THE BLACK HOLE–BULGE MASS RELATION IN MEGAMASER HOST GALAXIES^*

Our sample of megamaser disk galaxies with BH masses is taken from Greene et al. (2010), with most of the ${M}_{\mathrm{BH}}$ measurements provided by (Kuo et al. 2011, Table 1). We focus on these nine galaxies because they have Keplerian megamaser rotation curves and high-resolution imaging data, and thus well-determined ${M}_{\mathrm{BH}}$. While the BH mass we adopt for IC 2560 (${10}^{6.4\pm 0.4}\;{M}_{\odot }$; Kuo et al. 2011) is based on single-dish data, published and preliminary reductions of VLBI data yield log ${M}_{\mathrm{BH}}$/$\;{M}_{\odot }$ of 6.54 ± 0.06 (Yamauchi et al. 2012) and 6.64 ± 0.03 (J. Wagner et al. 2016, in preparation). If we were to adopt those values, then the results for the BH scaling relations (relation parameter and subsample offsets, see Section 5) would barely change (within a few percent of the uncertainties). Several of our targets are $\gt 50\;\mathrm{Mpc}$ away, and most of them were previously known or suspected to host small-scale structures (nuclear rings, disks, or bars) in addition to the bulge. High-resolution imaging is thus essential for a robust analysis. We do not include Circinus, NGC 1068, or NGC 4945 in this work, since comparable high-resolution data are not readily available for them, but we will consider the first two as a secondary sample in Section 5.

Table 1.  The Megamaser Sample

Galaxy	R.A.	decl.	D	Hubble Type	LH	Re	texp	Obs. Date	Wide-field Imaging
			(Mpc)		$({10}^{10}\;{L}_{\odot ,H})$	(kpc)	(s)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
IC 2560	10:16:18.7	−33:33:50	41.8	(R)SB(r)b	13.2	4.0	422	2010 Oct 23	UVIS F814W, LCO DuPont/Tek-I
NGC 1194	03:03:49.1	−01:06:13	52.0	SA0+	5.75	2.8	422	2011 Nov 23	APO3.5 m/NIC-K
NGC 2273	06:50:08.6	+60:50:45	26.0	SB(r)a:	3.47	1.4	422	2011 Jan 31	APO3.5 m/NIC-K
NGC 2960	09:40:36.4	+03:34:37	71.0	Sa?	7.76	1.9	422	2011 Jun 14	APO3.5 m/NIC-K
NGC 3393	10:48:23.4	−25:09:43	53.6	(R)SB(rs)	9.33	2.5	422	2011 Nov 11	UVIS F814W
NGC 4388	12:25:46.7	−12:39:44	19.0	SA(s)b:	3.09	1.4	422	2011 Jun 08	APO3.5 m/NIC-K
NGC 6264	16:57:16.1	−27:50:59	136.0	S?	8.71	4.0	422	2011 Jul 30	APO3.5 m/NIC-K
NGC 6323	17:13:18.1	−43:46:57	105.0	Sab	8.71	2.5	422	2011 Sep 01	WIYN/WHIRC-K
UGC 03789	07:19:30.9	−59:21:18	50.0	(R)SA(r)ab	5.37	2.2	422	2011 Sep 06	APO3.5 m/NIC-K

Note. Columns (1)–(5) give the galaxy name, coordinates, distance in Mpc, and Hubble Type (RC3 catalog, de Vaucouleurs et al. 1991). Column (6) gives the galaxy (total) H-band luminosity in units of ${10}^{10}\;{L}_{\odot ,H}$, and column (7) the galaxy effective radius in kiloparsecs. Both the L_H and R_e values result from our imaging data and multi-component fitting. The inner parts are imaged with HST/WFC3 in the F160W filter, with exposure times in seconds, and the dates are given in columns (8) and (9). In order to place constraints on the outer parts of the surface brightness that did not fit on the WFC3-IR FOV of $70\buildrel{\prime\prime}\over{.} 4\times 62\buildrel{\prime\prime}\over{.} 6$, we also include data that we obtained on the telescopes and instruments given in column (10).

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The high-resolution Hubble Space Telescope (HST) data (FWHM $=\quad 0\buildrel{\prime\prime}\over{.} 15$ in the H band corresponding to 50 pc at the median sample distance of 70 Mpc) were taken between 2010 October and 2011 November (see Table 1). We obtained HST/WFC3-IR imaging with filters F110W and F160W (similar to the 2MASS J and H bands) for each galaxy. Within the same program, we also acquired WFC-UVIS exposures in the F336W, F438W, and F814W filters (roughly the U, B, and I bands). We base our bulge luminosities and derived masses on the H-band data in order to reduce the uncertainties associated with dust obscuration and variations in stellar population, as compared to the optical bands. Indeed, many of the late-type galaxies in our sample are quite dusty and have complicated color profiles. We use the color information contained in the UVIS bands for a refined luminosity–mass conversion.

All of our galaxies were imaged in four exposures with F160W using sub-pixel dithering and a total exposure time of 422 s. They were co-added and cleaned of cosmic rays using the PyFits MultiDrizzle pipeline.⁸ In order to fit our five-band observations into two orbits, we utilize sub-arrays to avoid buffer dumps. The field of view (FOV) of the subarray is 70 × 62 arcsec, which is filled by the target in all cases. MultiDrizzle provides exposure time maps for the combined frame which we use to calculate the noise map needed for model fitting with galfit.

Since our HST data do not cover the outskirts of our target galaxies, we obtained additional wide-field imaging data. Most of these were ground-based K-band images which were acquired from 2010 to 2012 on the Apache Point Observatory (APO) and WIYN⁹ 3.5 m telescopes, using the NICFPS and WHIRC instruments, respectively (http://nicfps.colorado.edu/; Smee et al. 2011). In two fields (IC 2560 and NGC 3993), sufficiently deep NIR images were not available; here, we used HST WFC3 F814W and Las Campanas Observatory (LCO) du Pont 100-inch SITe2K-CCD I-band images. For details of the instruments, exposure times, and observing dates, see Table 1. Aside from providing valuable constraints on the derived galaxy parameters, and thus allowing robust fits to the complex morphologies that we encounter, their FOV is also large enough to allow reliable background subtraction, unbiased by galaxy light. In ground-based K-band images, these advantages are tempered by a bright ($\sim 14\;\mathrm{mag}\;{\mathrm{arcsec}}^{-2}$) background that is variable both spatially and temporally. A carefully designed observing strategy and data reduction is therefore required to achieve reliable background subtraction.

In taking the data, we apply a large-scale dither pattern, with the target first imaged near the detector center and then moved toward the corners of the FOV in a clockwise pattern. Before and after every on-target exposure, we perform an off-target exposure, and the whole pattern is repeated several times. This results in ∼25 science frames and twice the number of sky frames. With this strategy, we obtain a reliable reconstruction of the background, since every part of the detector remains unoccupied by the relatively large target galaxy at least in a sizeable fraction of the exposures, and we can simultaneously monitor the evolution of the background level and the two-dimensional structure in the background.

Using the dark and twilight flat frames, we identify bad pixels and mask them in all subsequent exposures. After flatfielding the raw frames, a background pattern (see bottom-left panel in Figure 1) persists, as does a much weaker, near-random pattern that corresponds to the expected pattern from variable non-uniform sky (atmospheric) emission. We ascribe the time-invariant portion of the residual background pattern to a discrepancy between the twilight flatfield image and the response of the detector to night sky illumination. Therefore, we need to subtract the mean background pattern that persists after the frames have been flatfielded with the twilight flat. The standard alternative, i.e., dome flatfield images, provides a significantly poorer approximation to the nighttime sky (and flatfield) pattern. Alternatively, we addressed the residual time-invariant background pattern by flatfielding using a "superflat," which is a flatfield image constructed from the images taken over the course of the night. However, we found no improvement in the background subtraction using this method. To achieve the required signal-to-noise ratio (S/N) in the flat requires summing over most of the images over the course of the night, but there is sufficient change in the background pattern with time that residual patterns remain after flatfielding with the "superflat."

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We construct an image of the mean residual background pattern as follows. We first normalize each frame by its mean background, and then take a pixel-by-pixel median over all of the normalized frames, including all sky frames and on-target frames when the target covers less then 40% of the FOV. By averaging so many frames, we can remove additional bad pixels and astronomical sources while retaining a high S/N in the averaged sky image. For the masking of intervening objects, we use source detection by the SExtractor software, combined with by-hand masks for bright stars and extended objects (galaxies). The mask for measuring the mean must be a combination of the masks of all frames, in order to avoid level offsets caused by large masked objects covering different parts of the detector on an uneven background. We subsequently subtract from each frame this "sky structure" image, scaled by the frame's background level.

This procedure is very effective at removing the residual near-constant background pattern (see Figure 1, bottom right panel). However, it requires that every part of the detector be uncontaminated by celestial sources, which renders the on-target frames unusable in some galaxies. For those fields, the sky pattern can still be reconstructed using the interleaved sky exposures. Naturally, for a successful background subtraction, we also need to measure the average sky level, apart from its spatial structure. For this, we use on-target measurements rather than the pure sky frames because the mean sky level fluctuates by $\sim 1 \%$ ($\sim 16\mbox{--}17\;\mathrm{mag}\;{\mathrm{arcsec}}^{-2}$) even on timescales of a minute or less.

After subtracting the sky structure and level, we coadd our frames. To that end, we re-detect all astronomical sources using SExtractor, use the resulting source catalogs to compute a third-order polynomial astrometric solution of the field distortion and true pointings (different from the coordinates found in the headers by $\sim 1^{\prime\prime}$ on average), and finally re-project and coadd the frames using SWarp.

After this first-pass sky subtraction and co-addition, we have an image that is much deeper than any individual frame, and hence offers a much better opportunity to mask faint sources (stars and small background galaxies) as well as low-level extended "wings" of bright stars and large galaxies. It also allows a better visual identification of large galaxies in the field. In fact, faint but previously unmasked source flux does sometimes leave visible imprints in the sky-subtracted frames which propagate to the first-pass stack. After obtaining the improved masks from the deep first-pass stack, we repeat the above procedure, but this time we use the deep mask projected onto the individual frames. This improves the sky structure model and removes remaining artifacts in the background.

We combine HST (H band) with ground-based images in order to provide sufficient constraints during the fitting process. We experimented and found that most of the real structures present in our galaxies cannot be analyzed reliably with galfit when either the ground-based or HST data are taken alone. For the medium-resolution (median FWHM $\sim \;0\buildrel{\prime\prime}\over{.} 8$), ground-based data, the cause is clear: small-scale structures are not resolved and a basic bulge plus disk model is the only feasible model in most cases. However, the HST data alone are also insufficient: the lack of data at large scales prevents a convergence of more complex models. In SB profile modeling, the need for large-scale information on both the galaxy light distribution and the background has been discussed in Peng et al. (2010).

We combine each co-added HST J- or H-band image with ground-based K-band data by first scaling the former to the latter: we measure the radial SB profiles in both, and pick by eye the part of the profile in which both overlap and exhibit the same shape. The matched profiles (Figure 2) show that the J-and H-band profiles are very similar to the K-band profiles, except in the very center (active galactic nucleus (AGN) light and dust) and around spiral arms (dust and young stellar populations), and the similarity of the profiles justifies our approach. After rescaling and background-subtracting the HST images using a linear fit to the profiles, $\langle {HST}\rangle =\langle {\rm{bkg}}\rangle \;+\langle {\rm{scale}}\rangle \ast \langle {\rm{ground}}\rangle$, we resample the ground-based image stack onto the HST WCS and replace K-band data with HST data where they exist. Similarly, we re-project, scale, and replace the noise and weight maps of K-band stacks with HST data where available.

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Although there is considerable interest in the correlations between BH mass and bulge luminosity or mass, there are few works that examine bulge masses in spiral galaxies with dynamical BH masses (they include Gadotti 2008; Hu 2008; Sani et al. 2011; Kormendy & Ho 2013). Often, spiral galaxies are excluded due to the difficulties in identifying robust bulge parameters (e.g., McConnell & Ma 2013). For one thing, the nuclei of spiral galaxies contain gas, dust, and ongoing or recent star formation (e.g., Carollo et al. 1997). These alone complicate the task considerably, since it is difficult to determine the true bulge parameters or mass-to-light ratio. However, it is even more difficult to determine exactly what bulge means in the context of these galaxies.

All of our galaxies contain a large-scale disk, and all show a steepening of the profile toward the center—a "bulge" by the most general definition. These central light excesses, however, show a wide range of physical properties, which are often more similar to disks than to classical bulges and elliptical galaxies: they are flattened like disks, tend to be fitted by an exponential profile (Andredakis & Sanders 1994) or Sérsic (1963) with low index (generally $n\lt 2$, see Fisher & Drory 2010), they show bars, dust, or spiral arms as disks do, and they have recent or ongoing star formation like disks (Carollo et al. 1997, and the review in Kormendy & Kennicutt 2004).

Together, these attributes are interpreted as evidence that the central light excess or bulge region is being built up slowly by secular, gas-rich processes such as bar or spiral arm transport. To distinguish these components from kinematically hot systems without gas or young stars (e.g., elliptical galaxies), these systems have come to be known as "pseudo-bulges," while bulges that have the characteristics of ellipticals are called "classical bulges." Because the classification of a bulge depends on how it formed, it is certainly possible that some late-type galaxies contain both a pseudo- and classical bulge component, with the former having low mass-to-light ratios and thus dominating the light (Nowak et al. 2010; Erwin et al. 2015). Thus, we first decompose these different components (e.g., Weinzirl et al. 2009; Laurikainen et al. 2010; Läsker et al. 2014a), and then ask which are of interest in the context of BH-bulge scaling relations.

We adopt the following dual approach. First, we consider a "basic" model, comprised of only a bulge and a large-scale disk, plus a nuclear point source if it can be included.¹⁰ In the basic fit, the small-scale components are mostly fit by the "bulge" component, and only to a small degree accounted for by the disk component. Therefore, the magnitude of this "basic bulge" represents an approximate upper limit to the true (classical) bulge magnitude.

With a basic model in hand, we construct a more complete model, including structures on small scales, which may help us to isolate a bulge component. We simultaneously model any central bars, rings, or disks, and look for an additional light component that is rounder and more centrally concentrated than the outer disk. If there is one, then we call this the "classical" bulge. In the future, we will improve these decompositions by combining spatially resolved kinematics (e.g., Greene et al. 2014) with our HST imaging.

We now describe our two-dimensional parametric modeling in more detail to model the central components in each galaxy.

Working in two dimensions allows us to make full use of the information contained in the data to reduce degeneracy, and is an important advantage over one-dimensional modeling for the complex galaxy structures considered here. Each two-dimensional model component is corrected for the effects of the point-spread function (PSF), and then the parameters of the model are optimized using ${\chi }^{2}$ minimization with the publicly available code galfit3 (Peng et al. 2010). At minimum (our "basic" model), the models include a bulge, a large-scale disk, and a central point-source model of the AGN and/or an unresolved nuclear star cluster in those cases where the bulge+disk model does not overestimate the central light already. In all of the megamaser host galaxies, more components are present. We identify these based on visual identification in the science image, the residual image of the basic model, and the radial profiles of SB, ellipticity (e), and position angle (PA).

An accurate PSF model is an important ingredient in the modeling. We construct a PSF model by combining a number of stars in our images, which gives us a model of the PSF that is local both in space and in time to the observations of the galaxy. In the Appendix, we describe various PSF comparisons to show that we are accurately recovering the PSF (see Figure 27 in the Appendix). Similarly, the masking of intervening objects, background subtraction, the availability of a sufficiently large image area around the target galaxy, and an appropriate noise image impact the feasibility and accuracy of the fit results. We describe these ancillary data in the Appendix B.

We follow wide-spread convention in prescribing the radial SB profile of Sérsic form for the bulge, as well as an exponential profile for the large-scale disk. The Sérsic profile is defined as

$$\begin{eqnarray}&&I{(R)={I}_{e}\mathrm{exp}\{-{b}_{n}[(R/{R}_{e})}^{1/n}-1]\},\end{eqnarray} \tag{ 1 }$$

in terms of three independent parameters: the effective radius R_e along the semimajor axis (SMA), the SB I_e at R_e, and the Sérsic index n. The value of b_n is numerically determined such that the area inside of R_e contains half of the total flux. The large-scale disk is modeled with an exponential profile, which is equivalent to a Sérsic profile with $n\equiv 1$, and the scale radius (R_s) is related to ${R}_{e}={b}_{n=1}{R}_{s}=1.678{R}_{s}$. The two-dimensional SB profile follows from (1) by additionally specifying the center $({x}_{0},{y}_{0})$, axis ratio ($q=1-e$), and PA of the elliptical isophotes. In galfit, I_e is replaced by the total magnitude of the profile, ${m}_{\mathrm{ser}}={m}_{0}-2.5\mathrm{log}{F}_{\mathrm{ser}}$, where ${m}_{0}$ is the photometric zeropoint and F_ser is the total flux, which is calculated by

$$\begin{eqnarray}&&{F}_{\mathrm{ser}}=2\pi {R}_{e}^{2}{{qI}}_{e}{{nb}}_{n}^{-2n}{e}^{{b}_{n}}{\rm{\Gamma }}(2n)\end{eqnarray} \tag{ 2 }$$

with ${\rm{\Gamma }}(2n)={\int }_{0}^{\infty }{x}^{2n-1}{e}^{-x}{dx}$ being the Gamma function.

The full image model is the sum of the fluxes from all of the included components. Apart from the two-dimensional PSF for the AGN, we exclusively employ profiles of Sérsic form, albeit with fixed Sérsic index if an exponential ($n\equiv 1$) or Gaussian ($n\equiv 0.5$) profile is desired. We sometimes use profile modifications, including Fourier modes, truncations, coordinate rotation, and bending modes. For more details on these perturbations, see Peng et al. (2010).

In Table 2, we list a selection of the resulting galfit parameters: component magnitudes, sizes (bulge R_e and disk R_s), and the bulge Sérsic index. Total apparent magnitudes are also listed (column 2).

Table 2.  galfit Best-fit Parameters of Galaxy Image Models

Galaxy	Total		Bulge						Disk				Psf		Additional Components
	mt		mb		${R}_{e}\;[^{\prime\prime} ]$		n		md		${R}_{s}\;[\;^{\prime\prime} \;]$		mp		mag and Type
	(2)		(3)		(4)		(5)		(6)		(7)		(8)		(9)
	bas	bul	bas	bul	bas	bul	bas	bul	bas	bul	bas	bul	bas	bul
IC 2560	8.83	8.62	10.71	11.50	0.99	0.59	2.9	1.5	9.04	9.65	6.2	5.6	⋯	16.33	13.44, 11.77, 11.72, 9.57 ND, XBul, SpRing, Env
NGC 1194	9.90	10.01	10.22	12.04	4.6	1.8	6.8	3.2	11.39	13.50	3.5	6.9	⋯	17.30	12.75, 10.32 Bar, Env
NGC 2273	9.13	9.04	10.96	10.81	0.25	0.33	1.0	2.0	9.36	9.75	1.4	2.2	14.84	15.24	12.85, 11.30, 11.31 NR, Bar, Spir
NGC 2960	10.36	10.35	11.24	11.01	0.68	15.8	4.0	1.0	12.02	10.89	3.1	2.1	⋯	14.84	12.44 ND
NGC 3393	9.46	9.55	10.19	11.20	1.6	0.62	3.5	2.3	10.24	10.77	5.5	1.6	17.63	15.94	13.65, 13.01, 10.57 Bar, SpRing, Env
NGC 4388	8.59	8.49	10.57	10.28	0.9	1.2	3.8	2.2	8.79	9.72	2.4	1.7	14.78	14.80	13.00, 10.43, 9.80 ND, SpRing, Env
NGC 6264	11.64	11.64	12.97	14.44	3.2	0.65	3.1	1.3	12.02	12.67	5.6	5.1	18.48	18.04	13.59, 12.72 Bar, SpRing
NGC 6323	11.08	11.08	14.05	14.14	0.75	0.66	1.2	1.1	11.16	11.82	4.2	3.4	17.45	17.40	13.05, 12.49 Ring, Spir
UGC 03789	9.98	10.00	11.47	11.50	0.51	0.8	1.5	3.3	10.31	11.07	3.1	2.3	15.89	16.63	13.25, 13.66, 12.58, 11.76 Bar, NR, Ring, Env

Note. In columns (2)–(8), we list H-band galaxy total magnitude, bulge magnitude, effective radius and Sérsic index, disk magnitude and scale radius, and the magnitude of the central point source. Each of those columns contains two values: the first one ("bas") derived from the basic decomposition (bulge, disk, and the central point source if it could be fitted), followed by the results of the full model ("bul"), which includes significant additional components and yields our best estimate of the "classical" bulge parameters by virtue of separating the non-bulge and pseudobulge components. The additional components' magnitudes of the full model are given in column (9), along with their morphology in abbreviated form: "NR" for nuclear ring, "ND" for nuclear disk, "IDisk" for inner disk, "XBul" for X-shaped/boxy bulge, "Bar," "Ring" for medium-large-scale ring, "Spir" for spiral modified by rotation, "SpRing" for spiral arms that nearly form a ring (no coordinate rotation fitted), and "Env" for envelope. See Table 3 for a short, and Section 3.3 for a detailed, presentation of those morphologies and classification criteria.

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Table 3.  Morphological Types of Non-standard Components

Abbreviation	Type	Description and Criteria
NR	nuclear ring	ring (see below) of $\lesssim 500\;\mathrm{pc}$ size, similar to nuclear disk with inner truncation
ND	nuclear disk	${R}_{e}\lesssim 500\;\mathrm{pc}$ Sérsic profile with $n\lesssim 1$, often not aligned with galaxy major axis
IDisk	inner disk	flattened as the main disk but smaller ($\sim 1\;\mathrm{kpc}$);
		only in NGC 2960 where it exhibits spiral arm substructure
XBul	X-shaped/boxy bulge	Sérsic with $1\lesssim n\lesssim 2$, $q\approx {q}_{\mathrm{disk}}$ and ${R}_{e}\sim 1\;\mathrm{kpc};$ identified in IC 2560
Bar	bar	Sérsic $n\lt 1$, generally elongated and often misaligned from major axis, in NGC 1194 probably seen down its long axis
Ring	ring	Sérsic with inner truncation and n = 0.5, fixed intermediate and large $\gtrsim 1\;\mathrm{kpc}$ scales
SpRing	spiral/ring	shows up in the profile as a ring but also spiral structure (tight winding) in the image, n fixed to 0.5 or 1.0
Spir	spiral	Sérsic profile with coordinate rotation to emulate spiral arms, sometimes fixed n = 0.5 or n = 1
Env	envelope	extended disk and/or a halo depending on ellipticity , accounts for flux excess above the main disk at large radii ($\gtrsim 5\;\mathrm{kpc}$), Sérsic n either fixed or free

Note. We list here the abbreviations and morphologies of non-standard (beyond bulge, disk and PSF) components we used while fitting galfit models to our galaxy images. Detailed descriptions of the morphological types, and the criteria we used to identify/classify them, are presented in Section 3.3.

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It is not trivial to determine the number and type of components to fit to these many-component profiles in the face of possible profile mismatches and parameter degeneracies. We generally begin with a very simple two-component model, and then examine the fit residuals, the ellipticity, and the PA profile to see whether additional components are warranted. We also refit, adding components in a different order, to be sure that GALFIT robustly converges on the same fit. The most challenging task is to find the most probable and physically realistic model while retaining acceptable alternatives for the systematic uncertainty estimate. Compared to this systematic (modeling) uncertainty, the formal parameter uncertainties from the ${\chi }^{2}$ derivatives are very small.

In the following subsections, we describe the most common subcomponents and how we identify them. Each is demonstrated graphically in Figure 3.

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3.3.1. Nuclear Disks

3.3.2. Bars

3.3.3. Rings

3.3.4. Spiral Arms

3.3.5. Envelopes

The uncertainty in our fitting is dominated not by measurement error, but rather by systematic uncertainty. In general, degeneracy or deficiency in our modeling dominates the uncertainty, but the background level can also play a significant role in some cases (e.g., NGC 4388).

3.4.1. Modeling Uncertainty

In the previous subsection and the Appendix, we describe our general approach to finding the most suitable model for a given galaxy image. Even given the high spatial resolution and depth of our data, and the complexity of our models, the true structure of the galaxy may not be fully represented. Thus, our choice of number of components and boundary conditions leaves a systematic uncertainty in the parameters we are interested in. This systematic parameter uncertainty originating in the choice of model is separate from the random uncertainties that originate in pixel noise. The latter are directly provided by galfit and are completely subdominant to the systematic modeling uncertainties.¹¹

We adopt a pragmatic approach and employ a handful (usually 2–4) of alternative models to our chosen best-fit model that we consider acceptable. This way, we obtain several alternative values for the resulting bulge parameter of interest (chiefly the magnitude) and take their standard deviation as a systematic uncertainty estimate. These values are presented in Table 4. Typical systematic uncertainty estimates are a few tenths of a magnitude. We use these uncertainties with the other systematic uncertainties added in quadrature to represent the measurement error in the derived bulge mass (${\text{}}{L}_{\mathrm{bul}}$ and ${\text{}}{M}_{\mathrm{bul}}$) when investigating the ${M}_{\mathrm{BH}}\mbox{--}{M}_{\mathrm{bul}}$ scaling relation in Section 5.

Table 4.  Systematic Uncertainties

Galaxy	Bulge								Disk		PSF
	mb				$\mathrm{log}({R}_{e}/\;\mathrm{kpc})$		$\mathrm{log}n$		md		mp
	psf	rsc	mod	tot	mod	tot	mod	tot	mod	tot	mod	tot
IC 2560	0.00	0.02	0.30	0.30	0.10	0.10	0.17	0.18	0.75	0.75	0.13	0.17
NGC 1194	0.06	0.08	0.54	0.54	0.40	0.42	0.11	0.11	0.19	0.45	8.37	8.37
NGC 2273	0.00	0.04	0.34	0.34	0.19	0.19	0.16	0.17	0.14	0.30	0.39	0.40
NGC 2960	0.11	0.02	0.08	0.14	0.06	0.08	0.14	0.17	0.02	0.05	0.29	0.31
NGC 3393	0.00	0.06	0.11	0.13	0.10	0.12	0.13	0.16	1.07	1.07	0.23	0.28
NGC 4388	0.00	0.31	0.51	0.60	0.11	0.32	0.06	0.24	0.45	0.79	0.12	0.19
NGC 6264	0.02	0.43	0.93	1.03	0.35	0.43	0.15	0.16	0.28	0.30	0.17	0.24
NGC 6323	0.01	0.51	0.52	0.73	0.23	0.55	0.21	0.47	0.32	4.02	0.47	0.54
UGC 03789	0.03	0.12	0.41	0.43	0.18	0.23	0.06	0.08	0.21	0.22	0.14	0.20

Note. Systematic uncertainties for five parameters of the full decompositions: the bulge magnitude, logarithmic effective radius, and Sérsic index (m_b, $\mathrm{log}({R}_{e}/\;\mathrm{kpc})$, and $\mathrm{log}n$), as well as the disk magnitude (m_d) and magnitude of the central point source (m_p). Each total ("tot") systematic error is the sum of the errors resulting from PSF model ("psf"), background and flux scaling ("rsc"), and model ("mod") systematic uncertainties, added in quadrature. In general, the modeling uncertainty (number and profiles of the model components, see Section 3.4.1) dominates the total systematic error, which is why PSF- and background/scaling-related errors (Sections 3.4.2 and 3.4.3) are shown only for the most important parameter in our study, m_b.

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3.4.2. PSF Uncertainty

3.4.3. Background Uncertainty

In order to facilitate direct comparison with early-type galaxies, we attempt to mitigate the variability in the mass-to-light ratio ${\rm{\Upsilon }}\equiv {M}_{\star }/L$ by using the galaxy color. Since the variation in ϒ with population properties and dust column density is decreased at NIR wavelengths, we choose F160W (nearly H band) to measure the luminosity, and derive ${{\rm{\Upsilon }}}_{H}\equiv {M}_{\star }/{L}_{H}$ based on optical colors. We use the color–ϒ relation from Bell et al. (2003), which determines conversions between a single galaxy color and the galaxy ϒ based on stellar population synthesis models and an assumed dust model. We also experimented with the two-color relations from Zibetti et al. (2009), but found that these conversions yielded unrealistically low ϒ values for some of the most massive ellipticals in our comparison sample, for whom the color is very red (Section 3.6). We note that many systematic uncertainties remain in stellar population synthesis modeling, particularly regarding the contribution to the near-infrared light from asymptotic giant branch stars (e.g., Maraston 2005; Conroy et al. 2009; Kriek et al. 2010; Zibetti et al. 2013). It is possible that the Bell et al. (2003) mass-to-light ratios are overestimates for the blue g − i color because their models do not treat these later stages of stellar evolution (e.g., Roediger & Courteau 2015).

Since we have measured the F435W (roughly B-band) and F814W (roughly I-band) magnitudes, we are closest in color to the g − i conversions to ${{\rm{\Upsilon }}}_{{\rm{H}}}$ from Bell et al. (2003). We derive a conversion between the HST colors and the Sloan Digital Sky Survey (SDSS; York et al. 2000) g − i system using simple stellar population models from the Padova group (Marigo et al. 2008), including extinction in each band in the A_V range 0–3. A tight linear relation is found (scatter of 0.05 mag) between the g − i and F438W − F814W color of

$$\begin{eqnarray}&&g-i=-0.443+0.738({\rm{F}}438{\rm{W}}-{\rm{F}}814{\rm{W}}).\end{eqnarray} \tag{ 3 }$$

Note that the F438W, F814W, F160W, and H-band magnitudes here are all in the Vega system, while the SDSS magnitudes are given in the AB system (Oke & Gunn 1983; Fukugita et al. 1996).

For both the basic and classical bulges, we measure the bulge color by defining a radial range over which the given component dominates the total flux. By using the same aperture on both bands, we can derive a color without performing full fits to each band. We ensure that PSF and AGN corrections are negligible by imposing a lower limit of $\gtrsim 2\;\mathrm{pix}$ (026) on the SMA of the aperture, which corresponds to ∼50 pc at the typical distance of 50 Mpc. The magnitudes for the entire galaxy (total) are measured from the total H-band magnitude within the WFC3-IR sky-subtracted image. We note that a more precise method for determining component colors would involve the simultaneous fitting of images in multiple bands, but this analysis is outside the scope of our study and will be left to future work.

The inferred colors are listed in Table 5, along with the inner and outer radii of the annuli in which bulge colors were measured, both for the basic and classical bulges. Table 6 shows the ${{\rm{\Upsilon }}}_{H}(g-i)$ that are derived from the Bell et al. (2003) models. The resulting $\mathrm{log}{M}_{\star }=\mathrm{log}{L}_{H}+\mathrm{log}{{\rm{\Upsilon }}}_{H}$ are given in Table 7 and used in Section 5 regarding their correlation with ${M}_{\mathrm{BH}}$.

Table 5.  Bulge and Total Colors

Galaxy	${a}_{1}[^{\prime\prime} ]$	${a}_{2}[^{\prime\prime} ]$	${a}_{1}[^{\prime\prime} ]$	${a}_{2}[^{\prime\prime} ]$	$F435-814W$			$F814-160W$			g − i			i − H			H − K
	bul		bas		bul	bas	tot	bul	bas	tot	bul	bas	tot	bul	bas	tot
IC 2560	0.28	5.89	0.28	7.85	2.83	2.79	2.14	1.70	1.67	1.58	1.65	1.62	1.14	2.46	2.42	2.31	0.26
NGC 1194	0.28	9.49	0.28	9.49	2.91	2.92	2.38	1.64	1.65	1.55	1.70	1.71	1.31	2.38	2.40	2.27	0.38
NGC 2273	0.28	5.89	0.28	4.03	2.38	2.25	2.33	1.78	1.80	1.57	1.31	1.22	1.28	2.56	2.58	2.30	0.29
NGC 2960	0.28	1.88	0.28	6.48	2.44	2.28	1.99	1.58	1.62	1.42	1.36	1.24	1.03	2.31	2.36	2.11	0.35
NGC 3393	0.28	3.33	0.28	9.49	2.09	2.21	2.06	1.62	1.59	1.59	1.10	1.19	1.08	2.36	2.32	2.32	0.28
NGC 4388	2.27	5.89	0.28	3.33	1.90	2.29	1.87	1.99	2.30	1.90	0.96	1.25	0.94	2.81	3.19	2.70	0.28
NGC 6264	0.28	1.41	0.28	4.87	2.32	2.49	1.79	1.61	1.62	1.56	1.27	1.39	0.88	2.35	2.36	2.29	0.33
NGC 6323	0.28	1.41	0.28	0.96	2.95	2.91	1.73	1.83	1.91	1.60	1.73	1.70	0.83	2.62	2.71	2.34	0.33
UGC 03789	0.27	4.67	0.28	4.43	2.03	2.01	1.94	1.69	1.67	1.47	1.06	1.04	0.99	2.45	2.42	2.18	0.27

Note. Bulge colors were measured in elliptical annuli bounded by a₁ and a₂ where the respective bulge component dominates, for the classical bulge ("bul") in our detailed decomposition and the Sérsic component in the basic Sérsic +exponential ("bas") decomposition. Meanwhile, total colors ("tot") were measured across the entire WFC3-IR FOV. Colors in the HST/WFC3 F435W, F814W, and F160W (similar to Johnson B, I, and 2MASS H) bands were converted to g − i and i − H as described in Section 3.5. The H − K color is taken from the 2MASS catalog and measured within the $20\;\mathrm{mag}\;{\mathrm{arcsec}}^{-2}$ isophote.

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Table 6.  Bulge and Total Mass-to-light Ratios

Galaxy	$\mathrm{log}{{\rm{\Upsilon }}}_{H}(g-i)$
	bul	bas	tot
IC 2560	0.11	0.10	0.02
NGC 1194	0.12	0.05	0.05
NGC 2273	0.05	0.03	0.04
NGC 2960	0.06	0.04	−0.00
NGC 3393	0.01	0.03	0.01
NGC 4388	−0.01	0.04	−0.02
NGC 6264	0.04	0.06	−0.03
NGC 6323	0.12	0.12	−0.04
UGC 03789	0.00	0.00	−0.01

Note. Logarithmic H-band mass-to-light ratios ($\mathrm{log}{{\rm{\Upsilon }}}_{H}(g-i)$) based on the Bell et al. (2003) prescription. The colors and decompositions on which these are based are listed in Table 5.

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Table 7.  Luminosities, Masses, and Sizes

Galaxy	$\mathrm{log}({M}_{\mathrm{BH}}/{M}_{\odot })$		$\mathrm{log}({L}_{H}/{L}_{\odot ,H})$			${({\rm{B}}/{\rm{T}})}_{L}$		$\mathrm{log}({M}_{\star }/{M}_{\odot })$				${({\rm{B}}/{\rm{T}})}_{M\star }$		$\mathrm{log}({R}_{e}/\;\mathrm{kpc})$
	val	err	bas	bul	tot	bas	bul	bas	bul	err	tot	bas	bul	bas	bul	tot
IC 2560	6.40	0.40	10.29	9.97	11.12	0.18	0.07	10.40	10.08	0.14	11.14	0.22	0.09	−0.14	−0.33	0.60
NGC 1194	7.82	0.05	10.67	9.94	10.76	0.74	0.15	10.72	10.39	0.20	10.81	0.74	0.38	0.58	−0.34	0.44
NGC 2273	6.88	0.05	9.77	9.83	10.54	0.19	0.19	9.82	9.88	0.12	10.58	0.19	0.20	−0.70	−0.56	0.15
NGC 2960	7.05	0.05	10.53	10.63	10.89	0.44	0.55	10.59	10.21	0.22	10.89	0.50	0.21	−0.28	0.73	0.29
NGC 3393	7.49	0.12	10.71	10.30	10.97	0.51	0.21	10.72	10.31	0.05	10.98	0.51	0.21	0.14	−0.21	0.40
NGC 4388	6.93	0.05	9.66	9.78	10.49	0.16	0.19	9.65	9.77	0.22	10.47	0.17	0.20	−0.11	-0.00	0.15
NGC 6264	7.45	0.05	10.41	9.82	10.94	0.30	0.08	10.45	9.86	0.41	10.91	0.35	0.09	0.33	−0.26	0.60
NGC 6323	6.96	0.05	9.75	9.72	10.94	0.06	0.06	9.87	9.84	0.27	10.90	0.09	0.09	−0.20	-0.24	0.40
UGC 03789	7.05	0.05	10.14	10.13	10.73	0.26	0.25	10.14	10.13	0.15	10.72	0.26	0.26	−0.36	-0.12	0.34

Note. BH masses (log ${M}_{\mathrm{BH}}/\;{M}_{\odot }$) and their errors, bulge and total H-band luminosities (log ${L}_{H}/{L}_{\odot ,H}$), the ratio of bulge-to-total luminosity [${(B/T)}_{L}$], stellar masses (log ${M}_{* }/\;{M}_{\odot }$), and effective H-band radii [$\mathrm{log}({R}_{e}/\;\mathrm{kpc})$] of our sample based on our galfit models. "Bas" indicates values based on basic bulge+disk(+point-source) models, while "bul" indicates those of the classical bulge parameters based on the full models. Bulge mass errors are based on the combined calibration, point-source, and modeling uncertainties (see Table 4). Luminosities were converted to masses via the color-based ${{\rm{\Upsilon }}}_{H}(g-i)$ (Bell et al. 2003) with colors measured on our HST/WFC3 F435W, F814W, and F160W images inside the appropriate apertures (bulge-dominated regions, see Section 4.4). The low B/T of the classical bulges conform to the late Hubble types of most of our targets. Alternative values for the $\mathrm{log}{M}_{\mathrm{BH}}$ of IC 2560 (6.54 ± 0.06, Yamauchi et al. 2012; and 6.643 ± 0.025, J. Wagner et al. 2016, in preparation) based on VLBI data instead of the single-dish based ${M}_{\mathrm{BH}}$ adopted here have no appreciable effect on the scaling relations (Section 5).

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The primary sample of megamaser disk galaxies that we have fit comprises nine disk galaxies of similar total stellar mass ($\sim {10}^{11}\;{M}_{\odot }$). We wish to compare the results for our megamaser sample with a larger sample of galaxies spanning a range of masses, morphologies, and ${M}_{\mathrm{BH}}$. Many works have performed two-dimensional image decomposition of the hosts of galaxies with dynamical BH mass measurements (e.g., Marconi & Hunt 2003; Sani et al. 2011; Beifiori et al. 2012; Vika et al. 2012). Here, we rely on the ${M}_{\mathrm{BH}}$–${\text{}}{L}_{\mathrm{bul}}$ data of Läsker et al. (2014b, L14 hereafter) because, of all of the available previous work, their image analysis and quality are closest to our current study. We will discuss the comparison with other literature data in Section 6. The Läsker et al. (2014b) sample comprises 35 galaxies of all Hubble types (4 spiral, 11 lenticular, and 20 elliptical galaxies) selected based on the availability of a reliable BH mass at the time the imaging data were taken. As in this paper, L14 provide the total photometry, results based on basic bulge+disk models, and detailed decompositions, all based on homogeneous deep sub-arcsecond-resolution K-band photometry. One of the galaxies in L14, NGC 4258, is the prototypical megamaser disk galaxy. In the following, we will include NGC 4258 in our sample of maser galaxies.

The sample from L14 is not identical to that of Kormendy & Ho (2013, KH13 hereafter). L14 include the gas emission-based ${M}_{\mathrm{BH}}$ measurements of PGC 49940 and Cygnus A, as well as those of NGC 2778, NGC 4261, NGC 6251, and NGC 7052, which were omitted by KH13 due to doubts about their ${M}_{\mathrm{BH}}$ reliability. Conversely, several ${M}_{\mathrm{BH}}$ measurements are included in KH13 that became available after the photometry for L14 was completed.

We again use the Bell et al. (2003) color conversions to calculate the stellar masses of the L14 sample. In this case, we do not have uniform HST color imaging for the objects. Instead, we use the SDSS photometry provided by the NASA-SDSS Atlas¹² (NSA hereafter; see, e.g., Blanton et al. 2011). Eighteen of the L14 galaxies have SDSS photometry. For these, we use the NSA single-component Sérsic fits for the optical galaxy magnitudes. We correct for galactic extinction (Schlafly & Finkbeiner 2011, retrieved using the NED¹³ ) and calculate a g − i color. For those galaxies which are not in the NSA catalog, we use the mean g − i color corresponding to the appropriate Hubble type: 1.17 mag (E), 1.15 mag (S0), and 1.0 mag (S).

The resulting H-band mass-to-light ratio ${{\rm{\Upsilon }}}_{H}(g-i)$ ranges from 0.99 to 1.06, and thus any assumptions made based on color likely have minor effects on the galaxy mass estimates. We calculate L_H from the L14 K-band magnitudes assuming the extinction-corrected $20\;\mathrm{mag}\;{\mathrm{arcsec}}^{-2}$-isophotal H − K color of the 2MASS database. We find good agreement between the masses derived in this manner and the empirical relation of Cappellari (2013), which fit a relation between the dynamical mass and M_K. The dynamical estimates are $0.2\;\mathrm{dex}$ higher on average and related to our color-based masses by a correlation with slope 0.9 but with negligible scatter. The higher dynamical masses are consistent with the presence of dark matter within R_e increasing with increasing galaxy mass. Similarly, our color-based masses are consistent with the values given in KH13, which are only $0.06\;\mathrm{dex}$ more massive on average with a scatter of only $0.15\;\mathrm{dex}$. The least certain masses are for the spirals where, again, the stellar population modeling harbors the most uncertainties. As one additional sanity check, we consider the five megamaser galaxies in the NSA catalog; deriving a stellar mass for them using the Bell et al. (2003) color relations and L_i, we find agreement at the $0.2\;\mathrm{dex}$ level, indicating that our stellar masses are all on the same relative scale.

In Section 5, we also consider three additional late-type galaxies: the Milky Way, Circinus, and NGC 1068 (the megamaser host NGC 4258 is already included in the L14 sample). In the first case, the BH mass is known more precisely than any other (e.g., Ghez et al. 2008; Gillessen et al. 2009) but the bulge mass is quite difficult to determine. In the other two systems, the BH masses are based on megamaser disk modeling, but the fidelity of ${M}_{\mathrm{BH}}$ has been questioned. In the case of NGC 1068, the rotation curve presented by Greenhill et al. (1996) is sub-Keplerian, perhaps because of a massive self-gravitating disk (Lodato & Bertin 2003). Circinus (Greenhill et al. 2003) may have an uncertain inclination (Ferrarese & Ford 2005).

The ${M}_{\mathrm{bul}}$ of the MW is taken from Kormendy & Ho (2013). The bulge magnitudes and masses for Circinus and NGC 1068 are based on the work of Sani et al. (2011). We convert their apparent $[3.6\;\mu {\rm{m}}]$ mag to ${M}_{\star }$ using their formula (5) in conjunction with ${\sigma }_{v}$ (dynamical mass), or their Equation (6) (empirical ${M}_{\star }\mbox{--}{L}_{3.6}$). For NGC 1068, both ${M}_{\star }$ values of the bulge are nearly identical; for Circinus, they differ by $0.5\;\mathrm{dex}$, and so we use their mean ($\mathrm{log}{\text{}}{M}_{\mathrm{bul}}/\;{M}_{\odot }=10.00$).

In Section 3, we described in detail the different physical components that are required to fully model the central regions of our megamaser disk galaxies. Because pseudo-bulges are defined by their formation history, and not by their appearance, we are forced to consider what properties might indicate a pseudobulge. Here, we primarily mean that we have identified structural components (nuclear rings or disks, as well as X-shaped/boxy bulges) that are associated with secular evolution. In the past, it has been shown that Sérsic indices $n\lt 2$ correlate with the presence of pseudo-bulges (e.g., Kormendy & Kennicutt 2004; Fisher & Drory 2010) as well as with low effective surface brightnesses at a given size (Gadotti 2009), and so we will also consider these specific criteria.

Below, we will go through the classification of each galaxy in detail (Section 4.4). Here, we simply summarize our main finding: all but one of the galaxies show unambiguous signatures of secular evolution. We find sub-kiloparsec disks, bars, or spirals in all galaxies with Hubble Type Sa or later (Table 1). We only identify one case (the lenticular galaxy NGC 1194) where there is no evidence for a pseudobulge. Thus, we are fairly confident that the large majority of these galaxies do contain a pseudobulge component.

As emphasized by Erwin et al. (2015), among others, the presence of pseudobulge components does not preclude the presence of a rounder, older, kinematically hot classical bulge. From the point of view of BH scaling relations, it may well be that this classical bulge component matters most (Nowak et al. 2010). Thus, we have attempted to use our photometric fitting to identify such components. In the next section, we characterize these putative classical bulge components using color, shape, and structural information.

We derive galactic-extinction-corrected luminosities and linear sizes from the apparent magnitudes and sizes presented in Table 2, assuming ${M}_{\odot ,H}$ = 3.32. As a reminder, the "basic" bulge is derived from a fit that includes just two or three components: disk, bulge, and central point source where it can be fit. The point source may arise from the contribution of an AGN or be stellar in nature (e.g., NGC 3384; Ravindranath et al. 2001; Graham & Driver 2007). Basic fits are indicated with the subscript "bas" in tables and figures. The "classical" bulge component is the roundest and highest n component in the multi-component fit. Classical bulge components are indicated with the subscript "bul" in figures and tables. Finally, the "total" magnitude and size are calculated as the sum of all of the components in our best-fit multi-component model. We list the resulting parameters in Table 7, along with the bulge-to-total ratios (B/T) for the classical and basic bulge measurements.

In general, the basic bulges are both more extended (mean effective radius $0.8\;\mathrm{kpc}$, ranging from 0.2 to $3.8\;\mathrm{kpc}$) and more luminous (0.5–5.1 $\times \quad {10}^{10}\;{L}_{\odot ,H}$) while the classical bulges, as they comprise only a single component of the galaxy central region, tend to be smaller (mean effective radius of $0.7\;\mathrm{kpc}$, ranging from 0.3 to $5.4\;\mathrm{kpc}$) and slightly fainter (0.5–4.3 $\times \quad {10}^{10}\;{L}_{\odot ,H}$). Likewise, the median B/T drops slightly from the basic bulge (30%) to the classical bulge (20%). Generally, these B/T values are completely consistent with our expectations for early-type spirals (e.g., Simien & de Vaucouleurs 1986; Laurikainen et al. 2010).

The g − i colors of the bulge and total galaxy are compared in Figure 4. As expected, the total color is always bluer than the bulge color, which avoids light from the large-scale disk component. We also check whether our detailed decompositions result in redder bulges than the basic decompositions. The latter tend to include central disks and rings, which are presumably younger and bluer. With our aperture measurements, however, classical bulges are not appreciably redder than the basic bulges. This similarity suggests that any color differences are too subtle for our crude method to discern, or that dust obscuration offsets real differences in the population.

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As discussed in Section 3, we model a putative classical bulge component in addition to the exponential kiloparsec-scale disk and any other identifiable morphological components, such as bars and nuclear disks. We attempt to understand the nature of the putative classical bulge components by examining their intrinsic flattening, Sérsic indices, and photometric scaling relations. Recall that in figures and tables, the classical bulge component is denoted as "bul."

4.3.1. Flattening

4.3.2. Sérsic n and the n–L Relation

The basic bulges are best fit by Sérsic indices ranging from 1.0 to 6.8 (Table 2). The presence of compact, disk-like central components (e.g., rings, disks, or bars) tends to drive up the value of n for the basic bulge components. When we perform more detailed decompositions, the effect of the nuclear components is mitigated, which generally leads to lower n. For example, in the galaxy NGC 4388, n drops from 3.8 to 2.2 when the highly inclined nuclear disk is modeled separately from the bulge. These classical bulge components have Sérsic $n\in [1.0,4.4]$, with four of the nine classical bulge candidates having $n\lt 2$ (IC 2560, NGC 2960, NGC 6264, NGC 6323). The classical bulges in Erwin et al. (2015) also tend to have $n\lt 2$, which suggests that a high Sérsic index is not a hard requirement for low-mass classical bulges using our photometric definition of a rounder, extra-light component (Section 3.1).

Most of the classical bulge Sérsic indices in our late-type galaxies follow the relation with ${L}_{{\rm{bulge}}}$ in early-type bulges (Figure 5, left panels). However, the $n\lt 2$ bulges have lower n for their luminosity than classical bulges in general. NGC 2960 is an interesting outlier. As suggested by Kormendy & Ho (2013), this galaxy may be a merger remnant. We find a kiloparsec-scale disk in NGC 2960 plus a nuclear disk with a steep profile, neither of which is easily interpreted as a classical bulge. If we instead consider its basic bulge (bottom left panel of Figure 5), then it falls in line with the general trend.

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4.3.3. The ${\mu }_{e}\mbox{--}{R}_{e}$ Relation

For each galaxy, we will summarize the evidence demonstrating that we have a pseudobulge, a classical bulge, or both. We established that in nearly all cases, megamaser disk host galaxies show unambiguous pseudobulge signatures in the form of nuclear rings, nuclear or inner ($\lesssim 1\;\mathrm{kpc}$) disks, central dust, and spiral structures. The presence of these components is our criterion for classifying a galaxy as containing a pseudobulge.

We have also attempted to isolate classical bulges. As criteria for classical bulge determination, we use the folloiwng: (1) shape: they should be rounder than the large-scale disk; (2) SB in relation to the effective radius: they should be close to the relation between ${\mu }_{e}$ and R_e defined by elliptical galaxies; and (3) Sérsic index: they should have high ($n\gt 2$) values. In our view, the Sérsic index is the least reliable discriminator of classical bulges due to the large scatter in the n–L plane. We determine that a galaxy contains a classical bulge if it satisfies two of these three criteria. For each galaxy, we assign a P to indicate a likely pseudobulge and a C to indicate a likely classical bulge.

IC 2560: IC 2560 is a relatively strongly inclined galaxy with a readily apparent X-shaped bar/bulge, which provides clear evidence for a pseudobulge component. We do identify a small classical bulge candidate that is rounder than the disk (q = 0.6 versus q = 0.4). The position in the ${\mu }_{e}\mbox{--}{R}_{e}$ diagram, which is close to the relation of early-type galaxies, likewise points toward a classical bulge, while the Sérsic index is somewhat low (n = 1.5). However, despite the above classical bulge indicators, given the dust and complexity of IC 2560 in the central regions, we cannot confirm that this small component is indeed a classical bulge. (P)

NGC 1194: This edge-on, bulge-dominated galaxy is difficult to fit robustly due to significant dust contamination and a likely bar. The basic and classical bulge fits are round and both have a high Sérsic index. The effective SB is not as high as in massive ellipticals, but is higher than expected for a pseudobulge based on the work of Gadotti (2009). Overall, we determine that NGC 1194 contains a classical bulge. We do not find any pseudobulge component. (C)

NGC 2273: While the ${\mu }_{e}\mbox{--}{R}_{e}$ position is consistent with expectations for classical bulges, the axis ratio of the putative classical bulge component matches that of the disk. The Sérsic index is intermediate with n = 2. The superposition of the candidate bulge component with the strong bar complicates significant detection of a classical bulge, and given the generally complex inner structure, we conclude that there is not sufficiently compelling evidence for a classical bulge component. NGC 2273 unambiguously contains pseudobulge components. From photometry, it has long been known to contain multiple rings and a nuclear disk (Erwin et al. 2003). More recently, kinematic evidence has confirmed that the central ∼200 pc is dominated by a disk (Barbosa et al. 2006; Falcón-Barroso et al. 2006). There is also a kiloparsec-scale bar component. (P)

NGC 2960: Apart from a large-scale smooth and round component, this galaxy contains two central disks: one nuclear and one $\sim 1\;\mathrm{kpc}$ sized with inset spiral structure. It is particularly challenging in this case to determine what component comprises the bulge. Treating the nuclear disk component as the classical bulge yields a very low Sérsic index but a high central SB. The other option was suggested by KH13; the galaxy may be an elliptical that just swallowed a spiral galaxy. In that case, the classical bulge may be the outer component and the inner ($1\;\mathrm{kpc}$) disk a recently acquired addition. The outer component is round, and the observed low ${\mu }_{e}$ is likely an artifact of the distortion to the center caused by the merger. Although this component technically does not satisfy our classical bulge requirements, we treat it as a classical bulge distorted by a merger. Since we detect an inner disk, it has a clear pseudobulge component. (CP)

UGC 3789: This galaxy is relatively face on, and so using the shape is challenging. However, given the high Sérsic index n = 3.3 and relatively high ${\mu }_{e}$, we identify a classical bulge component. We see clear signs for pseudobulge components in the nuclear and larger-scale rings. (CP)

NGC 3393: Similar to UGC 3789, this galaxy is close to face on. The classical bulge candidate is round and has a Sérsic index n = 2.3. Because the galaxy is face on, we cannot infer much about the intrinsic shape of the component. The high effective SB, combined with $n\gt 2$, argues for a classical bulge. NGC 3393 contains multiple rings and a bar. The evidence for pseudobulge components is clear. (CP)

NGC 4388: The classical bulge fit to this galaxy is rounder than the disk by a factor of two. However, given the low ${\mu }_{e}$ of the putative classical bulge, $n\approx 2$, and the significant dust extinction toward the galaxy center, we do not find a convincing classical bulge component. This well-known galaxy has a kiloparsec-scale bar that has been studied kinematically (Veilleux et al. 1999). On the smallest scales, we have identified a nuclear disk both from HST photometry and our NIR spectroscopy (Greene et al. 2014), which all points to a pseudobulge component. (P)

NGC 6264: One of the most distant galaxies in the sample, this galaxy clearly contains a kiloparsec-scale bar, and thus a pseudobulge component. The galaxy is close to face on, and so the axis ratio is not very constraining. The Sérsic index is low ($n\approx 1$), but ${\mu }_{e}$ is relatively high. Given the lack of consensus between the different indicators and the distance of the galaxy leading to extra degeneracy with the bar, we do not robustly identify a classical bulge. (P)

NGC 6323: We fit a very round central component as a classical bulge candidate. The combination of the low Sérsic index of $n\approx 1$ and the low SB suggest that we have not isolated a classical bulge component. In contrast, the structural properties of the bulge and the inner kiloparsec-scale disk/ring lead us to conclude that NGC 6323 harbors a pseudobulge (P).

Armed with these bulge classifications, luminosities, and stellar masses for our different stellar components, we now turn to the primary goal of this paper, i.e., the BH scaling relations.

In this subsection, we focus on the megamaser disk galaxies taken alone (including NGC 4258 from L14). Megamasers play two important roles. First and foremost, VLBI allows us to resolve much smaller spheres of influence than optical or NIR stellar- or gas-dynamical methods, and the usually near-perfect Keplerian rotation curves traced by the masers provide the most precise and accurate extragalactic BH mass measurements. Nuclear megamasers probe the full range of BH mass at a given galaxy property in a way that no other current technique can. Second, as a corollary, they allow us to probe BH mass in spiral galaxies where gas, dust, and typically small spheres of influence all conspire to make stellar or gas-dynamical techniques especially challenging.

The megamaser disk galaxies span a stellar mass range of $\mathrm{log}{M}_{* }/\;{M}_{\odot }=10.5$–11.1 (only a factor of four), and yet the BH masses span a range of $\mathrm{log}({M}_{\mathrm{BH}}/\;{M}_{\odot })\approx 6.4-7.8$, that is, a factor of 25. If we take the scaling relations measured for predominantly early-type galaxies from L14, then for the measured BH masses we expect a range in bulge mass of 10⁸–${10}^{10}\;{M}_{\odot }$, which corresponds to a range in bulge-to-total light (B/T) of 10⁻³ (for IC 2560) to 0.2 (NGC 1194), with a median value of 0.03. In contrast, galaxies of these Hubble types (S0-Sb) typically have ${\rm{B}}/{\rm{T}}\approx 0.1-0.2$ (Simien & de Vaucouleurs 1986; Laurikainen et al. 2010). It is already clear before we perform any fitting that these BHs would need to have very small classical bulge components if they were to obey the scaling relations seen in early-type galaxies. A similar conclusion was reached for the ${M}_{\mathrm{BH}}\mbox{--}{\sigma }_{* }$ relation by Greene et al. (2010; see also KH13 for other references).

The maser galaxies occupy a range of bulge masses of log ${M}_{* }/\;{M}_{\odot }=9.5-11$. The wide distribution in BH mass in a narrow range of galaxy properties¹⁴ shows us that there is not a tight correlation between ${M}_{\mathrm{BH}}$ and galaxy or bulge mass for galaxies with ${M}_{* }\lesssim {10}^{11}\;{M}_{\odot }$. Instead, the measured correlation found for early-type galaxies defines an upper envelope for the BH mass with many of the megamaser galaxies scattering below this relation. As we will quantify in the following subsections, this broad tail toward low ${M}_{\mathrm{BH}}$ appears to hold even when we consider bulge rather than total galaxy mass.

This tail to low BH mass, which is most clearly apparent in the megamaser disk galaxies, raises a more basic question about the scaling relations. We have to wonder whether the scaling relations reflect the true distribution in nature, or whether they reflect our inability to measure low-mass BHs in high-mass galaxies (Batcheldor 2010). Gültekin et al. (2011) explore the possibility that the ${M}_{\mathrm{BH}}\;\mbox{--}\;\sigma$ relation is only an upper envelope, since galaxies with unresolved gravitational spheres of influence may be preferentially missing. At high galaxy mass, ${\sigma }_{* }\gt 250\;\mathrm{km}\;{{\rm{s}}}^{-1}$ (corresponding roughly to $\sim {10}^{11}\;\;{M}_{\odot };$ e.g., Häring & Rix 2004), Gültekin et al. (2011) show that the existing dynamical BH mass sample is large enough to rule out a long tail to low ${M}_{\mathrm{BH}}$.¹⁵ However, at lower stellar velocity dispersion, a large range in ${M}_{\mathrm{BH}}$ at fixed galaxy property is what we observe. We discuss the possibility of bias in the low-mass galaxy sample, along with the possibility of bias in the megamaser disk galaxies, in Section 6.1. First, we quantitatively fit the relationships between ${M}_{\mathrm{BH}}$ and measured galaxy properties.

We use the IDL implementation of the Bayesian inference-based LINMIX_ERR (Kelly 2007) for fitting our BH scaling relations between ${M}_{\mathrm{BH}}$ and the galaxy properties. This routine naturally implements intrinsic scatter in the y-coordinate as part of the model, i.e., the relation is modeled as a probability distribution in (x, y) space. It renders a Markov Chain Monte Carlo (MCMC) realization of the posterior distribution of the linear relation parameters, which are the zeropoint (α), slope (β), and dispersion of the Gaussian intrinsic scatter (). We thus fit relations of the form

$$\begin{eqnarray}&&y=\alpha +\beta (x-{x}_{0})+{ \mathcal G }(\epsilon )\;,\end{eqnarray} \tag{ 4 }$$

where $y=\mathrm{log}({M}_{\mathrm{BH}}/{M}_{\odot })$, x are logarithmic luminosities or masses, i.e., $x=\mathrm{log}({L}_{H}/{L}_{\odot ,H}$) or $x=\mathrm{log}(M/{M}_{\odot })$, and $G(\epsilon )$ symbolizes a Gaussian probability distribution with dispersion . The x-offset x₀ is calculated before fitting as the mean of the x-coordinates of the data in order to reduce covariance between α and β. The linear relation (4) implies a power law between ${M}_{\mathrm{BH}}$ and L_H or M*, and $\beta =1$ corresponds to a linear relation between ${M}_{\mathrm{BH}}$ and the galaxy property. Some recent papers have suggested a broken power-law fit to BH scaling relations with bulge luminosity or mass (e.g., Graham & Scott 2015). This is an interesting possibility, but we do not have a sufficient sample size in this paper to address that possibility rigorously. The values quoted in Table 8 are the mean values of the parameters in the Markov Chain, and the given intervals delineate the 68% confidence interval of the drawn samples relative to the mean.

Table 8.  Scaling Relation Parameters $\mathrm{log}({M}_{\mathrm{BH}})\mbox{--}\mathrm{log}(x)$ with Galaxy Properties and Galaxy Subsamples

x	x0	α		β				${\rm{\Delta }}{a}_{\mathrm{mega}}$		${\epsilon }_{\mathrm{mega}}$		${\rm{\Delta }}{a}_{\mathrm{late}}$		${\epsilon }_{\mathrm{late}}$		${\rm{\Delta }}{a}_{\mathrm{low}}$		${\epsilon }_{\mathrm{low}}$
		val	err	val	err	val	err	val	err	val	err	val	err	val	err	val	err	val	err
${\text{}}{L}_{\mathrm{bul}}$	10.56	8.13	0.09	0.87	0.11	0.56	0.07	−0.63	0.21	0.90	0.11	−0.51	0.24	0.73	0.12	0.09	0.39	0.72	0.14
${\text{}}{L}_{\mathrm{bas}}$	10.64	8.12	0.09	0.99	0.13	0.57	0.07	−0.80	0.22	0.93	0.13	−0.58	0.24	0.76	0.13	0.04	0.37	0.76	0.13
${\text{}}{L}_{\mathrm{tot}}$	10.93	8.12	0.11	0.99	0.19	0.71	0.09	−1.13	0.21	1.35	0.11	−1.03	0.22	1.23	0.12	0.47	0.40	1.04	0.25
${\text{}}{M}_{\mathrm{bul}}$	10.66	8.12	0.08	0.88	0.10	0.52	0.06	−0.58	0.21	0.79	0.12	−0.49	0.22	0.70	0.12	−0.22	0.31	0.71	0.12
${\text{}}{M}_{\mathrm{bas}}$	10.74	8.13	0.09	0.98	0.12	0.56	0.07	−0.76	0.22	0.89	0.13	−0.57	0.24	0.74	0.14	0.05	0.34	0.74	0.11
${\text{}}{M}_{\mathrm{tot}}$	11.01	8.13	0.10	1.04	0.17	0.68	0.08	−1.05	0.20	1.25	0.11	−0.98	0.21	1.16	0.12	−0.04	0.36	0.84	0.12

Note. The first column identifies the quantity x that is, respectively, fitted by a relation $\mathrm{log}({M}_{\mathrm{BH}}/\;{M}_{\odot })=\alpha +\beta (\mathrm{log}(x/{x}_{\odot })-{x}_{0})+G(\epsilon )$ (Equation (4) in Section 5.2), where ${x}_{\odot }$ is ${L}_{\odot ,H}$ or ${M}_{\odot }$, and $G(\epsilon )$ denotes a Gaussian distribution with dispersion . Given in the second column is the offset x₀ (the inverse variance-weighted mean of all x), which is subtracted from the x before fitting in order to reduce covariance between α and β. All other parameters are fit to the data using LINMIX_ERR and the resulting Markov Chain Monte Carlo (MCMC) sample, which is evaluated for the mean ("val") and the standard deviation ("err," i.e., the size of the 68%-confidence interval). These parameters are as follows: the relation zeropoint (α), logarithmic slope (β), and log-scatter in the $y=\mathrm{log}({M}_{\mathrm{BH}}/\;{M}_{\odot })$-direction () for the fit to the entire sample of 44 objects, as well as the respective offset and intrinsic scatter of three subsamples: megamasers ("mega"), spiral galaxies ("late"), and low-mass galaxies ("low"). Low-mass galaxies always constitute half of the sample, i.e., those 22 galaxies for each relation with the lowest x values. The subsamples' offsets are relative to a relation fit to the data minus the subsample; the parameters of these relations are not shown here. The subsample scatter is relative to the offset relation with the same β as the main relation.

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When we combine the megamaser disk galaxies with L14, we obtain a large enough sample to split galaxies based on various properties and then ask where they fall in the BH-bulge mass plane. We will focus exclusively on the 44 galaxies (L14 and ours) that have dynamical BH mass measurements as described in Section 4.

We consider the following subsamples. We investigate the scaling of the 10 megamaser galaxies, which includes NGC 4258 from the L14 sample. We also group all late-type galaxies. Many works (Greene et al. 2008, 2010; Hu 2008; Gadotti 2009; Kormendy et al. 2011) have suggested that late-type galaxies with pseudo-bulges may obey different scaling relations than classical bulges, since secular evolution may not efficiently fuel BH growth. In practice, because there is considerable overlap between the late-type and pseudobulge samples (7/9 of our megamaser sample), we will only consider one late-type subsample comprising the eight non-S0 megamasers and the three additional spiral galaxies from L14. Finally, we consider a low-mass sample, since if the scaling relations arise from hierarchical merging via the central limit theorem (e.g., Peng 2007; Jahnke & Macciò 2011), then the scaling relations would break down at low mass. For this subsample, we simply take the 22 lowest-mass or lowest-luminosity galaxies.

We calculate the offset of each subsample from the "primary relation," which is the relation fit to the data excluding the respective subsample. For each Monte Carlo realization of the primary relation, the offset ${\rm{\Delta }}a$ (Table 8) is the weighted-mean $(y=\mathrm{log}{M}_{\mathrm{BH}})$-offset of the subsample from the primary relation. The weights are the y- and projected x-measurement errors, plus the intrinsic scatter in the relation, added in quadrature. We take into account the uncertainty in ${\rm{\Delta }}a$ by drawing it from its (Gaussian) error distribution around the weighted-mean offset. We subsequently determine the intrinsic scatter of the subsample () by iteratively varying its value, and adding it in quadrature to the measurement errors until ${\chi }^{2}=1$ for the given primary relation slope and subsample offset. We thus calculate ${\rm{\Delta }}a$ and for each element of the Markov chain, and the resulting ${\rm{\Delta }}a$ and distributions are evaluated for their mean and $1\sigma$ uncertainty. The offset for the maser sample is referred to as ${\rm{\Delta }}{a}_{{\rm{mega}}}$, while that for the late-type galaxies is ${\rm{\Delta }}{a}_{{\rm{late}}}$, and the low-mass sample is ${\rm{\Delta }}{a}_{{\rm{low}}}$.

There is another sample of spiral galaxies with indirect BH masses, based on reverberation mapping. A subsample of the reverberation-mapped AGNs have HST imaging that allows detailed bulge-disk decompositions (Bentz et al. 2009a). These fall in an inferred ${M}_{\mathrm{BH}}$ range of ${10}^{7}\mbox{--}{10}^{9}\;\;{M}_{\odot }$ that overlaps with the megamaser disks at the low-mass end. Many of the hosts are also disk galaxies. Bentz et al. (2009b) find that ${M}_{\mathrm{BH}}$ is quite tightly correlated with ${\text{}}{L}_{\mathrm{bul}}$ (even with no conversion to mass) and they do not observe the long tail to low ${M}_{\mathrm{BH}}$ that is seen with the megamaser galaxies. Interestingly, the scatter seen between ${M}_{\mathrm{BH}}$ and ${\sigma }_{* }$ is also smaller at ${M}_{\mathrm{BH}}\approx {10}^{7}\;\;{M}_{\odot }$ for the reverberation-mapped sources than the megamaser disk galaxies (e.g., Greene et al. 2010; Woo et al. 2010). We discuss this difference in Section 6.1.

We also note that there are two other prominent outliers in the BH-bulge scaling relations (S0 galaxies NGC 4342 and NGC 3998) that have apparently high ${M}_{\mathrm{BH}}$ for their stellar mass. In both galaxies, the bulge luminosity is strongly dependent on the adopted decomposition (for details, see Läsker et al. 2014a). However, even taking the total luminosity as an upper limit on ${\text{}}{L}_{\mathrm{bul}}$ still puts their ${M}_{\mathrm{BH}}$ above the ${M}_{\mathrm{BH}}$–${\text{}}{L}_{\mathrm{bul}}$ relation. In the case of NGC 3998, ${M}_{\mathrm{BH}}$ would be five times lower if the gas-dynamical measurement was adopted instead of the stellar-dynamical model, which is true for many galaxies with both stellar and gas dynamical measurements (see Walsh et al. 2012). The BH mass measurement in NGC 4342 is based on stellar dynamics. Here, the large ${M}_{\mathrm{BH}}$ for its (bulge) luminosity is similar to an emerging class of S0 galaxies that appear to have overly massive BHs for their stellar bulge mass (van den Bosch et al. 2012; Walsh et al. 2015, 2016). These galaxies tend to be very compact with large central velocity dispersions and fast rotation on large scales, live in rich environments, and may have very different formation histories than the megamaser galaxies studied here. However, they contribute to our overall conclusion that there is very significant scatter in ${M}_{\mathrm{BH}}$ for bulge masses $\lt 5\times {10}^{10}\;{M}_{\odot }$.

We begin by examining the "basic" bulge fit, in which we assume that the galaxy can be well fit by the combination of a bulge, disk, and possible point source (Figure 6, left). These fits represent an upper limit on the bulge component, and are also a good analog to fits in the literature to the SDSS (e.g., Lackner & Gunn 2012) and to higher-redshift galaxies (Bell et al. 2012). The expected range of H-band bulge luminosities for the megamaser disks, based on the scaling relations, is 10⁸–${10}^{10}\;{L}_{\odot }$. The observed range, in contrast, is much narrower ($3\times {10}^{9}\mbox{--}4\times {10}^{10}\;{L}_{\odot }$). If we measure the average offset in ${M}_{\mathrm{BH}}$ between the megamaser disks and the best-fit L14 relation (${\rm{\Delta }}{a}_{{\rm{mega}}}$ in Table 8, row 2), then we find a mean offset of $-0.8\pm 0.2\;\mathrm{dex}$ in BH mass from the best-fit relation.

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These galaxies tend to have recent or ongoing star formation in their nuclei, which biases the observed bulge luminosities to high values compared with the predominantly old stellar populations that dominate early-type galaxies. We attempt to mitigate these differences by transforming to stellar mass. We try to place both the literature and megamaser galaxies on the same stellar mass scale to facilitate direct comparison (Section 3.6). When considering stellar mass rather than luminosity (Figure 6, right; ${\rm{\Delta }}{a}_{{\rm{mega}}}$ in Table 8, row 5), we still see that the megamaser disks remain offset to smaller BH masses at a given bulge mass ($-0.8\pm 0.2\;\mathrm{dex}$).

If we instead examine the offset between the best-fit L14 relation and the spiral galaxy subset, rather than the megamaser subset, then the net offset in ${M}_{\mathrm{BH}}$ declines a bit, ${\rm{\Delta }}{a}_{{\rm{late}}}=-0.6\pm 0.2$ dex. The fact that the measured offset ${\rm{\Delta }}{a}_{{\rm{late}}}$ is smaller than ${\rm{\Delta }}{a}_{{\rm{mega}}}$ is interesting, and indicates a possible difference between the distribution of ${M}_{\mathrm{BH}}$ for megamaser disks and galaxies with stellar/gas-dynamical BH mass measurements.

In summary, when we consider the most general concept of a "bulge" as the centrally concentrated component that constitutes a light excess above the large-scale disk, we find a wide range of BH mass at fixed bulge mass and a significant offset from the early-type ${M}_{\mathrm{BH}}$–${\text{}}{M}_{\mathrm{bul}}$ relation for the megamaser disks and late-type galaxies in general. A qualitatively similar result has been seen before in late-type galaxies for the subset of pseudobulge galaxies (Greene et al. 2008; Hu 2008; Sani et al. 2011; Kormendy & Ho 2013).

In Section 4, we described in detail our attempt to isolate a classical bulge component in the maser disk galaxies. Considering the colors, shapes, and structures of the putative "classical" bulge components, we identified a classical bulge in four cases (NGC 1194, NGC 2960, NGC 3393, and UGC 3789).

We compare the BH and stellar mass for the confirmed classical bulges (solid symbols) in Figure 7. Obviously, these classical bulge components will, by construction, contain less stellar mass than the basic bulges (typically by $\sim 0.2\;\mathrm{dex}$), nominally improving the agreement with the elliptical galaxy ${M}_{\mathrm{BH}}$–${\text{}}{M}_{\mathrm{bul}}$ relation. Indeed, we see better agreement overall when plotting ${M}_{\mathrm{BH}}$ against classical rather than basic bulge measurement: the offset in ${M}_{\mathrm{BH}}$ is ${\rm{\Delta }}{a}_{{\rm{late}}}=-0.6\pm 0.2\;\mathrm{dex}$. However, if we focus only on those galaxies where we believe there is a secure classical bulge component (filled symbols in Figure 7), then we see that there is still a net offset toward lower ${M}_{\mathrm{BH}}$ at a given bulge mass. Thus, we tentatively conclude that simply identifying more robust classical bulges in these galaxies will not eradicate the trend toward higher scatter and lower ${M}_{\mathrm{BH}}$ at a given bulge mass. As noted by Sani et al. (2011) and Läsker et al. (2014a), it is still difficult to definitively rule out that observational issues (e.g., hidden nuclear star clusters or other small-scale components) are contaminating our measurements, but as the number of galaxies with HST data and high-fidelity dynamical BH masses increases, it becomes more and more clear that there is simply a very wide range of ${M}_{\mathrm{BH}}$ in these low-mass galaxies.

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There has been considerable interest in recent years in the relation between total stellar mass and ${M}_{\mathrm{BH}}$, with various claims that total stellar mass should also show a relationship with ${M}_{\mathrm{BH}}$ (Peng 2007), possibly even tighter than bulge mass (Jahnke & Macciò 2011), and one that does not evolve with redshift (Jahnke et al. 2009; Bennert et al. 2010, 2011; Cisternas et al. 2011). We examine the ${M}_{\mathrm{BH}}\mbox{--}{M}_{{\rm{tot}}}$ relation using the L14 and our megamaser samples in Figure 8. Focusing on the stellar mass range where the megamasers are found, we see the most striking mismatch between the range in ${M}_{\mathrm{BH}}$ ($2.5\;\mathrm{dex}$) and the range in stellar mass ($0.4\;\mathrm{dex}$). Thus, at a fixed stellar mass, galaxies may contain BHs with a wide range of mass. We do not see strong evidence that the total stellar mass to ${M}_{\mathrm{BH}}$ relation is tighter than others in the literature, and we see virtually no correlation at all below ${M}_{* }\approx {10}^{11}\;\;{M}_{\odot }$. Regardless, $\epsilon ({M}_{\mathrm{BH}}\mbox{--}{\text{}}{M}_{\mathrm{tot}})$ is still marginally consistent with $\epsilon ({M}_{\mathrm{BH}}\mbox{--}{\text{}}{M}_{\mathrm{bul}})$ (see Läsker et al. 2014b). We measure an offset between the megamasers and the best-fit L14 relation of ${\rm{\Delta }}a=-0.8\pm 0.2$ dex, which is similar to the apparent offset between active and quiescent BHs observed by Reines & Volonteri (2015).

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The megamaser disk galaxies span $1.5\;\mathrm{dex}$ in BH mass but only $0.6\;\mathrm{dex}$ in galaxy mass. Furthermore, the ratio of ${M}_{\mathrm{BH}}/{M}_{* }$ is, on average, considerably lower than what is seen in more massive elliptical and S0 galaxies. This long tail to low ${M}_{\mathrm{BH}}$ at fixed stellar mass is seen most conclusively in the maser disk samples, likely due to the difficulties of resolving the gravitational sphere of influence for low-mass BHs (Batcheldor 2010; Gültekin et al. 2011; van den Bosch et al. 2015). In the stellar mass range probed by the maser disks (${M}_{* }\lt {10}^{11}\;{M}_{\odot }$), in this paper we see a hint that stellar-dynamical, gas-dynamical, and reverberation-mapped samples do not truly sample the full range of ${M}_{\mathrm{BH}}$ at a given M_∗. In particular, only the megamaser disk galaxies extend to the lowest ${M}_{\mathrm{BH}}$ probed at a fixed galaxy mass. In the case of the stellar and gas-dynamical measurements, it is not surprising that the BHs do not sample the low-mass regime, since we cannot resolve their sphere of influence. Thus, we argue that only the megamaser disks reveal the true distribution of ${M}_{\mathrm{BH}}$ at a given galaxy property.

It is more difficult to pin down the origin of the difference between the maser and the reverberation-mapped sources. One possibility is a bias in the reverberation-based BH masses, which after all have been calibrated to follow the inactive ${M}_{\mathrm{BH}}\mbox{--}\sigma$ relation. Alternatively, the reverberation sources may also have a bias toward higher ${M}_{\mathrm{BH}}$ at a given galaxy mass, due to the preferential selection of the most luminous sources with correspondingly high-mass BHs. Until we come to a full understanding of this issue, it will be difficult to fully compare the scaling relations for single-epoch virial BH masses with dynamical BH masses (e.g., Graham & Scott 2015; Reines & Volonteri 2015).

Alternatively, the megamaser disk sample could have a bias toward lower ${M}_{\mathrm{BH}}$ at fixed galaxy property due to their selection as active galaxies if, for some reason, the megamaser disks pick out galaxies that are preferentially still growing toward the end state of the ${M}_{\mathrm{BH}}\mbox{--}\sigma$ relation. The megamaser disks are nearly the only active galaxies with dynamical BH masses, and so it is worth considering the possibility that masers select a non-representative sample. We argue against that possibility, repeating the arguments in Greene et al. (2010). The galaxies are found, on average, a factor of four below the relation between ${M}_{\mathrm{BH}}$ and ${L}_{{\rm{bulge}}}$. To erase this offset, at their current Eddington ratios of $\sim 10 \%$ (Greene et al. 2010), would require ∼1 Gyr of steady BH growth. On the other hand, the typical lifetimes of AGNs are likely shorter than this (Martini & Weinberg 2001) while pseudobulge growth times are much longer (Kormendy & Kennicutt 2004), and so how the megamaser disks would know to grow at this particular moment is difficult to understand. Furthermore, if such a bias impacted the maser galaxies, then we would expect to see the same effect in the reverberation-mapped sources, which we do not.

In principle, it is also possible that megamaser disk galaxies are biased against the most massive BHs (Reines & Volonteri 2015; van den Bosch et al. 2016). However, if there were a large sample of spiral galaxies with very massive BHs ($\gtrsim {10}^{8}\;\;{M}_{\odot }$), then we would likely know about them already from stellar- or gas-dynamical ${M}_{\mathrm{BH}}$ measurements.

Barring such biases, megamaser disks enable us to probe the underlying distribution of BH mass for spiral galaxies. The observations presented here apply (at minimum) to all BHs in spiral galaxies with ${M}_{* }\lt {10}^{11}\;{M}_{\odot }$. That is, at a fixed galaxy property, there is a large range of ${M}_{\mathrm{BH}}$, extending systematically below the relations defined by the early-type, massive galaxies.

We consider two explanations for the differences in scaling relations between the masers and early-type galaxies. One is that the scaling relations vary with galaxy morphology. In this picture, the formation history of the galaxy (e.g., the formation of a massive bulge) is tied to the fueling and feedback processes of the growing BH. For instance, galaxies that build their central bulges primarily with secular processes may never efficiently fuel their BHs (e.g., Gadotti 2008; Greene et al. 2008; Hu 2008). This would result in the observed offset to lower masses, along with significant scatter, preferentially among spirals. To test these possibilities, we urgently need BH mass measurements in more bulge-dominated, low-mass galaxies like M32. We also note the intruiging possibility raised by Saglia et al. (2016) that, at high enough mass density, the BHs in pseudo-bulges obey the same scaling relations

The other possibility is that the BH scaling relations are driven by merging via the central limit theorem, as advocated by Peng (2007) and Jahnke & Macciò (2011). In this picture, galaxies with fewer mergers do not converge to a tight scaling relation, leading to a strong dependence of scatter on the galaxy (or halo) mass. If we could measure the scatter in the scaling relations as a function of mass and morphology over the full range of ${M}_{\mathrm{BH}}$, then we could determine which of these scenarios is preferred. Unfortunately, we still have very few measurements at low mass, and vanishingly few in low-mass, early-type galaxies (M32, van den Bosch & de Zeeuw 2010; NGC 404, Seth et al. 2010, D. D. Nguyen et al. 2016, in preparation; NGC 4395, den Brok et al. 2015). It remains very challenging to distinguish these two possibilities.

Finally, there is the possibility that the scaling relations are completely artificial and actually just define an upper envelope that arises due to problems with the stellar and gas-dynamical methods. Others have considered this possibility (Batcheldor 2010; Gültekin et al. 2011; van den Bosch et al. 2015). In the coming decade, ALMA (Davis 2014) and 30m-class telescopes (Do et al. 2014) will provide an order of magnitude increase in angular resolution, allowing us to test this possibility. What we really need are megamaser disks in early-type galaxies. Searches thus far have not been successful (van den Bosch et al. 2016), but they are worth continuing.

Despite significantly increasing the sample of L* spiral galaxies with dynamical ${M}_{\mathrm{BH}}$ measurements, our samples at low mass and late-type morphology remain small. Thus, our conclusions are not yet definitive. While we did our best to identify classical bulges with photometric indicators, a combination of photometry and kinematics would undoubtedly work better (e.g., Erwin et al. 2015). Luckily, there are additional megamaser disk galaxies with Keplerian rotation curves and secure ${M}_{\mathrm{BH}}$ being observed with HST in Cycle 22 (P.I. Greene). We are also securing AO-assisted integral-field observations of the stellar and gas kinematics in five of these objects with SINFONI on the VLT (P.I. Greene). The combination of these two data sets should prove powerful in setting our results on firmer ground.

IC 2560 (Figures 9 and 10) contains a large-scale disk with well-defined spiral arms at intermediate radii. The disk is detectable out to $\sim 150^{\prime\prime}$ ($30\;\mathrm{kpc}$) along the major axis (with PA $=\;-50^\circ$) and has an axis ratio of ∼0.6; it grows rounder at larger radii. The tightly wound spiral arms range from 6 to 12 kpc (30''–60'') and broadly resemble a ring. The central X-shaped bulge/bar dominates the light inside $\sim 10^{\prime\prime}$ ($2\;\mathrm{kpc}$). Finally, the SB profile exhibits a "knee" at 1'' ($0.2\;\mathrm{kpc}$) that corresponds to a nuclear disk.

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The spiral ring and X-shaped bulge/bar are apparent in the residuals to the basic bulge+disk model (Figure 10). Thus, in our more complex fit, we introduce one component for the ring and one for the X-shaped bar/bulge. We also include a large-scale (extended) envelope, with a best-fit exponential scale radius of 47'' ($9.5\;\mathrm{kpc}$) to accommodate the obviously rounder outer component. Our best-fit model (Figure 9) also includes a faint nuclear disk that is exposed in the residual image and indicated by profile inflections around 1''. Although the formal ${\chi }^{2}$ improves only marginally when the disk is added, we see spiral structure associated with the nuclear disk in the residual image, and the disk model perfectly fits the apparent knee in the μ-profile at $\mathrm{SMA}\sim 1^{\prime\prime}$ ($0.2\;\mathrm{kpc}$). The bulge component changes when the nuclear disk is included, growing by $1^{\prime\prime}$ (a factor of two) and $0.34\;\mathrm{mag}$, as it is no longer trying to fit the very compact nuclear disk.

In the best-fit model, we fix the Sérsic index of the ring, envelope and nuclear disk to 1, 1, and 0.5, respectively. The ring is modified by an inner truncation. The X-shape is modeled by a fourth-order Fourier mode. Our estimate for the systematic (modeling) error of the classical bulge magnitude is $0.4\;\mathrm{mag}$, which we derive by considering the difference between the best-fit values from our reference model and several alternative models: allowing a free Sérsic index for first the envelope (bulge magnitude unchanged, ${n}_{\mathrm{env}}\to 0.6$), then the nuclear disk ($+0.3\;\mathrm{mag}$, ${n}_{\mathrm{nuc}.\mathrm{disk}}\to 0.8$), and finally the main disk ($-0.4\;\mathrm{mag}$, ${n}_{{\rm{d}}}\to 0.2$). We also construct alternative models by omitting from the model the nuclear disk (bulge $+0.3\;\mathrm{mag}$), or we omit the X-shaped pseudobulge ($-0.6\;\mathrm{mag}$).

Our high-resolution data allows us to cleanly separate the X-shaped bar/bulge from from a nuclear disk and the small, round (possibly classical) bulge. In the low-resolution and shallower Spitzer data of Sani et al. (2011), they are clearly fitting the disk and envelope together, since their disk is rounder than their bulge component. Likewise, their bulge component contains multiple components. Overall, they find a B/T of about 0.5, i.e., significantly higher than even the B/T of 0.18 in our basic model.

NGC 1194 (Figures 11 and 12) appears to be an S0 seen at relatively high inclination. The innermost region ($\sim 1^{\prime\prime}$ nucleus) is round, bright, and distinct from the flatter ($q\sim 0.5$) outer regions, which can be visually traced to about 90'' ($20\;\mathrm{kpc}$). The ellipticity profile features a local peak at $\sim 3^{\prime\prime}$ ($\sim 0.7\;\mathrm{kpc}$), followed by a trough at $\sim 8^{\prime\prime}$ ($2\;\mathrm{kpc}$). Subtracting the basic bulge+disk model additionally reveals a dust lane that is parallel to the major axis but offset by $\sim 4^{\prime\prime}$ to the south–west, as well as a minor-axis boxy light excess at $\sim 6^{\prime\prime} /1.5\;\mathrm{kpc}$.

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Turning to the basic model first, we see that there is no need for an AGN component as the central light is already slightly overestimated by the bulge+disk model. Out to $\sim 1^{\prime\prime}$, a major-axis excess in residual light may indicate an edge-on nuclear disk, while on larger scales ("$\sim 6^{\prime\prime} ;$ Figure 12) we may be seeing the residuals of an end-on bar. There is a local ellipticity peak $\sim 40^{\prime\prime}$ likely pointing to a disk component. At large radius, the basic model fits the extended light profile with the bulge (leading to a very high Sérsic index n = 6.8), but the best-fit bulge is too round to fit the outer component properly and leads to an over-extended profile at large radii compared with the profile in the data.

Our adopted model includes a bar-like component and an "envelope," in addition to a bulge, disk, and point source. The envelope, which has a best-fit Sérsic profile with n = 2, reduces the flux excess and axis ratio at the largest scales ($\gtrsim 100^{\prime\prime}$) compared to the basic bulge+disk model, and reduces the bulge Sérsic index (n = 3.2). The envelope is intermediate in flattening between bulge and disk: q = 0.5, versus 0.7 and 0.4, respectively. This outer component is as flattened as the inner disk and carries a large share of the total flux ($\sim 75 \%$), so that we surmise that it probably represents a large-scale, thick disk. Supporting this interpretation, there is also a large H i-disk in NGC 1194 (Sun et al. 2013). The bar-like component fits the apparent minor-axis excess on $\sim 10^{\prime\prime}$ scales. An additional $0\buildrel{\prime\prime}\over{.} 3$($80\;\mathrm{pc}$)-sized nuclear component can be fit and slightly improves the residuals, but we refrain from including it in our adopted model due to the complicated and dust-obscured center. However, we retain such a model with a nuclear component as an alternative that serves to estimate the systematic modeling errors of the model parameters.

Turning to the systematic errors, we find that the basic bulge is $1.8\;\mathrm{mag}$ brighter than the bulge component in our adopted model. If we remove just the envelope from the adopted model, then we obtain a $1.6\;\mathrm{mag}$ brighter bulge. Interestingly, if we add the putative nuclear component to the adopted model while constraining the envelope Sérsic index to n = 1 to reduce degeneracy, we again get a significantly brighter bulge than in our adopted model (by $0.8\;\mathrm{mag}$). Conversely, the bulge parameters barely change when we fit the large-scale disk with a Sérsic profile ($0.1\;\mathrm{mag}$ fainter bulge, and ${n}_{\mathrm{disk}}\to 0.8$). Finally, we explored whether masking of dust features (central, and particularly the lane parallel to the major axis) alters our results and found virtually no difference in parameters when applying the mask. In summary, these alternative models indicate a systematic bulge magnitude uncertainty of $0.8\;\mathrm{mag}$.

NGC 2273 (Figures 13 and 14) is a nearby ($26\;\mathrm{Mpc}$) spiral galaxy with several prominent rings and a central disk. Due to the proximity of the galaxy, the inner structure is well-resolved and the galaxy extends ∼100'' on the sky. At the largest radii ($\mathrm{SMA}\gtrsim 60^{\prime\prime} /7.5\;\mathrm{kpc}$), the light distribution is flattened ($q\sim 0.6$) with a major-axis PA of about $140^\circ$ E of N. The ends of the spiral arms are also visible. Further inward, the arms dominate the light. They are tightly wound, forming a broad ring at 10''–20'' (1.3–2.5 $\;\mathrm{kpc}$) along the SMA. The ellipticity of the ring is lower than that of the outer disk, and the PA is misaligned by about $+40^\circ$ from the outer disk. The spiral arms emerge from opposite sides of an apparent bar, which thickens to become lens-like toward the center. Located well inside this bar/bulge region at $\mathrm{SMA}=2^{\prime\prime}$ ($250\;\mathrm{pc}$) is a bright and slightly asymmetric nuclear ring and disk (Mulchaey et al. 1997; Erwin & Sparke 2003; Gu et al. 2003) with PA and axis ratio similar to the outer disk (see also, Petitpas & Wilson 2002; Barbosa et al. 2006; Falcón-Barroso et al. 2006). In the galaxy center, near the resolution limit, the brightness rises steeply. This feature appears round and is 1'' ($130\;\mathrm{pc}$) in diameter. It is either an inner bulge or a barely resolved star cluster.

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Starting with a basic bulge+disk+psf model (Figure 1), the best-fit bulge component traces the light of the nuclear ring, while the disk component broadly accounts for the main spiral arms. We improve on the basic model by adding a nuclear ring, bar, and spiral arms (Figure 2). We find a Gaussian profile with inner truncation for the nuclear ring and the spiral component. This choice fits the data better than an exponential and avoids the degeneracy of the more general Sérsic profile in the presence of the simultaneously adjustable truncation parameters. The bar component is a Sérsic with $n\sim 0.2$ and boxy isophotes (Fourier amplitude ${a}_{4}=-0.1$), as expected. The bulge and nuclear disk components are oriented along the (outer) major axis ($\sim 50^\circ$ E of N), while the bar component is rotated by a relative $+80^\circ$. The large-scale disk provides a good fit beyond $\gtrsim 20^{\prime\prime} (2.5\;\mathrm{kpc}$) aside from an additional faint large-scale spiral arm/ring pattern, which cannot be robustly modeled.

We bracket systematic uncertainties in our reference model with three additional models. Replacing the exponential disk by a Sérsic profile leads to a $0.2\;\mathrm{mag}$ reduction in the classical bulge light, and the disk index of n = 1.5 shows that the corresponding component indeed traces the exponential part of the profile. We test the effect of removing the bar, which was visually confluent with the bulge, and obtain a $0.6\;\mathrm{mag}$ increase in bulge flux. In this modification, the classical bulge R_e increases by a factor of two, becomes steeper (n = 3.8 versus the reference n = 2.1), and effectively accounts for most of the light inside the spiral ring. However, this model without a bar results in strongly increased residuals, and we thus prefer to include the bar. Finally, we test using a Sérsic profile for the nuclear ring and model a nuclear disk instead of the ring. We find virtually unchanged classical bulge parameters, but significantly elevated residuals in the latter case. The resulting low Sérsic index (0.1) of the disk also suggests that an inner truncation is appropriate to model the nuclear disk. In conclusion, we arrive at a conservative systematic uncertainy of $0.4\;\mathrm{mag}$ for the classical bulge magnitude of NGC 2273.

NGC 2960 (Figures 15 and 16) is a bulge-dominated galaxy with a kiloparsec-scale embedded disk. Its SMA is oriented $150^\circ$ east of north, and the average flattening is rather low, $q\sim 0.7$. The radial SB profile appears to exhibit a bulge-disk structure of a typical lenticular galaxy, with a prominent steepening of the profile inside $\sim 13^{\prime\prime}$ ($4.5\;\mathrm{kpc}$) and an exponential decline outside. However, two salient features distinguish NGC 2960 visually from a simple lenticular: the increase of ellipticity toward the center, and an inner ($\mathrm{SMA}\sim 8^{\prime\prime} /2.7\;\mathrm{kpc}$) flocculent and dusty disk. The residual image of a basic bulge+disk model (Figure 15) reinforces the impression of a dusty disk and reveals embedded asymmetric spiral structure. The residual image also shows that a highly inclined nuclear disk (residuals at $\mathrm{SMA}\lesssim 1\buildrel{\prime\prime}\over{.} 5/500\;\mathrm{pc}$) is responsible for the low ellipticity at the smallest radii. Both the nuclear disk and the kiloparsec-scale disk are indicated by separate ellipticity peaks ($e\sim 0.4$ respectively) at radii corresponding to their visual dominance.

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By contrast, the dominant large-scale (outermost) component is round ($q\sim 0.8$), smooth, and morphologically resembles an elliptical galaxy. We thus might interpret this large-scale component as the bulge despite its exponential profile. At the largest radii at which the light distribution can be traced, from 80'' ($30\;\mathrm{kpc}$) to 30'' ($10\;\mathrm{kpc}$), the profile again flattens and is marked by tidal or shell-like features that can be seen even in the science frames. These features indicate that NGC 2960 has undergone a recent interaction or merger which may have distorted the radial brightness profile of the bulge, resulting in a mostly exponential shape with a marked upturn only at the largest radii.

The basic bulge+disk model includes a flat "bulge" that over-predicts the central flux. To extract the bulge parameters more reliably, and to account for the disks, we add an additional nuclear component with a Sérsic profile (Figure 15). Both inner components converge to relatively compact profiles (n = 1.4 and 0.5). The comparison of this four-component model with the data profile makes it clear that both inner components trace the light of nuclear and kiloparsec-scale disk, and that the inner region is reasonably fit by these two components alone. We have also explored models with an additional central bulge, resulting in five components (including the central point source). However, the residuals barely improve, and the corresponding "bulge" component is still significantly flatter (q = 0.6) than the large-scale outer profile. We thus do not include this additional component. We have also accounted for the outermost, very flattened light by a separate component, but find that its inclusion does not affect the parameters of the other components.

Given these many complications, we do not find a clear classical bulge component in NGC 2960; instead, the center is fit by the sum of the two disks. We judge that the third, large-scale component corresponds best to a classical bulge, even with a low best-fit Sérsic $n\sim 1$. For comparison, Vika et al. (2012) have fit a two-component model, and interpreted the inner component as the bulge, which, given its size, presumably fits both the nuclear and the kiloparsec-scale disk simultaneously, and hence is more flattened than the outer component (the "disk" in their interpretation). The Vika et al. (2012) model hence corresponds to our basic model, which does not account for the separation of the two inner components and their clear disk morphology. We speculate that the kiloparsec-scale disk was recently accreted, and thus still contains gas and spiral structure. If we take one or both of the inner disks as the "bulge" instead, then the magnitude drops by 0.4–1.4 $\;\mathrm{mag}$. Other modifications, like allowing a Sérsic instead of an exponential profile for either disk, or including an envelope, have comparatively minor effects on the bulge parameters. The alternative models provide us with a $0.6\;\mathrm{mag}$ estimate of the systematic bulge magnitude uncertainty.

NGC 3393 (Figures 17 and 18) is a late-type galaxy that contains two prominent rings. It is probably seen face on based on the round outer disk, which extends to $\sim 80^{\prime\prime}$ ($21\;\mathrm{kpc}$). The large-scale disk is slightly lopsided toward $-50^\circ$ E of N, and features two asymmetric spiral arms with prominent star-forming regions. The arms barely connect to the galaxy center and broadly resemble a ring, which is clearly indicated by the peak in the SB profile at $40^{\prime\prime} /10\;\mathrm{kpc}$. The inner ring at intermediate radii ($\mathrm{SMA}=13^{\prime\prime} /3.5\;\mathrm{kpc}$) is much more elongated and has a lower axis ratio than the outer disk. The ring might be the star-forming boundary of a large-scale bar. The innermost region ($\lesssim 2^{\prime\prime} /0.5\;\mathrm{kpc}$) appears to be dominated by the bulge, i.e., a steep increase in the SB and round isophotes. It harbors yet another bar-like light distribution, with a PA $140^\circ$ E of N which is misaligned by $-20^\circ$ from the major axis defined by the inner ring.

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Fitting and removing the basic model (bulge+disk+nucleus, see Figure 18) exposes residuals from the bar and each ring. The basic fit yields an extended ($6\buildrel{\prime\prime}\over{.} 4/1.6\;\mathrm{kpc}$ and n = 3.5) "bulge" component that effectively accounts for all of the light at and inside the inner ring and is more flattened (q = 0.7) than the outer disk.

We improve the NGC 3393 model by adding separate components for the central bar and both rings. With n = 0.25 and q = 0.4, the bar is compact and flattened, as expected. We model the rings with Gaussian profiles (n = 0.5) but use an inner truncation so that the ring light does not eat away the disk. This, our best-fit model, has classical bulge parameters m = 11.2 mag, ${R}_{e}=2\buildrel{\prime\prime}\over{.} 4(0.6\;\mathrm{kpc})$, n = 2.6, and q = 0.97. This is $1\;\mathrm{mag}$ fainter than the bulge in the basic bulge+disk model, and $0.2\;\mathrm{mag}$ brighter than for the intermediate model without truncations. We adopt this difference as a rough estimate of the systematic bulge magnitude uncertainty.

NGC 4388 (Figures 19 and 20) is a spiral galaxy seen at high inclination (disk $q=0.35\;\to \;i\gtrsim 70^\circ$). The tightly wound spiral arms are visually defined between $\mathrm{SMA}\sim 30^{\prime\prime}$ and $50^{\prime\prime}$ (2.8 and $4.6\;\mathrm{kpc}$). They form a ring that can be identified in the SB and ellipticity profiles. In the center of NGC 4388, there is a bright, central ($\lesssim$ 25/200 pc) disk, seen almost edge-on with very low axis ratio, and at a $\sim -15^\circ$ misalignment from the large scale major axis. The entire region interior to the ring contains several dust lanes. Outside of the spiral/ring, the profile has two nearly exponential parts, with a change to a larger-scale radius (factor of several) and ellipticity (by ∼0.2) occurring at ∼80'' ($7\;\mathrm{kpc}$). We identify the inner exponential as the main disk, while the outer exponential "envelope" is identified as a very extended disk due to its high flattening ($q\sim 0.1$) and ∼100'' ($9\;\mathrm{kpc}$) scale radius.

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In addition to the bulge, disk, and nucleus (point source), we account for the nuclear disk, spiral arms, and envelope with exponential profiles. The spiral arms are modeled as a ring with an inner truncation. To reduce degeneracy, we chose an exponential instead of a Sérsic profile for the spiral ring, and force the bulge, disk, and envelope to share a common PA. The best-fit bulge of our adopted reference model is very round ($q\sim 0.8$, compared to the disk $q\sim 0.3$), has an intermediate Sérsic index n = 2.2, and boxy isophotes. The nuclear disk dominates the SB in the center, and the PA of the model component converges to the observed value, which provides confirmation that this component is suitably accounted for in our adopted model (see also the discussion of the nuclear disk from the kinematics as observed by SINFONI in Greene et al. 2014). The outer envelope also makes a significant difference to the fit in this case, changing the bulge magnitude by $-0.5\;\mathrm{mag}$.

Of the various models we fit, we note here the model with a Sérsic profile (instead of exponential) for the nuclear disk, a Sérsic for the main disk, and a model without the envelope component. These result in classical bulge magnitude changes of $+0.7$, −0.3, and $-0.5\;\mathrm{mag}$, respectively, and lead to a systematic bulge magnitude uncertainty estimate of $0.5\;\mathrm{mag}$. For reference, the classical bulge in the best-fit bulge+disk+point-source model is $0.3\;\mathrm{mag}$ fainter than in our adopted six-component model.

NGC 6264 (Figures 21 and 22) is dominated by a bar and a pair of smooth spiral arms. A distinct bulge is not immediately visible, but there is a small ($\sim 0\buildrel{\prime\prime}\over{.} 3/200\;\mathrm{pc}$) and round central light concentration embedded within the conspicuous bar. The bar is also apparent in the local maximum around 5'' ($3\;\mathrm{kpc}$) in the SB and ellipticity profiles at constant PA. Within $\sim 5^{\prime\prime}$ ($350\;\mathrm{pc}$), the PA profile shows a $\sim 10^\circ$ step, and grows considerably rounder toward smaller radii, suggesting that we are seeing an underlying bulge.

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The spiral arms are smooth and show little signs of star formation, perhaps due to the decreased spatial resolution ($\sim 100\;\mathrm{pc}$ at the distance of $136\;\mathrm{Mpc}$). The tightly wound spiral arms emerge from the ends of the bar, then become clearly defined at larger radii, and obtain full strength around SMA ∼10'' ($7\;\mathrm{kpc}$). This region is marked by a local maximum in the SB, ellipticity, and PA profiles, followed by a rapid brightness drop toward larger radii. At $\sim 30^{\prime\prime}$ ($20\;\mathrm{kpc}$), the SB profile transitions into a faint ($\sim 23\;\mathrm{mag}\;{\mathrm{arcsec}}^{-2}$) floor that we interpret as an envelope or halo that is traceable out to 50'' ($35\;\mathrm{kpc}$).

When fit with a basic model (bulge, disk, and point source), the "bulge" component is more flattened than the "disk" and appears to predominantly fit the light of the bar. Round residuals near the center expose an underlying rounder light distribution, i.e., the probable bulge. We add another Sérsic component to directly model the bar. The residuals in this second fit are greaty improved and we find a small bulge component (${R}_{e}=1^{\prime\prime} /0.7\;\mathrm{kpc}$, q = 0.7), and a larger flat (${R}_{e}=4^{\prime\prime} /2.6\;\mathrm{kpc}$, q = 0.4) and compact (Sérsic n = 0.5) component, as expected for a bulge and a bar. Using an exponential profile with inner truncation and power-law rotation, we model the spiral arms and the underlying exponential disk component. The adopted 4 + 1-component model (bulge, disk, bar, spiral, plus the nuclear point source) is a good fit aside from a possible outer envelope (or halo), which was too faint to be fit robustly. We choose not to account for the latter by another component, as it converges to a very large (${R}_{s}=100^{\prime\prime} /70\;\mathrm{kpc}$) scale, which suggests a degeneracy with the background uncertainty.

We experimented with alternatives to this adopted model and quote the change of bulge magnitude incurred by some of these modifications. Using a Sérsic instead of an exponential profile for the disk, or adding an exponential component for the envelope (halo), results in a 0.4 and $0.2\;\mathrm{mag}$ fainter bulge, respectively. Modeling the bar and bulge with only one Sérsic profile, but retaining the spiral component apart from the disk and AGN leads to a much brighter bulge ($-1.9\;\mathrm{mag}$) with classical bulge parameters that are close to those of the basic model parameters and differ by $-1.4\;\mathrm{mag}$ in m_bul from the reference model. As a conservative estimate, we thus assign a bulge magnitude uncertainty of $0.7\;\mathrm{mag}$.

NGC 6323 (Figures 23 and 24) is a spiral galaxy at high inclination with an apparent disk axis ratio of ∼0.4. There is a ring at SMA = 8'' ($4\;\mathrm{kpc}$), from which two flocculent and unequal-strength spiral arms emerge and extend to $\mathrm{SMA}\approx 10\;\mathrm{kpc}$ from the center. The main disk profile exhibits a weak truncation at $\mathrm{SMA}\gt 20\;\mathrm{kpc}$ that is recognizable in the image as the visible boundary of the disk. An inner ($4\;\mathrm{kpc}$) ring is clearly seen in the SB profile, delineating the transition from a low-ellipticity, bulge-dominated inner region to a flatter disk-dominated region. A nucleus or small bulge can be distinguished visually within the inner two arcseconds.

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The basic bulge+disk+nucleus model fares surprisingly well when emulating the radial profile. However, significant structure remains in the residual image, including spiral arms and a ring from which they appear to emerge, as well as a central misaligned, elongated structure whose ends coincide with the ring. We therefore construct a model that includes a spiral component modified by coordinate rotation and inner truncation, as well as a very compact, low-n Sérsic profile with high flattening that accounts for light between the bulge and the spiral arms and may be interpreted as a large-scale bar. This additional component also effectively removes the ring-like residuals at the onset of the spiral structure. Coincidentally, despite the addition of two components, the best-fit bulge parameters of the reference model are only marginally different from that of the basic model (${m}_{\mathrm{bul}}=15.5\;\mathrm{mag}$ instead of $15.4\;\mathrm{mag}$, and similarly for the bulge R_e and n). The bulge is about $2\;\mathrm{mag}$ fainter than the disk, ${R}_{e}=1\buildrel{\prime\prime}\over{.} 3$ ($0.65\;\mathrm{kpc}$) in size, and has a near-exponential profile. Allowing a fourth-order Fourier mode for the bulge isophotes gives a boxy shape (amplitude ∼0.1). The spiral is modified by Fourier modes (fourth order and lower), which enables fitting of the asymmetry in the spiral arms and a better convergence of the rotation function.

We explore multiple alternative models and find that, while formally increasing residuals (${\chi }^{2}$), for some of them the residual images and radial profile mismatches differ only in details. Removing the bar/ring component decreases the bulge brightness by $0.2\;\mathrm{mag}$, and omitting the spiral arm component instead changes m_bul by less then $0.1\;\mathrm{mag}$. Testing a model where the disk has a Sérsic profile instead of an exponential gives a $0.2\;\mathrm{mag}$ brighter bulge and a disk Sérsic index of 0.9. The lowest change in residuals, but biggest change in m_bul, occurs when we apply a truncation to the bar/ring instead of the spiral arm component, obtaining a $1\;\mathrm{mag}$ brighter and three times larger bulge, with n = 3.0 instead of 1.1. Taken together, these alternatives indicate a systematic m_bul uncertainty of $0.5\;\mathrm{mag}$.

UGC 3789 (Figures 25 and 26) is a late-type galaxy that is seen nearly face on and dominated by two rings, one close to the center at $\mathrm{SMA}=3\buildrel{\prime\prime}\over{.} 8$ ($900\;\mathrm{pc}$), and the second one at $\mathrm{SMA}=23^{\prime\prime}$ ($5.6\;\mathrm{kpc}$). Both rings contain star-forming regions and form the boundary of a disk, respectively, but the larger ring, as in NGC 3393, might as well delineate a large-scale bar. The inner ring is nearly round, while the second ring shows marked flattening and asymmetry. Two short spiral arms emerge at a PA $\approx 170^\circ$ but varies by several degrees from the center outwards. A third, weaker ring is discernible in the μ profile at $\sim 40^{\prime\prime}$ ($10\;\mathrm{kpc}$) and marks the edge of the visible large-scale disk.

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A basic bulge+disk+AGN model is clearly unsuitable to model this galaxy due to the luminous rings and bar. The "bulge" component fitted by the basic model largely fits the inner ring and is therefore very compact ($n\sim 1$). The "disk" in the basic model roughly accounts for the light of the second ring. In our best-fit model, the rings are modeled by Gaussian profiles with inner truncation, except for the outermost (third) ring, which is an untruncated Sérsic profile with low index ∼0.1 in the best-fit solution. Finally, the bar component becomes readily fit by a typical geometry ($q\sim 0.3$) and compact profile ($n\sim 0.3$).

The resulting reference model is a vast improvement over the basic model in terms of residuals and interpretation. Coincidentally, the bulge magnitude is almost identical to that of the basic model, but the bulge ${R}_{e}=3^{\prime\prime} /700\;\mathrm{pc}$ and n = 3.3 are $\sim 50 \%$ and 300% larger, respectively. Fitting the outer ring proves essential to keep the size of the main disk from growing extremely large. The truncation of the two inner rings improve the residuals considerably and allow bulge and disk to account for the central and inter-ring light. The following models are less precise representations of the data, but are still superior to the simple model and acceptable alternatives. When removing the outer ring, or the truncation of the second ring, the classical bulge magnitude differs by $-0.8\;\mathrm{mag}$ ($+0.2\;\mathrm{mag}$) from the reference model, respectively. Removing the truncation of the inner ring increases the residuals, but leaves M_bul nearly unchanged. Finally, we note that using a Sérsic profile for the main disk also leads to a very similar overall model, as the Sérsic index of the disk is $0.8\approx 1$ in the best fit. On average, these alternatives provide for a systematic uncertainty estimate of the bulge magnitude of $0.4\;\mathrm{mag}$.

In order to account for the effects of the PSF, galfit convolves each model with a PSF image. A scaled version of the PSF image is also used as a model of a point source (an AGN in our case). The accuracy of the PSF image effects the fit results of small-scale components near the galaxy center, including the bulge, and could in principle be important here. A PSF model can be provided by detailed modeling of the optical path and detector properties, as is commonly done for HST images. However, we found that the PSF that we obtained from TinyTim (Krist et al. 2010) is not adequate to describe the SB distribution of stars that we observe on our target fields. The problem is large enough to leave characteristic ring-like residuals near the galaxy centers after modeling, and to notably impact the AGN magnitude and bulge parameters in some of our targets. We therefore empirically derive the PSF using cutout images of non-saturated and isolated stars found on our (co-added) science frames. The co-addition of several such star cutouts improves the S/N and reduces the residual background uncertainty. It has the drawback of potentially broadening the PSF profile near the center due to finite pixel sampling and an unavoidable centering error (we do not resample onto fractional pixels). We tested the broadening incurred in our co-added image and find it to be marginal (see Figure 27).

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The PSF image must be large compared to the PSF FWHM to include most of the PSF image flux. We use a 43x43 pixel common cutout area, which is ∼27 times the FWHM of $0\buildrel{\prime\prime}\over{.} 2$ that we measure. Thus, our PSF image includes nearly 100% of the total PSF flux.

An image of the standard deviation of the flux per pixel (noise, or "sigma") is required to compute ${\chi }^{2}$. Providing a realistic estimate of the sigma map is necessary to obtain the "true" best-fit solution of a given model. We obtain the sigma image by first computing it on the ground-based and HST image stacks separately. This consists of measuring the background noise across the image as a whole (with objects masked) for the ground-based images, and adding in quadrature the Poisson noise from the object flux using the flux itself and the local effective gain. For the HST stacks, the noise can be computed since the four exposures are weighted evenly and all background levels are known precisely. Afterward, the two images are scaled and combined, with the HST data replacing ground-based data wherever it is available, and the noise maps are scaled accordingly.

Since we want to model the galaxy light unbiased by foreground and background objects, masks for the latter are indispensable. We create masks based on automatic object detection by SExtractor. We subsequently add masks by hand for stars that are particularly bright, and thus have extended PSF wings, or those that overlap with the galaxy and are hence not recognized by the automatic detection. In one case (UGC 3789), we opt not to mask the two stars near the galaxy center, but include them in our model and thereby avoid masking much of the area containing important constraints on the central profile. None of our fields are particularly crowded.