Discovery of a Low-redshift Hot Dust-obscured Galaxy

An optical spectrum for W1904+4853 was first obtained with the Low-Resolution Imaging Spectrometer (LRIS; Oke et al. 1995) at the Keck I Telescope on UT 2010 November 9. The spectrum was obtained with a total of 250 s integration on source with a 15 slit (seeing ∼15). The spectrum only covers 5800–10,320 Å due to the temporary malfunction of the blue arm camera of the LRIS during the observation. Strong Hα, Hβ, Hγ, and [O iii] 4959 and 5007 Å lines are well detected at redshift z = 0.415.

To investigate the Mg ii line, we reobserved W1904+4853 with the Double Spectrograph (DBSP) on the Palomar 200 inch Hale Telescope on UT 2020 July 24. We limit the spectrum from the blue and red arms of the spectrograph to rest-frame wavelengths 2500–3800 Å and 4100–7000 Å respectively, to minimize sensitivity losses at the edges of the observed spectral ranges. The 10 slit set to align with the parallactic angle of 110° was placed on the target, centered on the position R.A. =19^h04^m4504, decl. $=+48^\circ 53^{\prime} 08\buildrel{\prime\prime}\over{.} 9$ (J2000). The full DBSP spectrum with a total of 1200 s integration at a mean air mass of 1.1. The reduced spectrum is shown in Figure 1. The spectrum was processed and analyzed with IRAF, following the standard reduction procedures to account for bias and flat fielding. The spectrum was corrected for telluric absorption features and flux calibrated using the standard star BD+28 4211. The flux difference between the LRIS spectrum and the DBSP spectrum is less than 10%. The detailed line measurement process and redshift determination are discussed in Section 3.4. We note that the 2D spectrum of W1904+4853 from Palomar/DBSP does show a marginal extension along the slit. The FWHMs of emission lines are generally marginally extended at 16 and the continuum is slightly bigger with a size of 19, under the seeing condition of 15.

To construct the SED of W1904+4853 and estimate its bolometric luminosity, we gathered its photometric data at UV-to-submillimeter wavelengths from the GALEX 10.17909/ths3-nr82, Pan-STARRS 10.17909/s0zg-jx37, UKIRT, WISE 10.26131/IRSA1, AKARI 10.26131/IRSA180, IRAS 10.26131/IRSA11, and Spitzer 10.17909/mkcw-8w83 surveys. We also obtained near-IR (NIR) photometry from United Kingdom Infrared Telescope (UKIRT) and submillimeter flux measurements from James Clerk Maxwell Telescope (JCMT). The summary of the multiwavelength photometric data are given in Table 1 and plotted in Figure 2.

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2.2.1. NIR and Submillimeter Observations

2.2.2. Archival Photometric Data

W1904+4853 has strong and broad emission lines and faint continuum emission at optical wavelengths, similar to many high-z Hot DOGs (Wu et al. 2012; Assef et al. 2015; Tsai et al. 2015). These observed strong lines significantly contribute to the optical photometry and can obstruct the SED fitting if the used templates are constructed with weak-line conditions. To better model the SED of its host galaxy, we estimate the line-free continuum photometry by subtracting the emission-line contribution to the broadband photometry. The line-subtracted continuum flux and uncertainties are listed in Table 1.

We first assume that the broad emission lines are from the centrally concentrated and unresolved core region under the seeing condition, and the stellar continuum emission of the host galaxy is extended and marginally resolved as seen in the Pan-STARRS images (deconvolved FWHM ∼15 in the r band). The difference in the slit loss values for the components with different spatial extents in the DBSP's 10-slit spectrum and the seeing of ∼15 are significant and used to derive the intrinsic line-to-continuum ratios. These intrinsic ratios, which are lower than in the observed spectrum, are combined with the filter bandpasses (see Figure 3) to estimate the line-free continuum photometry. The Hα filter is not significantly contaminated by emission lines and therefore does not need this correction. While Mg ii falls in the U band, it only contributes ∼2% to the photometry, which is small compared to the ∼8% uncertainty of the U-band flux, so we did not correct this band.

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We consider the possibility of the NUV band being affected by strong emission lines. The UV fluxes in the GALEX NUV band is significantly higher than the best-fit model shown in Figure 2 (black open circle). One possibility is that the elevated NUV flux may be contaminated by the strong and redshifted C iv 1549 Å and C iii] 1909 Å lines at the range of 1400–2800 Å, which are often seen in high-z Hot DOGs (z > 1.5; Wu et al. 2012). We estimated C iii] and C iv emission contributes 16% of the observed NUV flux, based on the averaged equivalent widths of these lines seen in high-z Hot DOGs (P. R. M. Eisenhardt et al. 2023, in preparation), or up to 45% using the maximum equivalent widths seen.

The red MIR color, strong broad emission lines, and high luminosity of W1904+4853 suggest this system is mainly powered by an obscured AGN, as is thought to be true for high-redshift Hot DOGs (Eisenhardt et al. 2012; Assef et al. 2015; Tsai et al. 2015). Except for a few systems identified as blue Hot DOGs (Assef et al. 2016, 2020, 2022)—Hot DOGs with blue excess in their SEDs due to a small fraction of AGN blue light scattered through the dust cocoon, the emission of the powerful AGN is almost fully obscured. The rest-frame optical SED of Hot DOGs generally represents the host galaxy properties with little contribution from the deeply buried AGN.

To decompose the stellar components in the host galaxy, we employed the approach described by Assef et al. (2008, 2010) in which the SED of a galaxy is a linear combination of empirical spectral templates (Assef et al. 2010). The four empirical SED templates—"AGN" for an unreddened AGN, "E" for an elliptical galaxy (old stellar population), "Sbc" for a spiral galaxy (intermediate-aged stellar population), and "Im" (young starburst population) for an irregular galaxy—are used to model the SED of an AGN and its host galaxy in the rest-frame wavelength range from 0.03–30 μm (Assef et al. 2010). Each template can have an independent reddening applied.

These templates do not cover wavelengths longer than 30 μm in the rest frame. In addition to the host galaxy components, the SED of W1904+4853 (see Figure 2), like that of the Hot DOG population, is dominated by hot dust beyond a few microns in the rest frame, with significant emission to beyond 100 μm (Tsai et al. 2015). Therefore, to model the IR SED (>2 μm) we add an SPL dust distribution component, which was developed to describe dust emission for Hot DOGs (C.-W. Tsai et al. 2023, in preparation). The dust emission model assumes that dust number density is a simple power-law function of radius from the galaxy center, and the thermal dust emission is in equilibrium with the radiation received by the dust grain. In addition to the slope of the power law, the SPL model uses upper and lower dust temperature limits to represent the inner and outer cutoff of the dust distribution. The detailed best-fit SPL model is described in Section 4.1.

The dust component dominates the bolometric luminosity with its MIR and far-IR (FIR) emission. Other characteristics in the emission-line corrected SED of W1904+4853 are a steeper ascent in the rest frame NIR than expected for an unobscured stellar population, and a UV-optical continuum suggestive of a stellar population with relatively little obscuration. Motivated by these features, we modeled the SED for three different cases to assess the roles of AGN, dust, and star formation in W1904+4853. Each case assumed three components were present, one of which was the SPL dust model, with reddened Assef et al. (2010) templates used for the other two components. We assumed R_V = 3.1 and an SMC reddening law (Gordon et al. 2003) at short wavelengths and a Milky Way reddening law (Fitzpatrick & Massa 2007) at longer wavelengths.

Prior to the SED modeling process, the flux of each band was corrected for extinction from dust in the Milky Way (A_V = 0.19 mag; Schlegel et al. 1998; Fitzpatrick & Massa2007). We fit the SED using the Markov Chain Monte Carlo (MCMC) method provided by the Python package emcee (Foreman-Mackey et al. 2013), solving for the amplitude of the two template components and the SPL component simultaneously, along with the obscuration (for case 3 only the AGN obscuration was varied). A simple Gaussian function was used for the likelihood function with uninformative priors. The median value of the MCMC samples was adopted as the best-fit result of each parameter and the quoted "1σ" uncertainties are based on the samples' 16th and 84th percentiles in the marginalized distributions.

Case 1 assumes, in addition to the SPL hot dust component with the power-law index of dust radius distribution p = −0.82 ± 0.02, and higher temperature limit ${T}_{{\rm{h}}}={539}_{-6}^{+6}$ K, and lower temperature limit ${T}_{{\rm{c}}}\,=\,{37}_{-3}^{+3}$ K, host galaxy emission dominated by a young starburst population partially obscured by dust. We used two Im models to represent the young stellar population, with extinction applied to only one of them. This model as shown in Figure 2, provided the best SED fit (${\chi }_{\nu }^{2}\,=\,2.7$) of the three cases considered. The obscured starburst population has a substantial extinction of A_V ∼ 7.5 mag from the SED fit. The extinction toward a fraction of the young starburst population (Im template) is more reasonable than for the E or Sbc templates. This obscured stellar component provides a good match to the observed NIR bands, while the unobscured starburst dominates the shorter wavelength bands. In this case, the AGN is completely obscured and contributes no emission in the UV-optical wavelengths.

Case 2, like case 1, also assumes the SPL hot dust component and an unobscured starburst population are present, but replaces the obscured starburst with light transmitted through the dust around an obscured AGN. This model intends to use an obscured AGN SED to explain the relatively elevated NIR luminosity. The best-fit result again has a starburst population dominating the SED between 0.1 and 1.0 μm. The dusty AGN with extinction A_V ∼ 2.5 mag dominates the observed J, H, and K bands, but the fit here is not as good as for case 1, resulting in a significantly worse reduced chi-squared (${\chi }_{\nu }^{2}=10.5$).

Case 3 again assumes the SPL component is present, as well as a starburst component with a given A_V ∼ 7.5 mag obscuration, but replaces the unobscured starburst with a lightly obscured AGN component. This model mainly attributes the optical and UV emission from a lightly obscured AGN. The amplitude of the obscured starburst is a free parameter in the fitting. Some escaping AGN light is motivated by the broad emission lines seen in the optical, but the best-fit obscuration (A_V ∼ 0.9 mag) for an AGN producing the short wavelength light has a much higher reduced chi-squared (${\chi }_{\nu }^{2}=34$) than other cases. Like case 2, the fit in the observed NIR is worse than for case 1, and as shown in Figure 3, a mildly obscured AGN system cannot explain the change in the continuum from rest UV-to-optical wavelengths. However, the UV-optical continuum can be modeled by a young stellar population.

In summary, we examined three scenarios in the SED-fitting analysis. Case 1 includes an AGNs dust emission SPL model, an unobscured starburst model, and an obscured starburst population (A_V ∼ 7.5 mag) that dominates NIR emission. Case 2 contains an AGNs dust emission SPL model, an unobscured starburst model, and a highly obscured AGN (A_V ∼ 2.5 mag) that dominates NIR photometry. Case 3 has an AGNs dust emission SPL model, a lightly obscured AGN (A_V ∼ 0.9 mag) dominating optical-NIR photometry, and an obscured starburst (A_V ∼ 7.5 mag) contributing mainly to NIR wavelengths. The combination of SED models in case 1 yields the best-fit results. We adopt that scenario of case 1 in which an extremely obscured AGN with only hot dust emission is in a host galaxy with both obscured and unobscured starburst stellar population in the discussions in the rest of the paper. We cannot rule out, however, that light from the AGN scattered by gas or dust may contribute to the UV-to-NIR fluxes.

The bolometric luminosity of W1904+4853 was calculated using the emission-line subtracted photometric data shown in Figure 2. We obtain a lower limit of L_bol = 1.0 × 10¹³ L_⊙ for the bolometric luminosity using a power-law interpolation between photometric data, assuming no contributions from emission at wavelengths shorter or longer than the observed data. If the best-fit SED model (heavy gray line in Figure 2) between wavelengths of 0.03 and 1000 μm in the rest frame is adopted, the estimated bolometric luminosity is 1.1 × 10¹³ L_⊙, which is considered more representative of the total luminosity of W1904+4853 and is adopted as the bolometric luminosity in this paper. The IR dust emission, L(2–1000 μm), dominates this total luminosity (>99%). The systemic uncertainty of the total luminosity is considered to be ∼20% (Tsai et al. 2015) from the assumption of a slow-varying SED, which is more significant than the statistical uncertainty (<10%). We note that the S-band (2–4 GHz) luminosity of ∼ 6 × 10⁷ L_⊙ for W1904+4853 does not significantly contribute to the bolometric luminosity. In comparison with the optical luminosity (>10¹⁰ L_⊙), W1904+4853 can be classified as a radio-quiet system.

To check if W1904+4853 is variable in the MIR, we investigated its data in the unTimely catalog (Meisner et al. 2023), which contains 16 epochs of time-resolved WISE and NEOWISE co-adds from 2010–2020. We found that the difference in W2 magnitude between the first and last unTimely epochs is 0.077 ± 0.012, which is much higher than sources with comparable brightness in the same region of sky. Considering all 646 sources with 11.5 < W2 (first epoch) <12.5 in the same 156 × 156 WISE tile, only 10 sources showed a larger W2 change. After the second epoch, corresponding to 2010 November, the source has remained stable to ± 0.02 mag in W2. The difference between the first and last epochs in W1 magnitude is 0.000 ± 0.022, which is typical for sources of comparable W1 flux in the same WISE tile. WISE shows this source faded modestly in W2 (< 10%) in 2010, after which the source has remained stable. This result of a greater (but still small) variation in W2 compared to W1 is consistent with our SED modeling (Section 3.2), which AGN emission strongly dominates W2, while the host galaxy contributes significantly to W1. This suggests that, besides emission-line contamination, the bright GALEX photometry might also be due to a brighter episode in the source's past. We also examined the optical photometric data from Kepler-INT survey (g, r, and i; Greiss et al. 2012) and DESI Legacy Imaging Surveys (g, r, and z; Dey et al. 2019), and find no significant (>4σ) optical variability. We note that the z-band flux in the Legacy survey is significantly higher than that in the Pan-STARRS survey because the strong Hα line of W1904+4853 fully falls into the range of a wider z band in the Legacy survey.

The optical spectrum of W1904+4853 (Figure 1) shows well-detected Mg ii, [O ii], Hγ, Hβ, [O iii]4959 Å, [O iii]5007 Å, [O i], Hα, [N ii], and [S ii] emission lines. We used a power law to model the continuum emission, and single Gaussian, or two Gaussian profiles to model the emission lines. Table 2 summarizes the broad/narrow fitting schemes used for the selected lines. The emission-line fitting results are shown in Figure 4 and summarized in Table 3.

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Table 3. Emission Lines of W1904+4853

Line	Flux	$\mathrm{log}L$	$\mathrm{log}{L}_{\mathrm{bl}}$	△ vbl	FWHMbl	EWbl	$\mathrm{log}{L}_{\mathrm{nl}}$	△ vnl	FWHMnl	EWnl
	(10−16 erg cm−2 s−1)	(erg s−1)	(erg s−1)	(km s−1)	(km s−1)	(Å)	(erg s−1)	(km s−1)	(km s−1)	(Å)
Mg ii	9.5 ± 0.2	${41.77}_{-0.04}^{+0.03}$	${41.77}_{-0.04}^{+0.03}$	$-{160}_{-60}^{+60}$	${1600}_{-200}^{+200}$	${44}_{-3}^{+4}$	⋯	⋯	⋯	⋯
[O ii] λ3727	36.0 ± 0.3	${42.51}_{-0.01}^{+0.01}$	${42.25}_{-0.02}^{+0.01}$	$-{580}_{-30}^{+30}$	${1880}_{-50}^{+50}$	${161}_{-5}^{+5}$	${42.16}_{-0.02}^{+0.02}$	${164}_{-4}^{+4}$	${610}_{-10}^{+10}$	${130}_{-4}^{+4}$
Hγ	2.8 ± 0.2	${41.24}_{-0.07}^{+0.06}$	${40.80}_{-0.27}^{+0.19}$	$-{700}_{-300}^{+400}$	${1200}_{-500}^{+600}$	${6}_{-3}^{+4}$	${41.04}_{-0.13}^{+0.09}$	$-{10}_{-50}^{+40}$	${500}_{-100}^{+100}$	${11}_{-3}^{+3}$
Hβ	7.4 ± 0.2	${41.82}_{-0.02}^{+0.02}$	${41.52}_{-0.06}^{+0.05}$	$-{900}_{-100}^{+100}$	${2100}_{-300}^{+300}$	${36}_{-5}^{+4}$	${41.51}_{-0.01}^{+0.01}$	${25}_{-9}^{+9}$	${460}_{-30}^{+30}$	${35}_{-2}^{+3}$
[O iii] λ4959	6.9 ± 0.2	${41.53}_{-0.02}^{+0.02}$	${41.20}_{-0.04}^{+0.04}$	$-{500}_{-100}^{+100}$	${2200}_{-200}^{+200}$	${24}_{-3}^{+3}$	${41.25}_{-0.02}^{+0.02}$	$-{64}_{-5}^{+5}$	${430}_{-20}^{+20}$	${28}_{-2}^{+2}$
[O iii] λ5007	15.5 ± 0.2	${42.01}_{-0.02}^{+0.02}$	${41.68}_{-0.04}^{+0.04}$	$-{500}_{-100}^{+100}$	${2200}_{-200}^{+200}$	${70}_{-10}^{+10}$	${41.74}_{-0.02}^{+0.02}$	$-{63}_{-5}^{+5}$	${430}_{-20}^{+20}$	${83}_{-5}^{+6}$
[O i] λ6300	18.3 ± 0.3	${42.15}_{-0.01}^{+0.01}$	${41.95}_{-0.02}^{+0.02}$	$-{690}_{-50}^{+50}$	${2120}_{-60}^{+60}$	${117}_{-5}^{+5}$	${41.70}_{-0.03}^{+0.03}$	${122}_{-9}^{+9}$	${680}_{-30}^{+30}$	${65}_{-4}^{+4}$
[O i] λ6363	6.1 ± 0.2	${41.68}_{-0.01}^{+0.01}$	${41.56}_{-0.02}^{+0.02}$	$-{690}_{-50}^{+50}$	${2100}_{-60}^{+60}$	${47}_{-2}^{+2}$	${41.08}_{-0.05}^{+0.05}$	${121}_{-9}^{+9}$	${670}_{-30}^{+30}$	${16}_{-2}^{+2}$
[N ii] λ6548	⋯	${41.67}_{-0.01}^{+0.01}$	⋯	⋯	⋯	⋯	${41.67}_{-0.01}^{+0.01}$	${7}_{-2}^{+2}$	${627}_{-7}^{+7}$	${62}_{-1}^{+1}$
Hα	⋯	${43.00}_{-0.01}^{+0.01}$	${42.87}_{-0.01}^{+0.01}$	$-{540}_{-10}^{+10}$	${2810}_{-10}^{+10}$	${981}_{-7}^{+7}$	${42.44}_{-0.01}^{+0.01}$	${83}_{-1}^{+1}$	${602}_{-4}^{+4}$	${368}_{-4}^{+4}$
[N ii] λ6583	⋯	${42.13}_{-0.01}^{+0.01}$	⋯	⋯	⋯	⋯	${42.13}_{-0.01}^{+0.01}$	${7}_{-2}^{+2}$	${624}_{-7}^{+7}$	${182}_{-3}^{+3}$
[S ii] λ6716	⋯	${42.02}_{-0.02}^{+0.04}$	${41.76}_{-0.03}^{+0.07}$	$-{420}_{-40}^{+60}$	${1900}_{-50}^{+50}$	${80}_{-10}^{+10}$	${41.68}_{-0.02}^{+0.04}$	${177}_{-3}^{+3}$	${408}_{-9}^{+9}$	${65}_{-2}^{+2}$
[S ii] λ6731	⋯	${41.87}_{-0.06}^{+0.02}$	${41.66}_{-0.11}^{+0.04}$	$-{420}_{-40}^{+60}$	${1900}_{-50}^{+50}$	${60}_{-10}^{+10}$	${41.46}_{-0.02}^{+0.02}$	${177}_{-3}^{+3}$	${408}_{-9}^{+9}$	${40}_{-2}^{+2}$

Note. The fluxes were calculated by fitting one/two Gaussian profiles to the emission-line profiles, measuring the integrated flux under the profile. Mixing with other lines, the integrated flux of [N ii], Hα, and [S ii] cannot be estimated individually. L represents the emission-line luminosity derived from best-fit model and Δv represents the offset of the Gaussian center for each broad/narrow component with respect to the systemic redshift of z = 0.415 determined by multiple lines following the scheme of Eisenhardt et al. (2023, in preparation). Subscripts "bl" and "nl" indicate broad line and narrow line, respectively.

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The forbidden lines of W1904+4853 are generally broadened, asymmetric, and blueshifted. The broadened forbidden lines are generally considered evidence of ionized gas outflowing from an AGN at ≳ 10³ km s⁻¹ (Veilleux et al. 1994; Crenshaw & Kraemer 2000) instead of the virialized motions of clouds in the broad-line region (BLR). Following the analysis presented in Jun et al. (2020) for modeling the spectra of 12 Hot DOGs, the Balmer emission lines (Hα, Hβ, Hγ) and [O i], [O ii], [O iii], as well as [S ii] doublets of W1904+4853 are modeled with a single narrow (FWHM ≤1200 km s⁻¹) and a single broad (1200 km s⁻¹ ≤ FWHM ≤ 10,000 km s⁻¹) Gaussian profile. For [O i], [O iii], [S ii], and [N ii], we used the best-fit central wavelength of the stronger line in the doublet to constrain the weaker one with a fixed theoretical wavelength spacing and the same line width. In the fitting process, we fix the [O iii] doublet ratio to 2.99 (e.g., Storey & Zeippen 2000; Dimitrijević et al. 2007) and the [N ii] doublet ratio to 2.96 (e.g., Greene & Ho 2005; Wu et al. 2018; Jun et al. 2020). We are unable to measure the broad [N ii] emission because it is degenerate with other line components, so we choose to remove the broad [N ii] component from our analysis.

The Mg ii emission line is modeled with a Fe ii emission complex and a single Gaussian component (1G+1Fe) or a double-Gaussian (2G+1Fe) component. We adopted the Fe ii template from Tsuzuki et al. (2006). The Fe ii template from Vestergaard & Wilkes (2001) was also tested in our fitting process, but the results did not change significantly. Both the 1G+1Fe and 2G+1Fe models fit the Mg ii line reasonably well, but an F-test yields a probability p-value of 0.54, implying that there is no significant improvement by adding an additional Gaussian component. We therefore adopt the 1G+1Fe profile to model Mg ii line.

We did not correct for extinction based on the Balmer decrement (i.e., the ratio of Hα/Hβ) in this work because the contributions from the AGN and from star formation in the host galaxy cannot be easily disentangled. However, if we assume an intrinsic ratio of 2.86 for Hα/Hβ (e.g., Osterbrock 1989), the estimated A_V ∼ 4.6 mag is lower than the value derived from the AGN component in the SED analysis (A_V ∼ 20–60 mag; Eisenhardt et al. 2012; Assef et al. 2015, 2016). This implies that a significant fraction of the ionized hydrogen emission is from outflowing material and the host galaxy. Thus, in comparison with the AGN emission, the ionized hydrogen emission is overall experiencing less extinction.

W1904+4853 shows a rapidly rising SED around rest frame 4 μm as shown in Figure 2, followed by a gradual rise toward 100 μm, and a Rayleigh–Jeans falloff at FIR to submillimeter wavelengths. The IR radiation dominates the bolometric luminosity (L_IR = L_2–1000μm ∼ 1.1 × 10¹³ L_⊙). Similar to that of other high-z Hot DOGs (C. W. Tsai et al. 2023, in preparation), this SED shape suggests a continuous dust temperature distribution in the galaxy. The dust is heated to much hotter temperatures than in other IR-luminous galaxies. The high luminosity of W1904+4853 is due to the powerful, dust enshrouded AGN, with most energy released in the rest-frame MIR and FIR.

We applied a model with a single power-law (SPL) radial dust density distribution from Tsai et al. 2023, in preparation to fit the NIR to submillimeter SED. This SPL dust model assumes a continuous, spherically symmetric, optically thin dust cocoon in thermal equilibrium surrounding the central AGN. In addition to a scaling factor for matching the SED template with the observed fluxes, this model only relies on the representative hottest dust temperature (T_h), representative coldest dust temperature (T_c), and the power index p of the dust grain number density, with an assumed dust emissivity β = 1.5. The fitting result is shown as the gray curve in Figure 2. The best-fit SPL dust SED model suggests T_h = 539 ± 6 K, T_c = 37 ± 3 K, and the power-law index of dust grain number density with radius p = −0.82 ± 0.02. This model implies a total dust mass of ${5}_{-2}^{+3}\times {10}^{7}\,{M}_{\odot }$ for W1904+4853. These physical values are consistent with the range seen in high-z Hot DOGs (Tsai et al. 2023, in preparation).

Utilizing the SPL model, our estimate indicates that the radius of the dust with a temperature of T_h = 539 ± 6 K encircling the core of W1904+4853 is roughly 20 pc d, implying that the light-travel time is on the order of 100 yr. While hard photons can quickly destroy dust grains after the dust absorption, this represents the lower limit on the timescale for the hot dust to persist after exposure to the central heating AGN. The equilibrium between dust destruction and replenishment can prolong this timescale significantly.

With the assumption that the broad emission lines of the permitted lines are due to virialized motions of emitting gas around the central SMBH, the single-epoch mass of the BH M_BH can be estimated. As shown in Figure 1, the Hα and Hβ lines are both broad (FWHM >2000 km s⁻¹) and highly blueshifted (Δv < −500 km s⁻¹). These highly blueshifted Balmer lines could indicate that the emitting gas is outflowing (Jun et al. 2020), not suitable for M_BH estimate. In contrast, the Mg ii line shows a systematic broad line, much less blueshifted, implying that Mg ii light might originate around the SMBH and escape the dust cocoon through scattering (e.g., Assef et al. 2016, 2020). Outflows do not appear to significantly affect the Mg ii line shape for W1904+4853. However, we cannot rule out the possibility that the broad Mg ii line is associated with an outflow, rather than with the virialized gas around the SMBH. This caveat should be noted when considering the following discussions about the M_BH estimate based on the virialized Mg ii gas assumption. Assuming an Hα/Mg ii line ratio of 2.85 (Shen et al. 2011; Roig et al. 2014) and an equal line width, the corresponding broad Hα line would have a luminosity of 10^42.2 erg s⁻¹. This component cannot be well separated from the outflowing broad-line component in the line profile fitting. Thus, we cannot conclusively rule out the presence of the emission from the central viralized gas near the central AGN in the entangled broad Hα line emission.

The Mg ii line can be used to estimate BH masses (Wang et al. 2009; Tsai et al. 2018) and the calibration of Mg ii determined SMBH masses with respect to those from Hβ has been established (McLure & Dunlop 2004; Wang et al. 2009; Shen et al. 2011; Jun et al. 2015; Suh et al. 2015), assuming there is a close relationship between the BLR radius of the Mg ii emitting region and the AGN continuum luminosity. In this paper, we adopt the Mg ii-based SMBH mass formulation from Equation (10) of Wang et al. (2009):

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}\right) & = & (7.13\pm 0.27)+0.5\,\mathrm{log}\left(\displaystyle \frac{{L}_{3000}}{{10}^{44}\ \mathrm{erg}\ {{\rm{s}}}^{-1}}\right)\\ & & +(1.51\pm 0.49)\mathrm{log}\left(\displaystyle \frac{{\mathrm{FWHM}}_{\mathrm{Mg}\ \mathrm{II}}}{1000\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right),\end{array}\end{eqnarray} \tag{ 1 }$$

where L₃₀₀₀ is the intrinsic (unobscured) monochromatic luminosity from the central AGN at rest-frame 3000 Å (L_λ ≡ λ L_λ ), and FWHM_{Mg II} is the full width at half maximum of the Mg ii line profile.

The UV luminosity of W1904+4853 cannot be directly measured because of the high internal UV/optical extinction toward its central region. Instead, we estimate L₃₀₀₀ using L₃₀₀₀ ∼ 0.19 × L_bol based on the SED models for type 1 (broad-line) quasars from Richards et al. (2006). This implies L₃₀₀₀ = 2.1 × 10¹² L_⊙. With the FWHM of Mg ii of ${1600}_{-200}^{+200}$ km s⁻¹, Equation (1) yields $\mathrm{log}({M}_{\mathrm{BH}}/{M}_{\odot })$ = 8.4 ± 0.1 (stat.) ± 0.3 (sys.). We note that the FWHM of Mg ii in W1904+4853 is at the lower limit of measurements (< 2500 km s⁻¹) in Wang et al. (2009), with potential undersampling. To evaluate the reliability of Mg ii line in estimating BH mass for AGNs with FWHM spanning from 800–2500 km s⁻¹, we utilized the AGN sample from Coffey et al. (2019) and followed the methodological approach mentioned in Wang et al. (2009). The result is consistent with the reported systematic uncertainty of 0.3 dex (Wang et al. 2009).

For W1904+4853, the Eddington ratio $\eta \,=\,{L}_{\mathrm{AGN}}/{L}_{\mathrm{Edd}}\,=\,{1.4}_{-0.2}^{+0.3}$ (stat.)${}_{-0.7}^{+1.2}$ (sys.) for L_bol = 1.1 × 10¹³ L_⊙ and $\mathrm{log}({M}_{\mathrm{BH}}/{M}_{\odot })=8.4\pm 0.4$, assuming the bolometric luminosity is mainly from the obscured AGN. Systematic uncertainties from the SMBH mass estimate (Equation (1)) dominate the uncertainty in η. The extremely high luminosity of high-redshift Hot DOGs is thought to be powered by embedded SMBHs with accretion rates close to the Eddington limit (Tsai et al. 2018; Wu et al. 2018). W1904+4853 has a similarly high accretion rate, potentially exceeding the Eddington limit.

The UV-NIR SED (<1 μm) of W1904+4853, as described in Section 3, is dominated by the host galaxy because the AGN within is highly obscured. We used empirical SED templates to decompose the UV-NIR SED into two components: a starburst population and a highly obscured starburst population. The fitting result shows that the starburst component dominates the UV-optical SED, while a young stellar population with extinction dominates the observed NIR (J, H, and K) bands.

To further extract the properties of the host galaxies from the SED and optical spectrum, the following subsections discuss how the star formation rate (SFR) and stellar mass are estimated. The SFR is derived using the ultraviolet continuum emission (Section 4.3.1) and narrow component of [O ii] line emission (Section 4.3.2). We estimated the stellar mass according to the model from Bell et al. (2003) in Section 4.3.3.

4.3.1. UV-based SFR

4.3.2. [O ii]-based SFR

For moderately redshifted systems, optical observation of the [O ii]–3727 Å doublets (3726 Å and 3729 Å) provide an additional SFR tracer (Kennicutt 1998), although it is often affected by significant dust attenuation and suffers from large systematic uncertainties (i.e., Moustakas et al. 2006, and references therein). Using metallicities derived from the [N ii] λ6584/[O ii]λ3727 ratio, Zhuang & Ho (2019) refine a metallicity-dependent SFR estimator based on [O ii]. They applied this method to estimate the SFRs of a sample of ∼5500 type 2 AGNs, and the results are consistent with independent SFR obtained from the stellar continuum of the host galaxies. By removing the blueshifted component using the double-Gaussian decomposition of the observed [O ii] profile, the narrow [O ii] component provides an independent SFR tracer for W1904+4853.

We assume that the narrow [O iii] emission is driven by the AGN activity and the narrow [O ii] emission mainly arises from the star-forming region in the host galaxy. According to Zhuang & Ho (2019, Equation (7)), the calibrated [O ii] SFR for AGNs is

$$\begin{eqnarray}&&\begin{array}{l}{\mathrm{SFR}}_{[\mathrm{OII}]}({M}_{\odot }\,{\mathrm{yr}}^{-1})\\ =\ \displaystyle \frac{5.3\times {10}^{42}({L}_{[{\rm{O}}\ \mathrm{II}]}-0.109\,{L}_{[{\rm{O}}\ \mathrm{III}]})}{(-4373.14+1463.92x-163.045{x}^{2}+6.04285{x}^{3}),}\end{array}\end{eqnarray} \tag{ 2 }$$

where L_{[O II]} and L_{[O III]} are the total [O ii] and narrow [O iii] luminosities in erg s⁻¹, respectively. These numbers for W1904+4853 are corrected for the extinction from dust in the Milky Way and host galaxy (${A}_{{\rm{V}}}\,=\,{0.9}_{-0.1}^{+0.2}$ mag) as discussed in Section 4.3.1. The variable x in Equation (2) is the oxygen abundance $x\equiv \mathrm{log}({\rm{O}}/{\rm{H}})+12$. We adopt an oxygen abundance of 8.64, which is the average value of that in Seyfert 2 AGNs (Dors et al. 2020).

We note that W1904+4853 is significantly brighter than most of the galaxies in the Zhuang & Ho (2019) sample. Using the extinction-corrected emission-line luminosities, we estimate an SFR_{[O II]} of ∼45 M_⊙ yr⁻¹ for the host galaxy of W1904+4853. However, if a fraction of the [O ii] is shock ionized (Maddox 2018), the SFR_{[O II]} is an upper limit. We also note that the observed 610 km s⁻¹ line width of narrow [O ii] line emission is higher than the typical value in luminous starbursts (∼ < = 300 km s⁻¹; Banerji et al. 2011). This system could be at a late stage of dynamically settling in galaxy-galaxy merger event, as in the cases of ULIRGs (∼ 900 km s⁻¹; Chen et al. 2019).

4.3.3. Stellar Mass

4.4.1. Spectral Classification

The rest-frame optical SED of W1904+4853 shows little contribution from the powerful AGN although it dominates the IR emission. This suggests that the observed narrow emission lines potentially arise from ionized gas from the host galaxy. To distinguish the dominating photoionizing processes, we evaluate the emission-line ratios of W1904+4853 using standard BPT diagrams (e.g., Baldwin et al. 1981). As shown in Figure 5, we use three diagnostics which incorporate the ratios of [N ii]/Hα, [S ii]/Hα, [O i]/Hα, and [O iii]/Hβ (Kewley et al. 2001; Kauffmann et al. 2003; Kewley et al. 2006). The locations on the BPT diagrams are similar to those for the z = 0.83 Hot DOG J012611.96052909.6 (Jun et al. 2020) yet closer to the starburst region compared to the more luminous and distant Hot DOGs in Jun et al. (2020) with AGN dominance. These similarities indicate that W1904+4853 is rather complicated. The properties of W1904+4853 are highly consistent with that this system, like some red quasars, hosts powerful, obscured AGN and also strong star formation activity. For these red quasar systems, the high SFR may be enhanced by early galaxy interactions, making them located in the composite area of the BPT diagram (e.g., Ellison et al. 2016a, 2016b).

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4.4.2. Comparison with Star-forming Main Sequence

The main sequence (MS) of star formation in galaxies shows the correlation between SFR and stellar mass for star-forming galaxies (e.g., Brinchmann et al. 2004; Daddi et al. 2007; Elbaz et al. 2007; Noeske et al. 2007), which changes with redshift (e.g., Pannella et al. 2009; Whitaker et al. 2012; Moustakas et al. 2013; Schreiber et al. 2015). To compare W1904+4853 at z = 0.415 with the MS, we considered galaxies with redshift between 0.4 and 0.5 from the PRIsm MUlti-Object Survey (PRIMUS; Coil et al. 2011; Moustakas et al. 2013). We re-derived their SFRs and stellar masses using the same methods applied to W1904+4853 in Section 4.3 to avoid the systematic biases between SFR and stellar mass estimators. The result is shown in Figure 6. The large magenta point shows W1904+4853 with the lower limit of SFR calculated from the UV continuum of the SED model, while the small blue and red points are PRIMUS galaxies with SFRs. The large yellow point shows W1904+4853 with its SFR_UV derived using the BC03 model on the extinction-corrected host galaxy SED. We note that the density of quiescent galaxies in Figure 5 is much lower than reported in Moustakas et al. (2013) because using UV continuum to estimate the SFRs is unreliable for quiescent galaxies with depressed star formation. Those systems are omitted in the figure.

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As discussed in previous sections, the SED of W1904+4853's host galaxy is dominated by a starburst component. Considering extinction from the host galaxy, the SFRs estimated from the UV continuum and [O ii] line are both ≳45 M_⊙ yr⁻¹, significantly higher than the MS as shown in Figure 5. This result indicates that the activity of the obscured AGN in W1904+4853 has not yet significantly impacted the star formation activity of the host galaxy. The SMBH in W1904+4853, similar to high-z Hot DOGs (Eisenhardt et al. 2012; Wu et al. 2012; Tsai et al. 2018; Wu et al. 2018), has likely just been activated recently and is accreting in an extremely dusty environment while the whole galaxy is still experiencing an ongoing starburst episode.

4.4.3. Ionized Gas Outflows

The analysis of Section 4.2 implies that W1904+4853 hosts an SMBH that is accreting at close to the Eddington limit. Although the powerful, yet heavily obscured AGN in W1904+4853 drives a detectable outflow, the SFR is higher than in MS galaxies of similar mass and redshift, making the host galaxy a starburst system. The central AGN in W1904+4853 has not significantly hindered the host galaxy's star formation. The rapid AGN accretion hidden within the dust cocoon in the actively star-forming galaxy indicates that W1904+4853 is indeed a system in the transitional stage of galaxy evolution.

Assuming the number density of Hot DOGs is comparable to that of the unobscured QSOs with similar luminosities (Assef et al. 2015), the number of low-z Hot DOGs can be estimated from QSO surveys if the same relation still holds for the low-z systems. In SDSS DR7, ¹² there are nine type 1 QSOs at low redshift (z < 0.5) with L_bol ≥ 10¹³ L_⊙ from 11,663 deg² at z ∼ 0.365–0.465 (Abazajian et al. 2009). The comoving volume within z ∼ 0.365–0.465 is 11.121 Gpc³ (Wright 2006), indicating the volume density of type 1 QSOs is ∼3 Gpc⁻³ in this redshift range. Therefore, we expect ∼30 hyperluminous QSOs/Hot DOGs at z ∼ 0.365–0.465 for the whole sky based on these assumptions. W1904+4853 could yield a good model to inspire a comprehensive search for low-z obscured AGN systems such as low-z Hot DOGs.