Black hole scaling relations of active and quiescent galaxies: Addressing selection effects and constraining virial factors

TL;DR

This paper investigates the biases in black hole scaling relations caused by selection effects in local galaxy samples and constrains the virial factor to reconcile active and quiescent galaxy observations.

Contribution

It demonstrates that accounting for selection effects and adjusting the virial factor fvir aligns active galaxy black hole relations with intrinsic quiescent galaxy relations.

Findings

Selection effects bias quiescent galaxy black hole relations.

A virial factor of ~3.5 aligns AGN and quiescent relations.

Velocity dispersion primarily drives the Mbh-Mstar relation.

Abstract

Local samples of quiescent galaxies with dynamically measured black hole masses (Mbh) may suffer from an angular resolution-related selection effect, which could bias the observed scaling relations between Mbh and host galaxy properties away from the intrinsic relations. In particular, previous work has shown that the observed Mbh-Mstar (stellar mass) relation is more strongly biased than the Mbh-sigma (velocity dispersion) relation. Local samples of active galactic nuclei (AGN) do not suffer from this selection effect, as in these samples Mbh is estimated from megamasers and/or reverberation mapping-based techniques. With the exception of megamasers, Mbh-estimates in these AGN samples are proportional to a virial coefficient fvir. Direct modelling of the broad line region suggests that fvir~3.5. However, this results in a Mbh-Mstar relation for AGN which lies below and is steeper than the one observed for quiescent black hole samples. A similar though milder trend is seen for the Mbh-sigma relation. Matching the high-mass end of the Mbh-Mstar and Mbh-sigma relations observed in quiescent samples requires fvir~15 and fvir~7, respectively. On the other hand, fvir~3.5 yields Mbh-sigma and Mbh-Mstar relations for AGN which are remarkably consistent with the expected `intrinsic' correlations for quiescent samples (i.e., once account has been made of the angular resolution-related selection effect), providing additional evidence that the sample of local quiescent black holes is biased. We also show that, as is the case for quiescent black holes, the Mbh-Mstar scaling relation of AGN is driven by velocity dispersion, thus providing additional key constraints to black hole-galaxy co-evolution models.

Tables

Table 1. Table 1: List of the datasets used throughout this paper.

Data acronym	Method	Reference
	Active
H&K	Reverberation	Ho & Kim (2014)
MN&M	Single Epoch	Martín-Navarro & Mezcua (2018)
VdB	Single Epoch	van den Bosch (2016)
VdB	Masers	van den Bosch (2016)
G+	Masers	Greene et al. (2016)
B+	Single Epoch	Busch et al. (2014)
R&V	Single Epoch	Reines & Volonteri (2015)
B&MN	Single Epoch	Bentz & Manne-Nicholas (2018)
	Quiescent
Sa+	Dynamical	Savorgnan & Graham (2016)
K&H	Dynamical	Kormendy & Ho (2013)

Equations

$$r_{\mathrm{infl}}\equiv G{M}_{\mathrm{bh}}/{\sigma }^2.$$

$$M_{\mathrm{bh}}=f_{vir}\frac{r{\left(\Delta V\right)}^2}{G}.$$

$$\log \frac{M_{\mathrm{bh}}}{M_{\odot }}=8.54+1.18\log \left(\frac{M_{\mathrm{star}}}{10^{11}{M}_{\odot }}\right)$$

$$\log \frac{M_{\mathrm{bh}}}{M_{\odot }}=8.35+1.31\log \left(\frac{M_{\mathrm{star}}}{10^{11}{M}_{\odot }}\right),$$

$$\begin{gathered} \log \frac{M_{\mathrm{bh}}}{M_{\odot }}=7.574+1.946\log \left(\frac{M_{\mathrm{star}}}{10^{11}{M}_{\odot }}\right)-0.306 \\ \times {\left[\log \left(\frac{M_{\mathrm{star}}}{10^{11}{M}_{\odot }}\right)\right]}^2-0.011{\left[\log \left(\frac{M_{\mathrm{star}}}{10^{11}{M}_{\odot }}\right)\right]}^3, \end{gathered}$$

$$\Delta \log \frac{M_{\mathrm{bh}}}{M_{\odot }}=0.32-0.1\times \log \left(\frac{M_{\mathrm{star}}}{10^{12}{M}_{\odot }}\right).$$

$$\log \frac{M_{\mathrm{bh}}}{M_{\odot }}=8.51+5.09\left(\log \frac{{\sigma }_e}{\mathrm{km}{\mathrm{s}}^{-1}}-2.3\right),$$

$$\Delta (Y|X)\equiv \log Y-⟨\log Y|\log X⟩$$

$$\log M_{\mathrm{star},\mathrm{Bell}}=1.793+0.845\times \log M_{\mathrm{star},\mathrm{Zib}},$$

$$\sigma (R_e)={\sigma }_{\mathrm{SDSS}}(1.5")\times {\left(\frac{1.5"}{R_e}\right)}^{\gamma },$$

$$\begin{gathered} \gamma =-0.016366723+0.019136886\times n_{\mathrm{Ser}} \\ -0.0010648890\times {\left(n_{\mathrm{Ser}}\right)}^2. \end{gathered}$$

$$\frac{M_{\mathrm{star}}}{L_K}=K_0{\left(\frac{{\sigma }_e}{166\mathrm{km}{\mathrm{s}}^{-1}}\right)}^{0.45}\frac{M_{\odot }}{L_{\odot ,\mathrm{K}}}.$$

Full text

††pagerange: Black hole scaling relations of active and quiescent galaxies: Addressing selection effects and constraining virial factors– A††pubyear: 2018

1 Introduction

It has long been accepted that active galactic nuclei (AGN), the central powerhouses of the most energetic galaxies in the Universe, are powered by the release of gravitational energy during the accretion of material onto the supermassive black hole at their centres. The general consensus is that most, if not all, galaxies host a massive black hole and may go through an AGN “phase”. The latter may be self-regulating both the black hole growth and star formation in the host galaxy via some wind/jet driven feedback mechanisms (see reviews by, e.g., Shankar, 2009; Alexander & Hickox, 2012). Models predict that an AGN and its host may coevolve (e.g., Silk & Rees, 1998; Granato et al., 2004), leading to host characteristics such as galaxy bulge/total stellar mass ($M_{\rm bulge}$/$M_{\rm star}$) and/or central stellar velocity dispersion ($\sigma$) being linked to black hole mass ($M_{\rm bh}$). Probing these relations is a primary goal of modern cosmology because its understanding will be a crucial step towards a more complete view of galaxy evolution.

Many groups have quantified scaling relations between supermassive black hole masses and host galaxy properties, in the local Universe, using samples of quiescent galaxies (see, e.g., Ferrarese & Ford, 2005; Kormendy & Ho, 2013; Graham, 2016). However, Bernardi et al. (2007) showed that the $\sigma$-$M_{\rm star}$ relations defined by quiescent black hole samples differs from that defined by the bulk of the galaxies in the Sloan Digital Sky Survey (York et al., 2000, hereafter SDSS). van den Bosch et al. (2015) and Shankar et al. (2016) confirmed that quiescent samples are biased towards dense galaxies. As a result, it has been suggested that measurements of the $M_{\rm bh}$ scaling relations in these samples may be severely biased (e.g., Bernardi et al., 2007; Gültekin et al., 2009; Batcheldor, 2010; Morabito & Dai, 2012; Shankar et al., 2016).

In these galaxies, $M_{\rm bh}$ is estimated from the dynamics of stars near the black hole “sphere of influence” (e.g., Merritt & Ferrarese, 2001a)

[TABLE]

Since $r_{\rm infl}$ is small (order of parsecs), insufficient resolution prevents reliable black hole mass estimates or forces to target only the largest black holes, possibly leading to a selection bias. Shankar et al. (2016) used Monte Carlo simulations to show that this resolution-related selection effect has the potential to artificially increase the normalization of the $\sigma$-$M_{\rm star}$ and $M_{\rm bh}$-$\sigma$ relation by a factor of a few, and the $M_{\rm bh}$-$M_{\rm star}$ by an order of magnitude or more. Indeed, this selection effect alone can go a long way towards explaining why, to date, pulsar timing arrays have failed to detect any gravitational waves from supermassive black hole mergers (Sesana et al., 2016).

To gather more robust constraints on black hole-galaxy coevolution models, it is thus necessary to analyse samples that do not suffer from this resolution-related selection effect. In active galaxies, $M_{\rm bh}$ can be estimated spectroscopically from the kinematics of the broad line region or gas orbiting around the very inner regions around the central black hole (e.g., Ferrarese & Ford, 2005). However, except for masers for which black hole masses can be inferred from rotation curves (e.g., Ferrarese & Ford, 2005), for the vast majority of (Type 1) AGN, black hole masses are derived from the (presumed) virial motions of the broad line region gas cloud orbiting in the vicinity of the central compact object:

[TABLE]

In Equation 2, $r$ is the radius of the broad line region (BLR), which is derived from reverberation mapping (e.g., Blandford & McKee, 1982; Peterson, 1993), or reverberation-based methods that make use of the radius-luminosity relation (e.g., Bentz et al., 2006). The characteristic velocity $\Delta V$ is derived from the width of the emission lines (a common one is H$\beta$), and $G$ is the gravitational constant. As motions in the BLR are not perfectly Keplerian, a parameter $f_{vir}$ is included in Equation 2 to account for the uncertainties in kinematics, geometry and inclination of the clouds (e.g., Ho & Kim, 2014, and references therein). Systematically different values of $f_{vir}$ can be found if the virial masses (based on reverberation mapping campaigns) are computed using the full width at half maximum or dispersion of the emission line (e.g., Onken et al., 2004; Collin et al., 2006). In what follows, we will always refer to $f_{vir}$ as the virial factor calibrated on the line dispersion (i.e., second moment of the line profile) of H$\beta$ (e.g., Peterson et al., 2004).

A reasonable guess for $f_{vir}$ is obtained by matching the AGN black hole scaling relations to those of inactive black holes. Typical values for line dispersion-based $f_{vir}$ derived from the match to the $M_{\rm bh}$-$\sigma$ relation of quiescent black holes are in the range $f_{vir}\sim 4-5$ (e.g., Onken et al., 2004; Woo et al., 2010a; Grier et al., 2013; Batiste et al., 2017, and references therein). Although lower values for $f_{vir}$ have also been claimed (Graham et al., 2011), Ho & Kim (2014) invoke larger values, $f_{vir}\sim 6-10$, when comparing AGN in classical bulges to the quiescent sample of Kormendy & Ho (2013). In cases in which the BLR structure and dynamics have been modelled directly, the virial coefficient can be constrained directly from the data. Following the geometric and dynamic modelling put forward by Pancoast et al. (2014), Grier et al. (2017) have fitted the line dispersion of the H$\beta$ emission-line spectra of four sources finding a mean $f_{vir}\sim 3.5$ ($\log f_{vir}=0.54\pm 0.17$). Williams et al. (2018) have more recently confirmed an average value of $f_{vir}\sim 3.7$ ($\log f_{vir}=0.57\pm 0.19$) when fitting the H$\beta$ line dispersion of another seven AGN. The latter values are systematically lower than those found by, e.g, Ho & Kim (2014). Clearly, to date, there is no consensus on the best value of $f_{vir}$ for weighing black holes in AGN.

To use AGN as reliable probes of black hole-galaxy scaling relations, more secure determinations of $f_{vir}$ are required. The main aim of this work is to take a step in this direction. To this end, we analyse scaling relations in a variety of local AGN samples, so as to probe their level of bias with respect to a larger sample of local galaxies from the SDSS. We briefly describe how we homogenize the samples in Section 2, and provide full details in Appendix A. Section 3 presents scaling relations of the properties of the galaxies which host AGN – to address the question of whether these are a biased subset – before considering scaling relations with $M_{\rm bh}$ and their implications for $f_{vir}$. It should be noted in fact that, since resolution-related selection effects have a stronger impact on the quiescent $M_{\rm bh}$-$M_{\rm star}$ relation rather than on the $M_{\rm bh}$-$\sigma$ one (Shankar et al., 2016), if such selection effects are present, systematically different mean values of $f_{vir}$ should be derived when calibrating AGN samples against the $M_{\rm bh}$-$\sigma$ or the $M_{\rm bh}$-$M_{\rm star}$ relations of local inactive black hole samples. In this work we show that such a systematic offset in $f_{vir}$ is indeed present, but the offset can be removed by accounting for the resolution-related selection effect.

Throughout we adopt $h=0.7$, $\Omega_{m}=0.3$, $\Omega_{\Lambda}=0.7$ for the SDSS sample. All AGN samples considered here have black holes and host galaxy properties derived assuming identical or very similar cosmological parameters111The largest offset is found for the Ho & Kim (2014) sample who adopt $h=0.705$ and $\Omega_{m}=0.27$ for calibrating distances, which anyway induce only $\sim 0.5\%$ difference in distances at the redshifts of interest here..

2 Homogenizing different data sets

In this work we consider a number of serendipitous local AGN samples. These were collected at different flux limits and with different host galaxy morphologies. Therefore, it is important to homogenize them so that their $M_{\rm star}$ and $M_{\rm bh}$ values can be meaningfully compared. We clarify that throughout this paper $M_{\rm star}$ always refers to the total stellar mass of a galaxy, while $M_{\rm bulge}$ refers to its bulge stellar mass.

For our study, we correct all total stellar mass estimates so they correspond to $M_{\rm star}/L$ from Bell et al. (2003a) and a Chabrier (Chabrier, 2003) IMF, since this was the choice made by Shankar et al. (2016) in their study of the intrinsic (i.e., unbiased) black hole scaling relations. We make use of velocity dispersions222Unless otherwise noted, throughout this work $\sigma$ always refers to the velocity dispersion within one effective radius $R_{e}$, $\sigma_{e}\equiv\sigma(R_{e})$. $\sigma=\sigma_{e}=\sigma(R_{e})$ measured within the galaxy optical effective radius $R_{e}$. For the quiescent and some active black hole samples, we correct velocity dispersions measured within an aperture of radius $R$ to the value they are expected to have within an aperture of one effective radius using the Sérsic index-dependent correction $\sigma(R_{e})\propto(R/R_{e})^{\gamma(n_{\rm Ser})}$ (Bernardi et al., 2017b). Finally, if not otherwise specified (as for the sample from Martín-Navarro & Mezcua 2018), wherever relevant we assume $f_{vir}=3.5$, following the Lick Monitoring Project (Walsh et al., 2009) and the latest results of Grier et al. (2017) and Williams et al. (2018) when adopting the H$\beta$ line dispersion. The Appendix provides details of these corrections for the different samples we use. A list of the datasets considered in this work is given in Table 1.

3 Results

3.1 The $\sigma$-$M_{\rm star}$ relation of active galaxies

The first step of our analysis is to compare the $\sigma$-$M_{\rm star}$ relation of the different AGN samples among themselves and with that of a much larger sample of galaxies from the SDSS. The purpose of this check is twofold. First we ensure that, at least for the AGN samples with available (total) stellar mass and velocity dispersion measurements, the homogenizing corrections mentioned in Section 2, and expanded in Appendix A, provide consistent results. Second, we probe by how much, if at all, active host galaxies differ in terms of stellar mass and/or velocity dispersion from the general population of SDSS galaxies. In fact, as mentioned in Section 1, Bernardi et al. (2007) and Shankar et al. (2016) showed that local inactive galaxies with dynamical black hole mass measurements (open black and red squares and brown triangles in Figure 1) tend to have, on average, larger velocity dispersions compared to counterpart galaxies in the SDSS. This behaviour can be in large part explained by the selection effect imposed by limited telescope resolution power, which forces to preferentially target more massive black holes, predominantly hosted in galaxies with larger velocity dispersions (Shankar et al., 2016, 2017; Barausse et al., 2017).

Figure 1 shows333For simplicity, in this and in all subsequent Figures, to distinguish them from masers (labelled as “mas”), we label as “rev” all AGN samples in which black hole masses are based on direct reverberation mapping or reverberation-based (i.e., single-epoch virial) techniques. that reassuringly, after applying the proper homogenizing corrections in stellar mass and velocity dispersion, almost all the classical and pseudobulges from Ho & Kim (2014, filled red circles and green squares, respectively), the megamasers from Greene et al. (2016, filled cyan stars), and the active galaxies in the van den Bosch (2016, blue diamonds and cyan circles for reverberation-based and masers AGN, respectively) sample, fall within the scatter (see also Grier et al. 2013, their Figure 4, for a similar result) of the SDSS velocity dispersion-stellar mass relation (magenta long-dashed and dotted lines). For the SDSS galaxies we adopt the latest rendition of the Meert et al. (2015) galaxy sample, with light profiles extracted from Sérsic+exponential models and mass-to-light ratios from Mendel et al. (2013). We increase all stellar masses by an average 0.05 dex (see Figure A2 in Bernardi et al. 2017a) to account for the (small) difference at high stellar masses with the Bell et al. (2003b) mass-to-light ratios used by Shankar et al. (2016) and adopted as a reference in this work. Some of the lower mass pseudobulges from Ho & Kim (2014, green squares) and all the low-mass Seyferts from Martín-Navarro & Mezcua (2018, orchid upside down triangles) tend to have, on average, somewhat lower velocity dispersions at fixed stellar mass by $\lesssim 0.05-0.1$ dex, better lining up, as expected, with the SDSS $\sigma$-$M_{\rm star}$ relation of later-type galaxies (brown dashed line). The latter was calibrated out of the subsample of SDSS galaxies with a high probability $P$(Scd) $>0.7$ of being classified as late spirals according to the Bayesian automated classification of Huertas-Company et al. (2011).

In the right panel of Figure 1 we also include the black hole sample444We slightly correct the stellar masses in the Kormendy & Ho (2013) sample to match the $K$-band mass-to-light ratios to convert from dynamical to stellar masses and the same IMF (see text after Equation 12). Velocity dispersions are also corrected from $0.5R_{e}$ to $R_{e}$ following Cappellari et al. (2006). We note that such corrections are relatively small and, if neglected, would further exacerbate the tension between the Kormendy & Ho (2013) sample and the SDSS and van den Bosch (2016) galaxies. of elliptical galaxies from Kormendy & Ho (2013, red open squares). First off, it is relevant to note that the Kormendy & Ho (2013) ellipticals broadly overlap with the early-types from the Savorgnan & Graham (2016, open black squares) black hole sample and lie substantially above the mean $\sigma$-$M_{\rm star}$ relation of SDSS galaxies. Shankar et al. (2016) also showed that other samples of black holes in inactive galaxies (Beifiori et al., 2012; McConnell & Ma, 2013; Läsker et al., 2014) lie systematically above the SDSS $\sigma$-$M_{\rm star}$ relation, further supporting the view that such a mismatch is not a result of different choices in stellar mass calibrations and/or apertures, but an underlying selection effect affecting the sample of black holes in local inactive galaxies with dynamical mass measurement. It is particularly meaningful to compare the Kormendy & Ho (2013) ellipticals with the van den Bosch (2016) sample. Both samples adopt exactly the same mass-to-light ratio and span a similar range in stellar mass $10\lesssim\log M_{\rm star}/M_{\odot}\lesssim 11.5$, yet the Kormendy & Ho (2013) data points are placed at significantly larger velocity dispersions. Whilst some of the offset between the two samples can be ascribed to simple morphological segregation, being the van den Bosch (2016) AGN sample dominated by Seyfert-like galaxies which tend to be characterised by lower velocity dispersions (see left panel), still this effect is on average relatively small to account for the full offset. Within the SDSS later-type galaxies, in fact, only Scd galaxies tend to show a moderate offset of $\sim 0.1$ dex in velocity dispersion at fixed stellar mass with respect to the full SDSS galaxy population (left panel). On the other hand, Sab galaxies, which are much more common among (especially Type 1) Seyferts (e.g., Chen & Hwang, 2017), share, we checked, a very similar $\sigma$-$M_{\rm star}$ relation to the general population.

All in all, from Figure 1 we conclude that the samples of AGN considered in this work are not biased in terms of their velocity dispersions and stellar masses when compared to the SDSS galaxies. In this respect, being more faithful tracers of the local galaxy population, AGN samples appear as a more robust “training set” to probe the underlying scaling relations between black holes and their host galaxies. The systematic discrepancies, which we will discuss below, between the scaling relations of active and quiescent galaxies in view of Figure 1 should be mostly ascribed to selections rather than to physical effects. In the framework of the selection effects discussed above, if galaxies are offset in the SDSS $\sigma$-$M_{\rm star}$ relation, they should show a higher degree of bias in the $M_{\rm bh}$-$M_{\rm star}$ relation rather than in the $M_{\rm bh}$-$\sigma$ relation. As in fact evidenced from the Monte Carlo simulations by (Shankar et al., 2016), selecting sources with larger $\sigma$, above the mean $\sigma$-$M_{\rm star}$ correlation, would naturally correspond to substantially more massive black holes, due to the steepness and tightness of the underlying $M_{\rm bh}$-$\sigma$ relation. At fixed velocity dispersion the effect of the bias would be less prominent as correlations with the variable on which the selection was made (in this case $\sigma$) will naturally be less biased. However, the AGN samples considered in this work, which share a similar $\sigma$-$M_{\rm star}$ relation to SDSS galaxies, should present self-consistent black hole scaling relations in terms of velocity dispersion and stellar mass. We will show below that this is indeed the case.

Bentz & Manne-Nicholas (2018) have recently pointed out that the presence of bars in many local galaxies could induce a bias in the SDSS galaxy sample itself. Indeed the number of bars in the SDSS galaxies is significant (e.g., Consolandi, 2016). Bars, as also pointed out by Shankar et al. (2016), may increase velocity dispersions at fixed stellar mass (see also Graham et al. 2011 and Batiste et al. 2017). Nevertheless, even if such an effect is present, this would imply an intrinsic/unbiased SDSS $\sigma$-$M_{\rm star}$ relation lower in normalization than what plotted in Figure 1, which would exacerbate the tension with the local sample of black holes in quiescent galaxies. The good match with the AGN hosts tends to either disfavour the presence of a strong bar-induced bias in SDSS galaxies, or points to a similar fraction of barred galaxies among the different samples.

3.2 The $M_{\rm bh}$-$M_{\rm star}$ relation of local active galaxies

In each panel of Figure 2 we report the $M_{\rm bh}$-$M_{\rm star}$ relation from Shankar et al. (2016) of quiescent black holes as extracted from the Savorgnan & Graham (2016) sample with updated black hole masses from Kormendy & Ho (2013), and (total) stellar masses from full bulge-disc decompositions and 3.6 $\mu$m mass-to-light ratios $(M/M_{\odot})/(L/L_{\odot})=0.6$ from Meidt et al. (2014). The black open squares and brown triangles represent, as in Figure 1, early and late type galaxies, respectively. As discussed in Shankar et al. (2016), we retain from the original Savorgnan & Graham (2016) sample only the galaxies with secure black hole mass measurements and remove those sources classified as ongoing mergers, limiting the final sample to 48 galaxies out of which 37 are early-type galaxies (ellipticals or lenticulars). The black long-dashed and dotted lines are, respectively, the linear fits to the Savorgnan & Graham (2016) early type and full sample, respectively

[TABLE]

and

[TABLE]

while the grey area (corresponding to a scatter of $0.5$ dex) broadly brackets the uncertainty region around the observed $M_{\rm bh}$-$M_{\rm star}$ observed in local early-type quiescent galaxies. For completeness, we also plot the elliptical galaxies from the original Kormendy & Ho (2013, open red squares) sample which all lie within, if not even above, the grey band. We indeed verified that all the local quiescent black hole samples considered by Shankar et al. (2016) fall within the grey band.

The solid red line is instead the intrinsic/unbiased (or debiased) black hole mass versus total stellar mass ($M_{\rm bh}$-$M_{\rm star}$) relation proposed by Shankar et al. (2016)

[TABLE]

with a mass-dependent intrinsic scatter (yellow region) given by

[TABLE]

(Equation 5 is applicable to galaxies with stellar mass above $\log M_{\rm star}/M_{\odot}>10$). The Shankar et al. (2016) relation (labelled as “intrinsic”) is significantly lower in normalization and steeper than the relation that would be inferred by directly fitting the Savorgnan & Graham (2016) data (long-dashed and dotted lines). This different shape in the intrinsic $M_{\rm bh}$-$M_{\rm star}$ relation mainly reflects the curvature in the $\sigma$-$M_{\rm star}$ relation (Figure 1), and the fact that the black hole mass is tightly related to velocity dispersion. We note that, strictly speaking, the unbiased relation put forward by Shankar et al. (2016) has been calibrated against the SDSS early-type galaxies, and thus it should be preferentially compared to the black long-dashed line. Nevertheless, late-type galaxies become progressively subdominant at stellar masses $\log M_{\rm star}/M_{\odot}\gtrsim 10.5$ (e.g., Bernardi et al., 2013), and if included they would tend, if anything, to decrease the mean velocity dispersions by $\lesssim 0.05$ dex at the stellar masses considered in this work. In turn, the unbiased $M_{\rm bh}$-$M_{\rm star}$ relation would then be proportionally lower at fixed host stellar mass, thus further increasing the mismatch with the scaling relation of quiescent galaxies. In what follows we will thus continue to safely consider the yellow band as the region encompassing the intrinsic $M_{\rm bh}$-$M_{\rm star}$ relation of the full local central black hole population hosted in relatively massive galaxies.

It should be noted that in Figure 2 we include all the AGN data sets detailed in Appendix A. In the upper panels we include the classical and pseudobulges reverberation-based black hole masses from Ho & Kim (2014, filled red circles and green squares, respectively) and the low-mass Seyferts from Martín-Navarro & Mezcua (2018, orchid upside down triangles), in the middle panels the the megamasers from Greene et al. (2016, filled cyan stars), and the virial-based (i.e., single epoch) and masers from van den Bosch (2016, blue diamonds and cyan circles for reverberation-based and masers AGN, respectively), and in the lower panels the virial-based black holes in low-luminosity quasars from Busch et al. (2014, red filled squares), the virial-based AGN from Bentz & Manne-Nicholas (2018, purple circles), and the SDSS virial-based AGN from Reines & Volonteri (2015, green upside down triangles).

It is clear from the left panels of Figure 2 that when adopting a uniform virial factor of $f_{vir}=3.5$, as independently calibrated by Grier et al. (2017) and Williams et al. (2018) via direct broad line region modelling, the vast majority of the data tend to lie on average within the yellow band of Shankar et al. (2016). However, we stress that the latter is not a fit to the AGN samples. Indeed, some of the data sets present larger scatter than what implied by the yellow band, as evident for example in the Martín-Navarro & Mezcua (2018) and Reines & Volonteri (2015) sources. The Reines & Volonteri (2015) and van den Bosch (2016) samples also tend to be better fitted by a linear relation between black hole and stellar mass, somewhat flatter than the nearly quadratic one suggested by Equation 5. On the other hand, the Bentz & Manne-Nicholas (2018) sources are consistent with a similarly steep relation. It is worth noticing that some among the most massive ($M_{\rm star}\gtrsim 10^{11}\,M_{\odot}$) sources in Bentz & Manne-Nicholas (2018) lie above Equation 5, lining up with the observed $M_{\rm bh}$-$M_{\rm star}$ relation, though however the sample taken as a whole still points to an average lower $M_{\rm bh}$-$M_{\rm star}$ scaling relation. We note that Bentz & Manne-Nicholas (2018)’s choice of limiting the Sérsic index to $n_{\rm Ser}\leq 4$ could lead to underestimate the luminosities of their most massive galaxies which are usually characterized in SDSS by progressively higher Sérsic indices (e.g., Bernardi et al., 2014). In this respect, it is worth stressing that all the galaxies in the Busch et al. (2014) sample, which is a mixture of early- and late-type galaxies, all lie significantly below the observed scaling relations.

An average virial factor of $f_{vir}=3.5$ seems insufficient to reconcile active black holes to the scaling relations observed for quiescent black holes (black lines). As shown in the right panels of Figure 2, we would in fact need to increase the virial factor by more than an order of magnitude, e.g. $f_{vir}\gtrsim 15$, in order to be roughly consistent with the observed $M_{\rm bh}$-$M_{\rm star}$ relations (black dotted and long-dashed lines), at least around $\log M_{\rm star}/M_{\odot}\gtrsim 11$. At lower stellar masses the AGN data would require even higher virial factors due to the stronger steepness of their $M_{\rm bh}$-$M_{\rm star}$ relation. A more quantitative analysis of the appropriate virial factors needed to match the scaling relations of quiescent black holes will be presented in Section 3.4.

It is worth noticing that when increasing the virial factor only the virial-based black hole masses are proportionally varied but not the ones based on independent maser measurements. This creates a systematic discrepancy which is evident in the middle, right panel of Figure 2 between the masers by Greene et al. (2016, cyan stars) and van den Bosch (2016, cyan circles) with the virial-based black holes from the same van den Bosch (2016, blue diamonds) sample. This offset is not present when $f_{vir}=3.5$ is adopted (middle left panel), thus lending further support to the presence of a bias in inactive black holes.

Last but not least, in line with local quiescent black holes, all the AGN data sets considered in this work lack low black hole masses in massive hosts. The existence of a finite (though possibly large) scatter in the local scaling relations supports the view of an underlying black hole-host galaxy correlation (a “ridge” as labelled by Shankar et al. 2016), and disfavours the idea that local black hole-host scaling relations mark the upper envelope of a uniform distribution of black hole masses (e.g., Batcheldor, 2010).

3.3 The $M_{\rm bh}$-$\sigma$ relation of local active galaxies

In Figure 3 we present a similar comparison between quiescent and active galaxies as in Figure 2 but for the $M_{\rm bh}$-$\sigma$ relation. The open black squares and brown triangles are the early and late galaxies by Savorgnan & Graham (2016) with velocity dispersions originally taken from Hyperleda database (Paturel et al., 2003) with a nominal aperture of $0.595$ kpc. We thus correct via Equation 11 all their velocity dispersions to an aperture equal to one effective radius, with effective radii also self-consistently measured by Savorgnan & Graham (2016). A direct linear fit (see Appendix A in Shankar et al. 2017) to the quiescent early-type sample yields (black long-dashed line)

[TABLE]

with a scatter around $\sim 0.4$ dex (grey region). Equation 7 is close in both slope and normalization to Equation 5 in Kormendy & Ho (2013). The fit to the early-type black hole population is very similar (black long-dashed line) as both early- and late-type galaxies are less scattered in the $M_{\rm bh}$-$\sigma$ relation (e.g., van den Bosch, 2016, and references therein). The Monte Carlo simulations by Shankar et al. (2016) have revealed that assuming an underlying basic selection bias in the gravitational sphere of the central black hole yields an observed $M_{\rm bh}$-$\sigma$ offset from the intrinsic/unbiased one by $\sim 0.5$ dex but with a similar slope, if the intrinsic scatter is $\lesssim 0.3$ dex (their Figure 9). For our reference intrinsic/unbiased $M_{\rm bh}$-$\sigma$ relation we thus choose to adopt Equation 7 simply lowered in normalization by 0.5 dex (solid red line and yellow region). For completeness, as in previous Figures, we also report in Figure 3 the elliptical sample of Kormendy & Ho (2013, open red triangles) which are fully consistent with the observed $M_{\rm bh}$-$\sigma$ relation from the Savorgnan & Graham (2016) sample of quiescent galaxies (black lines).

Following the format of Figure 2, retaining the AGN samples for which we have published velocity dispersions, in the upper panels of Figure 3 we include the classical and pseudobulges reverberation-based black holes from Ho & Kim (2014, filled red circles and green squares, respectively) and the virial-based low-mass Seyferts from Martín-Navarro & Mezcua (2018, orchid upside down triangles), in the lower panels the megamasers from Greene et al. (2016, filled cyan stars), and the virial-based black holes and masers from van den Bosch (2016, blue diamonds and cyan circles for reverberation-based and masers AGN, respectively). In the left panels we assume a uniform virial factor $f_{vir}=3.5$ and $f_{vir}=8$ in the right panels. It is evident that, at least for galaxies with velocity dispersions above $\log\sigma/\rm km\,s^{-1}\gtrsim 1.9$, the former provides a better match to the unbiased relation, while the latter to the observed relation. More quantitative estimates of the appropriate virial scaling factors are given in Section 3.4. Above $\log\sigma/\rm km\,s^{-1}\gtrsim 1.9$, active black holes tend to follow a $M_{\rm bh}$-$\sigma$ relation similar in slope to the quiescent samples, in line with what also claimed by Woo et al. (2013b). At lower velocity dispersions, below $\log\sigma/\rm km\,s^{-1}\lesssim 1.9$, the Martín-Navarro & Mezcua (2018, orchid upside down triangles in the upper panels) sample tends to flatten out, as already noted by Martín-Navarro & Mezcua (2018), and also tend to become more scattered. Baldassare et al. (2016) on the other hand found that the lowest mass galaxies with AGN signatures in their sample fall within the extrapolations of the $M_{\rm bh}$-$\sigma$ of quiescent black holes. The main conclusions of this work anyway hold for galaxies with $\log\sigma/\rm km\,s^{-1}\gtrsim 1.9$, i.e. with stellar masses $\log M_{\rm star}/M_{\odot}\gtrsim 10$ according to the mean $\sigma$-$M_{\rm star}$ relation of SDSS galaxies (long-dashed line in Figure 1). The data on both active and quiescent galaxies become much more sparse below this threshold.

3.4 A distinct virial factor $f_{vir}$ for the observed $M_{\rm bh}$-$M_{\rm star}$ and $M_{\rm bh}$-$\sigma$ relations

In the previous sections we found that assuming an underlying virial factor of $f_{vir}=3.5$ provides a reasonable match to both the unbiased $M_{\rm bh}$-$M_{\rm star}$ and $M_{\rm bh}$-$\sigma$ relations put forward by Shankar et al. (2016). On the other hand, larger values of $f_{vir}$ are required to broadly match the observed scaling relations of black holes in quiescent galaxies. In particular, there is evidence for the need of a particularly large $f_{vir}$ when comparing with the observed $M_{\rm bh}$-$M_{\rm star}$ relation (right panels of Figure 2). In Figure 4 we provide a more thorough investigation into the distributions of virial factors $f_{vir}$ required to match both the observed (upper panels) and unbiased (lower panels) relations. For this purpose we choose the two reverberation-based data sets of classical/pseudobulges by Ho & Kim (2014, red solid lines) and the virial-based AGN by van den Bosch (2016, blue long-dashed lines). Both samples share a broad coverage in stellar mass and velocity dispersion, and are not biased with respect to the $\sigma$-$M_{\rm star}$ relation of SDSS galaxies (Figure 1). For each AGN sample and a given input $f_{vir}$ we then perform a linear fit to the $M_{\rm bh}$-$\sigma$ and $M_{\rm bh}$-$M_{\rm star}$ relations and compute their offsets with respect to the analogous relations for quiescent galaxies. Our methodology, which is slightly different from the one put forward by, e.g., Onken et al. (2004, their Equation 3), allows to determine the offsets between the active and quiescent populations in a given bin of stellar mass or velocity dispersion, particularly relevant when the slopes tend to be different, as in the $M_{\rm bh}$-$M_{\rm star}$ plane (Figure 2).

The left panels of Figure 4 show the displacement in $\log M_{\rm bh}$ between the $\log M_{\rm bh}-\log M_{\rm star}$ relation of quiescent and active galaxies computed at $\log M_{\rm star}/M_{\odot}=11$ as a function of the virial factor $f_{vir}$. Both samples suggest that, in agreement with Figure 2, only virial factors $f_{vir}\gtrsim 15$ tend to align the AGN with the quiescent galaxies within $\Delta\log M_{\rm bh}\lesssim 0.1$ dex in the $M_{\rm bh}$-$M_{\rm star}$ relation. The reference virial factor of $f_{vir}=3.5$ (vertical magenta dotted lines in Figure 4), in particular, would generate an offset of $\Delta\log M_{\rm bh}\sim 0.8$ dex, in order for the reverberation/virial-based AGN to line up to the relation observed in quiescent ellipticals. Note that we deliberately chose to compute the displacements at relatively high stellar masses $\log M_{\rm star}/M_{\odot}=11$ as at lower masses the match would require even higher $f_{vir}$ to bring AGN in line with the relation of quiescent galaxies, being the former steeper than the latter (see Section 3.2). In the right panels of Figure 4 we instead plot as a function of the virial factor $f_{vir}$ the displacement in $\log M_{\rm bh}$ between the $\log M_{\rm bh}-\log\sigma$ relation of quiescent and active galaxies computed at $\log\sigma/\rm km\,s^{-1}=2.2$, which is the mean velocity dispersion roughly corresponding to $\log M_{\rm star}/M_{\odot}=11$, following the SDSS $\sigma$-$M_{\rm star}$ relation (Figure 1). In this case the match between AGN and quiescent galaxies within $\Delta\log M_{\rm bh}\lesssim 0.1$ dex in the $M_{\rm bh}$-$\sigma$ relation is reached for $f_{vir}\gtrsim 7$, roughly a systematic factor of two lower than the $f_{vir}$ required to match the $M_{\rm bh}$-$M_{\rm star}$ relation.

This systematic difference in virial factors can be easily interpreted within, and in fact taken in support of, the framework of the selection bias considered by Shankar et al. (2016). As discussed with respect to Figure 1, this bias induces the selection of sources with velocity dispersions on average higher than regular counterpart SDSS galaxies of similar stellar mass. In turn, higher velocity dispersions would imply selecting on average higher mass black holes, given the strong dependence $M_{\rm bh}\propto\sigma^{4-5}$. Ultimately, this selection bias is expected to artificially increase the normalization of the black hole scaling relations, in particular of the $M_{\rm bh}$-$M_{\rm star}$ relation which is a direct reflection of the $\sigma$-$M_{\rm star}$ relation. In practise, the presence of such a bias requires a mean $f_{vir}$ factor systematically higher, by at least a factor of two, in the $M_{\rm bh}$-$M_{\rm star}$ than in the $M_{\rm bh}$-$\sigma$ relation. On the other hand, the same virial factors of $f_{vir}\sim 3-4$ are consistent with both the intrinsic relations within $\lesssim 0.1$ dex uncertainty (bottom panels of Figure 4). A $f_{vir}\sim 3-4$ also do not show the discrepancy between the masers and the reverberation-based black holes which appears instead when a higher $f_{vir}$ is adopted (compare the cyan stars and cyan circles in the middle, right panel of Figure 2).

3.5 Residuals in the active black hole scaling relations

It has been discussed by a number of groups (Bernardi et al., 2007; Shankar et al., 2016; van den Bosch, 2016; Barausse et al., 2017; Shankar et al., 2017) that velocity dispersion is a galactic property linked to black hole mass more fundamentally in terms of residuals than any other one, including stellar/bulge mass, light profile concentration, or effective radius. Residuals in pairwise correlations (Sheth & Bernardi, 2012) are in fact an effective methodology to probe underlying relations among variables. The left and right panels of Figure 5 report the $\Delta(M_{\rm bh}|M_{\rm bulge})$ vs $\Delta(\sigma|M_{\rm bulge})$ and $\Delta(M_{\rm bh}|\sigma)$ vs $\Delta(M_{\rm bulge}|\sigma)$, where

[TABLE]

is the residual in the $Y$ variable (at fixed $X$) from the log-log-linear fit of $Y(X)$ vs $X$, i.e. $\langle\log Y|\log X\rangle$.

For this test, analogously to what performed in Figure 4, we make use of the reverberation-based Ho & Kim (2014) and virial-based van den Bosch (2016) samples which share a broad coverage in stellar mass and velocity dispersion and are not biased with respect to the $\sigma$-$M_{\rm star}$ relation of SDSS galaxies. For the Ho & Kim (2014) sample in particular, we show results using bulge rather than total stellar masses, being the former more physically related to central velocity dispersion. We assume a constant $f_{vir}=3.5$ for all sources in both samples. To produce residuals we follow the procedure outlined in Shankar et al. (2016) and Shankar et al. (2017). For each residual we run 200 iterations, and at each iteration we eliminate two random objects from the original sample. From the full ensemble of realizations, we measure the mean slope and its 1$\sigma$ uncertainty.

Figure 5 clearly shows that black hole mass is strongly correlated with velocity dispersion at fixed bulge stellar mass with a Pearson coefficient $r=0.65$ (top left panel), while the correlation with bulge mass is negligible with $r=0.16$ at fixed velocity dispersion (right top panel). When computing residuals for only classical bulges (red circles, middle panels), the correlation with velocity dispersion becomes even more marked with a Pearson coefficient of $r=0.74$ while the one with bulge mass further decreases to $r=0.13$. Adopting total stellar masses in the Ho & Kim (2014) sample and/or their original values for $f_{vir}$ would produce even stronger residuals with velocity dispersion, further corroborating our results. The lower panels of Figure 5 show that the residuals extracted from the reverberation-based sample from van den Bosch (2016) still point to strong correlation with velocity dispersion ($r=0.68$) and a negligible one with (total) stellar mass ($r=0.06$).

These findings fully confirm and extend to local AGN the dominance of velocity dispersion in pairwise scaling relations put forward by Bernardi et al. (2007) and Shankar et al. (2016) for local quiescent black holes. The total slope of the $M_{\rm bh}$-$\sigma$ relation in AGN can be estimated as $M_{\rm bh}\propto\sigma^{\beta}M_{\rm star}^{\alpha}\propto\sigma^{\beta+\alpha\,\gamma}$, where $\gamma$ comes from $M_{\rm star}\propto\sigma^{\gamma}$. Since SDSS galaxies tend towards $\gamma\approx 2.2$ (Shankar et al., 2017), and the residuals in Figure 5 yield $\beta\sim 4-5$ and $\alpha\sim 0.1-0.2$, one obtains a total dependence of $M_{\rm bh}\propto\sigma^{4.2-5.5}$, consistent with models of black hole growth being regulated by energy/momentum-driven AGN feedback (e.g., Silk & Rees, 1998; Fabian, 1999; King, 2003; Granato et al., 2004).

4 Discussion and Conclusions

The first result of the present work is that the samples of local ($z<0.3$) AGN considered here with measured velocity dispersions and stellar masses are consistent, on average, with those from the SDSS galaxies (Figure 1). This is in stark contrast to samples of quiescent black holes, which are biased with respect to the full SDSS sample (Bernardi et al., 2007; Shankar et al., 2016). The second result concerns the factor $f_{vir}$ that is adopted to normalise black hole masses in reverberation-based AGN samples (e.g., Peterson, 1993). Values of order $f_{vir}\sim 15$ are required to match the selection-biased $M_{\rm bh}$-$M_{\rm star}$ relation of quiescent galaxies, whereas $f_{vir}\sim 3.5$, as derived from direct modelling of the broad line region (e.g., Williams et al., 2018, and references therein), is required to match the Shankar et al. (2016)’s estimate of the intrinsic relation for quiescent galaxies (Figure 2). Water masers, with black hole masses independent of any virial factor, also fall within the scatter of the unbiased relations by Shankar et al. (2016, cyan symbols in Figures 2 and 3).

A number of other groups had also found significant discrepancies between AGN samples, with virial factors $f_{vir}$ calibrated against some renditions of the $M_{\rm bh}$-$\sigma$ relation, and the observed $M_{\rm bh}$-$M_{\rm star}$ relation of quiescent black holes (e.g., Busch et al., 2014; Dasyra et al., 2007; Kim et al., 2008; Sarria et al., 2010; Falomo et al., 2014; Reines & Volonteri, 2015; Greene et al., 2016; Bentz & Manne-Nicholas, 2018), though without offering a convincing explanation for the nature of this puzzling offset. Reines & Volonteri (2015), in particular, carried out a detailed work to compare one of the largest local samples of broad-line AGN (244 sources) with virial black hole mass estimates, with the samples of quiescent galaxies from Kormendy & Ho (2013), as (re)proposed in the bottom panels of our Figure 2. After applying appropriate corrections to different total stellar mass estimates, they concluded that the substantial discrepancy ($\sim 1.2$ dex) in the normalization between the active and quiescent samples cannot be ascribed to only measurement errors. Indeed, they found that reconciling the two samples would require average virial factors of the order of $f_{vir}\gtrsim 40$, which is significantly beyond the typical uncertainties in $f_{vir}$. Bennert et al. (2011) also found evidence for a mean discrepancy between local active and inactive galaxies in terms of spheroidal luminosity (left upper panel of their Figure 17), though it tends to disappear when converting to stellar masses (middle upper panel of their Figure 17) most probably due to their specific choices of mass-to-light ratios.

We are thus not the first to report on an apparent discrepancy between scaling relations of active and quiescent local black hole samples (e.g., Reines & Volonteri, 2015). However, our work offers new insights into the origin of this discrepancy. In particular, it highlights the important role played by angular resolution-related selection effects on the quiescent sample. We showed in fact that the mean $f_{vir}$ required to match the selection-based $M_{\rm bh}$-$M_{\rm star}$ relation of quiescent black holes is systematically higher by a factor $\sim 2-3$ than that needed to match the $M_{\rm bh}$-$\sigma$ relation. However, once the selection effect has been accounted for, values of $f_{vir}\sim 3.5$ yield agreement with both relations. Ho & Kim (2014) also found evidence for a systematic difference in virial factors. They claimed that classical, more massive bulges, required $f_{vir}\sim 6.3$ to match the $M_{\rm bh}-\sigma$ relation of Kormendy & Ho (2013), and a virial factor of $f_{vir}\sim 9$ ($\sim 0.4$ dex higher) to match the $M_{\rm bh}$-$M_{\rm bulge}$ relation.

Previously, before the black hole mass revisions outlined in Kormendy & Ho (2013, and references therein), lower values of the $f_{vir}$ factors had been reported in the literature (see Section 1). For example, when comparing to the Woo et al. (2013a) $M_{\rm bh}$-$\sigma$ relation of quiescent black holes, Grier et al. (2013) retrieved a mean $f_{vir}\sim 4.3$. Shankar et al. (2016) reported that mean virial factors calibrated on the observed $M_{\rm bh}$-$\sigma$ relation should be reduced by a factor of $\sim 3$ to account for selection bias (see also Figure 3). They thus suggested that the mean virial factor could be of order unity based on the Grier et al. (2013) estimate of $f_{vir}\sim 4$. However, we here showed, in broad accordance with Ho & Kim (2014), that a more proper comparison with the most recent scaling relations of quiescent black holes suggests $f_{vir}\sim 10-12$ for a close match to the $M_{\rm bh}$-$\sigma$ relation (upper right panel of Figure 3), which would then imply a scaled $f_{vir}\sim 3.5-4$ to match the unbiased relation (left panels of Figure 3), in nice agreement with the independent estimate of $f_{vir}\sim 3.5$ by, e.g., Grier et al. (2017) and Williams et al. (2018). Finally, the correlation between $M_{\rm bh}$-$M_{\rm star}$ of the masers is more consistent with that of the reverberation-based black holes if a $f_{vir}\sim 3-4$ is adopted instead of a higher value.

It is very unlikely, also given the great diversity of AGN samples collected here, that the observed large offsets in black hole mass with respect to the observed relations of local quiescent black holes is a mere consequence of “infant” black holes still growing towards their final mass (e.g., Mathur et al., 2012), especially in the local Universe, vastly dominated by AGN with low characteristic Eddington ratios (e.g., Kauffmann & Heckman, 2009; Shankar et al., 2013). These findings instead lend further support to the presence of a strong bias in the local quiescent black hole sample, possibly caused by the limited telescope resolution power that artificially increases the normalization of the $\sigma$-$M_{\rm star}$ relation along with other scalings (e.g., Bernardi et al., 2007; Shankar et al., 2016, 2017). This bias has important consequences on a number of fronts, from implications for seeds and intermediate mass black holes (e.g., Graham, 2016; Shankar et al., 2016; Mezcua, 2017; Pacucci et al., 2018), gravitational waves (e.g., Sesana et al., 2016; Taylor et al., 2017; Chen et al., 2018; Joshi et al., 2018), to radiative/kinetic efficiencies (Shankar et al. 2019, submitted).

Reines & Volonteri (2015) pointed out that the quiescent subsample of later-type galaxies, especially pseudobulges, with dynamically-measured black holes tend to overlap with the black hole scaling relations in active galaxies. We do find a similar trend with the (few) late-type galaxies in the Savorgnan & Graham (2016) sample overlapping with our intrinsic black hole scaling relations (Figures 2 and 3). In our interpretation, the displacement, or lack thereof, between the relations of active and quiescent black holes can be explained by how much the host galaxies are outliers in the SDSS $\sigma$-$M_{\rm star}$ relation (Figure 1). Later-type galaxies, usually characterized by lower velocity dispersions at fixed stellar mass, will always be less biased than earlier-type galaxies, thus naturally appearing more consistent with the intrinsic scaling relations of black holes.

We stress that all the results presented here, including Equations 5 and 7, are mostly applicable to galaxies with (total) stellar mass $\log M_{\rm star}/M_{\odot}\gtrsim 10$ and velocity dispersion $\log\sigma/\rm km\,s^{-1}\ \gtrsim 1.9$. Although our AGN samples and SDSS data become rapidly more sparse and/or less robust below this limit, some efforts to probe black hole scaling relations at lower stellar masses have been attempted in recent years. Graham et al. (see, e.g., 2018, and references therein) suggest that a steepening should be present in the $M_{\rm bh}$-$M_{\rm star}$ relation at low stellar masses, while a flattening in the $M_{\rm bh}$-$\sigma$ relation seems to be more consistent with the data according to Martín-Navarro & Mezcua (2018) and Figure 3 (but see also Baldassare et al. 2016). In the context of further probing the correlations of active black holes at lower stellar masses, we also considered six low-mass galaxies from the Sloan Digital Sky Survey-IV Mapping Nearby Galaxies with AGN signatures (Penny et al., 2018). We computed stellar masses for these galaxies from their $r-i$ colours and the mass-to-light ratios from Bell et al. (2003b), decreased by 0.1 dex to convert to a Chabrier IMF. Velocity dispersion were corrected to an aperture of one effective radius using Equation 11, in which the Sérsic index was set to $n_{\rm Ser}=2$ (this choice does not have any impact on our results). Black hole masses were then inferred from Equation 7 lowered by 0.5 dex to convert to the intrinsic $M_{\rm bh}$-$\sigma$. We found the median black hole mass competing to a median host stellar mass of $\log M_{\rm star}/M_{\odot}\sim 9.7$, to be $\log M_{\rm bh}/M_{\odot}\sim 5.3$, which should be regarded more as an upper limit, as three galaxies have only assigned upper limits to their velocity dispersions. The median black hole mass in these dwarfs lies nicely within the $1\sigma$ of the intrinsic $M_{\rm bh}$-$M_{\rm star}$ relation reported in Figure 3. We have also compared with the sample of dwarfs included in Table 3 of Reines & Volonteri (2015), which yield, once converted to our reference mass-to-light ratio via Equation 9, a mean black hole mass of $\log M_{\rm bh}/M_{\odot}\sim 5.6\pm 0.5$ at $\log M_{\rm star}/M_{\odot}\sim 9.7$. The latter sample of dwarfs is $\sim 2\sigma$ above the extrapolation of Equation 5, possibly suggesting that a drop in black hole masses as marked as predicted by the extrapolation of our Equation 5 may be inconsistent with present data. In any event probing the $M_{\rm bh}$-$M_{\rm star}$ correlation at such low stellar masses falls beyond the parameter space probed by the Monte Carlo simulations performed by Shankar et al. (2016) which, as already stressed above, were based on relatively massive galaxies with $\log M_{\rm star}/M_{\odot}\gtrsim 10$. What is more relevant to emphasize in the context of the present paper is that all the dwarfs considered here fall an order of magnitude of more below the extrapolation of the observed $M_{\rm bh}$-$M_{\rm star}$ relation of quiescent black holes (grey region in Figure 2).

It is relevant to note that most of the data adopted here are extracted from samples of Type 1 AGN. We note, however, that recent work has proven Type 2 AGN to be characterized, if anything, by even lower scaling relations (e.g., Ricci et al., 2017a) which would further strengthen our claim for a bias in the $M_{\rm bh}$-$M_{\rm star}$ relation of dynamically measured quiescent supermassive black holes.

We have finally investigated into AGN samples at higher redshifts, with stellar masses/black hole masses derived from spectral energy decomposition analysis and single epoch spectroscopy (e.g., Chang et al., 2017; Delvecchio et al., 2017; Rowan-Robinson et al., 2017). In all cases we find the black holes to lie substantially below the local observed $M_{\rm bh}$-$M_{\rm star}$ relation. However, probing the presence of biases in the $M_{\rm bh}$-$M_{\rm star}$ relation at higher redshifts becomes increasingly less robust due to the possibility of sampling growing black holes, and/or due to intrinsic evolutionary effects in the $M_{\rm bh}$-$M_{\rm star}$ relation itself, and/or due to severe flux limitations (e.g., Bongiorno et al., 2014).

To conclude, in this work we showed that:

AGN hosts follow the $\sigma$-$M_{\rm star}$ correlation of SDSS galaxies, in stark contrast to quiescent galaxies with dynamical mass measurements of their black holes (Figure 1). This behaviour can be in large part explained by the selection effect imposed on the sample of quiescent galaxies by the limited telescope resolution power, which forces to preferentially target more massive, larger velocity dispersions black holes to allow for resolved dynamical mass modelling. 2. 2.

When adopting mean virial factors of $f_{vir}=3.5$ from direct modelling of the broad line region, distinct data sets of local active galaxies with accurate galaxy mass measurements all point to a $M_{\rm bh}$-$M_{\rm star}$ relation steeper and with a much lower normalization than the selection biased one observed for local quiescent black holes with dynamical mass measurements (Figure 2). 3. 3.

The same data sets of local active galaxies with also available velocity dispersion measurements, all point to a $M_{\rm bh}$-$\sigma$ relation, at least at $\log\sigma/\rm km\,s^{-1}\gtrsim 1.9$, with a similar slope but offset by a factor of $\sim 3$ from the selection biased one observed for local quiescent black holes with dynamical mass measurements (Figure 3). 4. 4.

The mean virial factors required for the AGN samples with reverberation-based black hole measurements to match the high-mass end of, respectively, the $M_{\rm bh}$-$\sigma$ and $M_{\rm bh}$-$M_{\rm star}$ relations of quiescent galaxies within $\lesssim 0.1$ dex accuracy are $f_{vir}\gtrsim 7$ and $f_{vir}\gtrsim 15$, substantially higher than the canonical $f_{vir}\sim 3.5$ (Figure 4). This systematic offset in $f_{vir}$ can be naturally explained within the framework of the same selection effects in the local sample of quiescent black holes, which tend to be more effective in the $M_{\rm bh}$-$M_{\rm star}$ rather than the $M_{\rm bh}$-$\sigma$ plane. 5. 5.

The residuals in the scaling relations of AGN show clear evidence for a strong intrinsic dependence of black hole mass on velocity dispersion but not on (bulge or total) stellar mass (Figure 5), in line with what observed in the sample of local inactive black holes (Shankar et al., 2016). These results support the finding of Bernardi et al. (2005) and Bernardi et al. (2011) who showed that $\sigma$ is the main driver of scaling relations with $M_{\rm star}$.

Acknowledgments

We warmly acknowledge Daniel Asmus, Misty Bentz, Angela Bongiorno, James Collinson, Ivan Delvecchio, Sebastian Hönig, Michael Koss, Mirko Krumpe, Isabella Lamberti, Achille Nucita, Michael Rowan-Robinson, and Andreas Schulze for a number of useful discussions and for kindly sharing their data. FS acknowledges partial support from a Leverhulme Trust Research Fellowship. VA acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 749348. MM acknowledges support from the Spanish Juan de la Cierva program (IJCI-2015-23944). FR acknowledges support from FONDECYT Postdoctorado 3180506 and CONICYT project Basal AFB-170002. FP acknowledges support from the NASA Chandra award No. AR8-19021A. We thank the referee for useful suggestions that helped to improve the clarity of the paper.

Appendix A AGN samples used in the main text

We here describe how we have corrected the stellar and black hole masses to a homogeneous system in our reference AGN samples. As in the main text, we here always refer to $f_{vir}$ as the virial factor calibrated on the line dispersion (i.e., second moment of the line profile) of H$\beta$ (e.g., Peterson et al., 2004). For virial black hole masses calibrated adopting the full width at half maximum (FWHM) of the H$\alpha$ line, we will instead denote the virial factors with the symbol $\epsilon$, following the convention put forward by Onken et al. (2004), which is roughly a factor of a few lower than $f_{vir}$. All the AGN samples considered in this work adopt as a reference the line dispersion of the broad H$\beta$ emission line, except for the samples by Reines & Volonteri 2015 and Martín-Navarro & Mezcua 2018, who adopt the FWHMs of the H$\alpha$ lines. Grier et al. (2017) have fitted the continuum H$\beta$ emission-line spectra finding that $f_{vir}\sim 3.5\,(\log f_{vir}=0.54\pm 0.17)$ and $\epsilon\sim 1.5\,(\log\epsilon=0.18\pm 0.23)$ when adopting the line dispersion and FWHM of the H$\beta$ line, respectively. Following Grier et al. (2017), in this work we use as our (mean) reference virial factors $f_{vir}=3.5$ and $\epsilon=1.51$. When adopting larger values of $f_{vir}$ (e.g., as in the right panels of Figure 2), we increase our reference $\epsilon$ proportionally to the ratio $f_{vir}/3.5$. We here assume the same equivalent virial factors apply to both the H$\alpha$ and the H$\beta$ emission lines. This is corroborated by Greene & Ho (2005), who found a tight linear correlation between the H$\alpha$ and H$\beta$ FWHMs with only a relatively small offset of $\lesssim 0.05$ dex between the two lines (their Figure 3), and also more recently by Ricci et al. (2017b, their Figure 1). This offset would correspond to a systematic difference in the implied black hole masses of $\lesssim 25\%$, which is much lower than the level of systematics discussed in this work. We now provide a brief description of each of the AGN samples considered in this work:

(1) Reines & Volonteri (2015) carried out a study of the black hole mass-host galaxy stellar mass relation of 262 broad-line AGN at $z\leq 0.055$, from the SDSS. Stellar masses were derived from the Zibetti et al. (2009) colour-dependent mass-to-light ratios. After correcting for a different IMF, Reines & Volonteri (2015) showed that the Zibetti et al. (2009) stellar masses present a mass-dependent offest with respect to the Bell et al. (2003b) stellar masses (their Figure 6, upper panel) which we approximate as

[TABLE]

which provides, in the range of interest here $9<\log M_{\rm star}<11.5$, a median offset of $\sim 0.21$ dex, as measured by Reines & Volonteri (2015). Reines & Volonteri (2015) calculated black hole masses from single-epoch virial estimators based on the H$\alpha$ emission line and luminosity, with a mean virial coefficient $\epsilon=1.075$ (Grier et al., 2013; Onken et al., 2004), which we correct to our reference value of $\epsilon=1.51$.

(2) Ho & Kim (2014) collected 43 reverberation mapping AGN with Sérsic (Sérsic, 1963) bulge-to-total decompositions on Hubble Space Telescope imaging. Bulge masses were then computed from the $B-R$ colour-dependent $M_{\rm star}/L$ from Bell et al. (2003b), and converted to total stellar masses using their tabulated values of bulge-to-total fractions. Bell et al. (2003b) adopted a “diet Salpeter” IMF, which we corrected to our reference Chabrier IMF subtracting 0.1 dex to all stellar masses (see Table 2 in Bernardi et al., 2010). We assign to all their stellar masses a typical statistical error of 0.15 dex (Bernardi et al., 2014). Ho & Kim (2014) took bulge velocity dispersions mostly from Nelson et al. (2004) and Woo et al. (2013b), who calibrated their velocity dispersions specifically at the effective radius. Other measurements adopted by Ho & Kim (2014) are from, e.g., Nelson & Whittle (1995), Ferrarese et al. (2001), or Woo et al. (2010b), who extracted spectra from 2” slits or a few arcsecond square apertures centred on the nucleus, similar to the aperture adopted in SDSS galaxies. As discussed by Ferrarese et al. (2001) and Nelson et al. (2004), these velocity dispersion measurements are effectively carried out at several kiloparsecs from the centre, probe the stellar bulge potential, and show relatively flat profiles (e.g., Merritt & Ferrarese, 2001b; Kormendy & Ho, 2013). We thus treat all their measured velocity dispersions as equivalent to those in our SDSS sample within one effective radius. As a further test, we also checked that fully consistent results are found in both the $\sigma$-$M_{\rm star}$ relation (Figure 1) and residuals (Figure 5), when adopting, wherever possible, velocity dispersions from the Hyperleda database (Paturel et al., 2003). Ho & Kim (2014) divided their sample into classical and pseudobulges based on their Sérsic index, for which they calibrated, respectively, $f_{vir}=6.3$ and $f_{vir}=3.2$ (based on the H$\beta$ line dispersion) when compared to the local $M_{\rm bh}$-$\sigma$ relation of inactive galaxies from Kormendy & Ho (2013). We instead adopt for all black hole masses in their sample a constant $f_{vir}=3.5$.

(3) Busch et al. (2014) performed aperture photometry and bulge-to-disc decompositions on near-infrared $J-$, $H-$, and $K-$band images of 20 low-luminosity type-1 quasars at $z\leq 0.06$ from the Hamburg/ESO survey. Stellar masses were calculated from parametric models based on inactive galaxy colours and using the Bell et al. (2003b) mass-to-light ratios, which we again correct to our reference Chabrier IMF subtracting 0.1 dex. Black hole masses were derived from the H$\beta$ line dispersion virial-based sample of Schulze et al. (2009) with $f_{vir}=3.85$ (Collin et al., 2006), which we rescale to $f_{vir}=3.5$.

(4) Greene et al. (2016) presented black hole masses and stellar velocity dispersion measurements for several local megamaser early-to-mid-type spiral galaxies, including those from the Saglia et al. (2016) sample. Black hole masses were derived by fitting a Keplerian rotation curve to the positions and velocities of the maser spots. Using SDSS data, stellar masses were obtained from the Bell et al. (2003b) mass-to-light ratios, for which we subtract a constant 0.1 dex. Velocity dispersions were extracted from spectra within a 2” aperture and were measured from the first two moments of the line-of-sight velocity dispersion. Analogously to the Ferrarese et al. (2001) measurements, even for this sample we do not apply any correction to the velocity dispersions when comparing to the SDSS $\sigma_{e}$.

(5) Martín-Navarro & Mezcua (2018) studied 127 low-mass Seyfert 1 galaxies with measured stellar masses from the SDSS spectral measurements and Bruzual & Charlot (2003) libraries with a Chabrier IMF, which are fully consistent with the stellar masses from Kauffmann et al. (2004) and systematically lower than those calibrated using Bell et al. (2003b) by $\sim 0.25$ dex (e.g., Bernardi et al., 2016). Black hole masses, derived from the H$\alpha$ virial relations of Woo et al. (2015, and references therein) with a mean virial factor of $\epsilon=1.12$ and $\epsilon=0.75$, respectively, are converted to our reference $\epsilon=1.51$. Velocity dispersions were extracted from SDSS and corrected for an aperture within one (exponential) effective radius via the usual scaling

[TABLE]

but using a Sérsic index-dependent slope (Bernardi et al., 2017b)

[TABLE]

We set the Sérsic index $n_{\rm Ser}=1$ in Equation 11, as the vast majority of the Martín-Navarro & Mezcua (2018) sample is heavily disc-dominated. Assuming a larger value for the Sérsic index such as $n_{\rm Ser}=2$ has a negligible effect on our results.

(6) van den Bosch (2016) compiled one of the largest samples of active and inactive supermassive black holes from the literature, counting 230 sources with black hole mass measurements from stellar dynamics, gas or CO dynamics, masers and reverberation mapping-based relations. In what follows, we will only consider the active galaxies from van den Bosch (2016) from masers and reverberation-based estimates. The latter are extracted from the original sample by Bentz & Katz (2015) who adopted a mean $f_{vir}=4.31$ from Grier et al. (2013, H$\beta$ line dispersion) which we rescale to $f_{vir}=3.5$. van den Bosch (2016) adopted, wherever possible, the closest approximation to $\sigma_{e}$ for the velocity dispersions (to which we assign typical statistical errors of 0.05 dex Bernardi et al. 2010), and uniformly applied Sérsic fits to the 2MASS $K_{s}$ band photometry. All galaxies in this sample, which excludes the most massive galaxies, are well resolved and detected in 2MASS according to van den Bosch (2016). Following van den Bosch (2016), galaxy luminosities were then converted to stellar masses via the velocity dispersion-dependent mass-to-light ratio from Kormendy & Ho (2013)

[TABLE]

Kormendy & Ho (2013) specify that the constant in Equation 12 should be $K_{0}\sim 1$ for the total dynamical mass-to-light ratios, and further detail that, following Into & Portinari (2013), it should be reduced to $K_{0}\sim 0.76$ when considering, as in this work, only the stellar component. We thus adopt the latter value for $K_{0}$. We further subtract a constant 0.05 dex from all stellar masses to account for the heavier (Kroupa, 2001) IMF adopted by Into & Portinari (2013). In the end, we find that galaxies with a Chabrier IMF and $\sigma_{e}=166\,\rm km\,s^{-1}$ have an average $M_{\rm star}/L_{K}\sim 0.676$, which is in excellent agreement with the mean $M_{\rm star}/L_{K}=0.67$ calculated by Longhetti & Saracco (2009). Indeed, we checked that equivalent results are found throughout even ignoring the (weak) dependence on velocity dispersion in Equation 12. We note that the van den Bosch (2016) maser subsample also includes the sources from Greene et al. (2016) but with independent measurements of the host stellar masses so we will still consider them as fully independent estimates.

(7) Bentz & Manne-Nicholas (2018) recently collected a sample of 37 active galaxies with high-resolution optical images from the Hubble Space Telescope with reverberation-based black hole masses with an average $f_{vir}=4.3$. Total luminosities are derived from Sérsic fits, though with a Sérsic index capped at $n_{\rm Ser}\leq 4$. We consider their mass-to-light ratios from Bell & de Jong (2001) who adopted a diet Salpeter. However, in this specific instance we do not substract their stellar masses by 0.1 dex to convert to a Chabrier IMF as Bell et al. (2003b) showed (their Figure 20, left panel) that at fixed optical galaxy colour the Bell & de Jong (2001) $M_{\rm star}/L$ are already systematically underestimated by (at least) $\sim 0.1$ dex with respect to those from Bell et al. (2003b).

Other AGN samples are available in the local Universe but are less suited to our purposes. For example, Nucita et al. (2017) presented X-ray AGN at $z\leq 0.055$ with black hole masses derived from the X-ray/radio fundamental plane relation (Merloni et al., 2003). However, the latter has already been shown to be biased, probably tracing the upper envelope of a much broader distribution (e.g., La Franca et al., 2010; Bonchi et al., 2013; Baldi et al., 2018; Martín-Navarro & Mezcua, 2018). Koss et al. (2017) presented the first catalogue and data release of the Swift-BAT AGN Spectroscopic Survey. However, their stellar masses were obtained by combining the SDSS Petrosian photometry with the Blanton & Roweis (2007) mass-to-light ratios both of which contribute to yield stellar masses a factor of $\gtrsim 2$ lower than the updated measurements adopted here (e.g., Bernardi et al., 2010, 2013). Nevertheless, we checked that after correcting stellar masses by a factor of two the Koss et al. (2017) sample lies well below the observed $M_{\rm bh}$-$M_{\rm star}$ relation of quiescent galaxies. Interestingly, Lamperti et al. (2017, see also Figure 8 in ) point to a discrepancy of up to an order of magnitude between black hole masses measured from virial relations and the $M_{\rm bh}$-$\sigma$ relation, in full agreement with the main conclusion of this work.