{+ 0.04}_{- 0.05}$	−20.96	3.55	0.30$^{+0.45}_{-0.18}$
NGC 2960	Sa?	n?	0.12$^{+0.005}_{-0.005}$	−23.85	3.06	3.5$^{+5.1}_{-2.1}$
NGC 2974	E	n	1.7$^{+ 0.2}_{- 0.2}$	−24.03	4.06	6.7$^{+5.7}_{-3.1}$
NGC 3079	SBc	n	0.024$^{+0.024}_{-0.012}$	−21.84	4.04	0.88$^{+1.28}_{-0.52}$
NGC 3115	S0	n	8.8$^{+ 10.0}_{- 2.7}$	−23.09	3.21	1.9$^{+2.7}_{-1.1}$
NGC 3227	SBa	n	0.14$^{+ 0.10}_{- 0.06}$	−22.60	2.73	0.93$^{+1.37}_{-0.56}$
NGC 3245	S0	n	2.0$^{+ 0.5}_{- 0.5}$	−22.63	3.26	1.24$^{+1.8}_{-0.7}$
NGC 3368	SBab	n	0.073$^{+0.015}_{-0.015}$	−22.29	3.15	0.86$^{+1.26}_{-0.51}$
NGC 3377	E5	n	0.77$^{+ 0.04}_{- 0.06}$	−22.87	3.78	2.0$^{+1.7}_{-0.9}$
NGC 3379	E1	y	4.0$^{+ 1.0}_{- 1.0}$	−23.87	3.94	5.4$^{+4.7}_{-2.5}$
NGC 3384	SB0	n	0.17$^{+ 0.01}_{- 0.02}$	−22.48	3.43	1.2$^{+1.7}_{-0.7}$
NGC 3393	SBa	n	0.34$^{+ 0.02}_{- 0.02}$	−23.89	3.68	4.9$^{+7.1}_{-2.9}$
NGC 3414	S0	n	2.4$^{+ 0.3}_{- 0.3}$	−22.98	3.58	2.0$^{+2.9}_{-1.2}$
NGC 3489	SB0	n	0.058$^{+0.008}_{-0.008}$	−21.95	3.26	0.66$^{+0.97}_{-0.40}$
NGC 3585	S0	n	3.1$^{+ 1.4}_{- 0.6}$	−23.94	3.67	5.1$^{+7.4}_{-3.0}$
NGC 3607	S0	n	1.3$^{+ 0.5}_{- 0.5}$	−23.53	3.06	2.6$^{+3.8}_{-1.5}$
NGC 3608	E2	y	2.0$^{+ 1.1}_{- 0.6}$	−23.56	3.43	3.2$^{+2.7}_{-1.5}$
NGC 3842	E	y	97$^{+ 30}_{- 26}$	−26.75	4.47	100$^{+86}_{-46}$
NGC 3998	S0	y?	8.1$^{+ 2.0}_{- 1.9}$	−22.37	3.96	1.4$^{+2.1}_{-0.9}$
NGC 4026	S0	n	1.8$^{+ 0.6}_{- 0.3}$	−22.22	3.34	0.88$^{+1.30}_{-0.53}$
NGC 4151	SBab	n	0.65$^{+ 0.07}_{- 0.07}$	−22.60	3.36	1.3$^{+1.9}_{-0.8}$
NGC 4258	SBbc	n	0.39$^{+ 0.01}_{- 0.01}$	−21.58	3.63	0.56$^{+0.82}_{-0.34}$
NGC 4261	E2	y	5.0$^{+ 1.0}_{- 1.0}$	−25.46	4.35	29$^{+25}_{-13}$
NGC 4291	E2	y	3.3$^{+ 0.9}_{- 2.5}$	−23.89	4.13	6.1$^{+5.2}_{-2.8}$
NGC 4342	S0	n	4.5$^{+ 2.3}_{- 1.5}$	−21.70	3.71	0.65$^{+0.96}_{-0.39}$
NGC 4388	Sb	n?	0.075$^{+0.002}_{-0.002}$	−23.57	3.50	3.3$^{+4.9}_{-2.0}$
NGC 4459	S0	n	0.68$^{+ 0.13}_{- 0.13}$	−22.90	3.75	2.0$^{+3.0}_{-1.2}$
NGC 4473	E5	n	1.2$^{+ 0.4}_{- 0.9}$	−24.02	4.13	6.9$^{+5.9}_{-3.2}$
NGC 4486a	E2	n	0.13$^{+ 0.08}_{- 0.08}$	−22.24	4.19	1.4$^{+1.2}_{-0.6}$
NGC 4552	E	y	4.7$^{+ 0.5}_{- 0.5}$	−24.25	3.94	7.7$^{+6.6}_{-3.6}$
NGC 4564	S0	n	0.59$^{+ 0.03}_{- 0.09}$	−22.10	3.61	0.90$^{+1.3}_{-0.5}$
NGC 4594	Sa	y	6.4$^{+ 0.4}_{- 0.4}$	−23.91	3.20	3.9$^{+5.7}_{-2.3}$
NGC 4596	SB0	n	0.79$^{+ 0.38}_{- 0.33}$	−22.84	3.64	1.8$^{+2.7}_{-1.1}$
NGC 4621	E	n	3.9$^{+ 0.4}_{- 0.4}$	−24.49	3.66	8.4$^{+7.2}_{-3.9}$
NGC 4649	E1	y	47$^{+ 10}_{- 10}$	−25.50	4.12	27$^{+23}_{-12}$
NGC 4697	E4	n	1.8$^{+ 0.2}_{- 0.1}$	−24.06	3.78	6.0$^{+5.2}_{-2.8}$
NGC 4736	Sab	n?	0.060$^{+0.014}_{-0.014}$	−21.54	3.17	0.43$^{+0.64}_{-0.26}$
NGC 4826	Sab	n?	0.016$^{+0.004}_{-0.004}$	−22.47	3.11	1.0$^{+1.5}_{-0.6}$
NGC 4889	cD	y	210$^{+ 160}_{- 160}$	−27.00	4.41	122$^{+105}_{-57}$
NGC 4945†	SBcd	n?	0.014$^{+0.014}_{-0.007}$	−20.60	4.21	0.30$^{+0.45}_{-0.18}$
NGC 5077	E3	y	7.4$^{+ 4.7}_{- 3.0}$	−25.40	4.49	29$^{+25}_{-13}$
NGC 5576	E3	n	1.6$^{+ 0.3}_{- 0.4}$	−24.50	4.24	11$^{+10}_{-5}$
NGC 5813	E	y	6.8$^{+ 0.7}_{- 0.7}$	−25.25	3.97	20$^{+17}_{-9}$
NGC 5845	E3	n	2.6$^{+ 0.4}_{- 1.5}$	−22.99	4.25	2.8$^{+2.4}_{-1.3}$
NGC 5846	E	y	11$^{+ 1}_{- 1}$	−25.32	4.21	24$^{+20}_{-11}$
NGC 6086	E	y	37$^{+ 18}_{- 11}$	−26.50	4.42	78$^{+67}_{-36}$
NGC 6251	E2	y?	5.9$^{+ 2.0}_{- 2.0}$	−26.57	4.73	96$^{+83}_{-44}$
NGC 6264	S?	n?	0.31$^{+0.004}_{-0.004}$	−23.61	3.57	3.6$^{+5.2}_{-2.1}$
NGC 6323	Sab	n?	0.10$^{+0.001}_{-0.001}$	−23.37	3.36	2.6$^{+3.8}_{-1.5}$
NGC 7052	E	y	3.7$^{+ 2.6}_{- 1.5}$	−25.97	4.73	55$^{+48}_{-26}$
NGC 7582	SBab	n	0.55$^{+ 0.26}_{- 0.19}$	−22.83	3.06	1.4$^{+2.0}_{-0.8}$
NGC 7768†	E	y	13$^{+ 5}_{- 4}$	−26.41	4.21	64$^{+55}_{-30}$
UGC3789	SBab	n?	0.11$^{+0.005}_{-0.005}$	−22.66	3.18	1.2$^{+1.8}_{-0.7}$

Note. † Galaxies for which we did not obtain new archangel photometry. Column (1): Galaxy identifier. Column (2): Morphological type. Column (3): Core type. y indicates the galaxy contains a core, n indicates the galaxy does not have a depleted core. ? indicates that the classification is based on the velocity dispersion. Column (4): Supermassive black hole mass. References are provided in GS13. Column (5): Inclination and dust corrected K_s absolute spheroid magnitude. For elliptical galaxies the typical uncertainty on K_{s, sph} is 0.25 mag. For disk galaxies this increases to 0.75 mag, due to the additional dust and bulge-to-total corrections. Column (6): (B − K_s ) spheroid color. Column (7): Spheroid stellar mass. For elliptical galaxies the typical uncertainty on M_{sph, *} is 0.2 dex, for disk galaxies this increases to 0.36 dex.

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Following GS13, apparent magnitudes were converted to absolute magnitudes using distance moduli primarily from the surface brightness fluctuation based measurements of Tonry et al. (2001), after applying the 0.06 mag correction of Blakeslee et al. (2002, see GS13 for a full list of references for the distance determinations). All magnitudes were corrected for Galactic extinction following Schlegel et al. (1998), cosmological redshift dimming, and K-corrections.

In addition to the standard corrections mentioned above, two further "corrections" were applied to the absolute magnitude of disk galaxies to derive spheroid magnitudes. Given the large sample size, individual spheroid fractions were not derived for each object, but instead a mean statistical correction was applied based on each object's morphological type and disk inclination. The relationship between the applied correction (for both dust and bulge fraction) is based on the galaxy's morphological type and inclination and is given by Equation (5) in GS13. The dust correction follows the method of Driver et al. (2008) and depends on the galaxy inclination and passband. The correction for the bulge-to-disk flux ratio was derived from the observed bulge-to-disk flux ratios presented in Graham & Worley (2008), as adapted slightly by GS13. The bulge-to-disk correction depends on morphological type and passband, and is given in Table 2 of GS13 for the B- and K_s -bands.

While the above prescription results in significant uncertainties for the spheroid magnitudes of individual bulges, the ensemble average correction is considerably more accurate, scaling with $\sqrt{N}$. Such a statistical correction is only now viable given the sufficiently large sample of supermassive black hole masses in disk galaxies that are available in the literature. Our updated inclination and dust corrected K_s -band spheroid magnitudes for the full sample are given in Table 1, the B-band values are given in Table 2 of GS13.

We use the absolute galaxy magnitudes of the elliptical galaxies and the inclination and dust corrected bulge magnitudes of the disk galaxies to derive stellar masses for all spheroids in our final sample of 75 galaxies. Using the optical–NIR (B − K_s ) color of the spheroids, we derive stellar mass-to-light ratios (M/L) using the relations presented in Bell & de Jong (2001). For the K_s -band stellar mass-to-light ratio, $M/L_{K_s}$ and the (B − K_s ) color, the relation is:

$$\begin{equation} \log {M/L}_{K_s} = -0.9586 + 0.2119 (B-K_s). \end{equation} \tag{ 2 }$$

We derive stellar mass-to-light ratios in the K_s -band as this ratio shows the smallest sensitivity to color in this band. For the range of B − K_s colors found in our sample, $M/L_{K_s}$ varies by a factor of two, compared to a factor of seven for the B-band mass-to-light ratio. K_s -band magnitudes also suffer the least from dust extinction, though as noted by Bell & de Jong (2001) the conversion to stellar mass based on an optical–NIR color is not significantly affected by dust. The final stellar masses for all 75 spheroids in our sample are given in Table 1.

Last, we note that for all 75 galaxies, GS13 identified them as either Sérsic or core-Sérsic galaxies. For the majority of galaxies this classification was based upon examination of their surface brightness profiles taken from Hubble Space Telescope (HST) imaging. For 19 galaxies without HST imaging GS13 assigned a core type based on the galaxy's velocity dispersion (see GS13 for further details, including a list of those objects with velocity dispersion based core type assignments). The most massive galaxies are typically core-Sérsic galaxies and the least massive galaxies are exclusively Sérsic galaxies; however, there is a significant region of overlap, with spheroids in the 10¹⁰–10¹¹  M_☉ region showing both profile types. For all of these galaxies in the overlap region the classification was based on their observed light profile.

2.1. Sources of Uncertainty on M_BH and M_{sph, *}

In Figure 3 we show the spheroid stellar mass plotted against the supermassive black hole mass for all galaxies in Table 1. We separate galaxies into Sérsic (filled blue symbols) and core-Sérsic (open red symbols). We fit separate linear regressions to the Sérsic and core-Sérsic galaxy subsamples, using the bces bisector regression of Akritas & Bershady (1996). This technique takes into account the measurement uncertainties in both black hole mass and stellar spheroid mass and accounts for (though does not determine) the intrinsic scatter. For the core-Sérsic galaxies the best-fitting symmetrical regression is

$$\begin{eqnarray} \log \frac{{M}_{\rm BH}}{{M}_\odot } &=& (0.97 \pm 0.14) \log \left(\frac{{M}_{\rm sph,*}}{3.0\times 10^{11}\, {M}_\odot }\right) \nonumber \\ && + (9.27 \pm 0.09), \end{eqnarray} \tag{ 3 }$$

and for Sérsic galaxies the best-fitting symmetrical regression is

$$\begin{eqnarray} \log \frac{{M}_{\rm BH}}{{M}_\odot } &=& (2.22 \pm 0.58) \log \left(\frac{{M}_{\rm sph,*}}{3.0\times 10^{10}\, {M}_\odot }\right) \nonumber \\ && + (7.89 \pm 0.18), \end{eqnarray} \tag{ 4 }$$

with rms residuals of 0.47 and 0.90 dex respectively in the log M_BH direction. These linear relations are shown in Figure 3 as the solid red and blue lines for the core-Sérsic and Sérsic galaxies, respectively. For comparison, the linear regression to the combined sample is shown as the black dashed line, which has a slope of 1.50  ±  0.12 (c.f. Laor 2001) and an rms residual of 0.67 dex. The best-fitting regressions for the two different types of galaxy have significantly different slopes that are not consistent with each other given the confidence intervals on the slopes. Sérsic galaxies follow an approximately quadratic relation, whereas core-Sérsic galaxies follow an approximately linear relation. This is in agreement with the analysis and conclusions of Graham (2012a) who studied the M_BH–M_{sph, dyn} relation.

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The bend or break in the M_BH–M_{sph, *} distribution occurs where the core-Sérsic and Sérsic relations overlap. This is at a spheroid stellar mass M_{sph, *} ∼ 3 × 10¹⁰  M_☉, corresponding to a black hole mass M_BH ∼ 2 × 10⁸  M_☉. The significance of this "break mass" will be discussed in Section 4. Here we simply note that very few Sérsic galaxies have M_BH greater than this break mass; equally no core-Sérsic galaxy has a black hole mass below this value.

Park et al. (2012) examined the effect of using different linear regression techniques on the M_BH–σ relation but their results are applicable to supermassive black hole scaling relations in general. They reported that three popular regression techniques, bces (as used in this work), a modified version of fitexy (Press et al. 1992; Tremaine et al. 2002), and a Bayesian technique developed by Kelly (2007), linmix_err, return consistent results. However, if the measurement uncertainties are larger than ∼15% in the ordinate when using the "forward" regression, they find that the bces routine may be biased to higher slopes (as was noted by Tremaine et al. 2002). Because of the significant uncertainties on many of our low-mass spheroid stellar masses (due to our statistical bulge-disk separation), we redetermined our core-Sérsic and Sérsic relations using the modified fitexy and the linmix_err linear regression methods to test the robustness of our result. Following GS13, we determine a symmetrical bisector regression from the linmix_err routine by determining the "forward" and "inverse" regressions, then determining the line that bisects those two regressions. Using the linmix_err method we find bisector slopes for the core-Sérsic and Sérsic samples of 1.10  ±  0.07 and 2.11  ±  0.46, respectively. We adopt a similar approach with fitexy; determining the "forward" and "inverse" regressions, then determining the bisector line. This method yields bisector regressions for the core-Sérsic and Sérsic samples with slopes of 1.08 and 2.48, respectively. With all three symmetric regression methods we find consistent best-fitting relations, and in all cases the slope for the Sérsic galaxies is greater than 2σ steeper than that for core-Sérsic galaxies. We conclude that our principal result—that core-Sérsic and Sérsic galaxies follow different M_BH–M_{sph, *} relations is robust against the choice of linear regression method.

The core-Sérsic/Sérsic classification is similar to the slow rotator/fast rotator (SR/FR) classification of Emsellem et al. (2007), though as discussed in Emsellem et al. (2011) the overlap between the two systems is not perfect. Of our objects, 33/75 are part of the ATLAS^3D survey (Cappellari et al. 2011) and have FR/SR classifications from Emsellem et al. (2011). We also examined the spheroid stellar mass versus supermassive black hole mass relation for these galaxies. We again fit linear regressions to the two samples of 9 SR and 24 FR galaxies. With this smaller sample we do not find significantly different slopes for the FR and SR samples; the slopes for the FR and SR samples are 1.71  ±  0.27 and 1.32  ±  0.44, respectively. While the slope for FRs is somewhat steeper, the difference is not significant given the formal uncertainty on the derived slopes. However, this may be caused by the galaxies with the most massive black holes and the least massive galaxies not having an FR/SR classification and therefore not being included in these regressions. This same sampling effect, where galaxies at the extremes of the supermassive black hole mass scaling relations were not well-sampled, led to a single log-linear relation being sufficient to describe the data in the past. It is only recently, where increased numbers of objects at the extremes of the relations have been added, has the bend in the supermassive black hole mass scaling relations become evident. Alternatively, the core-Sérsic/Sérsic classification may be more closely linked to the mechanism(s) responsible for black hole growth than the FR/SR classification. Indeed, FR lenticular galaxies with depleted cores are known to exist (Dullo & Graham 2013; Krajnović et al. 2013). A larger sample of galaxies with both measured supermassive black hole masses and kinematic classifications would be desirable.

From Equation (4), the expected variation of M_BH/M_{sph, *} with M_{sph, *} is close to linear for the Sérsic galaxies, with the black holes of more massive spheroids representing a larger fraction of their host spheroid's mass. In Figure 4 we show the ratio of supermassive black hole mass to spheroid stellar mass as a function of spheroid stellar mass. In previous studies which found $M_\mathrm{BH} \propto {M}_\mathrm{sph,*}^{\sim 1}$, this ratio was thought to be constant, with the supermassive black hole having a mass ∼0.15%–0.20% of its host spheroid's mass (Merritt & Ferrarese 2001; Marconi & Hunt 2003). Here we find that this remains approximately true for the core-Sérsic galaxies, albeit with M_BH ∼ 0.55% of M_{sph, *} (the relation for core-Sérsic galaxies is consistent with a slope of 1 hence a constant mass fraction). However, for Sérsic galaxies, we find that the average M_BH/M_{sph, *} is offset to a lower mean value of 0.3% for our particular sample's mass range and it also displays a large range, from ∼0.02%–2%.

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4.1. Comparison to Previous Studies

4.2. Scatter about the M_BH –M_{sph, *} Relation

4.3. Comparing Supermassive Black Hole and Nuclear Star Cluster Scaling Relations

Ferrarese et al. (2006a) and Wehner & Harris (2006) have argued that nuclear star clusters and supermassive black holes form a single class of central massive object (CMO) based on their allegedly common mass scaling relations, though recent studies (Balcells et al. 2007; Graham & Spitler 2009; Graham 2012b; Erwin & Gadotti 2012; Leigh et al. 2012; Scott & Graham 2013) have since argued against this scenario. We briefly re-examine the connection between nuclear star cluster and supermassive black hole scaling relations in the light of the bent M_BH–M_{sph, *} relation. In Figure 5 we show M_CMO versus M_{sph, *} for the Sérsic galaxies presented in this study and the nuclear star clusters presented in Scott & Graham (2013). The two lines show the best-fitting linear relations to the two samples. The M_NC–M_{sph, *} line is taken from Scott & Graham (2013) and has a slope of 0.88  ±  0.19. The relation for the nuclear star clusters is 2.3σ shallower than that for the supermassive black holes. This difference is more pronounced than that reported by Scott & Graham (2013), due to our improved bent supermassive black hole scaling relation, strongly suggesting that supermassive black holes and nuclear star clusters do not follow a common scaling relation and therefore do not have a common formation mechanism.

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4.4. The Growth of Supermassive Black Holes and Stellar Spheroids

The results in Section 3 represent a major revision to the accepted picture of the relationship between supermassive black holes and their host galaxies. Our results have significant implications for studies of how supermassive black holes and their hosts co-evolve over cosmic time; the detection of intermediate-mass supermassive black holes; and models of feedback from AGNs due to supermassive black hole growth.

We have examined the bent nature of the supermassive black hole mass–spheroid stellar mass relation for a large sample of 75 galaxies. We find that, when separating galaxies into core-Sérsic and Sérsic galaxies based on their central light profiles, they follow significantly different supermassive black hole scaling relations whose slopes are not consistent with one another. For the core-Sérsic galaxies $M_\mathrm{BH} \propto {M}_\mathrm{sph,*}^{0.97\,{\pm}\, 0.14}$, whereas for the Sérsic galaxies $M_\mathrm{BH} \propto {M}_\mathrm{sph,*}^{2.22\,{\pm}\, 0.58}$. These results are consistent with the expectation from a single log-linear supermassive black hole mass–host velocity dispersion relation combined with a bent relationship between host spheroid luminosity and host velocity dispersion. We find that the supermassive black hole mass is an approximately constant 0.55% of a core-Sérsic galaxy's spheroid stellar mass. The non-log-linear M_BH–M_{sph, *} relation implies that, for Sérsic galaxies, M_BH is not a constant fraction of the host spheroid mass, but represents an increasing fraction with increasing M_{sph, *}.

This research was supported by Australian Research Council funding through grants DP110103509 and FT110100263.