Tully–Fisher Distances and Dynamical Mass Constraints for 24 Host Galaxies of Reverberation-mapped AGNs

Spectroscopy of the H i 21 cm emission lines was acquired in 2013 (GBT13A-468; PI: Ou-Yang) and 2018/2019 (GBT18B-258; PI: Robinson) with the Robert C. Byrd Green Bank Telescope ⁷ (GBT). The observational setups and instrument selections are detailed in Paper I. In brief, both data sets were observed in position-switched mode with equal on–off exposure pairs and typical exposures of 60 s scans for GBT13A-468 and 120 s scans for GBT18B-258. All scans were broken into 3 s integrations to aid in radio frequency interference removal.

Spectral reduction was carried out with the GBTIDL suite (Marganian et al. 2006) v2.8 for GBT13A-468 and v2.10.1 for GBT18B-258. Each on–off pair was combined with the standard (ON–OFF)/OFF procedure, and all exposures for one source were accumulated and averaged into a single spectrum. Low-order polynomials were fit to and subtracted from the baselines before spectral measurements were conducted.

While we detected H i emission lines from 31 of the 44 AGN host galaxies that were observed, we limit the analysis here to the 24 galaxies that exhibit a rotationally broadened dual-horned profile shape, as this is needed to recover the disk velocity information for use in TF distance determinations. Additionally, we note that although we limit this sample to dual-horned profiles, the galaxy inclinations tend to be oriented more face-on (<45°) than the typical galaxies targeted for TF-based distances. The 24 galaxies are listed in Table 1.

Optical and near-infrared images of the AGN host galaxies have been compiled from several observatories, with the goal of separating the AGN contribution from the galaxy via two-dimensional surface brightness decomposition (described in Section 3). For all ground-based data, images were reduced and combined in IRAF ⁸ following standard procedures.

2.2.1. Previous Observations

2.2.2. New Observations

The TF relation for the optical bandpasses requires total, integrated galaxy magnitudes. Thus, with acceptable surface brightness models determined for each image, the image zero-points were then constrained in order to properly calibrate the model magnitudes. We achieved this by first modeling stars in the field that matched those in optical and near-infrared catalogs. The number of stars modeled was mainly dependent on how many were within the FOV, but was typically between 5 and 10. For all of our B- and V-band images, we drew stellar magnitudes from the AAVSO Photometric All-Sky Survey (APASS; Henden & Munari 2014; Henden et al. 2016), assuring none of the selected stars were flagged as variable. For NGC 6814 and Mrk 817, we utilized the R- and I-band field star magnitudes determined by Crimean Astrophysical Observatory imaging (Doroshenko et al. 2006).

For the remaining 12 galaxies in which data from the Crimean Observatory were not available, we collected r- and i-band stellar magnitudes first from the Sloan Digital Sky Survey (SDSS) data release 16 (Ahumada et al. 2020), or we collected the r- and i-band magnitudes from APASS. To transform the r and i magnitudes to R and I, we calculated synthetic photometry with the IRAF task synphot. We first estimated the spectral type of each star using the spectral classifications as a function of SDSS g−i (using g stellar magnitudes from either SDSS or APASS) color from Table 4 of Covey et al. (2007). Once the spectral type was assigned, we employed the corresponding stellar template from the Kurucz 1993 Atlas of Model Atmospheres (Kurucz 1993), and used synphot to calculate the difference between magnitudes of the template through the SDSS and Johnson–Cousins throughputs. The color differences were small for R and r, −0.05 < m_R − m_r < −0.26, and slightly larger for I and i, −0.06 < m_I − m_i < −0.76.

We adjusted the zero-point in Galfit to minimize the difference between the measured and expected magnitudes of the field stars, thus calibrating the photometry of the galaxy components as well. Lastly, we combined all the host-galaxy surface brightness components to determine total galaxy magnitudes, which are listed in Table 2.

We determine a typical uncertainty of 0.2 mag for the integrated galaxy magnitudes, consistent with Bentz & Manne-Nicholas (2018) based on our previous experience using Galfit as well as the level of agreement between fitting results to HST images of compact PG quasars (Veilleux et al. 2009). In some cases, poor seeing conditions or bright sky background induced higher uncertainty in the separation of AGN light from bulge light, or disk light from the sky contribution. For these cases, we assigned a slightly larger uncertainty of 0.3 mag to the final galaxy magnitudes (Mrk 79, NGC 2617 NGC 4748, Mrk 817, NGC 6814). We were unable to separate the disk light from sky contribution in the B-band images of Mrk 1044 and Mrk 6. Additionally for Mrk 1310, the seeing conditions coupled with focusing offsets in the B-band image caused substantial blending of the AGN and bulge light, thus we were unable to remove the AGN contamination. For these three galaxies, we omit the B-band data from our analysis.

Figure 1 displays selected B-band galaxy images, surface brightness models, and residuals, which show the range of quality in our surface brightness models of the ground-based images. For the most extended galaxies, like NGC 4593 and NGC 3783 (first and second column, respectively), we have good surface brightness models due to the larger size of the galaxy on the detector and hence, easier separation of each surface brightness component in the modeling process. More compact galaxies like NGC 4748 (third column) had surface brightness models of moderate quality, and the most compact galaxies, such as Mrk 817 (fourth column), had relatively poor quality surface brightness models. The quality of our models was mainly determined by comparing our galaxy V-band magnitudes to their HST V-band magnitudes. Good models had excellent agreement, usually within ∼0.01–0.02 mag. While moderate and poor models had larger discrepancies (∼0.1–0.3 mag), they are still in agreement within the larger uncertainties attributed to the compactness of the galaxy and the seeing conditions that complicated the modeling process of the ground-based images.

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The TF relation for the H band utilizes the H_−0.5 magnitude, which is calibrated for the aperture system $\mathrm{log}(A/{D}_{25}^{i})=-0.5$, where A is the aperture through which the galaxy intensity is measured and D₂₅ ⁱ is the galaxy diameter at the B-band 25 mag arcsec⁻² isophote, corrected for inclination (Aaronson et al. 1980). We employed the Ellipse task in IRAF to measure isophotes from our sky-subtracted, ground-based B-band images, with Galactic extinction corrections applied to the B-band magnitudes. We then fit an exponential disk function to the outer surface brightness profile to arrive at the semimajor axis in arcseconds at which the surface brightness reached 25 mag arcsec⁻². An example is shown in Figure 2, where the blue dashed line indicates the 25th mag arcsec⁻² surface brightness. For galaxies that had H-band imaging but did not have B-band images (Ark 120, SBS1116+583A, Zw 229-015), we utilized the relation between the radius at the 25 mag arcsec⁻² isophote (R₂₅) and the exponential disk scale length (R_d ) of R₂₅ = 3.2 R_d (Catinella et al. 2006; de Blok & Walter 2014) to estimate D₂₅ from our exponential disk profile fits. Lastly, our inclination corrections to the diameters follow the formula from the Second Reference Catalog of Bright Galaxies (de Vaucouleurs et al. 1976):

$$\begin{eqnarray}&&{D}_{25}^{i}={D}_{25}{\left(a/b\right)}^{-C},\end{eqnarray} \tag{ 2 }$$

where a/b is the ratio of major to minor axes, and Tully & Fouque (1985) determined C = 0.22 ± 0.03 based on their best fit to the deviations in H-band surface brightness as a function of galaxy inclination. H_−0.5-band magnitudes in addition to the galaxy radii and corresponding measurement method are listed in Table 2.

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Aaronson et al. (1980) originally assumed a typical uncertainty of 0.1 mag for their H_−0.5-band values. However, the aperture photometry for our sample was conducted on galaxy images in which we removed the AGN contamination in the surface brightness modeling process, which induces additional uncertainty in the total galaxy magnitude. Therefore, we conservatively adopt 0.2 mag uncertainty on all H_−0.5 magnitudes, consistent with our typical uncertainties on the AGN-free galaxy magnitudes for the optical bands.

The TF relation utilizes the width of the unresolved, rotationally broadened H i 21 cm emission line from late-type galaxies, which is directly related to the maximum rotation rate (Epstein 1964; Roberts 1969). We follow the method originally described by Tully & Fouque (1985), with the updated definition of the H i line width (Courtois et al. 2009), which includes corrections for instrumental and redshift broadening:

$$\begin{eqnarray}&&{W}_{m50}^{c}=\displaystyle \frac{{W}_{m50}}{(1+z)}-2{\rm{\Delta }}v\lambda ,\end{eqnarray} \tag{ 3 }$$

where z is the redshift of the H i line, Δv is the smoothed resolution of the spectrum, and λ is an empirically determined constant term given as λ = 0.25. We use the redshifts of the H i lines of our targets reported in Paper I. W_m50 is defined as the width of the H i profile at 50% of the mean flux over the range of spectral channels, which contain 90% of the H i flux. This new definition by Courtois et al. (2009) is preferred as it employs the mean flux rather than the peak, which makes the width measurement independent of the strengths of the flanks. Excluding 5% of the flux on either side of the profile also aids in separation of the profile wings from the noise. The line widths reported in Paper I are widths calculated at 50% and 20% over 100% of the flux. Therefore, we have remeasured the widths of our H i profiles using the updated definition and we list them in Table 3. An example of this measurement for the H i emission from NGC 4593 is shown in Figure 3.

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The corrected, observed width is then adjusted to agree statistically with twice the maximum rotational velocity, as the width of the H i line includes both redshifted and blueshifted gas motions. The translation is given as

$$\begin{eqnarray}\begin{array}{rcl}{W}_{\mathrm{mx}}^{2} & = & {\left({W}_{m50}^{c}\right)}^{2}+{\left({W}_{t,m50}\right)}^{2}[1-2{e}^{-{\left({W}_{m50}^{c}/{W}_{c,m50}\right)}^{2}}]\\ & & -2{W}_{m50}^{c}{W}_{t,m50}[1-{e}^{-{\left({W}_{m50}^{c}/{W}_{c,m50}\right)}^{2}}],\end{array}\end{eqnarray} \tag{ 4 }$$

where W_c,m50 = 100 km s⁻¹ and W_t,m50 = 9 km s⁻¹ are the values found by Courtois et al. (2009) to produce the best match between maximum rotation rate and adjusted H i line width. The width is then deprojected to edge-on orientation by

$$\begin{eqnarray}&&{W}_{\mathrm{mx}}^{i}={W}_{\mathrm{mx}}/{\sin }(i),\end{eqnarray} \tag{ 5 }$$

where i is the inclination of the galaxy disk.

The inclinations were generally derived from the axis ratios of the galaxy disk, as listed in Table 2. For most of the galaxies, we adopted the axis ratios reported by Bentz & Manne-Nicholas (2018). For NGC 4051 and NGC 4593, where the disk extended beyond the FOV of the HST image, we adopted the axis ratios from our Galfit models of the ground-based images. For NGC 4151, the spatially resolved H i study by Mundell et al. (1999) reveals the inclination of the H i disk to be 21°, much more face-on than the disk axis ratio that has been typically found in the optical based on the high surface brightness stellar distribution (∼0.6; de Vaucouleurs et al. 1976, 1991; Bentz & Manne-Nicholas 2018; see Section 5.4). We therefore adopt 21° as the true inclination of the H i disk for NGC 4151. We follow the standard prescription from the photo-visual analysis of Holmberg (1958) adopted by the main TF works in the literature (Tully & Fisher 1977; Tully & Pierce 2000; Tully et al. 2008, 2013):

$$\begin{eqnarray}&&\cos (i)={\left[({q}_{d}^{2}-{q}_{0,d}^{2})/(1-{q}_{0,d}^{2})\right]}^{1/2},\end{eqnarray} \tag{ 6 }$$

where q_d = b/a is the disk axis ratio and q_0,d is the intrinsic axial ratio of a disk galaxy viewed edge-on. Following Tully & Pierce (2000), we adopt q_0,d = 0.2 as the single, global value for the flattening. The uncertainties in the deprojected line widths increase as galaxy inclinations become more face-on. Consequently, the galaxies in this sample with the lowest inclination (NGC 2617, NGC 3783, NGC 6814) have the highest uncertainties in W_mx ⁱ .

The current calibrations for the B, R, H_−0.5 (Tully et al. 2008), and I-band (Tully & Courtois 2012) TF relations are as follows:

$$\begin{eqnarray}&&{M}_{B}^{b,i,k}=-19.99-7.27(\mathrm{log}{W}_{\mathrm{mx}}^{i}-2.5),\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&{M}_{R}^{b,i,k}=-21.00-7.65(\mathrm{log}{W}_{\mathrm{mx}}^{i}-2.5),\end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray}&&{M}_{I}^{b,i,k}=-21.39-8.81(\mathrm{log}{W}_{\mathrm{mx}}^{i}-2.5),\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&{M}_{{H}_{-0.5}}^{b,i,k}=-22.17-9.55(\mathrm{log}{W}_{\mathrm{mx}}^{i}-2.5),\end{eqnarray} \tag{ 10 }$$

where b, i, and k are the Galactic extinction, inclination, and redshift corrections, respectively, and the superscripts on the magnitudes indicate that the corresponding corrections have been applied. We estimate the extinction along the line of sight in each bandpass using the Schlafly & Finkbeiner (2011) recalibration of the Milky Way dust map of Schlegel et al. (1998).

The inclination correction is given by the expression ${A}_{i}^{\lambda }={\gamma }_{\lambda }\mathrm{log}(a/b)$, originally formulated by Tully et al. (1998) and subsequently used by Tully et al. (2008) and Tully & Courtois (2012), where λ is the passband, a/b is the ratio of major to minor axes of the galaxy disk, and γ is defined as

$$\begin{eqnarray}&&{\gamma }_{B}=1.57+2.75(\mathrm{log}{W}_{\mathrm{mx}}^{i}-2.5),\end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray}&&{\gamma }_{R}=1.15+1.88(\mathrm{log}{W}_{\mathrm{mx}}^{i}-2.5),\end{eqnarray} \tag{ 12 }$$

$$\begin{eqnarray}&&{\gamma }_{I}=0.92+1.63(\mathrm{log}{W}_{\mathrm{mx}}^{i}-2.5).\end{eqnarray} \tag{ 13 }$$

However, Tully et al. (1998) do not include a prescription for the H_−0.5 magnitudes. Sakai et al. (2000) approximated the correction as ${A}_{i}^{{H}_{-0.5}}=0.5{A}_{i}^{I}$, however, we adopt the original correction from Tully & Fouque (1985) of ${A}_{i}^{{H}_{-0.5}}=0.1{A}_{i}^{B}$ as it was derived from measurements in the H_−0.5 band.

Finally, the k-corrections for the B, R, and I bands utilized in the TF calibrations of Tully et al. (2008) and Tully & Courtois (2012) are described in Tully & Pierce (2000) and Chilingarian et al. (2010) for the optical bands and near-infrared band, respectively, and are as follows:

$$\begin{eqnarray}&&{A}_{k}^{B}=(3.6-0.36T)z,\end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray}&&{A}_{k}^{R}=[4.24(R-I)-1.10]z,\end{eqnarray} \tag{ 15 }$$

$$\begin{eqnarray}&&{A}_{k}^{I}=0.302z+8.768{z}^{2}-68.680{z}^{3}+181.904{z}^{4},\end{eqnarray} \tag{ 16 }$$

where T is the galaxy morphological type (1, 3, 5, and 7 corresponding to Sa, Sb, Sc, and Sd) and z is the redshift. The k-corrections in this work utilize the morphological classifications reported in Paper I and are listed in Table 4. Once more the H_−0.5 band lacks a prescription from Tully & Pierce (2000), thus we adopt the original k-correction from Aaronson et al. (1980) as ${A}_{k}^{{H}_{-0.5}}=1.9z$.

The TF relation has been calibrated for most optical and near-infrared bands (Tully et al. 2008; Tully & Courtois 2012), and most recently for SDSS and Wide-field Infrared Survey Explorer filters (Kourkchi et al. 2020). However, the Johnson V band has so far been neglected. We have therefore conducted the first calibration of the V-band TF relation.

We began by identifying the galaxies that were used to calibrate the most recent definitions of the optical TF relations (Tully et al. 2008). These included galaxies with distances determined from either Cepheid variable stars (26 galaxies), TRGB stars (13 galaxies), or SBF (7 galaxies). We then retrieved the V-band magnitudes for these galaxies from the Third Reference Catalogue of Bright Galaxies (RC3; de Vaucouleurs et al. 1991), the same source for the B-band magnitudes from the calibrations of Tully et al. (2008). These are purely observed magnitudes that have not been corrected for Galactic extinction, inclination-dependent extinction, or redshift. We followed Tully et al. (2008) and adopted the Schlegel et al. (1998) extinction corrections. We derived the inclination-dependent and redshift corrections in the V band following the same methods used to define them in B, R, and I. In-depth descriptions of the corrections and final calibration are available in the Appendix.

Tully et al. (1998) detailed the extinction corrections due to inclination in the B, R, and I bands. Following the same procedure and adopting the same formalism for the extinction parameter, ${A}_{i}^{\lambda }={\gamma }_{\lambda }\mathrm{log}(a/b)$, where a/b is inverse of the disk axis ratio, we find

$$\begin{eqnarray}&&{\gamma }_{V}=(1.01\pm 4.06)+(2.94\pm 1.09)(\mathrm{log}{W}_{{\rm\small{R}}}^{i}-2.5).\end{eqnarray} \tag{ 17 }$$

The method for deriving the k-corrections adopted by Tully & Pierce (2000) is not described, however, they are quite similar to the k-corrections based on the analysis of Frei & Gunn (1994). We therefore adopt the Frei & Gunn (1994) methodology and find a V-band k-correction of

$$\begin{eqnarray}&&{A}_{k}^{V}=(2.23-0.22T)z,\end{eqnarray} \tag{ 18 }$$

where T is the morphological type (1, 3, 5, and 7 again corresponding to Hubble types Sa, Sb, Sc, and Sd) and z is the redshift.

The extinction, inclination, and k-corrections were then applied to the apparent V magnitudes from RC3 of the Tully et al. (2008) calibrating sample. Using the accurate distances to these galaxies, which are based on Cepheids, TRGB, or SBF, we derived their absolute magnitudes. Finally, we fit a linear relationship between the absolute magnitudes and the H i line widths, following the formalism adopted for the other bandpasses. Our best-fit result is

$$\begin{eqnarray}&&{M}_{V}^{b,i,k}=(-20.39\pm 0.03)-(7.62\pm 0.15)(\mathrm{log}{W}_{\mathrm{mx}}^{i}-2.5).\end{eqnarray} \tag{ 19 }$$

We find a negligible change to the final result if we instead employ the updated Galactic extinction values from Schlafly & Finkbeiner (2011). When substituted, the slope and intercept shift slightly to −7.59 and −20.36, respectively. The calibrated relationship for the V band sits between the existing calibrated relationships for the B and R bands, and also agrees well with the recent TF calibrations of Kourkchi et al. (2020) for SDSS bands, especially when compared to g and r.

To constrain the TF distances, we utilized the deprojected H i line widths and calibrated TF relationships to derive absolute magnitudes for each galaxy in each available bandpass. We then calculated the distance moduli between our corrected apparent magnitudes and derived absolute magnitudes to constrain each distance. All corrected H i line widths and apparent magnitudes used in distance calculations are listed in Table 4, and the distance measurements for all bands are tabulated in Table 5.

Table 4. Corrected H i Line Widths and Magnitudes

Target	Morphology	W ${}_{\mathrm{mx}}^{i}$	${m}_{V}^{b,i,k}$ (HST)	${m}_{B}^{b,i,k}$	${m}_{V}^{b,i,k}$	${m}_{R}^{b,i,k}$	${m}_{I}^{b,i,k}$	${m}_{{H}_{-0.5}}^{b,i,k}$
(1)	(2)	(3)	(4)	5	(6)	(7)	(8)	(9)
Mrk 1044	SB(s)c	329.89 ± 28.33	14.02 ± 0.20	⋯	13.79 ± 0.20	13.56 ± 0.20	12.65 ± 0.20	⋯
Ark 120	Sb pec	549.21 ± 33.78	13.82 ± 0.20	⋯	⋯	⋯	⋯	11.71 ± 0.20
MCG+08-11-011	SBc	360.16 ± 11.95	10.93 ± 0.20	⋯	⋯	⋯	⋯	⋯
Mrk 6	Sb	565.76 ± 25.94	13.19 ± 0.20	⋯	12.96 ± 0.20	⋯	⋯	10.78 ± 0.20
Mrk 374	SBc	295.93 ± 22.24	13.93 ± 0.20	⋯	⋯	⋯	⋯	⋯
Mrk 79	SBb	261.91 ± 21.85	13.74 ± 0.20	13.77 ± 0.30	13.45 ± 0.20	12.95 ± 0.20	⋯	11.15 ± 0.20
NGC 2617	Sc	445.10 ± 149.27	12.53 ± 0.20	13.93 ± 0.30	12.68 ± 0.20	12.38 ± 0.20	⋯	⋯
NGC 3227	SAB(s) pec	448.88 ± 10.74	10.38 ± 0.20	11.00 ± 0.20	10.25 ± 0.20	9.85 ± 0.20	⋯	8.13 ± 0.20
SBS1116 + 583A	SBc	301.51 ± 41.10	15.45 ± 0.20	⋯	⋯	⋯	⋯	13.58 ± 0.20
NGC 3783	(R')SB(r)a	480.53 ± 120.76	11.71 ± 0.20	12.38 ± 0.20	11.65 ± 0.20	11.17 ± 0.20	⋯	⋯
Mrk 1310	Sbc	347.49 ± 24.08	14.67 ± 0.20	⋯	14.76 ± 0.20	14.13 ± 0.20	⋯	12.40 ± 0.20
NGC 4051	SAB(rs)bc	282.83 ± 15.66	9.87 ± 0.20	10.45 ± 0.20	9.97 ± 0.20	9.61 ± 0.20	⋯	8.52 ± 0.20
NGC 4151	(R')SAB(rs)ab	342.95 ± 56.31	10.69 ± 0.20	11.14 ± 0.20	10.52 ± 0.20	10.09 ± 0.20	9.66 ± 0.20	8.98 ± 0.20
NGC 4593	(R)SB(rs)b	437.95 ± 23.30	10.81 ± 0.21	11.51 ± 0.20	10.81 ± 0.20	10.29 ± 0.20	⋯	9.39 ± 0.20
NGC 4748	Sab	429.70 ± 23.25	13.17 ± 0.20	13.89 ± 0.30	12.80 ± 0.30	12.17 ± 0.20	⋯	10.86 ± 0.20
NGC 5548	(R')SA(s)0/a	534.08 ± 30.90	12.49 ± 0.20	13.08 ± 0.20	12.35 ± 0.20	12.03 ± 0.20	⋯	⋯
Mrk 817	SBc	549.93 ± 40.97	14.09 ± 0.20	14.76 ± 0.30	13.78 ± 0.30	13.38 ± 0.30	⋯	11.67 ± 0.20
Mrk 478	Sab	516.02 ± 163.75	15.24 ± 0.22	⋯	⋯	⋯	⋯	⋯
NGC 5940	SBc	327.54 ± 32.79	13.13 ± 0.20	⋯	⋯	⋯	⋯	⋯
Mrk 290	S0	376.64 ± 34.87	15.08 ± 0.20	⋯	⋯	⋯	⋯	⋯
Zw 229-015	(R)SBc	234.32 ± 21.15	14.71 ± 0.20	⋯	⋯	⋯	⋯	12.66 ± 0.20
1H1934-063	Sbc	286.26 ± 25.28	12.29 ± 0.20	13.30 ± 0.20	12.72 ± 0.20	12.33 ± 0.20	⋯	⋯
NGC 6814	SAB(rs)bc	388.09 ± 195.55	10.66 ± 0.20	11.46 ± 0.30	10.69 ± 0.20	10.20 ± 0.21	9.62 ± 0.20	9.71 ± 0.20
NGC 7469	(R')SAB(rs)a	335.80 ± 30.96	12.19 ± 0.20	12.60 ± 0.20	11.97 ± 0.20	11.83 ± 0.20	10.92 ± 0.20	9.76 ± 0.20

Note. The morphological classifications listed in Column 2 are consistent with those reported from Paper I. Column 3 lists the corrected H i line width in kilometers per second, which is statistically equal to twice the maximum rotation rate, deprojected to edge-on orientation (see Section 4.3). Columns 4–8 list the observed magnitudes in each band corrected for Galactic extinction, inclination-dependent extinction, and redshift (see Sections 5.1, 5.2).

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In Figure 4, we compare the ground-based distances to the distances based on the V-band HST apparent magnitudes due to their superior spatial resolution and lack of seeing effects. Within the uncertainties, we generally find close agreement between the distances derived from the different photometric bands. In addition to the superior image quality of the HST data, the models of the ground-based images were guided by, and in some cases held fixed to, the parameters determined from the HST images. The axis ratios from the models of the HST images were used to derive the deprojected H i line widths in most cases, except for NGC 4051 and NGC 4593 as we described in Section 4.3. Therefore, we prefer the distances based on the photometry derived from the HST images and quote them as our adopted TF distances in Table 5. We adopt a typical uncertainty of 20%, as used by CF1 and CF2 for TF-based distances. However, the ground-based photometry, especially when multiple bandpasses were available, can provide some additional insight into the uncertainties, so we list the uncertainty of the weighted mean as the final adopted uncertainty in cases where it was larger than 20% of the distance (3/24 galaxies). Though we employ the updated Galactic extinction values of Schlafly & Finkbeiner (2011), the calibrations of Tully et al. (2008) and Tully & Courtois (2012) utilized the previous values of Schlegel et al. (1998). We find a negligible change to our final distances if we instead employ the Schlegel et al. (1998) values, with a median fractional change of 0.4% for all galaxies in our sample.

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Peculiar velocities relative to the Hubble flow, or V _PEC , can be calculated as a check on the reliability of the TF distances. Galaxies in the local universe are generally observed to have V _PEC values ≲500 km s⁻¹ (Tully et al. 2008), therefore, larger values require additional scrutiny. We calculated the modified, cosmologically adjusted galaxy velocity ${V}_{{\rm\small{MOD}}}$, described in Tully et al. (2013, 2016) as

$$\begin{eqnarray}&&\begin{array}{l}{V}_{\mathrm{MOD}}={cz}[1+0.5(1-{q}_{0})z-(1/6)\\ \,\times \,\left(1-{q}_{0}-3{q}_{0}^{2}+1\right){z}^{2}],\end{array}\end{eqnarray} \tag{ 20 }$$

where z is the redshift with respect to the cosmic microwave background rest frame, q₀ = 0.5(Ω_M –2Ω_Λ), Ω_M = 0.27, and Ω_Λ = 0.73. This velocity includes relativistic corrections to the observed velocity assuming a ΛCDM cosmology, which are small for galaxies with z < 0.1, like our sample.

V _PEC is then calculated as

$$\begin{eqnarray}&&{V}_{\mathrm{PEC}}={V}_{\mathrm{MOD}}-{H}_{0}D,\end{eqnarray} \tag{ 21 }$$

where we adopt H₀ = 74 km s⁻¹ Mpc⁻¹ (Riess et al. 2019), and D is the adopted distance to the galaxy in megaparsecs.

The TF distances we have determined are the first redshift independent distances for many of the galaxies in our sample. However, in a select few cases there are previously measured distances with which we can compare our results, primarily by Cepheid and SBF methods, and second the Cosmicflows programs (CF1, CF2, CF3; Tully et al. 2008, 2013, 2016). Previous TF measurements have been reported for nine galaxies in our sample, mostly in the B band, yet none have taken into account the contamination of the predominantly blue AGN in the nucleus. As discussed in Section 3, the brightness contribution of an AGN can be significant and will bias the distance modulus toward smaller values, as we have found with the majority of TF distances discussed below. We have tabulated previous distance measurements with their respective methods in Table 6.

Mrk 1044: There are previously published distances for Mrk 1044 from the J-, H-, and K-band TF calibrations of Theureau et al. (2007) of 86.8 ± 18.4, 78.5 ± 17.0, and 68.5 ± 14.2 Mpc, respectively. We find a distance to Mrk 1044 of 81.3 ± 16.3 Mpc, which lies within the estimates of Theureau et al. (2007). Our surface brightness decomposition of the HST V-band image is mostly consistent with the decomposition of the same image from Wang et al. 2014, however, we find a larger exponential disk radius of 21.9'' compared to their value of 21.2''.

NGC 3227: NGC 3227 is interacting with its neighboring elliptical galaxy NGC 3226, which has an SBF distance measurement of 23.7 ± 2.6 Mpc from Tonry et al. 2001, with a slight correction from Blakeslee et al. 2010. NGC 3227 also has two previously reported B-band TF distance determinations: Bottinelli et al. 1984 reported a B-band distance of 15.2 Mpc, and Tully & Fisher (1988) reported an updated B-band distance of 20.6 ± 3.8. We report a distance of 24.3 ± 4.9 Mpc, which shows good agreement with the SBF measurement to its companion. The removal of the AGN contamination decreases the galaxy's apparent magnitude and results in the determination of a larger distance than both of the previous B-band TF determinations.

NGC 3783: NGC 3783 has a previous B-band TF estimate of 38.5 ± 14.2 Mpc (Tully & Fisher 1988) based on the diameter-H i line width relation. We report a slightly larger distance of 49.8 ± 10.0 Mpc. However, NGC 3783 is one of the most highly inclined systems in our sample, with an axis ratio of 0.96. Near face-on systems cause large uncertainties in W_mx ⁱ , and consequently a large uncertainty in the distance.

NGC 4051: There are numerous TF distance estimates for NGC 4051 with a large span of values, the most accurate of which is the recent Cepheids measurement by Yuan et al. (2020a) of 16.6 ± 0.3 Mpc. Sorce et al. (2014) reported a 3.6 μm TF distance of 8.8 ± 1.8 Mpc. B-band TF determinations span the range of 11.0−17.0 Mpc (de Vaucouleurs et al. 1981; Bottinelli et al. 1984, 1985; Tully & Fisher 1988; Tully et al. 2009). Finally, CF3 reports an I-band measurement of 11.0 ± 2.0 Mpc. Our distance is 9.5 ± 1.9 Mpc, surprisingly smaller than the previous TF distances given the removal of AGN contamination. The original axis ratio used by CF1 (and subsequently by CF2 and CF3) for NGC 4051 is 0.66, which is slightly more face-on than our constrained axis ratio of 0.58 from the ground-based surface brightness modeling (see Section 4.3). The higher inclination used by CF1 would produce a larger deprojected H i line width and subsequently brighter absolute magnitude predicted by the TF relation, thus resulting in a slightly larger distance of 10.9 Mpc.

NGC 4151: NGC 4151 has been studied by numerous groups in an attempt to constrain its distance, finding values that range from 4.5–20.3 Mpc (de Vaucouleurs et al. 1981; Bottinelli et al. 1984, 1985; Tully & Fisher 1988). The most accurate distance comes from a recent Cepheid study, which found 15.8 ± 0.4 Mpc (Yuan et al. 2020b). Almost all of the TF studies underpredict the distance, which seems to be caused by the adoption of an axis ratio of 0.6 when constraining the galaxy inclination. Resolved H i imaging of NGC 4151 (Mundell et al. 1999) suggests a much more face-on orientation of ∼21°. Adopting this value constrains our TF estimate of the distance to 18.6 ± 3.7 Mpc, slightly larger than but consistent with the Cepheids distance.

NGC 4593: Theureau et al. (2007) measured J-, H-, and K-band TF distances to NGC 4593 of ∼26 Mpc, which agrees fairly well with our finding of 28.5 ± 5.7 Mpc. Tully & Fisher (1988) estimated a much larger distance of 39.5 ± 14.5 Mpc based on the H i line width–diameter TF relation. However, as shown originally by Tully & Fisher (1977) and noted by Bottinelli et al. (1983), the diameter relation is much less accurate than the luminosity–H i line width relationship.

NGC 5548: The previous B-band TF measurement from Bottinelli et al. (1984) places NGC 5548 at a distance of 34.0 ± 8.8 Mpc. We find a distance of 45.0 ± 3.8 Mpc with a large V _PEC of 2104 ± 288 km s⁻¹. However, the large predicted V _PEC , in addition to the turbulent and low S/N H i profile, suggest this may not be a reliable distance. Ho et al. (2008) collected a higher S/N H i spectrum with W₂₀ = 321.1 ± 6.8 km s⁻¹. Using this measurement predicts D = 83.6 ± 16.7 Mpc with a more reasonable V _PEC = −753 ± 1242 km s⁻¹. We therefore adopt this distance for NGC 5548 and list it in Table 5.

NGC 6814: Bentz et al. (2019) recently reported a Cepheid-based distance to NGC 6814 of 21.6 ± 0.4 Mpc. There are also B-band TF estimates that range from 8.6–22.8 Mpc (Bottinelli et al. 1984; Tully & Fisher 1988). Even though NGC 6814 is almost perfectly face-on (with an axis ratio of 0.98) and therefore has a large uncertainty, the TF distance we predict of 22.1 ± 8.0 Mpc is in good agreement with the Cepheids value.

NGC 7469: NGC 7469 was host to SN 2008ec, a Type Ia supernova. Analysis of the supernova light curve by Koshida et al. (2017) and Ganeshalingam et al. (2013) constrained distances of 57.30–66.40 Mpc. There are also multiple TF distance determinations to NGC 7469, including a B-band measurement of 35.6 Mpc (Bottinelli et al. 1984) and JHK measurements of 50.0–59.6 Mpc (Theureau et al. 2007). However, in our analysis of the H i spectrum in Paper I, we commented on possible flux contribution to the blueshifted flank of NGC 7469 from companion galaxy IC 5283. Higher S/N emission line detections in the literature most likely include the flux contribution of the companion (Mirabel & Wilson 1984; Mirabel & Sanders 1988; Ho et al. 2008), while our lower S/N profile does not share the same signature. We have tested distances predicted using the W₂₀ measurements (with the ${W}_{{\rm\small{R}}}^{i}$ definition) from the literature to compare to our result. If 525.1 km s⁻¹ from Ho et al. (2008) is used, we calculate 140 Mpc. If we use 395 km s⁻¹ from Mirabel & Wilson (1984), the resulting distance is 91 Mpc. Using our width, our distance is 36.0 ± 7.2 Mpc with a V _PEC of 1949 ± 535 km s⁻¹. Due to the interaction of IC 5283 and uncertainty in the width of the emission line, resolved H i observations are necessary to both separate the interacting galaxies and improve on the current distance estimates which rely on the H i line width.

For all galaxies except Mrk 478, we are able to compare our distances to the distances predicted by the CF3 Distance-Velocity Calculator (CF3 DVC; Kourkchi et al. 2020) based on the velocity field from the Numerical Action Methods model (Shaya et al. 2017, D < 38 Mpc) and the Velocity and Density Field Model (Graziani et al. 2019, D < 200 Mpc). The CF3 DVC predicts a distance based on the Cosmicflows model of the local velocity field in a specific region of the sky. It also displays distances and velocities of known galaxy groups and clusters within the search region that define the local model, allowing us to analyze the density of matter in a particular region. The local gravitational interactions between a galaxy and its environment cause individual V _PEC values.

For Mrk 1044 (V _PEC = −1275 ± 1212), Ark 120 (V _PEC = −1855 ± 2394), SBS1116 + 583A (V _PEC = −1393 ±2030), NGC 4748 (V _PEC = −1513 ± 1219), and Mrk 290 (V _PEC = −2644 ± 2416), the V _PEC values we calculate agree with the range of peculiar velocities observed by CF1 within the large uncertainties. The peculiar velocities of Mrk 6 (V _PEC = −3625 ± 1873), Mrk 79 (V _PEC = 3181 ± 743), and Mrk 1310 (V _PEC = −2480 ± 1762) are large, but still within those observed by the larger CF2 and CF3 catalogs (maximum observed V _PEC of ∼4000 km s⁻¹), and could be caused by the mass distributions near each galaxy's position on the sky present in the CF3 catalog. We confirmed that the CF3 DVC shows known, localized mass concentrations occupying distributions of either smaller or larger distances than those predicted by the DVC. These suggest local gravitational wells, and the resultant blueshifts or redshifts would cause each galaxy to appear closer or farther, assuming the recessional velocities are equivalent to the Hubble flow.

For MCG+08-11-011, Mrk 374, Mrk 817, Mrk 478, NGC 5940, and Zw 229-015, however, we are unable to further check our TF distances with the CF3 DVC results (mostly due to the lack of clusters present in the CF3 catalog near the position of each galaxy) or any literature results. Within the uncertainties, these V _PEC constraints are all >1000 km s⁻¹, which we set as the cutoff for galaxies in which we were unable to analyze the local mass distribution. The same is true even if we adopt the uncertainty typically considered by Tully et al. (2008) of 20%. Our estimated distance for Mrk 478 is 282.2 Mpc, which is beyond the 200 Mpc limit of the CF3 DVC. Additionally, as previously discussed, any distance measurement which relies on current H i line width measurements of NGC 7469 is suspect. Thus, we have deemed the TF distances to these seven galaxies as uncertain, and have assigned each with the poor quality flag "c" in Table 5.

We note that the galaxy inclinations of the majority of this sample lie below the usual limit of 45° for TF studies in the literature, namely, the Cosmicflows programs. Systems with tendencies toward face-on orientations cause large uncertainties in the deprojected H i line widths, and consequently, high uncertainties on distance and V _PEC constraints. We also note that the majority of the outliers in Figure 5 have TF distance measurements far too small for their ${V}_{{\rm\small{MOD}}}$ given the Hubble flow for either value of H₀ we have displayed. The TF relation is calibrated with inactive galaxies, thus it is of interest to explore potential differences between active and inactive galaxies that could cause discrepancies in the predicted distances for this sample of AGN hosts.

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The analysis of color–magnitude diagrams for mass-matched samples of AGN and non-AGN hosts from the Chandra Deep Field North and South surveys by Xue et al. (2010) found that the star formation rates in active galaxies are typically a factor of ∼2–3 higher than quiescent galaxies for 0 < z < 1. Increased star formation has been shown to lead to an increase in surface brightness (e.g., Graves & Faber 2010; Mould 2020), and a higher surface brightness would lead to a brighter apparent magnitude, thus causing a galaxy to appear closer than it is. Additionally, in their study of the R-band TF relation for close galaxy pairs, Barton et al. (2001) found that triggered star formation is a significant contributor to the difference in slope from the TF relation. Whether higher star formation rates are caused by AGN activity or interactions, the observational effect would be consistent in that the galaxy would appear brighter than a comparable inactive or isolated galaxy, leading to a distance estimate that is biased low. Active galaxies might therefore be reasonably expected to show a larger scatter about the canonical TF relation.

All final TF distances are shown in the Hubble diagram in Figure 5, where the aforementioned uncertain distances are open circles, and the rest are closed circles. For the remainder of this work, we apply the redshift-based distances for MCG+08-11-011, Mrk 374, Mrk 817, Mrk 478, NGC 5940, and Zw 229-015, consistent with those reported in Paper I. We employ the SBF distance to NGC 3226 as the adopted distance to NGC 3227 (Tonry et al. 2001; Blakeslee et al. 2010), the Cepheid distance measurements to NGC 4051, NGC 4151, and NGC 6814 (Yuan et al. 2020a, 2020b; Bentz et al. 2019), and the average of the SN1a distances to NGC 7469 (Ganeshalingam et al. 2013; Koshida et al. 2017). Final adopted distances are tabulated in Table 7.

Table 7. Final Adopted Distances and Mass Estimates

Target	Distance	Ref	R HI	M BH	M*	M BARY	M DYN	M DM
	(Mpc)		(Kpc)	(M⊙)	(M⊙)	(M⊙)	(M⊙)	(M⊙)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
Mrk 1044	81.3 ± 16.3	1	8.10 ± 1.87	6.71 ${}_{-0.10}^{+0.12}$	10.02 ± 0.43	10.20 ± 0.32	10.71 ± 0.11	10.55 ± 0.22
Ark 120	161.2 ± 32.2	1	16.74 ± 4.39	8.07 ${}_{-0.06}^{+0.05}$	11.13 ± 0.22	11.18 ± 0.21	11.47 ± 0.11	11.15 ± 0.27
MCG+08-11-011	84.2 ± 6.9	2	39.45 ± 8.60	7.43 ${}_{-0.15}^{+0.15}$	11.10 ± 0.42	11.15 ± 0.39	11.47 ± 0.09	11.19 ± 0.38
Mrk 6	126.2 ± 25.2	1	30.63 ± 9.29	8.10 ${}_{-0.04}^{+0.04}$	11.05 ± 0.22	11.08 ± 0.21	11.76 ± 0.12	11.65 ± 0.16
Mrk 374	185.3 ± 7.0	2	41.08 ± 5.81	7.30 ${}_{-0.31}^{+0.31}$	10.84 ± 0.42	10.86 ± 0.41	11.32 ± 0.08	11.13 ± 0.28
Mrk 79	50.2 ± 10.0	1	13.10 ± 3.19	7.61 ${}_{-0.14}^{+0.11}$	10.13 ± 0.22	10.19 ± 0.20	10.72 ± 0.11	10.56 ± 0.17
NGC 2617	64.7 ± 19.5	1	12.70 ± 6.10	7.49 ${}_{-0.14}^{+0.14}$	10.54 ± 0.44	10.68 ± 0.36	11.17 ± 0.26	10.99 ± 0.37
NGC 3227	23.7 ± 2.6	3	17.89 ± 4.48	6.77 ${}_{-0.11}^{+0.08}$	11.04 ± 0.20	11.05 ± 0.20	11.32 ± 0.10	10.99 ± 0.27
SBS1116 + 583A	136.7 ± 27.3	1	11.23 ± 2.94	6.56 ${}_{-0.09}^{+0.08}$	10.48 ± 0.22	10.50 ± 0.22	10.77 ± 0.14	10.44 ± 0.32
NGC 3783	49.8 ± 10.0	1	23.98 ± 5.95	7.37 ${}_{-0.08}^{+0.08}$	11.08 ± 0.21	11.11 ± 0.20	11.51 ± 0.19	11.29 ± 0.30
Mrk 1310	118.7 ± 23.7	1	11.41 ± 2.78	6.21 ${}_{-0.09}^{+0.07}$	10.28 ± 0.22	10.38 ± 0.18	10.90 ± 0.11	10.75 ± 0.17
NGC 4051	16.6 ± 0.3	4	17.47 ± 1.94	6.13 ${}_{-0.16}^{+0.12}$	10.10 ± 0.19	10.19 ± 0.16	10.91 ± 0.06	10.82 ± 0.09
NGC 4151	15.8 ± 0.4	5	8.35 ± 1.13	7.56 ${}_{-0.05}^{+0.05}$	10.35 ± 0.19	10.41 ± 0.17	10.76 ± 0.13	10.50 ± 0.24
NGC 4593	28.5 ± 5.7	1	21.04 ± 6.45	6.88 ${}_{-0.10}^{+0.08}$	10.58 ± 0.22	10.60 ± 0.22	11.37 ± 0.12	11.29 ± 0.15
NGC 4748	82.2 ± 16.4	1	16.58 ± 5.21	6.41 ${}_{-0.18}^{+0.11}$	10.70 ± 0.22	10.73 ± 0.21	11.25 ± 0.12	11.09 ± 0.19
NGC 5548	83.6 ± 16.7	1	24.84 ± 5.96	7.72 ${}_{-0.02}^{+0.02}$	11.19 ± 0.22	11.20 ± 0.22	11.61 ± 0.10	11.40 ± 0.20
Mrk 817	130.8 ± 6.9	2	14.04 ± 2.74	7.59 ${}_{-0.07}^{+0.06}$	10.92 ± 0.19	10.93 ± 0.19	11.39 ± 0.10	11.21 ± 0.17
Mrk 478	342.7 ± 7.2	2	30.39 ± 4.19	7.40 ${}_{-0.18}^{+0.18}$	11.13 ± 0.42	11.17 ± 0.40	11.67 ± 0.22	11.51 ± 0.34
NGC 5940	141.6 ± 6.9	2	34.15 ± 4.94	7.04 ${}_{-0.06}^{+0.07}$	11.03 ± 0.29	11.07 ± 0.27	11.33 ± 0.10	10.98 ± 0.34
Mrk 290	162.3 ± 32.5	1	17.52 ± 4.24	7.28 ${}_{-0.06}^{+0.06}$	10.79 ± 0.30	10.81 ± 0.29	11.16 ± 0.12	10.90 ± 0.29
Zw 229-015	115.5 ± 6.9	2	28.16 ± 5.07	6.91 ${}_{-0.12}^{+0.07}$	10.26 ± 0.19	10.30 ± 0.18	10.95 ± 0.10	10.84 ± 0.13
1H1934-063	29.5 ± 5.9	1	5.57 ± 1.45	6.40 ${}_{-0.20}^{+0.17}$	10.15 ± 0.21	10.17 ± 0.21	10.42 ± 0.12	10.07 ± 0.31
NGC 6814	21.6 ± 0.4	6	11.91 ± 3.03	7.04 ${}_{-0.06}^{+0.06}$	10.33 ± 0.19	10.40 ± 0.16	11.02 ± 0.31	10.90 ± 0.38
NGC 7469	61.9 ± 3.3	7	17.06 ± 2.12	6.96${}_{-0.05}^{+0.05}$	10.78 ± 0.19	10.81 ± 0.18	11.05 ± 0.09	10.67 ± 0.28

Note. Final adopted distances and mass estimates for the AGN hosts in this study. The reference for each adopted distance in Column 3 is as follows: 1. TF distance; this work, 2. Redshift-based distances consistent with those reported in Paper I, adjusted for H₀ = 74 km s⁻¹, 3. SBF estimate to interacting companion NGC 3226 (Tonry et al. 2001), 4. Cepheids measurement (Yuan et al. 2020a), 5. Cepheids measurement (Yuan et al. 2020b), 6. Cepheids measurement (Bentz et al. 2019), 7. Average SN1a distance (Koshida et al. 2017; Ganeshalingam et al. 2013). The majority of black hole masses are from the RM database of Bentz & Katz (2015) (see Section 6.2). The calculations for M _BARY are detailed in Paper I, and M _DYN and M _DM are described in Section 6.

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Measurement of the maximum rotation rate (V_mx) of a disk galaxy allows the total enclosed mass of the system, or M _DYN , to be measured. H i is one of the best tracers of galaxy rotational velocity at the outer extents of the disk, as its distribution usually extends much farther than the high surface brightness stellar component (i.e., Walter et al. 2008; Ott et al. 2012; Koribalski et al. 2018). V_mx is most precisely measured from the flat portion of H i rotation curves (i.e., de Blok et al. 2008), however, the unresolved H i emission line is more commonly used as it requires far fewer observational resources to acquire.

The large-scale velocity dispersion of H i is negligible, ∼10 km s⁻¹, (Tamburro et al. 2009; Ianjamasimanana et al. 2012) relative to the rotational velocity. The broadening of the emission line is thus dominated by virial rotation, and the virial theorem describes the mass enclosed in the system as ${M}_{{\rm\small{DYN}}}=({{RV}}_{\mathrm{mx}}^{2})/{\rm{G}}$, where R is a characteristic radius and G is the gravitational constant. In our case, R is the radial extent of the H i distribution, and V_mx is equivalent to W_mx ⁱ /2, as Tully & Fouque 1985 have shown W_mx to be statistically equal to twice the maximum rotation rate.

There are multiple ways of estimating the H i radius in the literature. In their 21 cm study of 108 spiral galaxies, Broeils & Rhee (1997) found a relation between the H i radius and R₂₅. For galaxies where we have B-band images, we therefore adopt their relation of R _HI = (1.70 ± 0.16)R₂₅ with our R₂₅ measurements from B-band isophote analyses (see Section 5). In the cases where B-band data are unavailable for the sample (Ark 120, Mrk 374, SBS1116+583A, Mrk 478, NGC 5940, Mrk 290, Zw 229-015), we look to the collection of template disk galaxy rotation curves by Catinella et al. (2006) and de Blok & Walter (2014), and use the relation R₂₅ = 3.2 R_d , with the R_d measurements listed in Table 2. Combining these definitions yields R _HI = (5.4 ± 0.5) R_d , which agrees with the H i rotation curve analysis of de Blok & Walter (2014) that shows the maximum extent of all curves to be ∼5 R_d . Therefore, for the remainder of the sample that do not have B-band data, we adopt R _HI = (5.4 ± 0.5) R_d .

Additionally, Wang et al. (2016) recalibrated the relation between the diameter of the H i disk and H i mass, resulting in an extremely tight relationship over 5 orders of magnitude in mass. With this calibrated relationship, the integrated 21 cm H i flux measurement may be employed to estimate R _HI , as opposed to relying on the assumption of uniform scaling between the H i and optical sizes for all morphological types. We find a median fractional decrease of ∼18% in R _HI with this method compared to our adopted method of estimating R _HI , which is within our typical uncertainty of ∼24%.

A recent study by Trujillo et al. (2020) sought to derive a physically motivated galaxy radius definition. Such a radius would correspond to a clearly measurable galaxy property, and they suggest the radius at which the star formation threshold is reached (R₁). The gas density for this threshold is usually estimated to be ∼3–10 M_⊙ pc⁻² for gas-to-star transformation efficiencies of ∼100% (Schaye 2004). However, Trujillo et al. 2020 argued that if the efficiency is less than 100%, a more reasonable estimation is 1 M_⊙ pc⁻², which corresponds to an efficiency of ∼10%. H i has been observed to condense to molecular hydrogen at a threshold of ∼10 M_⊙ pc⁻² (Martin & Kennicutt 2001; Wong & Blitz 2002; Bigiel et al. 2008), and molecular clouds are the typical locations of star formation (e.g., Leroy et al. 2008). H i surface density should therefore be linked to star formation, and Trujillo et al. suggested that R₁ could be closely related to R _HI . To investigate this, we follow the prescriptions of Trujillo et al. (2020), which were derived from SDSS colors and a Chabrier initial mass function (Chabrier 2003), to transform the surface brightness profiles of the galaxies in our sample to stellar mass densities, and measure radii at 1 M_⊙ pc⁻². When compared to our R _HI estimates, we find an average ratio of R _HI to R₁ of ∼1.1, supporting the similarity between the two. We display the comparison between the two measurements in Figure 6. While we do not employ this method to estimate R _HI , and while our sample is somewhat small and we employ estimates rather than measurements of R _HI , the agreement between R₁ and R _HI may suggest a promising new avenue for constraining R _HI without resolved H i studies.

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With R _HI estimates for all galaxies in our sample, the total enclosed mass M _DYN is calculated by

$$\begin{eqnarray}&&{M}_{\mathrm{DYN}}=\left(\displaystyle \frac{{R}_{{HI}}{\left({W}_{\mathrm{mx}}^{i}/2\right)}^{2}}{G}\right),\end{eqnarray} \tag{ 22 }$$

with R _HI in units of kiloparsecs translated from the angular disk sizes by our adopted distances. The constraint on the amount of dark matter, then, is simply the difference between the total enclosed mass and luminous mass, M _BARY , calculated as

$$\begin{eqnarray}&&{M}_{\mathrm{DM}}={M}_{\mathrm{DYN}}-{M}_{\mathrm{BARY}},\end{eqnarray} \tag{ 23 }$$

where our M _BARY values are the sum of the gas mass and the stellar mass (M_*), or M _BARY = 1.4 M _HI + M_*. The factor of 1.4 on M _HI accounts for the contribution of helium. H i masses are adopted from Paper I, and the stellar masses are adopted from Bentz & Manne-Nicholas (2018) with a few additions in Paper I, both of which have been updated with our final adopted distances reported in this work. M_*, M _BARY , M _DYN , and M _DM are reported in Table 7.

All of the galaxies in this work belong to the sample of AGNs with direct black hole mass measurements from RM (Blandford & McKee 1982; Peterson 1993). RM measures the echo between the continuum variations of the nucleus, likely arising from the accretion disk, and the response of optically thick gas in the BLR moving at Doppler velocities. The time delay (τ) in the BLR variations is due to the extra path length traveled by the ionizing photons, and provides a measurement of the radius of the BLR (R _BLR ). When R _BLR is combined with the Doppler-broadened emission line width via the virial theorem, a constraint on the enclosed mass is obtained, the majority of which is due to the SMBH. The mass is given by

$$\begin{eqnarray}&&{M}_{\mathrm{BH}}=f\frac{c\tau {V}^{2}}{{\rm{G}}},\end{eqnarray} \tag{ 24 }$$

where c τ is the effective radius, V is the width of the broad emission line, G is the gravitational constant, and f is an order of unity scale factor accounting for the unknown geometry and kinematics of the unresolved BLR. We adopt 〈f〉 = 4.3 (Grier et al. 2013).

The majority of M _BH values are adopted from the AGN Black Hole Mass Database (Bentz & Katz 2015), and are the same as those used in our analysis in Paper I. For MCG+08-11-011, Mrk 374, and NGC 2617, we utilized the virial M _BH from Fausnaugh et al. (2017) and scaled them with 〈f〉 = 4.3. For Mrk 1044, we used the Hβ time delay from Hu et al. (2015) and the rms Hβ line width from Du et al. 2016 with our adopted 〈f〉 to arrive at an M _BH estimate. For NGC 5940, we adopt the rms line width from Barth et al. (2015) and time delay from Barth et al. (2013) to estimate M _BH . Lastly, the black hole masses for Mrk 478 and 1H1934-063 are based on current work on in-hand RM data (G. de Rosa 2020, private communication; M. C. Bentz et al. 2020, in preparation). All M _BH values are listed in Table 7.

The past two decades have revealed that the most fundamental form of the TF relation is the BTF relation, which shows a tightly correlated linear relation between rotational velocity and total baryonic mass over 5 decades of mass (McGaugh et al. 2000; McGaugh 2005; Lelli et al. 2015; Iorio et al. 2017). The mass contribution of gas in massive galaxies is small, therefore, the BTF relation is equivalent to the classic TF relation on the high mass end. As calculations of both gas and stellar masses, which constitute M _BARY , rely on distance, it is therefore of interest to compare our distances to those predicted by the BTF relation. Though some deviations from the relation have been observed, such as H i massive galaxies (M _HI ≳ 10¹⁰ M_⊙; Courtois et al. 2015) and H i-rich ultra-diffuse galaxies (Mancera Piña et al. 2019), the distances predicted by the BTF relation here are expected to be largely similar to those predicted by the TF relation, as the typical gas-to-stellar mass fraction for this sample is ∼13%. However, discrepancies may surface for a few galaxies with higher gas-to-stellar mass fractions (e.g., Mrk 1044, NGC 2617, Mrk 1310, Ark 120).

The BTF relation has been recently calibrated for several different definitions of rotational velocity measurement. We employ the calibration for our adopted velocity definition of W_m50 from Lelli et al. 2019, which has a slope of 3.62 ± 0.09 and an intercept of 2.33 ± 0.20. This agrees well with the examination of the BTF relation by Zaritsky et al. (2014) using the Spitzer Survey of Stellar Structure in Galaxies (Sheth et al. 2010), which found a slope of 3.5 ± 0.2. We employ the H i fluxes given in Table 3 for the H i mass estimates, with the scaling factor to convert H i mass to total gas mass of 1.33 for consistency with the BTF definition. We note that we use a scale factor of 1.33 here, rather than the value of 1.4 that we employ throughout the rest of this work, only to ensure that we calculate values in the same way as they were calculated in the calibration of the relation. Additionally, we note that the BTF relation employs the smaller scale factor of 1.33 as the helium contribution (which the scale factor accounts for) is assumed to be lower for the H i-rich calibrating sample of the BTF relation (McGaugh 2012 and references therein). We use the stellar mass-to-light ratios of Bell & de Jong (2001) to estimate M_*. A comparison between the BTF distances and TF distances is shown in Figure 7. A line of unity is drawn, and we find generally good agreement between the TF distances and those predicted by the BTF relation.

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The points in Figure 7 are labeled by H i emission line S/N, where profiles of S/N ≥ 10 are black circles, 5 < S/N ≤ 10 are blue squares, and S/N ≤ 5 are red diamonds. Mrk 290 and SBS1116 + 583A lie below the unity line, along with Ark 120 and Mrk 817, which lie below the line but agree within the uncertainties. The H i emission lines of these outliers all have a S/N < 5, which could result in underpredicting the flux and may be related to the cause of the discrepancies.

As described in Section 6, we utilize R _HI as the enclosing radius to estimate M _DYN for the galaxies in this sample. Here, we have examined the relationship between black hole mass and the total mass enclosed within the H i radius. The left panel of Figure 8 displays a clear trend between M _BH and M _DYN , with the best fit given by

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=(1.02\pm 0.35)\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{DYN}}}{{10}^{12}{M}_{\odot }}\right)+(6.95\pm 0.12),\end{eqnarray} \tag{ 25 }$$

with a scatter of (0.22 ± 0.09).

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Using the difference between the total enclosed mass and the luminous mass, we have also explored the relationship between M _BH and dark matter mass. We plot M _BH versus M _DM in the right panel of Figure 8 and find a weaker, but still significant, correlation. The best fit to the relation is given by

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=(1.08\pm 0.49)\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{DM}}}{{10}^{12}{M}_{\odot }}\right)+(7.15\pm 0.12),\end{eqnarray} \tag{ 26 }$$

with a scatter of (0.23 ± 0.11).

The average M _DM /M _DYN fraction is 62 ± 12%. However, we note that we are relying on the extent of the H i disk to measure M _DYN (and consequently M _DM ). The dark matter halo (DMH) is known to extend far beyond the visible radius, and thus we are probing only a fraction of the mass associated with each galaxy.

We have also attempted to estimate the total enclosed mass within the halo radius, or M _HALO . This includes estimates of the halo radius in relation to the H i radius and assumptions of the disk velocity at the halo radius (V _HALO ).

Kravtsov (2013) conducted a study relating R₂₀₀ to several galaxy radius definitions. R₂₀₀ is commonly treated as the radius of the DMH, and is the radius which encloses 200 times the critical density of the universe (ρ _CR (z)). Halo radius hereafter is assumed to be equivalent to R₂₀₀. Through abundance matching of halo mass functions (Tinker et al. 2008; Klypin et al. 2011) and stellar mass functions (Bernardi et al. 2010; Papastergis et al. 2012), they first defined a relationship between stellar mass and the halo mass enclosed within R₂₀₀, or M₂₀₀. M₂₀₀ was then estimated from M_⋆− M₂₀₀ for a sample of galaxies with measured stellar masses that span 8 decades in M_* and all morphological types (Misgeld & Hilker (2011); Leroy et al. (2008); Zhang et al. (2012)). R₂₀₀ was then estimated from M₂₀₀, where ${M}_{200}=(4\pi /3)200{\rho }_{{\rm\small{CR}}}(z){R}_{200}^{3}$. Kravtsov 2013 found R₂₅ = 0.048 R₂₀₀, which when combined with R _HI = (1.70 ± 0.16) R₂₅ (Broeils & Rhee 1997) yields R₂₀₀ ∼ (12.3 ± 1.2) R _HI .

Additionally, Lapi et al. (2018) derived global galaxy properties such as M₂₀₀ and R₂₀₀ for a sample of 546 nearby late-type galaxies (Persic & Salucci 1995) by constructing templates of the rotation curve compilations of Persic et al. (1996), Catinella et al. (2006), and Yegorova et al. (2011). Templates were derived as a function of I-band luminosity. By modeling a DMH profile (Burkert 1995), R₂₀₀ was derived by extrapolating the rotation curve to where the halo density reached ρ _CR (z). They then explored the relation between R₂₀₀ and the effective galaxy stellar radius R_e (assumed to be equivalent to 1.68 R_d ). While they quoted a polynomial form for the relationship, it is nearly linear within the sizeable scatter, except for a break in the trend toward smaller R₂₀₀ at R_e ∼ 4 kpc. Their best fit (approximated using solely the linear component) is log${R}_{e}=0.73\mathrm{log}{R}_{200}-0.91$, which yields R₂₀₀ ∼ (31.1 ± 1.6) R_e . Using their formula R_e ∼ 1.68 R_d and the relation R _HI ∼ (5.4 ± 0.5) R_d (Catinella et al. 2006; de Blok & Walter 2014) yields R₂₀₀ ∼ (9.7 ± 1.0) R _HI . Given the numerous approximations in both studies, we adopt R₂₀₀ ∼ (11 ± 1) R _HI , the average of the results of Kravtsov (2013) and Lapi et al. (2018).

In regards to V _HALO , if the DMH is assumed to have a constant density profile, it follows that the rotation curve would be flat out to R₂₀₀, thus, ${V}_{{\rm\small{HALO}}}\sim {W}_{\mathrm{mx}}^{i}/2$. This assumption is also adopted in the first derivation of a M _BH −M _HALO relation by Ferrarese (2002). Though for any density profile other than a constant, the disk circular velocity would decrease out to R₂₀₀, in which case ${W}_{\mathrm{mx}}^{i}/2$ would be an upper limit to V _HALO (as noted by Ferrarese 2002). The effect of the concentration parameter (the ratio of R₂₀₀ to a characteristic inner radius) of the DMH on disk circular velocity was explored in the ΛCDM simulation of Bullock et al. (2001). The median of concentration parameters in the simulation showed an approximately flat rotation curve out to ∼40 kpc. Additionally, The H i Nearby Galaxy Survey (Walter et al. 2008) measured flat rotation curves out to a maximum of ∼50 kpc, compared to the median R₂₀₀ estimate of Lapi et al. (2018) of ∼150 kpc. Therefore, we assume a flat rotation curve out to R₂₀₀, and as follows ${V}_{{\rm\small{HALO}}}\sim {W}_{\mathrm{mx}}^{i}/2$.

We thus calculate the total enclosed mass M _HALO with the same formalism used to estimate M _DYN . In Figure 9 we explore the relationship between M _BH and M _HALO . The best fit, which is displayed with the solid line, is

$$\begin{eqnarray}&&\mathrm{log}\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=(1.07\pm 0.37)\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{HALO}}}{{10}^{13}{M}_{\odot }}\right)+(7.97\pm 0.31),\end{eqnarray} \tag{ 27 }$$

with a scatter of (0.22 ± 0.10) dex. The average fraction of dark matter within R₂₀₀ is 97 ± 1%. The typical M _BH /M _HALO fraction is 10⁻⁵, but shows a trend with less massive black holes making up a smaller fraction of the total mass of the system, similar to what was found for M _BH /M_⋆ by Bentz & Manne-Nicholas (2018).

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To place the M _HALO estimates in context with other methods used to derive total enclosed galaxy mass, we first compare to the M _HALO estimates used to construct the globular cluster system mass–galaxy halo mass relation (Spitler & Forbes 2009). In that study, halo masses were estimated using M_⋆− M _HALO relations from weak gravitational lensing results (Hoekstra et al. 2005; Mandelbaum et al. 2006). The majority of the M _HALO estimates found by Spitler & Forbes (2009) fell within the range of ∼ 10¹⁰−10¹³ M_⊙ for a sample consisting of dE-, E-, S0-, and S-type galaxies. Additionally, the E-MOSAICS simulation (Bastian et al. 2020) of the globular cluster system mass–galaxy halo mass relation found that the majority of M _HALO constraints ranged from ∼10¹¹–10¹³ M_⊙. Comparatively, our sample of halo estimates span the right orders of magnitude for galaxies of similar morphological type.

We have compared our fit to several other estimates of the M _BH –M _HALO relation. Ferrarese (2002) utilized σ_⋆ measurements with the M _BH –σ_⋆ relation to constrain SMBH masses that spanned ∼10⁶−10⁹ M_⊙, along with several methods of estimating total gravitational mass, which fell within the range of ∼10¹¹−10¹⁴ M_⊙. We plot the first derivation (Equation (4) in Ferrarese 2002), which assumes ${V}_{{\rm\small{HALO}}}\sim {W}_{\mathrm{mx}}^{i}/2$, as the red dashed line in Figure 9. We find a shallower slope than Ferrarese (2002), even if we refit their relationship with their sample restricted to the same mass ranges we find. However, we employ direct measurements of M _BH , while those in Ferrarese (2002) were estimated from the M _BH −σ_⋆ relation. Additionally, we constrain W_mx ⁱ from unresolved H i line widths, while Ferrarese 2002 utilized V_mx measurements from rotation curves. The differences in both measurements are potential sources of discrepancy in the M _BH −M _HALO relations. Ferrarese 2002 described two other methods of estimating M _HALO , however, both assume nonconstant halo density profiles, and as such predict less massive DMHs and intercepts ∼0.5 dex and ∼1.5 dex smaller than what we find, respectively.

We also compare to the observationally constrained relation from Bandara et al. (2009). Their M _BH values were derived using σ_⋆ measurements and the M _BH –σ_⋆ relation, and total galaxy mass was estimated from strong gravitational lens modeling (Bolton et al. 2008). We plot their relation as the blue dotted–dashed line in Figure 9. We again find a slightly shallower slope in comparison (though the fits of our relation and Bandara et al. 2009 are statistically equivalent within the uncertainties). However, their study probes only the high mass end of both black hole and halo mass, with their sample spanning ∼10⁸−10⁹ M_⊙ in M _BH and ∼10¹³−10¹⁴ M_⊙ in M _HALO .

Lastly, we have compared our results to those of large, hydrodynamical simulations. Booth & Schaye (2010) explored correlations between M _BH −M_⋆ and M _BH –M _HALO , which they defined as the mass enclosed within a sphere of a mean density of 200ρ _CR (z). Their result is plotted as the purple dashed spaced line in Figure 9. The Illustris simulation also explored M _BH −M _HALO (where the definition of M _HALO is the same as that of Booth & Schaye 2010), and we plot the result of Mutlu-Pakdil et al. (2018) as the green dotted line. The intercepts of their relations differ by a decade, most likely due to the difference in DMH density profiles between the simulations. Pillepich et al. (2014) reported that the halo density profile for the Illustris galaxies is well characterized by a negative power law, which would result in less massive haloes due to the quicker drop-off in density. Interestingly, galaxies in the the upgraded IllustrisTNG simulation (Lovell et al. 2018, which incorporated a larger volume, higher resolution, and new physics such as black hole-driven winds) are a much better match to observations, with flat rotation curves out to large radii (∼60 kpc for M₂₀₀ = 10¹³ M_⊙). While the M _BH −M _HALO relationship has not yet been reexamined for IllustrisTNG, the flatter rotation curves will result in a larger enclosed mass within R₂₀₀ and may provide a better match to observationally constrained relationships such as the one we present here.