Black Hole–Galaxy Scaling Relationships for Active Galactic Nuclei with Reverberation Masses

HST imaging of the galaxies in our sample was acquired with the following instrument configurations: the Advanced Camera for Surveys (ACS) High Resolution Channel (HRC) through the F550M filter, the Wide Field Planetary Camera 2 (WFPC2) with the F547M filter, and the Wide Field Camera 3 (WFC3) through the F547M filter. The medium-band V filters were specifically chosen to avoid strong emission lines from the AGN and to sample a flat portion of the underlying host-galaxy spectrum. The details of these observations and the post-processing are described by Bentz et al. (2009a, 2013).

We also present here new WFC3 F547M images of eight galaxies in the sample (HST GO-11661 and GO-13816, PI Bentz). Three had not been previously observed, while prior imaging of five galaxies with the ACS HRC provided a field of view (290 × 250) that was too narrow to capture their extended morphologies. WFC3 provides a 27 × 27 field of view that is well matched to the galaxies in our sample, and a high spatial resolution with a pixel scale of 004. Each galaxy was observed for a single orbit, with a two-point dither pattern to fill in the gap between the detectors. At each point in the dither, a short and long exposure were obtained. The short exposures ensure an unsaturated measurement of the bright central AGN at each position, while the long exposures provide more depth for resolving the fainter, extended host galaxy.

The pipeline-reduced images were corrected for cosmic rays with LACosmic (van Dokkum 2001). Taking advantage of the linear nature of CCDs, we corrected for saturation of the AGN in the long exposures by clipping out the saturated pixels in the long exposures and replacing them with the same pixels from the short exposures taken at the same dither position, scaled up by the exposure time ratio. The individual exposures were then drizzled to a common reference and combined with AstroDrizzle.

Near-infrared imaging of 29 reverberation-mapped AGN host galaxies was obtained between fall 2011 and spring 2013 with the WIYN High-Resolution Infrared Camera (WHIRC) at the WIYN 3.5 m telescope.¹ The camera is a Raytheon Virgo HgCdTe with a pixel scale of 00986 and a field of view of 202'' × 202''. While broadband J, H, and Ks images were obtained for a subset of the sample, the majority of the observations were devoted to H-band images and we report those here.

The typical observing sequence involved many short observations of each target with a generous dither pattern between observations. This allowed for the removal of strong fringing in the H band, as well as bad pixels and cosmic rays.

Images were reduced in IRAF² following standard procedures. Strong fringing is a known problem for H-band images taken with WHIRC. We were able to correct for this effect by first median-combining a large number of dithered observations of a target, with each image scaled by the median sky level. Then we created a fringe mask from this combined image with the IRAF task objmasks. Finally, we used the mask with the rmfringe task to correct each image. After correcting for fringing, we computed the pixel offsets between dithered images, subtracted the mean sky background, and shifted and combined all of the images. For the final image of each object, we added back the average sky background that had been subtracted in the previous step, to ensure that the image statistics would be properly handled in the fitting process. In Figure 1 we show the final H-band images for three of our targets in comparison to the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) H-band images for the same galaxies. The improvement in depth and spatial resolution provided by the WHIRC images is immediately apparent, allowing for detection and characterization of faint surface brightness features, as well as better separation of distinct photometric components.

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We supplemented this sample with HST Near-Infrared Camera and Multi-Object Spectrometer (NICMOS) observations of eight additional PG quasars with the NIC2 camera through the F160W filter. Details of these observations are described by Veilleux et al. (2009). Drizzled and combined images were downloaded from MAST. For each image, we added back the subtracted sky background as recorded in the header, and then multiplied each image by the exposure time to return the image units to counts.

The optical HST magnitudes represent a few different medium-band V filters rather than a true broadband Johnson filter. For each object, we used synphot and a reddened, redshifted galaxy spectrum to determine the color difference between the filter used for the optical HST observations and a broadband V filter. We adopted the elliptical galaxy template spectrum of Kinney et al. (1996) for these calculations, but the use of an Sa or Sc galaxy spectrum does not significantly change our results. The color differences are small, −0.05 <m_V − m_HST < 0.13 mag. Similarly, we determined the difference between the F160W magnitudes from the NICMOS images and a "true" H-band magnitude using synphot and the tabulated passband for the H filter provided on the WHIRC filters webpage.³ These corrections were slightly larger in magnitude and were always in the same direction, showing a slight bias between the two filters, −0.15 < m_H − m_F160W <−0.12 mag.

The V and H magnitudes were then corrected for Galactic extinction along the line of sight based on the values determined from the Schlafly & Finkbeiner (2011) recalibration of the Schlegel et al. (1998) dust map of the Milky Way. Table 3 gives the extinction-corrected V- and H-equivalent apparent magnitudes for the integrated galaxies and for their bulges.

Table 3.  Bulge and Galaxy Magnitudes and Luminosities

Object	D	Vbulge	Vgalaxy	$\mathrm{log}\,{L}_{\mathrm{bulge}}$ (V)	$\mathrm{log}\,{L}_{\mathrm{galaxy}}$ (V)	Hbulge	Hgalaxy	$\mathrm{log}\,{L}_{\mathrm{bulge}}$ (H)	$\mathrm{log}\,{L}_{\mathrm{galaxy}}$ (H)
	(Mpc)	(mag)	(mag)	(L⊙)	(L⊙)	(mag)	(mag)	(L⊙)	(L⊙)
Mrk 335	109.5 ± 7.1	16.59	15.42	9.409 ± 0.098	9.861 ± 0.098	13.25	12.76	10.117 ± 0.098	10.312 ± 0.098
Mrk 1501	402.5 ± 7.5	17.22	15.40	10.325 ± 0.082	11.055 ± 0.082	14.17	13.53	10.872 ± 0.082	11.129 ± 0.082
PG 0026+129	653.1 ± 7.7	17.03	17.03	10.868 ± 0.081	10.868 ± 0.081	15.30	15.30	10.840 ± 0.081	10.840 ± 0.081
Mrk 590	112.1 ± 7.1	16.07	13.89	9.633 ± 0.097	10.494 ± 0.097	12.76	10.65	10.333 ± 0.097	11.177 ± 0.097
3C 120	140.9 ± 7.1	16.38	14.85	9.730 ± 0.091	10.327 ± 0.091	12.62	11.86	10.587 ± 0.091	10.891 ± 0.091
Akn 120	139.6 ± 7.1	14.89	13.95	10.311 ± 0.091	10.670 ± 0.091	11.87	11.18	10.879 ± 0.091	11.154 ± 0.091
Mrk 6	80.6 ± 7.1	14.97	13.55	9.770 ± 0.111	10.339 ± 0.111	11.24	10.86	10.658 ± 0.111	10.808 ± 0.111
Mrk 79	94.0 ± 7.1	15.64	13.80	9.657 ± 0.103	10.375 ± 0.103	12.27	11.14	10.376 ± 0.103	10.830 ± 0.103
PG 0844+349	279.4 ± 7.3	17.40	16.35	9.903 ± 0.083	10.330 ± 0.083	14.20	13.50	10.543 ± 0.083	10.823 ± 0.083
Mrk 110	150.9 ± 7.1	18.00	16.21	9.130 ± 0.090	9.823 ± 0.090	13.74	12.84	10.198 ± 0.090	10.557 ± 0.090
NGC 3227	23.5 ± 2.4	13.92	10.93	9.105 ± 0.119	10.301 ± 0.119	9.76	7.80	10.184 ± 0.119	10.970 ± 0.119
NGC 3516	37.1 ± 7.0	13.30	11.74	9.755 ± 0.182	10.379 ± 0.182	10.09	9.34	10.448 ± 0.182	10.747 ± 0.182
SBS 1116+583A	118.5 ± 7.1	18.50	15.48	8.696 ± 0.095	9.907 ± 0.095	15.42	12.60	9.315 ± 0.095	10.443 ± 0.095
Arp 151	89.2 ± 7.0	15.71	15.39	9.561 ± 0.105	9.691 ± 0.105	12.38	12.18	10.287 ± 0.105	10.367 ± 0.105
Mrk 1310	82.7 ± 7.0	16.37	14.81	9.230 ± 0.109	9.856 ± 0.109	13.19	12.41	9.899 ± 0.109	10.211 ± 0.109
NGC 4051	17.1 ± 3.4	14.70	10.07	8.515 ± 0.190	10.368 ± 0.190	11.99	8.18	9.016 ± 0.190	10.539 ± 0.190
NGC 4151	16.6 ± 3.3	13.78	10.72	8.858 ± 0.190	10.083 ± 0.190	10.41	8.12	9.622 ± 0.190	10.538 ± 0.190
Mrk 202	88.9 ± 7.1	17.15	15.30	8.982 ± 0.106	9.725 ± 0.106	13.55	12.61	9.818 ± 0.106	10.193 ± 0.106
NGC 4253	54.4 ± 7.0	16.44	13.10	8.835 ± 0.138	10.171 ± 0.138	12.96	10.86	9.628 ± 0.138	10.470 ± 0.138
PG 1226+023	735.7 ± 7.7	14.81	14.77	11.882 ± 0.081	11.882 ± 0.081	13.20	13.20	11.781 ± 0.081	11.781 ± 0.081
PG 1229+204	274.9 ± 7.3	16.04	15.59	10.430 ± 0.083	10.619 ± 0.083	12.91	12.67	11.045 ± 0.083	11.142 ± 0.083
NGC 4593	37.3 ± 7.5	13.17	11.12	9.812 ± 0.192	10.631 ± 0.192	9.84	8.66	10.553 ± 0.192	11.024 ± 0.192
NGC 4748	61.6 ± 7.0	14.58	13.39	9.688 ± 0.127	10.165 ± 0.127	10.94	10.77	10.546 ± 0.127	10.611 ± 0.127
PG 1307+085	718.7 ± 7.7	16.07	16.07	11.339 ± 0.081	11.339 ± 0.081	13.81	13.81	11.514 ± 0.081	11.514 ± 0.081
Mrk 279	129.7 ± 7.1	16.30	14.83	9.673 ± 0.093	10.246 ± 0.093	12.31	11.49	10.638 ± 0.093	10.964 ± 0.093
PG 1411+442	398.2 ± 7.4	16.69	16.71	10.511 ± 0.082	10.511 ± 0.082	13.67	13.67	11.062 ± 0.082	11.062 ± 0.082
PG 1426+015	383.9 ± 7.4	16.55	15.63	10.543 ± 0.082	10.909 ± 0.082	13.74	13.00	11.002 ± 0.082	11.299 ± 0.082
Mrk 817	134.2 ± 7.1	17.69	14.22	9.123 ± 0.092	10.519 ± 0.092	13.24	11.37	10.297 ± 0.092	11.044 ± 0.092
PG 1613+658	588.4 ± 7.6	15.91	15.87	11.220 ± 0.081	11.220 ± 0.081	12.79	12.79	11.750 ± 0.081	11.750 ± 0.081
PG 1617+175	507.4 ± 7.5	17.18	17.18	10.556 ± 0.081	10.556 ± 0.081	15.05	15.05	10.722 ± 0.081	10.722 ± 0.081
PG 1700+518	1463.3 ± 8.4	17.90	17.92	11.417 ± 0.080	11.417 ± 0.080	15.08	15.08	11.616 ± 0.080	11.616 ± 0.080
3C 390.3	243.5 ± 7.2	17.05	16.09	9.944 ± 0.084	10.313 ± 0.084	13.82	12.94	10.576 ± 0.084	10.929 ± 0.084
Zw 229-015	120.2 ± 7.2	16.93	14.82	9.342 ± 0.095	10.186 ± 0.095	13.89	12.38	9.940 ± 0.095	10.547 ± 0.095
NGC 6814	21.8 ± 7.0	14.47	10.66	8.823 ± 0.289	10.346 ± 0.289	11.18	8.47	9.549 ± 0.289	10.635 ± 0.289
Mrk 509	147.0 ± 7.1	⋯	14.87	⋯	10.344 ± 0.090	⋯	12.05	⋯	10.849 ± 0.090
PG 2130+099	274.7 ± 7.3	17.77	16.15	9.739 ± 0.083	10.395 ± 0.083	13.65	12.82	10.750 ± 0.083	11.082 ± 0.083
NGC 7469	68.8 ± 7.0	16.66	12.29	8.954 ± 0.119	10.701 ± 0.119	13.29	9.82	9.702 ± 0.119	11.088 ± 0.119

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Based on our previous experience with Galfit as well as comparison of our fitting results with those of Veilleux et al. (2009) for several of the PG objects, we assume a typical uncertainty of 0.20 mag for the integrated magnitudes of the galaxies. We also assume a typical uncertainty of 0.20 mag for the integrated magnitudes of the bulge components on their own. This is not to say that all the uncertainty is in the bulges, but rather that Galfit does a good job of recovering the total galaxy flux, even if there is some abiguity in how the light is divided between the various photometric components.

The galaxies in our sample span a range of distances covering 0.0 < z < 0.3. We used synphot to determine k-corrections for each galaxy in V and H so that we could compare z = 0-equivalent photometry and galaxy colors. In H, the relatively flat spectral energy distribution (SED) of a galaxy gives rise to small corrections ranging from −0.075 < k_H < −0.003 mag with a median of k_H = −0.028 mag. In V, however, there is significantly more structure to a galaxy SED, so the galaxies with the largest redshifts in our sample (z = 0.1–0.3) have k_V > 0.2 mag. The median is significantly smaller, however, at k_V = 0.061 mag.

After applying the k-corrections, we derive the V − H colors, both for the integrated light of the galaxy, which we report in Table 4, as well as for each individual component (e.g., bulge, bar, disk). The range of integrated galaxy colors is 1.2 < V − H < 3.3, with a median color of V − H = 2.6. Most of the sample is comprised of disk galaxies and, as expected, the V − H colors of the galaxy bulges are generally larger (redder) than the integrated colors of the entire galaxies by a median value of 0.75 mag.

Table 4.  Stellar and Black Hole Masses

	Bulge			Galaxy
Object	V − H	$\mathrm{log}{M}_{\mathrm{stars}}$ (Bd01)	$\mathrm{log}{M}_{\mathrm{stars}}$ (IP13)	V − H	$\mathrm{log}{M}_{\mathrm{stars}}$ (Bd01)	$\mathrm{log}{M}_{\mathrm{stars}}$ (IP13)	$\mathrm{log}{M}_{\mathrm{BH}}$
	(mag)	(M⊙)	(M⊙)	(mag)	(M⊙)	(M⊙)	(M⊙)
Mrk 335	3.22	10.22 ± 0.23	9.99 ± 0.30	2.58	10.17 ± 0.23	9.78 ± 0.30	${7.230}_{-0.044}^{+0.042}$
Mrk 1501	2.82	10.82 ± 0.23	10.49 ± 0.30	1.64	10.63 ± 0.23	10.00 ± 0.30	${8.067}_{-0.165}^{+0.119}$
PG 0026+129	1.38	10.24 ± 0.23	9.55 ± 0.30	1.38	10.24 ± 0.23	9.55 ± 0.30	${8.487}_{-0.119}^{+0.096}$
Mrk 590	3.19	10.42 ± 0.23	10.19 ± 0.30	3.16	11.25 ± 0.23	11.01 ± 0.30	${7.570}_{-0.074}^{+0.062}$
3C 120	3.59	10.83 ± 0.23	10.70 ± 0.30	2.86	10.86 ± 0.23	10.54 ± 0.30	${7.745}_{-0.040}^{+0.038}$
Akn 120	2.87	10.85 ± 0.23	10.53 ± 0.30	2.66	11.04 ± 0.23	10.68 ± 0.30	${8.068}_{-0.063}^{+0.048}$
Mrk 6	3.67	10.93 ± 0.23	10.82 ± 0.30	2.62	10.68 ± 0.23	10.31 ± 0.30	${8.102}_{-0.041}^{+0.037}$
Mrk 79	3.25	10.49 ± 0.23	10.27 ± 0.30	2.59	10.69 ± 0.23	10.31 ± 0.30	${7.612}_{-0.136}^{+0.107}$
PG 0844+349	3.05	10.58 ± 0.23	10.31 ± 0.30	2.68	10.72 ± 0.23	10.36 ± 0.30	${7.858}_{-0.230}^{+0.154}$
Mrk 110	4.12	10.64 ± 0.23	10.64 ± 0.30	3.27	10.68 ± 0.23	10.47 ± 0.30	${7.292}_{-0.097}^{+0.101}$
NGC 3227	4.15	10.64 ± 0.23	10.65 ± 0.30	3.12	11.03 ± 0.23	10.78 ± 0.30	${6.775}_{-0.112}^{+0.084}$
NGC 3516	3.18	10.53 ± 0.25	10.30 ± 0.32	2.37	10.52 ± 0.25	10.08 ± 0.32	${7.395}_{-0.061}^{+0.037}$
SBS 1116+583A	3.00	9.33 ± 0.23	9.05 ± 0.30	2.79	10.38 ± 0.23	10.05 ± 0.30	${6.558}_{-0.088}^{+0.081}$
Arp 151	3.27	10.40 ± 0.23	10.19 ± 0.30	3.14	10.44 ± 0.23	10.19 ± 0.30	${6.670}_{-0.054}^{+0.045}$
Mrk 1310	3.12	9.96 ± 0.23	9.71 ± 0.30	2.34	9.98 ± 0.23	9.53 ± 0.30	${6.212}_{-0.089}^{+0.071}$
NGC 4051	2.70	8.92 ± 0.25	8.56 ± 0.32	1.88	10.13 ± 0.25	9.56 ± 0.32	${6.130}_{-0.155}^{+0.121}$
NGC 4151	3.36	9.78 ± 0.25	9.59 ± 0.32	2.59	10.40 ± 0.25	10.01 ± 0.32	${7.555}_{-0.047}^{+0.051}$
Mrk 202	3.54	10.04 ± 0.23	9.90 ± 0.30	2.62	10.07 ± 0.23	9.69 ± 0.30	${6.133}_{-0.173}^{+0.166}$
NGC 4253	3.43	9.81 ± 0.24	9.64 ± 0.31	2.20	10.18 ± 0.24	9.70 ± 0.31	${6.822}_{-0.057}^{+0.050}$
PG 1226+023	1.20	11.11 ± 0.23	10.37 ± 0.30	1.20	11.11 ± 0.23	10.37 ± 0.30	${8.839}_{-0.113}^{+0.077}$
PG 1229+204	2.99	11.06 ± 0.23	10.77 ± 0.30	2.76	11.07 ± 0.23	10.73 ± 0.30	${7.758}_{-0.219}^{+0.175}$
NGC 4593	3.30	10.68 ± 0.25	10.48 ± 0.32	2.43	10.83 ± 0.25	10.40 ± 0.32	${6.882}_{-0.104}^{+0.084}$
NGC 4748	3.60	10.79 ± 0.24	10.66 ± 0.30	2.57	10.46 ± 0.24	10.07 ± 0.30	${6.407}_{-0.183}^{+0.110}$
PG 1307+085	1.89	11.11 ± 0.23	10.55 ± 0.30	1.89	11.11 ± 0.23	10.55 ± 0.30	${8.537}_{-0.161}^{+0.094}$
Mrk 279	3.86	10.98 ± 0.23	10.92 ± 0.30	3.24	11.07 ± 0.23	10.86 ± 0.30	${7.435}_{-0.133}^{+0.099}$
PG 1411+442	2.83	11.01 ± 0.23	10.69 ± 0.30	2.83	11.01 ± 0.23	10.69 ± 0.30	${8.539}_{-0.169}^{+0.125}$
PG 1426+015	2.60	10.87 ± 0.23	10.48 ± 0.30	2.42	11.10 ± 0.23	10.67 ± 0.30	${9.007}_{-0.164}^{+0.106}$
Mrk 817	4.38	10.84 ± 0.23	10.91 ± 0.30	2.76	10.97 ± 0.23	10.63 ± 0.30	${7.586}_{-0.072}^{+0.064}$
PG 1613+658	2.77	11.68 ± 0.23	11.34 ± 0.30	2.77	11.68 ± 0.23	11.34 ± 0.30	${8.339}_{-0.271}^{+0.164}$
PG 1617+175	1.87	10.31 ± 0.23	9.74 ± 0.30	1.87	10.31 ± 0.23	9.74 ± 0.30	${8.667}_{-0.128}^{+0.084}$
PG 1700+518	1.95	11.23 ± 0.23	10.69 ± 0.30	1.95	11.23 ± 0.23	10.69 ± 0.30	${8.786}_{-0.103}^{+0.091}$
3C 390.3	3.03	10.60 ± 0.23	10.33 ± 0.30	2.99	10.94 ± 0.23	10.66 ± 0.30	${8.638}_{-0.046}^{+0.040}$
Zw 229-015	2.95	9.94 ± 0.23	9.64 ± 0.30	2.35	10.32 ± 0.23	9.87 ± 0.30	${6.913}_{-0.119}^{+0.075}$
NGC 6814	3.27	9.67 ± 0.29	9.45 ± 0.35	2.17	10.34 ± 0.29	9.85 ± 0.35	${7.038}_{-0.058}^{+0.056}$
Mrk 509	⋯	⋯	⋯	2.71	10.76 ± 0.23	10.40 ± 0.30	${8.049}_{-0.035}^{+0.035}$
PG 2130+099	3.98	11.14 ± 0.23	11.11 ± 0.30	3.17	11.16 ± 0.23	10.92 ± 0.30	${7.433}_{-0.063}^{+0.055}$
NGC 7469	3.32	9.84 ± 0.23	9.64 ± 0.30	2.42	10.88 ± 0.23	10.45 ± 0.30	${6.956}_{-0.050}^{+0.048}$

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To convert the observed magnitudes to luminosities, we estimated D_L based on the apparent redshifts of the galaxies. We conservatively adopted an uncertainty of 500 km s⁻¹ in peculiar velocities for each distance estimate, based on the distribution of peculiar velocities derived by Tully et al. (2008). This works out to a 17% uncertainty at z = 0.01, and decreases as z increases. We caution that this uncertainty may still be significantly underestimated in the case of individual galaxies.

Four of the nearest galaxies in the sample have distances in the literature that were derived through other techniques. We summarize these distance measurements and their potential uncertainties in Bentz et al. (2013) but, in brief, they were generally retrieved from the Extragalactic Distance Database (Tully et al. 2009) and derived from an average of the distance moduli for galaxies within the same group. The exception is NGC 3227, where the distance measurement comes from an analysis of the surface brightness fluctuations of NGC 3226 (Tonry et al. 2001), with which it is interacting.

Adopted distances and their uncertainties are listed in Table 3.

We estimated the stellar M/L of each galaxy using the V − H color and the relationships tabulated by Bell & de Jong (2001) in their Table 1. Following their work, we assume solar absolute magnitudes of M_V = 4.82 (Cox 2000) and M_H = 3.37 (Worthey 1994) and we derive the expected stellar mass in the V and H passbands, which are identical and are listed as "$\mathrm{log}{M}_{\mathrm{stars}}$ (Bd01)" in Table 4. The uncertainties in the stellar masses are based on the propagated uncertainties in the photometry and the distances. The steeper dependency of M/L on bluer colors leads to uncertainties in the stellar masses that are roughly twice as large when based on the luminosity in V as for H. To be conservative, we adopt the larger uncertainties based on V.

We also estimated the stellar M/L of each galaxy using the relationships tabulated by Into & Portinari (2013), who used updated population synthesis models and applied prescriptions to more accurately account for thermally pulsing asymptotic giant branch stars, which can strongly affect near-infrared photometry of galaxies. We apply their "dusty" models (their Table 6) because we have not attempted to correct for dust internal to the galaxies, and the predominantly late types of the galaxies in our sample mean that they cannot be considered "dust free." Adopting the solar absolute magnitudes of M_V = 4.828 and M_H = 3.356 derived by Into & Portinari (2013) for consistency, we determined the expected stellar masses in the V and H passbands. Unlike the masses estimated from the relationships of Bell & de Jong (2001), the two passbands do not predict exactly the same stellar masses, but the differences are only at the 1% level. We adopted the stellar masses based on the luminosity in V, again because their larger propagated uncertainties make them a more conservative choice, and we list these in Table 4 as "$\mathrm{log}{M}_{\mathrm{stars}}$ (IP13)."

The stellar masses predicted by the relationships of Into & Portinari (2013) are typically a factor of 2.4 times smaller than those derived from the relationships tabulated by Bell & de Jong (2001), although for the smallest V − H colors in the sample, they can disagree by a factor of ∼4–5. Some of this difference can be attributed to the choice of a "diet" Salpeter initial mass function (IMF) used by Bell & de Jong and a Kroupa IMF adopted by Into & Portinari. If we adjust the M/L prescription of Bell & de Jong by −0.15 dex to better match a Kroupa IMF (Bell et al. 2003), then the agreement is better, although the stellar masses predicted by the Into & Portinari M/L relations are still typically 1.7 times smaller than those predicted by Bell & de Jong. This difference agrees with the factor-of-two lighter masses found by Into & Portinari when comparing their new stellar population models with previous models, which they attribute to updates like their treatment of thermally pulsing asymptotic giant branch stars. Kormendy & Ho (2013) also find that the M/L ratios predicted by Into & Portinari are, on average, a factor of 1.34 smaller than those predicted by the dynamics of the galaxy, although it is unclear how much of the discrepancy may be attributed to dark matter. Given the uncertainties in the methods, we report the results using both the Bell & de Jong and the Into & Portinari prescriptions throughout this work.

Black hole masses for all galaxies were drawn from the compilation of reverberation-based masses in the AGN Black Hole Mass Database (Bentz & Katz 2015). The basic technique of reverberation mapping (Blandford & McKee 1982; Peterson 1993) involves time-resolved spectrophotometry collected over a long time baseline and with dense time sampling (for nearby Seyferts, this typically amounts to daily sampling over a baseline of a few months). Variations in the continuum flux are "echoed" in the broad emission lines, and the time delay between the two is based on the light-travel time between the two regions where the signals arise, namely the accretion disk and the broad line region.

The black hole masses are determined as

$$\begin{eqnarray}&&{M}_{\mathrm{BH}}=f\displaystyle \frac{c\tau {V}^{2}}{G},\end{eqnarray} \tag{ 2 }$$

where cτ is the measured time delay for a broad emission line, V is the velocity width of that same emission line, and G is the gravitational constant. The factor f is an order-unity scaling factor that is necessary to account for the generally unknown geometry and detailed kinematics of the broad line region in the AGNs. The value of f ranges from 2.8 to 5.5 in the literature, with most current studies finding f ≈ 4. We adopted the scaling factor of $\langle f\rangle =4.3$ determined by Grier et al. (2013).

The relationship between black hole mass and bulge luminosity, ${M}_{\mathrm{BH}}\mbox{--}{L}_{\mathrm{bulge}}$ was one of the first black hole scaling relationships to be discovered (Kormendy & Richstone 1995). However, it was soon eclipsed by the ${M}_{\mathrm{BH}}\mbox{--}{\sigma }_{\star }$ relationship (Ferrarese & Merritt 2000; Gebhardt et al. 2000), which was initially reported to have a smaller intrinsic scatter and was therefore viewed as being the more fundamental scaling relationship. However, improvements in the black hole mass measurements, in particular, have led to much tighter ${M}_{\mathrm{BH}}\mbox{--}{L}_{\mathrm{bulge}}$ relationships in recent years where the reported scatter is similar to that of the ${M}_{\mathrm{BH}}\mbox{--}{\sigma }_{\star }$ relationship (Marconi & Hunt 2003; Gültekin et al. 2009). These studies have tended to focus on bulge-dominated galaxies while neglecting the late-type galaxies common among local Seyfert hosts.

A notable exception, however, is Wandel (2002), who drew photometry from the literature to investigate the ${M}_{\mathrm{BH}}\mbox{--}{L}_{\mathrm{bulge}}$ relationship for AGN host galaxies with black hole masses from reverberation mapping. A homogeneous reanalysis of the AGN black hole masses by Peterson et al. (2004) combined with consistent bulge photometry derived from high-quality HST imaging and galaxy photometric decompositions allowed Bentz et al. (2009b) to update the results of Wandel (2002), finding that ${M}_{\mathrm{BH}}\mbox{--}{L}_{\mathrm{bulge}}$ for disk-dominated active galaxies is similar in form and scatter to that of bulge-dominated galaxies with predominantly quiescent black holes and masses derived from dynamical modeling.

Here, we are able to improve upon the results of Bentz et al. (2009b) by extending the sample to lower black hole masses, increasing the number of galaxies included in the fit by 40%, and by examining the relationship in both the optical and the near-infrared. This last point is an important addition because it allows for the effects of dust and recent star formation on the photometry to be mitigated.

For each galaxy, we identified the photometric component most consistent with the expected properties of a bulge. In particular, we looked for a round (0.7 ≲ q ≲ 1.0) photometric component with Sérsic index n > 1.0 and r < r_disk. In one instance (Mrk 509), there was no such model component and so we do not include it here in the analysis of galaxy bulges. Mrk 509 is thus consistent with either a bulgeless disk galaxy or a disk galaxy with a compact bulge that we could not separate from the central AGN. Some of the PG quasars, on the other hand, were modeled by a single spheroidal component which we include as a "bulge" here. We do not attempt to discriminate between pseudobulges and classical bulges because we have limited kinematic information regarding the bulges of these galaxies. Numerous studies have shown that pseudobulge identification can be extremely uncertain when it is based solely on photometric information (e.g., Kormendy & Kennicutt 2004; Läsker et al. 2014). In the V band, we find the best-fit relationship between the black hole mass and bulge luminosity to be

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=(0.84\pm 0.10)\mathrm{log}\left(\displaystyle \frac{{L}_{V,\mathrm{bulge}}}{{10}^{10}{L}_{\odot }}\right)+(7.71\pm 0.08)\end{eqnarray} \tag{ 3 }$$

with a typical scatter of (0.23 ± 0.06) dex. This is similar to the slope found by Bentz et al. (2009b) using a smaller number of galaxies in the reverberation sample and covering a smaller range of black hole masses. The scatter is much decreased, however, from ∼0.4 dex to 0.23 dex.

In the H band, we find a best-fit relationship of

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=(1.05\pm 0.14)\mathrm{log}\left(\displaystyle \frac{{L}_{H,\mathrm{bulge}}}{{10}^{10}{L}_{\odot }}\right)+(7.06\pm 0.11)\end{eqnarray} \tag{ 4 }$$

with a typical scatter of (0.25 ± 0.07) dex. Surprisingly, the scatter in the near-infrared relationship is statistically equivalent to that of the optical relationship, suggesting that dust and/or recent star formation are not strong contributors to the intrinsic scatter in the relationship. As previously mentioned, however, there is still room for improvement in the distances, so it is likely that the scatter in both the optical and near-infrared relationships could be further decreased in the future through efforts to determine distances that do not rely on the galaxy redshift.

We display these relationships in Figure 3. The solid line shows the best fit, while the gray shaded regions show the uncertainties in the fit. We denote broad-line Seyferts 1s (BLS1s) with filled circles and narrow-line Seyferts 1s (NLS1s) with open circles. We follow the original definition of Osterbrock & Pogge (1985) and select NLS1s in cases where the broad Hβ emission line has FWHM < 2000 km s⁻¹. While the NLS1s tend to be associated with lower-mass black holes in lower-luminosity bulges, they exhibit the same scatter and general scaling relationship as the BLS1s. Some studies of NLS1s with black hole estimates have shown them to be significantly undermassive relative to BLS1s (e.g., Mathur et al. 2012), but we see no strong tendency for NLS1s to be undermassive relative to the other reverberation-mapped AGNs included here.

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Kormendy & Ho (2013) report a near-infrared ${M}_{\mathrm{BH}}\mbox{--}{L}_{\mathrm{bulge}}$ relationship in the 2MASS K_S band for quiescent galaxies that are ellipticals or contain classical bulges, and for which black hole masses have been determined through dynamical modeling. They find a slightly steeper slope of 1.21 and a scatter of 0.31 dex, both of which are consistent within the errors with our finding for the active galaxy sample in H. The slightly higher intercept for their sample compared to ours is increased by the color difference between the H and K bands, given that galaxies are typically somewhat brighter in K than H.

While Kormendy & Ho (2013) do not report a fit to the ${M}_{\mathrm{BH}}\mbox{--}{L}_{\mathrm{bulge}}$ relationship in V, they do tabulate bulge absolute magnitudes in V. We fit the V-band relationship matching their accepted sample and adopted uncertainties and find a slope that agrees with their value reported for the K_s band, which is steeper than the slope that we find in V for the active galaxy sample. The intercept is also somewhat higher, although the fit to their sample agrees with our findings for the active galaxy sample at the low-mass end. The fits to the Kormendy & Ho (2013) sample are shown as black dashed lines in Figure 3. It is important to note that the active and quiescent samples primarily probe different regions of parameter space in this plot: the active galaxy sample is heavily dominated by galaxies with M_BH < 10⁸ M_⊙, while the vast majority of galaxies in the quiescent sample have M_BH > 10⁸ M_⊙.

Läsker et al. (2016) report deep H-band imaging and surface brightness decompositions for a sample of nine megamaser galaxies with accurate black hole masses. We find that the megamasers are contained wholly within the scatter of the active galaxy sample presented here in the H band. With the good agreement between the active galaxies, the megamasers, and the quiescent galaxy sample, we therefore refit the ${M}_{\mathrm{BH}}\mbox{--}{L}_{\mathrm{bulge}}$ relationship in H with all three samples combined. Based on the typical galaxy properties in 2MASS reported by Jarrett (2000), we adopt $\langle H-{K}_{s}\rangle =0.3$ mag for the quiescent sample, which should account for any average color offset between the two filters (although we note that the scatter in H − K_s values is typically ∼0.2 mag, even for galaxies with a specific morphological type). The best fit is

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=(1.31\pm 0.09)\mathrm{log}\left(\displaystyle \frac{{L}_{H,\mathrm{bulge}}}{{10}^{10}{L}_{\odot }}\right)+(7.27\pm 0.08)\end{eqnarray} \tag{ 5 }$$

with a typical scatter of 0.26 ± 0.05 dex. While Läsker et al. (2016) do not report V-band measurements for the megamaser sample, we can investigate the ${M}_{\mathrm{BH}}\mbox{--}{L}_{\mathrm{bulge}}$ relationship in V for the active and quiescent samples combined. When we do, we find a best fit of

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=(1.13\pm 0.08)\mathrm{log}\left(\displaystyle \frac{{L}_{V,\mathrm{bulge}}}{{10}^{10}{L}_{\odot }}\right)+(8.04\pm 0.06)\end{eqnarray} \tag{ 6 }$$

with a typical scatter of (0.24 ± 0.05) dex. These fits are displayed as the red long-dashed lines in Figure 3. In both the H and V bands, the best fit for the combined sample has an almost identical scatter to that found for the active sample alone, even though the combination of the samples more than doubles the number of points being fit and extends the range of M_BH by an order of magnitude. This may indicate that the galaxies in all three samples are drawn from the same parent population.

We also examined the relationship between black hole mass and total luminosity of the host galaxy. We find a clear correlation between these two measurements, in both the optical and the near-infrared. The best-fit relationships are found to be

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=(1.25\pm 0.22)\mathrm{log}\left(\displaystyle \frac{{L}_{V,\mathrm{galaxy}}}{{10}^{11}{L}_{\odot }}\right)+(8.26\pm 0.16)\end{eqnarray} \tag{ 7 }$$

in the V band, with a typical scatter of (0.34 ± 0.09) dex, and

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=(1.56\pm 0.24)\mathrm{log}\left(\displaystyle \frac{{L}_{H,\mathrm{galaxy}}}{{10}^{11}{L}_{\odot }}\right)+(7.75\pm 0.10)\end{eqnarray} \tag{ 8 }$$

in the H band, with a typical scatter of (0.32 ± 0.09) dex.

While the scatter is somewhat higher than that of the ${M}_{\mathrm{BH}}\mbox{--}{L}_{\mathrm{bulge}}$ relationship, the fact that there is still a relatively tight relationship found when the total galaxy luminosity is used (see Figure 4) suggests that bulge/disk decompositions can be avoided when estimating black hole masses from broadband photometry of disk galaxies, but with a loss of some accuracy. This may be of particular interest for large photometric surveys that are operational or coming online soon (e.g., LSST), where automated measurements will be key to making sense of the large data sets that will be produced.

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Our best-fit relationships for active galaxies may again be compared to the Kormendy & Ho (2013) sample of quiescent galaxies. The best-fit relationships based on their tabulated measurements in V and K_s have similar slopes and scatter to our findings, but their intercepts are significantly higher. This appears to stem from the differences in morphology between their sample and ours, as well as the different ranges of M_BH between the two samples. While the intercepts for the ${M}_{\mathrm{BH}}\mbox{--}{L}_{\mathrm{bulge}}$ relationships traced by the active galaxy sample show good agreement with the quiescent galaxies, two-thirds of the galaxies in the Kormendy & Ho (2013) sample are ellipticals. Thus, the ${M}_{\mathrm{BH}}\mbox{--}{L}_{\mathrm{galaxy}}$ relationships for their sample are very similar to the ${M}_{\mathrm{BH}}\mbox{--}{L}_{\mathrm{bulge}}$ relationships, because two-thirds of the points between them are exactly the same. On the other hand, the active galaxy sample is dominated by later-type galaxies where the bulge contributes a smaller fraction of the integrated galaxy light, and so the best-fit ${M}_{\mathrm{BH}}\mbox{--}{L}_{\mathrm{bulge}}$ and ${M}_{\mathrm{BH}}\mbox{--}{L}_{\mathrm{galaxy}}$ relationships that we find for the active galaxies are quite different from each other.

We looked at the bulge-to-total ratios for the active galaxy sample and investigated whether splitting the sample into "early" (B/T > 0.5) and "late" (B/T < 0.5) types uncovered any offsets or separations among the sample that may lead to better agreement with the quiescent galaxy sample. The only obvious difference between these two subsamples is that the "early" types have more massive black holes than the "late" types, and so a cut in B/T is similar to a cut in M_BH and does not improve the agreement. As before, we also investigated the location of the Läsker et al. (2016) megamasers and find that they are wholly contained within the H-band scatter of the active galaxy sample. If we again combine the active, quiescent, and megamaser samples as before, we find best fits of

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=(1.33\pm 0.17)\mathrm{log}\left(\displaystyle \frac{{L}_{V,\mathrm{galaxy}}}{{10}^{11}{L}_{\odot }}\right)+(8.89\pm 0.13)\end{eqnarray} \tag{ 9 }$$

in the V band, with a typical scatter of (0.55 ± 0.09) dex, and

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=(1.54\pm 0.18)\mathrm{log}\left(\displaystyle \frac{{L}_{H,\mathrm{galaxy}}}{{10}^{11}{L}_{\odot }}\right)+(8.22\pm 0.08)\end{eqnarray} \tag{ 10 }$$

in the H band, with a typical scatter of (0.52 ± 0.08) dex. Thus, while the scatter is significantly increased when galaxies of all morphological types are treated equally, it is likely more representative of the true uncertainty on black hole mass estimates from the total galaxy luminosity.

The relationship between black hole mass and bulge stellar mass is expected to be the physical basis for the ${M}_{\mathrm{BH}}\mbox{--}{L}_{\mathrm{bulge}}$ relationship, where bulge light traces mass. A variety of methods have been used to investigate this relationship in the past, often with the aim of decoupling the ${M}_{\mathrm{BH}}\mbox{--}{M}_{\mathrm{bulge}}$ relationship from any dependence on the ${M}_{\mathrm{BH}}\mbox{--}{L}_{\mathrm{bulge}}$ relationship so they can be studied independently.

For example, Magorrian et al. (1998) carried out axisymmetric dynamical models to constrain the bulge mass and the black hole mass simultaneously. Marconi & Hunt (2003) measured effective bulge radii from 2MASS imaging for quiescent galaxies with dynamical black hole masses. The bulge radii were combined with σ_* to predict M_bulge under the assumption that bulges behave similarly to isothermal spheres. Häring & Rix (2004), on the other hand, numerically solved the spherical Jeans equation while matching published luminosity and σ_* profiles for quiescent galaxies with dynamical black hole masses.

We can examine this relationship for active galaxies by estimating the bulge stellar mass from its optical−near-infrared color and the M/L prescriptions described above. The best-fit relationship between the black hole mass and the stellar mass of the bulge, based on the Bell & de Jong (2001) M/L predictions, is found to be

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=(1.06\pm 0.24)\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{bulge}}}{{10}^{10}{M}_{\odot }}\right)+(7.02\pm 0.17)\end{eqnarray} \tag{ 11 }$$

with a typical scatter of (0.39 ± 0.12) dex.

If we estimate M/L using the prescriptions of Into & Portinari (2013), we find the best fit to be

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=(0.80\pm 0.30)\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{bulge}}}{{10}^{10}{M}_{\odot }}\right)+(7.36\pm 0.15)\end{eqnarray} \tag{ 12 }$$

with a typical scatter of (0.55 ± 0.16) dex. These relationships are displayed in Figure 5.

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For a direct comparison with the quiescent galaxy sample, we recalculated the bulge masses based on the absolute V magnitudes of the bulges and the V − K_s colors tabulated by Kormendy & Ho (2013) with the M/L prescriptions of both Bell & de Jong (2001) and Into & Portinari (2013). Because Kormendy & Ho (2013) only provide an integrated V − K_s color for each galaxy, we note that we would expect there to be a bias in the bulge masses derived for the disk galaxies in their sample because of the different colors of bulges and disks. The best-fit relationships for the quiescent galaxies are shown as the black dashed lines in Figure 5.

While the active galaxy sample displays a linear relationship between M_BH and bulge stellar mass, the quiescent galaxy relationships are considerably steeper. The two samples agree better using the M/L prescriptions of Bell & de Jong (2001), although both prescriptions show agreement between the samples at the low-mass end.

The megamaser sample of Läsker et al. (2016) reports M_bulge based on near-infrared HST and ground-based imaging and the M/L prescriptions of Bell et al. (2003), which allows for a simple comparison with our results. We again find that all nine megamasers are contained wholly within the scatter of the active galaxy sample, with no apparent offsets in bulge mass or black hole mass.

Noting that there is good agreement between the active, quiescent, and megamaser samples, we also fit the ${M}_{\mathrm{BH}}\mbox{--}{M}_{\mathrm{bulge}}$ relationship with all three samples combined. Assuming the Bell & de Jong (2001) M/L prescriptions, the best-fit relationship is

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=(1.50\pm 0.13)\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{bulge}}}{{10}^{10}{M}_{\odot }}\right)+(7.16\pm 0.11)\end{eqnarray} \tag{ 13 }$$

with a scatter of (0.27 ± 0.06) dex. The red long-short dashed line in the left panel of Figure 5 displays this fit. While the slope is considerably steeper than that found for the active galaxy sample, they only disagree at the ∼1σ level. Furthermore, there is good agreement with the gray shaded region (which denotes the uncertainty on the fit to the active sample alone) over the range sampled by the active galaxies. This appears to indicate that all three samples may be drawn from the same parent population of galaxies.

We also compared our results to those of simulated galaxies. Some caution must be taken when interpreting such comparisons, because cosmological galaxy simulations are generally tuned to match a set of observables. For example, the slope of the ${M}_{\mathrm{BH}}\mbox{--}{M}_{\mathrm{bulge}}$ relationship is not expected to be affected by such tuning, but the intercept is. Furthermore, there is no agreement on the best way to separate the bulges of late-type galaxies from their disks in simulations, where the resolution is often a limiting factor, so the simulated galaxies are either compared to samples of massive early-type galaxies where M_bulge ≈ M_galaxy (e.g., Schaye et al. 2015; Steinborn et al. 2015) or a prescription is applied to estimate the bulge contribution.

Sijacki et al. (2015) used the high-resolution hydrodynamical Illustris simulations to explore the predicted ${M}_{\mathrm{BH}}\mbox{--}{M}_{\mathrm{bulge}}$ relationship for galaxies. The total stellar mass within the stellar half-mass–radius was used as a proxy for the bulge mass. This simplification does not take into account different bulge mass fractions of galaxies, nor the fact that some galaxies may not have a bulge at all. Additionally, the Illustris simulations assumed a Chabrier IMF, which can be compared to a "diet" Salpeter like that employed by Bell & de Jong (2001) by adding 0.093 dex (Gallazzi et al. 2008). To compare with a Kroupa IMF like that employed by Into & Portinari (2013), on the other hand, we subtracted 0.057 dex (Bell et al. 2003; Herrmann et al. 2016). The best-fit relationship of Sijacki et al. (2015), with the IMF scaled appropriately, is displayed as the blue long-dashed lines in Figure 5. With a reported slope of 1.21, it is in good agreement with our findings, especially when we adopt the Bell & de Jong (2001) M/L prescriptions.

The large-volume Horizon-AGN simulations, which adopt a Salpeter IMF, were analyzed by Volonteri et al. (2016). To separate the bulge contribution, they tried various prescriptions, including examining the kinematics and also adopting a double Sérsic model for each galaxy, where the indices for the two Sérsic profiles were chosen to be [1.0, 1.0], [1.0, 4.0], or [1.0, 1.0 or 4.0]. The slope of the relationship based on these various prescriptions ranges from 0.75 to 1.05, which is in good agreement with our findings for the active galaxies using either the Bell & de Jong (2001) or Into & Portinari (2013) M/L prescriptions, although it is somewhat in tension with our results for the combined active, quiescent, and megamaser samples. This tension may result from incompleteness in the Horizon-AGN simulation for black holes with M_BH ≲ 2 × 10⁷ M_⊙, which is the region probed by many of the active galaxies.

In the same way, we can examine the best-fit relationship between the black hole mass and the total stellar mass of the galaxy. When we adopt the Bell & de Jong (2001) M/L predictions, we find a best fit of

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=(1.69\pm 0.46)\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{stars}}}{{10}^{11}{M}_{\odot }}\right)+(8.05\pm 0.18)\end{eqnarray} \tag{ 14 }$$

with a typical scatter of (0.38 ± 0.13) dex.

If we instead estimate M/L using the prescriptions of Into & Portinari (2013), we find the best fit to be

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=(1.34\pm 0.55)\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{stars}}}{{10}^{11}{M}_{\odot }}\right)+(8.49\pm 0.41)\end{eqnarray} \tag{ 15 }$$

with a typical scatter of (0.49 ± 0.17) dex. These relationships are displayed in Figure 6.

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Interestingly, the ${M}_{\mathrm{BH}}\mbox{--}{M}_{\mathrm{stars}}$ relationship based on the Into & Portinari (2013) M/L values is similar to that found by Reines & Volonteri (2015) for inactive black holes residing in ellipticals and classical bulges. This would seem to contradict their finding that active galaxies lie below the relationship defined by local quiescent galaxies, although a direct comparison is somewhat difficult given that they used M/L prescriptions of Zibetti et al. (2009), who employ a different initial mass function than Into & Portinari (2013).

We therefore recalculated the ${M}_{\mathrm{BH}}\mbox{--}{M}_{\mathrm{stars}}$ relationship for local quiescent galaxies based on the absolute V magnitudes and the V − K_s colors tabulated by Kormendy & Ho (2013), using both the Bell & de Jong (2001) and Into & Portinari (2013) M/L prescriptions for direct comparison with the active galaxies in our sample. The best fits are shown as the dashed lines in Figure 6. Using the Bell & de Jong prescription, we find a nearly identical slope for the quiescent galaxies compared to the active galaxies, but an intercept that is 0.75 dex higher, supporting the findings of Reines & Volonteri (2015) that active galaxies fall below quiescent galaxies in this parameter space. However, using the Into & Portinari prescription instead, we find a slightly steeper slope for the quiescent galaxies which, when coupled with the intercept, show the two samples to be in general agreement at the low-mass end while diverging at the high-mass end.

If we again combine the active sample with the quiescent galaxies and the megamasers, we find a best-fit relationship of

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=(1.84\pm 0.25)\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{stars}}}{{10}^{11}{M}_{\odot }}\right)+(8.40\pm 0.09)\end{eqnarray} \tag{ 16 }$$

with a scatter of (0.44 ± 0.10) dex. This fit is denoted with the red long-short dashed line in the left panel of Figure 6. Once again, the consistency with the results derived solely from the active galaxies seems to indicate that all of these subsamples may be drawn from the same parent population.

Recently, Shankar et al. (2016) investigated the potential for selection bias among the quiescent galaxy sample using Monte Carlo simulations and a large sample of galaxies drawn from the Sloan Digital Sky Survey. They concluded that the quiescent galaxy sample is selected from an upper "ridgeline" in the distribution of normal galaxy properties, leading to a bias of a factor of ∼3 in the normalization of the ${M}_{\mathrm{BH}}\mbox{--}{\sigma }_{\star }$ relationship. If such a bias exists, that would argue against our choice of scaling factor for reverberation-based masses in the active galaxy sample, and would instead argue for f ≈ 1. Interestingly, when we adopt f = 1 for the scaling of reverberation-based M_BH, and examine the ${M}_{\mathrm{BH}}\mbox{--}{M}_{\mathrm{stars}}$ relationship based on the M/L prescriptions of Bell & de Jong (2001), we find that the active galaxy sample closely follows the predicted unbiased relationship in Equation (6) of Shankar et al. (2016). The stellar masses predicted by Into & Portinari (2013), however, are undermassive compared to the predicted relationship, even when accounting for the slight differences in assumed IMF. However, it appears that bars will affect the measurements of effective radii (Meert et al. 2015) and possibly velocity dispersion (Batiste et al. 2017) that are adopted for the "unbiased" SDSS sample considered by Shankar et al. (2016). These effects will be strongest at the low-mass end, where most of the active galaxies in our sample are found, thus complicating the interpretation for reverberation-based masses. Furthermore, forward modeling of velocity-resolved reverberation signals by Pancoast et al. (2014) and Grier et al. (2017) has constrained the geometry and kinematics of the broad line region and the black hole mass for nine AGNs, independent of any f factor. Both studies recover modeling-based black hole masses that agree well with M_BH values derived from traditional reverberation analysis and the use of f ≈ 4 (as described in Section 4.5). These findings argue against the use of f = 1 for the proper scaling of reverberation masses, but do not rule out that there may be biases present in the quiescent galaxy sample.

Unlike for the ${M}_{\mathrm{BH}}\mbox{--}{M}_{\mathrm{bulge}}$ relationship, comparisons with simulated galaxies are much simpler when the entire galaxy stellar mass is used because the issues with bulge–disk decompositions are avoided, although the caveats related to the tuning of parameters in the simulations remain. Mutlu-Pakdil et al. (2018) recently examined the relationships between black holes and large-scale galaxy properties for z = 0 spiral galaxies in the Illustris simulations. Using the same IMF corrections described in the previous section, we compare our best-fit ${M}_{\mathrm{BH}}\mbox{--}{M}_{\mathrm{stars}}$ relationships to theirs (blue long-dashed lines in Figure 6) and we find excellent agreement, especially when we adopt the Bell & de Jong (2001) M/L prescriptions, which may argue against any potential bias in the reverberation-based M_BH scaling. Volonteri et al. (2016) examined the ${M}_{\mathrm{BH}}\mbox{--}{M}_{\mathrm{stars}}$ relationship for galaxies from the Horizon-AGN simulation, and found a slope that is somewhat shallower than we have found, although the low-mass end of their relationship may be biased by incompleteness. Steinborn et al. (2015) used the Magneticum Pathfinder Simulations to examine the ${M}_{\mathrm{BH}}\mbox{--}{M}_{\mathrm{stars}}$ relationship, excluding simulated galaxies for which M_BH < 5 × 10⁷ M_BH. Perhaps unsurprisingly, their reported best-fit relationship (with a slope of 1.09) agrees with the most massive black holes in the active galaxy sample (M_BH ≳ 10⁸ M_⊙), but diverges at lower black hole masses, predicting a larger M_BH at fixed M_stars, similar to the findings of Volonteri et al. (2016).

Many large photometric surveys that are currently in operation or are upcoming will collect photometry in multiple filters. Considering that these surveys may need to be treated in an automated fashion, the stellar mass of the galaxy based on its color appears to be a better predictor of black hole mass than the total galaxy luminosity in a single filter. This can be seen from the decreased scatter in the ${M}_{\mathrm{BH}}\mbox{--}{M}_{\mathrm{stars}}$ relationship for the combined active, quiescent, and megamaser samples (0.44 ± 0.10 dex) relative to the ${M}_{\mathrm{BH}}\mbox{--}{L}_{\mathrm{galaxy}}$ relationship (∼0.53 ± 0.09 dex).

Finally, we investigated the typical fraction of black hole mass to stellar mass for each galaxy. We find a median value of M_BH/M_stars = 0.0005 ± 0.0049; however, we also find a very clear relationship between M_BH/M_stars and M_BH, while there appears to be no obvious relationship between M_BH/M_stars and M_stars (see Figure 7).

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For comparison, we derived the black hole mass fractions for the quiescent galaxy sample of Kormendy & Ho (2013) and found a median value of M_BH/M_stars = 0.0058 ± 0.0077. At first glance, this would appear to demonstrate that active galaxies host undermassive black holes compared to quiescent galaxies. However, the samples cover different M_BH ranges, with the active galaxy sample skewed toward lower M_BH, while the quiescent galaxy sample is skewed to higher M_BH (see Figure 8), and M_BH/M_stars seems to depend strongly on M_BH. For a better comparison between the two samples, we binned the galaxies in each sample by M_BH with bins of width 0.5 dex. For each bin with three or more objects, we computed the median black hole mass to stellar mass fraction. Figure 8 shows the median M_BH/M_stars as a function of M_BH for the two samples, with the active sample in red and the quiescent sample in black. The majority of the overlap between the samples exists within the range 10⁷ < M_BH/M_⊙ < 10⁹, with the range extending to lower black hole masses in the active galaxy sample, and extending to higher black hole masses in the quiescent galaxy sample. We have adopted M_stars based on the M/L predictions of Bell & de Jong (2001) in Figure 8 but, while the values slightly change, the overall trend is the same if we adopt M_stars based on the Into & Portinari (2013) M/L values. The two samples show broad agreement, both in the overall trend—with more massive black holes comprising larger mass fractions of their galaxies—and with the typical values for the black hole mass fraction at a fixed value of M_BH. While there seems to be a tendency for the active galaxies to lie slightly below the quiescent galaxies in the expected black hole mass fraction at a fixed black hole mass, the values agree within the standard deviation for each bin, and the small and uneven number of objects in each bin make it difficult to draw firm conclusions about any apparent offset between the two samples. Notably, the trend appears to continue across the full range of black hole masses probed by either sample.

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We also examined the megamaser sample of Läsker et al. (2016) for comparison. Adopting the same bins for the megamaser sample as for the above two samples, we show the median M_BH/M_stars in blue in Figure 8. There is no apparent offset between the megamaser and the reverberation samples, nor with the extension of the quiescent sample to lower black hole masses. Läsker et al. (2016) noted in their study that the megamaser galaxies appeared to probe a lower M_BH at fixed galaxy mass than the reverberation sample (as reported by Bentz et al. 2009a), but this discrepancy has been completely erased with the larger sample and extended range of M_BH and galaxy properties presented here.

The scaling of M_BH/M_stars as a function of M_BH was previously noticed by Trakhtenbrot & Netzer (2010). Using large samples of local non-AGN galaxies and AGN galaxies at z ≈ 0.15, 1, 2 and scaling relationships to predict M_stars and M_BH, they found that M_BH/M_stars ∝ (0.7 ± 0.1)M_BH. A formal fit to the active, quiescent, and maser galaxies examined here finds

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\mathrm{stars}}}=(0.71\pm 0.04)\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{BH}}}{{10}^{8}{M}_{\odot }}\right)-(2.80\pm 0.04)\end{eqnarray} \tag{ 17 }$$

with a typical scatter of (0.04 ± 0.02) dex, which agrees well with a formal fit to the active galaxies alone, and to the estimated slope reported by Trakhtenbrot & Netzer (2010).

Interestingly, we find the same scaling between M_BH/M_stars and M_BH among simulated galaxies from Illustris. Vogelsberger et al. (2014) provide black hole masses and galaxy stellar masses for two subsamples of representative "red" and "blue" galaxies from the Illustris simulation. The "blue" galaxies preferentially occupy the lower M_BH range that is probed here by the active and megamaser samples, and the "red" galaxies preferentially occupy the upper M_BH range probed by the quiescent galaxies. The scaling in M_BH/M_stars as a function of M_BH in the simulated galaxies matches the observed galaxies extremely well in both slope and offset.

It is clear from these studies that the commonly used assumption of a constant M_BH/M_stars is incorrect in the local universe and possibly up to z ≈ 2. Attempts to search for cosmic evolution of black holes and host galaxies, or to search for differences in the evolutionary paths of distinct galaxy samples, should be careful to account for this scaling when the samples are not matched in M_BH.

We suggest that the physical meaning of this scaling may be related to differences in feedback efficiency as a function of galaxy mass. High-resolution and zoom-in simulations of individual galaxies show that supernova feedback is extremely effective at prohibiting black hole growth at early times (e.g., Dubois et al. 2015; Anglés-Alcázar et al. 2017; Trebitsch et al. 2018). Once the host galaxy reaches a critical mass (M_stars ≈ 10⁹–10¹⁰ M_⊙; Dubois et al. 2015; Anglés-Alcázar et al. 2017), supernova feedback can no longer restrict the gas flow to the nucleus and the black hole will undergo a period of rapid growth, effectively "catching up" with the galaxy. This period of rapid growth is short-lived, however, because AGN feedback soon becomes important and the black hole then regulates its own growth and the continued growth of the galaxy (e.g., Dubois et al. 2015; McAlpine et al. 2017). In this scenario, we may currently be witnessing the rapid growth phase for low-mass black holes in the local universe.