The Black Hole Mass–Color Relations for Early- and Late-type Galaxies: Red and Blue Sequences

Our investigation of correlations between the SMBH mass (M_BH) and (UV−[3.6]) galaxy color uses UV and 3.6 μm magnitudes that are determined in a homogeneous manner for a large sample of galaxies with measured SMBH masses. Henceforth, we refer to the (UV−[3.6]) color as ${ \mathcal C }$. Bouquin et al. (2015, 2018) provided FUV (λ_eff ∼ 1526 Å), NUV (λ_eff ∼ 2267 Å), and 3.6 μm asymptotic magnitudes for a sample of 1931 nearby galaxies taken from the Spitzer Survey of Stellar Structure in Galaxies (S⁴G) sample (Sheth et al. 2010). They used UV and near-infrared (3.6 μm) imaging data obtained with the GALEX, (Martin et al. 2005; Gil de Paz et al. 2007) and the Infrared Array Camera on the Spitzer Space Telescope, respectively. We use the SMBH sample presented in van den Bosch (2016, his Table 2). They publish a compilation of directly measured SMBH masses (M_BH), half-light radii (R_e), and total K_s-band luminosities (L_k) for a large sample of 245 galaxies. We selected all galaxies that were in common with Bouquin et al. (2018) and van den Bosch (2016), resulting in a sample of 67 galaxies studied in this paper. Homogenized mean central velocity dispersions (σ) and morphological classifications (elliptical E, elliptical-lenticular E-S0, lenticular S0, lenticular-spiral S0-a, and spiral S) of the sample galaxies were obtained from Hyperleda⁵ (Paturel et al. 2003; Makarov et al. 2014). In the analysis of the scaling relations (Tables 1–4), the galaxies are divided into two broad morphological classes, early-type galaxies (9 Es, 2 E-S0s, 2 S0s, and 7 S0-a) and late-type galaxies (47 Ss). Most of our late-type galaxies are disk dominated. The full list of galaxies and their properties are presented in Appendix C.

In Figure 1 we determine potential sample selection biases by comparing M_BH, R_e, and L_k of our sample and those of another 178 known galaxies with measured black hole masses using data from van den Bosch (2016, his Table 2). Both the early- and late-type galaxies in our sample probe a wide range in M_BH, R_e, and L_k to allow a robust investigation of the ${M}_{\mathrm{BH}}-{ \mathcal C }$ relations. We also find that our early- and late-type galaxies span a wide range in stellar mass (M_*,k), Figure 1(c). We compute the galaxy stellar masses using L_k and assuming the K_s-band mass-to-light ratio M_*/L_k = 0.10σ^0.45 (van den Bosch 2016). Late-type galaxies in our sample have M_*,k that range from 10⁹M_⊙ to 2 × 10¹¹M_⊙, and for 75% of them, M_*,k/M_⊙ ≳ 2 × 10¹⁰. For the early-type galaxies, 10¹⁰ ≲ M_*,k/M_⊙ ≲ 10¹², and 90% of these galaxies have M_*,k/M_⊙ ≳ 2 × 10¹⁰. It worth noting that the GALEX/S⁴G sample galaxies (Bouquin et al. 2018) were chosen to have radio-derived radial velocities of V_radio < 3000 Km s⁻¹ in HyperLEDA. The sample therefore lacks H i-poor extremely massive galaxies, including brightest cluster galaxies (BCGs).

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Our selected sample of 67 galaxies includes 64 galaxies with SMBH masses (M_BH) that are determined from stellar, gas, or maser kinematic measurements. For the remaining 3 galaxies (NGC 4051, NGC 4593, and NGC 5273), M_BH measurements were based on reverberation mapping (Bahcall et al. 1972; Peterson 1993). Of the 67 galaxies, 62 harbor black holes that are supermassive (i.e., M_BH ≳ 10⁶M_⊙); see Appendix C. While the remaining 5 sample galaxies have 2 × 10⁴M_⊙ ≲ (M_BH) ≲ 3 × 10⁵M_⊙, we also refer to these black holes as SMBHs. The sample includes 25 galaxies with M_BH upper limits, comprised of 23 late-type galaxies and 2 early-type galaxies. We discuss the effect of including upper limits on the black hole scaling relations in Section 3. The uncertainties on M_BH were taken from van den Bosch (2016).

Bouquin et al. (2015, 2018) used the 3.6 μm surface brightness profiles from Muñoz-Mateos et al. (2015) to determine the 3.6 μm magnitudes for their galaxies. They extracted the UV surface brightness profiles of the galaxies following the prescription of Muñoz-Mateos et al. (2015). Briefly, the sky levels in galaxy images were first determined, then the images were masked to avoid bright foreground and background objects (Bouquin et al. 2018, their Section 3.1). The FUV, NUV, and 3.6 μm radial surface brightness profiles were then extracted using a series of elliptical annuli with fixed ellipticity and position angle, after the innermost regions, R < 3'', were excluded (Bouquin et al. 2015, 2018; Muñoz-Mateos et al. 2015). Each annulus has a width of 6'', and measurements were taken up to 3× the major axis of the galaxy D25 elliptical isophote. To derive the FUV, NUV, and 3.6 μm asymptotic magnitudes from the corresponding surface brightness profiles, Bouquin et al. (2018) extrapolated the growth curves. The UV and 3.6 μm data reach depths of ∼27 mag arcsec⁻² and ∼26.5 mag arcsec⁻², respectively, allowing the growth curves to flatten out for most galaxies. The method yielded robust asymptotic magnitudes with errors that are within the FUV and NUV zero-point uncertainties of 0.05 and 0.03 AB mag (Morrissey et al. 2007).

The FUV, NUV, and 3.6 μm (total) asymptotic magnitudes of our sample were corrected for Galactic extinction by Bouquin et al. (2015, 2018) using the E(B − V) reddening values taken from Schlegel et al. (1998). For the analyses in the paper, we define the total galaxy luminosity as the sum of the luminosities of the bulge and disk, excluding additional galaxy structural components such as bars and rings. The bulk of the galaxies in our sample are multicomponent systems. Fractional luminosities of the individual structural components are needed to obtain accurate bulge and disk magnitudes from the total asymptotic magnitudes. We note that from here on, the term "bulge" is used when we refer to the spheroids of elliptical galaxies and to the bulges of disk galaxies. Fortunately, Salo et al. (2015) performed detailed 2D multicomponent decompositions of 3.6 μm images of all our galaxies into nuclear sources, bulges, disks, and bars, and they presented fractional bulge and disk luminosities that we use to calculate the 3.6 μm bulge and disk magnitudes. For two galaxies (NGC 3368 and NGC 4258) with poor fits in Salo et al. (2015), the 3.6 μm fractional luminosities were taken from Savorgnan & Graham (2016). The bulge-to-disk flux ratio (B/D) of a galaxy depends on the observed wavelength and galaxy morphological type (e.g., Möllenhoff 2004; Möllenhoff et al. 2006; Graham & Worley 2008; Kennedy et al. 2016). The UV B/T and D/T tabulated in Appendix C were derived using the 3.6 μm B/D together with the (extrapolation of the) B/D passband-morphological type diagram from Möllenhoff (2004, his Figure 5).

For the disk galaxies, we additionally applied the inclination-dependent (i) internal dust attenuation corrections from Driver et al. (2008, their Equations (1) and (2) and Table 1) to determine dust-corrected bulge and disk magnitudes. Because Driver et al. (2008) did not provide 3.6 μm dust corrections, we rely on the prescription for their reddest bandpass (i.e., K) to correct the 3.6 μm magnitudes. These corrections are given by

$$\begin{eqnarray}&&{m}_{\mathrm{bulge},\mathrm{UV}}^{\mathrm{corr}}={m}_{\mathrm{bulge},\mathrm{UV}}^{\mathrm{obs}}-1.10-0.95{\left[1-\cos (i)\right]}^{2.18},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{m}_{\mathrm{disk},\mathrm{UV}}^{\mathrm{corr}}={m}_{\mathrm{disk},\mathrm{UV}}^{\mathrm{obs}}-0.45-2.31{\left[1-\cos (i)\right]}^{3.42},\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{m}_{\mathrm{bulge},3.6}^{\mathrm{corr}}={m}_{\mathrm{bulge},3.6}^{\mathrm{obs}}-0.11-0.79{\left[1-\cos (i)\right]}^{2.77},\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{m}_{\mathrm{disk},3.6}^{\mathrm{corr}}={m}_{\mathrm{disk},3.6}^{\mathrm{obs}}-0.04-0.46{\left[1-\cos (i)\right]}^{4.23},\end{eqnarray} \tag{ 4 }$$

where cos(i) = b/a, i.e., the minor-to-major axis ratios, which were computed for our galaxies from the minor and major galaxy diameters given in the NED database.

For each sample galaxy, we derived the dust-corrected total galaxy magnitude as

$$\begin{eqnarray}&&{m}_{\mathrm{total}}^{\mathrm{corr}}=-2.5\mathrm{log}({10}^{-0.4{m}_{\mathrm{disk}}^{\mathrm{corr}}}+{10}^{-0.4{m}_{\mathrm{bulge}}^{\mathrm{corr}}}).\end{eqnarray} \tag{ 5 }$$

Analyses of the black hole–color relations can be affected by uncertainties on the bulge, disk, and total magnitudes (Section 3.1 and Appendix C), which are dominated by systematic errors. We account for four potential sources of systematic uncertainty. Uncertainties on the UV and 3.6 μm asymptotic magnitudes are introduced by dust contamination, imperfect sky background determination, and poor masking of bright sources (Bouquin et al. 2018). The disk galaxies have uncertainties due to our dust correction. There is also a need to account for uncertainties on the 3.6 μm B/T and D/T (Salo et al. 2015) used to covert the asymptotic magnitudes into disk, bulge, and total magnitudes. For the UV magnitudes, an additional source of systematic uncertainty is the derivation of the B/T and D/T (Section 3.1). The total uncertainties associated with the UV and 3.6 μm magnitudes were calculated by adding the individual contributions to the error budget in quadrature. Appendix C lists total magnitudes and associated errors for our sample galaxies. The quoted magnitudes are in the AB system unless noted otherwise.

Inherent differences in the employed statistical methods may systematically affect the derived black hole scaling relations, and it is therefore vital to explore this issue. We performed linear regression fits to ${M}_{\mathrm{BH}}-{ \mathcal C }(={m}_{\mathrm{UV}}^{\mathrm{corr}}-{m}_{3.6}^{\mathrm{corr}}$), M_BH − L_3.6, and M_BH − σ data using three traditional regression techniques: the bivariate correlated errors and intrinsic scatter (bces) code (Akritas & Bershady 1996), the Bayesian linear regression routine (linmix_err, Kelly 2007), and the ordinary least-squares (ols) code (Feigelson & Babu 1992); see Figures 2 and 3. The bces routine (Akritas & Bershady 1996) was implemented in our work using the python module by Nemmen et al. (2012). While the bces and linmix_err methods take into account the intrinsic scatter and uncertainties in M_BH and the host galaxy properties, only the latter can process "censored" data, e.g., black hole mass upper limits. The ols routine does not account for errors; we use this method to provide ${M}_{\mathrm{BH}}-{ \mathcal C }$ relations independent of measurement errors.

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In an effort to assess the robustness of the above linear regression fits, we additionally performed symmetric MCMC Bayesian linear regression fits for our (${M}_{\mathrm{BH}},{ \mathcal C }$) data, which account for black hole mass upper limits (see Appendix A).

Fitting the Y = βX + α line with the bces, linmix_err, and ols codes, we present the results from the $Y| X$, $X| Y$, and bisector regression analyses (Tables 1–3). We also present the results from our symmetric MCMC Bayesian regressions (Table 1). The $Y| X$ and $X| Y$ regressions minimize the residuals around the fitted regression lines in the Y and X directions, respectively. The symmetrical bisector line bisects the $Y| X$ and $X| Y$ lines. The linmix_err code does not return bisector regressions, thus we computed the the slope of the line that bisects the $Y| X$ and $X| Y$ lines. Throughout this work, we focus on the relations from the symmetrical bces bisector regressions (Figures 2 and 3).

Table 1.  ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}$ Scaling Relations for Early- and Late-type Galaxies

			Y = βX+α, X = ${{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}$ −6.5, Y = log MBH
			early-type galaxies, Figure 2, left
Regression method	$Y| X$		$X| Y$		Bisector		r	Δ (dex)	(dex)	N
	α	β	α	β	α	β
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
BCES	8.12 ± 0.18	1.28 ± 0.40	8.30 ± 0.31	2.65 ± 0.82	8.18 ± 0.20	1.75 ± 0.41	0.61	0.86	⋯	18
linmix_err	8.15 ± 0.22	1.25 ± 0.44	8.34 ± 0.23	2.47 ± 0.84	⋯	1.71 ± 0.51	⋯	⋯	0.69 ± 0.20	18
OLS	8.10 ± 0.17	1.04 ± 0.30	8.32 ± 0.27	2.59 ± 0.77	8.17 ± 0.18	1.57 ± 0.27	⋯	0.87	⋯	18
					Symmetric
MCMC	⋯	⋯	⋯	⋯	8.27 ± 0.25	2.06 ± 0.63	⋯	0.85	⋯	18
			Y = βX+α, X = ${{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}-$ 3.3, Y = log MBH
			late-type galaxies, Figure 2, left
	$Y| X$		$X| Y$		Bisector		r	Δ (dex)	(dex)	N
	α	β	α	β	α	β
BCES	7.01 ± 0.13	0.82 ± 0.20	7.06 ± 0.19	1.35 ± 0.36	7.03 ± 0.14	1.03 ± 0.13	0.60	0.87	⋯	45
linmix_err	7.07 ± 0.13	0.87 ± 0.26	7.09 ± 0.13	1.59 ± 0.38	⋯	1.17 ± 0.27	⋯	⋯	0.69 ± 0.22	45
OLS	6.97 ± 0.12	0.62 ± 0.16	7.10 ± 0.22	1.82 ± 0.36	7.02 ± 0.14	1.05 ± 0.12	⋯	0.87	⋯	45
					Symmetric
MCMC	⋯	⋯	⋯	⋯	6.95 ± 0.11	0.87 ± 0.17	⋯	0.81	⋯	45
			Y = βX+α, X = ${{ \mathcal C }}_{\mathrm{NUV},\mathrm{tot}}-$ 5.0, Y = log MBH
			early-type galaxies, Figure 2, right
	$Y| X$		$X| Y$		Bisector		r	Δ (dex)	(dex)	N
	α	β	α	β	α	β
BCES	8.07 ± 0.15	1.57 ± 0.36	8.21 ± 0.29	2.74 ± 0.99	8.12 ± 0.17	1.95 ± 0.28	0.70	0.72	⋯	19
linmix_err	8.10 ± 0.20	1.66 ± 0.55	8.19 ± 0.20	2.63 ± 0.79	⋯	2.04 ± 0.60	⋯	⋯	0.66 ± 0.18	19
OLS	8.06 ± 0.15	1.27 ± 0.28	8.18 ± 0.24	2.65 ± 0.68	8.11 ± 0.16	1.76 ± 0.20	⋯	0.68	⋯	19
					Symmetric
MCMC	⋯	⋯	⋯	⋯	8.06 ± 0.26	2.33 ± 0.74	⋯	0.82	⋯	19
			Y = βX+α, X = ${{ \mathcal C }}_{\mathrm{NUV},\mathrm{tot}}-$ 2.7, Y = log MBH
			late-type galaxies, Figure 2, right
	$Y| X$		$X| Y$		Bisector		r	Δ (dex)	(dex)	N
	α	β	α	β	α	β
BCES	6.96 ± 0.15	1.24 ± 0.35	6.96 ± 0.17	1.61 ± 0.33	6.96 ± 0.15	1.38 ± 0.23	0.65	0.86	⋯	45
linmix_err	7.02 ± 0.12	1.08 ± 0.30	8.32 ± 0.27	1.86 ± 0.41	⋯	⋯	⋯	⋯	0.66 ± 0.18	45
OLS	6.94 ± 0.12	0.82 ± 0.17	6.94 ± 0.18	1.94 ± 0.35	6.94 ± 0.13	1.24 ± 0.13	⋯	0.83	⋯	45
					Symmetric
MCMC	⋯	⋯	⋯	⋯	6.90 ± 0.13	1.35 ± 0.26	⋯	0.85	⋯	45

Note. Correlation between SMBH mass (M_BH) and total UV−[3.6] color (${{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}})$ for our early- and late-type galaxies with directly measured M_BH. ${{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}$ = m_FUV − m_3.6μm, ${{ \mathcal C }}_{\mathrm{NUV},\mathrm{tot}}$ = m_NUV − m_3.6μm, where m_FUV, m_NUV and m_3.6μm are the FUV, NUV, and m_3.6μm total apparent magnitudes of the galaxies (Table C1). Column (1) lists the regression method. Columns (2) and (3) are the intercepts (α) and slopes (β) from the ($Y| X$) regressions. Columns (4) and (5) are α and β obtained from the $Y| X$ regression fits, while Columns (6) and (7) show α and β from the symmetrical bisector regressions. The preferred slopes and intercepts are highlighted in bold. Column (8) lists the Pearson correlation coefficient (r). Column (9) lists the rms scatter around the fitted bces bisector relation in the log M_BH direction (Δ). Column (10) lists the intrinsic scatter (), see the text for details. Column (11) lists the number of data points contributing to the regression fits.

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In this section, we investigate the correlations between M_BH and total (i.e., bulge+disk) colors ${{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}$ ($={m}_{\mathrm{FUV},\mathrm{total}}^{\mathrm{corr}}\,-{m}_{3.6,\mathrm{total}}^{\mathrm{corr}}$) and ${{ \mathcal C }}_{\mathrm{NUV},\mathrm{tot}}$ (=${m}_{\mathrm{NUV},\mathrm{total}}^{\mathrm{corr}}-{m}_{3.6,\mathrm{total}}^{\mathrm{corr}}$) for our sample of 67 galaxies that is comprised of 20 early-type galaxies and 47 late-type galaxies (Appendix C). In Figure 2 we plot these correlations (Table C1) with data points that are color-coded based on morphological type. The regression analyses reveal that early- and late-type galaxies define two distinct red and blue sequences with markedly different slopes in the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ diagrams, regardless of the applied regression methods (Table 1). We find that the slopes for early- and late-type galaxies are different at the ∼2σ level (Appendix A), and the significance levels for rejecting the null hypothesis that these two morphological types have the same slope are 1.7%–6.7%. We note in passing that this trend of different slopes for early- and late-type galaxies holds for the correlations between M_BH and the bulge colors of the two Hubble types (${{ \mathcal C }}_{\mathrm{UV},\mathrm{bulge}}$, Dullo et al. 2020). For both early- and late-type galaxies, the ${{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}$ and M_BH data correlate with a Pearson correlation coefficient r ∼ 0.60 (Table 1). The ${{ \mathcal C }}_{\mathrm{NUV},\mathrm{tot}}$ and M_BH data have Pearson correlation coefficients r ∼ 0.70 and 0.65 for early- and late-type galaxies, respectively. In the ${M}_{\mathrm{BH}}-{ \mathcal C }$ regression analyses, we have excluded one early-type galaxy (NGC 2685) and 2 late-type galaxies (NGC 3310 and NGC 4826) that are offset from the relations by more than three times the intrinsic scatter (Figure 2). The early-type galaxy NGC 5018 was also excluded from the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{FUV}}$ relations, resulting in 18 early-type galaxies. These four outliers have peculiar characteristics that are discussed in Appendix B.1.

Symmetrical bces bisector fits to the (${M}_{\mathrm{BH}},{{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}$) and (${M}_{\mathrm{BH}},{{ \mathcal C }}_{\mathrm{NUV},\mathrm{tot}}$) data yield relations for early-type galaxies with slopes of 1.75 ± 0.41 and 1.95 ± 0.28, respectively (Table 1), such that M_BH ∝ (L_FUV,tot/L_3.6,tot)^{−4.38±1.03} and M_BH ∝ (L_NUV,tot/L_3.6,tot)^{−4.88±0.70}. This is to be compared with the derived bces bisector ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}$ and ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{NUV},\mathrm{tot}}$ relations for the late-type galaxies having shallower slopes of 1.03 ± 0.13 and 1.38 ± 0.23, such that M_BH ∝ (L_FUV,tot/L_3.6,tot)^{−2.58±0.33} and M_BH ∝ (L_NUV,tot/L_3.6,tot)^{−3.45±0.58}.

With the assumption that the UV-to-3.6 μm luminosity ratio (L_UV/L_3.6) is a proxy for the sSFR, (e.g., Bouquin et al. 2018), this implies that the growth of black holes in late-type galaxies has a steeper dependence on sSFR (i.e., ${M}_{\mathrm{BH}}\propto {\mathrm{sSFR}}_{\mathrm{FUV}}^{-2.58}$) than early-type galaxies (${M}_{\mathrm{BH}}\propto {\mathrm{sSFR}}_{\mathrm{FUV}}^{-4.38}$). That is, at a given value of the sSFR, late-type galaxies tend to have more massive black holes than early-type galaxies. The caveat of using FUV magnitudes as a proxy for the current SFR is that a significant fraction of the FUV light in ∼5% of massive early-type galaxies may come from extreme horizontal branch stars and not from young upper main-sequence stars. This phenomenon is called the "UV upturn" (e.g., Code & Welch 1979; O'Connell 1999; Yi et al. 2011). This is likely due to the rarity of very massive early-type galaxies in our sample. Nonetheless, we found that none of our early-type galaxies are UV upturns when we used the criteria given by Yi et al. (2011, their Table 1). Because the FUV band is more sensitive to the galaxy SFR than the NUV band, the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}$ relations are systematically shallower than the corresponding ${M}_{\mathrm{BH}}\,-{{ \mathcal C }}_{\mathrm{NUV},\mathrm{tot}}$ relations, although they are consistent with overlapping 1σ uncertainties (Table 1).

The root-mean-square (rms) scatter (Δ) around the fitted bces bisector relations in the log M_BH direction is Δ_FUV,early ∼ 0.86 dex, Δ_FUV,late ∼ 0.87 dex, Δ_NUV,early ∼ 0.72 dex, and Δ_NUV,late ∼ 0.86 dex. We report intrinsic scatters () for our ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ relations as derived by linmix_err to be _FUV,early ∼ 0.69 ± 0.20, _FUV,late ∼ 0.69 ± 0.22, _NUV,early ∼ 0.66 ± 018, and _NUV,late ∼ 0.66 ± 0.18.

As noted previously, the linmix_err code and MCMC Bayesian analysis—which account for the 24 galaxies (22 late-type galaxies and 2 early-type galaxies) with M_BH upper limits—yield ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ relations consistent with the bces regression analyses (Table 1). Nonetheless, we checked for a potential bias for the late-type galaxies due to the inclusion of M_BH upper limits by rerunning the bces bisector regression analysis on the 23 (=45–22) late-type galaxies with more securely measured M_BH. We find that the slopes, intercepts, and Δ of the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ relations are only weakly affected by the exclusion of M_BH upper limits.⁶ Including the upper limits in the black hole scaling relations is useful (Gültekin et al. 2009) because they also follow the M − σ relation that is traced by galaxies with more securely measured M_BH (Figure 3).

We can compare our work to that of Terrazas et al. (2017, their Figures 1 and 2), who used SFRs determined based on IRAS far-infrared imaging and reported an inverse correlation between sSFR and SMBH mass for 91 galaxies with measured black hole masses. Although they did not separate the galaxies into late- and early-types, their full sample seems to follow a single M_BH − sSFR relation with no break. This contradicts our results. To explain this discrepancy, we split the galaxies in Terrazas et al. (2017) by morphology and find that their late-type galaxies (which constitute one-third of the full sample) reside at the low-mass end of their M_BH−sSFR relation and span very small ranges in SMBH mass (4 × 10⁶ ≲ M_BH/M_⊙ ≲ 10⁸) and in sSFR (10⁻¹¹ ≲ sSFR/yr⁻¹ ≲ 8 × 10⁻⁹). This is inadequate to establish the blue ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ sequence (Figure 2). Furthermore, we note that the far-IR (FIR) flux may underestimate the actual SFR for low-mass late-type galaxies because most of the UV photons of these galaxies are unobscured by dust and are thus not reprocessed to FIR wavelengths (Catalán-Torrecilla et al. 2015). We also find that the Terrazas et al. (2017) early-type M_BH − sSFR relation has more scatter than ours. We suspect that this may be due to a variable contamination of the IRAS FIR emissions in massive galaxies by the AGN⁷ that heats the surrounding dust. While the dusty AGN in some massive galaxies might led to an increase in the SFR values based on FIR luminosities (e.g., Catalán-Torrecilla et al. 2015; Toba et al. 2017), star formation activities are likely the dominant contributor to the SFR values reported by Terrazas et al. (2017) because AGN contamination is mainly responsible for the larger scatter observed in their M_BH − sSFR relation.

In Figure 2 we have shown for the first time, to our knowledge, a correlation between SMBH mass and total (i.e., bulge+disk) colors for early- and late-type galaxies. For this correlation to be evident, it is important that the color is determined using a wide wavelength baseline. In this section, we present correlations between M_BH and velocity dispersion (σ) and 3.6 μm total luminosity (L_3.6,tot) for the same galaxy sample to allow a direct statistical comparison with the ${M}_{\mathrm{BH}}-{ \mathcal C }$ relations (Figure 3 and Table 2). Assuming a 10% uncertainty⁸ on σ, the bces bisector regression yields M_BH − σ relations with slopes 5.42 ± 0.90, 4.49 ± 0.48, and 4.65 ± 0.35 for the early-type galaxies and late-type galaxies, and for the full ensemble. These relations are in good agreement with each other within their 1σ uncertainties. The late-type galaxies NGC 5055 and NGC 5457, which are the most deviant outliers in the M_BH − σ diagram, were excluded. The unification of early- and late-type galaxies in the M_BH − σ diagram has been reported before (e.g., Beifiori et al. 2012; Graham & Scott 2013; van den Bosch 2016; Dullo et al. 2020, submitted). The M_BH − σ relations (Table 2) are consistent with those from Gültekin et al. (2009), Beifiori et al. (2012), McConnell & Ma (2013), Kormendy & Ho (2013), and Graham & Scott (2013).⁹

Table 2.  M_BH − σ Relation

	Y = βX+α, X = log σ−2.2, Y = log MBH (early-type, Figure 3, left)
Regression method	$Y| X$		$X| Y$		Bisector		r	Δ (dex)	(dex)	N
	α	β	α	β	α	β
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
bces	7.84 ± 0.14	4.33 ± 0.80	7.81 ± 0.23	7.10 ± 1.58	7.84 ± 0.16	5.42 ± 0.90	0.72	0.67	0.70 ± 0.16	20
	Y = βX+α, X = log σ−2.0, Y = log MBH (late-type, Figure 3, left)
	$Y| X$		$X| Y$		Bisector		r	Δ (dex)	(dex)	N
	α	β	α	β	α	β
bces	6.98 ± 0.10	4.00 ± 0.53	7.00 ± 0.11	5.00 ± 0.99	6.98 ± 0.10	4.49 ± 0.48	0.75	0.70	0.63 ± 0.10	45
	Y = βX+α, X = log σ−2.0, Y = log MBH (all galaxies, Figure 3, left)
	$Y| X$		$X| Y$		Bisector		r	Δ (dex)	(dex)	N
	α	β	α	β	α	β
bces	6.99 ± 0.09	4.23 ± 0.40	6.92 ± 0.10	5.39 ± 0.72	6.96 ± 0.09	4.65 ± 0.35	0.78	0.68	0.62 ± 0.07	65

Note. Similar to Table 1, but here showing linear regression analyses of the correlation between SMBH mass (M_BH) and velocity dispersion (σ).

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To determine the M_BH − L_3.6,tot relation, we converted the inclination and dust-corrected 3.6 μm total apparent magnitudes into absolute magnitudes (M_3.6,tot, Appendix C) using distances given in van den Bosch (2016). The bces bisector M_BH − L_3.6,tot relation for the full sample of 67 galaxies was performed without accounting for the error on M_3.6,tot, yielding ${M}_{\mathrm{BH}}\propto {L}_{3.6,\mathrm{tot}}^{1.23\pm 0.15}$ (Figure 3 and Table 3). Graham & Scott (2013) reported two distinct M_BH − L relations for the bulges of Sérsic galaxies (${M}_{\mathrm{BH}}\propto {L}_{{{\rm{K}}}_{{\rm{s}}},\mathrm{bulge}}^{2.73}$) and core-Sérsic galaxies (${M}_{\mathrm{BH}}\propto {L}_{{{\rm{K}}}_{{\rm{s}}},\mathrm{bulge}}^{1.10}$). Because only 7 galaxies were identified as core-Sérsic galaxies (see Figure 4), we refrained from separating the galaxies into Sérsic and core-Sérsic galaxies in the M_BH − L_3.6,tot diagram.

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Table 3.  M_BH − L_3.6,tot Relation

	Y = βX+α, X = M3.6,tot +18.5, Y = log MBH (all galaxies, Figure 3, right)
Regression method	$Y| X$		$X| Y$		Bisector		r	Δ (dex)	(dex)	N
	α	β	α	β	α	β
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
bces	6.96 ± 0.11	−0.37 ± 0.06	6.80 ± 0.17	−0.65 ± 0.12	6.88 ± 0.12	−0.49 ± 0.06	−0.66	0.84	0.69 ± 0.09	67

Note. Similar to Table 1, but here showing linear regression analyses of the correlation between the SMBH masses (M_BH) and the 3.6 μm total absolute magnitude of the galaxies (M_3.6,tot), see the text for details.

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Because a different number of galaxies was used to define the ${M}_{\mathrm{BH}}-{ \mathcal C }$, M_BH − σ and M_BH − L relations, a direct comparison of the strength and scatter of the relations is difficult. Nonetheless, the correlation between the color ${{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ and black hole mass M_BH (r ∼ 0.60–0.70, see Table 1) is slightly weaker than that between the stellar velocity dispersion σ and M_BH (r ∼ 0.72–0.78, Table 2). These two relations have comparable intrinsic scatter (see Tables 1 and 2). In terms of scatter in the log M_BH direction, the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ relations typically have 5%–27% more scatter (i.e., Δ ∼ 0.72–0.87 dex) than the M_BH − σ relations (Δ ∼ 0.68–0.70 dex). The M_BH − σ relation appears to be the most fundamental SMBH scaling relation. However, the M_BH − σ relations for late- and early-type galaxies are not notably offset from each other. This contrasts with the formation models of galaxies, which predict that the SMBH growth in the two Hubble types is completely different (see Section 4.5). Furthermore, Dullo et al. (2020, submitted) showed that the M_BH − σ relation tends to underpredict the actual black hole masses for the most massive galaxies with M_* ≳ 10¹²M_⊙. In contrast, the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ relations are in accordance with galaxy formation models (Section 4.5).

In the comparison between the ${M}_{\mathrm{BH}}-{ \mathcal C }$ and M_BH − L relations, these two relations display a similar level of strength and vertical scatter (Table 3, r ∼ 0.60–0.70 and Δ ∼ 0.72–0.87 dex for ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ and r ∼ −0.66, and Δ ∼ 0.84 dex for M_BH − L_3.6,tot). In passing we note that the existence of the M_BH − L relation coupled with the red sequence and blue cloud traced by early- and late-type galaxies in the color–magnitude diagram does not necessitate a correlation between the black hole mass and galaxy color.

For comparison, our ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ relation for the 47 late-type galaxies is stronger (r ∼ 0.60–0.65, and Δ ∼ 0.87 dex) than the M_BH − M_*,tot relation based on 3.6 μm data by Davis et al. (2018) for their sample of 40 late-type galaxies (r ∼ 0.47 and Δ ∼ 0.79 dex).

As noted in the Introduction, the SMBH scaling relations may differ depending on the galaxy core structure (i.e., core-Sérsic versus Sérsic type). We identify seven core-Sérsic galaxies (6 Es + 1 S) in our sample with partially depleted cores published in the literature: NGC 1052 (Lauer et al. 2007), NGC 3608, NGC 4278, and NGC 4472 (Dullo & Graham 2012, 2014), and NGC 4374, NGC 4594, and NGC 5846 (Graham & Scott 2013). They are among the reddest (${{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}\gtrsim 6$) galaxies in our sample with massive SMBHs (M_BH ≳ 10⁸M_⊙), Figure 4. While structural analyses of high-resolution Hubble Space Telescope images are needed to identify a partially depleted core (or lack thereof) in the remaining sample galaxies (e.g., Dullo & Graham 2013, 2014; Dullo et al. 2016, 2017, 2018, the majority (∼80%) of our spiral galaxies have σ ≲ 140 km s⁻¹, and they are likely Sérsic galaxies with no partially depleted cores (e.g., Dullo & Graham 2012, 2013, 2014; Dullo et al. 2017). For early-type galaxies, we did not find bends or offsets from the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ relations because of core-Sérsic or Sérsic galaxies (Figure 4).

To locate our galaxies in color–color diagrams, we used the classification by Bouquin et al. (2018, their Section 4.4). These authors compared the FUV−NUV and NUV–[3.6] colors to separate their galaxies into red, intermediate, and blue sequences. Figure 5 shows excellent coincidence between the red and blue ${M}_{\mathrm{BH}}-{ \mathcal C }$ early- and late-type morphological sequences (Sections 3.4) and the canonical color–color relation (red/intermediate) and blue sequences, respectively, with only three exceptions (NGC 2685, NGC 4245, and NGC 4594). The case of NGC 2685 was discussed in Appendix B.1.4. NGC 4245 is a barred S0-Sa galaxy with a prominent ring (Treuthardt et al. 2007). The spiral Sa NGC 4594 (also referred to as the Sombrero Galaxy) exhibits properties similar to massive early-type galaxies. Spitler et al. (2008) found that the number of blue globular clusters in NGC 4594 is comparable to massive early-type galaxies. Moreover, Jardel et al. (2011) noted that the galaxy dark matter density and core radius resemble those expected for early-type galaxies with massive bulges. It is the only red-sequence spiral in our sample (Bouquin et al. 2018), which is also unique in being the only core-Sérsic late-type galaxy in the sample. Interestingly, Figure 5 reveals that all the intermediate-sequence galaxies (Bouquin et al. 2018) reside to the left of the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ relation that is defined by early-type galaxies.

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It is of interest to assess the robustness of black hole masses that are estimated using the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}$ and ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{NUV},\mathrm{tot}}$ relations found in this work. We do so using literature FUV, NUV, and 3.6 μm magnitudes for a selected sample of 11 galaxies with direct SMBH masses that are not in our sample (see Table 4). These 11 galaxies were not included in the main sample because we endeavor to establish the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ relations using homogeneously determined UV and 3.6 μm magnitudes. In this way, the observed trends in the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ diagrams (Figure 2) cannot be attributed to differences in methods and/or data sources. We use the black hole mass measurement of NGC 205 by Nguyen et al. (2019), and for the remaining 10 galaxies, the SMBH masses are taken from van den Bosch (2016). Of the 11 galaxies, 9 are in common between Jeong et al. (2009) and Savorgnan & Graham (2016). Jeong et al. (2009, their Table 1) published total apparent FUV and NUV magnitudes derived from growth curves for the galaxies, while Savorgnan & Graham (2016, their Table 2) presented their 3.6 μm galaxy apparent magnitudes¹⁰ that were computed using their best-fitting structural parameters. We also included the low-mass elliptical galaxy NGC 205 and the Seyfert SAm bulgeless galaxy NGC 4395 (Filippenko & Ho 2003; Peterson et al. 2005). NGC 205 potentially harbors the lowest central black hole mass measured for any galaxy to date (Nguyen et al. 2019), and NGC 4395 is known to be an outlier from the M_BH − σ diagrams (e.g., Davis et al. 2017). For NGC 205, we use the UV and 3.6 μm magnitudes from Gil de Paz et al. (2007) and Marleau et al. (2006), respectively. For NGC 4395, the total UV and 3.6 μm magnitudes are from Dale et al. (2009) and Lee et al. (2011); a caveat here is that these magnitudes are not corrected for internal dust attenuation.

Table 4.  SMBH Masses

Galaxy	Type	${{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$	log (MBH/M⊙)	log (MBH/M⊙)
		(AB mag)	(directly measured)	(predicted)
		(FUV/NUV)		(FUV/NUV)
(1)	(2)	(3)	(4)	(5)
NGC 0205	E5 pec	4.61/2.67	${3.83}_{-1.83}^{+1.18}$	4.85/3.58
NGC 0524	SA0	7.30/5.48	${8.94}_{-0.05}^{+0.05}$	9.68/9.02
NGC 0821	E6	7.02/4.69	${8.22}_{-0.21}^{+0.21}$	9.13/7.64
NGC 1023	SB0	6.64/5.01	${7.62}_{-0.05}^{+0.05}$	8.39/8.20
NGC 4395	SAm	1.49/1.37	${5.54}_{-0.54}^{+0.54}$	5.17/5.29
NGC 4459	SA0	6.56/5.03	${7.84}_{-0.09}^{+0.09}$	8.24/8.23
NGC 4473	E5	6.80/4.93	${7.95}_{-0.24}^{+0.24}$	8.71/8.06
NGC 4552	E	6.24/5.33	${8.70}_{-0.05}^{+0.05}$	7.61/8.76
NGC 4564	E6	6.34/4.77	${7.95}_{-0.12}^{+0.12}$	7.91/7.78
NGC 4621	E5	7.18/5.78	${8.60}_{-0.09}^{+0.09}$	9.41/9.55
NGC 5845	E	6.38/5.30	${8.69}_{-0.16}^{+0.16}$	7.89/8.71

Note. Column (1) lists the galaxy name. Column (2) lists the morphological type from the NED database. Column (3) lists the total FUV–[3.6] and NUV–[3.6] colors (${{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}$ and ${{ \mathcal C }}_{\mathrm{NUV},\mathrm{tot}}$). Columns (4) list the directly measured SMBH masses. Column (5) lists black hole masses predicted using the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}$ and ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{NUV},\mathrm{tot}}$ relations (Table 1) and the appropriate colors given in Column (3). We assign a typical uncertainty of 0.85 dex to log (M_BH) for these predicted black hole masses.

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Before applying our ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ relations to estimate M_BH, we homogenize the FUV, NUV, and 3.6 μm data from the literature by comparing our magnitudes with those from Jeong et al. (2009) and Savorgnan & Graham (2016) for galaxies in common with them. We find that compared to our magnitudes, the Jeong et al. (2009) total FUV and NUV magnitudes are fainter by typically 0.52 mag, while the galaxy magnitudes from Savorgnan & Graham (2016) are brighter by typically 0.18 mag. Having applied these corrections (i.e., m_UV = m_UV,Jeo − 0.52 and m_3.6 = m_3.6,Sav + 0.18) for the 9 early-type galaxies, we computed the ${{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}$ and ${{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}$ colors listed in Table 4.

Figure 6 reveals good agreement between the directly measured M_BH and predicted M_BH determined using ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}$ and ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{NUV},\mathrm{tot}}$ relations for the 10 galaxies in Table 4. On average, $| \mathrm{log}({M}_{\mathrm{BH},\mathrm{predicted}}/{M}_{\mathrm{BH},\mathrm{measured}})| \sim 0.67\,\mathrm{dex}\pm 0.29\,\mathrm{dex}(\mathrm{FUV})$ and ∼0.32 dex ± 0.29 dex (NUV). In Figure 6 the direct black hole mass appears to correlate better with that predicted using the NUV color than using the FUV color, and for the massive early-type galaxies, this may be due to contributions to the FUV flux from the extreme horizontal branch stars (see Section 3.4). The approach of using homogenized galaxy colors obtained through different methods may introduce some systematic errors in the determination of M_BH. We caution that when the ${M}_{\mathrm{BH}}-{ \mathcal C }$ relations are used to predict black hole masses, one should use FUV, NUV, and 3.6 μm magnitudes that are obtained in a homogeneous way. Furthermore, the ${M}_{\mathrm{BH}}-{ \mathcal C }$ relations should not be used to predict black hole masses in galaxies that are highly inclined (e.g., edge-on) and obscured with dust.

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As noted in the introduction, a clear benefit of the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ relation is its applicability to early- and late-type galaxies, including those with low central velocity dispersions (σ ≲ 100 km s⁻¹) and with small or no bulges. Moreover, photometry has the advantage of being cheaper than spectroscopy. Using our relations (Table 1) together with galaxy colors derived from the Bouquin et al. (2018, their Table 1) asymptotic FUV, NUV, and 3.6 μm magnitudes, we tentatively predict black hole masses in a sample of 1382 GALEX/S⁴G galaxies (Table D1) with no measured black hole masses, see Appendix D. We show that late-type galaxies with ${{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}\lesssim 1.33$ AB mag or ${{ \mathcal C }}_{\mathrm{NUV},\mathrm{tot}}\lesssim 1.28$ AB mag may harbor IMBHs (M_BH ∼ 100–10⁵M_⊙). Similarly, early-type galaxies with ${{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}\lesssim 4.68$ AB mag or ${{ \mathcal C }}_{\mathrm{NUV},\mathrm{tot}}\lesssim 3.4$ AB mag are potential IMBH hosts. While Sloan Digital Sky Survey (SDSS) velocity dispersion measurements are available for hundreds of thousands of galaxies and one can use them together with the M_BH − σ relation to estimate black hole masses, as cautioned by the SDSS Data Release¹¹ 12 (Alam et al. 2015), velocity dispersion values lower than 100 km s⁻¹ reported by SDSS are below the resolution limit of the SDSS spectrograph and are regarded as unreliable. Note that galaxies with σ ≲ 100 km s⁻¹ are expected to have low stellar masses (M_* ≲ 2 × 10¹⁰M_⊙), and such galaxies make up a significant fraction of the SDSS galaxy sample (Chang et al. 2015, see their Figure 9). In addition, the SDSS spectra measure the light within a fixed aperture of radius 15, thus the SDSS velocity dispersion values of more distant galaxies can be systematically lower than those of similar nearby galaxies.

By morphologically splitting the sample galaxies, we have demonstrated that late-type hosts do not correlate with SMBHs in the same manner as early-type hosts (Table 1). This can be reconciled very well with the prediction that early- and late-type galaxies have fundamentally different formation histories (e.g., White & Rees 1978; Khochfar & Burkert 2001; Steinmetz & Navarro 2002; Kauffmann et al. 2003b; Kormendy & Kennicutt 2004; Schawinski et al. 2010, 2014; Dullo & Graham 2014; Tonini et al. 2016; Davis et al. 2018; Dullo et al. 2019). For example, the red and blue ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{FUV},\mathrm{tot}}$ relations are such that M_{BH,early-type} ∝ (L_FUV,tot/L_3.6,tot)^−4.38 and M_BH,late-type ∝ (L_FUV,tot/L_3.6,tot)^−2.58. Given that L_UV/L_3.6 is a good proxy for the sSFR, (Bouquin et al. 2018. their Appendix B), this therefore implies that both early- and late-type galaxies exhibit log-linear inverse correlations between M_BH and sSFR, the latter having a steeper dependence on sSFR than the former (see Table 1 and Figure 2).

A correlation between M_BH and sSFR is expected. Observations have shown that bright quasars and local Seyferts tend to reside in strong starburst galaxies or in galaxies with ongoing star formation (e.g., Sanders et al. 1988; Kauffmann et al. 2003a; Alexander et al. 2005; Lutz et al. 2008; Netzer 2009; Wild et al. 2010; Rosario et al. 2012; Barrows et al. 2017; Yang et al. 2017). Other findings lending further support to the link between star formation and SMBH growth are the correlation between black hole accretion rate and host galaxy SFR (e.g., Heckman et al. 2004; Merloni et al. 2004; Hopkins & Quataert 2010; Chen et al. 2013; Madau & Dickinson 2014; Sijacki et al. 2015; Yang et al. 2017), the inverse correlation between sSFR and specific SMBH mass (Terrazas et al. 2017), and the trend between SMBH mass and host galaxy star formation histories over cosmic time (e.g., Martín-Navarro et al. 2018; van Son et al. 2019).

Within the self-regulated SMBH growth model, the correlation between SMBH masses and the host galaxy properties (e.g., stellar luminosity, McLure & Dunlop 2002; Marconi & Hunt 2003) is interpreted as reflecting a link between the growth of SMBHs and star formation events in the host (Silk & Rees 1998; Fabian 1999; King 2003; Di Matteo et al. 2005; Murray et al. 2005; Springel et al. 2005; Croton et al. 2006; Hopkins et al. 2006; Schawinski et al. 2006; Cattaneo et al. 2009; Weinberger et al. 2017). In this scenario, the same cold gas reservoir that fuels the AGN/quasar feeds starburst events. The energy or momentum released by the AGN/quasar can heat the interstellar medium and cause the expulsion of gas from the host galaxy, shutting off star formation and halting accretion onto the SMBH. However, whether AGN accretion and star formation are precisely coincidental is unclear (e.g., Ho 2005).

We (see also Dullo et al. 2020, submitted) argue that the significantly different ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{FUV}}$ relations for early- and late-type galaxies (i.e., the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{FUV}}$ red and blue sequences) suggest that the two Hubble types follow two distinct channels of SMBH growth: the former is driven by a major merger, and the latter involves (major merger) free processes (see Hopkins & Hernquist 2009). This broadly agrees with Schawinski et al. (2010, 2014).

The standard cosmological formation paradigm is that SMBHs in early-type galaxies are built up during the period of rapid galaxy growth at high redshift (z ∼ 2–5) when the major gas-rich mergers of disk galaxies (e.g., Toomre & Toomre 1972; White & Rees 1978) drive gas infall into the nuclear regions of the newly formed merger remnant, leading to starburst events and AGN accretion processes (e.g., Barnes & Hernquist 1991, 1996; Naab et al. 2006a; Hopkins & Quataert 2010; Knapen et al. 2015). Accretion onto more massive SMBHs triggers stronger AGN feedback, which is efficient at quenching star formation rapidly. The position of an early-type galaxy on the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV}}$ red sequence is therefore dictated by the complex interplay between the details of its SMBH growth, efficiency of AGN feedback, regulated star formation histories, and major merger histories; this is not set by simple hierarchical merging (Peng 2007; Jahnke & Macciò 2011).

Massive early-type galaxies (i.e., total stellar mass M_*,k ∼ 8 × 10¹⁰M_⊙–10¹²M_⊙) with M_BH ≳ 10⁸M_⊙ and ${{ \mathcal C }}_{\mathrm{FUV}}\gtrsim 6.3$ mag, at the high-mass end of the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV}}$ red sequence (Figure 2, Section 4.3), are consistent with the scenario where a (gas-rich) major merger at high redshift drives intense bursts of star formation, efficient SMBH growth, and ensuing quenching of star formation by strong AGN feedback on short timescales (e.g., Thomas et al. 2005, 2010; de La Rosa et al. 2011; McDermid et al. 2015; Segers et al. 2016). This is accompanied by a few (0.5–2) successive gas-poor (dry) major mergers since z ∼ 1.5–2 (e.g., Bell et al. 2004, 2006; Khochfar & Silk 2009; Dullo & Graham 2012, 2013, 2014; Man et al. 2012; Rodriguez-Gomez et al. 2015), involving low level star formation¹² (i.e., "red but not strictly dead," see de La Rosa et al. 2011; Davis et al. 2019; Habouzit et al. 2019) detected by the GALEX FUV and NUV detectors (e.g., Gil de Paz et al. 2007; Bouquin et al. 2018). The bulk of these objects are core-Sérsic elliptical galaxies, a fraction of which may gradually grow stellar disk structures and transform into massive lenticular galaxies (Dullo & Graham 2013; Graham 2013; Dullo 2014; Graham et al. 2015; de la Rosa et al. 2016).

As for the less massive (Sérsic) early-type galaxies (M_*,k ∼ 10¹⁰M_⊙ − 2 × 10¹¹M_⊙) with lower SMBH masses (10⁶M_⊙ ≲ M_BH ≲ 10⁸M_⊙) and ${{ \mathcal C }}_{\mathrm{FUV}}\lesssim 6.3$ mag (Figure 2, Section 4.3), they likely grow primarily via gas-rich (wet) major mergers and form their stellar populations over an extended period of time (Thomas et al. 2005, 2010; de La Rosa et al. 2011; McDermid et al. 2015). Our findings disfavor a scenario where Sérsic early-type galaxies with intermediate colors are late-type galaxies quenching star formation and moving away from the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{FUV}}$ blue sequence. Collectively, core-Sérsic and Sérsic early-type galaxies define a red sequence in the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{FUV}}$ diagram. Lacking the most luminous and massive BCGs with M_*,k ≳ 10¹²M_⊙ in our sample, we note that our ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV}}$ relation is not constrained at the highest-mass end. Becausesuch galaxies are generally expected to have negligible star formation (Dullo 2019), the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV}}$ relations, the ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{FUV}}$ in particular, may not apply to them. Our interpretation of the assembly of the red sequence for early-type galaxies is in accordance with the "downsizing" scenario, where more massive galaxies form stars earlier and over a shorter timescale than less massive galaxies (e.g., Cowie et al. 1996; Brinchmann & Ellis 2000; Cattaneo et al. 2008; Pérez-González et al. 2008; Pannella et al. 2009).

The (major merger) free scenario—secular processes and minor mergers—may be naturally consistent with the observed late-type ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{FUV}}$ blue sequence (Figure 2, Section 4.3) and dynamically cold stellar disks of late-type galaxies. Recently, Martin et al. (2018a) reported that massive SMBHs in disk galaxies can grow primarily via secular processes with small contributions (i.e., only 35% of the SMBH mass) from mergers. We tentatively hypothesize that secular-driven processes involving nonaxisymmetric stellar structures, such as bars and spiral arms, can trigger a large inflow of gas from the large-scale disk into nuclear regions of late-type galaxies, slowly feeding SMBHs and fueling star formation (e.g., Kormendy 1993, 2013; Kormendy & Kennicutt 2004; Fisher & Drory 2008; Leitner 2012; Cisternas et al. 2013; Tonini et al. 2016; Dullo et al. 2019). Barred galaxies make up the bulk (∼62%) of the late-type galaxies in our sample (Figure 4). In addition, gas-rich minor mergers have been suggested in the literature to trigger enhanced star formation and SMBH growth in late-type galaxies without destroying the disks (Simmons et al. 2013, 2017; Kaviraj 2014a, 2014b; Martin et al. 2018a, 2018b). The question remains, however, whether pure (major merger) free processes could be the main mechanism for the formation of late-type galaxies with massive bulges and high-velocity dispersion, as in the case of NGC 4594.

As noted above, we find that core-Sérsic¹³ and Sérsic galaxies collectively define a single early- or late-type morphology sequence, in agreement with the conclusions by Sahu et al. (2019a), Dullo (2019), and Dullo et al. (2020, submitted). Moreover, Savorgnan et al. (2016) reported a blue spiral galaxy M_BH − M_*,bulge sequence using their sample of 17 spiral galaxies (see also Davis et al. 2018, their Section 2.2).

We remark that bulgeless spirals and spiral galaxies with classical bulges or pseudo-bulges all follow the blue late-type ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV}}$ relations (Figure 2). Pseudo-bulges are typically hosted by late-type galaxies and a few early-type galaxies, while classical bulges are generally associated with early-type galaxies and massive late-type galaxies. A key point to note here is that the relatively high sSFR for pseudo-bulges coupled with the steeper dependence of SMBH masses on sSFRs for late-type galaxies likely explain why pseudo-bulges seem to obey a different M_BH − σ relation than classical bulges (e.g., Kormendy & Ho 2013). This also explains why bulgeless spirals and low-mass spirals are offset from the M_BH − L_Bulge, M_BH − M_*,Bulge, and M_BH − σ relations defined by the massive early- and late-type galaxies, as reported in the literature (e.g., Greene et al. 2008, 2010, 2016; Baldassare et al. 2017, Caglar et al. 2020).

We have performed linear regression fits to the (${M}_{\mathrm{BH}},{{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$) data set by applying a Bayesian statistical inference with an MCMC technique.¹⁴ The regression fits take into account errors in M_BH and ${{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ and an additional spread that is not explained by the error bars. The MCMC runs were implemented in our work through the Stan programming language¹⁵ (e.g., Carpenter et al. 2017). In addition to the slope, intercept, and dispersion, the model parameters include "true" color and SMBH mass values. In our implementation, the observed SMBH mass upper limits were modeled by drawing samples from an asymmetric normal distribution centered around the true values, with the standard deviation having an upper wing that equals the error bar of the measurements and a lower wing with a much larger size. The regression fits thus probe a large range in SMBH masses for galaxies with SMBH upper limits. For the Bayesian analysis, we used noninformative prior distributions (e.g., Gelman et al. 2013) and confirmed that the results did not depend on the choice of the prior details.

Figure A1 shows the results of the Bayesian linear regressions. The shaded regions indicate the 95% highest density interval (HDI) for the derived fits. Note that the HDIs are not symmetric because the derived parameters exhibit skewed posterior distributions. The dotted lines mark the 1σ and 3σ intervals for the additional real dispersion that is not explained by the error bars (Figure A1). The probability distribution functions (PDFs) for these additional dispersions are not symmetrical, and the derived values exhibit 95% HDIs of 0.00 and 0.74, and 0.14 and 0.68 for the early- and late-type galaxies. For the former, the additional dispersion is not significantly different from zero, therefore the observed dispersion could be fully explained by the error bars. In contrast, an additional real dispersion is needed for the latter to explain the residuals from the fitted relation.

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In Figure A2 we show the PDF for the disparity in slope between early- and late-type ${M}_{\mathrm{BH}}-{{ \mathcal C }}_{\mathrm{UV},\mathrm{tot}}$ relations obtained by applying the linear Bayesian regression fits. The PDFs are determined using all the individual steps of the computed chains, thus avoiding any assumption about the probability distribution of the derived parameters. We find that the significance levels for rejecting the null hypothesis that both morphological types have the same slope are 1.7% and 6.7% for the FUV and NUV relations, respectively.

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Five galaxies in our sample are offset notably from the ${M}_{\mathrm{BH}}-{ \mathcal C }$ relations (Figure 2).

B.1.1. NGC 2685

B.1.2. NGC 3310

B.1.3. NGC 3368

B.1.4. NGC 4826

B.1.5. NGC 5018