MEASURING THE MASS OF THE CENTRAL BLACK HOLE IN THE BULGELESS GALAXY NGC 4395 FROM GAS DYNAMICAL MODELING

The center of NGC 4395 was imaged with Hubble Space Telescope (HST)/Wide Field Camera 3 (WFC3) in seven filter bands, ranging from the ultraviolet (UV) to the near-infrared (NIR). Instead of a broad V band, we used the medium-wide F547M filter to exclude most bright emission lines. The observations are summarized in Table 1. Each filter band consisted of at least four exposures with different dither positions. These data are part of a larger survey to infer the formation mechanisms of the nearest NSCs and have already been presented in Carson et al. (2015); however, to obtain optimal spatial resolution and better noise characteristics, we use a slightly different procedure to reduce the data.

Table 1.  Summary of HST/WFC3 Observations

	Expose Time	Zeropoint	${A}_{\lambda }^{{\rm{a}}}$
Band	(s)	(mag)	(mag)
F275W	8 × 150	22.6322	0.094
F336W	4 × 254	23.4836	0.077
F438W	4 × 148	24.9738	0.062
F547M	4 × 120	24.7477	0.050
F814W	4 × 100	24.6803	0.026

Note.

^aThe extinction values ${A}_{\lambda }$ were obtained from Schlafly & Finkbeiner (2011).

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We drizzled the flat-fielded optical/UV images using the drizzlepac package in pyraf. We found good results in terms of resolution and noise by drizzling the optical images with a Lanczos3 kernel (with pixfrac set to 1 pixel). The World Coordinate System of the images was aligned to that of the F438W band using the tweakreg package, after which the aligned flat-fielded images were re-drizzled. The spatial alignment between the optical/UV bands is better than 0.1 pixel.

Although we also imaged NGC 4395 in the NIR with HST/WFC3, we did not use these data for this work since they have slightly lower resolution, whereas the separation of the active galactic nucleus (AGN) contribution from the light of the NSC requires superior resolution.

In addition to the WFC3 data, we also use archival HST/Advanced Camera for Surveys (ACS) F606W and F814W wide field camera (WFC) data. The F606W filter is important for identifying line emission since it contains Hα. The F814W ACS data are necessary to make a F606W–F814W color map. We drizzled the F606W and F814W data on the same grid as the WFC3 data so that we were able to use these data to mask emission line regions in the WFC3 images.

2.1.1. Point-spread Function (PSF)

NGC 4395 was observed in the K band with Gemini/NIFS, an NIR image-slicing integral field spectrograph on Gemini-north (McGregor et al. 2003) with ALTAIR laser guide star adaptive optics. A nearby star was used to tune the slow focus for these observations. Data were taken on three separate nights in 2010: March 28, May 5, and May 22. Exposures were taken in an object–sky–object sequence, and a total of 12 × 600 s on-source exposures were taken. A telluric calibrator with a spectral type of A0V was taken on each night and used to remove telluric absorption.

Filippenko & Ho (2003) tried to measure the velocity dispersion of the NSC to constrain the black hole mass, but could only obtain an upper limit on the dispersion of 30 km s⁻¹. To get a better measurement of the dispersion, we observed the NGC 4395 nucleus with NIRSPEC at the Keck II telescope. Unfortunately, the CO bandheads, which are typical of evolved stellar populations, were absent, probably because of the continuum emission of the AGN, so that we were unable to obtain a dispersion measurement from them. Since we do not use the NIRSPEC data for our analysis, we present the details of these data and the reduction procedures in Appendix A together with the details of our attempt to measure the dispersion from the CO bandheads in the NIFS data.

2.2.1. NIFS Data Reduction and PSF Determination

The data were reduced as described by Seth et al. (2010); initial reduction was done using tools from the IRAF Gemini package that were modified to enable propagation of the variance spectrum. The cubes were rebinned to a pixel size of $0\buildrel{\prime\prime}\over{.} 05\times 0\buildrel{\prime\prime}\over{.} 05$ using our own IDL version of NIFCUBE to make final data cubes for each night. The 12 data cubes were then combined after shifting the May data to match the March 28 data's barycentric velocity. The line-spread function (LSF) of the data was determined by reducing the sky cubes and combining them in the same fashion as the science data; the sky lines in each spatial pixel (spaxel) were then fit to Gaussians to obtain the variation in LSF across the chip; the FWHM of the LSF ranged from 4.0 to 5.0 Å across the chip with a median of 4.5 Å, a typical spectral resolving power of $\lambda /{\rm{\Delta }}\lambda \sim 4800$ at the wavelength of the H₂ 1–0 S(1) line used in our analysis.

The intensity, velocity, and velocity dispersion of the H₂ 1–0 S(1), H₂ 1–0 Q(1), and Brγ lines were determined by fitting each line with a Gaussian. We found that close to the center of the cluster, the Brγ line did not have a Gaussian shape, but could be fitted by two Gaussians: one with a narrow component ($\sigma \approx 40$ km s⁻¹) and one with a broad component ($\sigma \approx 300$ km s⁻¹). The width of the broad component suggests the emission originates from the BLR.

We used a Bayesian criterion to tell us where the data warranted a two-component fit to the Brγ line. At these positions, the Brγ line was fitted by a double Gaussian. To constrain the central potential of NGC 4395, we use the H₂ 1–0 S(1), which has the highest signal-to-noise ratio (S/N) of the two H₂ lines. The H₂ 1–0 S(1) kinematic maps are shown in Figure 1. Although gas velocity dispersions can only be accurately determined for dispersions higher than ∼15 km s⁻¹, we note that our results are not sensitive to the dispersion of the disk (see Section 5).

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To model the PSF for the kinematics, we use the continuum emission from the AGN. This is justified since we know from the absence of the CO bandheads that the continuum emission is made up almost completely of non-stellar emission (see Appendix A for more details). We have checked the width of the continuum against that of the flux from the broad-line Brγ emission and a star in the field. The FWHMs of these other components agree with the value of the continuum emission.

We note that, as in Seth et al. (2010), the PSF can be modeled as a combination of a Gaussian (with FWHM = 016), describing the instrumental PSF, and a Moffat profile, describing the seeing: ${\rm{\Sigma }}(r)={{\rm{\Sigma }}}_{0}/[{(1+{(R/{R}_{d})}^{2})}^{4.765}].$ We use ${R}_{d}=0\buildrel{\prime\prime}\over{.} 95$. The inner core of the PSF is slightly broader than the one used by Seth et al. (2010), which is probably due to the nucleus of NGC 4395, which was used for tip/tilt correction during the observations, being less bright. For the dynamical modeling, we decompose the profile into a multi-Gaussian expansion (MGE; Emsellem et al. 1994) since it allows for an easy deprojection.

The most obvious way to get rid of the emission line regions is by masking them out. We identify all central pixels in the F606W–F814W color map that are bluer than 0.38 mag and create a bad pixel map for Galfit based on these pixels.

We fit the light distribution of the NSC with a combination of a Sérsic profile and a point source. We first determine the Sérsic index and effective radius in the F547M band and then keep those fixed between different bands. We find a Sérsic index n = 2.25 and ${R}_{\mathrm{eff}}\simeq 3.6$ pc. We note that these values for the Sérsic are not atypical for NSCs: the Milky Way NSC has $n\approx 3$ and M32 has $n\approx 2.3$ (Graham & Spitler 2009).

Instead of masking the regions, we can also try to model and subtract the emission line contribution in each filter. We tried to do this two ways. The first method, which we dub "iterative residual subtraction," makes use of the fact that the emission line regions show up as strongly positive residuals after fitting. For each band, we identified strongly positive residuals from our Galfit fit, with the bluest pixels still masked, as emission line regions. The thus created "emission line map" was then subtracted from the original image, which was then fit again with Galfit. This procedure was iterated a few times. It is a priori not clear that this procedure only identifies the non-axisymmetric emission since fitting with the wrong NSC model can also lead to the removal of stellar emission. We were therefore very careful in identifying at which intensity to clip, which unfortunately leads to some arbitrariness.

The final structural parameter data show a somewhat more compact NSC, with Sérsic index n = 4.4 and effective radius ${R}_{\mathrm{eff}}=3$ pc. The NSC is 0.07 mag brighter in the F814W band than with the masking method. Although it may seem counterintuitive that subtraction of the residuals would lead to a brighter NSC, the overall curvature and compactness of the surface brightness profile are significantly changed, resulting in this change in brightness.

Inspection of the F275W image suggests that the narrow-line emission contamination is most prominent in the F275W band, possibly due to the lack of stellar emission in these bands. Its isophotes are the most non-circular and resemble those of the Brγ emission in the NIR. Instead of masking the emission line regions, we therefore attempt to remove the emission line regions by subtracting the F275W image from the redder bands after appropriate scaling. Since the diffraction pattern in the F275W band is different from the other bands, we first subtract the central point source from the F275W band.

To scale the emission of the F275W band to the other bands, we assume that the emission line region is the narrow-line emission of the AGN. We therefore use a typical narrow-line emission spectrum from the well-studied nearby Seyfert 2 galaxy NGC 1068 (Spinelli et al. 2006) to determine the flux ratio between the F275W band and the redder bands. Subtracting the scaled point-source-subtracted F275W image from the other bands gave surprisingly good results in the F547M band, whereas the F814W band required another 5% scaling in the flux of the F275W band.

The best-fitting Sérsic profile, determined in the F547M band, has Sérsic index n = 1.4 and ${R}_{\mathrm{eff}}=4.4$ pc. The luminosity of the NSC is lower than for the other two methods: compared to the masking method the NSC is 30% fainter in the reddest band and in the bluer bands even more. We note that it is possible that some of the subtracted F275W emission is in fact stellar.

We summarize the structural parameters found for the four different colors using the three different methods, together with the results of Carson et al. (2015), in Table 2. To assess which method describes the cluster profile the best, we compare how the models fit the outer, unmasked portion of the NSC. We avoid consideration of the inner parts of the fit because the iterative residual subtraction gives a low ${\chi }^{2}$ by construction. We therefore decided to calculate a ${\chi }_{\nu }^{2}$ with

$$\begin{eqnarray}&&{\chi }^{2}=\displaystyle \sum _{i\in \mathrm{Good}\;\mathrm{pixels}}\displaystyle \frac{{({I}_{i}-{\mathrm{Model}}_{i})}^{2}}{{\sigma }_{i}^{2}},\end{eqnarray} \tag{ 2 }$$

where the good pixels are all unmasked pixels (determined from the bad pixel map of the masking method) in an annulus of 4–20 pixels from the cluster center, corresponding to roughly 1–5 ${R}_{\mathrm{eff}}$. Here, ${I}_{i}$, Model_i, and ${\sigma }_{i}$ denote the observed intensity, model intensity, and observational uncertainty of each pixel value.

The masking and iterative residual subtraction method have the lowest ${\chi }^{2}$ per pixel values (4.3 and 4.1); the ${\chi }^{2}$ of the F275W subtraction method is slightly higher (4.7). Given the small difference in performance between the masking method and the iterative subtraction method, we adopt the simpler approach and use the results from the masking method as our preferred NSC parameters in our dynamical modeling. To get a sense of the systematic uncertainty in our BH mass measurements due to the poorly constrained NSC profile, we also perform dynamical modeling using NSC parameters from the other two methods. The profiles of all uncolvolved Sérsic models of the NSC are shown in Figure 3, as well as a PSF-convolved model including the central point-source emission.

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As a first attempt, we fit an SSP to the magnitudes derived with the Galfit fits. The photometric uncertainties on the data are small, typically 1%. This uncertainty does not reflect the systematic errors such as model mismatch or remaining line emission. The uncertainty therefore represents a lower limit on the real uncertainty.

We use the ${\chi }^{2}$ as our figure of merit for the fits. For each age and metallicity in the library, we calculate the predicted magnitudes, given a stellar mass. An M/L is then calculated by dividing the F814W luminosity by the mass, which can be different by a few percent from the theoretical M/L from the stellar library since it allows for a statistical error in the F814W band luminosity.

Figure 4 shows a probability distribution function of the fitted M/L_F814W. The best-fitting SSP is old and metal poor. The ${\chi }^{2}$ of individual fits is not perfect in the sense that the reduced ${\chi }_{\nu }^{2}\gt 1$. An old metal-poor population provides a better fit than a younger metal-rich population. The age and metallicity of the NSC in this scenario would be consistent with the NSC being built up from accreted globular clusters (Lotz et al. 2001; Antonini 2013).

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Although it is possible that the NSC formed from old metal-poor globular clusters, sitting at the galaxy center it is very likely to have been exposed to gas accretion and subsequent star formation (Seth et al. 2006; Walcher et al. 2006). A more physical mass model of the NSC should therefore include the possibility of an additional younger population. We therefore consider CSP fits where we assume that the NSC is built up from two components: an old and metal-poor component, which probably contains most of the mass and a younger component with equal or higher metallicity. For each possible combination of metallicities and ages, we calculate the best-fitting weights of the two stellar populations from our four photometric bands and use this to obtain a likelihood and an M/L in the F814W band for each metallicity and age combination. We show the normalized likelihoods of the fitted M/L_F814W from CSPs as a thick solid line in Figure 4, together with the 68% confidence interval. For SSP fits, an M/L_F814W up to 2 was allowed. For composite populations, higher M/Ls are also allowed. The reason for this is that it is now possible to fit the red part with an old metal-rich population, which has a slightly higher M/L than the old metal-poor population. We note that it is possible that the emission line contamination in the blue bands mimics a young stellar population. Whether this contamination is from young stars or emission lines is in reality not very relevant though because neither would contain much mass.

The best-fit CSP models have a main component of solar metallicity and intermediate age (3 Gyr) combined with a young component. This would point to a scenario in which the nuclear stellar cluster was built up locally from enriched gas and continues forming stars, albeit at a low level.

Observations of globular clusters suggest that SSP models with a standard IMF may not accurately predict the M/L of old systems (Strader et al. 2009, 2011). Although we do not know how the nucleus of NGC 4395 formed, the colors of the cluster are consistent with those of globular clusters, thus motivating us to examine empirical constraints on the M/L from globular clusters.

We use the sample of GCs in M31 of Strader et al. (2011) for which dynamical masses have been calculated. We then look up the corresponding I-band magnitudes in the Revised Bologna Catalogue (Galleti et al. 2004); correct these for extinction, as in Strader et al.; and convert the I-band magnitude to F814W magnitude. This yields 177 unique sources, for which we can determine the M/L in the F814W band. As in Strader et al., we use the virial mass as an indicator of the dynamical mass of the cluster.

It is known that the M/L of globular clusters varies as a function of luminosity; low-mass globulars are sensitive to dynamical processes that can alter their M/L (Kruijssen & Mieske 2009). We therefore chose to use only globular clusters heavier than 10⁶ ${M}_{\odot }$ and with color $0.8\lt V-I\lt 1.0$ since our $V-I$ color determination of NGC 4395's cluster is the most robust and least affected by possible additional young stellar populations. We show the distribution of empirical M/L_F814W inferred for these 14 clusters in Figure 4.

The empirical M/L_F814W of the GCs varies from 0.5 to 3.0 ${M}_{\odot }$/L${}_{\odot }$ and peaks between ~1 and 1.5 ${M}_{\odot }$/${L}_{\odot }$, consistent with the M/Ls from the theoretical stellar populations analysis. We note that including GCs with colors outside our chosen color range does not change the peak value or width of the histogram. As the sources shown here are the most massive GCs, it is possible that some of these contain MBHs and therefore have elevated M/L (Mieske et al. 2013; Seth et al. 2014). Nevertheless, we can conclude that the empirically derived I-band M/L of massive GCs and the M/L of NGC 4395's NSC derived from stellar population synthesis modeling are in excellent agreement with each. Therefore, for our dynamical modeling, we use the constraint from the CSP modeling that the M/L_F814W is 1.3 ± 0.6 (1σ uncertainty).

Our dynamical models have the following free parameters.

• 1.  
  The dynamical M/L of the NSC in the F814W band. We use a logarithmic scale between 0.5 and 5.
• 2.  
  The mass of the IMBH. We assume that this mass is between 10³ and 10⁷ ${M}_{\odot }$ logarithmically scaled.
• 3.  
  The inclination of the system. Although Kinemetry provides us with an ellipticity of each ring, which we convert to an inclination, we also try out configurations with a constant (possibly negative) angle added to all rings and with all rings fixed to a single inclination value.

Each point in this parameter space corresponds to a dynamical model. The likelihood of each data pixel is calculated from the squared difference of the observed and predicted velocity divided by the uncertainty of the observed velocity. In Figure 1, a bright region is visible west of the nucleus at offset 0.5–1.5 arcsec. We exlude therefore all pixels with X offset higher than 1.0 arcsec from the fit. We also exclude velocities with uncertainties higher than 5 km s⁻¹. For these uncertainties, fluctuations in the sky can cause systematic errors in our velocity determinations. This mainly affects isolated pixels of low S/N in Figure 1.

We created dynamical models for 25 different inclinations, each sampling 25 × 25 models in black hole mass and M/L. The M/L and black hole mass were sampled logarithmically. Figure 7 shows the likelihood of these models, projected by taking the maximum likelihood along the inclination axis or the M/L axis. Our dynamical models seem to prefer a configuration in which the gas disk has M/L${}_{{\rm{F}}814{\rm{W}}}=1.3$ and inclination of 37°. The M/L_F814W value is in good agreement with the stellar population analysis above. The reduced ${\chi }_{\nu }^{2}$ of our best-fit model is 3.9. A ${\chi }_{\nu }^{2}$ value $\gt 1$ is not unexpected with our simplifying modeling assumptions. We therefore scale the ${\chi }^{2}$ of our models so that the best-fit model has ${\chi }_{\nu }^{2}=1$. For our 3σ confidence limits, we select models for which the rescaled ${\chi }^{2}$ is within ${\rm{\Delta }}{\chi }^{2}=14$ (3 degrees of freedom) of our best-fit model's ${\chi }^{2}$.

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We have combined the results of the CSP models with dynamical constraints. In Figure 8, we show the results of this combination. The 1σ contours do not change much compared to the fits based on dynamical models only since the best-fit dynamical models agreed almost exactly with the best-fit stellar population synthesis models, the joint analysis helps to exclude models with low inclination and low black hole mass. From the combined modeling of the stellar populations of the NSC and the dynamics of the molecular gas, we find a best-fit black hole mass of $M={4}_{-3}^{+8}\times {10}^{5}$ M_⊙ (3σ uncertainties). The velocity field of the best-fit model is shown in Figure 6. For the parameters of this model, we also did the full line modeling so that we could calculate the dispersion field. The central dispersion is accurately reproduced by this model, together with the depressions in dispersion along the H₂ disk, without adding any intrinsic dispersion for the gas. This shows that our modeling of a cold disk is justified.

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The modeling results for different structural parameters of the NSC are shown in Figures 11 and 12 in Appendix B. For the iterative residual subtraction method, we find a BH mass similar to $M={3}_{-2.4}^{+7}\times {10}^{5}$ M_⊙, which is very close to the mass found using the masking method. The F275W subtraction method for determining the potential gives a higher black hole mass of $M={7}_{-5}^{+8}\times {10}^{5}$ M_⊙.

Several components of our modeling procedure are prone to systematic errors; the structural parameters of the cluster are uncertain, we are making simplifying assumptions about the shape of the potential, and it is possible that the observed gas does not trace the gravitational potential.

The largest uncertainty comes from our poor knowledge of the structural parameters of the cluster. Despite this, dynamical modeling with the different structural models from Section 3 for the potential of the NSC yields best-fit black hole masses that agree with our preferred model to within 1σ. However, our analysis relies critically on the assumption that we can separate the continuum emission of the AGN, which is ${L}_{{\rm{F}}814{\rm{W}}}\approx 1.3\times {10}^{6}$ ${L}_{\odot }$, from the stellar emission of the cluster ${L}_{{\rm{F}}814{\rm{W}}}\approx 1.6\times {10}^{6}$ ${L}_{\odot }$.

The kinematic signature observed in the H₂ gas does not necessarily have to be a rotating disk; it could also be tracing a weak outflow. However, there are a number of lines of evidence that suggest this is unlikely.

• 1.  
  The H₂ emission in other Seyfert galaxies is known to trace gas disk components (e.g., Hicks et al. 2009, 2013; Riffel et al. 2009).
• 2.  
  The analysis of the velocity field with Kinemetry shows that the velocity along each ellipse follows almost a perfect cosine. An outflow would not necessarily have the same signal.
• 3.  
  Wrobel & Ho (2006) present radio continuum observations of the central parsecs of NGC 4395 and find an elongated structure, possibly an outflow, along a P.A. of 28°, more or less orthogonal to the rotation axis of the H₂ disk. The orientation of this jet structure suggests a disk interpretation for the H₂ gas instead of an outflow.

In our models, we assume that the cluster is spherical and that the gas is not pressure supported. Loosening the first assumption could lower the black hole mass by a few percent. Introducing a pressure component will increase the black hole mass.

With the exception of M32 (Verolme et al. 2002), NGC 7457 (Gebhardt et al. 2003), and M60-UCD1 (Seth et al. 2014), very few dynamical mass measurements of MBHs in galaxies with low velocity dispersions exist (Kormendy & Ho 2013; McConnell & Ma 2013). For most galaxies with dispersion below 100 km s⁻¹, masses have been determined using the reverberation mapping method. The formula to determine the mass is usually written as

$$\begin{eqnarray}&&{M}_{\mathrm{BH}}=f\displaystyle \frac{(c{\rm{\Delta }}t){({\rm{\Delta }}v)}^{2}}{G},\end{eqnarray} \tag{ 9 }$$

where ${\rm{\Delta }}t$ is a delay time between variation of continuum and line. The first bracketed term is thus a measure of distance from the black hole. ${\rm{\Delta }}v$ is a proxy of the average rms velocity of the line-emitting gas. For non-Gaussian line shapes, it is not clear what quantity should be used here, FWHM or σ. Virialization normalization factor f is usually called the f-factor and is often calibrated against the M–σ relation for high-mass AGNs (but see Ho & Kim 2014).

Three mass estimates for the black hole in NGC 4395 were carried out using this technique, but with different data. Peterson et al. (2005) used the C iv line in the UV to estimate the time lag and converted this to a black hole mass using f = 5.5 (based on high-mass AGNs) and using the velocity dispersion σ of the line for ${\rm{\Delta }}v$ (which in this case was very similar to the FWHM). This mass measurement was confirmed by Desroches et al. (2006) using Hα RM, although their measurement was not significant. Edri et al. (2012) used broadband reverberation mapping, which targets an individual line, in this case Hα, but uses a broadband filter to measure the variation in the line. These authors used f = 0.75, based on a simple virial estimate of a spherical BLR, and used instead the FWHM of the line. Our black hole mass estimate is in agreement with the estimate by Peterson et al., suggesting that a high f-factor may be applicable in this particular case.

In addition to the RM estimates, several additional BH mass estimates have been made for NGC 4395. Several of these studies use estimates of the BLR size from the AGN continuum and then use a line width to derive a mass. Lira et al. (1999) estimate the black hole mass to be 5 × 10⁵ M_⊙(assuming a distance to NGC 4395 of 5 Mpc), based on the width of the Hβ line and their estimate of the bolometric luminosity of the AGN; Kraemer et al. (1999) estimate a mass of $1.5\times {10}^{5}$ M_⊙ (at 2.6 Mpc distance) based on Hβ and a size estimate of the BLR from photoionization models. Using Hβ and the BLR size–luminosity relation of Kaspi et al. (2000), Filippenko & Ho (2003) estimate a mass 10⁴ M_⊙. Most recently, La Franca et al. (2015) estimated a mass of 2 × 10⁵ M_⊙ based on the width of the Paβ line.

A relation between black hole mass, bolometric luminosity, and break frequency of the X-ray power spectrum has also been developed (McHardy et al. 2006). In NGC 4395, the break frequency was measured to be ∼2 × 10⁻³ Hz (Vaughan et al. 2005). If we use the bolometric luminosity from Lira et al. (1999; $1.2\times {10}^{41}$ erg s⁻¹), we find a black hole with mass $M=5\times {10}^{4}$ M_⊙, which is significantly lower than our estimate. However, there are some indications that the X-ray luminosity is underestimated due to extinction (Nardini & Risaliti 2011) so that it is possible that the bolometric luminosity is in fact higher, which would increase NGC 4395's black hole mass estimate from the McHardy relation.

NGC 4395 is currently the only bulgeless galaxy with a dynamically measured black hole mass. Here, we compare this galaxy to two similar bulgeless galaxies that appear to lack MBHs.

At a distance of 4.4 Mpc, NGC 4395's absolute magnitude is ${M}_{B}=-17.65$ mag and ${M}_{V}=-18.10$ mag, slightly less luminous than M33, and similar to NGC 4244, a highly inclined Sc galaxy that lies at the same distance from Earth. NGC 4244 and NGC 4395 have similar maximum rotation velocities (${V}_{\mathrm{max}}\approx 90$ km s⁻¹; Olling 1996; Swaters et al. 1999) that are 20 km s⁻¹ lower than M33's. Although all three galaxies have similar morphological properties, NGC 4395 is the only galaxy with an obvious MBH. The upper limit on the mass of the MBH in NGC 4244 is 5 × 10⁵ M_⊙ (De Lorenzi et al. 2013) and for M33 is as low as a few thousand solar masses (Gebhardt et al. 2001; Merritt et al. 2001). The masses of the NSCs in M33 (1.4–2.1 × 10⁶ M_⊙; Kormendy & McClure 1993; Hartmann et al. 2011) and NGC 4395 are essentially the same, whereas the NSC of NGC 4244 is five times heavier ($1.1\times {10}^{7}$; Hartmann et al. 2011; De Lorenzi et al. 2013). Despite having a black hole at its center, NGC 4395 has succeeded in producing an ordinary NSC with a mass typical of those in late-type galaxies (Seth et al. 2008). NGC 4395's I-band central surface brightness is, as expected, slightly lower than M33's. The only obvious difference between NGC 4395 and these other two galaxies is the kinematic lopsidedness of NGC 4395. Lopsidedness, however, is not an uncommon feature among late-type spiral galaxies (Matthews et al. 1998).

It is interesting to see how NGC 4395's black hole mass fits in with scaling relations of MBHs in more massive galaxies. NGC 4395 is not a dispersion-dominated galaxy, and we do not know the value of its velocity dispersion. Comparing it to the M–σ relation would thus not be very useful. However, Kormendy & Ho (2013) derive a relation between black hole mass and the K-band luminosity of the bulge (M–L), with which we can compare our measurement. In Appendix C, we perform a photometric decomposition of NGC 4395. Although we believe that the central upturn in the light profile of NGC 4395 is due to a bar, we can use the luminosity of the bar as an upper limit on the luminosity of the bulge and compare the black hole mass with this upper limit. We do not know the K-band luminosity of the bar. To convert our i-band measurement of $L=4.1\times {10}^{7}$ ${L}_{\odot }$ to K band, we use $i-I=0.4$ (Jordi et al. 2006) and $I-K=2$, which is common for old stellar populations and is probably redder than the actual color of the bar (Peletier & de Grijs 1998). Formula 2 in Kormendy & Ho (2013) then predicts a black hole mass $M=1.6\times {10}^{5}$ M_⊙. Given the intrinsic width of the M–L relation and the uncertainties in our black hole mass measurement, we conclude that although a factor of three higher, our mass measurement is not inconsistent with the M–L relation.

We presented dynamical models of the center of the nearest Seyfert 1 galaxy NGC 4395. NGC 4395 was the first bulgeless galaxy known to host an AGN and still has the most secure detection of an intermediate-mass black hole (M $\lt {10}^{6}$ M_⊙), although with considerable discussion about its exact mass.

Our high-resolution HST/WFC3 data enabled us to model the morphology and M/L of the compact NSC at the center of NGC 4395. After correcting for the asymmetric contribution of emission lines to the cluster light, we find that the cluster is almost spherical (in projection). The range of M/L of the cluster that we inferred from CSP models is in excellent agreement with those found for globular clusters in M31.

Combining our HST imaging data with adaptive optics assisted NIR integral field data of the cluster, we model the dynamics of the molecular gas. Our best-fitting dynamical models contain an intermediate-mass black hole with mass $M={4}_{-3}^{+8}\times {10}^{5}$ M_⊙ (3σ uncertainties). We characterize the influence of the uncertainty in the stellar potential on our measurement and find that it leads to changes in the black hole mass by less than 1σ. Our mass estimate is in excellent agreement with the mass estimate from reverberation mapping by Peterson et al. (2005), but significantly higher than the more recent estimate from Edri et al. (2012) and estimates based on accretion.