Extreme Nature of Four Blue-excess Dust-obscured Galaxies Revealed by Optical Spectroscopy

In Noboriguchi et al. (2019), 571 DOGs were selected by combining ∼105 deg² imaging data obtained from the HSC-SSP ¹⁸ (g, r, i, z, and y), VIKING (Z, Y, J, H, and Ks), and ALLWISE (W1, W2, W3, and W4) surveys. The eight BluDOGs were defined among the DOG sample with the smallest observed-frame optical slope (α_opt < 0.4, where α_opt is the observed-frame optical spectral index of the power-law fits to the HSC g-, r-, i-, z-, and y-band fluxes, ${f}_{\nu }\propto {\lambda }^{{\alpha }_{\mathrm{opt}}}$). We selected the four brightest BluDOGs (r_AB < 23: see Table 1) as the targets of our spectroscopic observations presented in this paper.

We executed the observations by using Faint Object Camera and Spectrograph (FOCAS; Kashikawa et al. 2002) installed on the Subaru Telescope of the National Astronomical Observatory of Japan, and FORS2 (Appenzeller et al. 1998) installed on the Very Large Telescope (VLT-UT1) of the European Southern Observatory (ESO). We present the observation log in Table 2.

2.2.1. Subaru FOCAS

2.2.2. VLT FORS2

2.2.3. Spectrophotometric Recalibration

Figure 1 shows the reduced spectra of the four BluDOGs. In order to measure the emission-line properties, we divide the emission lines into six groups as follows: (1) Lyα1216, N v λ1240, and Si ii λ1263, (2) Si iv λ1397 and O iv]λ1402, (3) He ii λ1640 and O iii]λ1663, and (4) Al iii λ1857, Si iii]λ1892, and C iii]λ1909, (5) C iv 1549, and (6) Mg ii. We fit the emission lines in each group simultaneously, with a linear continuum model subtracted from the observed spectrum. We adopt a single-Gaussian profile for Ly α, N v, Si ii, Si iv, O iv], O iii], Al iii, Si iii, and Mg ii. The C iii] of J1202 is fitted with a single-Gaussian profile, while those of J0907 and J1207 are fitted with a double-Gaussian profile. For the fit around the Si iv and O iv] of J1202, we added an additional Gaussian profile to reproduce the observed broad component. We fit C iv and He ii with double-Gaussian profiles, and denote the blue and red components with the suffixes of "_B" and "_R," respectively. Additionally, we fit the doublet absorption lines observed around the C iv emission lines of J1202 and J1443. The C iv absorption lines observed at λ_obs = 5916.8 and 5926.6 Å for J1202 and those at λ_obs = 6678.8 and 6689.9 Å for J1443 are fitted using the Voigt profile, respectively. The doublet absorption line ratio is fixed as 2:1 (Feibelman 1983). The best values and standard deviations for emission and absorption lines parameters are estimated by using scipy.optimize.curve_fit, ¹⁹ while we calculate the FWHM of emission lines with a double Gaussian by using a Monte Carlo method. For this Monte Carlo simulation, we created 10,000 mock spectra using the noise arrays of the observed spectra, and calculated the mean and standard deviation of the line properties. The results for emission lines are listed in Tables 3–6. For the absorption lines, the observed-frame EWs and redshifts of the doublet absorption lines on the J1202 C iv emission line are 47.7 ± 19.6 Å, 23.6 ± 9.7 Å, and 2.822, respectively, while the observed-frame EWs and redshift of the doublet absorption lines on J1443 C iv emission line are 14.0 ± 6.3 Å, 6.94 ± 3.14 Å, and 3.314, respectively. Therefore, the comoving distance between J1202 and its C iv absorber is 8.73 Mpc, while that between J1443 and its C iv absorber is 2.79 Mpc.

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The flux ratios of N v/Lyα and N v/C iv for J1443 are 3.9 and 1.8, respectively, whereas the values for the typical quasar (Vanden Berk et al. 2001) are 0.02 and 0.10. One possible reason for these unusual flux ratios in J1443 is the presence of absorption lines, which absorb most of the Lyα and the C iv fluxes around the peak. The unusual flux ratios cannot be explained by the dust reddening, given too small wavelength separations among the emission lines of Lyα, N v, and C iv.

Figure 2 shows the best-fit models to the C iv emission lines in the four BluDOGs. We adopt the C iv redshift taking C iv_R + C iv_B into account as the systemic redshift of the targets. The determined systemic redshifts of J0907, J1202, J1207, and J1443 are 2.258 ± 0.002, 2.830 ± 0.002, 2.511 ± 0.001, and 3.317 ± 0.006, respectively.

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Figure 1 suggests the very large EW of the emission lines. The average rest-frame EW (REW) of the C iv line of the four BluDOGs is 160 ± 33 Å, ∼7 times higher than the average of SDSS type 1 quasars (23.8 ± 0.1 Å; Vanden Berk et al. 2001). Here, we investigate the effect of the large REWs on the HSC g- and r-band magnitudes.

First, we calculate the expected magnitudes at the g and r bands from an extrapolation of the power-law fit to the longer-wavelength bands (i, z, y, Z, Y, J, H, Ks, W1, W2, W3, and W4). Figure 3 clearly shows that the observed g- and r-band magnitudes exceed the extrapolation of the power-law fit. The excesses of the g-band magnitudes for J0907, J1202, J1207, and J1443 are 1.27, 1.13, 1.48, and 0.88 mag, and those for the r-band excesses are 0.47, 0.44, 0.65, and 0.40 mag, respectively.

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Furthermore, we estimate the effect of the strong emission lines, based on their observed-frame EWs and the bandwidths (BWs) of the HSC g and r bands. The BWs of the HSC g and r bands are 1468 and 1508 Å (Kawanomoto et al. 2018), respectively. By taking all of the emission lines (Tables 3–6) covered by the HSC g band (4000–5500 Å) and r band (5500–7000 Å) into account, the total observed-frame EWs for J0907, J1202, J1207, and J1443 in the g band are 604, 258, 608, and 1380 Å, respectively, while those in the r band are 129, 836, 329, and 721 Å (Table 7). Note that the total observed-frame EWs in the g band are lower limits because our optical spectra do not cover the entire wavelength range of the band (Section 2.2) and thus some emission lines are not taken into account in the derived total observed-frame EWs. Especially Lyα, the strongest emission line in the rest-frame UV spectrum of typical AGNs, is not covered in our spectra of J0907, J1202, and J1207, thus, the total observed-frame EWs for these three objects are largely underestimated. ²⁰ Since the magnitude excess by the emission lines is given by ${\rm{\Delta }}\mathrm{mag}=2.5\mathrm{log}(1+\mathrm{EW}/\mathrm{BW})$, the estimated effects in the g band for J0907, J1202, J1207, and J1443 are 0.37, 0.18, 0.38, and 0.72 mag, respectively. Similarly, the estimated effects of emission lines to the r-band magnitudes are 0.09, 0.48, 0.21, and 0.42 mag, respectively (see Table 7 for a summary). We will discuss the implication of these estimates in Section 4.2.

We need to estimate dust extinction, E(B − V) of AGN radiation, and ${L}_{\mathrm{bol}}^{\mathrm{AGN}}$ to calculate the SMBH mass and Eddington ratio. Since Balmer decrement or other spectral measures of E(B − V) are not available, we perform a spectral energy distribution (SED) fitting to the broadband photometry to estimate the E(B − V) and ${L}_{\mathrm{bol}}^{\mathrm{AGN}}$. In this work, we utilize the new version of Code Investigating GAlaxy Emission (CIGALE; Burgarella et al. 2005; Noll et al. 2009; Boquien et al. 2019) called X-CIGALE (Yang et al. 2020), to perform the SED fit in a self-consistent framework by considering an energy balance between the UV/optical absorption and IR emission. X-CIGALE generates the best-fit model, including the stellar, AGN, and SF components that fit the photometric data in the rest-frame UV to far-infrared (FIR) bands. We utilize the Herschel Space Observatory (Pilbratt et al. 2010) Astrophysical Terahertz Large Area Survey (H-ATLAS; Eales et al. 2010; Bourne et al. 2016; Valiante et al. 2016) data observed with the Photodetector Array Camera and Spectrometer (PACS; Poglitsch et al. 2010) at 100 and 160 μm and with Spectral and Photometric Imaging REceiver (SPIRE; Griffin et al. 2010) at 250, 350, and 500 μm in the FIR, in addition to optical, NIR, and MIR data obtained by Subaru HSC, VISTA, and WISE. The 1σ limiting fluxes at 100, 160, 250, 350, and 500 μm are 44, 49, 7.4, 9.4, and 10.2 mJy, respectively (Valiante et al. 2016).

To search for the H-ATLAS counterpart of the four BluDOGs, we adopt a search radius of 10'' by following Toba et al. (2019) (and Toba et al. 2022). Accordingly, we found the counterparts of two BluDOGs (J1202 and J1207). The separation between the HSC position and the H-ATLAS counterpart position is 094 for J1202, and 97 for J1207. The relatively large separation in the latter case suggests the counterpart being a coincidental detection. There are two WISE sources around J1207 (Figure 4); one probably corresponds to J1207 itself (the angular separation between the HSC and WISE potions is 065) and another is located 19'' away in the northeast direction. The H-ATLAS source is located between these two WISE sources, and thus the FIR fluxes given in the H-ATLAS catalog are possibly attributed to the two WISE sources. Therefore, we regard the H-ATLAS fluxes of J1207 as the upper limit. For the remaining two BluDOGs (J0907 and J1443), we adopt 5σ upper limit fluxes.

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As for the optical–MIR photometric data, we utilize g, r, i, z, y (HSC-SSP), Z, Y, J, H, Ks (VIKING DR2), W1, W2, W3, and W4 (ALLWISE) bands (see Noboriguchi et al. 2019). Note that the signal-to-noise ratios (S/Ns) in these bands are more than 5, except for the W4 band with an S/N more than 3 because we adopted such an S/N cut in the selection of the DOGs (Noboriguchi et al. 2019). Since the g- and r-band photometries are significantly affected by the strong emission lines (see Figure 1 and Tables 3–6), which cannot be treated properly in X-CIGALE, we corrected for their contribution by referring to the estimates given in Table 7.

The models and parameters of X-CIGALE adopted in this work are summarized in Table 8. We assume a delayed star formation history (SFH; Ciesla et al. 2015) with the e-folding times of the main stellar population (τ_main) and late starburst population (τ_burst), mass fraction of the late burst population (f_burst), and age of the main stellar population (age_main) and the late burst (age_burst). As the stellar population, we assume the initial mass function of Chabrier (2003), solar metallicity, and a 10 Gyr separation between young and old stellar populations (Age_separation). The nebular emission model (Inoue 2011) is characterized by the ionization parameter (U), fractions of Lyman continuum photons escaping the galaxy (f_esc) and absorbed by dust (f_dust) and line width. We utilize a modified dust attenuation model presented by Boquien et al. (2019). The dust attenuation model for the continuum is taken from Calzetti et al. (2000) with the extension taken from Leitherer et al. (2002) between the Lyman break and 1500 Å. The emission lines are attenuated with a Milky Way extinction with R_V = 3.1 (Cardelli et al. 1989). We assumed E(B − V)_continuum = 0.44 E(B − V)_line, following Calzetti et al. (2000). The E(B − V)_line is varied between 3 and 10. We utilize the SKIRTOR model as the AGN emission model, which takes the geometric parameters of the AGN into account and also allows us to incorporate the effect of extinction by the polar dust. The parameters of the AGN model are the average edge-on optical depth at 9.7 μm (τ_9.7), the torus density parameters (p and q; Stalevski et al. 2016), the angle between the equatorial plane and the edge of the torus (oa), the ratio of the maximum to minimum radii of the dust torus (R_ratio), the fraction of total dust mass inside clumps (M_cl), the inclination (i), the AGN fraction (f_AGN), the extinction law, color excess ($E(B\,-V{)}_{\mathrm{polar}\ \mathrm{dust}}^{\mathrm{AGN}}$), dust temperature (${T}_{\mathrm{polar}\ \mathrm{dust}}^{\mathrm{AGN}}$), and emissivity index of the polar dust.

Table 8. Parameters Adopted in the X-CIGALE Fit

Parameter	Value
Delayed SFH (Ciesla et al. 2015)
τmain [Myr]	100, 250, 500
τburst [Myr]	10, 50
fburst	0.0, 0.5, 0.99
Agemain [Myr]	500, 800, 1000
Ageburst [Myr]	1, 5, 10
Single Stellar Population (Bruzual & Charlot 2003)
IMF	Chabrier (2003)
Metallicity	0.02
Ageseparation [Myr]	10
Nebular Emission (Inoue 2011)
$\mathrm{log}U$	−2.0
fesc	0.0
fdust	0.0
Line width [km s−1]	300.0
Dust Attenuation (Calzetti et al. 2000)
E(B − V)line	3, 4, 5, 6, 7, 8, 9, 10
fE(B−V)	0.44
λUV, bump [nm]	217.5
FWHMUV, bump [nm]	35.0
AUV, bump	0.0
δ	0.0
Extinction law of emission lines	the Milky Way
RV	3.1
Dust Emission (Dale et al. 2014)
AGN fraction	0.0
αIR, AGN	0.0625, 0.2500, 2.0000
AGN Model (Stalevski et al. 2016)
τ9.7	3, 7
p	1.0
q	1.0
oa [deg]	10, 20, 30, 40, 50, 60, 70, 80
Rratio	20
Mcl	0.97
i [deg]	0, 10, 20, 30, 40,
	50, 60, 70, 80, 90
fAGN	0.1, 0.3, 0.5, 0.7, 0.9
Extinction law of polar dust	Calzetti et al. (2000)
$E(B-V{)}_{\mathrm{polar}\ \mathrm{dust}}^{\mathrm{AGN}}$	0.1, 0.2, 0.3, 0.4, 0.5
${T}_{\mathrm{polar}\ \mathrm{dust}}^{\mathrm{AGN}}$ [K]	600, 700, 800, 900,
	1000, 1100, 1200, 1300, 1400
Emissivity of polar dust	1.6

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The best-fit SED models are shown in Figure 5. The reduced χ² of the fits are 1.38, 3.19, 0.93, and 1.74 for J0907, J1202, J1207, and J1443, respectively. The best-fit values and associated errors for $E(B-V{)}_{\mathrm{polar}\ \mathrm{dust}}^{\mathrm{AGN}}$ and ${L}_{\mathrm{bol}}^{\mathrm{AGN}}$ are estimated with the Bayesian-like strategy presented in Noll et al. (2009), and are reported in Table 9. On the other hand, we cannot quantitatively constrain the parameters of the host galaxies because the E(B − V) values are too large and the optical parts in their SEDs are dominated by their AGN emission (see Figure 5).

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Table 9. Physical Properties of the Four BluDOGs

	HSC J0907	HSC J1202	HSC J1207	HSC J1443
Redshift	2.258 ± 0.002	2.830 ± 0.002	2.511 ± 0.001	3.317 ± 0.006
$E(B-V{)}_{\mathrm{polar}\ \mathrm{dust}}^{\mathrm{AGN}}$	0.26 ± 0.05	0.33 ± 0.04	0.30 ± 0.02	0.20 ± 0.01
${L}_{\mathrm{bol}}^{\mathrm{AGN}}$/L⊙	(6.11 ± 0.95) × 1012	(6.11 ± 1.18) × 1013	(7.95 ± 1.47) × 1012	(2.52 ± 0.13) × 1013
MBH (C iv)/M⊙	(1.69 ± 0.17) × 108	(4.95 ± 0.30) × 108	(1.11 ± 0.08) × 108	(5.48 ± 0.86) × 108
MBH (Mg ii)/M⊙	(9.85 ± 1.80) × 107	⋯	⋯	⋯
λEdd (C iv)	1.10 ± 0.20	3.75 ± 0.76	2.19 ± 0.43	1.40 ± 0.23

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We have detected the C iv emission line for all four BluDOGs and the Mg ii emission line for J0907, both of which are widely used to calculate the SMBH mass of type 1 AGNs. Note that the systematic uncertainty is larger in the C iv-based SMBH mass than in the Mg ii-based SMBH mass, due to a powerful outflow sometimes seen in the C iv velocity profile (e.g., Baskin & Laor 2005; Netzer 2015; Coatman et al. 2017). We calculate the single-epoch mass of SMBHs with the C iv and Mg ii emission lines, following the calibrations given in Vestergaard & Peterson (2006) and Vestergaard & Osmer (2009), respectively:

$\begin{eqnarray}&&{M}_{\mathrm{BH}}={10}^{6.66}{\left(\displaystyle \frac{\mathrm{FWHM}({\rm{C}}\,{\rm\small{IV}})}{{10}^{3}\ \mathrm{km}\ {{\rm{s}}}^{-1}}\right)}^{2}{\left(\displaystyle \frac{\lambda {L}_{\lambda }(1350{\rm{\mathring{\rm{A}} }})}{{10}^{44}\ \mathrm{erg}\ {{\rm{s}}}^{-1}}\right)}^{0.53}{M}_{\odot },\end{eqnarray} \tag{ 1 }$

and

$\begin{eqnarray}&&{M}_{\mathrm{BH}}={10}^{6.86}{\left(\displaystyle \frac{\mathrm{FWHM}(\mathrm{Mg}\,{\rm\small{II}})}{{10}^{3}\ \mathrm{km}\ {{\rm{s}}}^{-1}}\right)}^{2}{\left(\displaystyle \frac{\lambda {L}_{\lambda }(3000{\rm{\mathring{\rm{A}} }})}{{10}^{44}\ \mathrm{erg}\ {{\rm{s}}}^{-1}}\right)}^{0.5}{M}_{\odot },\end{eqnarray} \tag{ 2 }$

where FWHM(C iv), FWHM(Mg ii), λ L_λ (1350Å), and λ L_λ (3000Å) are the FWHM of the C iv and Mg ii velocity profile, and the monochromatic luminosity at 1350 and 3000 Å, respectively. Note that we use the FWHM of C iv_R + C iv_B as the FWHM of the C iv. We cannot eliminate the possibility that the estimated SMBH masses are overestimated because the C iv profiles are affected by nucleus outflows (Section 4.1). For estimating the reddening-corrected monochromatic luminosity, we use the optical spectra presented in Section 3.1. We converted the spectra to the rest-frame, dereddened them with $E(B\,-V{)}_{\mathrm{polar}\ \mathrm{dust}}^{\mathrm{AGN}}$ derived in the SED fit, and masked out emission and absorption lines as well as pixels with negative values. Then, we fit a power-law continuum model to the spectra and estimate the monochromatic luminosities from the best fits. The estimated λ L_λ (1350) of J0907, J1202, J1207, and J1443 are (1.54 ±0.05) × 10⁴⁵, (9.64 ± 0.27) × 10⁴⁵, (3.06 ± 0.06) × 10⁴⁵, and (2.93 ± 0.03) × 10⁴⁵ erg s⁻¹, respectively. The λ L_λ (3000) of J0907 is estimated to be (1.45 ± 0.04) × 10⁴⁵ erg s⁻¹.

The resultant SMBH masses are summarized in Table 9. It should be noted that the C iv-based M_BH and Mg ii-based M_BH of J0907 is not consistent within the statistical error. This is probably attributable to a systematic error, especially in the C iv-based M_BH, known to be accompanied by a large systematic error (∼0.5 dex; see, e.g., Shen 2013). Hereafter, we use only the C iv-based M_BH, since it is measured in all the four BluDOGs.

We found that the redshifts of the four BluDOGs are in the range of 2.2 ≲ z_sp ≲ 3.3. They are systematically higher than the typical redshifts of DOGs (z_sp = 1.99 ± 0.45; Dey et al. 2008; Pope et al. 2008). One possible reason for this systematically high redshift is a selection effect related to the blue-excess criterion. When we select BluDOGs from the parent DOG sample, the g- and r-band magnitudes show an excess of the expected magnitudes estimated by the power-law extrapolation from the i band to the W4 band. Thus, we may select DOGs in a preferred redshift range where strong emission lines such as Lyα and C iv shift into the two bands (see Section 4.2 for more quantitative assessments). The reason for the underestimated photometric redshift (∼1; Noboriguchi et al. 2019) is the unusual emission lines with the large REW.

The detected emission lines have large velocity widths, ≳2000 km s⁻¹ in most cases. This suggests that the broad-line region (BLR) of the BluDOGs is not completely obscured; in other words, the observed BluDOGs are classified as type 1 AGNs. This is an unexpected result because their very red color between optical and MIR suggests the heavily obscured nature. One possible interpretation is that we are looking at a phase where the surrounding dust is just blown away by the nuclear activity (outflow, radiation pressure, or both), as discussed further in Section 4.3. It should be noted that the type 1 nature is seen not only in the presented BluDOGs but also in some other DOGs (e.g., Toba & Nagao 2016; Toba et al. 2017a; Zou et al. 2020). Systematic spectroscopic observations for the whole population of DOGs are required to study the nature of obscuration occurring in various populations of DOGs.

As shown in Figure 2, the velocity profile of the observed C iv lines shows a notable excess feature in the blue wing. Such an excess in the C iv velocity profile has been observed in other type 1 AGNs and interpreted as a result of powerful nuclear outflows (e.g., Baskin & Laor 2005; Netzer 2015; Coatman et al. 2017). To evaluate quantitatively how the nuclear outflow in BluDOGs is strong compared to ordinary AGNs, we examine the asymmetry parameter (α_β ) defined by De Robertis (1985) as

$\begin{eqnarray}&&{\alpha }_{\beta }=\displaystyle \frac{{\lambda }_{c}(3/4)-{\lambda }_{c}(1/4)}{{\rm{\Delta }}\lambda (1/2)},\end{eqnarray} \tag{ 3 }$

where λ_c (h) and Δλ(1/2) are the central wavelengths at which the flux falls to the h time of the peak flux and FWHM of the broad profile, respectively. The positive and negative values of α_β express the blue and red excesses, respectively. The derived values of α_β for J0907, J1202, J1207, and J1443 are 0.216, 0.102, 0.246, and 0.051, respectively. As a reference, the C iv velocity profile in the composite spectrum of SDSS type 1 quasars given by Vanden Berk et al. (2001) shows α_β = 0.110. Thus, J0907 and J1207 may possess a significant nuclear outflow that is more powerful than typical quasars.

In order to compare α_β of the BluDOG with that of another dusty AGN population, we fitted the C iv profile of 97 core ERQs (ERQs with REW(C iv) >100 Å) in Hamann et al. (2017) and measured α_β by adopting a single or double-Gaussian profile. The core ERQ sample consists of 80 objects without broad absorption lines (BALs) and 17 objects with BALs, and we investigate the statistics of α_β for the two subsamples separately because the BAL feature can affect the C iv line profile. Here, we exclude J1443 from the BluDOG sample when comparing the α_β index because its velocity profile is largely affected by narrow absorption lines (hereafter the limited-BluDOG sample to infer the three BluDOGs; i.e., J0907, J1202, and J1207). Figure 6 shows the cumulative fraction of α_β for the limited BluDOGs, core ERQs without BALs, and core ERQs with BALs. The averaged values of the limited BluDOGs, core ERQs without BALs, and core ERQs with BALs are 0.15 ± 0.08, 0.02 ± 0.13, and 0.01 ± 0.09, respectively. We performed the Kolmogorov–Smirnov test (K-S test) to examine the statistical significance of the difference in α_β among the samples. The p-values of the limited-BluDOG-core ERQs without BALs, and limited-BluDOG-core ERQs with BALs are 0.0178 and 0.0175, respectively. Thus, we conclude that the distributions of α_β of the limited BluDOGs and core ERQs with/without BALs are marginally different with >2σ significance. This suggests that the BluDOGs show a nuclear outflow that is possibly more powerful than the nuclear outflow in core ERQs with/without BALs.

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We also focus on the kurtosis index (kt₈₀) defined as follows (see Hamann et al. 2017 for details): kt₈₀ = Δv(80%) /Δv(20%), where Δv(x%) is the velocity width at x% of the peak flux height. In addition to α_β , this kt₈₀ index is useful to characterize the C iv wing (a more prominent blue wing results in a smaller kt₈₀). By using the best-fit double-Gaussian profile of the BluDOGs, kt₈₀ of J0907, J1202, J1207, and J1443 are 0.276, 0.313, 0.252, and 0.440, respectively. Again we exclude J1443 from the BluDOG sample when comparing the kt₈₀ index with the discussion of the α_β index. For comparison, the kt₈₀ of a single Gaussian is $\sqrt{1-\tfrac{2\mathrm{ln}(2)}{\mathrm{ln}(5)}}$ (∼0.37), whereas most quasars have kt₈₀ ∼ 0.15–0.30 (see Figure 7 in Hamann et al. 2017). The limited BluDOGs, core ERQs without BALs, and core ERQs with BALs show kt₈₀ = 0.28 ± 0.03, 0.33 ± 0.06, and 0.34 ± 0.05, respectively (see also Figure 7). Note that the C iv profile of the 41 core ERQs without BALs and seven core ERQs with BALs is fitted by a single Gaussian, which is the reason why many objects have kt₈₀ ∼ 0.37 as shown in Figure 7. The C iv velocity profiles of core ERQs with/without BALs are roughly consistent with the Gaussian without a blue wing. However, the kt₈₀ index of the limited BluDOGs is less than $\sqrt{1-\tfrac{2\mathrm{ln}(2)}{\mathrm{ln}(5)}}$, suggesting that their C iv line profile has a wing. We performed the K-S test to examine the statistical significance of the difference in kt₈₀ among the samples. The p-values of the limited-BluDOGs-core ERQs without BALs, and limited-BluDOGs-core ERQs with BALs are 0.0637 and 0.0175, respectively. Therefore, we conclude that the distributions of kt₈₀ between the samples of the limited BluDOGs and core ERQs with/without the BAL feature are marginally different with >2σ significance.

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It has been reported that AGNs with a high Eddington ratio tend to show a Lorentzian-line velocity profile in BLR lines (e.g., Moran et al. 1996; Véron-Cetty et al. 2001; Collin et al. 2006; Zamfir et al. 2010). Therefore, the small kt₈₀ value of BluDOGs can be caused by the contribution of extended Lorentzian wings instead of the asymmetric blue wing. For a symmetric Lorentzian profile, kt₈₀ ∼ 1/16 (much smaller than a Gaussian profile, kt₈₀ ∼ 0.37) and α_β = 0 are expected. However, the BluDOGs are inconsistent with this expectation (Figure 8). Figure 8 also shows that the BluDOGs follow the trend made by core ERQs with/without BALs in the kt₈₀–α_β plane, while a systematic deviation of BluDOGs toward (α_β , kt₈₀) = (0, 0) is expected if a Lorentzian component significantly contributes to the C iv line of BluDOGs. Thus, we conclude that extended Lorentzian wings do not affect the C iv line profile of BluDOGs, but the small kt₈₀ of BluDOGs is caused by the asymmetric blue excess due to the stronger nuclear outflow than that of ERQs.

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As we summarized in Table 7, the blue excess in J1443 can almost be explained by the contribution of the strong emission lines. This is also the case for J1202 by taking into account the additional contribution of unobserved Lyα to the g band. On the other hand, the blue excess of the remaining two BluDOGs cannot be explained only by the contribution of BLR emission lines. Figure 3 strongly suggests that a part of the excess flux comes from the continuum emission, which deviates at ≲7000 Å from the extrapolation of the power-law fit. These results demonstrate the complexity and diversity of BluDOGs; systematic exploration of a larger sample is required to statistically understand the origin of the blue excess.

Not only REW(C iv), but the REW of other BLR emission lines are also systematically larger than observed in typical type 1 quasars (see Tables 3–6, Figure 9, and also Table 2 in Vanden Berk et al. 2001). Such a trend may be explained if the observed BluDOGs have lower UV luminosity than typical quasars owing to the Baldwin effect (Baldwin 1977; Kinney et al. 1990; Baskin & Laor 2004), i.e., the negative correlation between the REWs and the continuum luminosities of quasars. Figure 10 shows the four BluDOGs in the C iv REW versus λ L_λ (1350 Å) diagram. Note that the REW of J1443 (114 ± 24 Å) is somewhat smaller than that of the remaining three BluDOGs (148 ± 12, 203 ± 10 and 173 ± 9 Å for J0907, J1202, and J1207, respectively; see Tables 3–6). This is partly because of an underestimation of the C iv flux caused by the absorption features. The figure also shows SDSS type 1 quasars with reliable measurement of C iv REW (EWCIV/e_EWCIV > 5) and without BALs (BAL < 1) taken from Shen et al. (2011). Since the Baldwin effect does not significantly depend on redshift (e.g., Dietrich et al. 2002; Croom et al. 2002; Niida et al. 2016), we do not adopt any redshift criterion to select the SDSS quasars so that a wide luminosity range is covered. We also use another comparison sample taken from the WISE/SDSS selected hyper-luminous quasar sample (WISSH; Bischetti et al. 2017; Vietri et al. 2018), ²¹ in order to add objects at the high-luminosity end.

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Figure 10 clearly shows that the C iv REWs of BluDOGs are larger than the comparison samples at a given UV luminosity. The excess REW over the average relation of the Baldwin effect (shown with a green solid line in Figure 10) for J0907, J1202, J1207, and J1443 are 0.29, 0.66, 0.44, and 0.26 dex, respectively. This excess is larger than the scatter of the comparison samples (see red plots in Figure 10). Therefore, the large REW seen in the BluDOGs is not due to the Baldwin effect.

The averages and standard deviations of REW(C iv) for core ERQs and ERQ-like objects are 178 ± 74 and 86 ± 45 Å, respectively (Hamann et al. 2017). The distributions of REW(C iv) and (i − W3)_AB color for BluDOGs are consistent with these of core ERQs, although most core ERQs and ERQ-like objects do not show a blue-wing profile in C iv (Section 4.1). Hamann et al. (2017) proposed a scenario in which the large REW of ERQs is possibly due to the spatially extended geometry of BLRs caused by the powerful nuclear outflow. If the obscuration is heavier for the accretion disk than for the BLRs, which have extended geometry, the continuum emission is more heavily extinct than the BLR emission lines and thus the observed-frame EW becomes larger. Such a scenario may also apply to BluDOGs. Unfortunately, it is not observationally feasible to confirm this idea by resolving the spatial structure of BLRs in ERQs or BluDOGs due to the required angular resolution, even with JWST or existing ground-based interferometers. Without spatially resolving them, a possible approach is the velocity-resolved reverberation mapping of the geometry and kinematics of BLR clouds (e.g., Horne et al. 2004; Denney et al. 2009; Li et al. 2013; Kollatschny et al. 2014; Pancoast et al. 2014).

To understand the nature of BluDOGs, especially in the context of the major-merger scenario for the quasar evolution, we compare the SMBH accretion of the four BluDOGs with other AGN populations. Figure 11 presents a diagram of L_bol versus the SMBH mass. As in Section 4.2, SDSS quasars (Shen et al. 2011) and WISSH quasars (Vietri et al. 2018) are used as comparison samples. For the SDSS quasars, we select only non-BAL quasars (BAL < 1) with the uncertainty of L_bol and M_BH less than 0.5 dex (e_logBHCV < 0.5&e_logLbol < 0.5), and adopt the C iv-based SMBH mass for a fair comparison with those of the BluDOGs. We also plot samples of 28 ERQs (Perrotta et al. 2019), five Hot DOGs (Wu et al. 2018), two power-law DOGs (Melbourne et al. 2011), and one Compton-thick (CT) DOG (Toba et al. 2020). Hot DOGs are DOGs with a special color of WISE (very faint in the 3.4 and 4.5 μm bands, but bright in the longer bands; Eisenhardt et al. 2012; Wu et al. 2012), while power-law DOGs are DOGs with a featureless power-law SED from the optical to MIR (e.g., Dey et al. 2008; Bussmann et al. 2012; Toba et al. 2015; Noboriguchi et al. 2019). The CT DOG was identified by the Nuclear Spectroscopic Telescope Array (Harrison et al. 2013) from the SDSS-WISE DOG sample. All but the CT DOGs have spectroscopic redshifts. The SMBH masses of the ERQs and the WISSH quasars are estimated from Hβ, while those of the Hot DOGs and the DOGs are estimated from Hα. The SMBH mass of the CT DOG was estimated by Toba et al. (2020) from the stellar mass by using an empirical relation between the stellar mass and SMBH mass (Kormendy & Ho 2013). Since Perrotta et al. (2019) and Melbourne et al. (2011) did not correct the absorption of dust, the M_BH of ERQs and DOGs are lower limits.

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Figure 11 shows that the four BluDOGs are more luminous than the other AGN populations at a given SMBH mass, or equivalently, they have lower-mass SMBHs than the other AGN populations at a given bolometric luminosity. This suggests that the SMBH growth in the BluDOGs is more rapid than AGNs in comparison samples. Indeed, the Eddington ratios (λ_Edd) of J0907, J1202, J1207, and J1443 are 1.10 ±0.20, 3.89 ± 0.78, 2.19 ± 0.44, and 1.40 ± 0.23, respectively (Table 9), with the average value of 2.26. In other words, the SMBHs in the BluDOGs are now in the stage of the Eddington-limit or super-Eddington accretion. Even if the intrinsic SMBH masses are lower than those estimated (Section 3.4), the conclusion of this study remains qualitatively unchanged. The higher Eddington ratios compared to other populations suggest that the SMBHs in BluDOGs are in the most rapidly evolving phase during the entire evolutionary history of SMBHs. In the gas-rich major-merger scenario of Hopkins et al. (2008), the peak of the AGN activity (i.e., the mass growth of SMBHs) corresponds to the transition phase from the optically thick to optically thin quasars, where the surrounding dust is blown out by the powerful AGN activity. Note that optically thick quasars in the major-merger scenario should be recognized as type 2 quasars in optical (the BLR cannot be observed due to the heavy dust reddening). Since optically thick quasars in the final stage of the evolution can be recognized as both type 1 and type 2, due to the orientation effect toward the dusty torus, the observed type 1 nature suggests the object is not in the early (optically thick) stage in the major-merger evolutionary scenario. Preferentially in AGNs with high λ_Edd, a blue-wing feature tends to be observed (e.g., Aoki et al. 2005; Komossa et al. 2008). The observed characteristics of the BluDOGs such as the type 1 nature and the blue-wing feature of the C iv velocity profile are consistent with the picture that BluDOGs are in such a peak stage of the SMBH evolution.

To discuss the evolutionary relation among populations of dusty galaxies (BluDOGs, core ERQs, and Hot DOGs), we focus on E(B − V) and kt₈₀. E(B − V) for BluDOGs, core ERQs (Hamann et al. 2017), and Hot DOGs (Wu et al. 2018) are 0.273 ± 0.049, 0.242 ± 0.127, and 4.781 ± 1.986, respectively. The E(B − V) of the Hot DOGs is significantly larger than that of the BluDOG and core ERQ samples, suggesting the Hot DOGs are thought to be in a heavily obscured phase. Since the kt₈₀ of BluDOGs is smaller than that of core ERQs (Section 4.1), and the kt₈₀ of MIR-detected quasars is close to that of BluDOGs (Figure 1 of Monadi & Bird 2022), the BluDOG phase is thought to be close to the optically thin quasar phase. Therefore, it is suggested that the evolutionary path of various AGN populations is "Hot DOGs—core ERQs—BluDOGs—optically thin quasars."

For AGNs in general, the mass accretion efficiency (η) is defined as the following:

$\begin{eqnarray}&&\eta =\displaystyle \frac{{L}_{\mathrm{bol}}}{\dot{M}{c}^{2}},\end{eqnarray} \tag{ 4 }$

where $\dot{M}$ is the mass accretion rate. By multiplying the $\dot{M}$ and lifetime of BluDOGs (t_life), we can roughly estimate the accreted mass (M_acc) in the BluDOG phase. Bian & Zhao (2003) estimated $\mathrm{log}\eta =-1.61$ of Seyfert 1 galaxies and Palomar–Green quasars by assuming that the geometrically thin and optically thick standard α-prescription accretion disk model (Shakura & Sunyaev 1973). By assuming $\mathrm{log}\eta =-1.61$ and t_life = 1 Myr (Noboriguchi et al. 2019), the estimated M_acc of J0907, J1202, J1207, and J1443 are about 1.68 × 10⁷, 1.68 × 10⁸, 2.19 × 10⁷, and 6.93 × 10⁷ M_⊙. The SMBH masses reached when the SMBH masses of the BluDOGs are increased by the observed mass accretion rate during the typical lifetime of BluDOGs (${M}_{\mathrm{BH}}^{+}={M}_{\mathrm{BH}}+{M}_{\mathrm{acc}}$) of J0907, J1202, J1207, and J1443 are 1.86 × 10⁸, 6.63 × 10⁸, 1.32 × 10⁸, and 6.17 × 10⁸ M_⊙, respectively. Therefore, the SMBH mass of BluDOGs increases by ∼20% during the short BluDOG phase, suggesting that BluDOGs are actually in a rapidly glowing phase.

Figure 12 shows the Eddington ratios of various populations of AGNs as a function of redshift. The excess of λ_Edd of the four BluDOGs is more significant than the scatter of the λ_Edd distribution, suggesting that BluDOGs are a special class of AGNs that harbor SMBHs in the most actively evolving phase. Then, why is such a class of AGNs only found in a limited redshift range, 2.2 < z_sp < 3.3? A possible reason comes from their selection criteria, as briefly mentioned in Section 4.1. Since the BluDOGs are selected by the blue excesses, which are largely caused by the contribution of strong BLR emission lines, the resultant redshift distribution would be biased such that the blue bands contain strong emission lines. It is also not clear whether the entire population of DOGs has systematically larger λ_Edd than ordinary type 1 quasars, due to the paucity of spectroscopic data. In order to reveal the total picture of the dust-enshrouded evolution of SMBHs, more systematic spectroscopic observations for various populations of BluDOGs and DOGs are needed.

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