NuSTAR Observations of a Heavily X-Ray-obscured AGN in the Dwarf Galaxy J144013+024744

There are multiple ways to estimate the mass of the central BH in galaxies. For instance, bulge-dominated galaxies are expected to trace the M_• − σ_⋆ relation to an acceptable accuracy. Schutte et al. (2019) studied J1440 using deep Hubble Space Telescope (HST)/WFC3 observations and found that J1440 is an Sa galaxy with dim spiral regions in the disk (see Figure 2). J1440 was found to have a classical bulge with a bulge Sérsic index (Sersic 1968) of n = 1.6, while the Sérsic index for the disk component was n = 0.75. Supported by the presence of a prominent bulge component, we utilize the M_• − σ_⋆ relation derived for low-mass BHs by Xiao et al. (2011): $\mathrm{log}({M}_{\bullet })=(7.68\pm 0.08)+(3.32\pm 0.22)\mathrm{log}({\sigma }_{\star }/200$ km s⁻¹). For J1440, this leads to an estimated BH mass of M_• = 10^5.5±0.2 M_⊙ (based on σ_⋆ = 44 ± 4 km s⁻¹ from Barth et al. 2008).

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The BH mass can also be estimated from the velocity dispersion of the AGN broad-line region using single-epoch spectra, which is done by assuming the broad-line region gas to be virialized and to follow empirical BH radius–luminosity relations. R13 used the broad Hα line to obtain a viral BH mass estimate of M_• = 10^5.2 M_⊙ (see Figure 3 for the fitting of the optical spectrum).

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The two M_• measurements discussed here are consistent with each other within their respective uncertainties, and both are in the range of what is conventionally considered as an IMBH (<10⁶ M_⊙).

In this section, we utilize the existing photometric data of J1440 ²⁰ to estimate the physical properties of the galaxy such as its stellar mass, luminosity, star formation rate (SFR), and metallicity using CIGALE. The photometric data we used are as follows: far- and near-UV from GALEX (Kron flux density in an elliptical aperture), optical from SDSS (SDSS model C), near-IR from the Two Micron All Sky Survey (2MASS XSC), and IR from WISE (Profile-fit), Spitzer-MIPS (point-source function flux density), and IRAS (fixed aperture). These photometric data are initially fitted with the modules accounting for the host galaxy emission only. The best-fit spectral energy distribution (SED) deviates from the data significantly at the IR wavelengths, with a poor fit statistic of ${\chi }_{\mathrm{reduced}}^{2}=4.06$. This suggests that the galaxy-only modules are not sufficient for J1440. We then include an AGN component, Fritz2006, which is an AGN template library composed of an isotropic point-source emission component and a thermal and scattering dust torus emission component (see Fritz et al. 2006; Boquien et al. 2019, for details). This greatly reduced the disagreement between the data and best-fit SED in the IR wavelengths (see Figure 4), with an improved fit statistic of ${\chi }_{\mathrm{reduced}}^{2}=1.12$ (for Z = 0.004, ²¹ we discuss the fit statistics for different values of Z later in this section). To confirm the need for an AGN component, we utilized the Akaike information criterion (AIC; Akaike 1974). AIC can be expressed as AIC = χ² + 2k, where χ² determines the goodness of fit and was 17.95 for the model including an AGN component and 64.97 for the model with no AGN (galaxy only). AIC penalizes for extra degrees of freedom through k. As we are interested in ΔAIC, the value of Δk on adding the AGN component was 7. A significant result (3σ) is obtained when AIC changes by 7 (see Yang et al. 2018 and references therein). For J1440, ΔAIC = AIC_{no AGN}–AIC_AGN was 33.02, which was highly significant and confirmed that an AGN component is required to explain the SED of J1440 (the lower the value of AIC, the better the fit).

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For our SED fitting involving both the galactic and AGN components, we explored three different values of metallicity: Z = 0.0004, 0.004, and 0.02. ²² The ${\chi }_{\mathrm{reduced}}^{2}$ for these three metallicities are 0.91, 1.12, and 1.6, respectively. We note that the measurement of metallicities based on photometric SED fits might have limited accuracy, and the spectroscopic measurements can also be challenging owing to the presence of an AGN. However, galaxies with mass similar to J1440 are expected to have lower metallicities than their more massive counterparts, as suggested by the mass–metallicity relation (e.g., Tremonti et al. 2004; Gao et al. 2018). Since the reduced χ² for Z = 0.0004 and Z = 0.004 are both acceptable, we consider the recent study by Ma et al. (2016), who used high-resolution cosmological zoom-in simulations to study the mass–metallicity relation over a wide range of stellar mass and redshift. Using their redshift-dependent mass–metallicity relation and the best-fit M_⋆ for J1440, the expected metallicity for J1440 is Z = 0.0039, which is consistent with our choice of metallicity in the CIGALE SED fitting and implies that J1440 is a galaxy with subsolar metallicity. The galactic and AGN properties estimated from the CIGALE SED fitting (for Z = 0.004) are as follows:

• 1.  
  M_⋆ = 10^9.20±0.05 M_⊙ (this stellar mass obtained by CIGALE is slightly lower than that obtained by R13 (M_⋆ = 10^9.40 M_⊙) using the kcorrect code that fits broadband fluxes using stellar population synthesis models).
• 2.  
  SFR = 0.42 ± 0.24 M_⊙ yr⁻¹. The SFR and M_⋆ values place J1440 on the star-forming main sequence based on, e.g., Whitaker et al. (2012).
• 3.  
  L_AGN = (4.33 ± 0.35) × 10⁴³ erg s⁻¹ (AGN bolometric luminosity).

We list the input parameter ranges and the best-fit values for all the CIGALE modules in Table 1.

We also compared the SFR obtained from CIGALE with that obtained from the polycyclic aromatic hydrocarbon (PAH) emission (O'Dowd et al. 2009). These complex molecules often break apart when subjected to high-energy photons from the AGN (Schweitzer et al. 2006); therefore, their presence can be used to determine the SFR and the temperature of the dust since these molecules can only form in the colder region of the galaxy (see H17 and references therein). H17 estimated the SFR for J1440 from the PAH features at 7.7 and 11.3 μm. The SFR value of 0.16 ± 0.10 M_⊙ yr⁻¹ was lower but within the uncertainty range of SFR estimated from CIGALE.

J1440 was targeted by XMM-Newton in 2006 (XMM-Newton ObsID = 0400570101) with an exposure of 22.92 ks (Thornton et al. 2009), and was also targeted by Chandra in 2015 for ≈6 ks (Chandra ObsID = 17035). The XMM-Newton data were found to be heavily background dominated above 1 keV as suggested by the 4XMM catalog, which is based on the XMM data analysis pipeline provided by the XMMSOC (Webb et al. 2020). The target was strongly detected in the <1 keV bands with $\mathrm{DET}\_\mathrm{ML}\gt 150$. ²³ However, for harder bands the detection likelihood rapidly drops from ∼26 for 1–2 keV to ∼8 and ∼5 for 2–4.5 keV and 4.5–12 keV bands, respectively. While the source is likely to be detected in the 1–2 keV band according to the 4XMM pipeline software, there are only ∼3 ± 6 counts in the 1–2 keV band within our spectral extraction region, essentially rendering spectral fitting infeasible beyond 1 keV. Note that the $\mathrm{DET}\_\mathrm{ML}$ values represent the likelihood for the source to be detected according to the algorithm of emldetect, and XMMSOC suggests a minimum of $\mathrm{DET}\_\mathrm{ML}=10$ for a reliable detection. ²⁴ Monte Carlo simulations also suggest that the true reliability of a given $\mathrm{DET}\_\mathrm{ML}$ value can be nontrivial. For instance, studies in deep XMM-Newton surveys suggest that the $\mathrm{DET}\_\mathrm{ML}$ values required for a hard (2–12 keV) band source to be detected with a 99.7% (3σ) reliability are ≈10 (Chen et al. 2018) or higher (Ni et al. 2021). Due to the background-dominated spectrum for this target, Thornton et al. (2009) were only able to analyze the <1 keV spectrum, where they found the object to be dominated by a diffuse plasma model (see Thornton et al. 2009, for details).

The Chandra data were also heavily dominated by the soft X-ray emission with only one >2 keV count (see Table 2 in Baldassare et al. 2017), which is effectively a nondetection. Due to the low counts in the Chandra data, no spectral analysis was done in Baldassare et al. (2017). They also found that the soft X-ray flux for this object is consistent with the expected value derived based on the scaling relation between SFR and X-ray luminosity for high-mass X-ray binaries (see their Section 4.1 for details).

Both XMM-Newton and Chandra data suggest that the soft X-ray component for J1440 is not dominated by the X-ray emission from the X-ray corona near the accretion BH, but rather is associated with the host galaxy stellar activity or the diffuse emission in the narrow-line regions (e.g., Bianchi et al. 2006; Bogdán et al. 2017). However, Thornton et al. (2009) suggested that the discrepancy between the soft X-ray emission and the L_{[Oiii] λ5007)}−L_{2−10 keV} relation established by Panessa et al. (2006) may imply some level of X-ray obscuration for J1440. This is investigated with NuSTAR observations discussed in the subsequent sections.

The target J1440 was observed on 2020-09-02 for ≈100 ks with NuSTAR, with an obsid 60601028002. The data were processed using HEAsoft v6.29, ²⁵ while nupipeline was used to produce cleaned and calibrated event lists. To account for the background enhancement due to the South Atlantic Anomaly, we set SAA = strict and Tentacle = yes. We selected the source and a source-free background using 4500-radius circular regions centered at (α, δ) = (14^h40m1266, + 02d47m4153) and (14h40m0947, + 02d49m4956), respectively (Figure 5). Nuproduct was used to extract the X-ray spectra of our target from the event files. We generated the spectra for the two Focal Plane Modules (FPM) on board NuSTAR, namely, FPMA and FPMB. The net count rate in the 3–79 keV range for FPMA was 1.56 × 10⁻³ ± 4.76 × 10⁻⁴ counts s⁻¹, while that for FPMB was 1.63 × 10⁻³ ± 5.01 × 10⁻⁴ counts s⁻¹. The cleaned exposure times for FPMA and FPMB were 85.94 and 84.63 ks, respectively.

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To measure the source significance, we followed the algorithm adopted by Mullaney et al. (2015) and Lansbury et al. (2017), which operates on the false-probability images generated based on the NuSTAR background and science images (see Section 2.3 of Mullaney et al. 2015, for further details). The results for the source detection algorithm for the 3–8 keV, 8–24 keV, 3–24 keV, and 30–50 keV bands are summarized in Table 2.

From Table 2, we can infer that the source has significant detections in the 3–8 keV, 8–24 keV, and 3–24 keV bands and is not detected at 30–50 keV. For the 3–24 keV band, where the source is detected most strongly, the source shows a stronger detection in FPMA over FPMB due to lower background.

Before delving into complex physical models, we evaluate the parameters with a simple absorbed power-law model and Pexmon model. The absorbed power-law model in Sherpa can be written as xstbabs × (xszphabs × xszpowerlw).Here xstbabs accounts for Galactic absorption and was set to 2.9 × 10²⁰ cm⁻². ²⁷ xszphabs × xszpow is the redshifted absorbed power law. The best-fit power-law model parameters suggest the source to be heavily obscured with $\mathrm{log}({N}_{{\rm{H}}}/{\mathrm{cm}}^{-2})={23.54}_{-0.28}^{+0.21}$ (0.16, 0.50, and 0.84 quantiles) and a fit statistic (Cstat/dof) of 507.35/521. The unabsorbed and absorbed 2–10 keV X-ray luminosities for the absorbed power-law model are $\mathrm{log}({L}_{2-10}(\mathrm{erg}\,{{\rm{s}}}^{-1}))={41.41}_{-0.15}^{+0.12}$ and $\mathrm{log}({L}_{2-10}(\mathrm{erg}\,{{\rm{s}}}^{-1}))={40.93}_{-0.10}^{+0.09}$, respectively (see Figure 7 for spectral fit and residual). If metallicity (Z = 0.006) is included in the absorbed power-law model (using xsvphabs), the obscuring column density increases to $\mathrm{log}({N}_{{\rm{H}}}/{\mathrm{cm}}^{-2})={24.04}_{-0.28}^{+0.19}$.

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We also modeled the X-ray spectrum using the Pexmon model, which combines a power law of a fixed cutoff energy with reflection from neutral Compton reflector and fluorescence lines. The model in Sherpa can be written as xstbabs × (xszphabs × xspexmon). We set the inclination angle to 85°, though a different inclination angle did not significantly affect our results. Other parameters of Pexmon were set to their default values. The reflection coefficient of Pexmon was set to R = −1 to simulate a reflection-dominated model, while the cutoff energy was fixed at 400 keV. The column density of $\mathrm{log}({N}_{{\rm{H}}}/{\mathrm{cm}}^{-2})={21.47}_{-0.99}^{+1.16}$ was poorly constrained, as we were unable to obtain a Gaussian posterior distribution. We then fixed the reflection coefficient to R = +1 to include the power-law component. This configuration of Pexmon produced a well-constrained column density (see Figure 8). Since a simple absorbed power law or a Pexmon model does not capture the physics of an obscuring torus, we use physical models to constrain the properties of a physical torus.

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RXTorus is a model of obscuring torus that has a variable ratio of radius of minor to major axis of the torus. The RXTorus model allows for different metallicities of the AGNs (ranging from Z = 0.006 to Z = 0.04) and hence can be used to model low-metallicity AGNs, particularly those in the dwarf galaxies. Moreover, it also allows for disentanglement of its line-of-sight column density and equatorial column density, which it can measure up to 10²⁵ cm⁻². The photon index can vary between Γ = 1 and Γ = 3. The model in Sherpa can be written as ²⁸ xstbabs × (RXTorus-cont-0.3 × xscutoffpl + RXTorus-rprc-0.3). Here RXTorus-cont-0.3 ∗ xscutoffpl is the absorbed power-law component, RXTorus-rprc-0.3 is the reprocessed component that includes scattering and fluorescence emission, and 0.3 represents the metallicity in the unit of solar metallicity of these modules (Z = 0.006). ²⁹ In BXA, we created log-uniform priors for RXTorus normalization, column density, and background normalization associated with the FPMA detector, while a uniform prior was created for the inner-to-outer radius ratio of torus (r/R). The photon index, cutoff energy, and column density of all the modules were linked. The cutoff energy was set at 200 keV, the default value of the RXTorus model. The inclination angle was set to 90° to simulate an edge-on viewing; however, we do not find significant changes in the posterior distribution for different inclination angles.

We show the X-ray fitting results for the phenomenological and physical models in Figure 7. The best-fit parameters of the models discussed in this work are listed in Table 3. We also show the posterior distribution of the best-fit column densities for all the models used in this work in Figure 8. All these models indicate the object to be heavily obscured. For the two phenomenological models simple absorbed power law and Pexmon (R = + 1), the column densities are $\mathrm{log}({N}_{{\rm{H}}}/{\mathrm{cm}}^{-2})$ = ${23.54}_{-0.28}^{+0.21}$ and ${23.52}_{-0.29}^{+0.19}$, respectively. For the low-metallicity RXTorus model (Z = 0.006), the best-fit column density almost reaches the Compton-thick regime with $\mathrm{log}({N}_{{\rm{H}}}/{\mathrm{cm}}^{-2})$ = ${23.85}_{-0.25}^{+0.22})$. The log-likelihood function that BXA uses to compare models was consistent within margins of error. We do not find significant changes in the column density when a variable inclination angle is used. However, a variable photon index leads to a poor constraint on the column density; hence, it was fixed to Γ = 2.13. We note that the default cutoff energies are not the same between the physical model and the phenomenological models. However, as demonstrated by Baloković et al. (2020), the intrinsic cutoff energies span a wide range from 140 to 500 keV for 68% of their large sample of AGNs with high-quality NuSTAR and Swift/XRT data. In addition, the spectral fit statistics for their sample do not improve significantly even if the cutoff energy was allowed to vary freely. Therefore, the different cutoff energies are unlikely to qualitatively change our results.

Table 3. Posterior Estimates for Different Models

Model	Abs.Powerlw	Pexmon(R = +1)	RXTorus
$\mathrm{log}\left(\tfrac{{N}_{{\rm{H}}}}{{\mathrm{cm}}^{-2}}\right)$	${23.54}_{-0.28}^{+0.21}$	${23.52}_{-0.29}^{+0.19}$	${23.85}_{-0.25}^{+0.22}$
$\mathrm{log}({\mathrm{Norm}}_{\mathrm{zero}})$	$-{4.15}_{-0.15}^{+0.12}$	$-{4.22}_{-0.14}^{+0.12}$	$-{3.98}_{-0.20}^{+0.25}$
$\mathrm{log}({\mathrm{Norm}}_{\mathrm{PCA}})$	${2.74}_{-0.03}^{+0.03}$	${2.74}_{-0.03}^{0.03}$	${2.74}_{-0.03}^{+0.03}$
(CStat/dof)source+bkg	508.39/521	510.14/526	510.56/521
(CStat/dof)bkgonly	393.91/521	393.36/521	393.34/521
$\mathrm{log}({L}_{2-10}$ (erg s−1))	${41.41}_{-0.15}^{+0.12}$	${41.38}_{-0.14}^{+0.12}$	${41.62}_{-0.19}^{+0.23}$
$\mathrm{log}(Z)$	−461.65 ± 0.47	−461.12 ± 0.44	−460.26 ± 0.46

Note. The range corresponds to 0.5 quantile with upper bounds corresponding to 0.84 quantile, while lower bound corresponds to 0.16 quantile. Here $\mathrm{log}({\mathrm{Norm}}_{\mathrm{zero}})$ represents the normalization for the zeroth-order power law, and $\mathrm{log}({\mathrm{Norm}}_{\mathrm{PCA}})$ is the normalization for the PCA-based background model associated with FPMA detector.

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We also show the combined model plot (binned for better display) and the Quantile–Quantile plot (Q–Q plot) of the unbinned data to compare between the absorbed power law and the RXTorus model (Figure 9). All these models explain the data acceptably well, but the models deviate from the data at higher (≳20 keV) energies, possibly due to the high background noise. To quantitatively assess the goodness of the fit, we performed a two-sample Anderson–Darling (AD) test (Anderson & Darling 1954). A two-sample AD test measures the distance between the two cumulative distribution by estimating the square of the difference of the two functions multiplied by a weight function. Since the model was derived from the data, we performed bootstrapping with 2000 iterations to estimate the p-value. These values are quoted in the right panel of Figure 9. The lower AD stat and a higher p-value indicate that the data and model are drawn from the same distribution and corroborate our findings from the Q–Q plot that RXTorus with its subsolar metallicity provides the best fit to the data. In Figure 10 (left) we show the spectral fitting results for the source+background and background-only models. Both the source and background models seem to explain the data reasonably well. The unconvolved model components (Figure 10, right) for the RXTorus models show that the overall spectrum is dominated by an absorbed power-law component; however, a nonnegligible scattered and fluorescence component is present in the best-fit spectra of physical models. We reiterate that we did not make use of the soft X-ray data from XMM-Newton or Chandra and did not include an additional component to account for the <3 keV emission, due to the lack of high-quality soft X-ray data and the fact that the >3 keV emission for this source cannot be explained with typical diffuse X-ray emission components such as apec. A high-quality <3 keV X-ray spectrum is needed to further constrain the spectral properties such as the intrinsic photon index and the strength of the scattered and reflected components.

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To assess whether the X-ray luminosity of J1440 might have a non-AGN origin, we calculate the expected luminosity from high-mass X-ray binaries (HMXBs) and low-mass X-ray binaries (LMXBs). We used the empirical relation derived by Lehmer et al. (2010), along with the SED-derived SFR and stellar mass discussed in Section 2.2, and find L_LMXB = (1.4 ± 0.2) × 10³⁸ erg s⁻¹ and L_HMXB = (6.8 ± 4) erg s⁻¹. We compare this with the 2–10 keV intrinsic luminosity for each model (see Table 3) calculated using Sherpa's "calc_energy_flux" command. This command was applied to the power-law component of the model to obtain the intrinsic luminosity. We find that the intrinsic 2–10 keV X-ray luminosities (Table 3) are ≳2 orders of magnitude higher than those expected from X-ray binaries (XRBs). Therefore, the X-ray spectrum of J1440 is unlikely to suffer from significant XRB contamination.

We summarize the key results of our X-ray spectral analysis below:

• 1.  
  The intrinsic X-ray luminosities for the models discussed in this work are much higher than the expected contribution from X-ray binaries, which strongly supports the presence of a hard X-ray AGN despite the faint soft X-ray fluxes found in the literature (Thornton et al. 2009; Baldassare et al. 2017).
• 2.  
  All the models indicate the object to be heavily obscured. For the simple absorbed power-law model and Pexmon (R = +1) model, the column densities are $\mathrm{log}({N}_{{\rm{H}}}/{\mathrm{cm}}^{-2})$ = ${23.54}_{-0.28}^{+0.21}$ and ${23.52}_{-0.29}^{+0.19}$, respectively. For the RXTorus model with a low metallicity, the best-fit column density nearly reaches the Compton-thick regime with $\mathrm{log}({N}_{{\rm{H}}}/{\mathrm{cm}}^{-2})$ = ${23.85}_{-0.25}^{+0.22}$.
• 3.  
  The geometry of the torus was poorly constrained, as we were unable to obtain a Gaussian posterior distribution for the geometry parameter in the RXTorus model. The 0.16, 0.50, and 0.84 quantiles for the ratio of inner to outer radius parameter for the RXTorus model was ${0.47}_{-0.25}^{+0.29}$. We need more good-quality data to constrain the geometry of the obscuring torus.
• 4.  
  Qualitatively, the spectra of J1440 are dominated by the absorbed power-law component based on the results from the physical model, but high-quality soft X-ray data and higher signal-to-noise ratio NuSTAR spectra are needed to further constrain the spectral properties.

As discussed in Section 3, our data quality prohibits us from exploring the full range of the X-ray power-law photon index Γ. We choose the value informed by the multiwavelength data, specifically the AGN bolometric luminosity. For an accreting SMBH, its bolometric luminosity is tied to the global accretion rate, which can affect the seed photon emission and can modulate the X-ray spectral slope (e.g., Shemmer et al. 2006; Ishibashi & Courvoisier 2010). A linear relation between Eddington ratio (λ) and photon index has been documented in the past for systems accreting at high Eddington ratios (e.g., Shemmer et al. 2006, 2008; Brightman et al. 2013; Yang et al. 2015; Trakhtenbrot et al. 2017). In Brightman et al. (2013), the relation can be expressed as ${\rm{\Gamma }}=(0.32\pm 0.05)\mathrm{log}\lambda \,+(2.27\pm 0.06)$. For J1440, the bolometric luminosity derived from [Oiii] λ5007 is $\mathrm{log}({L}_{\mathrm{bol}}/\mathrm{erg}\ {{\rm{s}}}^{-1})=43.96\pm 0.60$ based on the Stern & Laor (2012) empirical relation. Similarly, the bolometric luminosity derived from [Oiv] 25.89 μm based on Goulding et al. (2010) is $\mathrm{log}({L}_{\mathrm{bol}}/\mathrm{erg}\ {{\rm{s}}}^{-1})=42.94\pm 0.40$. We also calculated the bolometric luminosity directly by integrating the best-fit SED described in Section 2.2 to be $\mathrm{log}({L}_{\mathrm{bol}}^{\mathrm{SED}}/\mathrm{erg}\ {{\rm{s}}}^{-1})=43.64\pm 0.04$. These values are consistent with each other within the ∼1σ uncertainty. Using the bolometric luminosity from [Oiv] 25.89 μm and the BH mass obtained from the broad Hα line, we estimate the Eddington ratio of J1440 to be λ ∼ 0.37. This translates to a photon index of Γ = 2.13 ± 0.06 under the assumption of the Γ − λ relation from Brightman et al. (2013).

A higher photon index for high Eddington ratio, lower-M_• systems has been found in the literature (e.g., Porquet et al. 2004; Done et al. 2012; Baldassare et al. 2017), as low-M_• systems may have a higher accretion disk temperature with thermal emission extending into the soft X-ray energies. Moreover, one can argue that the X-ray photon index could be softer, as J1440 shows the presence of the [Oiv] 25.89 μm emission line, which requires an abundance of EUV photons to ionize, and the presence of these EUV photons has been linked to soft X-ray fluxes (Timlin III et al. 2021; Telfer et al. 2002).

While X-ray spectral analysis is an ideal way to confirm the presence of obscuring material in an AGN, the scarcity of sensitive X-ray instruments has limited such observations to only a small number of sources with deep X-ray observations. One commonly adopted practice to find candidate X-ray-obscured AGNs in large surveys is to compare the observed X-ray luminosity and AGN luminosity indicators at other wavelengths, assuming that these different AGN luminosity indicators follow simple scaling relations derived for unobscured type 1 sources. In Figure 11, we compared the 2–10 keV intrinsic luminosity with that from the [Oiii] λ5007 (Barth et al. 2008), [Oiv] 25.89 μm (H17), and 6 μm (estimated from the SED fits) mid-IR luminosity. The solid orange line represents the L_2–10 keV versus L_{[Oiii] λ5007} relation obtained by Panessa et al. (2006), where the linear relation can be expressed as $\mathrm{log}\left(\tfrac{{L}_{2-10\,\mathrm{keV}}}{\mathrm{erg}\,{{\rm{s}}}^{-1}}\right)=(1.22\pm 0.06)\mathrm{log}\left(\tfrac{{L}_{[{\rm{O}}{\rm\small{}}\mathrm{III}(5007\mathring{\rm{A}} )}}{\mathrm{erg}\,{{\rm{s}}}^{-1}}\right.+(-7.34\pm 2.53).$ Similarly, the solid red line shows the L_2–10 versus L_6μm relation obtained by Chen et al. (2017). This equation can be expressed as $\mathrm{log}\left(\tfrac{{L}_{2-10\,\mathrm{keV}}}{\mathrm{erg}\,{{\rm{s}}}^{-1}}\right)=(0.84\pm 0.03)\times \mathrm{log}\left(\tfrac{{L}_{6\mu {\rm{m}}}}{{10}^{45}\mathrm{erg}\,{{\rm{s}}}^{-1}}\right)+(44.60\pm 0.01)$. The solid blue line represents the L_bol versus L_{[Oiv] 25.89 μm} relation obtained by Goulding et al. (2010), which can be expressed as $\mathrm{log}\left(\tfrac{{L}_{\mathrm{bol}}}{{10}^{44}\mathrm{erg}/{\rm{s}}}\right)=(0.38\pm 0.09)\,+(1.31\pm 0.09)\times \mathrm{log}\left(\tfrac{{L}_{[{\rm{O}}[\,\mathrm{IV}]](25.89\mu {\rm{m}})}}{{10}^{41}\mathrm{erg}\,{{\rm{s}}}^{-1}}\right)$. Here we use an X-ray bolometric correction factor of 25 (Brightman et al. 2017) to convert the relation between L_{2−10 keV} and L_[Oiv].

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With the intrinsic X-ray luminosity and N_H measured for J1440 with NuSTAR, we can assess how effective these different AGN luminosity indicators can be when used to identify heavily obscured AGNs when combined with X-ray observations. For this purpose, we calculated the absorbed 2–10 keV X-ray luminosity by fitting the FPMA data with a simple absorbed power-law model mentioned in Section 3.1, which leads to $\mathrm{log}\left(\tfrac{{L}_{2-10\ \mathrm{keV}}^{\mathrm{abs}}}{\mathrm{erg}\,{{\rm{s}}}^{-1}}\right)=40.93$. If we assumed that the intrinsic AGN X-ray luminosity follows the aforementioned empirical relations, N_H values estimated using the ratio between ${L}_{2-10\ \mathrm{keV}}^{\mathrm{abs}}$ and L_[Oiii] or L_6μm would be at least an order of magnitude higher than what we obtained from X-ray spectral fitting analysis. On the other hand, the ratio between ${L}_{2-10\,\mathrm{keV}}^{\mathrm{abs}}$ and [Oiv] 25.89 μm predicts a column density of $\mathrm{log}\left(\tfrac{{N}_{{\rm{H}}}}{{\mathrm{cm}}^{-2}}\right)=23.4$, which is more consistent with the best-fit N_H with phenomenological and physical models described in Section 3. The results are shown in Figure 11. One plausible explanation is that the higher ionization potential of [Oiv] (59.4 eV) makes it a better AGN luminosity tracer in dwarf galaxies owing to the more significant host galaxy contamination effects in lines with lower ionization energy such as [Oiii] (35 eV) (e.g., Meléndez et al. 2008). As for L_6μm, we see nonnegligible contributions from dust emission associated with stellar activity in the mid-IR wavelength of the best-fit SED. Given the limited photometric coverage in the mid-IR, it is possible that the best-fit AGN SED is still contaminated by the host galaxy contribution. Moreover, if [Oiv] 25.89 μm lines are thought to be the better measure of the bolometric luminosity, then CIGALE seems to be overpredicting the bolometric and consequently 6 μm luminosities.

The ratio between the optical–UV and X-ray luminosity for AGNs has been actively studied in the past, particularly in the parameterized form between the luminosity densities at 2500 Å and 2 keV: α_OX = −0.383 $\mathrm{log}\left(\tfrac{{L}_{2500\mathring{\rm{A}} }}{{L}_{2\mathrm{keV}}}\right)$ (Tananbaum et al. 1979). For typical, type 1 AGNs, a clear correlation has been established between α_OX and L_2500Å (e.g., Just et al. 2007; Lusso et al. 2010), suggesting that typical AGNs share a common radiation mechanism. However, it is not clear whether this relation extends to AGNs powered by less massive BHs in dwarf galaxies. For instance, the dwarf galaxies in the Baldassare et al. (2017) sample generally deviate from the linear relation, which was primarily attributed to the difficulties in separating AGN emission from that of the host galaxy in such systems (see Section 3.2 of Baldassare et al. 2017). The target studied in this work, J1440, is a part of the Baldassare et al. (2017) sample and was found to have an α_OX lower than the empirical α_OX − L_2500Å relation for typical AGNs by at least ≈0.6. Here we recalculate α_OX for J1440 using the intrinsic 2 keV luminosity based on the best-fit model using NuSTAR data. The UV–optical emission of J1440 is heavily suppressed as shown in Figure 4; therefore, we calculated L_2500Å using the power-law relation f_ν ∝ ν^−0.44, where we utilized the flux at 5100 Å estimated from the Hα emission line (see Section 4 of Dong et al. 2012 for details of this method).

We find an updated α_OX value for J1440 of α_OX = −1.26. This is consistent with the value expected from the Just et al. (2007) relation within the margin of error. We attribute the different α_OX values between our work and that from Baldassare et al. (2017), α_OX = −1.6, to the presence of AGN obscuration for this object, and the soft X-ray data observed on Chandra and XMM-Newton might have been due to stellar activity of the host galaxy or photoionization of the gas in the AGN narrow-line regions; hence, only the hard X-ray data can give a reliable estimate of intrinsic 2–10 keV X-ray luminosity for heavily obscured AGNs owing to its higher penetrating power. At least for J1440, the IMBH-powered AGN appears to have an optical–UV to X-ray spectral slope similar to typical AGNs. We note that the L_2500Å we estimated using empirical relations likely has large uncertainties, but it is consistent with the L_2500Å value measured using HST photometry by Baldassare et al. (2017), although the direct photometry measurement is also likely highly uncertain owing to host galaxy contamination. Previous studies of low-mass AGN samples such as Dong et al. (2012) and Baldassare et al. (2017) have found a significant fraction of their sample to deviate away from the empirical α_OX − L_2500Å relation. The results from J1440 shown here suggest that at least some of the low-mass AGNs still follow the typical α_OX relation when obscuration and host galaxy contamination are properly corrected. A NuSTAR follow-up of these low-mass AGNs is thus warranted to study the extension of α_ox in low-mass regimes.

Recently Fernández-Ontiveros & Munoz-Darias (2021) studied the IR emission-line ratios for AGNs selected from the Spitzer IRS archive. They found that the ratio between emission lines of different ionizing energies can be used as a proxy of the "hardness" of the ionizing source (i.e., [Neii] 12.81 μm/([Neii] 12.81 μm+[Oiv] 25.89 μm); see their Equation (1)). The EUV photons from the accretion disk in rapidly accreting systems can excite high-excitation lines such as [Oiv] 25.89 μm from the accretion disk, while the low-excitation lines such as [Neii] 12.81 μm become more significant in systems that lack the strong UV continuum, as they are accreting in a lower state. This transition between different accretion states is commonly seen in XRBs, as their X-ray spectral hardness and count rates cycle through different accretion states (e.g., Fender et al. 2004). However, these transitions are not well studied in the case of AGNs, although some studies suggest that changing-look quasars might be a manifestation of change of state similar to XRBs (Noda & Done 2018). Despite potential uncertainties associated with original sample selection bias, as well as local physical conditions, the mid-IR line ratio provides a useful tool for inferring the "hardness" for AGNs with heavily suppressed and/or soft X-ray emission dominated by host galaxy stellar activity. With the Spitzer IRS emission-line measurements from H17, ³⁰ we can calculate the line ratio defined above to be ≈0.6. Since the Eddington ratio of J1440 is high (λ_Edd ≈ 0.37), it could imply that J1440 is currently in the soft accretion state and is transitioning into the hard accretion state. It is possible that [Neii] 12.81 μm has more contamination from the host galaxy for a dwarf galaxy such as J1440. Future spatially resolved observations with JWST's MIRI might help with determining the nuclear line and continuum fluxes, which will reveal more information regarding its accretion mechanisms.