#  A Wide and Deep Exploration of Radio Galaxies with Subaru HSC (WERGS). IV.
Rapidly Growing (Super-)Massive Black Holes in Extremely Radio-Loud Galaxies

Kohei Ichikawa Frontier Research Institute for Interdisciplinary Sciences,
Tohoku University, Sendai 980-8578, Japan  Astronomical Institute, Tohoku
University, Aramaki, Aoba-ku, Sendai, Miyagi 980-8578, Japan  Max-Planck-
Institut für extraterrestrische Physik (MPE), Giessenbachstrasse 1, D-85748
Garching bei Müunchen, Germany  Takuji Yamashita National Astronomical
Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Yoshiki
Toba Department of Astronomy, Kyoto University, Kitashirakawa-Oiwake-cho,
Sakyo-ku, 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
Tohru Nagao Research Center for Space and Cosmic Evolution, Ehime University,
2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan  Kohei Inayoshi Kavli
Institute for Astronomy and Astrophysics, Peking University, Beijing 100871,
China  Maria Charisi  TAPIR, California Institute of Technology, 1200 E.
California Blvd., Pasadena, CA 91125, USA  Wanqiu He Astronomical Institute,
Tohoku University, Aramaki, Aoba-ku, Sendai, Miyagi 980-8578, Japan  Alexander
Y. Wagner Center for Computational Sciences, University of Tsukuba, 1-1-1
Tennodai, Tsukuba, Ibaraki 305-8577, Japan  Masayuki Akiyama Astronomical
Institute, Tohoku University, Aramaki, Aoba-ku, Sendai, Miyagi 980-8578, Japan
Bovornpratch Vijarnwannaluk  Astronomical Institute, Tohoku University,
Aramaki, Aoba-ku, Sendai, Miyagi 980-8578, Japan  Xiaoyang Chen Astronomical
Institute, Tohoku University, Aramaki, Aoba-ku, Sendai, Miyagi 980-8578, Japan
Masaru Kajisawa Research Center for Space and Cosmic Evolution, Ehime
University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan  Taiki Kawamuro
National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo
181-8588, Japan  Chien-Hsiu Lee NSF’s National Optical-Infrared Astronomy
Research Laboratory, Tucson, AZ 85719, USA  Yoshiki Matsuoka  Research Center
for Space and Cosmic Evolution, Ehime University, 2-5 Bunkyo-cho, Matsuyama,
Ehime 790-8577, Japan  Malte Schramm  National Astronomical Observatory of
Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Hyewon Suh Subaru
Telescope, National Astronomical Observatory of Japan (NAOJ), 650 North
A’ohoku Place, Hilo, HI 96720, USA  Gemini Observatory/NSF’s NOIRLab, 670 N.
A’ohoku Place, Hilo, Hawaii, 96720, USA  Masayuki Tanaka National Astronomical
Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Hisakazu
Uchiyama  National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka,
Tokyo 181-8588, Japan  Yoshihiro Ueda Department of Astronomy, Kyoto
University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan  Janek
Pflugradt  Astronomical Institute, Tohoku University, Aramaki, Aoba-ku,
Sendai, Miyagi 980-8578, Japan  Hikaru Fukuchi  Astronomical Institute, Tohoku
University, Aramaki, Aoba-ku, Sendai, Miyagi 980-8578, Japan

(Received May 3, 2020; Revised July 19, 2021; Accepted August 5, 2021)

###### Abstract

We present the optical and infrared properties of 39 extremely radio-loud
galaxies discovered by cross-matching the Subaru/Hyper Suprime-Cam (HSC) deep
optical imaging survey and VLA/FIRST 1.4 GHz radio survey. The recent
Subaru/HSC strategic survey revealed optically-faint radio galaxies (RG) down
to $g_{\mathrm{AB}}\sim 26$, opening a new parameter space of extremely radio-
loud galaxies (ERGs) with radio-loudness parameter of $\log\mathcal{R_{\rm
rest}}=\log(f_{1.4\mathrm{GHz,rest}}/f_{g,\mathrm{rest}})>4$. Because of their
optical faintness and small number density of $\sim 1~{}$deg-2, such ERGs were
difficult to find in the previous wide but shallow, or deep but small area
optical surveys. ERGs show intriguing properties that are different from the
conventional RGs: (1) most ERGs reside above or on the star-forming main-
sequence, and some of them might be low-mass galaxies with
$\log(M_{\star}/M_{\odot})<10$. (2) ERGs exhibit a high specific black hole
accretion rate, reaching the order of the Eddington limit. The intrinsic
radio-loudness ($\mathcal{R_{\mathrm{int}}}$), defined by the ratio of jet
power over bolometric radiation luminosity, is one order of magnitude higher
than that of radio quasars. This suggests that ERGs harbor a unique type of
active galactic nuclei (AGN) that show both powerful radiations and jets.
Therefore, ERGs are prominent candidates of very rapidly growing black holes
reaching Eddington-limited accretion just before the onset of intensive AGN
feedback.

galaxies: active — galaxies: nuclei — quasars: supermassive black holes —

††journal: ApJ††facilities: VLA, Herschel, WISE, Subaru/HSC††software: astropy
(Astropy Collaboration et al., 2013), Matplotlib (Hunter, 2007), Pandas
(McKinney, 2010)

##  1 Introduction

The formation of supermassive black holes (SMBHs) and their growth across the
cosmic time are fundamental questions in modern astronomy. In the local
universe at $z\sim 0$, the mass of SMBH ($M_{\mathrm{BH}}$) and their host
properties show tight correlations for the SMBH mass range of
$6\lesssim\log(M_{\mathrm{BH}}/M_{\odot})\lesssim 10$ with a scatter of
$\sigma\sim 0.3$ dex (e.g., Magorrian et al., 1998; Gebhardt et al., 2000;
Ferrarese & Merritt, 2000; Tremaine et al., 2002; Marconi & Hunt, 2003; Häring
& Rix, 2004; Sani et al., 2011; Kormendy & Ho, 2013; McConnell & Ma, 2013).
Such a tight correlation is considered to be established by a balance of
feeding and feedback processes between the central SMBHs and the host
galaxies.

Local Radio galaxies have been primary targets for investigating the effect of
SMBHs on the host galaxies because powerful radio galaxies or radio-loud
active galactic nuclei (AGN) mainly reside in massive galaxies whose star-
formation is quenched, with the presence of strong jets dispersing the
interstellar medium (e.g., Morganti et al., 2005; Holt et al., 2008; Nesvadba
et al., 2017), or producing cavities in the host galaxies (e.g., Rafferty et
al., 2006; McNamara & Nulsen, 2007; Bîrzan et al., 2008; Blandford et al.,
2019). Those radio galaxies tend to show a low accretion rate, i.e., Eddington
ratio of $\lambda_{\mathrm{Edd}}<10^{-2}$, suggesting that the energy release
is dominated by the kinetic power by jet, not by the radiation from AGN
accretion disk.

However, the situation may be different at $z>1$. Using over $10^{3}$ radio
AGN selected from the Very Large Array (VLA)-COSMOS 3 GHz large project
(Smolčić et al., 2017a), Delvecchio et al. (2018) demonstrated that SMBH
accretion in radio-bright
($L_{\mathrm{1.4GHz}}>10^{25}~{}\mathrm{W}~{}\mathrm{Hz}^{-1}$) AGN becomes
more radiatively efficient ($\lambda_{\mathrm{Edd}}>10^{-2}$) at $z>1$. They
reside in star-forming galaxies, which contain plenty of cold gas. This
picture of radio AGN is completely different from those seen in the local
universe in the same radio luminosity range (e.g., Hickox et al., 2009).
Still, the survey volume of VLA-COSMOS surveys is small so that they may be
missing a rare, but radio-bright population. The FIRST survey is the best tool
to explore such a radio bright end since it covers half the sky with the VLA
at 1.4 GHz (e.g., Becker et al., 1995; Helfand et al., 2015). However, cross-
matching the VLA/FIRST sources with the SDSS survey catalog identified optical
counterparts in only 30% of the radio sources (Ivezić et al., 2002; Best &
Heckman, 2012).

Recent Subaru/Hyper Suprime-Cam (HSC; Miyazaki et al., 2018) strategic survey
shed light on such a situation. We have conducted a search for optically-faint
radio-galaxies (RGs) using the Subaru HSC survey catalog (Aihara et al.,
2018b) and the VLA/FIRST radio continuum catalog, and we have found a large
number ($>3\times 10^{3}$ sources) of RGs at $z\sim 0$–$5$ (Yamashita et al.,
2018, 2020). The project is called Wide and deep Exploration of Radio Galaxies
with Subaru/HSC (WERGS; Yamashita et al., 2018). Yamashita et al. (2018)
demonstrated that over 60% of populations now have reliable optical
counterparts thanks to deep HSC/optical imaging. Figure 1 shows that the WERGS
sample spans a wide range of optical magnitude $g_{\mathrm{AB}}=18-26$ and
radio-loudness parameter of $\log\mathcal{R_{\rm
rest}}=\log(f_{1.4\mathrm{GHz,rest}}/f_{g~{}{\rm band,rest}})=1$–$6$ (e.g.,
Ivezić et al., 2002).

Our particular interest is the new parameter space of optically faint RGs that
are extremely radio-loud galaxies (ERGs) with $\log\mathcal{R_{\rm rest}}>4$.
Previously known radio quasars have a peak of radio-loudness at
$\log\mathcal{R_{\rm rest}}=2$–$3$, and rarely contain any sources with
$\log\mathcal{R_{\rm rest}}>4$ (Ivezić et al., 2002; Inoue et al., 2017).
Therefore, the optical emission of ERGs seems not originate from the AGN
accretion disk anymore probably due to dust obscuration of the nuclei, but it
traces the stellar-component of the host galaxies (e.g., Terashima & Wilson,
2003). Given that the optical band is very faint with median magnitudes of
$\left<g_{\mathrm{AB}}\right>\sim 24.5$, ERGs might have smaller stellar mass
than previously known radio sources. Considering the very small number density
of ERGs ($\sim 1$ source deg-2), it is not surprising that deep but smaller
volume surveys (such as VLA-COSMOS Smolčić et al., 2017a, b) have rarely
detected such ERGs, and the very wide SDSS survey (e.g., SDSS-selected radio
galaxies Best & Heckman, 2012) could not detect ERGs either because of their
shallow sensitivity down to only $g_{\mathrm{AB}}\sim 22$.

In this study, we will explore the physical properties of ERGs. Toba et al.
(2019) already compiled multi-wavelength data covering the optical, IR, and
radio band for the WERGS sample, and derived physical parameters of host
galaxies such as stellar mass, star-formation rate as well as the AGN
luminosity estimated from the mid-IR bands. By using this data set, we will
explore the AGN and host galaxy properties of the ERGs. Thoroughout this
paper, we adopt the same cosmological parameters as Yamashita et al. (2018)
and Toba et al. (2019); $H_{0}=70$ km s-1 Mpc-1, $\Omega_{\mathrm{M}}=0.27$,
and $\Omega_{\Lambda}=0.73$.

Figure 1:  $\log\mathcal{R_{\rm rest}}$ versus rest $g$ band magnitude of our
sample. The original WERGS sample obtained by Yamashita et al. (2018) is shown
with gray circles. The finally selected 987 WERGS sample with
$\log\mathcal{R_{\rm rest}}<4$ used in this study (we call the sample “NRGs”
in the text) and 39 ERGs (the sample with $\log\mathcal{R_{\rm rest}}>4$) are
shown with blue circles, and orange stars, respectively. The vertical dashed-
line indicates the magnitude limit of the SDSS survey at $g_{\mathrm{AB}}=22$.

Figure 2:  Luminosity of WERGS sample as a function of redshift. The points
are the same as in Figure 1. (left) Rest-frame radio luminosity $\log
L_{\mathrm{1.4GHz}}$ ($\mathrm{W}~{}\mathrm{Hz}^{-1}$) as a function of
redshift, where $L_{\mathrm{1.4GHz}}$ is obtained from VLA/FIRST (Helfand et
al., 2015), and the $k$-correction was made by Yamashita et al. (2018) based
on redshift. The horizontal dashed line is a luminosity cut we adopt to
exclude galaxies with strong starbursts. The faint cyan and orange circle
points are data obtained from FIRST-SDSS (Best & Heckman, 2012) and VLA-COSMOS
(Smolčić et al., 2017a), respectively. (Right) IR AGN luminosity
$L_{\mathrm{AGN,IR}}$ (erg s-1) as a function of redshift. For the entire
WERGS population, we plot the sources only when it is included in Toba et al.
(2019), in which the IR AGN luminosity was measured.

##  2 Sample Selection and Properties

Our initial sample is based on the WERGS sample ($\sim 3600$ sources;
Yamashita et al., 2018), which compiled the HSC Subaru Strategic Program (HSC-
SSP) optical counterparts of the VLA/FIRST data. Here, we briefly summarize
the WERGS sample and the reader should refer to Yamashita et al. (2018) for
the WERGS catalog and Toba et al. (2019) for the IR catalog of the WERGS
sample. We also describe further selection criteria imposed on the sample,
which are suitable for this study. The number of WERGS sources after each
sample selection cut is also summarized in Table 1.

###  2.1 WERGS Sample

####  2.1.1 VLA/FIRST

The VLA/FIRST survey contains radio imaging data at 1.4 GHz with a spatial
resolution of 5.4 arcsec (Becker et al., 1995; White et al., 1997), which
completely covers the footprint of the HSC-SSP Wide-layer (see the text
below). Yamashita et al. (2018) utilized the final release catalog of FIRST
(Helfand et al., 2015) with the flux limit of $>1$ mJy, and extracted 7072
FIRST sources in the HSC-SSP footprint.

####  2.1.2 Subaru/HSC-SSP data

The HSC-SSP is an ongoing wide and deep imaging survey covering five broadband
filters ($g$-, $r$-, $i$-, $z$-, and $y$-band; Aihara et al., 2018b; Bosch et
al., 2018; Furusawa et al., 2018; Kawanomoto et al., 2018; Komiyama et al.,
2018; Huang et al., 2018), consisting of three layers (Wide, Deep, and
UltraDeep). Yamashita et al. (2018) utilized the Wide-layer S16A data release,
which contains observations from 2014 March to 2016 January with a field
coverage of 154 deg2 (based on six fields; XMM-LSS, GAMA09H, WIDE12H, GAMA15H,
HECTOMAP, and VVDS), and forced photometry of $5\sigma$ limiting magnitude
down to $26.8,26.4,26.4,25.5,$ and $24.7$ for $g,r,i,z,$ and $y$-band,
respectively (Aihara et al., 2018a). The average seeing in the $i$-band is
$0.6$ arcsec, and the astrometric root mean squared uncertainty is about 40
mas. After removing spurious sources flagged by the pipeline, Yamashita et al.
(2018) cross-matched the FIRST sources with a search radius of 1 arcsec.
Yamashita et al. (2018) also required detections with $\mathrm{S/N}>5$ in the
$r$-, $i$-, and $z$-bands to qualify as an optical counterpart. This initial
sample of Yamashita et al. (2018) comprised 3579 sources.

We then applied additional cuts to this sample. To remove radio galaxies from
the initial WERGS sample whose radio emission might be dominated by the star-
formation of host galaxies, and not by the AGN, we set a lower-limit to radio-
luminosity of $L_{\mathrm{1.4GHz}}>10^{24}$ $\mathrm{W}~{}\mathrm{Hz}^{-1}$,
which is equivalent to the radio-emission from the host galaxies with a star-
formation rate of $\mathrm{SFR}\approx 250~{}M_{\odot}$ yr-1 (Condon, 1992;
Condon et al., 2013). This cut is also supported by a steep decline of radio
luminosity function of starburst galaxies above $L_{\mathrm{1.4GHz}}=10^{23}$
$\mathrm{W}~{}\mathrm{Hz}^{-1}$ (e.g., Kimball et al., 2011; Tadhunter, 2016;
Padovani, 2016). This criterion reduces the sample size to 3147.

Next, we limit our sample to compact sources in the radio band. This is
important in order to reduce false optical identification by mismatching the
optical sources with the locations of spatially extended radio-lobe emission.
Yamashita et al. (2018) discussed this and categorized radio compact sources
using the ratio of the total integrated radio flux density to the peak radio
flux density $f_{\mathrm{int}}/f_{\mathrm{peak}}$. They treated the source as
compact if the ratio fulfills either of two following equations,

$\displaystyle f_{\mathrm{int}}/f_{\mathrm{peak}}$
$\displaystyle<1+6.5\times(f_{\mathrm{peak}}/\mathrm{rms})^{-1}$ (1)
$\displaystyle\log(f_{\mathrm{int}}/f_{\mathrm{peak}})$ $\displaystyle<0.1,$
(2)

where $f_{\mathrm{peak}}/\mathrm{rms}$ is the S/N, and rms is a local rms
noise in the FIRST catalog, and the above two equations are obtained from the
study by Schinnerer et al. (2007) (see also the original criterion: Ivezić et
al., 2002). We set an additional conservative requirement that there shall be
no FIRST source in the surrounding 1 arcmin (corresponding to $\lesssim 500$
kpc at $z\sim 1$) to select the isolated radio core emission and avoid
coincident matching with radio lobes of other nearby FIRST sources. This
reduces the sample to 2583 sources.

A further ten sources were removed in crowded regions of the HSC footprint due
to multiple HSC detections within $<1$ arcsec of the HSC counterpart, bringing
the sample down to 2573 sources.

Finally, we restricted the sample to sources with spectroscopic redshift
(spec-$z$; $z_{\mathrm{spec}}$) or reliable photometric redshift (photo-$z$;
$z_{\mathrm{phot}}$) values. The spec-$z$ were obtained from SDSS DR12 (Alam
et al., 2015), the GAMA project DR2 (Driver et al., 2011; Liske et al., 2015),
and WiggleZ Dark Energy Survey project DR1 (Drinkwater et al., 2010). In this
study, we limit the sample to the spec-$z$ range $0.3<z_{\mathrm{spec}}<1.6$
to cover the same redshift range as the photo-$z$ sample. For the sources
without spec-$z$, we utilized the photo-$z$ estimated using the `Mizuki` SED-
fitting code which is one of the standard photo-$z$ packages for the HSC-SSP
survey. The method utilizes the photometries of the five HSC-SSP bands (see
Tanaka, 2015; Tanaka et al., 2018, for more details) for the SED fitting.
Yamashita et al. (2018) discussed that the HSC-SSP photo-$z$ derived by
`MIZUKI` is reliable for $z_{\mathrm{phot}}<1.6$ based on comparison with
spectroscopic redshift in the COSMOS field. In addition, the redshift of
sources with $z_{\mathrm{phot}}<0.3$ are sometimes erroneous because they lack
the Balmer break tracer in the HSC optical bands. Therefore, we limit the
sample to $0.3<z_{\mathrm{phot}}<1.6$. We further imposed requirements based
on the reliable photo-$z$ fitting quality (reduced $\chi^{2}<3$,
$\sigma/z_{\mathrm{phot}}<0.2$, and $\sigma/(1+z_{\mathrm{phot}})<0.1$),
following Toba et al. (2019). The resulting WERGS sample contains 1770
sources. Given that our sample largely relies on photo-$z$ results, we further
discussed how possible erroneous photo-$z$ might affect our main results in
Appendix A.

Table 1: Summary of the sample selection cut in this study

(1) | (2) | (3) |
---|---|---|---
Selection | No. of WERGS sources | No. of ERGs |
Parent WERGS sample of Yamashita et al. (2018) | 3579 | 273 |
$L_{\mathrm{1.4GHz}}>10^{24}$ W Hz-1 | 3147 | 270 |
compact radio sources | 2792 | 208 |
No nearby multiple FIRST sources in $<1$ arcmin | 2583 | 192 |
No nearby multiple HSC sources in $<1$ arcsec | 2573 | 187 |
Redshift range at $0.3<z<1.6$ | 2286 | 145 |
Good photo-$z$ quality | 1770 | 79 |
IR available region by Toba et al. (2019) | 1055 | 39 |
$q_{\mathrm{IR}}<1.68$ (final sample) | 1026 | 39 |

††footnotetext:  Notes.— The number of sources after the each selection cut
staring from the parent sample to the final one used in this study. The
details are summarized at Section 2.1.2 and 2.2.

###  2.2 WERGS IR catalog

To study the AGN and host galaxy properties in WERGS, Toba et al. (2019)
compiled optical, near-IR, mid-IR, far-IR, and radio data for the WERGS
sample. Toba et al. (2019) performed spectral energy distribution (SED)
fitting with `CIGALE` (Boquien et al., 2019), and inferred physical
properties, including the IR luminosity contributed from AGN (IR AGN
luminosity; $L_{\mathrm{AGN,IR}}$), dust extinction corrected stellar-mass
($M_{\star}$), and SFR estimated from the decomposed host galaxy IR
emission111The catalog containing physical parameter of Toba et al. (2019) is
available at http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=J/ApJS/243/15.
For the estimation of $L_{\mathrm{AGN,IR}}$, Toba et al. (2019) considered the
contamination of Synchrotron radiation in the IR bands by extrapolating the
power-law from the radio bands. Thus, $L_{\mathrm{AGN,IR}}$ is obtained purely
from the dust emission heated by AGN. The bolometric AGN luminosity is
estimated by using the conversion $L_{\mathrm{AGN,bol}}\simeq 3\times
L_{\mathrm{AGN,IR}}$ (Delvecchio et al., 2014; Inayoshi et al., 2018). Because
Toba et al. (2019) restricted themselves to objects in an area of $\sim 95$
deg2, in which mutli-wavelength information from $u$-band to far-IR was
available, our sample is reduced to 1055 sources.

Some of the selected sources have intensive star formation rates, reaching
$\mathrm{SFR}\approx 250M_{\odot}$ yr-1, so we applied an additional cut to
remove possible star-formation dominated radio galaxies using the ratio of IR
and radio luminosity ($q_{\mathrm{IR}}$; Helou et al., 1985; Ivison et al.,
2010) defined by

$q_{\mathrm{IR}}=\log\left(\frac{L_{\mathrm{IR}}/3.75\times
10^{12}}{L_{\mathrm{1.4GHz}}}\right),$ (3)

where $L_{\mathrm{IR}}$ is the total IR luminosity in units of W derived from
`CIGALE` and $3.7\times 10^{12}$ is the frequency in Hz corresponding to 80
$\mu$m, which makes $q_{\mathrm{IR}}$ a dimensionless quantity. We set
$q_{\mathrm{IR}}<1.68$ (Del Moro et al., 2013) to select radio excess (meaning
jet-emission dominated) sources. As a result, our final sample reduces to 1026
sources, and the resulting final number of ERGs fulfilling
$\log\mathcal{R_{\rm rest}}>4$ is 39 sources, and they are shown in orange
stars in Figure 1. We refer to the remaining 987 WERGS sources with
$1<\log\mathcal{R_{\rm rest}}<4$ as “normal radio galaxies (NRGs)” (shown with
blue circles in Figure 1) hereafter.

Table 1 shows the number of sources for the full WERGS sample and the ERGs
after each selection cut. ERGs suffers the photo-$z$ quality cut more than the
full WERGS sample because ERGs contain a relatively large fraction of
optically faintest sources with $i_{\mathrm{AB}}>25$, which sometimes makes
the reliable photo-$z$ estimation difficult. The IR selection cut is another
main factor in reducing the number of sources. This is mainly because the
region available for the IR data is limited in the area of $\sim 95$ deg2 out
of the 154 deg2 (Toba et al., 2019). Note that this IR selection reduces the
similar fraction of sources for the full WERGS sample (60%) and ERGs (55%).

##  3 Results

We summarize the properties of the obtained 39 ERGs with IR detections. First,
we show the basic differences between ERGs and NRGs. Then, we show the
properties of ERGs on SMBHs and host galaxies.

###  3.1 Basic Sample Properties

####  3.1.1 $\log\mathcal{R_{\rm rest}}$ vs. $g$-band magnitude

Figure 1 shows the distribution of the radio-loudness parameter
$\mathcal{R_{\rm rest}}$ as a function of the rest-frame $g$-band magnitude
($g_{\mathrm{AB}}$). The vertical dashed-line at $g_{\mathrm{AB}}=22$
indicates the SDSS magnitude limit (e.g., Ivezić et al., 2002). Since most
ERGs are fainter than the SDSS limit, Subaru/HSC has enabled us to investigate
this unique population for the first time. Figure 1 also shows that most ERGs
are very faint in the optical, with median magnitudes of $\langle
g_{\mathrm{AB}}\rangle=24.5$. The current 8 m class telescopes are
sufficiently sensitive to obtain spec-$z$ for the bright end of the ERGs
sample down to $g_{\mathrm{AB}}\approx 24.0$, and with 30 m class telescopes,
spec-$z$ can be obtained for sources down to $g_{\mathrm{AB}}\approx 26.0$.

Figure 3:  (Left) The relation between SFR and stellar-mass ($M_{\star}$) of
the WERGS sample. The both values are obtained from the SED fitting by Toba et
al. (2019). The blue circles represent the NRGs. The orange and red stars
represent ERGs at $z>1$ and $z<1$, respectively. The large points show the
average of each sample. The shaded area is the expected main-sequence region
from $z=0.3$ (minimum) to $z=1.6$ (maximum) with the scatter of $\sigma=0.35$
at $z=0.3$ and $\sigma=0.24$ at $z=1.6$, which is obtained from Pearson et al.
(2018). The redshift evolution of the relation is summarized in Figure 10.
(Right) Redshift dependence of the ratio SFR/SFR(MS) of the WERGS sample. The
1$\sigma$ scatter is shown with the orange shaded area, which is also obtained
from Pearson et al. (2018).

####  3.1.2 $L$–$z$ plane

Figure 2 shows the radio and IR AGN luminosities of our sample as a function
of redshift. The 1.4 GHz radio luminosity ($L_{\mathrm{1.4GHz}}$ W Hz-1) is
taken from Yamashita et al. (2018) or Toba et al. (2019), in which the
integrated flux density ($f_{\mathrm{int}}$) obtained by the VLA/FIRST final
catalog (Helfand et al., 2015) is used, and $k$-correction is applied by
assuming a power-law radio spectrum with $f_{\nu}\propto\nu^{\alpha}$, where
$\alpha$ is estimated with
$\alpha=\log(f_{\mathrm{1.4GHz}}/f_{\mathrm{150MHz}})/\log(\nu_{\mathrm{1.4GHz}}/\nu_{\mathrm{150MHz}})$
for the objects having TGSS 150 MHz data (Intema et al., 2017), and
$\alpha=-0.7$ for all others (e.g., Condon, 1992).

As shown in the left panel of Figure 2, ERGs show relatively high radio
luminosities with a median of
$\langle\log(L_{\mathrm{1.4GHz}}/\mathrm{W~{}Hz{{}^{-1}}})\rangle=26.3$, which
is one order of magnitude higher than that of the NRGs
($\langle\log(L_{\mathrm{1.4GHz}}/\mathrm{W~{}Hz{{}^{-1}}})\rangle=25.1$). On
the other hand, in terms of the IR AGN luminosity shown in the right panel,
there is no clear difference between ERGs and the NRGs
$\langle\log(L_{\mathrm{AGN,IR}}/\mathrm{erg}~{}\mathrm{s}^{-1})\rangle=44.9$
for ERGs and
$\langle\log(L_{\mathrm{AGN,IR}}/\mathrm{erg}~{}\mathrm{s}^{-1})\rangle=44.6$
for the NRGs. We therefore assume ERGs to be intrinsically radio-louder
sources than NRGs, and we will discuss this in Section 4.1.

Figure 4:  The stellar-mass ($M_{\star}$) as a function of the radio
luminosity $\log L_{\mathrm{1.4GHz}}$. The points are the same as in Figure 1.

###  3.2 Host Galaxy Properties

The left panel of Figure 3 shows the distribution of our RGs in the SFR and
$M_{\star}$ plane, where both values are obtained from the optical+IR SED
fitting with `CIGALE` (Toba et al., 2019). It is known that most star-forming
galaxies follow the main-sequence (MS) whose normalization moves upward with
redshift, as galaxies are more gas-rich at higher $z$ (e.g., Brinchmann et
al., 2004; Noeske et al., 2007; Elbaz et al., 2011; Whitaker et al., 2012;
Schreiber et al., 2015a). Above the MS, galaxies are referred to as starburst
galaxies, producing stars more efficiently than regular star-forming galaxies.
Pearson et al. (2018) measured the SFR and $M_{\star}$ using multi-wavelength
data from UV to far-IR employing the `CIGALE` code, and their MS is delineated
with the shaded area in Figure 3, whose bottom and top boundaries correspond
to redshifts of $z=0.3$ and $z=1.6$ with the scatter of $\sigma=0.35$ at
$z=0.3$ and $\sigma=0.24$ at $z=1.6$, respectively. In this study, we define
the sources as starburst galaxies if they are located above the yellow shaded
MS area, which is roughly consistent with the criteria in previous studies
(e.g., Elbaz et al., 2011).

Considering that our sample spans a wide redshift range in $0.3<z<1.6$ and
their rapid redshift evolution of MS, redshift dependence is a key factor to
understand the relation in the left panel of Figure 3. Therefore we also
calculate the ratios between the observed SFRs and those predicted from the MS
relations at a given stellar-mass, that is SFR/SFR(MS), and its redshift
dependence is shown in the right panel of Figure 3. We also compile how the
SFR and $M_{\star}$ relation evolves with redshift in Appendix B and Figure 10
(top panels).

Figure 3 shows several sequences of sources, notably at around sSFR$\sim
10^{-10.5}$, $\sim 10^{-9}$, and $\sim 10^{-8}$ yr-1, and the sources locate
scarcely between the sequences. This does not originate from the properties of
nature, but more mainly from the complications of the limited bin numbers of
the SED fitting parameters of star-forming history (SFH). In our case, the
most notable contribution is considered to be $f_{\mathrm{burst}}$; mass
fraction of the burst population. Toba et al. (2019) set a limited parameter
binning of $f_{\mathrm{burst}}=0.001,0.1$, and $0.3$, which is roughly
corresponding to the bindings at sSFR$\sim 10^{-10.5},10^{-9},$ and $10^{-8}$
yr-1. This banding might disappear once we follow the same SFH parameter
binning of Pearson et al. (2018), which was impossible for our studies because
of the additional parameters of AGN and radio components which increase the
computational time exponentially. Therefore instead we assume that SFRs in
this study have large uncertainty of $\sim 0.5$ dex. Please see the more
detailed discussion on the choice of the SFH parameters and their effects on
the SFR estimations (e.g., Schreiber et al., 2015b; Ciesla et al., 2017;
Pearson et al., 2018).

Although our SFR estimation by Toba et al. (2019) might harbor large
uncertainties as discussed above, Figure 3 shows three important suggestions.
One is that most ERGs are distributed above the MS by a factor of $\sim 10$
(see the right panel), suggesting that most ERGs are in starburst mode and
they contain a copious amount of gas. This is indirect evidence for the
availability of cold gas supply fueling both star-formation, and the central
SMBHs. The specific star-formation rate defined by
$\mathrm{sSFR}=\mathrm{SFR}/M_{\star}$ reaches $\mathrm{sSFR}\sim 10^{-8}$
yr-1 for ERGs, suggesting that ERGs are in a rapid stellar-mass assembly phase
with mass doubling times of only $\sim 100$ Myr. This value is also comparable
to one starburst duration (e.g., McQuinn et al., 2010) and thus most of the
stellar component is expected to be dominated by a very young population.

Second, the onset of AGN feedback on the host galaxies has apparently not
(yet) happened to most ERGs considering their location above the MS. This
indicates a different picture from the conventional local RGs, which show a
preference of massive host galaxies ($M_{\star}>10^{11}M_{\odot}$) and fall
below the MS because their strong AGN feedback quenches star formation (e.g.,
Seymour et al., 2007). Note that our sample requires IR detections for the
`CIGALE` SED fitting to derive stellar-mass and SFR, therefore the WERGS not
detected in IR do not appear in Figure 3. In addition to that, our sample
requires radio compact morphologies, which removes a large population of
local, radio-extended RGs. These two selection criteria may introduce a
selection bias, since it is possible that these IR non-detection or radio
extended sources are clustered below the SF main-sequence. It is nonetheless
intriguing that ERGs are located at the top edge of the distribution within
the WERGS sample with IR detections.

The third point is that, if we limit ourselves to the sources with $z<1$ (red
star points), most of these are clustered at the low-$M_{\star}$ end,
typically at $\log M_{\star}/M_{\odot}<10$. This suggests that the low-$z$
subsample of ERGs is potentially important with regard to the study of BH
seeds. Considering that all of our sources fulfill (1)
$L_{\mathrm{1.4GHz}}>10^{24}$ $\mathrm{W}~{}\mathrm{Hz}^{-1}$, that is, they
lie above the threshold where their radio luminosity could be produced by star
formation, as discussed in Section 2.1.2, and (2) the radio-excess selection
with $q_{\mathrm{IR}}<1.68$, their radio emission can only be achieved by the
AGN jet, requiring the existence of a SMBH at the center. Therefore, ERGs
contain massive BH candidates residing in low-mass galaxies.

Figure 4 shows the distribution of ERGs and NRGs in the $M_{\star}$ and
$L_{\mathrm{1.4GHz}}$ plane, and illustrates the third point above from a
different aspect. ERGs populate regions of comparatively small stellar-mass
and high $L_{\mathrm{1.4GHz}}$, showing that higher $\mathcal{R_{\rm rest}}$
sources tend to have smaller $M_{\star}$ as well as higher
$L_{\mathrm{1.4GHz}}$. The combined results from above and from Figure 1
suggest that smaller $M_{\star}$ sources tend to observed as optically fainter
sources, and are therefore observed as high $\mathcal{R_{\rm rest}}$ sources.
We will discuss this point later in Section 4.1.

Figure 5:  sBHAR properties for ERGs and NRGs in this study. The colors and
symbols are same as in Figure 1. (Left) the distribution of sBHAR. The median
of sBHAR is
$\langle\log(\mathrm{sBHAR}/\mathrm{erg}~{}\mathrm{s}^{-1}~{}M_{\odot}^{-1})\rangle=35.3$
for ERGs and
$\langle\log(\mathrm{sBHAR}/\mathrm{erg}~{}\mathrm{s}^{-1}~{}M_{\odot}^{-1})\rangle=34.0$
for NRGs. (Right) The relation between sBHAR and $M_{\star}$. The two straight
lines are the expected Eddington-limits $\lambda_{\mathrm{Edd}}=1$ using
Equation (4; gray dashed line) and using Equation (5; black dot-dashed line).
The redshift evolution of the relation is summarized in the middle panels of
Figure 10.

###  3.3 SMBH Properties: Relation between sBHAR and $M_{\star}$

Considering that most ERGs are very faint
($\left<g_{\mathrm{AB}}\right>=24.5$) in optical, as shown in Figure 1 and
Section 3.1.1, obtaining the BH virial mass from spectroscopy (e.g., McLure &
Dunlop, 2004) is time-consuming and difficult even if they are type-1 AGN.
This means that the direct measurement of the Eddington ratio
($\lambda_{\mathrm{Edd}}\equiv L_{\mathrm{AGN,bol}}/L_{\mathrm{Edd}}$, where
$L_{\mathrm{Edd}}$ is Eddington luminosity $L_{\mathrm{Edd}}\simeq 1.26\times
10^{38}(M_{\mathrm{BH}}/M_{\odot})$ erg s-1), is difficult at this stage.
Instead, we investigate the SMBH properties through the specific black hole
accretion rate (hereafter, sBHAR), which may be considered a proxy for the
Eddington ratio. The sBHAR is conventionally defined as
$\mathrm{sBHAR}=L_{\mathrm{AGN,bol}}/M_{\star}$
$\mathrm{erg}~{}\mathrm{s}^{-1}~{}M_{\odot}^{-1}$ (e.g., Mullaney et al.,
2012). The left panel of Figure 5 shows the distribution of sBHAR for ERGs and
NRGs. The median sBHAR of ERGs is
$\langle\log(\mathrm{sBHAR}/\mathrm{erg}~{}\mathrm{s}^{-1}~{}M_{\odot}^{-1})\rangle=35.3$,
which is an order of magnitude higher than that of the NRGs with
$\langle\log(\mathrm{sBHAR}/\mathrm{erg}~{}\mathrm{s}^{-1}~{}M_{\odot}^{-1})\rangle=34.0$.
Based on Best & Heckman (2012), the boundary of radiatively inefficient and
efficient AGN is at an Eddington ratio of $\log\lambda_{\mathrm{Edd}}\sim-2$,
which corresponds to
$\log(\mathrm{sBHAR}/\mathrm{erg}~{}\mathrm{s}^{-1}~{}M_{\odot}^{-1})=32$–$33$.
Thus, almost all of our sources are considered to be radiatively efficient
AGN.

This difference in sBHAR between the two subgroups is more pronounced in the
right panel of Figure 5, showing sBHAR as a function of $M_{\star}$. To
illustrate the dependence of $M_{\star}$ and $\lambda_{\mathrm{Edd}}$ on sBHAR
more clearly, we use local scaling relations between $M_{\mathrm{BH}}$ and
$M_{\star}$. Previous studies assumed a constant ratio of
$M_{\mathrm{BH}}/M_{\mathrm{bulge}}=(1.5-2.0)\times 10^{-3}$ (Marconi & Hunt,
2003; Häring & Rix, 2004) and $M_{\mathrm{bulge}}\approx M_{\star}$ for
simplicity (Aird et al., 2012; Mullaney et al., 2012; Delvecchio et al., 2018;
Aird et al., 2019). In this study, we apply stellar-mass dependent values for
$M_{\mathrm{BH}}$ with $M_{\mathrm{BH}}\propto M_{\star}^{\beta}$, where
$\beta=1.4$ (KH13; Kormendy & Ho, 2013) and $\beta=1.05$ (RV15; Reines &
Volonteri, 2015). With this relation, sBHAR can be written as a function of
$\lambda_{\mathrm{Edd}}$ and $M_{\star}$ by

$\displaystyle\mathrm{sBHAR(KH13)}=4.6\times
10^{35}\lambda_{\mathrm{Edd}}\left(M_{\star}/10^{10}~{}M_{\odot}\right)^{0.4},$
(4) $\displaystyle\mathrm{sBHAR(RV15)}=3.2\times
10^{34}\lambda_{\mathrm{Edd}}\left(M_{\star}/10^{10}~{}M_{\odot}\right)^{0.05}.$
(5)

The right panel of Figure 5 exhibits that ERGs are more clustered in the high
Eddington ratio regime. The expected median Eddington ratio by using Eq. (4)
is $\left<\log\lambda_{\mathrm{Edd}}\right>\approx-0.4$. Some sources appear
to exceed the Eddington limit. NRGs cover a broader range in sBHAR, and some
massive galaxies with $M_{\star}>10^{11}M_{\odot}$ fall into the radiatively
in-efficient regime with $\lambda_{\mathrm{Edd}}<-2$.

We caution that the above discussion does not take into account the redshift
evolution of the $M_{\mathrm{BH}}$–$M_{\star}$ relation, which has been
suggested in some studies (e.g., Woo et al., 2008; Merloni et al., 2010; Ding
et al., 2020). In this case, the estimated $M_{\mathrm{BH}}$ becomes larger at
a given $M_{\star}$, and the resulting Eddington ratio becomes smaller.
Assuming the evolutional trend of Merloni et al. (2010), with
$M_{\mathrm{BH}}/M_{\star}(z)\propto(1+z)^{0.68}$, and using a median redshift
for the ERGs of $\langle z\rangle=1.1$, the normalization of sBHAR becomes
slightly smaller by a factor of 1.6. As shown in Figure 5, this difference
does not change our overall result. Although there are other significant
uncertainties and possible systematics of the expected
$\lambda_{\mathrm{Edd}}$ values, under the basic assumptions of Equations (4)
or (5), our results suggest that higher $\mathcal{R_{\rm rest}}$ sources have
higher sBHAR, and ERGs might contain sources achieving super-Eddington
accretion. We will discuss this point in Section 4.1.

In summary, our results indicate that ERGs exhibit high sBHAR with the
expected Eddington ratio of
$\left<\log\lambda_{\mathrm{Edd}}\right>\approx-0.4$, and some ERGs may be
experiencing a super-Eddington phase. In addition, ERGs are likely starburst
galaxies and their stellar-mass is relatively lower than NRGs. ERGs appear to
be in a phase preceding the onset of AGN feedback. If we limit the sample to
$z<1$, most ERGs are low-mass galaxies with $M_{\star}<10^{10}M_{\odot}$.
Therefore, lower-$z$ ERGs are also candidates of massive, rapidly growing BHs.

##  4 Discussion

Figure 6:  The distribution of
$L_{\mathrm{jet}}/\mathrm{erg}~{}\mathrm{s}^{-1}$ (left),
$L_{\mathrm{jet}}/L_{\mathrm{AGN,bol}}$, an indicator of intrinsic
$\mathcal{R_{\mathrm{int}}}$ (middle), and $\eta_{\mathrm{jet}}$ assuming the
radiative efficiency of 0.1 (right). The color is same as in Figure 1.  Figure
7:  The relationship between
$L_{\mathrm{jet}}/L_{\mathrm{AGN,bol}}=\mathcal{R_{\mathrm{int}}}$ and sBHAR.
The yellow shaded area represents the corresponding $\lambda_{\mathrm{Edd}}=1$
region assuming that $M_{\mathrm{BH}}$ is based on the
$M_{\mathrm{BH}}$–$M_{\star}$ relation by Kormendy & Ho (2013). The symbols
are same as those in Figure 1, but other WERGS sources are shown with color
gradation based on $\mathcal{R_{\rm rest}}$ in the range of
$1<\log\mathcal{R_{\rm rest}}<4$. The redshift evolution of the relation is
summarized in the bottom panels of Figure 10.

###  4.1 What Does High $\mathcal{R_{\rm rest}}$ Mean?

Figures 1 and 2 indicate that ERGs or high $\mathcal{R_{\rm rest}}$ sources
tend to trace optically-faint, but radio-loud AGN. In addition, Figure 4 shows
that higher $\mathcal{R_{\rm rest}}$ tends to pick up relatively lower
stellar-mass population. This means that the selection of ERGs using
$\mathcal{R_{\rm rest}}$ has a preference of selecting smaller $M_{\star}$
and, therefore, $\mathcal{R_{\rm rest}}$ using optical bands does not seem to
trace AGN accretion disk emission in the optical band. This is not a new
result, but it is a long-standing issue surrounding the use of the optical
radio-loudness $\mathcal{R_{\rm rest}}$: it is strongly affected by host
galaxy contamination and/or the nuclear obscuration around the SMBHs
(Terashima & Wilson, 2003; Ho, 2008). This raises the question of whether ERGs
are intrinsically radio-loud or not.

To investigate this, we estimate the “intrinsic” radio-loudness
$\mathcal{R_{\mathrm{int}}}$; the energy balance between the jet and
accretion-disk defined by
$\mathcal{R_{\mathrm{int}}}=L_{\mathrm{jet}}/L_{\mathrm{AGN,bol}}$, which is
frequency-independent, and also free from the contamination of host galaxy
component, unlike $\mathcal{R_{\rm rest}}$ (e.g., Terashima & Wilson, 2003).
For the accretion disk luminosity, we use the bolometric AGN luminosity
$L_{\mathrm{AGN,bol}}$ obtained from the IR AGN luminosity
($L_{\mathrm{AGN,IR}}$), since $L_{\mathrm{AGN,IR}}$ is derived from IR SED
decomposition, which traces the re-radiation of the dust powered by AGN and is
mostly insusceptible to absorption (Gandhi et al., 2009; Asmus et al., 2015;
Ichikawa et al., 2012, 2017, 2019).

The total jet power of the AGN ($L_{\mathrm{jet}}$) can be estimated from the
radio luminosity of the compact core or from the total radio emission (Willott
et al., 1999; Cavagnolo et al., 2010; O’Sullivan et al., 2011). We adopt the
relation between $L_{\mathrm{jet}}$ and $L_{\mathrm{1.4GHz}}$ of Cavagnolo et
al. (2010),

$\displaystyle L_{\mathrm{jet}}=7.3\times
10^{43}~{}(L_{\mathrm{1.4GHz}}/10^{24}~{}\mathrm{W}~{}\mathrm{Hz}^{-1})^{0.70}~{}\mathrm{erg}~{}\mathrm{s}^{-1}.$
(6)

Note that the above equation is derived with the assumption that most radio
sources have a spectral index of $\alpha=0.8$. This value is almost consistent
with the median value of our WERGS sample; $\alpha=0.65$ for the sources with
detections at both TGSS 150 MHz and VLA/FIRST 1.4 GHz, or the fiducial value
of $\alpha=0.7$ for the sources whose radio band detection is only in one band
(i.e., VLA/FIRST 1.4 GHz only) (Condon, 1992). Shabala & Godfrey (2013)
recently investigated the effect of the radio source size in the jet power
estimation, and found the dependence on the source size to be $\propto
D^{0.58}$, suggesting that the effect of the source size is small. Since our
sample is selected only for radio-compact emission in VLA/FIRST with a spatial
resolution of $\sim 5$ arcsec (or $\lesssim 20$ kpc at $z\sim 1$) this again
mitigates the size dependence; otherwise the sources are ultra-compact
sources.

The left panel of Figure 6 shows the distribution of $L_{\mathrm{jet}}$,
spanning $44.0<\log(L_{\mathrm{jet}}/\mathrm{erg}~{}\mathrm{s}^{-1})<46.4$,
and the median values are $\left<\log
L_{\mathrm{jet}}/\mathrm{erg}~{}\mathrm{s}^{-1}\right>=45.4$ for ERGs and
$\left<\log L_{\mathrm{jet}}/\mathrm{erg}~{}\mathrm{s}^{-1}\right>=44.6$ for
NRGs, which is equivalent to the radio-loud quasar level (e.g., Best et al.,
2005; Inoue et al., 2017). This is naturally expected since we apply the
simple conversion relation (Eq. 6), all of our sources are selected based on
VLA/FIRST detection with the $>1$ mJy flux limit, and the radio luminosity
range is similar to that of the FIRST-SDSS sample, although they are located
in relatively higher-$z$ (see Figure 2).

This high $L_{\mathrm{jet}}$ is powerful enough to produce a radio jet with
the size of $\gtrsim 10$ kpc that can disperse the interstellar medium (e.g.,
Nesvadba et al., 2017) and create cavities in the galactic inster-stellar
medium and larger scale intergalactic environment to possibly quench star-
formation in host galaxies (e.g., McNamara & Nulsen, 2007). Given the compact
radio sizes of the sources in our sample ($<5$ arcsec or $\lesssim 20$ kpc at
$z\sim 1$) and given the fact that the host galaxies are still in an active
star-forming phase (Figure 3), ERGs and the WERGS sources above or on the SF
main-sequence may still be in the phase before the onset of huge kinetic radio
feedback.

The middle panel of Figure 6 shows the distribution of
$\mathcal{R_{\mathrm{int}}}$, and the median values of the two populations are
$\left<\log\mathcal{R_{\mathrm{int}}}\right>=0.0$ for ERGs, and
$\left<\log\mathcal{R_{\mathrm{int}}}\right>=-0.5$ for NRGs. For half of the
ERGs, $\mathcal{R_{\mathrm{int}}}>1$, that is, the jet kinetic power is higher
than the radiation from the accretion disk. The physical properties of higher
$\mathcal{R_{\rm rest}}$ sources are more clearly illustrated in Figure 7,
which shows the distribution of ERGs and other WERGS sources in the
$\mathcal{R_{\mathrm{int}}}$–sBHAR plane. The yellow shaded area is the region
corresponding to $\lambda_{\mathrm{Edd}}=1$ assuming Equation (4) for the
range of $8<\log(M_{\star}/M_{\odot})<12$. The other WERGS sources are shown
with a color gradation in $\log\mathcal{R_{\rm rest}}$, with higher
$\mathcal{R_{\rm rest}}$ lying toward the top right of the plot. This means
that higher $\mathcal{R_{\rm rest}}$ sources tend to have both higher
$\lambda_{\mathrm{Edd}}$ and higher $\mathcal{R_{\mathrm{int}}}$. It is well
known that radio galaxies are more radio-loud as the Eddington-scaled
accretion rate decreases, producing the sequence from the top left region
toward the bottom right one in Figure 7 (Ho, 2002; Merloni & Heinz, 2007;
Panessa et al., 2007; Sikora et al., 2007, 2013; Ho, 2008), and overall NRGs
also follow this trend. However, ERGs are located in the top right part of the
plane, suggesting that ERGs contain rapidly growing BH in the center, and at
the same time harbor powerful, compact radio-jets.

These radio galaxies are different from the conventional radio galaxies in the
local universe (Seymour et al., 2007). Delvecchio et al. (2018) recently found
that high-$z$ ($z>1.5$) radio galaxies discovered in the VLA/COSMOS survey
tend to have high Eddington ratios with $\log\lambda_{\mathrm{Edd}}>-2$ and
that they are also starforming or starburst galaxies. This is consistent with
the properties of our overall WERGS sample (see also Toba et al., 2019), and
thus ERGs occupy the extreme end of highly accreting BHs in radio galaxies.

###  4.2 $\eta_{\mathrm{jet}}$ and the Origin of Radio Emission in ERGs

Figure 7 indicates that ERGs are a very interesting population, showing both
radiative (high $\lambda_{\mathrm{Edd}}$) and jet-efficient (high
$\mathcal{R_{\mathrm{int}}}$) emission, which were missed in previous surveys.
To investigate the jet properties in more detail, we here discuss the jet
efficiency of ERGs and compare the obtained values with other radio sources.
The jet production efficiency is defined as

$\eta_{\mathrm{jet}}=L_{\mathrm{jet}}/\dot{M}_{\mathrm{BH}}c^{2}=\eta_{\mathrm{rad}}L_{\mathrm{jet}}/L_{\mathrm{AGN,bol}}$
(7)

where $\eta_{\mathrm{rad}}$ is the radiation efficiency of an AGN accretion
disk, $c$ is the speed of light, and $\dot{M}_{\mathrm{BH}}$ is the mass
accretion rate onto the SMBH through the disk. In the following, we adopt a
canonical value of $\eta_{\mathrm{rad}}=0.1$ based on the Soltan-Paczynski
argument (Soltan, 1982).

The distribution of $\eta_{\mathrm{jet}}$ is shown in the right panel of
Figure 6. The median values are $\left<\log\eta_{\mathrm{jet}}\right>=-1.0\pm
0.3$ for ERGs and $\left<\log\eta_{\mathrm{jet}}\right>=-1.5\pm 0.4$ for NRGs.
These values are slightly higher or consistent with the nearby radio AGN
population ($\log\eta_{\mathrm{jet}}\sim-1.5$) whose host galaxies are massive
($M_{\star}>10^{11}M_{\odot}$; Nemmen & Tchekhovskoy, 2015). However, the
local radio AGN population generally has much smaller Eddington ratios of
$\log\lambda_{\mathrm{Edd}}<-2$. This population would be located in the top
left region in Figure 7, so they are clearly different from ERGs. The
$\eta_{\mathrm{jet}}$ of ERGs is higher by a factor of $\sim 10$ compared to
the SDSS radio quasar population, whose radio jet efficiency lies at
$\left<\log\eta_{\mathrm{jet}}\right>=-2.0\pm 0.5$ (e.g., van Velzen & Falcke,
2013; Inoue et al., 2017). Considering that the SDSS radio quasars on average
show $\log\lambda_{\mathrm{Edd}}\sim-1$, those radio quasars would be located
at the bottom-center to bottom-right of Figure 7, which is again different to
the distribution of ERGs. Therefore, the disk-jet connection may be
fundamentally different from the standard disk model, which conventionally
describes the quasar/AGN accretion disk emission.

One possible origin of this high production efficiency of radiation and jets
is that the accretion disk of ERGs is actually in the “radiatively
inefficient” state, but the physical origin of radiative inefficiency is
different from the disks in the local radio galaxies. For example, the ERGs
may be undergoing more rapid mass accretion (so called slim disk model;
Abramowicz et al., 1988). Recent radiation hydrodynamical simulations suggest
that when the mass accretion rate significantly exceeds the Eddington rate,
radiation is effectively trapped within the accreting matter and advected to
the central BH before escaping by radiative diffusion. As a result, the
emergent radiation luminosity is saturated at the order of $L_{\mathrm{Edd}}$
(i.e., $\eta_{\mathrm{rad}}\lesssim 0.1$ at $\gg\dot{M}_{\mathrm{Edd}}$) and
the accretion flow turns into a radiatively inefficient state even with a
super-Eddington accretion rate (e.g., Ohsuga et al., 2005, 2009; McKinney et
al., 2014; Inayoshi et al., 2016; Takeo et al., 2020). This phase is
considered to be a key process of the BH seed growth in the high-$z$ ($z>6$)
universe to describe the already known massive high-$z$ SMBHs (e.g., Mortlock
et al., 2011; Wu et al., 2015; Bañados et al., 2018; Onoue et al., 2019).

In the situation that the accretion rate is well above the Eddington rate, a
relativistic jet can be launched by the Blandford-Znajek mechanism if large-
scale magnetic fields exist in the innermost region (Blandford & Znajek, 1977;
Tchekhovskoy et al., 2011). The jet behavior of these extreme cases has been
investigated by several authors (Sadowski et al., 2014; Sadowski & Narayan,
2015) using a 3D general relativistic radiation magneto-hydrodynamical
simulation (GRRMHD) code. They find that, in these (super-)Eddington accretion
phase, BHs emit a significant amount of radiation and jet energy, and both the
radiation and jet power approach around the Eddington limit, which appears to
be the case for ERGs and the sources in the top right region in Figure 7 (see
also Blandford et al., 2019). Thus, the study of ERGs at $z\sim 1$ will be
complementary to studies utilizing the next generation instruments capable of
observing seed BHs in the early universe at $z\gtrsim 7$ (Haiman et al., 2019)
in the investigations of the growth of seed BHs.

Figure 8:  A schematic view of the relationship between $M_{\mathrm{BH}}$ and
$M_{\star}$. The local relations by Kormendy & Ho (2013) and Reines &
Volonteri (2015) are shown as dot-dashed (black; the fiducial relation in this
study) and solid-line (gray), respectively. The orange shaded region
represents the range of over-massive BH, which is at least one order of
magnitude higher than the local relations (Case 1 in Section 4.3), and the
region is delineated by $10^{8}<M_{\star}/M_{\odot}<10^{10}$ and
$10^{-2}<M_{\mathrm{BH}}/M_{\star}<1$. The blue shaded region represents the
range of under-massive BH, in which host galaxies form first, and BH grow
later (Case 2 in Section 4.3). This region is delineated by
$10^{8}<M_{\star}/M_{\odot}<10^{10}$ and $10^{-2}<M_{\mathrm{BH}}/M_{\star}$
and smaller than the local relation by Reines & Volonteri (2015). The red
shaded region represents the forbidden region where the BH cannot exceed
$M_{\mathrm{BH}}\lesssim 3\times 10^{10}M_{\odot}$ (Inayoshi & Haiman, 2016;
Ichikawa & Inayoshi, 2017).

###  4.3 Alternative Scenarios: If ERGs Do Not Follow Local Scaling Relations
between $M_{\mathrm{BH}}$ and $M_{\star}$

The discussion related to the Eddington ratio depends on the $M_{\mathrm{BH}}$
estimation, which in turn relies on the local scaling relation of Kormendy &
Ho (2013). However, it is not obvious that this relation also holds in the
low-mass end in which many ERGs probably reside. Although the current data
cannot give any constraints on this issue and a more detailed study is beyond
the scope of this paper, we discuss two alternative scenarios, in which our
galaxies are above (case one) or below (case two) the correlation between
$M_{\mathrm{BH}}$ and $M_{\star}$ as shown in Figure 8.

Case one reflects the possibility that ERGs might host over-massive BHs
compared to the relation by Kormendy & Ho (2013), with the BH-to-stellar-mass
ratio $f_{\mathrm{b,\star}}\equiv M_{\mathrm{BH}}/M_{\star}\gtrsim 10^{-2}$
(see the orange shaded area in Figure 8). In this case, concerns surrounding
super-Eddington accretion discussed in Section 3.3 and 4.1 are alleviated: the
median Eddington ratio for ERGs can be parametrized by
$\langle\lambda_{\mathrm{Edd}}\rangle\simeq
0.17~{}(f_{\mathrm{b,\star}}/0.01)^{-1}$.

In addition, the possible future growth path in the plane of $M_{\mathrm{BH}}$
and $M_{\star}$ can be discussed by assuming the current BH/stellar mass
assembly rate. Since the radiation efficiency is $\eta_{\mathrm{rad}}=0.1$ in
the sub-Eddington regime, the BH accretion rate is estimated as
$\dot{M}_{\mathrm{BH}}=L_{\mathrm{AGN,bol}}/(\eta_{\mathrm{rad}}c^{2})\simeq
1.7\times 10^{-3}f_{\mathrm{b,\star}}^{-1}\dot{M}_{\mathrm{Edd}}$, where the
median Eddington ratio above is substituted (note that this equation is valid
at $f_{\mathrm{b,\star}}\gtrsim 1.7\times 10^{-3}$). Comparing the BH
accretion rate to the sSFR of ERGs (sSFR$=\mathrm{SFR}/M_{\star}\simeq
10^{-8}~{}\mathrm{yr}^{-1}$; see Figure 3), we obtain
$\dot{M}_{\mathrm{BH}}/\mathrm{SFR}\simeq 4\times 10^{-3}$, which is
independent of the choice of $f_{\mathrm{b,\star}}$. Therefore, the BH-galaxy
mass ratio for ERGs is expected to approach a canonical value observed in the
local universe (e.g., $f_{\mathrm{b,\star}}\sim 3\times 10^{-3}$; Kormendy &
Ho, 2013). This evolutional path might be analogous to that of known high-$z$
luminous quasars whose SMBHs are likely over-massive compared to the local
relation with $10^{-2}\lesssim f_{\mathrm{b,\star}}\lesssim 2\times 10^{-1}$
(e.g., Wang et al., 2013, 2016; Trakhtenbrot et al., 2015; Decarli et al.,
2018).

Case two considers the possibility that ERGs might host very under-massive BHs
with $f_{\mathrm{b,\star}}\lesssim 10^{-3}$–$10^{-4}$ as shown in the blue
shaded region in Figure 8. For instance, the overall normalization for late-
type galaxies may be considerably lower than for the local relation of early-
type galaxies (e.g., Reines & Volonteri, 2015; Läsker et al., 2016; Greene et
al., 2019). This “galaxy grows first, BH come later” phase may occur because
gas accretion onto the BHs is quite inefficient due to efficient stellar
feedback, e.g., star formation-driven outflows, and the shallow halo potential
until the stellar-mass reaches a critical value of $M_{\star}\sim
10^{10.5}M_{\odot}$ (e.g., Bower et al., 2017; Habouzit et al., 2017).
However, once the galaxy reaches the critical mass, above which star
formation-driven outflows no longer prevent the gas accretion to the galactic
nuclei, they abruptly switch to a rapid growth phase in the absence of
feedback, and finally merge into the local relation. ERGs with
$M_{\star}\gtrsim 10^{10.5}M_{\odot}$ might be in such a rapidly growing
phase.

The scenario above looks promising but it is worth discussing the critical
mass value because the stellar mass of most ERGs actually lies below the
expected critical mass. Beside, Figure 5 shows that the median sBHAR (and
therefore $\lambda_{\mathrm{Edd}}$) tends to be higher for less massive ERGs
with the median Eddington ratio of $\langle\lambda_{\mathrm{Edd}}\rangle\simeq
1.7~{}(f_{\mathrm{b,\star}}/10^{-3})^{-1}$, suggesting that the extreme BH
growth is possible (at least temporally) even in lower mass galaxies. This
discrepancy may reflect that there are missing understanding on the physics of
AGN feedback and gas feeding in low mass galaxies.

Another interesting point in the second scenario is that the Eddington ratio
for several ERGs becomes as high as $\lambda_{\mathrm{Edd}}\sim 10^{2}$.
Recent numerical simulations suggest that for a highly magnetized accretion
disk around a rapidly spinning BH, the disk transits into a magnetically
arrested disk (MAD) state and produces high radiative luminosity (e.g.,
McKinney et al., 2014; Sadowski & Narayan, 2015). Through the emission
process, the level of high luminosity could be achieved only when the BH mass
accretion exceeds $\sim 10^{3}~{}\dot{M}_{\mathrm{Edd}}$ (Inayoshi et al.
2016; see also Figure 5 in Inayoshi et al. 2019). Therefore, if this scenario
is true, future follow-up observations of those ERGs with such high Eddington
ratios would reveal the properties of possibly hyper-Eddington accreting BHs
(Takeo et al., 2020).

###  4.4 Prospects for AGN Feedback in Low-Mass Galaxies through ERGs

In recent years, the theoretical study of AGN feedback has been extended to
low-mass galaxies (Silk, 2017). This was motivated mainly by the increasing
number of intriguing observational results showing signs of AGN feedback in
low-mass galaxies (Nyland et al., 2017; Penny et al., 2018; Kaviraj et al.,
2019; Dickey et al., 2019; Mezcua et al., 2019). Our results show that the jet
power of $L_{\mathrm{jet}}>10^{44}$ erg s-1 in ERGs is equivalent to that
produced from radio quasars and local radio AGN residing in massive galaxies.
This suggests the presence of a strong jet that can disperse or even expel the
interstellar medium (e.g., Morganti et al., 2005; Holt et al., 2008; Nesvadba
et al., 2017) or produce cavities in the host galaxies, which are often
observed in the local massive counterparts (e.g., Rafferty et al., 2006;
McNamara & Nulsen, 2007; Bîrzan et al., 2008; Blandford et al., 2019). On the
other hand, low stellar-mass ERGs are still in a starburst phase, indicative
of a substantial gas reservoir, and lacking clear signatures of negative AGN
feedback222Numerical simulations suggest that mechanical feedbacks associated
with jets would impact upon their host galaxies with a significant delay time,
which might be marginally longer than the typical AGN lifetime (Costa et al.,
2018).

To investigate whether such a negative feedback from the jet is effective in
the host galaxies, it is necessary to obtain high spatial resolution radio
images that resolve the host galaxy down to scales of $<10$ kpc (Reines et
al., 2020). Our sample of compact radio sources from VLA/FIRST with a spatial
resolution of $\sim 5$ arcsec only provide poor upper-bounds of the radio jet
size of $<40$ kpc at $z\sim 1$. Future higher quality observations with sub-
arcsecond resolution will provide more insight into the effect of the jet on
the host galaxy.

Given that the BH mass of ERGs might reach the massive BH range below
$M_{\mathrm{BH}}\sim 10^{6}M_{\odot}$, studying the properties of ERGs gives a
window into understanding seed BH growth in the high-$z$ universe. Some
observational studies recently suggested that AGN feedback might also have
positive effect on the host galaxies, and intensive in situ star formation is
ignited in the outflowing gas launched by the AGN (Maiolino et al., 2017).
Recent numerical simulations of jet-driven feedback also predict star-
formation triggered on galaxy scales by the overpressure of the jet during the
first few Myrs of strong interaction between the jet and the interstellar
medium (Wagner & Bicknell, 2011; Wagner et al., 2016; Gaibler et al., 2012;
Mukherjee et al., 2018). If the radio jets in low-mass galaxies have a
positive impact on both star formation and BH growth, then radio-selected AGN
in low-mass galaxies are an intriguing population for understanding the BH and
stellar mass assembly in the environment of shallow potential low-mass
galaxies.

###  4.5 Wide Area Radio and Optical Surveys; Potential for Discovering
Previously Missed Populations

The small number density of ERGs ($\sim 1$ source deg-2) and their optical
faintness of $i_{\mathrm{AB}}\sim 25$ suggest that ERGs were easily missed in
previous optical surveys of radio sources. Our work shows that ERGs can be
discovered with wide ($>100$ deg2) and deep ($i_{\mathrm{AB}}\lesssim 26$)
optical follow-up observations of radio sources. The number of known ERGs will
increase in near future, once the Subaru/SSP survey is complete, covering an
area of $\sim 10^{3}$ deg2. The upcoming Subaru/Prime Focus Spectrograph (PSF;
Takada et al., 2014) will conduct extensive optical and near-IR spectroscopic
follow-up observations in the footprint of the HSC-SSP field, providing
spec-$z$ information of ERGs with $i_{\mathrm{AB}}\lesssim 24$. The
forthcoming LSST survey (Ivezić et al., 2019) will cover half of the sky, and
it will also increase the number of sources by another order of magnitude,
resulting in $\sim 10^{4}$ sources. A significant fraction of these ERGs will
also be expected to reside in low-mass galaxies. Therefore, the combination of
wide area (either shallow or deep) radio and deep optical imaging and
spectroscopic surveys will give us a statistically large number of massive BH
candidates in the coming years.

Massive BH searches have been conducted with multi-wavelength data; optical
spectroscopy using broad H$\alpha$ emission (Greene & Ho, 2004, 2007; Xiao et
al., 2011) or narrow emission line ratios (e.g., Barth et al., 2008; Reines et
al., 2013), mid-IR ($W1-W2$) colors in WISE (Satyapal et al., 2014; Sartori et
al., 2015; Secrest et al., 2015; Kaviraj et al., 2019), X-ray observations
(e.g., Schramm et al., 2013; Baldassare et al., 2015; Mezcua et al., 2016;
Chen et al., 2017; Kawamuro et al., 2019), as well as through studies of the
AGN flux variability based on the properties that lower luminosity AGN have
stronger variability amplitude (Morokuma et al., 2016; Baldassare et al.,
2018, 2019; Elmer et al., 2020; Kimura et al., 2020). On the other hand, radio
surveys have rarely been used for searching massive BHs in low-mass galaxies.

Recently, Reines et al. (2020) employed the radio-survey approach to search
for massive BHs by using VLA/FIRST and conducting VLA high spatial resolution
follow-up observations of local dwarf galaxies at $z<0.1$, and found more than
10 candidates. One remarkable result was that most radio cores were not
located at the center of the host, but off-nucleus, a possible signature of a
previous merger. If the detection of an off-nucleus core is indeed the
consequence of a galaxy merger, it indicates that the orbital decay of a black
hole through dynamical friction is inefficient in this BH mass range,
resulting in a population of BHs that fail to reach the galactic center within
a Hubble time, since major mergers in dwarf galaxies becomes rare at $z<3$
(Fitts et al., 2018). Currently there are many theoretical implication
regarding wandering BHs (Comerford & Greene, 2014; Blecha et al., 2016;
Tremmel et al., 2018; De Rosa et al., 2020; Guo et al., 2020; Ricarte et al.,
2021b, a). High spatial resolution radio imaging can pin down the locations of
such wandering BHs, and large-scale statistical studies may provide insights
into the frequency and environment of wandering BHs through the combination of
LSST and VLA/FIRST or the ongoing VLASS (Lacy et al., 2020), which will
achieve a sensitivity down to $0.1$ mJy at 2–4 GHz, giving an order of
magnitude deeper radio observations than VLA/FIRST.

###  4.6 Do Blazars Contaminate ERGs?

It could be argued that blazars might contaminate the sample of ERGs, and that
therefore the optical emission is dominated by the jet component. Based on the
known blazar sequence in the radio and optical bands (Fossati et al., 1998;
Donato et al., 2001; Inoue & Totani, 2009; Ghisellini et al., 2017), the
observed radio-loudness of blazars is in the range of
$\log\mathcal{R}_{\mathrm{obs}}\sim 1.5-3$. This range is obtained by using
the luminosity range of $L_{\mathrm{1.4GHz}}=10^{41-43}$ erg s-1 and shifting
redshift to the range of $z\sim 0$–$5$. Therefore, blazars cannot reproduce
extreme radio-loudness reaching $\log\mathcal{R_{\rm rest}}>4$. Blazar
contamination is unlikely also from the point of the observed optical
magnitude. Considering that all ERGs are VLA/FIRST selected with a flux limit
of $>1$ mJy, the expected observed magnitude of blazars based on the blazar
sequence is high with a peak around $i_{\mathrm{AB}}=21$, and all cases are at
$i_{\mathrm{AB}}<23.5$ even when changing the luminosity range of the blazar
SEDs and also shifting the redshift range to $z=0$–$5$. Based on these
arguments, the contamination of blazars to ERGs is unlikely.

##  5 Conclusion

The long-missing optical counterparts of radio-bright ($f_{\nu}>1$ mJy at 1.4
GHz) VLA/FIRST population have been constructed by Yamashita et al. (2018) by
utilizing the wide ($>100$ deg2) and deep ($i_{\mathrm{AB}}<26$) Subaru/HSC
SSP survey (named WERGS). The WERGS catalog contains a unique radio galaxy
population with $\log\mathcal{R_{\rm rest}}>4$, or extremely radio-loud
galaxies (ERGs). The number density of ERGs indicates that they are a very
rare population ($\sim 1$ source deg-2), and therefore it is not surprising
that ERGs were missed in previous optical counterpart surveys of the radio
sources. Combining multi-wavelength data in optical, IR, and radio bands (Toba
et al., 2019), we have compiled a sample of 39 ERGs and 987 NRGs with radio-
loudness is $1<\log\mathcal{R_{\rm rest}}<4$.

We have investigated the properties of these unique ERGs and found the
following key results:

  1. 1.

Although the estimated SFRs are sensitive to assumed SFHs, and they might have
large uncertainties with $\sim 0.5$ dex, all ERGs are likely in the star-
forming or starburst phase reaching specific star-formation rate of
$\mathrm{sSFR}\sim 10^{-8}$ yr-1, suggesting that ERGs might be in a rapid
stellar-mass assembly phase with mass doubling times of $\sim 100$ Myr.
Besides, their stellar mass is relatively small, including the low-mass
galaxies with $M_{\star}<10^{10}M_{\odot}$.

  2. 2.

IR detected ERGs are in a rapid BH accretion phase with high specific black
hole accretion rate (sBHAR) with the expected Eddington ratio
$\left<\log\lambda_{\mathrm{Edd}}\right>\approx-0.4$, and some ERGs may be
experiencing a super-Eddington phase.

  3. 3.

Sources with higher $\mathcal{R_{\rm rest}}$ tend to have both higher sBHAR
(and thus higher $\lambda_{\mathrm{Edd}}$) and higher intrinsic radio-loudness
$\mathcal{R_{\mathrm{int}}}$. This paints a different picture of radio
galaxies compared to conventionally known local radio galaxies with low
$\lambda_{\mathrm{Edd}}$. ERGs represent a population of unique radio galaxies
characterized by both high $\lambda_{\mathrm{Edd}}$ and high radio power.

  4. 4.

The jet efficiencies of ERGs are typically $\eta_{\mathrm{jet}}\sim 0.1$,
which is similar to local radio AGN residing in massive galaxies, whereas it
is an order of magnitude higher than the values estimated for SDSS radio-loud
quasars. This indicates that, although the accretion disk is reaching super-
Eddington accretion, it is in a radiatively inefficient phase (possibly in a
slim disk configuration) due to rapid mass accretion onto the central BH.

We thank the anonymous referee for helpful suggestions that strengthened the
paper. We thank Yoshiyuki Inoue for providing us the blazar sequence SED
templates. This work is supported by Program for Establishing a Consortium for
the Development of Human Resources in Science and Technology, Japan Science
and Technology Agency (JST) and is partially supported by Japan Society for
the Promotion of Science (JSPS) KAKENHI (18K13584 and 20H01939; K. Ichikawa,
18J01050 and 19K14759; Y. Toba, 16H03958, 17H01114, 19H00697; T. Nagao,
17J09016: T. Kawamuro, 19K03862: A. Y. Wagner). M. Charisi acknowledges
support from the National Science Foundation (NSF) NANOGrav Physics Frontier
Center, award number 1430284. 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 the 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.lsst.org
This paper is based on data collected at the Subaru Telescope and retrieved
from the HSC data archive system, which is operated by Subaru Telescope and
Astronomy Data Center (ADC) at NAOJ. Data analysis was in part carried out
with the cooperation of Center for Computational Astrophysics (CfCA), NAOJ.
The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been
made possible through contributions by 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, the 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 grant No.
AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the
Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.

##  Appendix A How Much Do Wrong Photo-$z$ Affect Our Results?

Figure 9:  The $k$-correction for different physical quantities as a function
of redshift. The SED template obtained by Hickox et al. (2017) (type-1: black
solid line, and type-2: dashed red line) is used for the $k$-correction
estimation. (Left)
$\mathcal{R}_{\mathrm{int,obs}}/\mathcal{R}_{\mathrm{int,rest}}=(f_{\mathrm{\nu,1.5GHz,obs}}/f_{\mathrm{\nu,12\mu
m,obs}})/(f_{\mathrm{\nu,1.5GHz,rest}}/f_{\mathrm{\nu,12\mu m,rest}})$.
(Right) sBHAR(obs)/sBHAR(rest)$=(f_{\mathrm{\nu,12\mu
m,obs}}/f_{\nu,i~{}\mathrm{band,obs}})/(f_{\mathrm{\nu,12\mu
m,rest}}/f_{\nu,i~{}\mathrm{band,rest}})$.

Our results on ERGs rely on photo-$z$ estimates, which affect physical values
calculated using luminosity distance, e.g., stellar-mass and luminosities.
Unfortunately, because most of our sources are optically faint, there are no
spec-$z$ confirmed ERGs in our sample. A concern is how erroneous photo-$z$
estimates may affect our results.

If our photo-$z$ values are severely under-estimated, it is clear that the
absolute physical values such as stellar-mass, with the dependence of
luminosity distance of $D_{L}^{2}$, have been underestimated, and therefore
the results on low-mass BH mass and low-mass galaxy arguments discussed in
Section 4.4 are no longer valid. One situation this might happen is that our
photo-$z$ estimation at $z\sim 0.3$–$0.5$ is not tracing the Balmer break at
$\sim 4000$ Å, but actually the Lyman break at $z\sim 3$–$4$ (e.g., Tanaka et
al., 2018).

On the other hand, physical quantities obtained from the ratios of two
physical quantities have weaker redshift dependences. For both
$\mathcal{R_{\mathrm{int}}}$ and sBHAR, the luminosity distance dependence is
canceled out. The remaining $z$-dependent factor is the $k$-correction between
the observed flux and the rest frame flux. The physical quantities
$L_{\mathrm{jet}}$, $L_{\mathrm{AGN,IR}}$ (and therefore
$L_{\mathrm{AGN,bol}}$), and $M_{\star}$, can be mainly traced by one-band
flux (densities) of FIRST 1.5 GHz tracing radio Synchrotron emission
($f_{\mathrm{\nu,1.5GHz}}$), WISE MIR band(s) tracing the peak of AGN dust
emission ($f_{\nu,12\mu\mathrm{m}}$), and $i$-band tracing stellar emission
($f_{\nu,i~{}\mathrm{band}}$). Therefore, each physical quantity can be
written as
$\mathcal{R_{\mathrm{int}}}=L_{\mathrm{jet}}/L_{\mathrm{AGN,bol}}\propto
f_{\mathrm{\nu,1.5GHz}}/f_{\nu,12\mu\mathrm{m}}$ and
sBHAR$=L_{\mathrm{AGN,bol}}/M_{\star}\propto
f_{\nu,12\mu\mathrm{m}}/f_{\nu,i~{}\mathrm{band}}$. We checked and confirmed
the proportionality of these ratios in our sample.

We then investigated the $k$-correction by seeeing how much these observed
values change as a function of redshift. In the radio-band, we assumed the
same power-law $f_{\nu}\propto\nu^{\alpha}$ with $\alpha=-0.7$. In the optical
and IR band, we used the quasar SED templates obtained by Hickox et al.
(2017), which contain two templates of type-1 and type-2 quasars, whose
optical band is dominated by accretion disk and stellar-component,
respectively. Since the SED extends only down to 2000 Å, we extrapolated the
SED with $\alpha=-0.5$ for type-1 QSOs and $\alpha=-2.4$ for type-2 QSOs in
order to smoothly connect the SED template (eg., see also Richards et al.,
2006; Polletta et al., 2007, for other SED templates). Given their high radio-
loudness and as we discussed in Section 3, the SED of ERGs is likely similar
to type-2 QSOs, whose optical emission is dominated by the stellar-component.

Figure 9 shows the $k$-correction of each physical value as a function of
redshift. The $k$-correction changes by a factor of up to 4.5 for
$\mathcal{R_{\mathrm{int}}}$ and factor of $3$ for sBHAR even when the targets
are shifted at $z\sim 4$. This suggests that an erroneous photo-$z$ does not
strongly affect our overall results for $\mathcal{R_{\mathrm{int}}}$ and
sBHAR.

##  Appendix B Redshift dependence of our results

Figure 10:  The same relations but with redshift-divided sample of $0.3<z<0.8$
(Left), $0.8<z<1.2$ (Center), and $1.2<z<1.6$ (Right) overlapped with the
total sample ($0.3<z<1.6$) in gray. (Top) The relation between SFR and
stellar-mass ($M_{\star}$) and the symbols are same with Figure 3. (Middle)
The relation between sBHAR and $M_{\star}$, same with Figure 5. (Bottom) The
relationship between
$L_{\mathrm{jet}}/L_{\mathrm{AGN,bol}}=\mathcal{R_{\mathrm{int}}}$ and sBHAR,
same with Figure 7.

The physical properties between ERGs and NRGs are explored in Section 3 and
discussed in Section 4. As shown in Figure 2, NRGs distribute smoothly in a
wide redshift range at $0.3<z<1.6$, while ERGs are slightly clustered at
$z>0.8$. Thus, one might wonder whether the difference in physical parameters
between ERGs and NRGs is caused by the redshift difference. We here split the
sample into the three redshift bins ($z=0.3$–$0.8$, $0.8$–$1.2$, and
$1.2$–$1.6$) for mitigating such redshift dependence and then compare the key
parameters of the two populations.

The top panels show the relations between SFR and $M_{\star}$, which are
similar to ones with Figure 3. Most of the NRGs reside below the MS in the
$0.3<z<0.8$, then the fraction of sources on and above the MS increases as a
function of redshift. On the other hand, ERGs always locate the lower
$M_{\star}$ range in each redshift bin and most of them are above the MS
(except several sources on and below the MS). Considering that the stellar-
mass is estimated from the photometries mainly in the optical or near-IR
bands, the deeper Subaru/HSC photometreis enable us to find this smaller
stellar-mass population as shown in Figure 4.

The middle panels show the relations between sBHAR and $M_{\star}$, which are
the redshift-divided version of Figure 5. At $0.3<z<0.8$, most of the NRGs are
located at low sBHAR and high $M_{\star}$ cluster region where
$\mathrm{sBHAR}/\mathrm{erg}~{}\mathrm{s}^{-1}~{}M_{\odot}^{-1}\sim 10^{33.5}$
and $M_{\star}\sim 10^{11.5}M_{\odot}$, and then they move to higher sBHAR
sequence with redshift. On the other hand, ERGs always locate at the top edge
of the sequence, keeping high sBHAR values and sometimes reaching the sBHAR
equivalent to $\lambda_{\mathrm{Edd}}\sim 1$.

Finally, the bottom panels show the relation between
$\mathcal{R_{\mathrm{int}}}$ and sBHAR, which are the redshift-divided ones of
Figure 7. Most of the NRGs are located at the top left region at $0.3<z<0.8$,
and then the population moves to higher sBHAR and smaller
$\mathcal{R_{\mathrm{int}}}$ sequence, moving to bottom-center or bottom-right
of the panel. This is a consistent view of local radio galaxies at lower-$z$
and radio quasar population at higher-$z$ as discussed in Section 4.2. On the
other hand, ERGs reside in the top right part of the plane, and does not show
a redshift evolution, because of its extreme selection cut of
$\log\mathcal{R_{\rm rest}}>4$, limiting the sample only in the top right area
of the panel.

## References

  * Abramowicz et al. (1988) Abramowicz, M. A., Czerny, B., Lasota, J. P., & Szuszkiewicz, E. 1988, ApJ, 332, 646
  * Aihara et al. (2018a) Aihara, H., Armstrong, R., Bickerton, S., et al. 2018a, PASJ, 70, S8
  * Aihara et al. (2018b) Aihara, H., Arimoto, N., Armstrong, R., et al. 2018b, PASJ, 70, S4
  * Aird et al. (2019) Aird, J., Coil, A. L., & Georgakakis, A. 2019, MNRAS, 484, 4360
  * Aird et al. (2012) Aird, J., Coil, A. L., Moustakas, J., et al. 2012, ApJ, 746, 90
  * Alam et al. (2015) Alam, S., Albareti, F. D., Allende Prieto, C., et al. 2015, ApJS, 219, 12
  * Asmus et al. (2015) Asmus, D., Gandhi, P., Hönig, S. F., Smette, A., & Duschl, W. J. 2015, MNRAS, 454, 766
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33
  * Bañados et al. (2018) Bañados, E., Venemans, B. P., Mazzucchelli, C., et al. 2018, Nature, 553, 473
  * Baldassare et al. (2018) Baldassare, V. F., Geha, M., & Greene, J. 2018, ApJ, 868, 152
  * Baldassare et al. (2019) —. 2019, arXiv e-prints, arXiv:1910.06342
  * Baldassare et al. (2015) Baldassare, V. F., Reines, A. E., Gallo, E., & Greene, J. E. 2015, ApJ, 809, L14
  * Barth et al. (2008) Barth, A. J., Greene, J. E., & Ho, L. C. 2008, AJ, 136, 1179
  * Becker et al. (1995) Becker, R. H., White, R. L., & Helfand, D. J. 1995, ApJ, 450, 559
  * Best & Heckman (2012) Best, P. N., & Heckman, T. M. 2012, MNRAS, 421, 1569
  * Best et al. (2005) Best, P. N., Kauffmann, G., Heckman, T. M., & Ivezić, Ž. 2005, MNRAS, 362, 9
  * Bîrzan et al. (2008) Bîrzan, L., McNamara, B. R., Nulsen, P. E. J., Carilli, C. L., & Wise, M. W. 2008, ApJ, 686, 859
  * Blandford et al. (2019) Blandford, R., Meier, D., & Readhead, A. 2019, ARA&A, 57, 467
  * Blandford & Znajek (1977) Blandford, R. D., & Znajek, R. L. 1977, MNRAS, 179, 433
  * Blecha et al. (2016) Blecha, L., Sijacki, D., Kelley, L. Z., et al. 2016, MNRAS, 456, 961
  * Boquien et al. (2019) Boquien, M., Burgarella, D., Roehlly, Y., et al. 2019, A&A, 622, A103
  * Bosch et al. (2018) Bosch, J., Armstrong, R., Bickerton, S., et al. 2018, PASJ, 70, S5
  * Bower et al. (2017) Bower, R. G., Schaye, J., Frenk, C. S., et al. 2017, MNRAS, 465, 32
  * Brinchmann et al. (2004) Brinchmann, J., Charlot, S., White, S. D. M., et al. 2004, MNRAS, 351, 1151
  * Cavagnolo et al. (2010) Cavagnolo, K. W., McNamara, B. R., Nulsen, P. E. J., et al. 2010, ApJ, 720, 1066
  * Chen et al. (2017) Chen, C. T. J., Brandt, W. N., Reines, A. E., et al. 2017, ApJ, 837, 48
  * Ciesla et al. (2017) Ciesla, L., Elbaz, D., & Fensch, J. 2017, A&A, 608, A41
  * Comerford & Greene (2014) Comerford, J. M., & Greene, J. E. 2014, ApJ, 789, 112
  * Condon (1992) Condon, J. J. 1992, ARA&A, 30, 575
  * Condon et al. (2013) Condon, J. J., Kellermann, K. I., Kimball, A. E., Ivezić, Ž., & Perley, R. A. 2013, ApJ, 768, 37
  * Costa et al. (2018) Costa, T., Rosdahl, J., Sijacki, D., & Haehnelt, M. G. 2018, MNRAS, 479, 2079
  * De Rosa et al. (2020) De Rosa, A., Vignali, C., Bogdanović, T., et al. 2020, arXiv e-prints, arXiv:2001.06293
  * Decarli et al. (2018) Decarli, R., Walter, F., Venemans, B. P., et al. 2018, ApJ, 854, 97
  * Del Moro et al. (2013) Del Moro, A., Alexander, D. M., Mullaney, J. R., et al. 2013, A&A, 549, A59
  * Delvecchio et al. (2014) Delvecchio, I., Gruppioni, C., Pozzi, F., et al. 2014, MNRAS, 439, 2736
  * Delvecchio et al. (2018) Delvecchio, I., Smolčić, V., Zamorani, G., et al. 2018, MNRAS, 481, 4971
  * Dickey et al. (2019) Dickey, C., Geha, M., Wetzel, A., & El-Badry, K. 2019, arXiv e-prints, arXiv:1902.01401
  * Ding et al. (2020) Ding, X., Silverman, J., Treu, T., et al. 2020, ApJ, 888, 37
  * Donato et al. (2001) Donato, D., Ghisellini, G., Tagliaferri, G., & Fossati, G. 2001, A&A, 375, 739
  * Drinkwater et al. (2010) Drinkwater, M. J., Jurek, R. J., Blake, C., et al. 2010, MNRAS, 401, 1429
  * Driver et al. (2011) Driver, S. P., Hill, D. T., Kelvin, L. S., et al. 2011, MNRAS, 413, 971
  * Elbaz et al. (2011) Elbaz, D., Dickinson, M., Hwang, H. S., et al. 2011, A&A, 533, A119
  * Elmer et al. (2020) Elmer, E., Almaini, O., Merrifield, M., et al. 2020, MNRAS, arXiv:2002.02468
  * Ferrarese & Merritt (2000) Ferrarese, L., & Merritt, D. 2000, ApJ, 539, L9
  * Fitts et al. (2018) Fitts, A., Boylan-Kolchin, M., Bullock, J. S., et al. 2018, MNRAS, 479, 319
  * Fossati et al. (1998) Fossati, G., Maraschi, L., Celotti, A., Comastri, A., & Ghisellini, G. 1998, MNRAS, 299, 433
  * Furusawa et al. (2018) Furusawa, H., Koike, M., Takata, T., et al. 2018, PASJ, 70, S3
  * Gaibler et al. (2012) Gaibler, V., Khochfar, S., Krause, M., & Silk, J. 2012, Mon. Not. R. Astron. Soc., 425, 438
  * Gandhi et al. (2009) Gandhi, P., Horst, H., Smette, A., et al. 2009, A&A, 502, 457
  * Gebhardt et al. (2000) Gebhardt, K., Bender, R., Bower, G., et al. 2000, ApJ, 539, L13
  * Ghisellini et al. (2017) Ghisellini, G., Righi, C., Costamante, L., & Tavecchio, F. 2017, MNRAS, 469, 255
  * Greene & Ho (2004) Greene, J. E., & Ho, L. C. 2004, ApJ, 610, 722
  * Greene & Ho (2007) —. 2007, ApJ, 667, 131
  * Greene et al. (2019) Greene, J. E., Strader, J., & Ho, L. C. 2019, arXiv e-prints, arXiv:1911.09678
  * Guo et al. (2020) Guo, M., Inayoshi, K., Michiyama, T., & Ho, L. C. 2020, ApJ, 901, 39
  * Habouzit et al. (2017) Habouzit, M., Volonteri, M., & Dubois, Y. 2017, MNRAS, 468, 3935
  * Haiman et al. (2019) Haiman, Z., Brandt, W. N., Vikhlinin, A., et al. 2019, BAAS, 51, 557
  * Häring & Rix (2004) Häring, N., & Rix, H.-W. 2004, ApJ, 604, L89
  * Helfand et al. (2015) Helfand, D. J., White, R. L., & Becker, R. H. 2015, ApJ, 801, 26
  * Helou et al. (1985) Helou, G., Soifer, B. T., & Rowan-Robinson, M. 1985, ApJ, 298, L7
  * Hickox et al. (2017) Hickox, R. C., Myers, A. D., Greene, J. E., et al. 2017, ApJ, 849, 53
  * Hickox et al. (2009) Hickox, R. C., Jones, C., Forman, W. R., et al. 2009, ApJ, 696, 891
  * Ho (2002) Ho, L. C. 2002, ApJ, 564, 120
  * Ho (2008) —. 2008, ARA&A, 46, 475
  * Holt et al. (2008) Holt, J., Tadhunter, C. N., & Morganti, R. 2008, Mon. Not. R. Astron. Soc., 387, 639
  * Huang et al. (2018) Huang, S., Leauthaud, A., Murata, R., et al. 2018, PASJ, 70, S6
  * Hunter (2007) Hunter, J. D. 2007, Computing In Science & Engineering, 9, 90
  * Ichikawa & Inayoshi (2017) Ichikawa, K., & Inayoshi, K. 2017, ApJ, 840, L9
  * Ichikawa et al. (2017) Ichikawa, K., Ricci, C., Ueda, Y., et al. 2017, ApJ, 835, 74
  * Ichikawa et al. (2012) Ichikawa, K., Ueda, Y., Terashima, Y., et al. 2012, ApJ, 754, 45
  * Ichikawa et al. (2019) Ichikawa, K., Ricci, C., Ueda, Y., et al. 2019, ApJ, 870, 31
  * Inayoshi & Haiman (2016) Inayoshi, K., & Haiman, Z. 2016, ApJ, 828, 110
  * Inayoshi et al. (2016) Inayoshi, K., Haiman, Z., & Ostriker, J. P. 2016, MNRAS, 459, 3738
  * Inayoshi et al. (2018) Inayoshi, K., Ichikawa, K., & Haiman, Z. 2018, ApJ, 863, L36
  * Inayoshi et al. (2019) Inayoshi, K., Visbal, E., & Haiman, Z. 2019, arXiv e-prints, arXiv:1911.05791
  * Inoue et al. (2017) Inoue, Y., Doi, A., Tanaka, Y. T., Sikora, M., & Madejski, G. M. 2017, ApJ, 840, 46
  * Inoue & Totani (2009) Inoue, Y., & Totani, T. 2009, ApJ, 702, 523
  * Intema et al. (2017) Intema, H. T., Jagannathan, P., Mooley, K. P., & Frail, D. A. 2017, A&A, 598, A78
  * Ivezić et al. (2002) Ivezić, Ž., Menou, K., Knapp, G. R., et al. 2002, AJ, 124, 2364
  * Ivezić et al. (2019) Ivezić, Ž., Kahn, S. M., Tyson, J. A., et al. 2019, ApJ, 873, 111
  * Ivison et al. (2010) Ivison, R. J., Magnelli, B., Ibar, E., et al. 2010, A&A, 518, L31
  * Kaviraj et al. (2019) Kaviraj, S., Martin, G., & Silk, J. 2019, MNRAS, 489, L12
  * Kawamuro et al. (2019) Kawamuro, T., Ueda, Y., Ichikawa, K., et al. 2019, ApJ, 881, 48
  * Kawanomoto et al. (2018) Kawanomoto, S., Uraguchi, F., Komiyama, Y., et al. 2018, PASJ, 70, 66
  * Kimball et al. (2011) Kimball, A. E., Kellermann, K. I., Condon, J. J., Ivezić, Ž., & Perley, R. A. 2011, ApJ, 739, L29
  * Kimura et al. (2020) Kimura, Y., Yamada, T., Kokubo, M., et al. 2020, arXiv e-prints, arXiv:2004.08835
  * Komiyama et al. (2018) Komiyama, Y., Obuchi, Y., Nakaya, H., et al. 2018, PASJ, 70, S2
  * Kormendy & Ho (2013) Kormendy, J., & Ho, L. C. 2013, ARA&A, 51, 511
  * Lacy et al. (2020) Lacy, M., Baum, S. A., Chandler, C. J., et al. 2020, PASP, 132, 035001
  * Läsker et al. (2016) Läsker, R., Greene, J. E., Seth, A., et al. 2016, ApJ, 825, 3
  * Liske et al. (2015) Liske, J., Baldry, I. K., Driver, S. P., et al. 2015, MNRAS, 452, 2087
  * Magorrian et al. (1998) Magorrian, J., Tremaine, S., Richstone, D., et al. 1998, AJ, 115, 2285
  * Maiolino et al. (2017) Maiolino, R., Russell, H. R., Fabian, A. C., et al. 2017, Nature, 544, 202
  * Marconi & Hunt (2003) Marconi, A., & Hunt, L. K. 2003, ApJ, 589, L21
  * McConnell & Ma (2013) McConnell, N. J., & Ma, C.-P. 2013, ApJ, 764, 184
  * McKinney et al. (2014) McKinney, J. C., Tchekhovskoy, A., Sadowski, A., & Narayan, R. 2014, MNRAS, 441, 3177
  * McKinney (2010) McKinney, W. 2010, in Proceedings of the 9th Python in Science Conference, ed. S. van der Walt & J. Millman, 51 – 56
  * McLure & Dunlop (2004) McLure, R. J., & Dunlop, J. S. 2004, MNRAS, 352, 1390
  * McNamara & Nulsen (2007) McNamara, B. R., & Nulsen, P. E. J. 2007, ARA&A, 45, 117
  * McQuinn et al. (2010) McQuinn, K. B. W., Skillman, E. D., Cannon, J. M., et al. 2010, ApJ, 724, 49
  * Merloni & Heinz (2007) Merloni, A., & Heinz, S. 2007, MNRAS, 381, 589
  * Merloni et al. (2010) Merloni, A., Bongiorno, A., Bolzonella, M., et al. 2010, ApJ, 708, 137
  * Mezcua et al. (2016) Mezcua, M., Civano, F., Fabbiano, G., Miyaji, T., & Marchesi, S. 2016, ApJ, 817, 20
  * Mezcua et al. (2019) Mezcua, M., Suh, H., & Civano, F. 2019, MNRAS, 488, 685
  * Miyazaki et al. (2018) Miyazaki, S., Komiyama, Y., Kawanomoto, S., et al. 2018, PASJ, 70, S1
  * Morganti et al. (2005) Morganti, R., Tadhunter, C. N., & Oosterloo, T. a. 2005, Astron. Astrophys., 444, L9
  * Morokuma et al. (2016) Morokuma, T., Tominaga, N., Tanaka, M., et al. 2016, PASJ, 68, 40
  * Mortlock et al. (2011) Mortlock, D. J., Warren, S. J., Venemans, B. P., et al. 2011, Nature, 474, 616
  * Mukherjee et al. (2018) Mukherjee, D., Bicknell, G. V., Wagner, A. Y., Sutherland, R. S., & Silk, J. 2018, Mon. Not. R. Astron. Soc., 479, 5544
  * Mullaney et al. (2012) Mullaney, J. R., Daddi, E., Béthermin, M., et al. 2012, ApJ, 753, L30
  * Nemmen & Tchekhovskoy (2015) Nemmen, R. S., & Tchekhovskoy, A. 2015, MNRAS, 449, 316
  * Nesvadba et al. (2017) Nesvadba, N. P. H., De Breuck, C., Lehnert, M. D., Best, P. N., & Collet, C. 2017, Astron. Astrophys. Suppl. Ser., 599, A123
  * Noeske et al. (2007) Noeske, K. G., Weiner, B. J., Faber, S. M., et al. 2007, ApJ, 660, L43
  * Nyland et al. (2017) Nyland, K., Davis, T. A., Nguyen, D. D., et al. 2017, ApJ, 845, 50
  * Ohsuga et al. (2009) Ohsuga, K., Mineshige, S., Mori, M., & Kato, Y. 2009, PASJ, 61, L7
  * Ohsuga et al. (2005) Ohsuga, K., Mori, M., Nakamoto, T., & Mineshige, S. 2005, ApJ, 628, 368
  * Onoue et al. (2019) Onoue, M., Kashikawa, N., Matsuoka, Y., et al. 2019, ApJ, 880, 77
  * O’Sullivan et al. (2011) O’Sullivan, E., Giacintucci, S., David, L. P., et al. 2011, ApJ, 735, 11
  * Padovani (2016) Padovani, P. 2016, A&A Rev., 24, 13
  * Panessa et al. (2007) Panessa, F., Barcons, X., Bassani, L., et al. 2007, A&A, 467, 519
  * Pearson et al. (2018) Pearson, W. J., Wang, L., Hurley, P. D., et al. 2018, A&A, 615, A146
  * Penny et al. (2018) Penny, S. J., Masters, K. L., Smethurst, R., et al. 2018, MNRAS, 476, 979
  * Polletta et al. (2007) Polletta, M., Tajer, M., Maraschi, L., et al. 2007, ApJ, 663, 81
  * Rafferty et al. (2006) Rafferty, D. A., McNamara, B. R., Nulsen, P. E. J., & Wise, M. W. 2006, ApJ, 652, 216
  * Reines et al. (2020) Reines, A. E., Condon, J. J., Darling, J., & Greene, J. E. 2020, ApJ, 888, 36
  * Reines et al. (2013) Reines, A. E., Greene, J. E., & Geha, M. 2013, ApJ, 775, 116
  * Reines & Volonteri (2015) Reines, A. E., & Volonteri, M. 2015, ApJ, 813, 82
  * Ricarte et al. (2021a) Ricarte, A., Tremmel, M., Natarajan, P., & Quinn, T. 2021a, arXiv e-prints, arXiv:2107.02132
  * Ricarte et al. (2021b) Ricarte, A., Tremmel, M., Natarajan, P., Zimmer, C., & Quinn, T. 2021b, MNRAS, 503, 6098
  * Richards et al. (2006) Richards, G. T., Lacy, M., Storrie-Lombardi, L. J., et al. 2006, ApJS, 166, 470
  * Sadowski & Narayan (2015) Sadowski, A., & Narayan, R. 2015, MNRAS, 453, 3213
  * Sadowski et al. (2014) Sadowski, A., Narayan, R., McKinney, J. C., & Tchekhovskoy, A. 2014, MNRAS, 439, 503
  * Sani et al. (2011) Sani, E., Marconi, A., Hunt, L. K., & Risaliti, G. 2011, MNRAS, 413, 1479
  * Sartori et al. (2015) Sartori, L. F., Schawinski, K., Treister, E., et al. 2015, MNRAS, 454, 3722
  * Satyapal et al. (2014) Satyapal, S., Secrest, N. J., McAlpine, W., et al. 2014, ApJ, 784, 113
  * Schinnerer et al. (2007) Schinnerer, E., Smolčić, V., Carilli, C. L., et al. 2007, ApJS, 172, 46
  * Schramm et al. (2013) Schramm, M., Silverman, J. D., Greene, J. E., et al. 2013, ApJ, 773, 150
  * Schreiber et al. (2015a) Schreiber, C., Pannella, M., Elbaz, D., et al. 2015a, A&A, 575, A74
  * Schreiber et al. (2015b) —. 2015b, A&A, 575, A74
  * Secrest et al. (2015) Secrest, N. J., Satyapal, S., Gliozzi, M., et al. 2015, ApJ, 798, 38
  * Seymour et al. (2007) Seymour, N., Stern, D., De Breuck, C., et al. 2007, ApJS, 171, 353
  * Shabala & Godfrey (2013) Shabala, S. S., & Godfrey, L. E. H. 2013, ApJ, 769, 129
  * Sikora et al. (2013) Sikora, M., Stasińska, G., Kozieł-Wierzbowska, D., Madejski, G. M., & Asari, N. V. 2013, ApJ, 765, 62
  * Sikora et al. (2007) Sikora, M., Stawarz, Ł., & Lasota, J.-P. 2007, ApJ, 658, 815
  * Silk (2017) Silk, J. 2017, ApJ, 839, L13
  * Smolčić et al. (2017a) Smolčić, V., Novak, M., Bondi, M., et al. 2017a, A&A, 602, A1
  * Smolčić et al. (2017b) Smolčić, V., Delvecchio, I., Zamorani, G., et al. 2017b, A&A, 602, A2
  * Soltan (1982) Soltan, A. 1982, MNRAS, 200, 115
  * Tadhunter (2016) Tadhunter, C. 2016, A&A Rev., 24, 10
  * Takada et al. (2014) Takada, M., Ellis, R. S., Chiba, M., et al. 2014, PASJ, 66, R1
  * Takeo et al. (2020) Takeo, E., Inayoshi, K., & Mineshige, S. 2020, arXiv e-prints, arXiv:2002.07187
  * Tanaka (2015) Tanaka, M. 2015, ApJ, 801, 20
  * Tanaka et al. (2018) Tanaka, M., Coupon, J., Hsieh, B.-C., et al. 2018, PASJ, 70, S9
  * Tchekhovskoy et al. (2011) Tchekhovskoy, A., Narayan, R., & McKinney, J. C. 2011, MNRAS, 418, L79
  * Terashima & Wilson (2003) Terashima, Y., & Wilson, A. S. 2003, ApJ, 583, 145
  * Toba et al. (2019) Toba, Y., Yamashita, T., Nagao, T., et al. 2019, ApJS, 243, 15
  * Trakhtenbrot et al. (2015) Trakhtenbrot, B., Urry, C. M., Civano, F., et al. 2015, Science, 349, 168
  * Tremaine et al. (2002) Tremaine, S., Gebhardt, K., Bender, R., et al. 2002, ApJ, 574, 740
  * Tremmel et al. (2018) Tremmel, M., Governato, F., Volonteri, M., Pontzen, A., & Quinn, T. R. 2018, ApJ, 857, L22
  * van Velzen & Falcke (2013) van Velzen, S., & Falcke, H. 2013, A&A, 557, L7
  * Wagner & Bicknell (2011) Wagner, A. Y., & Bicknell, G. V. 2011, Astrophys. J., 728, 29
  * Wagner et al. (2016) Wagner, A. Y., Bicknell, G. V., Umemura, M., Sutherland, R. S., & Silk, J. 2016, Astron. Nachr., 337, 167
  * Wang et al. (2013) Wang, R., Wagg, J., Carilli, C. L., et al. 2013, ApJ, 773, 44
  * Wang et al. (2016) Wang, R., Wu, X.-B., Neri, R., et al. 2016, ApJ, 830, 53
  * Whitaker et al. (2012) Whitaker, K. E., van Dokkum, P. G., Brammer, G., & Franx, M. 2012, ApJ, 754, L29
  * White et al. (1997) White, R. L., Becker, R. H., Helfand, D. J., & Gregg, M. D. 1997, ApJ, 475, 479
  * Willott et al. (1999) Willott, C. J., Rawlings, S., Blundell, K. M., & Lacy, M. 1999, MNRAS, 309, 1017
  * Woo et al. (2008) Woo, J.-H., Treu, T., Malkan, M. A., & Bland ford, R. D. 2008, ApJ, 681, 925
  * Wu et al. (2015) Wu, X.-B., Wang, F., Fan, X., et al. 2015, Nature, 518, 512
  * Xiao et al. (2011) Xiao, T., Barth, A. J., Greene, J. E., et al. 2011, ApJ, 739, 28
  * Yamashita et al. (2020) Yamashita, T., Nagao, T., & Ikeda, H. 2020, ApJ submitted
  * Yamashita et al. (2018) Yamashita, T., Nagao, T., Akiyama, M., et al. 2018, ApJ, 866, 140