Modeling the Spectral Energy Distribution of the Active Galactic Nucleus inside NGC 4395

We study the broadband spectral energy distribution (SED) of the prototypical low-mass active galactic nucleus (AGN) in NGC 4395. We jointly model the optical through mid-IR SED with a combination of galaxy and AGN light, and find that on arcsecond scales the AGN dominates at most wavelengths. However, there is still some ambiguity about emission from the galaxy, owing partially to the strong short-term variability of the black hole. We investigate the use of smooth- and clumpy-torus models in order to disentangle the nuclear IR emission, as well as exploring the use of poloidal wind emission to account for the blue spectral slope observed in the near-IR. Even when simultaneously fitting the full optical–IR spectral range, we find that degeneracies still remain in the best-fit models. We conclude that high-spatial-resolution and wider-wavelength coverage with the JWST is needed to understand the mid-IR emission in this complex, highly variable object, which is the best nearby example to provide a blueprint to finding other low-mass AGNs via their mid-IR emission in the future.


Introduction
Supermassive black holes (SMBHs) are ubiquitous in the centers of massive galaxies, with mass ranges of 10 6 -10 9 M e (e.g., Kormendy & Ho 2013).On the opposite extreme are stellar-mass black holes exhibiting masses on the order of 10 1 -10 2 M e , formed from the deaths of massive stars (Remillard & McClintock 2006).It is therefore reasonable to suspect that a further population of black holes should exist in the mass regime between both extremes, the so-called "intermediate-mass" black holes (IMBHs).
Those seeds that do not continue to grow beyond this point should leave behind relic IMBHs with M BH ≈ 10 2 -10 5 M e , which should provide clues to their formation.To date, direct evidence for only one such IMBH has been found with M BH ≈ 150 M e (Abbott et al. 2020).These are therefore prime science objectives of the next-generation gravitational-wave observatories such as LISA (Amaro-Seoane et al. 2015), sensitive to detecting the first black hole seeds out to redshifts z ∼ 20 at masses 10 4 -10 7 M e to investigate SMBH formation at cosmic dawn (e.g., Bellovary et al. 2019).
In the interim, the challenge is to identify IMBH candidates using electromagnetic signatures.While possible dynamical detections of IMBHs in globular clusters have been reported (e.g., Gebhardt et al. 2005;Lützgendorf et al. 2013), in every case there are contradictory masses in the literature (e.g., Tremou et al. 2018), highlighting how challenging it will be to detect such objects should they exist.Beyond the Local Group, there are a handful of dynamical detections of M BH ≈ 10 5 M e black holes (Nguyen et al. 2018(Nguyen et al. , 2019)).To reach statistical samples still requires looking for signatures of accretion, as has been attempted with optical spectroscopy (e.g., Reines et al. 2013;Moran et al. 2014), X-ray (Miller et al. 2015;Pardo et al. 2016;She et al. 2017), and optical variability (Baldassare et al. 2018).
Additional information may come from focusing on the restframe IR emission from putative low-mass black holes.Highionization mid-IR emission lines that are relatively insensitive to dust obscuration and host-galaxy dilution effects are very effective at identifying active galactic nuclei (AGNs) arising from low-mass black holes (Satyapal et al. 2007;Goulding & Alexander 2009).The mid-IR continuum from AGNs is dominated by emission from a dusty "torus" of gas and dust that absorbs UV light from the accretion disk and reemits in the IR.
Over the past decade, adaptive optics and interferometry have provided a new level of understanding of the torus region.We now appreciate that smooth-torus models cannot simultaneously fit the spectral shape and Si absorption of AGNs (e.g., Netzer 2015); we will further confirm this finding here even for a low-mass low-luminosity AGN (LLAGN) such as NGC 4395.Furthermore, high-resolution imaging shows that the torus comprises at least two components, a disk-like and a poloidal component.A compelling possibility is that the poloidal component arises from a wide-angle outflow or wind component (e.g., Hönig & Kishimoto 2017).However, diskwind models of the torus have not been extended to low black hole mass before.Both for the purposes of identifying new low-mass black holes and for understanding the geometry and dependence on physical parameters, it is thus crucial to model Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
the tori of lower-mass systems.We make a start on this goal here with the AGN in NGC 4395.
The central IMBH powering the AGN at the heart of NGC 4395, a type I Seyfert galaxy at a distance of ∼4 Mpc (Thim et al. 2004), is one of the nearest and best-studied IMBH candidates in a galaxy nucleus.NGC 4395 houses a relatively low-luminosity AGN (Filippenko & Sargent 1989;Filippenko & Ho 2003) with L bol ∼ 10 40 erg s −1 (Peterson et al. 2005) and a current black hole mass estimate of 3.5 × 10 5 M e (den Brok et al. 2015), although Woo et al. (2019) posit the mass to be much lower at ∼10 4 M e .Perhaps due to its low mass and/or low luminosity (Elitzur & Ho 2009), this AGN is one of the most variable known (Moran et al. 2005), varying at X-ray energies by a factor ∼3 on 2-3 hr timescales (Kammoun et al. 2019).
The goal of this paper is to compile and investigate the near-UV to mid-IR spectral energy distribution (SED) of the central region of NGC 4395, and model the photometry with a combination of templates representing the host galaxy, the accretion disk, and the dusty torus to yield insight into lowluminosity AGN architecture.In Section 2, we introduce all the data sets and apertures that we use; in Section 4, we present the broadband fits with clumpy-torus models; and in Section 5, we put NGC 4395 in the context of other samples of AGNs with fitted torus parameters, and summarize our conclusions.

The Broadband Spectral Energy Distribution of NGC 4395
To model the combined galaxy and AGN SED of NGC 4395, we make use of photometric and spectroscopic data sets covering the near-UV to the mid-IR (0.2-38.0 μm; see Table 1).We revisit the previously published SED from Moran et al. (1999) with a set of new observations.There are two significant challenges in modeling the full SED of such a lowluminosity AGN.The first is that there is an unknown contribution from galaxy light that is likely both wavelength and aperture dependent.The second is that the AGN varies on significantly different timescales across the UV-IR wavelength range, making nonsimultaneous SEDs challenging to interpret (e.g., Vaughan et al. 2005;Burke et al. 2020).We confront these challenges directly in Section 3, but describe here various choices that we made to mitigate aperture mismatch.
At the highest spatial resolution, we harness broadband imaging from the UVIS and IR channels of the Wide Field Camera 3 (WFC3) on the Hubble Space Telescope (HST) along with near-IR imaging from the ground to pin down the likely contribution from galaxy light within our modeled aperture (Section 4.1).Specifically, NGC 4395 harbors a nuclear star cluster (NSC) at its center (e.g., Carson et al. 2015) that contributes some fraction of the light at all wavelengths.Using the HST image, Carson et al. (2015) have spatially decomposed the contributions from the NSC and nonthermal AGN light in the optical/near-IR wavelengths, giving us our best handle on the relative contributions of each component.
Over the full wavelength range, we also consider spectroscopy from the Infrared Spectrograph (IRS) on the Spitzer Space Telescope (previously published in Hood et al. 2017) and the Sloan Digital Sky Survey (SDSS), as well as photometric measurements from the IRAC camera on Spitzer.
In this section, we present salient details about each data set that we include in the model.

Spitzer Infrared Array Camera Data
We use data from the cryogenic mission of the Spitzer Infrared Array Camera (IRAC), observed through IRAC channels 1 and 2 (Ch1 and Ch2, respectively) with central wavelengths of 3.6 and 4.5 μm, respectively.These observations (Program ID: 40204) were performed in Cycle 7. Individual frames (exposure times ∼26.8 s) were mosaicked using MOPEX and were processed and calibrated using the IRAC Pipeline; cryogenic data were calibrated with IRAC Pipeline S18.18.0.Mosaicking resulted in a new pixel scale of ∼0 6 × 0 6, for a combined field of view of approximately ¢ ´¢ 30. 4 28. 5. Aperture photometry was performed on the 3.6 and 4.5 μm IRAC data.Here we choose not to perform direct point-spread function (PSF) fitting as point sources in the mosaicked IRAC images (∼0 6 pixel −1 ) are undersampled.Photometry was conducted using the PhotUtils v0.6 package in Astropy v3.1.1.We extracted surface-brightness profiles in Ch1 and Ch2 centered at the position of the AGN.To closely match other available multiwavelength data, we extract photometry from within a 3″ aperture.The observed surface-brightness profile extends significantly beyond that expected from a simple PSF, which we model here as a simple Gaussian.Within r ∼ 1 5 (5 pixel diameter), the enclosed flux is higher than that expected from a point source.At the distance of NGC 4395, the AGN component is a point source, but the surrounding NSC is well resolved (e.g., Carson et al. 2015).We find that ∼33% of the light is therefore likely to come from stars in the NSC.The statistical uncertainties on these measurements were determined to be significantly smaller than the systematic uncertainty (∼10%) expected from performing photometry on mosaicked Spitzer images (see the IRAC Handbook); hence, we conservatively adopt ∼10% uncertainties on each of these IRAC measurements.
NGC 4395 has been observed on four separate occasions in Ch1 and Ch2 during the cold and warm phases of the Spitzer mission.Across the ≈6 yr baseline, the typical variability was only ∼8% from the mean in both Ch1 and Ch2, with the maximal amplitude of variability being observed in Ch2 of ∼21% across the whole range of observations.Hence, in the case of the IRAC observations, AGN variability is captured within our assumed photometric uncertainties.

Spitzer Infrared Spectrograph Spectra
To extend the resolution and wavelength range of our analyses, we further include archival low-resolution (R ∼60-127) mid-IR spectra (5.2-38.0μm) from Spitzer/IRS included in our fitting.The coadded and preprocessed, background-subtracted, and calibrated data were retrieved from the NASA/IPAC Infrared Science Archive (IRSA) archive.The data had been processed with IRS Pipeline S18.18.0.To account for the different aperture sizes, the individual spectral orders from the short-low (SL) and long-low (LL) modules were matched using the overlapping wavelength coverage between the orders.The width of the SL slit (3 7) is similar to the aperture size used in our IRAC photometry, and hence we anchor the aperture corrections to the flux in the second SL spectral order.
Directly mixing spectroscopy and photometry in SED fitting can produce statistically incoherent results due to the overweighting of the spectral elements in the fit.Hence, we artificially lower the resolution of the Spitzer/IRS data and produce synthetic photometry that captures the main features and spectral shape seen in the IRS data, such as polycyclic aromatic hydrocarbons (PAHs) and silicates in absorption/ emission.We separate the combined Spitzer/IRS spectrum into 20 synthetic top-hat filters with widths δλ = 1.2 μm in the range 5.7-18.9μm and 2.4 μm in the range 18.9-38.1 μm.Uncertainties are estimated from the rms of the spectral values within the synthetic filter.

Sloan Digital Sky Survey Spectrophotometry
Our mid-IR spectrophotometric measurements produced from the Spitzer/IRS data may include contributions from both the central AGN and dust reemission of starlight that resides within the 3″-width slit.To encompass similar AGN +stellar contributions at optical wavelengths, we include the well-matched 3″ fiber spectroscopy available in the 7th Data Release (DR7) of the SDSS (Abazajian et al. 2009).
Following our methodology for the Spitzer/IRS spectroscopy, we construct synthetic spectrophotometry from the DR7 spectrum using constant transmission bandpasses in 10 spectral regions.We avoid prominent emission lines that are not fitted by continuum models.Uncertainties were calculated from the standard deviation of the flux density of the individual spectral elements in the bandpass.See Table 2 for the central wavelengths, bandpass widths, and spectrophotometric measurements in each filter.

Hubble Space Telescope/Wide Field Camera 3 UVIS Photometry
HST provides the highest-resolution look at the AGN+NSC combination in the center of NGC 4395.We make use of fiveband HST/WFC3 UVIS photometry from Carson et al. (2015) in the F275W, F336W, F438W, F547M, and F814W filters.Carson et al. (2015) use the HST imaging to construct surfacebrightness profiles of the galaxy center, and use GALFIT (Peng et al. 2002(Peng et al. , 2010) ) to fit a combined point source and Sérsic profile (Sérsic 1963) to simultaneously model the emission from the AGN and the NSC.Carson et al. (2015) model the HST data used in this paper to find an F814W effective radius of 4.56 pc (∼0 2).We anchor our model of the galaxy contribution to the SED using the photometry of the NSC, which dominates the galaxy light on the 3″ scales used to construct the broadband SED.

Near-IR Photometry
In the near-IR, we use HST/WFC3-IR (F127M, F153M; Carson et al. 2015) and ground-based K-band (2.2 μm) photometry (FWHM∼1 1) from the Multicolor Imaging Photometer mounted on the 2 m telescope of the Multicolor Active Galactic NUclei Monitoring (MAGNUM) project at the Haleakala Observatories in Hawaii (Minezaki et al. 2006).
We take the mean of these photometric data, and to encompass the variability seen in these measurements into our SED modeling, we take their standard deviation as the measurement "uncertainty."

Zwicky Transient Facility Photometry
Constraints on optical variability can be deduced using data from the Zwicky Transient Facility (ZTF), measured through gri bands spanning a wavelength range of approximately 4000-9000 Å, and represent observations over a span of 694,

Apertures and Variability
As mentioned above, the contribution from starlight is challenging to disentangle from AGN light, especially given the low luminosity of the AGN in NGC 4395.Our overall approach is therefore to jointly model the AGN+galaxy light within a uniform aperture of ∼3″.The width of the SL slit on the Spitzer IRS (3.7″) is similar to the fiber width used in recording our SDSS spectrophotometry of 3″, and, hence, we anchor the aperture corrections to the flux in the second SL spectral order.
An even greater challenge, which cannot be fully addressed with the current data, is the variability of the AGN.NGC 4395 is one of the most variable AGNs known in the X-ray (e.g., Vaughan et al. 2005), and it has been observed to vary on timescales of minutes to years in the UV, optical, and near-IR bands (e.g., Minezaki et al. 2006;Peterson 2014;Burke et al. 2020).Ideally, we would like a simultaneous measurement of the source across all wavelengths, to model the source in the same luminosity state.However, this is currently unavailable, and so in what follows we attempt to bracket the range of possible flux densities in bands with multiepoch observations.
There have been studies of the optical through near-IR variability of NGC 4395 that provide some insight into its variability amplitude.Minezaki et al. (2006) recorded intranight J-, K-, and H-band variations on the order of 10%, with larger flux variations in optical to near-IR bands across days to months.Specifically, the K-band point used in our study, recorded 11 times over 345 days, was observed to fluctuate between 1.663 ± 0.434 mJy.Using the ZTF, Figure 1 demonstrates that the minimum and maximum ZTF points differ by a factor of about 1.6.More notably, the minimum ZTF points on record are consistent with the measured HST NSC photometry from Carson et al. (2015) on comparable spatial scales.Our interpretation is that the lowest flux points in the ZTF data represent a low state of the AGN when the optical light is actually galaxy dominated, providing additional confirmation of our assumed galaxy fluxes as well as the range of AGN luminosities we might expect.
We will assume that the mid-IR varies on scales longer than a decade, supported by the lack of variability that we see in the few epochs of IRAC imaging (Section 2).The torus surrounding the AGN is thought to extend to parsec scales, translating to a very long light-crossing time, and therefore long mid-IR variability timescale.However, given the lowmass nature of NGC 4395, we of course do not know whether the mid-IR variability timescale is also commensurately short, as suggested by the correlation between mid-IR to optical lag and luminosity (Yang et al. 2020).We present the above observations in Figure 1 along with their respective dates of observation.

Spectral Energy Distribution Fitting
We now turn to the main task of the paper, to jointly fit the AGN and galaxy light.To this end, we use the X-ray module adaptation to the Python-based Code for Investigating GALaxy Emission (X-CIGALE; Noll et al. 2009;Serra et al. 2011;Yang et al. 2020) to self-consistently model the contributions to the UV-IR SED of NGC 4395 from the galaxy star formation history, dust, AGN accretion disk, and torus.Specifically, we use the stellar population models from Bruzual & Charlot (2003) combined with a Chabrier (2003) initial mass function (IMF) and a delayed, exponentially declining star formation history.These optical/UV models are combined with a Calzetti et al. (2000) attenuation law, which is balanced by dust reemission in the IR following the empirical models of Dale et al. (2014).The free parameters associated with each model component are summarized in Table 3.
Motivated by prior studies of AGNs showing that the torus is inhomogenous (Krolik & Begelman 1988;Elitzur & Shlosman 2006;Nenkova et al. 2008aNenkova et al. , 2008c;;Mullaney et al. 2011;Netzer 2015), we parameterize the AGN component of the SED with skirtor AGN models (Stalevski et al. 2012;Camps & Baes 2015;Stalevski et al. 2016).The skirtor model assumes a clumpy geometry, parameterized by the average edge-on optical depth of the disk t, the radial powerlaw exponent that governs dust density p l , the angular filling factor q, the half-opening angle θ, the ratio of the maximum to minimum radii R, and the inclination i.Through a radiative- 0.0, 0.5, 1.0, 1.5 0.5 q 0.0, 0.5, 1.0, 1. transfer model, the output SED consists of two components, primary emission from the disk and an anisotropic dust component (Table 3).We will compare the relative successes of clumpy models over smooth ones in Section 4.3.Furthermore, in Section 4.4, we will show that while the clumpy-torus model shows dramatic improvements over the smooth-torus models previously implemented by CIGALE, there are still aspects of the SED, in particular the 3-6 μm slope, that are not well modeled, leading us to also explore clumpy-torus models with a disk and wind component (Hönig & Kishimoto 2017).
To mitigate degeneracies between the AGN and galaxy contributions to the SED (Section 3), we proceed in two steps.First, we place empirical limits on the galaxy SED using our highest-spatial-resolution (HST+MAGNUM) data, for which the AGN and NSC components have been modeled separately (Section 3).Second, we take the allowed range of stellar continuum parameters from the initial galaxy-only fit, and refine the fit by simultaneously modeling the AGN and hostgalaxy components over our full spectral baseline, subject to the constraint that the galaxy component must provide a good fit to the HST data.

Nuclear Star Cluster Spectral Energy Distribution Fitting
The presence of an NSC at the center of NGC 4395 (Filippenko & Ho 2003) translates into a nonnegligible stellar contribution to the overall SED within 3″ (Section 3).We first fit the HST photometry with X-CIGALE, fitting only for the galaxy and dust parameters, and turning off the AGN component entirely.We emphasize that the NSC luminosity from Carson et al. (2015) is consistent with the low end of the ZTF photometry, suggesting this is a reasonable assumed level for galaxy light on this spatial scale.
A plot of the best-fit SED model is shown in Figure 2. The model falls satisfactorily within the HST error bars, with a χ 2 value of 2.2 with 7°of freedom.This fit exhibits a bolometric dust luminosity of ∼4.9 × 10 39 erg s −1 and an unabsorbed stellar luminosity of 1.6 × 10 40 erg s −1 .The best-fit parameters are tabulated in Table 3 and suggest that the NSC emission is dominated by a weakly absorbed (A V ∼ 0.1), older (∼9 Gyr old) stellar population with no additional evidence for a recent burst of star formation.These results are supported by the presence of a prominent 4000 Å break in the SED.Our approach in the rest of this section is to use this fit as a measure of true galaxy (dust+stellar emission) in NGC 4395.As there is degeneracy between AGN and galaxy light within the SDSS +Spitzer/IRS, in our analyses we limit the fitting range for the stellar component such that this component continues to reproduce the HST NSC data as described below.

AGN + Nuclear Star Cluster Spectral Energy Distribution Fitting
Using the range of best-fit parameters from Section 4.1 as limits, we jointly model our full range of multiwavelength data for the combined galaxy and AGN emission.Specifically, we include the spectrophotometry extracted from the SDSS and Spitzer spectroscopy, combined with the K-band MAGNUM measurement and the photometry extracted from the Spitzer IRAC imaging.Since we consider the fit from the previous section to be our best guess of the true level of galaxy light, we must simultaneously fit the global photometry to the overall SED as well as the HST photometry to the dust+stellar SEDs.We input the best-fit galaxy parameters from above as a starting position for a global fit that solves for both an AGN and galaxy component.We fit the galaxy parameters, the overall AGN amplitude (fracAGN), and the six torus parameters; the results of this fit are shown in Figure 3.This is a successful fit, but does not necessarily enforce a good fit (in a χ 2 sense) between the HST data and the galaxy model.To enforce this additional constraint, we tune the galaxy amplitude manually using fracAGN, which is a measure of the fraction of light contributed by the AGN relative to the total IR luminosity at 3-1000 μm.We run X-CIGALE across fixed values of 0 < fracAGN < 1, fix five of the six torus parameters to their best-fit values, and leave one free for the program to fit.We repeat this process for all six torus parameters.Then, we examine the best-fit model with a fracAGN that exhibits the minimum χ 2 between the HST photometry and the stellar+dust model SED.Four of the six torus parameters that most affect the SED are shown in Figure 4. We find that the results of this minimum χ 2 analysis converge on the same best-fit torus parameters as the global allfree fit and to the same value fracAGN = 0.6, exhibiting an AGN luminosity of 1.4 × 10 40 erg s −1 , consistent with that found previously (∼1.9 × 10 40 erg s −1 ) from considering the UV/optical SED (Moran et al. 1999).
These additional limited free-parameter fits confirm that the model with all parameters free is in satisfactory agreement with the HST NSC data, with a reduced χ 2 of 2.944.The best-fit model highlights a significant contribution from starlight to the optical portion of the SED, anchored by the spectrophotometry extracted from the 3″ SDSS fiber.By contrast, the best-fit model suggests that there is little galaxy contribution to the mid-IR spectrum.We also find that the IRS spectrum is well fit by the model; the spectrum exhibits a smooth, featureless continuum, with subdominant PAH features and the absence of a silicate feature at 9.7 μm.
To further investigate possible degeneracy between torus parameters, we then fix the best-fit model and scan over each torus parameter to examine how they affect the shape of our model SED.As silicate features in AGN SEDs are produced in the innermost black-hole-facing surface of the torus, the parameters most directly responsible for altering the shape of the near to mid-IR spectrum are the torus opening angle and line-of-sight inclination.We show a representative selection of the SED fits at alternating orientations and geometries in Figure 5.In general, we find that the photometry best favors models with wide torus opening angles and face-on inclinations.As inclination increases and the torus becomes edge-on, obscuration removes blue continuum from the AGN, pushing our fit to face-on configurations.
With this more complete understanding of the parameter space, we present the full range of allowed geometries and orientations in Figure 6, which shows the χ 2 map of our SDSS +IRS+MAGNUM spectrophotometry relative to the overall best-fit SED model across half-opening angles 0°< θ < 80°a nd inclinations 0°< i < 90°.The model strongly prefers extremes of the allowed parameters, with a half-opening angle of θ = 70°and an inclination of i = 10°, indicating a face-on configuration.Inclination and opening angle combinations looking through the torus are heavily disfavored.We conclude that the torus of NGC 4395 is very well constrained to be (a) clumpy, (b) face-on, and (c) wide angle.This model makes a strong prediction that at wavelengths beyond ∼20 μm dust emission from the galaxy will outshine dust from the torus.It would be useful to test this prediction with longer-wavelength data.

Investigating the Use of Alternative Torus Models
To this point, we have focused on the use of clumpy-torus models to reproduce the observed IR emission, as these have become more commonplace in the recent literature, and are understood to better represent IR emission from tori, particularly when the highest-spatial-resolution data are available (see Ramos Almeida & Ricci 2017 and Hönig 2019 for reviews).The skirtor model that we have employed thus far is a two-phase model using both smooth and clumpy distributions for the dust.Such two-phase models were designed in part based on the predictions of hydrodynamical simulations showing that the torus is likely a multiphase structure (e.g., Schartmann et al. 2014).
Here we replace the skirtor model in X-CIGALE with the smooth-torus models of Fritz et al. (2006).The Fritz et al. (2006) model assumes a smooth, flared-disk dust torus geometry, parameterized by the line-of-sight inclination (where edge-on is Ψ = 0°), optical depth (τ), the ratio of the maximumto-minimum radii, the opening angle, and the density distribution of the dust contained within the torus.Through a radiative-transfer model the output AGN SED consists of three components: primary emission from the disk, a dust-scattered component, and a dust-reemitted component.We perform consistent analyses to those outlined in the previous sections using this Fritz smooth-torus model.The results of the fit are shown as the dashed line in Figure 3.Most notably, this best-fit model produces a silicate emission feature at 9.7 μm, which is in stark contrast to the observed Spitzer/IRS spectrum, as well as the best-fit skirtor clumpy model.Furthermore, we find increased residuals blueward of λ < 20 μm.We further investigate this in Figure 5, where we show that for the smooth-torus model fits, only face-on inclinations provide the necessary blue UV/optical continua for the AGN, but in turn produce strong Si-emission features that are not observed in the IR.By contrast, even moderately inclined tori that reduce the Si feature produce little to no UV continua.Thus, we conclude that a smooth-torus alone cannot simultaneously provide the needed blue/UV light from a face-on torus and accommodate the lack of Si emission in NGC 4395.Only clumpy torii with high covering fractions can simultaneously yield negligible silicate emission or absorption and the blue continuum of an unobscured AGN.
We also conduct a complementary investigation of strictly clumpy models from the CLUMPY family of torus SEDs (Nenkova et al. 2008b(Nenkova et al. , 2008d)).The CLUMPY model assumes a heterogenous distribution of dusty clouds quantified similarly as the skirtor models.The added relevant parameters control the average number of clouds along radial equatorial rays N 0 , and the torus thickness parameter σ, the latter of which is the most analogous to the half-opening angle θ.Through a radiative-transfer model based on the DUSTY code (Ivezic et al. 1999a(Ivezic et al. , 1999b;;Nenkova et al. 2000Nenkova et al. , 2001Nenkova et al. , 2002a)), the output the AGN SED consists of a torus component and an input AGN spectrum.We fit the Spitzer/IRS spectrophotometry against the CLUMPY SED models while fixing the stellar and dust components to the SED to those suggested from our forwardmodeling process in Sections 4.1 and 4.2.
We present the region occupied by the 10 closest-fitting models in shaded gray, alongside the best-fitting model in green in Figure 7.The best-fit CLUMPY model represents a torus of inclination i = 50°, angular torus thickness σ = 25°, and radial extent Y ≡ R out /R in = 100.Similar to the fritz models, the closest CLUMPY models all insist on a silicate emission feature at 9.7 μm, in disagreement with the observed Spitzer/IRS spectrum as well as the best-fit skirtor clumpy model.From analyses of intermediate-type AGNs with CLUMPY-torus models in the literature (García-Bernete et al. 2019), NGC 4395 shows similar inclination angles to those of more luminous type 1.5 Seyferts.However, these external CLUMPY fits show incomparable angular and radial extents and disagreement on the presence of silicate features.Overall, analyses invoking CLUMPY-torus models produce a wide variety of potential radial extents and predict low inclination angles, while simultaneously predicting narrow opening angles (Ramos Almeida et al. 2009;Alonso-Herrero et al. 2011;Audibert et al. 2017).The latter is in contrast to the predictions using the skirtor model.From the overall geometry and lack of prominent silicate features predicted by the skirtor fits, we find that their two-phase torus models are the most proximate in describing the SED of the AGN in NGC 4395.

The Incompleteness of the Clumpy-torus Model
While the two-phase clumpy-torus model does a better job of reproducing the lack of Si emission or absorption with the steep mid-IR slope compared with a simpler smooth torus, the fit is not particularly good in the 3-6 μm region of the spectrum.This is a known deficiency of clumpy-torus models (e.g., García-González et al. 2017;Hönig & Kishimoto 2017;González-Martín et al. 2019).In particular, Hönig & Kishimoto (2017) argue that, to account for the additional near-IR emission, a second torus component is required.This second component is seen in interferometric observations of some nearby AGNs (e.g., Burtscher et al. 2013;López-Gonzaga et al. 2016).Hönig & Kishimoto (2017) present torus models that explicitly include a poloidal wind component, and argue that the wind emission dominates the mid-IR emission, while a blue near-IR spectral slope (the so-called "blue bump") is dominated by the outer accretion disk.An example of such a "wind" model is implemented in the CAT3D-WIND SED library.
We follow a similar methodology to that implemented previously (e.g., Hernán-Caballero et al. 2015;García-González et al. 2017;Hönig & Kishimoto 2017) and perform a nonparametric test to elucidate if a wind model can reproduce the observed mid-IR parameters in NGC 4395.For consistency with these previous studies, we use the DeblendIRS package (Hernán-Caballero et al. 2015) to empirically decompose the Spitzer/IRS spectra into its "pure-AGN," "pure-stellar," and "pure-interstellar" subcomponents.From the AGN component, we then measure the near-IR and mid-IR spectral slopes (α NIR and α MIR , respectively) and the equivalent width of the silicate feature.
In Figure 8, we show NGC 4395 in α NIR and α MIR space.We compare with a range of models produced in CAT3D-WIND, with relatively thin (scale heights of 0.1 and 0.2) face-on disks with inclination angles of 15 o and 30 o (similar to those found in our earlier analyses), and varying fractions of the polar-wind contribution to the mid-IR emission ( f wind = {0.15,0.30, 0.45, 0.60}).We include models with a varying number ).For all models, we assume a radial power-law slope of a = −2.5, and a half-opening angle and angular width of the wind θ W = 45°and σ θ = 15°, as these produced the most meaningful results based on the NGC 4395 measurements.
We find that it is possible to explain the location of NGC 4395 in α NIR -α MIR space with reasonable CAT3D-WIND models, particularly those invoking high f wind fractions.Interestingly, the NGC 4395 measurements are consistent with the region in the CAT3D-WIND models where the Si absorption transitions to emission, which is also consistent with our observations.The level of Si absorption (−S Si ∼ 0.1-0.2) observed in NGC 4395 is also similar to the models and data presented in García-González et al. (2017) for other type 1.8/1.9AGNs.We further note that the α MIR slope is significantly steeper than α NIR owing to the existence of the near-IR blue blump; this feature cannot be reproduced by the no-wind CAT3D models.Hönig & Kishimoto (2017) use the existence of AGNs in the space where α NIR is bluer than α MIR to argue that the wind model is needed to describe real AGNs.This need for a wind in some sources is also in accord with interferometric observations of a small handful of nearby Seyfert galaxies, where a polar component is imaged in the torus-emitting region (e.g., Raban et al. 2009;Hönig et al. 2012;Tristram et al. 2014;Leftley et al. 2018).
Our measurements of NGC 4395 throughout this study are in broad agreement with those most recently found for the CAT3D-WIND and smooth-torus models of this galaxy by García-Bernete et al. (2022), albeit that those authors utilize only mid-IR data from 8 to 10 m-class ground-based telescopes for their study.By contrast, the best-fit two-phase skirtor model in García-Bernete et al. (2022) is that of a completely edge-on torus, which is inconsistent with our findings here.We do not have a full explanation for this difference, as the SED shapes reported by them are similar to those considered here.At the same time, it is important to note that García-Bernete et al. (2022) do not use the results for NGC 4395 in their wider study of hard-X-ray-detected AGNs, presumably due to the inconsistency they find between the different model parameters and overall poor fits for NGC 4395.Consistent with our findings here, García-Bernete et al. (2022) also show that the CAT3D-WIND model produces the best overall fit to NGC 4395 when the near-IR data are also considered in their fitting.

Discussion and Conclusion
In the previous sections, we determined that the preferred geometry for the obscuring material surrounding the central black hole in NGC 4395 involves a semi-coherent structure of many individual optically thick clouds (Nenkova et al. 2002b(Nenkova et al. , 2008c)), a so-called clumpy-torus model that we parameterized using the skirtor library in X-CIGALE.Due mainly to the differing line-of-sight heating and radiativetransfer effects of the clouds, these models tend to produce less pronounced silicate absorption features for accretion disks that are viewed edge-on, and a wider range of mid-IR spectral slopes.
Over the past decade, the idea of a polar-wind component to the torus has also gained support, both due to spatially resolved observations of a poloidal component to the torus (e.g., Tristram et al. 2014)    Theoretically, we do expect that radiation pressure can drive winds in dusty environments (e.g., Thompson et al. 2015).Recently, Venanzi et al. (2020) presented simulations of radiation-pressure driving from dusty disks in the torus region of AGNs.They show that the potential for driving a wind will depend on N H , which scales with the amount of material available to be driven by the wind, and the Eddington ratio, which encodes how much radiation pressure is available to act against the gravity of the AGN.There is a sweet spot where N H is moderate (logN H ≈ 22-23 cm −2 ), and the Eddington ratio is relatively high (∼10%), where they expect the radiation pressure is strong enough to drive a wind.
Interestingly, García-Bernete et al. (2022) find some support for this picture by fitting the SEDs of tens of local AGNs with near-IR+mid-IR spectroscopy.They find the dusty wind model to be a better fit to moderately obscured AGNs (e.g., Seyfert type 1.5-1.8)and usually not required in type 2 (more heavily obscured) systems.NGC 4395, which is classified as a Seyfert type 1.8, and through careful modeling of its X-ray spectral shape, has been determined to show evidence for partial covering by variable cold absorbers producing a logN H ∼ 22-23 cm −2 (Nardini & Risaliti 2011;Kammoun et al. 2019), and, hence, seems to fit into this picture rather nicely.
Our current study is still limited by two main issues: (i) the lack of simultaneity across all of the wave bands, and (ii) the spatial/spectral resolution of the mid-IR data out beyond 20 μm.However, with the advent of the JWST, we are now in a position to obtain a much higher resolution view of the torus region in NGC 4395, which hopefully can serve as a template for future searches.With its subarcsecond resolution, JWST will be a powerful tool in accurately decomposing IR spectra where AGN light dominates into the actual AGN signal and its stellar and galactic contaminants.High-resolution studies of the near-IR may provide insight into possible winds, silicates, and graphites in the torus, whereas observations at longer, mid-IR wavelengths will determine whether there is a luminous star-forming feature as predicted by CIGALE.The Mid-InfraRed Instrument should be able to measure the hottest bit of this dusty continuum, place limits on possible PAH features, and constrain silicate features apart from any spectral contaminants.These studies of low-luminosity AGN spectral features will facilitate future surveys searching for IMBHs, shed light on the processes that allow massive black holes to form, and in turn gain insight into the complexities of galaxy evolution.
624, and 78 nights respectively, encompassing 2018 March 15-2020 January 15.We note that Burke et al. (2020) also use the Transiting Exoplanet Survey Satellite to measure optical variability in NGC 4395 on timescales <1 month.

Figure 1 .
Figure1.Left: a compilation of various observations of NGC 4395, listed with corresponding apertures and dates of observation.We include published data from the Lick Observatory(Desroches et al. 2006), the HST/WFC3 NSC photometry fromCarson et al. (2015), and UV data fromPeterson et al. (2005), in addition to the archival SDSS, Spitzer/IRS, and MAGNUM K-band data used in this study.To yield insight into the intrinsic optical variability of the AGN, the minimum and maximum gri-band photometry from the ZTF have been overplotted as red bars.For reference,Elvis et al. (1994) quasar templates normalized to the Spitzer IRS spectrum at 12 μm have been overplotted.Right: ZTF point-source photometry for NGC 4395 in the g-, r-, and i-bands (blue, green, and red points, respectively).The day-long UV/optical variability is similar in both the g and r bands with ∼0.48 mags (AB).

Figure 2 .
Figure2.The best-fit stellar-only model SED, fitted using the HST/WFC3 NSC photometry fromCarson et al. (2015).We overplot the minimum and maximum archival ZTF photometry, which we argue represents a minimum and maximum state of the AGN in NGC 4395.The HST photometry for the NSC are consistent with the minimum ZTF points, giving reassurance that the photometry representing the NSC have negligible AGN contamination.

Figure 3 .
Figure 3. X-CIGALE SED modeling of the Spitzer/IRAC photometry (black triangles) and SDSS and Spitzer/IRS spectrophotometry described in Section 2. Total best-fit SED, UV/optical stellar component, dust stellar component, and smooth-torus model are shown with black, blue, red, and green lines, respectively.For illustration purposes only, overlaid are the HST and MAGNUM high-spatial-resolution photometric data described in Sections 2.4 and 2.5, as well the SDSS and Spitzer/IRS spectra.These points used in the forward-modeling process fit the data with a reduced χ 2 = 2.71.

Figure 4 .
Figure 4.The χ 2 of the HST/WFC3 photometry to the fitted galaxy model plotted against the fraction of the fitted AGN model at 9.7 μm, shown for different values for four of the most relevant skirtor torus parameters.We seek the minimum χ 2 value to ensure that the best-fit parameters that shape the global model SED in Figure 3 encompass a model galaxy in satisfactory agreement with the NSC photometry.All models exhibit minimum χ 2 values at an AGN fraction of approximately 60%, suggesting that the best-fit parameterization of the torus is in sufficient agreement with the global SDSS +IRS photometry as well as the galactic anchor specified in Section 4.1.

Figure 5 .
Figure 5.The different X-CIGALE model SED fits with alternating values for opening angle θ and inclination angle i.The SDSS and Spitzer/IRS spectrum as well as the HST/WFC3 NSC photometry have been overplotted for consistency.Note that the models demonstrate a diminishing optical component of the AGN with increasing inclination, presumably due to a line of sight passing through the obscuring torus.

Figure 6 .
Figure 6.χ 2 distribution of orientation angle (i) and half-opening angle (θ), derived from the modeled galaxy to the high spatial resolution (HST) described in Section 4.1.The heat map highlights clear preference for extremes of allowed parameters, preferring an almost perfectly face-on inclination of 10°a nd a large half-opening angle of 70°.Combinations of inclination and opening angle with the line of sight passing through the torus are heavily disfavored.

Figure 7 .
Figure 7. SED comparison of the Spitzer/IRAC photometry (black triangles) and Spitzer/IRS spectrophotometry, against the CLUMPY-torus models.The UV/optical stellar component and dust stellar component predicted by X-CIGALE are denoted in blue and red, respectively.In gray are the space of 10 CLUMPY AGN SEDs closest in fit to the IRS spectrum, with the best-fitting SED represented in green.For illustrative purposes, the Spitzer/IRS spectrum is overlaid in orange.

Table 1 A
List of Observations Used in This Study

Table 2 A
List of Photometry Used for Model SED Fitting

Table 3 A
List of Inputs and Outputs from CIGALE for Our Full SED Modeling Study