# Extreme nature of four blue-excess dust-obscured galaxies revealed by
optical spectroscopy

Akatoki Noboriguchi School of General Education, Shinshu University, 3-1-1
Asahi, Matsumoto, Nagano 390-8621, Japan  Frontier Research Institute for
Interdisciplinary Sciences, Tohoku University, 6-3 Aramaki, Aoba-ku, Sendai,
Miyagi 980-8578, Japan  Graduate School of Science and Engineering, Ehime
University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan  Tohru Nagao
Research Center for Space and Cosmic Evolution, Ehime University, 2-5 Bunkyo-
cho, Matsuyama, Ehime 790-8577, Japan  Yoshiki Toba National Astronomical
Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Department
of Astronomy, Kyoto University, Kitashirakawa-Oiwake-cho, Kyoto 606-8502,
Japan  Academia Sinica Institute of Astronomy and Astrophysics, 11F of
Astronomy-Mathematics Building, AS/NTU, No.1, Section 4, Roosevelt Road,
Taipei 10617, Taiwan  Research Center for Space and Cosmic Evolution, Ehime
University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan  Kohei Ichikawa
Frontier Research Institute for Interdisciplinary Sciences, Tohoku University,
6-3 Aramaki, Aoba-ku, Sendai, Miyagi 980-8578, Japan  Masaru Kajisawa Graduate
School of Science and Engineering, Ehime University, 2-5 Bunkyo-cho,
Matsuyama, Ehime 790-8577, Japan  Nanako Kato  Graduate School of Science and
Engineering, Ehime University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577,
Japan  Toshihiro Kawaguchi Department of Economics, Management and Information
Science Onomichi City University, Hisayamada 1600-2, Onomichi, Hiroshima
722-8506, Japan  Hideo Matsuhara  Institute of Space and Astronautical
Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo-ku,
Sagamihara, Kanagawa 252-5210, Japan  Department of Space and Astronautical
Science, The Graduate University for Advanced Studies, SOKENDAI, 3-1-1
Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan  Yoshiki Matsuoka
Research Center for Space and Cosmic Evolution, Ehime University, 2-5 Bunkyo-
cho, Matsuyama, Ehime 790-8577, Japan  Kyoko Onishi Department of Space, Earth
and Environment, Chalmers University of Technology, Onsala Observatory, SE-439
92 Onsala, Sweden  Masafusa Onoue Kavli Institute for the Physics and
Mathematics of the Universe (Kavli IPMU, WPI), The University of Tokyo, 5-1-5
Kashiwanoha, Kashiwa, Chiba 277-8583, Japan  Kavli Institute for Astronomy and
Astrophysics, Peking University, Beijing 100871, China  Max-Planck-Institut
für Astronomie, Königstuhl 17, D-69117, Heidelberg, Germany  Nozomu Tamada
Graduate School of Science and Engineering, Ehime University, 2-5 Bunkyo-cho,
Matsuyama, Ehime 790-8577, Japan  Koki Terao Subaru Telescope, National
Astronomical Observatory of Japan, 650 North A’ohoku Place, Hilo, HI 96720,
USA  Astronomical Institute, Tohoku University, 6-3 Aramaki, Aoba-ku, Sendai,
Miyagi 980-8578, Japan  Yuichi Terashima Graduate School of Science and
Engineering, Ehime University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577,
Japan  Research Center for Space and Cosmic Evolution, Ehime University, 2-5
Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan  Yoshihiro Ueda Department of
Astronomy, Kyoto University, Kitashirakawa-Oiwake-cho, Kyoto 606-8502, Japan
Takuji Yamashita National Astronomical Observatory of Japan, 2-21-1 Osawa,
Mitaka, Tokyo 181-8588, Japan

###### Abstract

We report optical spectroscopic observations of four blue-excess dust-obscured
galaxies (BluDOGs) identified by Subaru Hyper Suprime-Cam. BluDOGs are a sub-
class of dust-obscured galaxies (DOGs, defined with the extremely red color
$(i-[22])_{\rm AB}\geq 7.0$; Toba et al. 2015), showing a significant flux
excess in the optical $g$\- and $r$-bands over the power-law fits to the
fluxes at the longer wavelengths. Noboriguchi et al. (2019) has suggested that
BluDOGs may correspond to the blowing-out phase involved in a gas-rich major
merger scenario. However the detailed properties of BluDOGs are not understood
because of the lack of spectroscopic information. In this work, we carry out
deep optical spectroscopic observations of four BluDOGs using Subaru/FOCAS and
VLT/FORS2. The obtained spectra show broad emission lines with extremely large
equivalent widths, and a blue wing in the C iv line profile. The redshifts are
between 2.2 and 3.3. The averaged rest-frame equivalent widths of the C iv
lines are $160\pm 33$ Å, $\sim$7 times higher than the average of a typical
type-1 quasar. The FWHMs of their velocity profiles are between 1990 and 4470
${\rm km\ s^{-1}}$, and their asymmetric parameters are 0.05 and 0.25. Such
strong C iv lines significantly affect the broad-band magnitudes, which is
partly the origin of the blue excess seen in the spectral energy distribution
of BluDOGs. Their estimated supermassive black hole masses are $1.1\times
10^{8}<M_{\rm BH}/M_{\odot}<5.5\times 10^{8}$. The inferred Eddington ratios
of the BluDOGs are higher than 1 ($1.1<\lambda_{\rm Edd}<3.8$), suggesting
that the BluDOGs are in a rapidly evolving phase of supermassive black holes.

galaxies: active — galaxies: evolution — infrared: galaxies — quasars: general
— techniques: spectroscopic

††software: Astropy, Astro-SCRAPPY, X-CIGALE, Numpy,
Scipy.optimaize.curve_fit, Recipe flexible execution workbench
(Reflex)††facilities: Subaru (FOCAS, HSC), VLT (FORS2), VISTA, WISE, and
Herschel (PACS, SPIRE)

##  1 Introduction

In the last two decades, observations of low-redshift galaxies have revealed
tight correlations between the mass of supermassive black holes (SMBHs) and
the host galaxy properties such as bulge mass (e.g., Magorrian et al. 1998;
Ferrarese & Merritt 2000; Gebhardt et al. 2000; Tremaine et al. 2002; Marconi
& Hunt 2003; Kormendy & Ho 2013; Ding et al. 2020). Such scaling relations
suggest the so-called co-evolution between galaxies and SMBHs. It has been
argued that a major merger of gas-rich galaxies triggers active star-forming
activity and subsequent mass accretion onto SMBHs (e.g., Sanders et al. 1988;
Hopkins et al. 2008; Treister et al. 2012; Goulding et al. 2018). In this
scenario, the merging two galaxies first evolve into a dusty star-forming (SF)
galaxy. Then it evolves into a dusty active galactic nucleus (AGN) as gas
accretion to the nuclear region triggers the activity of SMBHs. Finally, a
dusty AGN evolves into an optically-thin quasar after the surrounding dust is
blown out by the powerful AGN outflow. The most active period of such SF and
AGN activity is generally heavily obscured by dust, which prevents us from
investigating these phases observationally.

By combining optical, near-infrared (NIR), and mid-infrared (MIR) catalogs
obtained from the Subaru Hyper Suprime-Cam (HSC; Miyazaki et al. 2018)-Subaru
Strategic Program (SSP; Aihara et al. 2018), the VISTA Kilo-degree Infrared
Galaxy survey (VIKING; Arnaboldi et al. 2007), and the Wide-field Infrared
Survey Explorer (WISE; Wright et al. 2010) all-sky survey (ALLWISE; Cutri
2014), Toba et al. (2015, 2017b) and Noboriguchi et al. (2019) selected dusty
SF galaxies and/or powerful AGNs as dust-obscured galaxies (DOGs; Dey et al.
2008; Fiore et al. 2008; Bussmann et al. 2009; Desai et al. 2009; Bussmann et
al. 2011). DOGs are defined with a very red optical-MIR color ($(i-[22])_{\rm
AB}\geq 7.0$; Toba et al. 2015). DOGs represent a transition phase from a gas-
rich major merger to an optically-thin quasar in the gas-rich major merger
scenario (Dey et al. 2008), suggesting that some DOGs are expected to have
buried AGNs. Recently, eight blue-excess DOGs (BluDOGs; Noboriguchi et al.
2019) were discovered from the HSC-selected DOGs based on their optical
spectral slopes (i.e., $\alpha_{\rm opt}<0.4$, where $\alpha_{\rm opt}$ is the
observed-frame optical spectral index for the HSC $g$-, $r$-, $i$-, $z$-, and
$y$-bands in the power-law fit, $f_{\nu}\propto\lambda^{\alpha_{\rm opt}}$),
and are a very rare population (eight BluDOGs out of 571 HSC-selected DOGs).
Noboriguchi et al. (2019) suggested that the BluDOGs with such blue excess may
be in the blowing-out phase involved in the gas-rich major merger scenario.
However, the detailed properties of BluDOGs are not well understood because of
the lack of spectroscopic information. Spectroscopic observations will give us
accurate redshifts, and thus reliable AGN luminosities as a measure of the
accretion rates, as well as the SMBH masses.

Another interesting population that may represent the transition phase between
optically-thick AGNs and optically-thin quasars is extremely red quasars
(ERQs; e.g., Ross et al. 2015; Hamann et al. 2017; Perrotta et al. 2019;
Villar Martín et al. 2020). ERQs were identified by combining the optical
photometric data of Sloan Digital Sky Survey (SDSS; York et al. 2000), the
optical spectroscopic data from SDSS-III (Eisenstein et al. 2011) Baryon
Oscillation Spectroscopic Survey (BOSS; Dawson et al. 2013), and the MIR
photometric data of WISE catalog. They are also defined with very red optical
to MIR colors ($F_{\nu}(24{\rm\mu m})/F_{\nu}(R)\geq 1000$), and their spectra
show broad emission lines with extremely large equivalent widths (Ross et al.
2015; Hamann et al. 2017). Hamann et al. (2017) refined the definition of ERQs
as $(i-[12])_{\rm AB}>4.6$111All of the BluDOGs also satisfy the criterion of
the ERQ (see Table 1)., and reported notable blue-wing features in their C iv
profiles, which suggests the presence of powerful outflow. However, the ERQ
sample is limited to optically bright objects since their selection requires
SDSS spectra. Detailed studies of optically-faint populations in the
transition phase between the optically-thick and optically-thin stages are
required to understand the whole scenario of the merger-driven evolution of
SMBHs. Therefore, it is important to execute the spectroscopic observations
for BluDOGs and to research their spectroscopic properties.

In this work, we present the results of spectroscopic observations and
subsequent analyses of four BluDOGs. This paper is organized as follows. We
describe sample selection of our targets and observations in Section 2. In
Section 3, we present properties of the detected emission lines, the estimated
dust extinctions, bolometric luminosities of an AGN ($L^{\rm AGN}_{\rm bol}$),
and SMBH masses ($M_{\rm BH}$). The discussion on the large equivalent widths
of the C iv emission, their SMBH mass, and Eddington ratios is given in
Section 4. Then we give a brief summary in Section 5. Throughout this paper,
the adopted cosmology is a flat universe with $H_{0}=70\ {\rm km\ s^{-1}\
Mpc^{-1}}$, $\Omega_{M}=0.3$, and $\Omega_{\Lambda}=0.7$. Unless otherwise
noted, all magnitudes refer to the AB system.

Table 1: Photometric data of BluDOGs Name | HSC $r$-band | HSC $i$-band | WISE $W3$-band | WISE $W4$-band
---|---|---|---|---
| [AB mag] | [AB mag] | [AB mag] | [AB mag]
HSC J090705.64$+$020955.8 (HSC J0907) | 22.56$\pm$0.01 | 22.59$\pm$0.01 | 16.06$\pm$0.13 | 14.89$\pm$0.34
HSC J120200.84$-$011846.4 (HSC J1202) | 20.92$\pm$0.00 | 20.87$\pm$0.00 | 14.47$\pm$0.04 | 13.46$\pm$0.10
HSC J120728.71$-$005808.4 (HSC J1207) | 22.12$\pm$0.01 | 22.31$\pm$0.01 | 16.28$\pm$0.16 | 15.01$\pm$0.36
HSC J141435.21$+$003547.4 | 23.32$\pm$0.02 | 23.11$\pm$0.02 | 17.24aaThe magnitude is a 95% confidence upper limit.
https://wise2.ipac.caltech.edu/docs/release/allwise/expsup/sec2_1a.html | 15.33$\pm$0.33
HSC J143727.40$-$011726.5 | 23.17$\pm$0.02 | 23.10$\pm$0.01 | 16.94$\pm$0.23 | 15.37$\pm$0.31
HSC J144333.84$-$000830.3 (HSC J1443) | 22.34$\pm$0.01 | 22.24$\pm$0.01 | 16.14$\pm$0.10 | 15.04$\pm$0.23
HSC J144813.65$+$002244.3 | 23.55$\pm$0.02 | 23.43$\pm$0.02 | 16.83$\pm$0.16 | 15.37$\pm$0.34
HSC J144900.84$+$002350.2 | 23.95$\pm$0.03 | 23.74$\pm$0.02 | 17.15$\pm$0.22 | 15.47$\pm$0.36
Table 2: Observation log Name | Exp. time [s] | Date | Standard star | Instrument
---|---|---|---|---
HSC J0907 | 900$\times$2 | 2019 October 8 | G191-B2B | FOCAS (Subaru)
| 600$\times$1 |  |  |
HSC J1202 | 900$\times$6 | 2019 February 27 | LTT 6248 | FORS2 (VLT)
HSC J1207 | 900$\times$12 | 2019 March 1, 2, 6 | LTT 4816 | FORS2 (VLT)
HSC J1443 | 900$\times$12 | 2019 March 7, 8 | LTT 4816, EG 274 | FORS2 (VLT)

##  2 Sample and the data

###  2.1 Sample selection

In Noboriguchi et al. (2019), 571 DOGs were selected by combining $\sim$105
deg2 imaging data obtained from the survey of HSC-SSP222 We utilize the
photometric data of S16A HSC-SSP, which was released internally within the HSC
survey team and is based on data obtained from 2014 March to 2016 April. ($g$,
$r$, $i$, $z$, and $y$), VIKING ($Z$, $Y$, $J$, $H$, and $Ks$), and ALLWISE
($W1$, $W2$, $W3$, and $W4$). The eight BluDOGs were defined among the DOG
sample with the smallest observed-frame optical slope ($\alpha_{\rm
opt}\textless 0.4$, where $\alpha_{\rm opt}$ is the observed-frame optical
spectral index of the power-law fits to the HSC $g$, $r$, $i$, $z$, and
$y$-band fluxes, $f_{\nu}\propto\lambda^{\alpha_{\rm opt}}$). We selected the
four brightest BluDOGs ($r_{\rm AB}<23$: see Table 1) as the targets of our
spectroscopic observations presented in this paper.

###  2.2 Spectroscopic observations and data reductions

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

####  2.2.1 Subaru FOCAS

By using FOCAS, we observed HSC J090705.64$+$020955.8 (hereafter J0907) on
October 8th in 2019, with airmass $\sim$1.76 and seeing $\sim$0.5 arcsec. We
used the 300B grism and the SY47 filter to cover $\lambda_{\rm
obs}\sim$4700–9200 Å, with the resultant spectral resolution of $R\sim$800 for
the used 0″.8-width slit. To reduce the obtained data, we performed bias
correction, flat fielding with dome flat, removal of cosmic-rays, spectral
extraction, sky subtraction, wavelength calibration, and flux calibration with
a standard star (G191-B2B) using the Python packages of `Astropy` and `Numpy`.
For removing cosmic-rays, we utilized `Astro-SCRAPPY` (McCully & Tewes 2019).
`Astro-SCRAPPY` is based on the algorithm of `L.A.Cosmic`, which removes
cosmic-rays based on a variation of Laplacian edge detection (van Dokkum
2001). The final spectrum is an inverse-variance weighted mean of the
individual shots, corrected for the Galactic extinction (Schlegel et al.
1998).

####  2.2.2 VLT FORS2

By using FORS2, we observed HSC J120200.84$-$011846.4, HSC
J120728.71$-$005808.4, and HSC J144333.84$-$000830.3 (hereafter J1202, J1207,
and J1443, respectively) between February 27th and March 8th, 2019. We used
the GRISM_600RI$+19$ and the GG435 filter to cover $\lambda_{\rm
obs}\sim$5200–8000 Å, which results in the spectral resolution of $R\sim$1500
with 0″.7-width slit. The typical airmasses of the observations for J1202,
J1207, and J1443 were 1.17, 1.24, and 1.12, and the typical seeing sizes were
$\sim$1.0, 0.5, and 0.5 arcsec, respectively. For the data reduction, we
utilized the `Recipe flexible execution workbench` (`Reflex`; Freudling et al.
2013) software. `Reflex` performed bias correction, flat fielding with dome
flat, sky subtraction, removing cosmic-rays, spectral extraction, wavelength
calibration, and flux calibration with a standard star (LTT 6248, LTT 4816,
and EG 274). The final spectrum of each target is the inverse-variance
weighted mean of the individual shots, corrected for the Galactic extinction.

Figure 1: The reduced spectra of the BluDOGs. The spectra are for J0907,
J1202, J1207 and J1443 from the top to bottom. Detected lines are marked by
arrows and labels.

####  2.2.3 Spectrophotometric re-calibration

We re-calibrated the reduced spectra to match the HSC photometry, in order to
correct for the effects of the slit loss of the flux, systematic errors in the
photometric and spectroscopic calibrations, and any other possible systematic
errors. In our observations, the spectra cover the wavelength range of the HSC
$r$-band. We calculate the calibration factor, $f_{\rm photo\\_calib}=F_{{\rm
photo}\\_r}/F_{{\rm spec}\\_r}$, where $F_{{\rm photo}\\_r}$ and $F_{{\rm
spec}\\_r}$ are the photometric and spectroscopic fluxes in the HSC $r$-band.
The derived calibration factors of J0907, J1202, J1207, and J1443 are 0.97,
1.50, 1.40, and 1.36, respectively. We multiply the spectra with the derived
calibration factors.

##  3 Results

Figure 2: Spectral fits to the C iv emission lines of the BluDOGs. The top
left, top right, bottom left, and bottom right show the C iv emission lines of
J0907, J1202, J1207, and J1443, respectively. The green, magenta, red, blue,
and black lines represent the observed spectrum, linear fit to the continuum
emission, two Gaussians for the red and blue components, and best-fit model,
respectively. The orange line on the J1202 and J1443 panels represents the C
iv doublet absorption line. The horizontal black bars denote the wavelength
range used to fit the continuum emission. In each panel, the lower part
presents the residual of the best-fit, with the same flux scale as in the
upper part.

###  3.1 Emission-line measurements

Figure 1 shows the reduced spectra of the four BluDOGs. In order to measure
the emission-line properties, we divide emission lines into six groups as
follows; (1) Ly$\alpha$1216, N v$\lambda$1240, and Si ii$\lambda$1263, (2) Si
iv$\lambda$1397 and O iv]$\lambda$1402, (3) He ii$\lambda$1640 and O
iii]$\lambda$1663, and (4) Al iii$\lambda$1857, Si iii]$\lambda$1892, and C
iii]$\lambda$1909, (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 ${\alpha}$, 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 add 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 $\lambda_{\rm obs}$ = 5916.8 Å and 5926.6 Å for J1202 and those at
$\lambda_{\rm obs}$ = 6678.8 Å 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_fit333https://docs.scipy.org/doc/scipy/reference/, while
we calculate full width at half maximum (FWHM) of emission lines with 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 calculate the mean and standard deviation of the line properties. The
results for emission lines are listed in Tables 3–6. For absorption lines, the
observed-frame equivalent widths and redshifts of the doublet absorption lines
on the J1202 C iv emission line are 47.7$\pm$19.6 Å, 23.6$\pm$9.7 Å, and
2.822, respectively, while the observed-frame equivalent widths and redshift
of the doublet absorption lines on J1443 C iv emission line are 14.0$\pm$6.3
Å, 6.94$\pm$3.14 Å, and 3.314, respectively. Therefore, the co-moving 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.

The flux ratios of N v/Ly$\alpha$ 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 of these unusual flux ratios in
J1443 is the presence of absorption lines, which absorb most of the Ly$\alpha$
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
emission lines of Ly$\alpha$, N v, and C iv.

Figure 2 showcases 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$\pm$0.002, 2.830$\pm$0.002,
2.511$\pm$0.001, and 3.317$\pm$0.006, respectively.

###  3.2 Emission-line contributions to the HSC $g$\- and $r$-band magnitudes

Figure 1 suggests the very large equivalent width (EW) of the emission lines.
The average rest-frame EW (REW) of the C iv line of the four BluDOGs is
$160\pm 33$ Å, $\sim$7 times higher than the average of SDSS type-1 quasars
($23.8\pm 0.1$ 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.

Furthermore, we estimate the effect of the strong emission lines, based on
their observed-frame EWs and the band widths (BW) 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 (4000–5500Å) and $r$-band
(5500–7000Å) 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 Ly$\alpha$, 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 3
objects are largely underestimated444The Ly$\alpha$ line of J0907 is at the
shorter edge of the HSC $g$-band coverage but the flux contribution to the
$g$-band magnitude is likely to be significant owing to its broad nature..
Since the magnitude excess by the emission lines is given by $\Delta{\rm
mag}=2.5\log{(1+EW/BW)}$, 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 from these estimates in Section 4.2.

Table 3: The detected lines of J0907

Line name |  $\lambda_{\rm rest}$ [Å] | $z_{\rm line}$ |  $FWHM_{\rm rest}$ [Å] |  $F_{\rm line}$ [${\rm erg\ s^{-1}\ cm^{-2}}$] |  $EW_{\rm rest}$ [Å] |  $v_{\rm width}$ [${\rm km\ s^{-1}}$]
---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7)
C iv_R | 1549.5 | 2.258$\pm$0.001 | 12.8$\pm$0.7 | (1.10$\pm$0.07)E$-$15 | 118$\pm$10 | 2470$\pm$130
C iv_B | 1549.5 | 2.227$\pm$0.004 | 13.8$\pm$2.5 | (2.87$\pm$0.60)E$-$16 | 31.5$\pm$6.7 | 2670$\pm$490
C iv_R + C iv_B | 1549.5 | 2.258$\pm$0.002 | 15.2$\pm$0.8 | (1.39$\pm$0.09)E$-$15 | 148$\pm$12 | 2940$\pm$150
He ii_R | 1640.4 | 2.260$\pm$0.002 | 3.63$\pm$2.32 | (3.50$\pm$2.36)E$-$17 | 4.43$\pm$3.01 | 663$\pm$425
He ii_B | 1640.4 | 2.235$\pm$0.005 | 38.1$\pm$5.9 | (2.13$\pm$0.48)E$-$16 | 26.8$\pm$6.3 | 6960$\pm$1080
He ii_R + He ii_B | 1640.4 | 2.260$\pm$0.002 | 5.54$\pm$1.29 | (2.48$\pm$0.53)E$-$16 | 31.4$\pm$7.0 | 1010$\pm$240
O iii] | 1663.5 | 2.264$\pm$0.001 | 3.29$\pm$1.69 | (4.49$\pm$1.48)E$-$17 | 5.84$\pm$1.98 | 593$\pm$305
Si iii | 1892.0 | 2.258$\pm$0.002 | 4.03$\pm$4.16 | (2.97$\pm$2.55)E$-$17 | 3.56$\pm$3.06 | 639$\pm$659
C iii]_R | 1908.7 | 2.261$\pm$0.005 | 30.3$\pm$5.3 | (2.34$\pm$0.66)E$-$16 | 28.2$\pm$8.1 | 4760$\pm$830
C iii]_R | 1908.7 | 2.258$\pm$0.002 | 6.19$\pm$3.04 | (6.50$\pm$3.21)E$-$17 | 7.83$\pm$3.89 | 971$\pm$477
C iii]_R + C iii]_B | 1908.7 | 2.258$\pm$0.003 | 11.6$\pm$1.7 | (2.99$\pm$0.73)E$-$16 | 36.0$\pm$9.0 | 1830$\pm$260
Mg ii | 2799.1 | 2.259$\pm$0.001 | 17.6$\pm$1.6 | (2.44$\pm$0.29)E$-$16 | 49.0$\pm$7.3 | 1890$\pm$170

Note. — Column (1): Line name, (2): Rest-frame wavelength of the line, (3):
Line redshift, (4): Rest-frame FWHM, (5): Line flux, (6): Rest-frame EW, (7):
Velocity width after the correction for the instrumental broadening.

Table 4: The detected lines of J1202

Line name |  $\lambda_{\rm rest}$ [Å] | $z_{\rm line}$ |  $FWHM_{\rm rest}$ [Å] |  $F_{\rm line}$ [${\rm erg\ s^{-1}\ cm^{-2}}$] |  $EW_{\rm rest}$ [Å] |  $v_{\rm width}$ [${\rm km\ s^{-1}}$]
---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7)
Si iv | 1393.8 | 2.831$\pm$0.001 | 4.27$\pm$0.73 | (1.56$\pm$0.33)E$-$16 | 5.55$\pm$1.17 | 919$\pm$157
Broad componenta | — | — | — | (1.23$\pm$0.13)E$-$15 | — | 4970$\pm$170
O iv] | 1399.9 | 2.842$\pm$0.001 | 9.90$\pm$0.87 | (5.13$\pm$0.68)E$-$16 | 18.1$\pm$2.4 | 2120$\pm$190
C iv_R | 1549.5 | 2.831$\pm$0.001 | 15.0$\pm$0.4 | (5.46$\pm$0.26)E$-$15 | 177$\pm$9 | 2900$\pm$70
C iv_B | 1549.5 | 2.793$\pm$0.002 | 13.0$\pm$1.0 | (7.98$\pm$1.03)E$-$16 | 27.7$\pm$3.6 | 2510$\pm$190
C iv_R + C iv_B | 1549.5 | 2.830$\pm$0.002 | 16.0$\pm$0.5 | (6.26$\pm$0.28)E$-$15 | 203$\pm$10 | 3100$\pm$90
He ii_R | 1640.4 | 2.838$\pm$0.002 | 11.0$\pm$1.7 | (1.68$\pm$0.47)E$-$16 | 5.06$\pm$1.43 | 2010$\pm$310
He ii_B | 1640.4 | 2.806$\pm$0.005 | 21.1$\pm$3.4 | (3.16$\pm$0.55)E$-$16 | 9.31$\pm$1.64 | 3870$\pm$620
He ii_R + He ii_B | 1640.4 | 2.834$\pm$0.004 | 25.5$\pm$2.5 | (4.84$\pm$0.73)E$-$16 | 14.5$\pm$2.2 | 4650$\pm$450
O iii] | 1663.5 | 2.852$\pm$0.003 | 7.57$\pm$2.94 | (2.06$\pm$1.07)E$-$17 | 0.661$\pm$0.343 | 1360$\pm$530
Al iii | 1858.8 | 2.839$\pm$0.002 | 21.5$\pm$2.4 | (3.05$\pm$0.41)E$-$16 | 10.5$\pm$1.4 | 3470$\pm$390
Si iii | 1892.0 | 2.819$\pm$0.004 | 13.6$\pm$5.5 | (9.40$\pm$4.81)E$-$17 | 3.19$\pm$1.64 | 2160$\pm$870
C iii] | 1908.7 | 2.835$\pm$0.002 | 30.6$\pm$1.9 | (1.01$\pm$0.07)E$-$15 | 33.5$\pm$2.4 | 4810$\pm$300

Note. — See Table 3 for the description of each column.

aThe observed-frame wavelength, continuum flux, and FWHM of the broad
component are 5349.5$\pm$2.0 Å, (7.36$\pm$0.12)E$-$18 ${\rm erg\ s^{-1}\
cm^{-2}}$ Å-1, and 88.9$\pm$2.9 Å, respectively. See Section 3.1 for details.

Table 5: The detected lines of J1207

Line name |  $\lambda_{\rm rest}$ [Å] | $z_{\rm line}$ |  $FWHM_{\rm rest}$ [Å] |  $F_{\rm line}$ [${\rm erg\ s^{-1}\ cm^{-2}}$] |  $EW_{\rm rest}$ [Å] |  $v_{\rm width}$ [${\rm km\ s^{-1}}$]
---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7)
C iv_R | 1549.5 | 2.512$\pm$0.001 | 7.87$\pm$0.43 | (1.02$\pm$0.08)E$-$15 | 74.2$\pm$6.0 | 1520$\pm$80
C iv_B | 1549.5 | 2.500$\pm$0.001 | 20.2$\pm$0.5 | (1.36$\pm$0.09)E$-$15 | 99.3$\pm$6.9 | 3900$\pm$90
C iv_R + C iv_B | 1549.5 | 2.511$\pm$0.001 | 10.3$\pm$0.4 | (2.39$\pm$0.12)E$-$15 | 173$\pm$9 | 1990$\pm$70
He ii_R | 1640.4 | 2.511$\pm$0.001 | 6.53$\pm$1.12 | (6.61$\pm$1.50)E$-$17 | 5.32$\pm$1.21 | 1190$\pm$210
He ii_B | 1640.4 | 2.499$\pm$0.002 | 17.7$\pm$1.3 | (1.47$\pm$0.24)E$-$16 | 11.7$\pm$1.9 | 3240$\pm$240
He ii_R + He ii_B | 1640.4 | 2.509$\pm$0.002 | 11.6$\pm$1.2 | (2.13$\pm$0.28)E$-$16 | 17.2$\pm$2.3 | 2120$\pm$220
O iii] | 1663.5 | 2.516$\pm$0.002 | 12.2$\pm$2.4 | (3.70$\pm$0.95)E$-$17 | 3.18$\pm$0.82 | 2200$\pm$430
Al iii | 1858.8 | 2.508$\pm$0.002 | 19.7$\pm$1.7 | (9.09$\pm$1.02)E$-$17 | 9.23$\pm$1.04 | 3180$\pm$280
Si iii | 1892.0 | 2.511$\pm$0.003 | 10.7$\pm$4.9 | (2.64$\pm$1.60)E$-$17 | 2.79$\pm$1.69 | 1690$\pm$770
C iii]_R | 1908.7 | 2.510$\pm$0.001 | 12.9$\pm$1.4 | (1.69$\pm$0.25)E$-$16 | 18.2$\pm$2.7 | 2030$\pm$220
C iii]_B | 1908.7 | 2.503$\pm$0.002 | 42.0$\pm$2.9 | (4.02$\pm$0.65)E$-$16 | 43.1$\pm$7.0 | 6600$\pm$450
C iii]_R + C iii]_B | 1908.7 | 2.509$\pm$0.002 | 19.6$\pm$1.2 | (5.71$\pm$0.70)E$-$16 | 61.4$\pm$7.5 | 3080$\pm$180

Note. — See Table 3 for the description of each column.

Table 6: The detected lines of J1443

Line name |  $\lambda_{\rm rest}$ [Å] | $z_{\rm line}$ |  $FWHM_{\rm rest}$ [Å] |  $F_{\rm line}$ [${\rm erg\ s^{-1}\ cm^{-2}}$] |  $EW_{\rm rest}$ [Å] |  $v_{\rm width}$ [${\rm km\ s^{-1}}$]
---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7)
Ly ${\alpha}$ | 1215.7 | 3.341$\pm$0.003 | 10.7$\pm$2.6 | (5.28$\pm$1.31)E$-$16 | 64.3$\pm$17.3 | 2650$\pm$640
N v | 1240.8 | 3.312$\pm$0.001 | 16.8$\pm$0.6 | (2.06$\pm$0.09)E$-$15 | 242$\pm$23 | 4070$\pm$160
Si ii | 1262.6 | 3.326$\pm$0.003 | 16.0$\pm$1.9 | (1.24$\pm$0.17)E$-$16 | 13.6$\pm$2.0 | 3790$\pm$450
Si iv | 1393.8 | 3.324$\pm$0.010 | 16.4$\pm$3.2 | (3.18$\pm$1.01)E$-$16 | 33.8$\pm$10.7 | 3520$\pm$700
O iv] | 1399.9 | 3.339$\pm$0.008 | 12.9$\pm$2.5 | (1.74$\pm$1.11)E$-$16 | 18.6$\pm$11.8 | 2760$\pm$540
C iv_R | 1549.5 | 3.328$\pm$0.005 | 14.2$\pm$1.6 | (6.15$\pm$1.74)E$-$16 | 60.0$\pm$17.0 | 2740$\pm$310
C iv_B | 1549.5 | 3.296$\pm$0.007 | 15.7$\pm$2.3 | (5.47$\pm$1.67)E$-$16 | 54.9$\pm$16.8 | 3030$\pm$440
C iv_R + C iv_B | 1549.5 | 3.317$\pm$0.006 | 23.1$\pm$1.8 | (1.16$\pm$0.24)E$-$15 | 114$\pm$24 | 4470$\pm$350
He ii_R | 1640.4 | 3.337$\pm$0.001 | 6.48$\pm$1.56 | (3.23$\pm$1.01)E$-$17 | 3.24$\pm$1.02 | 1180$\pm$290
He ii_B | 1640.4 | 3.307$\pm$0.004 | 20.3$\pm$2.9 | (9.15$\pm$1.53)E$-$17 | 9.25$\pm$1.56 | 3710$\pm$530
He ii_R + He ii_B | 1640.4 | 3.335$\pm$0.003 | 20.1$\pm$2.5 | (1.24$\pm$0.18)E$-$16 | 12.4$\pm$1.9 | 3680$\pm$460

Note. — See Table 3 for the description of each column.

Table 7: Emission-line contribution and excess magnitude to the power-law fit
in the $g$\- and $r$-band

|  $g$-band |  $r$-band
---|---|---
| Total EWs |  $\Delta$mag | Excess mag | Total EWs |  $\Delta$mag | Excess mag
| [Å] | [AB mag] | [AB mag] | [Å] | [AB mag] | [AB mag]
HSC J0907 |  $>$604 |  $>$0.37 | 1.27 | 129 | 0.09 | 0.47
HSC J1202 |  $>$258 |  $>$0.18 | 1.13 | 836 | 0.48 | 0.44
HSC J1207 |  $>$608 |  $>$0.38 | 1.48 | 329 | 0.21 | 0.65
HSC J1443 | 1380 | 0.72 | 0.88 | 721 | 0.43 | 0.40

Note. — $\Delta$mag: $2.5\log{(1+EW/BW)}$, Excess mag: The excesses of the
$g$\- and $r$\- band magnitudes between the observed magnitudes and the
expected magnitudes from an extrapolation of the power-law fit to the longer
wavelength bands.

Figure 3: The SED of J0907 (top), J1202 (middle upper), J1207 (middle lower),
and J1443 (bottom). The red dots denote the $g$\- and $r$-band magnitudes,
while the blue dots denote the longer-wavelength optical and near-infrared
magnitudes that are used for the power-law fit (black line). The green lines
represent the observed spectra. Figure 4: J1207 images in the WISE $W1$-band
(left) and H-ATLAS 250 $\mu$m-band (right). The orange stars, green crosses,
and red cross denote source detections in the HSC-SSP, ALLWISE, and H-ATLAS
catalogs, respectively. The size of each image is 60″$\times$ 60″, centered at
the HSC position of J1207.

###  3.3 Estimating the dust extinction

We need to estimate dust extinction, $E(B-V)$ of AGN radiation, and $L^{\rm
AGN}_{\rm bol}$ to calculate the SMBH mass and Eddington ratio. Since Balmer
decrement or other spectral measures of $E(B-V)$ is not available, we perform
the SED fitting to the broad-band photometry to estimate the $E(B-V)$ and
$L^{\rm AGN}_{\rm bol}$. 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 fits 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; Valiante et al. 2016; Bourne et
al. 2016) data observed with Photodetector Array Camera and Spectrometer
(PACS; Poglitsch et al. 2010) at 100 and 160 $\mu$m and with Spectral and
Photometric Imaging REceiver (SPIRE; Griffin et al. 2010) at 250, 350, and 500
$\mu$m in the FIR, in addition to optical, NIR, and MIR data obtained by
Subaru HSC, VISTA, and WISE. The 1$\sigma$ limiting fluxes at 100, 160, 250,
350, and 500 $\mu$m 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 arcsec 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
0.94 arcsec for J1202, and 9.7 arcsec 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 0.65 arcsec) and another is located at 19 arcsec away to the north-
east 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 the
5$\sigma$ upper limit fluxes.

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 SNRs in these
bands are more than 5, except for the $W4$-band with SNR more than 3 because
we adopted such SNR cut in the selection of DOGs (Noboriguchi et al. 2019).
Since the $g$\- and $r$-band photometry 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.

Table 8: Parameters adopted in the X-CIGALE fit  Parameter | Value
---|---
Delayed SFH (Ciesla et al. 2015)
${\tau}_{\rm main}$ [Myr] | 100, 250, 500
${\tau}_{\rm burst}$ [Myr] | 10, 50
$f_{\rm burst}$ | 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)
$\log{U}$ |  $-$2.0
$f_{\rm esc}$ | 0.0
$f_{\rm dust}$ | 0.0
Lines width [${\rm km\ s^{-1}}$] | 300.0
Dust attenuation (Calzetti et al. 2000)
$E(B-V)_{\rm line}$ | 3, 4, 5, 6, 7, 8, 9, 10
$f_{E(B-V)}$ | 0.44
$\lambda_{\rm UV,bump}$ [nm] | 217.5
FWHMUV,bump [nm] | 35.0
$A_{\rm UV,bump}$ | 0.0
$\delta$ | 0.0
Extinction law of emission lines | the Milky Way
$R_{V}$ | 3.1
Dust emission (Dale et al. 2014)
AGN fraction | 0.0
$\alpha_{\rm IR,AGN}$ | 0.0625, 0.2500, 2.0000
AGN model (Stalevski et al. 2016)
$\tau_{9.7}$ | 3, 7
$p$ | 1.0
$q$ | 1.0
$oa$ [deg] | 10, 20, 30, 40, 50, 60, 70, 80
$R_{\rm ratio}$ | 20
$M_{\rm cl}$ | 0.97
$i$ [deg] | 0, 10, 20, 30, 40,
| 50, 60, 70, 80, 90
$f_{\rm AGN}$ | 0.1, 0.3, 0.5, 0.7, 0.9
Extinction law of polar dust | Calzetti et al. 2000
$E(B-V)^{\rm AGN}_{\rm polar\ dust}$ | 0.1, 0.2, 0.3, 0.4, 0.5
$T^{\rm AGN}_{\rm polar\ dust}$ [K] | 600, 700, 800, 900,
| 1000, 1100, 1200, 1300, 1400
Emissivity of polar dust | 1.6

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 ($\tau_{\rm main}$)
and late starburst population ($\tau_{\rm burst}$), mass fraction of the late
burst population ($f_{\rm burst}$), and age of the main stellar population
(Agemain) and the late burst (Ageburst). As the stellar population, we assume
the initial mass function of Chabrier (2003), solar metallicity, and 10-Gyr
separation between young and old stellar population (Ageseparation). The
nebular emission model (Inoue 2011) is characterized by the ionization
parameter ($U$), fractions of Lyman continuum photons escaping the galaxy
($f_{\rm esc}$) and absorbed by dust ($f_{\rm dust}$), 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 $E(B-V)_{\rm
continuum}=0.44E(B-V)_{\rm line}$, following Calzetti et al. (2000). The
$E(B-V)_{\rm line}$ is varied between 3 and 10. We utilize the SKIRTOR model
as the AGN emission model, which takes 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 $\mu$m ($\tau_{9.7}$), 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
($R_{\rm ratio}$), the fraction of total dust mass inside clumps ($M_{\rm
cl}$), the inclination ($i$), the AGN fraction ($f_{\rm AGN}$), the extinction
law, color excess ($E(B-V)^{\rm AGN}_{\rm polar\ dust}$), dust temperature
($T^{\rm AGN}_{\rm polar\ dust}$), and emissivity index of the polar dust.

The best-fit SED models are shown in Figure 5. The reduced $\chi^{2}$ 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 $E(B-V)^{\rm
AGN}_{\rm polar\ dust}$ and $L^{\rm AGN}_{\rm bol}$ are estimated with a
Bayesian-like strategy presented in Noll et al. (2009), and are reported in
Table 9. On the other hands, 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).

Figure 5: The results of the SED fitting for the four BluDOGs. The upper left,
upper right, lower left and lower right panels show the results of J0907,
J1202, J1207, and J1443, respectively. The black, blue, green, red, and orange
lines represent the best-fit model, stellar component (with dust attenuation),
AGN component, SF component (FIR re-emission from the dust heated by SF), and
nebular component, respectively. The magenta plots represent the photometric
data. The arrows denote 5$\sigma$ upper limit flux.

###  3.4 Measurement of the SMBH mass

Table 9: Physical properties of the four BluDOGs | HSC J0907 | HSC J1202 | HSC J1207 | HSC J1443
---|---|---|---|---
Redshift | $2.258\pm 0.002$ | $2.830\pm 0.002$ | $2.511\pm 0.001$ | $3.317\pm 0.006$
$E(B-V)^{\rm AGN}_{\rm polar\ dust}$ | $0.26\pm 0.05$ | $0.33\pm 0.04$ | $0.30\pm 0.02$ | $0.20\pm 0.01$
$L^{\rm AGN}_{\rm bol}$/$L_{\odot}$ | $(6.11\pm 0.95)\times 10^{12}$ | $(6.11\pm 1.18)\times 10^{13}$ | $(7.95\pm 1.47)\times 10^{12}$ | $(2.52\pm 0.13)\times 10^{13}$
$M_{\rm BH}$ (C iv)/$M_{\odot}$ | $(1.69\pm 0.17)\times 10^{8}$ | $(4.95\pm 0.30)\times 10^{8}$ | $(1.11\pm 0.08)\times 10^{8}$ | $(5.48\pm 0.86)\times 10^{8}$
$M_{\rm BH}$ (Mg ii)/$M_{\odot}$ | $(9.85\pm 1.80)\times 10^{7}$ | — | — | —
$\lambda_{\rm Edd}$ (C iv) | $1.10\pm 0.20$ | $3.75\pm 0.76$ | $2.19\pm 0.43$ | $1.40\pm 0.23$

We have detected the C iv emission line for all the four BluDOGs and 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:

$\displaystyle M_{\rm BH}$ $\displaystyle=$ $\displaystyle
10^{6.66}\Big{(}\frac{{\rm FWHM(C~{}{\sc IV})}}{10^{3}\ {\rm km\
s^{-1}}}\Big{)}^{2}\Big{(}\frac{\lambda L_{\lambda}(1350{\rm\AA})}{10^{44}\
{\rm erg\ s^{-1}}}\Big{)}^{0.53}M_{\odot},$

and

$\displaystyle M_{\rm BH}$ $\displaystyle=$ $\displaystyle
10^{6.86}\Big{(}\frac{{\rm FWHM(Mg~{}{\sc II})}}{10^{3}\ {\rm km\
s^{-1}}}\Big{)}^{2}\Big{(}\frac{\lambda L_{\lambda}(3000{\rm\AA})}{10^{44}\
{\rm erg\ s^{-1}}}\Big{)}^{0.5}M_{\odot},$

where FWHM(C iv), FWHM(Mg ii), $\lambda L_{\lambda}(1350{\rm\AA})$ and
$\lambda L_{\lambda}(3000{\rm\AA})$ are the FWHM of the C iv and Mg ii
velocity profile, and the monochromatic luminosity at 1350 Å 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 possiblility 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, de-reddened them with $E(B-V)^{\rm AGN}_{\rm
polar\ dust}$ 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 $\lambda L_{\lambda}$(1350) of J0907, J1202,
J1207, and J1443 are $(1.54\pm 0.05)\times 10^{45}$, $(9.64\pm 0.27)\times
10^{45}$, $(3.06\pm 0.06)\times 10^{45}$, and $(2.93\pm 0.03)\times 10^{45}$
${\rm erg\ s^{-1}}$, respectively. The $\lambda L_{\lambda}$(3000) of J0907 is
estimated to be $(1.45\pm 0.04)\times 10^{45}$ ${\rm erg\ s^{-1}}$.

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

##  4 Discussion

###  4.1 Spectral features and nuclear outflows

We found that the redshifts of the four BluDOGs are in the range of
$2.2\lesssim z_{\rm sp}\lesssim 3.3$. They are systematically higher than the
typical redshifts of DOGs ($z_{\rm sp}=1.99\pm 0.45$; 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
$i$-band to $W4$-band. Thus we may select DOGs in a preferred redshift range
where strong emission lines such as Ly$\alpha$ and C iv shifts into the two
bands (see Section 4.2 for more quantitative assessments). The reason for the
underestimated photometric redshift ($\sim 1$; Noboriguchi et al. 2019) is the
unusual emission lines with the large REW.

The detected emission lines have large velocity widths, $\gtrsim 2000\ {\rm
km\ s^{-1}}$ 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 mid-IR 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 more 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 populations 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 show 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
($\alpha_{\beta}$)” defined by De Robertis (1985) as

$\displaystyle\alpha_{\beta}$ $\displaystyle=$
$\displaystyle\frac{\lambda_{c}(3/4)-\lambda_{c}(1/4)}{\Delta\lambda(1/2)},$
(3)

where $\lambda_{c}(h)$ and $\Delta\lambda(1/2)$ are the central wavelength at
which the flux falls to a $h$ time the peak flux and FWHM of the broad
profile, respectively. The positive and negative values of $\alpha_{\beta}$
express the blue and red excesses, respectively. The derived values of
$\alpha_{\beta}$ 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 $\alpha_{\beta}=0.110$. Thus J0907, and J1207 may possess a significant
nuclear outflow that is more powerful than typical quasars.

In order to compare $\alpha_{\beta}$ 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 $\alpha_{\beta}$ by
adopting a single or double Gaussian profile. The core ERQ sample consists of
80 objects without BAL and 17 objects with BAL, and we investigate the
statistics of $\alpha_{\beta}$ 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 $\alpha_{\beta}$ index because its velocity
profile is largely affected by narrow absorption lines (hereafter the limited-
BluDOG sample to infer the 3 BluDOGs; i.e., J0907, J1202, and J1207). Figure 6
shows the cumulative fraction of $\alpha_{\beta}$ for the limited-BluDOGs,
core ERQs without BAL, and core ERQs with BAL. The averaged values of the
limited-BluDOGs, core ERQs without BAL, and core ERQs with BAL are
0.15$\pm$0.08, 0.02$\pm$0.13, and 0.01$\pm$0.09, respectively. We performed
the Kolmogorov-Smirnov test (KS-test) to examine the statistical significance
of the difference in $\alpha_{\beta}$ among the samples. The p-values of the
limited-BluDOGs-core ERQs without BAL, and limited-BluDOG-core ERQs with BAL
are 0.0178 and 0.0175, respectively. Thus we conclude that the distributions
of $\alpha_{\beta}$ of the limited-BluDOGs and core ERQs with/without BAL are
marginally different with $>2$ sigma significance. This suggests that the
BluDOGs show nuclear outflow that is possibly more powerful than the nuclear
outflow in core ERQs with/without BAL.

Figure 6: Cumulative distribution of the $\alpha_{\beta}$ indices for the
limited-BluDOGs (see the main text; blue line), core ERQs without BAL (green
line), and core ERQs with BAL (orange line). The red dashed line denotes the
$\alpha_{\beta}$ index measured for the composite spectrum of SDSS type-1
quasars. Figure 7: Cumulative distribution of the $kt_{80}$ indices for the
limited-BluDOGs (blue line), core ERQs without BAL (green line), and core ERQs
with BAL (orange line). The red dashed line denotes the $kt_{80}$ index for
the single Gaussian profile.

We also focus on the kurtosis index ($kt_{80}$) defined as follows (see Hamann
et al. 2017 for detailes): $kt_{80}=\Delta v$(80%) $/\Delta v$(20%), where
$\Delta v$($x$%) is the velocity width at $x$% of the peak flux height. In
addition to $\alpha_{\beta}$, this $kt_{80}$ index is useful to characterize
the C iv wing (a more prominent blue wing results in smaller $kt_{80}$). By
using the best-fit double Gaussian profile of the BluDOGs, $kt_{80}$ 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 $kt_{80}$
index as the discussion of the $\alpha_{\beta}$ index. For comparison,
$kt_{80}$ of a single Gaussian is $\sqrt{1-\frac{2\ln(2)}{\ln(5)}}$ ($\sim
0.37$), whereas most quasars have $kt_{80}\sim 0.15$–$0.30$ (see Figure 7 in
Hamann et al. 2017). The limited-BluDOGs, core ERQs without BAL, and core ERQs
with BAL show $kt_{80}=0.28\pm 0.03$, $0.33\pm 0.06$, and $0.34\pm 0.05$,
respectively (see also Figure 7). Note that the C iv profile of 41 core ERQs
without BAL and 7 core ERQs with BAL is fitted by a single Gaussian, which is
the reason why many objects have $kt_{80}\sim 0.37$ as shown in Figure 7. C iv
velocity profiles of core ERQs with/without BAL are roughly consistent with
the Gaussian without a blue wing. However, the $kt_{80}$ index of the limited-
BluDOGs is less than $\sqrt{1-\frac{2\ln(2)}{\ln(5)}}$, suggesting that their
C iv line profile has a wing. We performed the KS-test to examine the
statistical significance of the difference in $kt_{80}$ among the samples. The
p-values of the limited-BluDOGs-core ERQs without BAL, and limited-BluDOGs-
core ERQs with BAL are 0.0637 and 0.0175, respectively. Therefore, we conclude
that the distributions of $kt_{80}$ between the samples of the limited-BluDOGs
and core ERQs with/without BAL feature are marginally different with $>2$
sigma significance.

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 $kt_{80}$ value of BluDOGs can be caused by the contribution of extended
Lorentzian wings instead of the asymmetric blue wing. For a symmetric
Lorentzian profile, $kt_{80}\sim 1/16$ (much smaller than a Gaussian profile,
$kt_{80}\sim 0.37$) and $\alpha_{\beta}=0$ are expected. However, the BluDOGs
are inconsistent with this expectation (Figure 8). This Figure 8 also shows
that the BluDOGs follow the trend made by core ERQs with/without BAL in the
$kt_{80}-\alpha_{\beta}$ plane, while a systematic deviation of BluDOGs toward
($\alpha_{\beta}$, $kt_{80}$) = (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 $kt_{80}$ of BluDOGs is caused by the asymmetric blue excess due to
the stronger nuclear outflow than that of ERQs.

Figure 8: The $kt_{80}$ vs. $\alpha_{\beta}$ plot for the limited-BluDOGs
(blue dots), core ERQs without BAL (green dots), and core ERQs with BAL
(orange dots). The black solid line and dashed line denote the $kt_{80}$
values of single Gaussian and single Lorentzian, respectively. Note that 41
core ERQs without BAL and 7 core ERQs with BAL are fitted with a single
Gaussian, and they are plotted at ($\alpha_{\beta}$, $kt_{80}$) = (0,
$\sqrt{1-\frac{2\ln(2)}{\ln(5)}}$).

###  4.2 Large equivalent widths of the CIV emission

As we summarized in Table 7, the blue excess in J1443 can be almost explained
by the contribution of the strong emission lines. This is also the case for
J1202 by taking into account of the additional contribution of unobserved
Ly$\alpha$ to $g$-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 $\lesssim$7000Å 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.

Figure 9: Rest-frame EW ratio vs. rest-frame wavelength. REW ratios are
defined as REWs of objects over REWs from the composite spectrum of SDSS
type-1 quasar measured by Vanden Berk et al. (2001). The red, blue, green, and
orange plots show the REW ratios of J0907, J1202, J1207, and J1443,
respectively. Figure 10: Rest-frame EW of the C iv vs. the monochromatic
luminosity at 1350 Å. Blue and orange dots represent the four BluDOGs and
WISSH quasars (Vietri et al. 2018). The grey 2D histogram represents the
number density of the SDSS quasars (Shen et al., 2011). The green line
represents the linear fit to the distribution of the SDSS quasars. The red
plots show the mean and standard deviation in luminosity bins with 0.5 dex
width. The numbers of the SDSS quasars in the individual bins are shown at the
bottom of the panel.

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 on the C
iv REW vs. $\lambda L_{\lambda}$(1350Å) diagram. Note that the REW of J1443
($114\pm 24$ Å) is somewhat smaller than that of the remaining three BluDOGs
($148\pm 12$, $203\pm 10$ and $173\pm 9$ 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 broad absorption lines (`BAL < 1`) taken from Shen et al. (2011).
Since the Baldwin effect does not significantly depend on redshift (e.g.,
Croom et al. 2002; Dietrich 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)555The C iv REW and C iv line luminosity of WISSH quasars
are given by Vietri et al. (2018). To calculate $L_{\lambda}$(1350Å) of WISSH
quasars, we assume that the continuum spectrum of WISSH quasars is a power-law
and adopt the following formula:  $\displaystyle L_{\lambda}({\rm 1350\AA})$
$\displaystyle=$ $\displaystyle\frac{L^{\rm line}({\rm C~{}{\sc
IV}})}{REW({\rm C~{}{\sc
IV}})}\times\Big{(}\frac{1350}{1549}\Big{)}^{\alpha_{\lambda}},$ (4) where
$L_{\lambda}({\rm 1350\AA})$, $L^{\rm line}({\rm C~{}{\sc IV}})$, and
$\alpha_{\lambda}$ are the monochromatic luminosity at 1350 Å, the line
luminosity of C iv, and power-law index, respectively. Here we adopt
$\alpha_{\lambda}=-1.7$ (Vanden Berk et al., 2001) as the power-law index. ,
in order to add objects at the high-luminosity end.

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 are
not due to the Baldwin effect.

The averages and standard deviations of REW(C iv) for core ERQs and ERQ-like
objects are $178\pm 74$ and $86\pm 45$ Å, respectively (Hamann et al., 2017).
The distributions of REW(C iv) and $(i-W3)_{\rm AB}$ color for BluDOGs are
consistent with these of core ERQs although the most of 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 that the large REW of ERQs are 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 the JWST or
exisiting 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).

###  4.3 Possible extreme accretion and the nature of BluDOGs

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 is a diagram of $L_{\rm
bol}$ vs. 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 $L_{\rm bol}$ and $M_{\rm BH}$ 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), 5 Hot DOGs (Wu et al., 2018), 2 power-law DOGs
(Melbourne et al., 2011), and 1 Compton-thick (CT) DOG (Toba et al., 2020).
Hot DOGs are DOGs with a special color of WISE (very faint in the 3.4 $\mu$m
and 4.5 $\mu$m 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 optical to mid-IR (e.g., Dey et al., 2008; Bussmann et al., 2012;
Toba et al., 2015; Noboriguchi et al., 2019). The CT DOG was identified by
Nuclear Spectroscopic Telescope Array (Harrison et al., 2013) from SDSS-WISE
DOGs sample. All but the CT DOG have spectroscopic redshifts. The SMBH masses
of the ERQs and the WISSH quasars are estimated from H$\beta$, while those of
the Hot DOGs and the DOGs are estimated from H$\alpha$. 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 $M_{\rm BH}$ of ERQs and DOGs are lower
limits.

Figure 11: The SMBH mass vs. the bolometric luminosity diagram. The filled-
blue stars and gray contour denote the BluDOGs and SDSS quasars, while the
filled hexagons with green, orange, purple, cyan, and light green colors
denote ERQs (Perrotta et al., 2019), WISSH quasars (Vietri et al., 2018), Hot
DOGs (Wu et al., 2018), DOGs (Melbourne et al., 2011, 2012), and a CT DOG
(Toba et al., 2020), respectively. The red dashed lines represent a constant
Eddington ratio of $\lambda_{\rm Edd}=$ 0.01, 0.1, 1.0, and 10.0.

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 ($\lambda_{\rm Edd}$) of J0907, J1202,
J1207, and J1443 are $1.10\pm 0.20$, $3.89\pm 0.78$, $2.19\pm 0.44$, and
$1.40\pm 0.23$, 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 whole 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
$\lambda_{\rm Edd}$, 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 $kt_{80}$.
$E(B-V)$ for BluDOGs, core ERQs (Hamann et al., 2017), and hot DOGs (Wu et
al., 2018) are $0.273\pm 0.049$, $0.242\pm 0.127$, and $4.781\pm 1.986$,
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 $kt_{80}$ of BluDOGs is smaller than
that of core ERQs (Section 4.1), and the $kt_{80}$ of Mid-IR 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 ($\eta$) is defined as
following:

$\displaystyle\eta$ $\displaystyle=$ $\displaystyle\frac{L_{\rm
bol}}{\dot{M}c^{2}},$ (5)

where $\dot{M}$ is the mass accretion rate. By multiplying the $\dot{M}$ and
lifetime of BluDOGs ($t_{\rm life}$), we can roughly estimate the accreted
mass ($M_{\rm Acc}$) in the BluDOGs phase. Bian & Zhao (2003) estimated
$\log\eta=-1.61$ of Seyfert 1 galaxies and Palomar-Green quasars by assuming
that the geometrically-thin and optically-thick standard $\alpha$-prescription
accretion disk model (Shakura & Sunyaev 1973). By assuming $\log\eta=-1.61$
and $t_{\rm life}=1$ Myr (Noboriguchi et al., 2019), the estimated $M_{\rm
Acc}$ of J0907, J1202, J1207, and J1443 are about $1.68\times 10^{7}$,
$1.68\times 10^{8}$, $2.19\times 10^{7}$, and $6.93\times 10^{7}\ M_{\odot}$.
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
($M^{+}_{\rm BH}=M_{\rm BH}+M_{\rm Acc}$) of J0907, J1202, J1207, and J1443
are $1.86\times 10^{8}$, $6.63\times 10^{8}$, $1.32\times 10^{8}$, and
$6.17\times 10^{8}\ M_{\odot}$, respectively. Therefore the SMBH mass of
BluDOGs increases by $\sim$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 $\lambda_{\rm Edd}$ of the four BluDOGs is
more significant than the scatter of the $\lambda_{\rm Edd}$ distribution,
suggesting that BluDOGs are a special class of AGNs that harbor SMBHs in the
most actively evolving phase. Then, why such a class of AGNs is found only in
a limited redshift range, $2.2<z_{\rm sp}<3.3$? A possible reason comes from
their selection criteria, as briefly mentioned in Sec 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 whole population of DOGs have systematically larger
$\lambda_{\rm Edd}$ than ordinary type-1 quasars, due to the paucity of the
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.

Figure 12: The redshift vs. the Eddington ratio diagram. The filled-blue stars
and hexagons are the same as in Figure 11. The gray 2D histogram represents
the number density of SDSS quasars (Shen et al., 2011). The red plots show the
mean and standard deviation of $\lambda_{\rm Edd}$ in redshift bins with the
width of $\Delta z=0.5$. The numbers shown at the upper part denote the
numbers of SDSS quasars in the redshift bins.

##  5 CONCLUSION

We carried out spectroscopic observations of the four BluDOGs selected by
Noboriguchi et al. (2019) using Subaru/FOCAS and VLT/FORS2. The analysis of
the obtained spectroscopic data revealed the following spectroscopic
properties of the BluDOGs:

  1. 1.

The rest-frame UV spectra of the BluDOGs show broad ($\gtrsim$2000 ${\rm km\
s^{-1}}$) emission lines. This suggests that the BLRs of the BluDOGs are not
completely obscured, albeit the very dusty nature inferred from their optical-
IR SED.

  2. 2.

The C iv lines of the BluDOGs show a significant blue wing, which is more
prominent than in ordinary SDSS type-1 quasars. This suggests a presence of
powerful nuclear outflow at the spatial scale of the BLR in the BluDOGs.

  3. 3.

The REWs of their BLR lines are very large, REW(C iv)$\sim$160 Å, $\sim$7
times larger than the average of SDSS type-1 quasars. Such strong lines cause
the flux excess of the two BluDOGs in the HSC $g$\- and $r$-bands, while blue
continuum emission also contributes the blue excess in the remaining two
objects. The large REWs are not explained by the Baldwin effect. A possible
origin is a powerful nuclear outflow in the BluDOGs causing a selective
obscuration of the nuclear region, as suggested for ERQs.

  4. 4.

The Eddington ratios of the BluDOGs are higher than 1.0 and are systematically
larger than other AGN populations. The mass accretion onto the SMBH in BluDOGs
is in the mode of the Eddington-limit or super-Eddington accretion.

All of the above results support the scenario that BluDOGs represent a
population of AGNs in the transition phase from optically thick to optically
thin quasars, i.e., in the blowing-out phase of the major-merger scenario for
the SMBH evolution. The spectroscopic properties of the BluDOGs are similar to
those of ERQs. For further understandings of the complete picture, more
systematic spectroscopic observations are crucial, not only of BluDOGs but
also of the whole population of DOGs.

The authors gratefully acknowledge the anonymous referee for a careful reading
of the manuscript and very helpful comments. This study is based on data
collected at Subaru Telescope, which is operated by the National Astronomical
Observatory of Japan, and observations collected at the European Southern
Observatory under a ESO programme 0102.B-0614(A). We are honored and grateful
for the opportunity of observing the Universe from Maunakea, which has the
cultural, historical and natural significance in Hawaii. The Hyper Suprime-Cam
(HSC) collaboration includes the astronomical communities of Japan and Taiwan,
and Princeton University. The HSC instrumentation and software were developed
by the National Astronomical Observatory of Japan (NAOJ), the Kavli Institute
for the Physics and Mathematics of the Universe (Kavli IPMU), the University
of Tokyo, the High Energy Accelerator Research Organization (KEK), the
Academia Sinica Institute for Astronomy and Astrophysics in Taiwan (ASIAA),
and Princeton University. Funding was contributed by the FIRST program from
Japanese Cabinet Office, the Ministry of Education, Culture, Sports, Science
and Technology (MEXT), the Japan Society for the Promotion of Science (JSPS),
Japan Science and Technology Agency (JST), the Toray Science Foundation, NAOJ,
Kavli IPMU, KEK, ASIAA, and Princeton University. This paper makes use of
software developed for the Large Synoptic Survey Telescope. We thank the LSST
Project for making their code available as free software at
http://dm.lsstcorp.org. The Pan-STARRS1 Surveys (PS1) have been made possible
through contributions of the Institute for Astronomy, the University of
Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its
participating institutes, the Max Planck Institute for Astronomy, Heidelberg
and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns
Hopkins University, Durham University, the University of Edinburgh, Queen’s
University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las
Cumbres Observatory Global Telescope Network Incorporated, the National
Central University of Taiwan, the Space Telescope Science Institute, the
National Aeronautics and Space Administration under Grant No. NNX08AR22G
issued through the Planetary Science Division of the NASA Science Mission
Directorate, the National Science Foundation under Grant No. AST-1238877, the
University of Maryland, and Eotvos Lorand University (ELTE) This publication
has made use of data from the VIKING survey from VISTA at the ESO Paranal
Observatory, program ID 179.A-2004. Data processing has been contributed by
the VISTA Data Flow System at CASU, Cambridge and WFAU, Edinburgh. This
publication makes use of data products from the Wide-field Infrared Survey
Explorer, which is a joint project of the University of California, Los
Angeles, and the Jet Propulsion Laboratory/California Institute of Technology,
funded by the National Aeronautics and Space Administration. Herschel is an
ESA space observatory with science instruments provided by European-led
Principal Investigator consortia and with important participation from NASA.
This research made use of Astropy,666http://www.astropy.org a community-
developed core Python package for Astronomy (Astropy Collaboration et al.,
2013, 2018). We would like to thank Enago (www.enago.jp) for the English
language review and Kohei Iwashita for helpful discussion. This study was
financially supported by the Japan Society for the Promotion of Science (JSPS)
KAKENHI grant Nos. 19J10458, 21H01126 (A.N.), 16H03958, 17H01114, 19H00697,
20H01949 (T.N.), 18J01050, 19K14759, 22H01266 (Y. Toba), 20H01939 (K.I.), and
20K04014 (Y. Terashima).

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