11institutetext: School of Astronomy and Space Science, Nanjing University,
Nanjing 210093, China
11email<EMAIL_ADDRESS><EMAIL_ADDRESS>22institutetext: Key
Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry
of Education, Nanjing 210093, China 33institutetext: Kavli Institute for
Astronomy and Astrophysics, Peking University, Beijing 100871, China
44institutetext: Department of Astronomy, School of Physics, Peking
University, Beijing 100871, China 55institutetext: Department of Pure and
Applied Physics, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555,
Japan

# The fundamental plane of black hole activity for low-luminosity radio active
galactic nuclei across $0<z<4$

Yijun Wang 1122 0000-0002-1010-7763 Tao Wang 1122 0000-0002-2504-2421 Luis C.
Ho 3344 0000-0001-6947-5846 Yuxing Zhong 55 Bin Luo 1122

###### Abstract

Context. The fundamental plane of back hole activity describes the correlation
between radio luminosity ($L_{\rm R}$), X-ray luminosity ($L_{\rm X}$), and
black hole mass ($M_{\rm BH}$). It reflects a connection between accretion
disc and jet. However, the dependence of the fundamental plane on various
physical properties of active galactic nuclei (AGNs) and host galaxies remains
unclear, especially for low-luminosity AGNs, which is important for
understanding the accretion physics in AGNs.

Aims. Here we explore the dependence of the fundamental plane on radio-
loudness, Eddington-ratio ($\lambda_{\rm Edd}$), redshift, and galaxy star-
formation properties (star forming galaxies and quiescent galaxies) across
$0.1<z\leq 4$ for radio AGNs. Based on current deep and large surveys, our
studies can extend to lower luminosities and higher redshifts.

Methods. From the deep and large multi-wavelength surveys in the GOODS-N,
GOODS-S, and COSMOS/UltraVISTA fields, we constructed a large and homogeneous
radio AGN sample consisting of 208 objects with available estimates for
$L_{\rm R}$ and $L_{\rm X}$. Then we divided the radio AGN sample into 141
radio-quiet AGNs and 67 radio-loud AGNs according to the radio-loudness
defined by the ratio of $L_{\rm R}$ to $L_{\rm X}$, and explored the
dependence of the fundamental plane on different physical properties of the
two populations, separately.

Results. The ratio of $L_{\rm R}$ to $L_{\rm X}$ shows a bimodal distribution
which is well described by two single gaussian models. The cross point between
these two gaussian components corresponds to a radio-loudness threshold of
$\log(L_{\rm R}/L_{\rm X})=-2.73$. The radio-quiet AGNs have significantly
larger Eddington ratio than the radio-loud AGNs. Our radio-quiet and radio-
loud AGNs show significantly different fundamental plane which is $\log L_{\rm
R}=(0.55\pm 0.05)\log L_{\rm X}+(0.28\pm 0.06)\log M_{\rm BH}+(13.54\pm 2.27)$
for the radio-quiet AGNs, and $\log L_{\rm R}=(0.82\pm 0.08)\log L_{\rm
X}+(0.07\pm 0.08)\log M_{\rm BH}+(5.24\pm 3.33)$ for the radio-loud AGNs. For
both radio-quiet and radio-loud AGNs, the fundamental plane does not show a
significant dependence on redshift and galaxy star-formation properties, while
it shows a significant dependence on $\lambda_{\rm Edd}$.

Conclusions. The fundamental plane sheds important light on the accretion
physics of central engines. Radio-quiet AGNs at $0.01<\lambda_{\rm Edd}<0.1$
are consistent with a combination of advection dominated accretion flow (ADAF)
and a synchrotron jet model, while at $0.1<\lambda_{\rm Edd}<1$, they mainly
follow the synchrotron jet model. Radio-loud AGNs are consistent with a
combination of ADAF and the synchrotron jet model at $\lambda_{\rm Edd}<0.01$,
and agree with the synchrotron jet model at $0.01<\lambda_{\rm Edd}<0.1$, and
follow a combination of the standard thin disc and a jet model at
$\lambda_{\rm Edd}>0.1$.

###### Key Words.:

galaxies: active – galaxies: general – galaxies: nuclei – radio continuum:
galaxies – X-rays: galaxies

##  1 Introduction

Accreting supermassive black holes (SMBHs), also known as active galactic
nuclei (AGNs), emit immense energy across the whole electromagnetic spectrum
which are believed to have a great impact on the growth and evolution of host
galaxies (Fabian, 2012; King & Pounds, 2015, for reviews). Thus, AGNs are
ideal laboratories to explore both accretion physics around black holes and
their connection with host galaxies. Accretion physics around black holes are
found to be scale-invariant across black hole mass scale from $\sim 10$ solar
masses of X-ray binaries (XRBs) to $10^{6}\sim 10^{10}$ solar masses of SMBHs
(Merloni et al., 2003; Falcke et al., 2004; Done & Gierliński, 2005; McHardy
et al., 2006; Körding, 2014; Ruan et al., 2019). One of the most prominent
pieces of evidences to support the unification of XRBs and SMBHs is the
fundamental plane of black hole activity (Merloni et al., 2003; Falcke et al.,
2004, and references therein) that is characterized by a non-linear empirical
relation given by radio luminosity, X-ray luminosity and black hole mass. The
radio luminosity is thought to be related with jet activities (Begelman et
al., 1984), while the ratio of X-ray luminosity to black hole mass is usually
taken as a tracer for accretion rate of disc (Haardt & Maraschi, 1991; Liu &
Qiao, 2022). Thus, the fundamental plane connecting XRBs and SMBHs suggests a
similar disc-jet connection across different mass scales (e.g., Merloni et
al., 2003; Falcke et al., 2004; Plotkin et al., 2012; Dong et al., 2014). The
fundamental plane also provides an approach to estimating black hole mass
directly through radio luminosity and X-ray luminosity (e.g., Merloni et al.,
2003, and references therein).

However, a growing number of studies focusing only on the fundamental plane of
AGNs demonstrate that different types of AGN, such as low-ionization nuclear
emission line regions (LINERS), Seyferts, and quasars, show different
fundamental planes (e.g., Yuan et al., 2009; Gültekin et al., 2009b; Bonchi et
al., 2013; Saikia et al., 2015; Nisbet & Best, 2016; Fan & Bai, 2016; Xie &
Yuan, 2017; Li & Gu, 2018; Bariuan et al., 2022). These results indicate that
the fundamental plane may depend on the accretion state of disc or be
sensitive to the adopted sample of black holes (Plotkin et al., 2012). In
order to increase sample sizes, the majority of above-mentioned studies about
the fundamental plane used a combination of radio-quiet and radio-loud AGNs.
For the first time, Wang et al. (2006) and Li et al. (2008) studied the
fundamental plane in broad-line radio-quiet and radio-loud AGNs separately.
More recently, Bariuan et al. (2022) focused on radio-quiet and radio-loud
quasars. These works all found that radio-quiet and radio-loud AGNs show quite
different fundamental planes and follow different theoretical accretion models
given by Merloni et al. (2003). Due to limitations of data, these works mainly
focus on high-luminosity radio-loud and radio-quiet AGNs. Thanks to the deep
and large multi-wavelength surveys in the GOODS-N, the GOODS-S, and the
COSMOS/UltraVISTA fields (e.g., Owen, 2018; Alberts et al., 2020; Smolčić et
al., 2017; Liu et al., 2018; Jin et al., 2018), we can extend the fundamental
plane studies to low-luminosity radio-quiet and radio-loud AGNs.

Due to the limitation of sample sizes, in the past it is difficult to make
detailed analysis for the dependence of the fundamental plane on other
physical properties, such as 1) Eddington ratio, 2) redshift, and 3) galaxy
star-formation properties, especially for low-luminosity AGNs. These studies
may be crucial to our understanding of why different types of AGNs exhibit
different fundamental planes. 1) “Eddington ratio”: Observational evidences
show that radio-quiet and radio-loud AGNs have different fundamental planes
(Wang et al., 2006; Li et al., 2008; Bariuan et al., 2022), and radio-loudness
exhibits a negative correlation with Eddington ratio (Ho, 2002; Panessa et
al., 2007; Sikora et al., 2007). This demonstrates that the fundamental plane
may depend on Eddington-scaled accretion rate, which is still lack of
quantitative studies until now. 2) “Redshift”: AGN accretion rate density
peaks at $z\sim$ 2, and declines toward local universe (see Aird et al., 2010;
Madau & Dickinson, 2014, for a review), which may give rise to different
accretion physics at different cosmic time. The majority of previous works
studied the fundamental plane at low redshift ($z<0.5$), while some of them
extended to high redshift but only for high-luminosity AGNs (Wang et al.,
2006; Li et al., 2008; Bariuan et al., 2022). For low-luminosity AGNs, it is
still unclear about the dependence of the fundamental plane on redshift. 3)
“Galaxy star-formation properties”: Radio AGNs hosted by star forming galaxies
(SFGs) and quiescent galaxies (QGs) have different cosmic evolutions for AGN
incident rate (e.g., Janssen et al., 2012; Kondapally et al., 2022; Wang et
al., 2024, hereafter “Paper I”) and radio luminosity functions (Kondapally et
al., 2022, Paper I). Given that SFGs and QGs may perform different fueling
mechanisms toward central SMBHs (e.g., Kauffmann & Heckman, 2009; Kondapally
et al., 2022; Ni et al., 2023), radio activities of central engines may depend
on the fueling mechanisms of their host galaxies. Further, it still remains
unclear that whether the fueling mechanisms affect the disc-jet connection
characterized by the fundamental plane.

In this work, we first introduce a parent radio AGN sample from the GOODS-N,
the GOODS-S, and the COSMOS/UltraVISTA fields selected by Paper I across
$0.1<z\leq 4$ (Section 2). For these radio AGNs, we collect available
measurements for radio luminosity and X-ray luminosity from our previous works
and other literature works, and infer black hole mass from stellar mass
(Section 3). Next we divide our sample into radio-quiet and radio-loud AGN
subsamples according to the radio loudness defined by the relative strength of
the radio and X-ray emission (Section 4). Then we fit the fundamental plane
for the radio-quiet and radio-loud AGN subsamples separately (Section 5).
Further, we give a brief summary about the fundamental plane studies and
discuss the dependence of the fundamental plane on Eddington ratio, redshift,
and galaxy star-formation properties (Section 6). In Section 6, we also
discuss the central engines for radio-quiet and radio-loud AGNs. Finally, we
summarize our conclusions in Section 7. Throughout this paper, we assume a
Chabrier (2003) initial mass function (IMF) and a flat cosmology with the
following parameters: $\Omega_{\rm m}=0.3$, $\Omega_{\Lambda}=0.7$, and
$H_{0}=70\ \rm{km}\ \rm{s}^{-1}\ \rm{Mpc}^{-1}$.

##  2 Parent radio AGN sample

###  2.1 GOODS-N and COSMOS fields

For the GOODS-N and the COSMOS/UltraVISTA fields, our parent radio AGN sample
was derived from Paper I, which consists of 102 radio AGNs from the GOODS-N
and 881 radio AGNs from the COSMOS/UltraVISTA across $0.1<z<4$ selected by the
infrared-radio correlation (IRRC; e.g., Helou et al., 1985; Condon, 1992, and
references therein). We refer to Section 4 in Paper I for more details about
sample selections and here we just give a brief introduction. IR emission and
radio emission of the star formation process have a mutual origin from
activities of massive stars (Condon, 1992; Dubner & Giacani, 2015), which
results in a tight correlation between each other (IRRC). The IRRC is usually
defined by the ratio ($q_{\rm TIR}$) of rest-frame 8–1000 $\mu$m IR luminosity
($L_{\rm{TIR}}$) to rest-frame 1.4 GHz radio luminosity ($L_{1.4\rm{GHz}}$)
which is in a form of $q_{\rm{TIR}}=\log[L_{\rm{TIR}}/(L_{1.4\rm{GHz}}\times
3.75\times 10^{12}\ \rm{Hz})]$ (Helou et al., 1985). AGNs may have extra radio
emission from nuclear activities, such as jets (Panessa et al., 2019, for a
review). Therefore, radio AGNs usually exhibit a radio excess relative to the
IRRC and have a smaller $q_{\rm{TIR}}$ value compared to that of star
formation. In Paper I, we define a $q_{\rm{TIR}}$ threshold
($q_{\rm{TIR,AGN}}$) to select radio AGNs (see details in Paper I). A radio
source will be selected as a radio AGN if its $q_{\rm{TIR}}$ value is lower
than $q_{\rm{TIR,AGN}}$. In addition, $L_{1.4\rm{GHz}}$ was derived from Paper
I which is calculated by the radio flux from the deep VLA 1.4 GHz (GOODS-N;
Owen, 2018) or 3 GHz radio surveys (COSMOS; Smolčić et al., 2017) assuming a
radio spectral index of $-0.8$ (e.g., Yang et al., 2022). $L_{\rm TIR}$ was
derived from Paper I which is estimated by the broadband spectral energy
distribution (SED) fitting. In the SED fitting process, the far-infrared (FIR)
and submillimeter data are derived from the “super de-blended” photometry Liu
et al. (2018); Jin et al. (2018) ensuring a more precise estimate for the IR
luminosity.

###  2.2 GOODS-S field

We also selected a radio AGN sample from the GOODS-S field following Paper I
to enlarge our sample. We first derived radio data at 3 GHz from Alberts et
al. (2020) which contains 712 sources with signal-to-noise ratio (S/N) larger
than 3. Then we cross-matched this 3 GHz catalog with the ultraviolet-optical-
mid-infrared (UV-optical-MIR) catalog from Guo et al. (2013) by a match radius
of 1 arcsec. This UV-optical-MIR catalog covers the wavelength range between
0.4 and 8 $\mu$m, and contains 34,930 sources over 171 arcmin2. After cross-
matching, 414 (out of 712) radio objects in Alberts et al. (2020) have
UV/optical/MIR counterparts in Guo et al. (2013). Following selection criteria
in Paper I ($0.1<z\leq 4.0$ and S/N of radio flux $\geq 5$), we selected out
366 radio sources from the 414 objects as our radio sources sample in the
GOODS-S field to make further analysis. Next we collected MIR-FIR data in the
GOODS-S field from Wang et al. (in prep.). Based on the similar “super de-
blended” photometry method in the GOODS-N and COSMOS fields, Wang et al. (in
prep.) obtained photometry at MIR band (Spitzer 16 and 24 $\mu$m) and “super
de-blended” photometry at FIR band (Herschel 100, 160, 250, 350, and 500
$\mu$m) for 1881 objects. We also utilized the submillimeter data derived from
SCUBA-2 850 $\mu$m survey (Cowie et al., 2018), Atacama Large
Millimeter/submillimeter Array (ALMA) 870 $\mu$m survey (Tadaki et al., 2020),
and ALMA 1.1 mm survey (Gómez-Guijarro et al., 2022). Further, we cross-
matched the radio sources sample in the GOODS-S field with the MIR-FIR catalog
(Wang et al. in prep.) by a match radius of 1 arcsec, with the SCUBA-2 850
$\mu$m survey by a radius of 5 arcsec, with the ALMA 870 $\mu$m survey by a
radius of 1 arcsec, with the ALMA 1.1 mm survey by a radius of 1.5 arcsec. For
the 366 sources in the radio sources sample, 324 objects have MIR-FIR
counterparts in Wang et al. (in prep.). Of these, 27 (out of 324) objects have
SCUBA-2 850 $\mu$m detections, 12 (out of 324) objects have ALMA 870 $\mu$m
detections, and 35 (out of 324) objects have ALMA 1.1 mm detections. For the
above-mentioned 324 objects that have multi-wavelength data from UV-optical-
MIR to FIR-submillimeter-radio bands, we performed broadband SED fitting with
Code Investigating GALaxy Emission (cigale 2022.0; Burgarella et al., 2005;
Noll et al., 2009; Boquien et al., 2019; Yang et al., 2020, 2022) to estimate
various galaxy properties (such as $L_{\rm TIR}$ and stellar mass
$M_{\star}$). We refer to Appendix A in Paper I for parameter settings about
the SED fitting. Finally, we followed Paper I to select a parent radio AGN
sample in the GOODS-S field including 71 sources across $0.1<z\leq 4.0$ (see
brief introduction in Section 2.1 and detailed analysis in Section 4 of Paper
I).

##  3 Derived quantities

###  3.1 Black hole mass ($M_{\rm BH}$)

In this work we estimated black hole mass through an indirect way that is
based on the correlation between black hole mass and total stellar mass
($M_{\rm BH}$-$M_{\star}$ relation; e.g., Greene et al., 2020, for a review).
Here $M_{\star}$ was estimated by the broadband SED fitting (see details in
Paper I for the GOODS-N and COSMOS fields, and see details in Section 2.2 for
the GOODS-S field). Most of our radio AGN sample are hosted by ellipticals.
Thus, we used the $M_{\rm BH}$-$M_{\star}$ relation in a form of $\log(M_{\rm
BH}/M_{\odot})=(7.89\pm 0.09)+(1.33\pm 0.12)\times\log(M_{\star}/3\times
10^{10}M_{\odot})$ from Greene et al. (2020) for local early-type galaxies.
The $M_{\star}$ in this work was estimated based on a Chabrier (2003) IMF,
while Greene et al. (2020) adopted a diet Salpeter IMF (Bell et al., 2003).
Thus, we divided our $M_{\star}$ by a constant value of 1.14 (Madau &
Dickinson, 2014; van der Wel et al., 2007) to convert values from the Chabrier
(2003) IMF to the diet Salpeter IMF. In addition, Li et al. (2023) found that
the $M_{\star}$-$M_{\rm BH}$ relation does not show a significant evolution
with redshift across $0<z<3.5$. Therefore, we applied the local
$M_{\star}$-$M_{\rm BH}$ relation from Greene et al. (2020) to the whole
redshift range in this work ($0.1<z<4$). The uncertainties of $M_{\rm BH}$
were inferred from the parameters errors of $M_{\rm BH}$-$M_{\star}$ relation
(Greene et al., 2020) using the propagation of error method.

Figure 1: Distribution of the ratio of the rest-frame 5 GHz radio luminosity
($L_{\rm R}$) to the rest-frame 2–10 keV X-ray luminosity ($L_{\rm X}$) for
the entire final radio AGNs sample (Panel A), the radio-quiet (RQ) AGN
subsample (Panel B), and the radio-loud (RL) AGN subsample (Panel C). The
green solid curve in Panel (A) represents the best-fit model to the entire
distribution, which consists of two single Gaussian models (the blue dash-
dotted curve and the red dotted curve). The vertical dark-gray dashed line in
all panels represents the cross point between two single models, which is
defined as the radio-loudness threshold to divide radio-loud and radio-quiet
AGNs in this work. The vertical light-gray dashed line in Panel (A) represents
the radio-loudness threshold in Panessa et al. (2007), which is obtained by a
sample consisting of local Seyferts and low luminosity radio galaxies (LLRGs).
The blue and red histograms in Panel (B) represent the radio-quiet AGNs hosted
by SFGs and QGs, respectively, while in Panel (C), they represent the radio-
loud AGNs hosted by SFGs and QGs, respectively.

###  3.2 Rest-frame 5 GHz radio luminosity ($L_{\rm R}$)

To get a pure radio luminosity for AGNs, radio luminosity from star formation
($L_{\rm{SF}}$) should be subtracted from the total radio luminosity. The
$L_{\rm{SF}}$ can is estimated by the IRRC in the form of

$L_{1.4\rm{GHz},\rm{SF}}=L_{\rm{TIR}}/(3.75\times 10^{12}\ {\rm Hz}\times
10^{q_{\rm{TIR}}})$ (1)

(Helou et al., 1985), where $L_{\rm TIR}$ is the rest-frame 8–1000 $\mu$m IR
luminosity, $L_{1.4\rm{GHz},\rm{SF}}$ is the rest-frame 1.4 GHz radio
luminosity from star formation in the unit of erg s-1 Hz-1, and $q_{\rm{TIR}}$
is the IRRC index for the star-formation. The $q_{\rm{TIR}}$ is found to
depend on redshift (Magnelli et al., 2015; Delhaize et al., 2017; Novak et
al., 2017; Enia et al., 2022) and stellar mass (Delvecchio et al., 2022). For
consistency, here we used the relation obtained in our Paper I which is in a
form of $q_{\rm{TIR}}=(2.62\pm 0.08)\times(1+z)^{-0.08\pm 0.03}$. In Paper I,
we did not consider a $M_{\star}$-dependent IRRC as it does not have a
significant impact on our results.

Then the rest-frame 5 GHz radio luminosity from AGN (hereafter $L_{\rm R}$; in
the unit of erg s-1) is calculated by

$L_{\rm R}=\frac{4\pi D_{L}^{2}}{(1+z)^{1+\alpha_{\rm
AGN}}}\times\left(\frac{5\ {\rm GHz}}{\nu_{\rm obs}}\right)^{\alpha_{\rm
AGN}}\times(S_{\nu,\rm{obs}}-S_{\nu,\rm{SF}})\times 5\ {\rm GHz},$ (2)

where $D_{L}$ is the luminosity distance (in the unit of centimeter), $z$ is
the redshift, $\alpha_{\rm AGN}$ is the radio spectral index for AGNs that is
assumed to be $-0.5$ (e.g., de Gasperin et al., 2018; Bariuan et al., 2022),
$\nu_{\rm obs}$ is the observed frequency (in the unit of GHz), and
$S_{\nu,\rm{obs}}$ (in the unit of erg s-1 cm-2 Hz-1) is the observed
integrated flux densities at $\nu_{\rm obs}$. For the GOODS-N,
$S_{\nu,\rm{obs}}$ at $\nu_{\rm obs}=1.4$ GHz was derived from Owen (2018)
(see Section 2.1 or Paper I). For the GOODS-S, $S_{\nu,\rm{obs}}$ at $\nu_{\rm
obs}=3$ GHz was derived from Alberts et al. (2020) (see Section 2.2). For the
COSMOS, $S_{\nu,\rm{obs}}$ at $\nu_{\rm obs}=3$ GHz was derived from Smolčić
et al. (2017) (see Section 2.1 or Paper I). Here $S_{\nu,\rm{SF}}$ is the flux
densities at $\nu_{\rm obs}$ attributed to the star formation, which is
calculated by

$S_{\nu,\rm{SF}}=L_{1.4\rm{GHz},\rm{SF}}\ \frac{(1+z)^{1+\alpha_{\rm
SF}}}{4\pi D_{L}^{2}}\ \left(\frac{\nu_{\rm obs}}{1.4\ {\rm
GHz}}\right)^{\alpha_{\rm SF}}$ (3)

(Condon, 1992), where $L_{1.4\rm{GHz},\rm{SF}}$ is given by Equation 1 and
$\alpha_{\rm SF}$ is the radio spectral index for star formation that is
assumed to be $-0.8$ (e.g., Yang et al., 2022). The uncertainties of $L_{\rm
R}$ were inferred from the flux uncertainties given by the above-mentioned
radio surveys using the propagation of error method.

In some literature works, the rest-frame 5 GHz radio luminosity in the
fundamental plane refers to the nuclear radio emission from a compact radio
core in order to compare with X-ray emission that are mainly from central
engine. However, VLA 1.4 GHz or 3 GHz surveys in the GOODS-N, the GOODS-S, and
the COSMOS fields do not have high enough spatial resolution to resolve the
compact radio core. Even so, their spatial resolutions still ensure that the
radio flux is measured on the top of the galaxy rather than the large-scale
jet. In addition, nearly 20% of our sample have radio detections with higher
spatial resolution, such as VLA 10 GHz Pilot Survey in the GOODS-N field
(average spatial resolution of $0.22^{\prime\prime}\approx 1.76$ kpc at $z=1$;
Murphy et al., 2017) and VLA 6 GHz Survey in the GOODS-S field (average
angular resolution of $0.62^{\prime\prime}\times 0.31^{\prime\prime}\approx
4.97\ {\rm kpc}\times 2.48$ kpc at $z=1$; Alberts et al., 2020; Lyu et al.,
2022). These objects do not show significant large-scale jet structures.
Furthermore, we utilized the ratio of peak radio flux to total radio flux as a
proxy for compactness to select out a sample only including objects with
relatively compact structure (including 110 sources). We found that using this
compact objects subsample does not change our results comparing to using the
entire sample. In order to ensure a large sample to make analysis, in this
work we used the entire sample and do not consider whether the rest-frame 5
GHz radio luminosity is strictly derived from a spatially-resolved compact
core.

Figure 2: Distribution of physical properties for the radio-quiet (RQ) AGNs
(blue histogram) and radio-loud (RL) AGNs (red histogram) used to study the
fundamental plane of black hole activity, including: (A) redshift, (B) rest-
frame 2–10 keV X-ray luminosity from AGNs ($L_{\rm X}$), (C) rest-frame 5 GHz
radio luminosity from AGNs ($L_{\rm R}$), (D) specific star formation rate
(sSFR), (E) black hole mass ($M_{\rm BH}$) inferred from stellar mass, (F)
Eddington ratio ($\lambda_{\rm Edd}$).

###  3.3 Rest-frame 2–10 keV X-ray luminosity ($L_{\rm X}$)

X-ray data in the GOODS-N were mainly derived from the 2 Ms Chandra Deep
Field-North (CDF-N) survey (Xue et al., 2016). Xue et al. (2016) estimated the
absorption-corrected rest-frame 0.5–7 keV luminosity assuming an intrinsic
photon index of $\Gamma=1.8$ (typical value for the X-ray spectrum of AGNs;
Tozzi et al., 2006). Then we cross-matched our parent radio AGN sample in the
GOODS-N (102 objects, see Section 2.1) with the 2 Ms CDF-N survey by a match
radius of 1.5 arcsec. A total of 46 (out of 102) objects have X-ray
counterparts and their intrinsic 2–10 keV luminosities used in this work are
calculated by the intrinsic 0.5–7 keV luminosity from Xue et al. (2016) under
the assumption of $\Gamma=1.8$. Among these 46 objects, 17 sources have been
performed with systematic X-ray spectral analysis in Li et al. (2019)
($\Gamma$ is a free parameter in the fit and $\Gamma=1.80\pm 0.08$ for these
objects). Therefore, for these 17 sources, their intrinsic 2–10 keV
luminosities were derived from Li et al. (2019).

X-ray data in the GOODS-S were mainly derived from the 7 Ms Chandra Deep
Field-South (CDF-S) survey (Luo et al., 2017). Similar to the GOODS-N, the
absorption-corrected rest-frame 0.5–7 keV luminosities in the GOODS-S are
estimated by assuming an intrinsic photon index of $\Gamma=1.8$ (Luo et al.,
2017). We cross-matched our parent radio AGN sample in the GOODS-S (71
objects, see Section 2.2) with the 7 Ms CDF-S survey by a match radius of 1.5
arcsec. A total of 48 (out of 71) objects have X-ray counterparts and their
intrinsic 2–10 keV luminosities used in this work are calculated by the
intrinsic 0.5–7 keV luminosity from Luo et al. (2017) under the assumption of
$\Gamma=1.8$. Among these 48 objects, 23 sources have been performed with
systematic X-ray spectral analysis in Liu et al. (2017) ($\Gamma$ is a free in
the fit and $\Gamma=1.81\pm 0.09$). Therefore, for these 23 sources, their
intrinsic 2–10 keV luminosities were derived from Liu et al. (2017).

X-ray data in the COSMOS were mainly derived from the X-ray spectral fitting
for the 4.6 Ms Chandra COSMOS-Legacy survey (Marchesi et al., 2016) that gives
the intrinsic 2–10 keV luminosity. We cross-matched our parent radio AGN
sample in the COSMOS/UltraVISTA (881 objects, see Section 2.1) with the 4.6 Ms
Chandra COSMOS-Legacy survey by a match radius of 1.5 arcsec. A total of 117
(out of 881) objects have X-ray counterparts with available estimates for the
intrinsic 2–10 keV luminosity ($\Gamma=1.85\pm 0.62$). Among these 117
objects, 8 objects are classified as Compton-thick AGN by Lanzuisi et al.
(2018). For these 8 objects, we used their obscuration-corrected intrinsic
2–10 keV luminosity from Lanzuisi et al. (2018) to make the subsequent
analysis.

The above-mentioned 2–10 keV luminosity refers to the total X-ray luminosity
from the entire galaxy ($L_{\rm 2-10keV,tot}$). In order to get the pure X-ray
luminosity from AGNs, X-ray radiation from XRBs should be subtracted. X-ray
luminosities of XRBs have been found to correlate with star formation rate
(SFR) and stellar mass (Grimm et al., 2003; Lehmer et al., 2010; Mineo et al.,
2012, 2014), which also shows an evolution with redshift (Lehmer et al.,
2016). Here we used the relation of

$\frac{L_{\rm 2-10keV,XRBs}}{{\rm erg\
s^{-1}}}=10^{29.3}(1+z)^{2.19}\frac{M_{\star}}{M_{\odot}}+10^{39.4}(1+z)^{1.02}\frac{{\rm
SFR}}{M_{\odot}\ {\rm yr}^{-1}}$ (4)

derived from Lehmer et al. (2016) based on the 6Ms CDF-S survey. The
$M_{\star}$ and SFR in this relation were estimated assuming a Kroupa (2001)
IMF while we used the Chabrier (2003) IMF throughout this work. Therefore, we
first divided our $M_{\star}$ and SFR by a constant factor of 1.06 (Speagle et
al., 2014) to convert values from the Chabrier (2003) IMF to the Kroupa (2001)
IMF. Then we applied the scaled $M_{\star}$ and SFR into Equation 4 to get the
X-ray luminosity from XRBs. Finally, the pure X-ray luminosity from AGNs
(hereafter $L_{\rm X}$; in the unit of erg s-1) can be calculated by

$L_{\rm X}=L_{\rm 2-10keV,tot}-L_{\rm 2-10keV,XRBs},$ (5)

where $L_{\rm 2-10keV,XRBs}$ is calculated by Equation 4. The uncertainties of
$L_{\rm X}$ were inferred from the flux uncertainties given by the above-
mentioned X-rays surveys using the propagation of error method.

Considering the available estimates for $M_{\star}$, $L_{\rm R}$ and $L_{\rm
X}$ ($L_{\rm X}$ in Equation 5 is required to be greater than 0), we selected
out a radio AGNs sample including 208 objects (46 objects in the GOODS-N, 45
objects in the GOODS-S, and 117 objects in the COSMOS/UltraVISTA) that are
utilized in the subsequent analysis for the fundamental plane. The basic
information for these 208 objects are summarized in Table A1. In addition, for
the radio AGNs without X-ray counterparts in the aforementioned X-ray surveys,
we estimated their 2–10 keV X-ray luminosity upper limits by the X-ray
detection limit in these three fields (Xue et al., 2016; Luo et al., 2017;
Civano et al., 2016) assuming $\Gamma=1.8$. The X-ray detection limit is
$2.0\times 10^{-16}$ erg cm-2 s-1 in the 0.5–7 keV band for the GOODS-N (Xue
et al., 2016), $1.9\times 10^{-17}$ erg cm-2 s-1 in the 0.5–7 keV band for the
GOODS-S (Luo et al., 2017), and $1.5\times 10^{-15}$ erg cm-2 s-1 in the 2–10
keV band for the COSMOS (Civano et al., 2016).

##  4 Final sample of Radio-loud and Radio-quiet AGNs

In this work, our final radio AGN sample used to make the fundamental plane
analysis consists of the above-mentioned 208 objects which have available
estimates for $L_{\rm R}$, $L_{\rm X}$, and inferred $M_{\rm BH}$ from
$M_{\star}$. Then we utilized the radio-loudness defined by the relative
strength of the radio and X-ray emission ($R_{\rm X}$; e.g., Terashima &
Wilson, 2003; Panessa et al., 2007; Ho, 2008) to divide radio-loud and radio-
quiet AGNs in this work. The ratio of $L_{\rm R}$ to $L_{\rm X}$ is shown in
Panel (A) of Fig. 1. The $\log(L_{\rm R}/L_{\rm X})$ distribution shows a
bimodal shape which is attributed to radio-quiet and radio-loud AGNs,
respectively. Then we used two single Gaussian components to model the double
peaks (see the blue dash-dotted line and red dotted line in Panel A of Fig.
1), and used their cross point as the radio-loudness threshold (see the
vertical dark-gray dashed line in Panel A of Fig. 1) to divide radio-quiet and
radio-loud AGNs in this work. This radio-loudness threshold ($R_{\rm X,T}$) is

$R_{\rm X,T}=\log(L_{\rm R}/L_{\rm X})_{\rm cross\ point}=-2.73.$ (6)

It is consistent with the result in Panessa et al. (2007) that is obtained
based on a sample of 47 local Seyferts and 16 local low-luminosity radio
galaxies (see the vertical light-gray dashed line in Panel A of Fig. 1).
Finally, we selected out 141 radio-quiet AGNs (68% of the final radio AGN
sample) and 67 radio-loud AGNs (32% of the final radio AGN sample). The
physical properties of these radio-quiet and radio-loud AGNs are shown in Fig.
2.

Figure 3: Comparison of the predicted rest-frame 5 GHz luminosity from the
best-fit fundamental plane (x axis) and the observed rest-frame 5 GHz
luminosity (y axis) for the radio-quiet AGNs (left panel) and the radio-loud
AGNs (right panel). The black dashed line in each panel represents the 1:1
line. The dark-red empty triangles in the right panel represent the radio-loud
AGNs with only upper limits for $L_{\rm X}$ (see parameter calculation in
Section 3.3 and see sample selection in Section 5).

  * (1)

Both the radio-loud and radio-quiet AGN subsamples have a similar redshift
range between 0.1 and 4, while the median redshift is 0.9 for the radio-loud
AGNs and 1.2 for the radio-quiet AGNs (see Panel A of Fig. 2).

  * (2)

The range of $\log[L_{\rm X}\ (\rm{erg\ s}^{-1})$] for our radio-quiet AGN
sample is between $40.9$ and $45.2$ with a median of $44.0$, while for our
radio-loud AGN sample, it is between $39.9$ and $44.7$ with a median of $42.4$
(see Panel B of Fig. 2). The radio-quiet AGN sample has significantly larger
$L_{\rm X}$ than the radio-loud AGN sample.

  * (3)

The range of $\log[L_{\rm R}\ (\rm{erg\ s}^{-1})$] for the radio-quiet AGN
sample is between $37.9$ and $41.5$ with a median of $40.0$, while for the
radio-loud AGN sample, it is between $38.4$ and $43.4$ with a median of $40.5$
(see Panel C of Fig. 2). The radio-quiet AGN sample has slightly lower $L_{\rm
R}$ than the radio-loud AGN sample.

  * (4)

The range of specific star formation rate (sSFR) for our radio-quiet AGN
sample is between $0.001$ and $100$ Gyr-1 with a median of 0.60 Gyr-1, while
for our radio-loud AGN sample, it is between $0.003$ and 17 Gyr-1 with a
median of 0.12 Gyr-1 (see Panel D of Fig. 2). Here SFR was derived from Paper
I which is estimated by the broadband SED fitting. The radio-quiet AGN sample
has slightly higher sSFR than the radio-loud AGN sample.

  * (5)

The range of $\log[M_{\rm BH}/M_{\odot}]$ for the radio-quiet AGN sample is
between $5.35$ and $9.62$ with a median of $8.36$, while for the radio-loud
AGN sample, it is between $4.28$ and $9.70$ with a median of $8.58$ (see Panel
E of Fig. 2). The radio-quiet AGN sample has slightly lower $M_{\rm BH}$ than
the radio-loud AGN sample.

  * (6)

The Eddington ratio ($\lambda_{\rm Edd}$) is defined as $\lambda_{\rm
Edd}=L_{\rm bol}/L_{\rm Edd}$ where $L_{\rm bol}$ is the bolometric luminosity
and $L_{\rm Edd}$ is the Eddington luminosity. The bolometric luminosity is
converted from X-ray luminosity by a bolometric correction factor that is
related to the luminosity (e.g., Duras et al., 2020). For our sample, this
correction factor is around 20 (Duras et al., 2020). Therefore, here $L_{\rm
bol}$ is calculated by $L_{\rm bol}=L_{\rm X}\times 20$. The Eddington
luminosity is defined as $L_{\rm Edd}=1.3\times 10^{38}\ M_{\rm BH}/M_{\odot}$
in the unit of erg s-1 (Rybicki & Lightman, 1979). The range of $\lambda_{\rm
Edd}$ for our radio-quiet AGN sample is between $2.3\times 10^{-5}$ and $51$
with a median of $0.06$, while for our radio-loud AGN sample, it is between
$10^{-5}$ and $1.0$ with a median of $0.001$ (see Panel F of Fig. 2). The
radio-quiet AGN sample has significantly larger $\lambda_{\rm Edd}$ than the
radio-loud AGN sample, which is consistent with the negative correlation
between radio-loudness and Eddington ratio (e.g., Ho, 2002; Panessa et al.,
2007; Sikora et al., 2007).

Table 1: Best-fitting parameters of the fundamental plane of black hole
activity for radio-quiet and radio-loud AGNs in this work.

[.5]() | $N_{\rm sources}$ | $\xi_{\rm X}$ | $\xi_{\rm M}$ | $b$ | $\sigma_{\rm R}$
---|---|---|---|---|---
[.5]() |  | Radio-quiet AGNs |  |
[.5]() Total | 141 | $0.55\pm 0.05$ | $0.28\pm 0.06$ | $13.54\pm 2.27$ | 0.37
$\lambda_{\rm Edd}\leq 10^{-1.5}$ | 63 | $0.63\pm 0.09$ | $0.33\pm 0.15$ | $9.76\pm 3.42$ | 0.31
$\lambda_{\rm Edd}>10^{-1.5}$ | 78 | $0.52\pm 0.13$ | $0.26\pm 0.08$ | $14.99\pm 5.54$ | 0.40
$0.1<z\leq 1.0$ | 56 | $0.53\pm 0.07$ | $0.27\pm 0.08$ | $14.43\pm 3.36$ | 0.35
$1.0<z\leq 4.0$ | 85 | $0.36\pm 0.09$ | $0.30\pm 0.07$ | $21.79\pm 3.83$ | 0.37
Hosted by SFGs | 116 | $0.45\pm 0.07$ | $0.32\pm 0.07$ | $17.63\pm 3.14$ | 0.39
Hosted by QGs | 25 | $0.67\pm 0.06$ | $0.18\pm 0.08$ | $9.23\pm 2.89$ | 0.22
[.5]() |  | Radio-loud AGNs |  |
[.5]() Total | 67 | $0.82\pm 0.08$ | $0.07\pm 0.08$ | $5.24\pm 3.33$ | 0.34
$\lambda_{\rm Edd}\leq 10^{-2.5}$ | 40 | $0.57\pm 0.14$ | $0.24\pm 0.18$ | $14.07\pm 5.43$ | 0.33
$\lambda_{\rm Edd}>10^{-2.5}$ | 27 | $0.90\pm 0.19$ | $0.07\pm 0.17$ | $1.77\pm 7.39$ | 0.35
$0.1<z\leq 1.0$ | 37 | $0.83\pm 0.09$ | $0.03\pm 0.09$ | $4.98\pm 3.82$ | 0.31
$1.0<z\leq 4.0$ | 30 | $0.81\pm 0.16$ | $0.20\pm 0.19$ | $4.61\pm 7.00$ | 0.37
Hosted by SFGs | 32 | $0.78\pm 0.13$ | $0.13\pm 0.12$ | $6.15\pm 5.30$ | 0.36
Hosted by QGs | 35 | $0.85\pm 0.09$ | $-0.08\pm 0.16$ | $5.17\pm 4.05$ | 0.32
111 $N_{\rm sources}$ represents the number of sources. The best-fit
parameters for the fundamental plane correspond to the correlation coefficient
of X-ray luminosity $\xi_{\rm X}$, the correlation coefficient of black hole
mass $\xi_{\rm M}$, and constant offset $b$ (see Equation 7). Parameter
$\sigma_{\rm R}$ denotes the scatter of the observed $L_{\rm R}$ relative to
the predicted value from the best-fit fundamental plane.

##  5 Fitting the fundamental plane for radio-loud and radio-quiet AGNs

Following Merloni et al. (2003), we defined the fundamental plane of black
hole activity as

$\log L_{\rm R}=\xi_{\rm X}\log L_{\rm X}+\xi_{\rm M}\log M_{\rm BH}+b,$ (7)

where $L_{\rm R}$ is the rest-frame 5 GHz radio luminosity (in the unit of erg
s-1), $L_{\rm X}$ is the rest-frame 2–10 keV X-ray luminosity (in the unit of
erg s-1), $M_{\rm BH}$ is the black hole mass (in the unit of $M_{\odot}$).
Then we use the the ordinary least squares (OLS) Linear Regression method in
the Python package scikit-learn (Pedregosa et al., 2011) to fit the data set.
Further, we ran the fitting process with 4000 iterations to take the
uncertainties of both dependent and independent variables into account. Next
we take the variable $L_{\rm X}$ as an example to show the detailed analysis
process. In our sample, the $i$th object has the observed $L_{{\rm X,obs},i}$
with an uncertainty of $\sigma_{i}$. In the $j$th fitting process, value of
the variable used for fitting ($L_{{\rm X,fit},i,j}$) was randomly selected
from a normal distribution centered at $L_{{\rm X,obs},i}$ with a variance of
$\sigma_{i}$. We made the same value selection for the variables $L_{\rm R}$
and $M_{\rm BH}$. Thus, in the $j$th fitting process, the $i$th object had
$L_{{\rm X,fit},i,j}$, $L_{{\rm R,fit},i,j}$, and $M_{{\rm BH,fit},i,j}$.
After the $j$th fitting, the best-fit parameters were given as $\xi_{{\rm
X,}j}\pm\sigma_{{\rm X,}j}$, $\xi_{{\rm M,}j}\pm\sigma_{{\rm M,}j}$, and
$b_{\rm j}\pm\sigma_{b,j}$. Finally, fitting with 4000 iterations produced a
nearly symmetric distribution for each fitting coefficient. Then we used the
mean of the distribution as the best-fit coefficient, while the error was
derived from the integrated variance from both fitting process and observed
uncertainties. Next we take parameter $\xi_{\rm X}$ as an example. The best-
fit $\xi_{\rm X}$ was calculated by $\sum_{j=1}^{4000}\xi_{{\rm X,}j}/4000$
(written as $\bar{\xi}_{\rm X}$ hereafter), while its error was calculated by
$\sqrt{\sum_{j=1}^{4000}(\xi_{{\rm X,}j}-\bar{\xi}_{\rm
X})^{2}/4000+\left(\sum_{j=1}^{4000}\sigma_{{\rm X,}j}/4000\right)^{2}}$. Then
we did the same calculation for both $\xi_{\rm M}$ and $b$.

We performed the above fitting process for our radio-quiet and radio-loud AGN
samples separately. We found a best-fit fundamental plane of

$\log L_{\rm R}=(0.55\pm 0.05)\log L_{\rm X}+(0.28\pm 0.06)\log M_{\rm
BH}+(13.54\pm 2.27)$ (8)

for the radio-quiet AGN sample, and

$\log L_{\rm R}=(0.82\pm 0.08)\log L_{\rm X}+(0.07\pm 0.08)\log M_{\rm
BH}+(5.24\pm 3.33)$ (9)

for the radio-loud AGN sample. The best-fit coefficients and their errors are
summarized in Table 1. The comparison between the observed $L_{\rm R}$ and the
predicted $L_{\rm R}$ by the best-fit fundamental plane is shown in Fig. 3.
The significantly different fundamental plane between radio-quiet and radio-
loud AGNs, and their comparison with literature works are discussed in details
in Section 6.1. For the radio AGNs with only upper limits for X-ray
luminosity, we estimated their radio-loudness lower limits according to the
ratio of $L_{\rm R}$ to $L_{\rm X}$-upper-limits. Therefore, from these
sources, we selected out 76 radio-loud AGNs with only upper limits for X-ray
luminosity (see the dark-red triangles in Fig. 3) based on the previously
defined radio-loudness threshold (see Equation 6). These radio-loud AGNs are
greatly consistent with the fundamental plane (see Equation 9) obtained with
the aforementioned radio-loud AGN sample (see Fig. 3).

Figure 4: Comparison of the best-fit correlation coefficients $\xi_{X}$ and
$\xi_{M}$ of the fundamental plane. Our results for the radio-quiet (RQ) AGNs
and radio-loud (RL) AGNs samples are shown as the dark-red filled star and the
dark-red empty star, respectively. The results from literature works are shown
as comparisons, including Merloni et al. (2003) (Merloni+2003), Falcke et al.
(2004) (Falcke+2004), Plotkin et al. (2012) (Plotkin+2012), Dong et al. (2014)
(Dong+2014), Yuan et al. (2009) (Yuan+2009), Gültekin et al. (2009b)
(G$\rm\ddot{u}$ltekin+2009), Saikia et al. (2015) (Saikia+2015), Nisbet & Best
(2016) (Nisbet & Best 2016), Xie & Yuan (2017) (Xie & Yuan 2017), Bonchi et
al. (2013) (Bonchi+2013), Li & Gu (2018) (Li & Gu 2018), Fan & Bai (2016) (Fan
& Bai 2016), Wang et al. (2006) (Wang+2006), Li et al. (2008) (Li+2008),
Bariuan et al. (2022) (Bariuan+2022). Purple symbols represent studies based
on a sample consisting of both X-ray binaries (XRBs) and local AGNs. Blue
symbols represent studies based on local low-luminosity AGNs (LLAGNs). Yellow
symbols represent studies for other types of AGNs. Red symbols represent
studies for radio-quiet (filled symbols) and radio-loud (empty symbols) AGN
separately. The theoretically predicted correlation coefficients are derived
from Merloni et al. (2003) with the electron spectral index $p=2$, which are
shown as a circle with a square in the center for the advection dominated
accretion flow (ADAF), a circle with a pentagon in the center for a
synchrotron jet model, and a circle with a diamond in the center for the
standard Shakura-Sunyaev disc model. For the theoretically predicted
correlation coefficients, empty gray symbols and filled gray symbols represent
the predictions based on a radio spectral index of $0$ and $-0.5$,
respectively, and the dashed lines connecting the empty and filled symbols
represent the tracks of $\xi_{\rm X}$ and $\xi_{\rm M}$ due to the variation
of radio spectral index.

##  6 Discussion

The comparison between the best-fit correlation coefficients $\xi_{\rm X}$ and
$\xi_{\rm M}$ of the fundamental plane can characterize the accretion physics
of central engines (Merloni et al., 2003). In the $\xi_{\rm X}$–$\xi_{\rm M}$
diagram (see Fig. 4, Fig. 5, and Fig. 6), the theoretically predicted
correlation coefficients are derived from Merloni et al. (2003) with the
electron spectral index $p=2$. These theoretical models are advection
dominated accretion flow (ADAF; a radiatively inefficient accretion flow;
Narayan & Yi, 1994; Yuan, 2001; Yuan & Narayan, 2014, for a review), the
synchrotron jet model producing radio emission by the optically thin
synchrotron radiation from jet, and the standard Shakura-Sunyaev disc model
(Shakura & Sunyaev, 1973; Pringle, 1981, for a review). Next we give a brief
summary about the studies for the fundamental plane in Section 6.1 and further
discuss the dependence of the fundamental plane on Eddington ratio (Section
6.2), redshift (Section 6.3), and galaxy star-formation properties (Section
6.4). Combining our and literature works, we investigate the central engines
of radio-quiet and radio-loud AGNs in Section 6.5.

###  6.1 A brief summary about the fundamental plane studies

Merloni et al. (2003), Falcke et al. (2004), Plotkin et al. (2012), and Dong
et al. (2014) all studied the fundamental plane based on a sample consisting
of both X-ray binaries (XRBs) and local AGNs (see the purple symbols in Fig.
4). Merloni et al. (2003), Falcke et al. (2004), and Plotkin et al. (2012) got
a consistent result about the fundamental plane of nearly all types of AGNs
but with a primary focus of low-luminosity AGNs (LLAGNs), showing that these
populations yield an ADAF model. On the other hand, Dong et al. (2014) showed
a significantly different pattern that their bright AGNs with higher Eddington
ratio are in line with the predictions of the disc model. Thus, such a
difference indicates that different types of AGNs may have different
fundamental plane.

Furthermore, many studies of the fundamental plane only focus on AGNs. Some
works studied the fundamental plane of local LLAGNs (Yuan et al., 2009;
Gültekin et al., 2009a; Saikia et al., 2015; Nisbet & Best, 2016; Xie & Yuan,
2017, see blue symbols in Fig. 4). Gültekin et al. (2009a), Saikia et al.
(2015), and Nisbet & Best (2016) obtained consistent results (ADAF model) with
those in Merloni et al. (2003) and Falcke et al. (2004), while Yuan et al.
(2009) and Xie & Yuan (2017) exhibited different results. The LLAGNs samples
in Gültekin et al. (2009a), Saikia et al. (2015), and Nisbet & Best (2016)
have relatively higher Eddington ratio than those in Yuan et al. (2009) and
Xie & Yuan (2017), which might explain the different results among them. In
addition, X-ray-selected AGN ($L_{\rm X}>10^{42}\ \rm{erg}\ \rm{s}^{-1}$)
(Bonchi et al., 2013), low-excitation radio-loud AGN (Li & Gu, 2018), and
young radio AGNs (Fan & Bai, 2016) show a similar fundamental plane with
LLAGNs (see yellow symbols in Fig. 4).

Figure 5: Comparison of the best-fit correlation coefficients $\xi_{X}$ and
$\xi_{M}$ of the fundamental plane for Eddington-ratio subsamples (A),
redshift subsamples (B), and galaxy-star-formation-property subsamples (C).
The theoretically predicted correlation coefficients for ADAF, jet model, and
disc model are same as Fig. 4, which are shown here respectively as triangles,
pentagons, and stars. In each panel, filled symbols represent radio-quiet (RQ)
AGNs and empty symbols represent radio-loud (RL) AGNs. In Panel (A), “TW”,
“B22”, “D14”, “W06”, and “L08” means results from this work, Bariuan et al.
(2022), Dong et al. (2014), Wang et al. (2006), Li et al. (2008),
respectively.

In addition, many works explore the fundamendal plane of radio-quiet and
radio-loud populations separately (Wang et al., 2006; Li et al., 2008; Bariuan
et al., 2022). Both Wang et al. (2006) and Li et al. (2008) utilized broad-
line AGNs samples and they got a consistent result about the fundamental plane
within 1$\sigma$ uncertainty (see Fig. 4). They all found that radio-quiet and
radio-loud AGNs show quite different fundamental planes. Radio-quiet AGNs
favor the ADAF model coupled with a synchrotron jet model, while the radio-
loud AGNs favor a combination of the disc model with the synchrotron jet
model. More recently, Bariuan et al. (2022) found that for luminous quasars,
radio-quiet and radio-loud subsets also have different fundamental planes.
Therefore, these works demonstrate that the fundamental plane depends on the
radio loudness of AGNs.

We also separately studied the fundamental plane of radio-quiet and radio-loud
AGNs. Comparing to the literature works (Wang et al., 2006; Li et al., 2008;
Bariuan et al., 2022), our samples have relatively lower X-ray luminosity,
lower radio luminosity, and lower Eddington ratio. We also found that there is
a different fundamental plane between radio-quiet and radio-loud AGNs. Our
low-luminosity radio-quiet AGNs show a slightly different fundamental plane
than the high-luminosity radio-quiet AGNs from Wang et al. (2006), Li et al.
(2008), and Bariuan et al. (2022), while our low-luminosity radio-loud AGNs
present a significantly different result than the high-luminosity radio-loud
AGNs from these literature works (see Fig. 4). These results indicate that the
fundamental plane may have a dependence on Eddington ratio (see details in
Section 6.2).

###  6.2 Eddington-ratio dependence for the fundamental plane

We split our radio-quiet AGN subsample into two Eddington-ratio subsets:
$\lambda_{\rm Edd}\leq 10^{-1.5}$ (with a median value of $0.01$) and
$\lambda_{\rm Edd}>10^{-1.5}$ (with a median value of $0.2$). Our radio-loud
AGN subsample was split into two Eddington-ratio subsets: $\lambda_{\rm
Edd}\leq 10^{-2.5}$ (with a median value of $0.0003$) and $\lambda_{\rm
Edd}>10^{-2.5}$ (with a median value of $0.02$). The best-fit parameters for
the fundamental plane of these subsets and the source number in each subset
are summarized in Table 1. The comparison between $\xi_{\rm X}$ and $\xi_{\rm
M}$ is shown in Panel A of Fig. 5. For the radio-quiet AGN sample, both the
low-Eddington-ratio subset ($\lambda_{\rm Edd}\leq 10^{-1.5}$; the yellow
filled square in Panel A of Fig. 5) and high-Eddington-ratio subset
($\lambda_{\rm Edd}>10^{-1.5}$; the blue filled circle in Panel A of Fig. 5)
agree with an ADAF model coupled with a synchrotron jet model. For the radio-
loud AGN sample, the low-Eddington-ratio subset ($\lambda_{\rm Edd}\leq
10^{-2.5}$; the red empty diamond in Panel A of Fig. 5) can be explained by an
ADAF model coupled with a jet model, while the high-Eddington-ratio subset
($\lambda_{\rm Edd}>10^{-2.5}$; the yellow empty square in Panel A of Fig. 5)
mainly follows a jet model. For comparison, $\xi_{\rm X}$ and $\xi_{\rm M}$
from Wang et al. (2006) (W06), Li et al. (2008) (L08), and Bariuan et al.
(2022) (B22) are shown in Panel A of Fig. 5. In addition, we also analyzed the
fundamental plane for the radio-quiet AGN sample from Dong et al. (2014) (D14)
whose best-fit parameters are also shown in Panel A of Fig. 5. Our samples and
samples from these literature works have different Eddington ratio and follow
different fundamental planes (see Panel A of Fig. 5). According to these
results, we found that for both radio-quiet AGNs and radio-loud AGNs, their
fundamental planes may depend on Eddington ratio.

Figure 6: Cartoon illustrating the model for the central engine of radio-quiet
AGNs and radio-loud AGNs. Black solid lines represent the theoretically
predicted correlation coefficients for ADAF, jet, and standard thin disc
models, which are same as Fig. 4 and Fig. 5. The upper colored arrow
represents the observational results for radio-quiet (RQ) AGNs, while the
lower colored arrow represents the observational results for radio-loud (RL)
AGNs. The different colors of the arrow represent different Eddington ratio
($\lambda_{\rm Edd}$) and the direction of the arrow means from low
$\lambda_{\rm Edd}$ to high $\lambda_{\rm Edd}$. Radio-quiet AGNs at
$0.01<\lambda_{\rm Edd}<0.1$ are consistent with a combination of ADAF and a
synchrotron jet model (ADAF+jet model), while at $0.1<\lambda_{\rm Edd}<1$,
they mainly follow the synchrotron jet model (Jet model). Radio-loud AGNs are
consistent with a combination of ADAF and a synchrotron jet model (ADAF+jet
model) at $\lambda_{\rm Edd}<0.01$, and agree with the synchrotron jet model
(Jet model) at $0.01<\lambda_{\rm Edd}<0.1$, and follow the standard thin disc
coupled with a jet model (Disc+jet model) at $\lambda_{\rm Edd}>0.1$.

###  6.3 Redshift dependence for the fundamental plane

We further studied the fundamental plane of radio-quiet and radio-loud AGN
subsamples by splitting them into two redshift subsets: $0.1<z\leq 1$ and
$1<z\leq 4$. For each subset, the best-fit parameters and source numbers are
summarized in Table 1. For both radio-loud AGNs and radio-quiet AGNs, there
seems to be no signifiant redshift dependence for the fundamental plane (see
Panel B of Fig. 5). For luminous AGNs (such as broad-line AGNs and quasars),
Li et al. (2008) found no significant dependence on redshift for both radio-
quiet and radio-loud subsets across $0<z<2.5$, while Bariuan et al. (2022)
only observed a redshift dependence for radio-loud subset across $0.1<z<5$. In
the future, larger samples across a broad luminosity range and a wide redshift
range are required to draw a firm conclusion about the redshift dependence.

###  6.4 Galaxy-star-formation-property dependence for the fundamental plane

For the first time, we studied the galaxy-star-formation-property (SFGs and
QGs) dependence for the fundamental plane whose best-fit parameters and source
numbers are summarized in Table 1. We adopted the UVJ selection criteria in
Schreiber et al. (2015) to decide galaxy types (SFG or QG). Here the UVJ
magnitudes of our sample were derived from literature works (GOODS-N: Barro et
al. 2019; GOODS-S: Straatman et al. 2016; COSMOS: Weaver et al. 2022). Radio
AGNs hosted by SFGs and QGs have different cosmic evolutions for AGN incident
rate (e.g., Janssen et al., 2012; Kondapally et al., 2022, Paper I) and radio
luminosity functions (Kondapally et al., 2022, Paper I). In addition, SFGs and
QGs have different gas contents that may perform different fueling mechanisms
toward central SMBHs (e.g., Kauffmann & Heckman, 2009; Kondapally et al.,
2022; Ni et al., 2023). However, as Panel (C) of Fig. 5 shows, neither the
radio-loud AGNs nor the radio-quiet AGNs show a significant dependence on the
galaxy star-formation properties, which indicates that galaxy star-formation
properties may not a major factor to affect the fundamental plane and the
disc-jet connection may not depend on the fueling mechanisms of host galaxies.
In addition, nearly 82% of radio-quiet AGNs are hosted by SFGs and 18% of the
radio-quiet AGNs are hosted by QGs (see Table 1 and Panel B of Fig. 1), while
the fraction of the radio-loud AGNs hosted by SFGs and QGs are both around 50%
(see Table 1 and Panel C of Fig. 1).

###  6.5 Central engine for radio-quiet and radio-loud AGNs

As we mentioned in Section 6.1, radio-quiet AGNs and radio-loud AGNs are found
to follow different fundamental planes, which may correspond to different
accretion physics for the central engine (see Fig. 4). In Fig. 6, we show a
cartoon illustrating the central engines of radio-quiet AGNs and radio-loud
AGNs based on the observational results.

According to the observational evidences from our work and literature works
(see details in Section 6.2), radio-quiet AGNs at $0.01<\lambda_{\rm Edd}<0.1$
are consistent with a combination of ADAF and a synchrotron jet model, while
at $0.1<\lambda_{\rm Edd}<1$, they mainly follow the synchrotron jet model
(see Panel A in Fig. 5 or the cartoon illustration in Fig. 6). For radio-quiet
AGNs at other $\lambda_{\rm Edd}$ ranges, more observational data are required
to verify this trend in the future. Wang et al. (2022a) studied the ambient
circumnuclear medium of six radio-quiet AGNs with $0.05<\lambda_{\rm Edd}<0.5$
based on the high-resolution X-ray analysis for warm absorber outflows. The
density profile of the ambient circumnuclear medium shows that for these six
radio-quiet AGNs, the accretion physics from 0.01 parsec to a few parsec
(corresponding to a physical scale from the broad-line region to the torus;
Wang et al., 2022b) are consistent with the standard thin disc model. One
possible reason for the difference between this work and Wang et al. (2022a)
is that for different physical scales. The fundamental plane describes the
disc-jet or corona-jet connection in the innermost region of the accretion
flow (Merloni et al., 2003), which reflects the accretion physics around
several Schwarzschild radius (e.g., Alston et al., 2020) (corresponding to
about $10^{-4}$ parsec assuming a $10^{8}\ M_{\odot}$ black hole). Thus, the
physical scale we target in this work is much smaller than that in Wang et al.
(2022a).

Radio-loud AGNs are consistent with a combination of ADAF and a synchrotron
jet model at $\lambda_{\rm Edd}<0.01$, and agree with the synchrotron jet
model at $0.01<\lambda_{\rm Edd}<0.1$, and follow the standard thin disc
coupled with a jet model at $\lambda_{\rm Edd}>0.1$ (see Panel A in Fig. 5 or
the cartoon illustration in Fig. 6). The result for the high-$\lambda_{\rm
Edd}$ radio-loud AGN is consistent with that in Zhong et al. (2023) who found
that the extremely powerful radio jets are a result of either the spectral
transition from ADAF to a thin disc or a super-Eddington accretion.

##  7 Summary and conclusions

We investigated the fundamental plane of black hole activity based on a large
radio AGN sample selected from the GOODS-N, the GOODS-S, and the
COSMOS/UltraVISTA fields across $0.1<z\leq 4$. This radio AGN sample consists
of 208 objects with available estimates for rest-frame 5 GHz radio luminosity
($L_{\rm R}$) and rest-frame 2–10 keV X-ray luminosity ($L_{\rm X}$), and
inferrer black hole mass ($M_{\rm BH}$) from stellar mass (Section 3). Then we
divided this radio AGN sample into 141 radio-quiet AGNs and 67 radio-loud AGNs
(Section 4), and studie their fundamental planes separately (Section 5).
Further, we summarized the current studies about the fundamental plane
(Section 6.1). Finally, we explored the dependence of the fundamental plane on
Eddington ratio (Section 6.2), redshift (Section 6.3), and galaxy star-
formation properties (Section 6.4), and discussed the central engines of
radio-quiet and radio-loud AGNs (Section 6.5). The main conclusions are shown
as follows:

  1. (i)

The ratio of $L_{\rm R}$ to $L_{\rm X}$, also known as a tracer for radio-
loudness, shows a bimodal distribution which can be well described by two
single Gaussian models (Fig. 1). The cross point between these two Gaussian
components, that is $\log(L_{\rm R}/L_{\rm X})=-2.73$, is defined as a radio-
loudness threshold to divide radio-quiet and radio-loud AGN in this work.

  2. (ii)

Our Radio-quiet AGNs have larger X-ray luminosity, lower radio luminosity, and
significantly larger Eddington ratio comparing to our radio-loud AGNs.

  3. (iii)

Our radio-quiet and radio-loud AGNs show significantly different fundamental
plane which is $\log L_{\rm R}=(0.55\pm 0.05)\log L_{\rm X}+(0.28\pm 0.06)\log
M_{\rm BH}+(13.54\pm 2.27)$ for the radio-quiet AGNs, and $\log L_{\rm
R}=(0.82\pm 0.08)\log L_{\rm X}+(0.07\pm 0.08)\log M_{\rm BH}+(5.24\pm 3.33)$
for the radio-loud AGNs (Fig. 3 and Table A1). Our radio-quiet AGNs can be
explained by an ADAF model coupled with a synchrotron jet model, while our
radio-loud AGNs mainly agree with a synchrotron emitting jet model (Fig. 4).

  4. (iv)

For both radio-quiet and radio-loud AGNs, the fundamental plane shows a
significant dependence on Eddington ratio (Panel A in Fig. 5), while it
presents no significant dependence on redshift and galaxy star-formation
properties (SFGs and QGs) (Panels B and C in Fig. 5, respectively).

  5. (v)

Radio-quiet and radio-loud AGNs at different accretion states have different
fundamental planes (Fig. 4) corresponding to different central engines (Fig.
6). Radio-quiet AGNs at $0.01<\lambda_{\rm Edd}<0.1$ are consistent with a
combination of ADAF and a synchrotron jet model, while at $0.1<\lambda_{\rm
Edd}<1$, they mainly follow the synchrotron jet model (Fig. 6). Radio-loud
AGNs are consistent with a combination of ADAF and a synchrotron jet model at
$\lambda_{\rm Edd}<0.01$, and agree with the synchrotron jet model at
$0.01<\lambda_{\rm Edd}<0.1$, and follow the standard thin disc coupled with
the jet model at $\lambda_{\rm Edd}>0.1$ (Fig. 6).

###### Acknowledgements.

We thank Stefano Marchesi and Giorgio Lanzuisi for kind help to access the
COSMOS-Legacy survey data. This work is supported by the National Natural
Science Foundation of China (Project No. 12173017 and Key Project No.
12141301). LCH was supported by the National Science Foundation of China
(11991052, 12011540375, 12233001), the National Key R&D Program of China
(2022YFF0503401), and the China Manned Space Project (CMS-CSST-2021-A04, CMS-
CSST-2021-A06).

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Table A1: Radio AGN sample used in the analysis for the fundamental plane of black hole activity. (1) Survey name: “GOODSN” for the GOODS-N field, “GOODSS” for the GOODS-S field, “COSMOS” for the COSMOS/UltraVISTA field; (2) ID from Liu et al. (2018) (or Barro et al. 2019) for the GOODS-N, from Guo et al. (2013) for the GOODS-S, from Jin et al. (2018) for the COSMOS; (3) Right Ascension; (4) Declination; (5) Redshift; (6) Radio-loudness type: “RQ” for radio-quiet AGN, “RL” for radio-loud AGN; (7) Rest-frame 5 GHz radio luminosity from AGN; (8) Rest-frame 2–10 keV X-ray luminosity from AGN; (9) Black hole mass inferred from stellar mass; (10) Eddington ratio; (11) Host galaxy star-formation properties: “SFG” for star-forming galaxy, “QG” for quiescent galaxy; (12) Specific star formation rate.  [.5]()Survey | ID | R.A. | Decl. | $z$ | Type | $\log\left(\frac{L_{\rm R}}{{\rm erg}\ {\rm s}^{-1}}\right)$ | $\log\left(\frac{L_{\rm X}}{{\rm erg}\ {\rm s}^{-1}}\right)$ | $\log\left(\frac{M_{\rm BH}}{M_{\odot}}\right)$ | $\log\lambda_{\rm Edd}$ | Host galaxy | $\log\left(\frac{{\rm sSFR}}{{\rm Gyr}}\right)$
---|---|---|---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12)
GOODSN | 90 | 189.069981 | 62.104166 | 1.141 | RQ | $39.81\pm 0.05$ | $42.72\pm 0.14$ | $8.51\pm 0.12$ | $-2.61$ | SFG | $-106.78$
GOODSN | 896 | 189.206901 | 62.127243 | 1.610 | RQ | $40.47\pm 0.02$ | $44.56\pm 0.01$ | $7.03\pm 0.14$ | $0.72$ | SFG | $0.90$
GOODSN | 1211 | 189.135673 | 62.133290 | 1.994 | RQ | $40.42\pm 0.03$ | $43.52\pm 0.05$ | $5.54\pm 0.26$ | $1.17$ | SFG | $2.03$
GOODSN | 1464 | 189.312283 | 62.139902 | 0.825 | RL | $41.11\pm 0.01$ | $42.10\pm 0.14$ | $6.81\pm 0.16$ | $-1.52$ | QG | $0.40$
GOODSN | 2085 | 189.289291 | 62.143789 | 0.907 | RL | $40.19\pm 0.01$ | $42.33\pm 0.07$ | $8.93\pm 0.13$ | $-3.41$ | QG | $-2.06$
GOODSN | 2351 | 189.050155 | 62.149980 | 2.220 | RQ | $40.13\pm 0.10$ | $43.37\pm 0.07$ | $8.62\pm 0.12$ | $-2.07$ | SFG | $-1.22$
GOODSN | 2955 | 189.125229 | 62.156647 | 0.954 | RQ | $39.51\pm 0.03$ | $43.10\pm 0.05$ | $7.10\pm 0.14$ | $-0.81$ | QG | $-4.67$
GOODSN | 3629 | 189.065078 | 62.162943 | 1.263 | RL | $39.70\pm 0.06$ | $42.11\pm 0.19$ | $8.75\pm 0.12$ | $-3.45$ | SFG | $-0.79$
GOODSN | 3919 | 189.027641 | 62.164241 | 0.638 | RQ | $39.76\pm 0.03$ | $43.57\pm 0.05$ | $8.23\pm 0.10$ | $-1.48$ | SFG | $-1.09$
GOODSN | 4316 | 189.071192 | 62.169817 | 0.846 | RQ | $39.46\pm 0.05$ | $43.08\pm 0.02$ | $8.16\pm 0.10$ | $-1.89$ | SFG | $-0.89$
GOODSN | 4345 | 189.049043 | 62.170740 | 0.851 | RQ | $39.15\pm 0.06$ | $44.12\pm 0.05$ | $7.51\pm 0.11$ | $-0.21$ | SFG | $-0.35$
GOODSN | 4593 | 189.028576 | 62.172613 | 2.505 | RQ | $40.71\pm 0.02$ | $43.92\pm 0.11$ | $9.00\pm 0.14$ | $-1.90$ | QG | $-1.70$
GOODSN | 4663 | 189.114607 | 62.173937 | 0.761 | RQ | $38.82\pm 0.09$ | $42.92\pm 0.04$ | $7.27\pm 0.11$ | $-1.17$ | SFG | $-1.22$
GOODSN | 5157 | 189.033868 | 62.176641 | 0.679 | RQ | $39.95\pm 0.01$ | $43.05\pm 0.05$ | $7.97\pm 0.09$ | $-1.73$ | QG | $-4.87$
GOODSN | 5195 | 189.341015 | 62.176583 | 0.979 | RQ | $39.61\pm 0.06$ | $43.51\pm 0.05$ | $8.54\pm 0.11$ | $-1.85$ | SFG | $-0.82$
GOODSN | 6135 | 189.066879 | 62.185503 | 1.619 | RQ | $39.74\pm 0.06$ | $44.35\pm 0.01$ | $7.86\pm 0.12$ | $-0.32$ | SFG | $-1.06$
GOODSN | 6226 | 189.179527 | 62.185702 | 3.230 | RQ | $37.85\pm 0.07$ | $43.16\pm 0.09$ | $5.39\pm 0.25$ | $0.96$ | SFG | $-2.72$
GOODSN | 6694 | 189.135303 | 62.184818 | 0.519 | RL | $38.87\pm 0.07$ | $40.70\pm 0.35$ | $8.66\pm 0.12$ | $-4.78$ | QG | $-2.99$
GOODSN | 8109 | 189.266607 | 62.199309 | 3.406 | RQ | $40.59\pm 0.04$ | $44.44\pm 0.11$ | $8.07\pm 0.10$ | $-0.44$ | QG | $-1.00$
GOODSN | 8513 | 189.420565 | 62.200105 | 1.168 | RQ | $39.90\pm 0.06$ | $44.05\pm 0.01$ | $8.77\pm 0.13$ | $-1.53$ | SFG | $-0.36$
GOODSN | 11541 | 189.153773 | 62.222334 | 3.110 | RQ | $40.57\pm 0.05$ | $44.22\pm 0.10$ | $8.07\pm 0.10$ | $-0.66$ | SFG | $0.56$
GOODSN | 11561 | 189.200329 | 62.219182 | 0.475 | RQ | $38.45\pm 0.07$ | $41.57\pm 0.05$ | $8.03\pm 0.10$ | $-3.28$ | QG | $-4.05$
GOODSN | 11595 | 189.231040 | 62.219797 | 0.955 | RQ | $39.39\pm 0.04$ | $42.61\pm 0.04$ | $8.60\pm 0.11$ | $-2.80$ | QG | $-2.73$
GOODSN | 12953 | 189.073650 | 62.228983 | 0.534 | RQ | $38.50\pm 0.08$ | $41.69\pm 0.11$ | $8.15\pm 0.10$ | $-3.27$ | QG | $-2.84$
GOODSN | 13456 | 189.351104 | 62.233248 | 0.474 | RQ | $39.71\pm 0.07$ | $42.72\pm 0.02$ | $7.90\pm 0.10$ | $-2.00$ | SFG | $-4.46$
GOODSN | 14007 | 189.193116 | 62.234636 | 0.961 | RQ | $40.38\pm 0.02$ | $43.97\pm 0.01$ | $8.63\pm 0.12$ | $-1.47$ | SFG | $-1.43$
GOODSN | 14094 | 189.426126 | 62.238412 | 1.554 | RL | $39.95\pm 0.04$ | $42.41\pm 0.15$ | $7.49\pm 0.10$ | $-1.89$ | SFG | $-0.74$
GOODSN | 14559 | 189.403676 | 62.241388 | 2.158 | RQ | $40.44\pm 0.03$ | $44.53\pm 0.02$ | $8.05\pm 0.11$ | $-0.33$ | SFG | $-0.32$
GOODSN | 16450 | 189.220352 | 62.245578 | 0.321 | RL | $39.22\pm 0.02$ | $40.81\pm 0.08$ | $8.53\pm 0.11$ | $-4.53$ | QG | $-3.38$
GOODSN | 16517 | 188.989304 | 62.254510 | 2.423 | RQ | $39.88\pm 0.10$ | $44.12\pm 0.05$ | $8.16\pm 0.10$ | $-0.85$ | SFG | $0.06$
GOODSN | 16574 | 189.065980 | 62.254315 | 2.690 | RQ | $40.18\pm 0.07$ | $44.46\pm 0.06$ | $8.89\pm 0.13$ | $-1.25$ | SFG | $-2.45$
GOODSN | 17162 | 189.095584 | 62.257403 | 2.583 | RQ | $40.43\pm 0.03$ | $44.76\pm 0.01$ | $6.66\pm 0.21$ | $1.29$ | SFG | $2.02$
GOODSN | 17217 | 189.318220 | 62.253422 | 0.559 | RL | $39.67\pm 0.01$ | $41.33\pm 0.12$ | $8.56\pm 0.11$ | $-4.04$ | QG | $-1.76$
GOODSN | 17242 | 189.334881 | 62.256554 | 0.937 | RL | $39.14\pm 0.07$ | $41.82\pm 0.15$ | $8.60\pm 0.11$ | $-3.59$ | QG | $-2.66$
GOODSN | 18204 | 189.175812 | 62.262626 | 0.858 | RQ | $39.94\pm 0.03$ | $42.85\pm 0.03$ | $8.51\pm 0.11$ | $-2.48$ | SFG | $-0.72$
GOODSN | 18583 | 189.270299 | 62.267106 | 1.890 | RQ | $39.91\pm 0.06$ | $44.20\pm 0.01$ | $8.11\pm 0.10$ | $-0.73$ | SFG | $-0.31$
GOODSN | 22096 | 189.543917 | 62.291455 | 1.256 | RQ | $39.83\pm 0.07$ | $44.18\pm 0.02$ | $8.26\pm 0.10$ | $-0.89$ | QG | $-6.93$
GOODSN | 22224 | 189.319477 | 62.292585 | 1.146 | RQ | $40.12\pm 0.01$ | $44.11\pm 0.01$ | $7.48\pm 0.11$ | $-0.18$ | SFG | $-0.41$
GOODSN | 23451 | 189.393419 | 62.303323 | 2.241 | RQ | $39.99\pm 0.07$ | $43.22\pm 0.12$ | $8.41\pm 0.11$ | $-1.99$ | QG | $-1.66$
GOODSN | 23652 | 189.247165 | 62.309045 | 2.199 | RL | $42.39\pm 0.01$ | $43.60\pm 0.06$ | $8.37\pm 0.10$ | $-1.59$ | QG | $-5.90$
GOODSN | 23856 | 189.254555 | 62.352667 | 0.800 | RL | $40.34\pm 0.01$ | $41.99\pm 0.15$ | $8.82\pm 0.13$ | $-3.64$ | QG | $-6.10$
GOODSN | 24659 | 189.413983 | 62.350082 | 0.837 | RQ | $39.55\pm 0.05$ | $43.87\pm 0.01$ | $5.35\pm 0.27$ | $1.71$ | QG | $1.75$
GOODSN | 24879 | 189.281190 | 62.363283 | 1.450 | RQ | $39.90\pm 0.08$ | $44.35\pm 0.01$ | $8.56\pm 0.12$ | $-1.03$ | SFG | $-0.34$
GOODSN | 25194 | 189.256368 | 62.340213 | 2.990 | RQ | $40.69\pm 0.04$ | $44.05\pm 0.12$ | $8.88\pm 0.13$ | $-1.64$ | SFG | $-0.06$
GOODSN | 27062 | 189.324500 | 62.315479 | 2.237 | RQ | $39.95\pm 0.07$ | $44.34\pm 0.01$ | $7.30\pm 0.14$ | $0.22$ | SFG | $0.84$
GOODSN | 27423 | 189.168911 | 62.309187 | 1.146 | RL | $40.61\pm 0.01$ | $41.82\pm 0.20$ | $8.61\pm 0.11$ | $-3.60$ | SFG | $-1.93$
GOODSS | 25734 | 53.111521 |  $-$27.695987 | 0.734 | RQ | $39.22\pm 0.07$ | $42.95\pm 0.04$ | $8.22\pm 0.13$ | $-2.09$ | SFG | $-0.92$
GOODSS | 25273 | 53.101073 |  $-$27.690674 | 0.534 | RQ | $38.99\pm 0.04$ | $42.59\pm 0.03$ | $8.57\pm 0.13$ | $-2.79$ | QG | $-2.78$
GOODSS | 24497 | 53.110392 |  $-$27.676539 | 1.031 | RQ | $39.48\pm 0.09$ | $43.98\pm 0.02$ | $6.85\pm 0.17$ | $0.32$ | SFG | $1.39$
GOODSS | 24012 | 53.174944 |  $-$27.663675 | 0.152 | RL | $38.86\pm 0.03$ | $40.46\pm 0.13$ | $7.72\pm 0.13$ | $-4.08$ | QG | $-1.20$
GOODSS | 23922 | 53.167050 |  $-$27.659599 | 0.733 | RQ | $39.23\pm 0.08$ | $43.38\pm 0.05$ | $8.18\pm 0.10$ | $-1.61$ | QG | $-5.86$
GOODSS | 23259 | 53.040437 |  $-$27.713362 | 0.733 | RL | $40.33\pm 0.01$ | $42.18\pm 0.04$ | $8.95\pm 0.14$ | $-3.58$ | QG | $-2.78$
GOODSS | 23153 | 53.138691 |  $-$27.709999 | 1.213 | RQ | $39.44\pm 0.07$ | $43.42\pm 0.05$ | $7.49\pm 0.13$ | $-0.88$ | SFG | $-5.86$
GOODSS | 22879 | 53.186044 |  $-$27.700681 | 0.709 | RL | $39.46\pm 0.02$ | $41.41\pm 0.20$ | $8.01\pm 0.10$ | $-3.41$ | QG | $-1.85$
GOODSS | 20859 | 53.152971 |  $-$27.735114 | 0.666 | RQ | $38.74\pm 0.07$ | $42.96\pm 0.02$ | $7.68\pm 0.10$ | $-1.53$ | SFG | $-5.86$
GOODSS | 20447 | 53.045478 |  $-$27.737492 | 1.615 | RL | $41.84\pm 0.00$ | $44.27\pm 0.01$ | $8.97\pm 0.14$ | $-1.51$ | SFG | $-0.92$
GOODSS | 20219 | 53.094107 |  $-$27.740510 | 0.738 | RQ | $39.61\pm 0.05$ | $43.31\pm 0.71$ | $8.35\pm 0.11$ | $-1.86$ | SFG | $-0.30$
GOODSS | 19892 | 53.079375 |  $-$27.741624 | 3.356 | RL | $39.99\pm 0.06$ | $42.27\pm 0.22$ | $8.51\pm 0.13$ | $-3.05$ | SFG | $0.06$
GOODSS | 18638 | 53.121828 |  $-$27.752702 | 1.831 | RQ | $39.67\pm 0.07$ | $42.59\pm 0.19$ | $8.15\pm 0.13$ | $-2.37$ | SFG | $-0.30$
GOODSS | 18166 | 53.124914 |  $-$27.758302 | 1.209 | RQ | $39.43\pm 0.06$ | $43.89\pm 0.02$ | $6.58\pm 3.24$ | $0.49$ | SFG | $1.36$
GOODSS | 17206 | 53.015224 |  $-$27.767690 | 0.574 | RQ | $39.40\pm 0.05$ | $43.09\pm 0.04$ | $8.59\pm 0.12$ | $-2.31$ | QG | $-8.21$
GOODSS | 16985 | 53.093923 |  $-$27.767722 | 1.730 | RQ | $39.73\pm 0.08$ | $43.81\pm 0.05$ | $8.23\pm 0.10$ | $-1.23$ | SFG | $-0.33$
GOODSS | 16599 | 53.119720 |  $-$27.772304 | 0.738 | RL | $40.11\pm 0.01$ | $42.15\pm 0.05$ | $8.35\pm 0.14$ | $-3.01$ | QG | $-18.46$
GOODSS | 16375 | 53.044947 |  $-$27.774393 | 1.610 | RL | $40.82\pm 0.01$ | $42.11\pm 0.10$ | $9.16\pm 0.15$ | $-3.86$ | QG | $-5.86$
GOODSS | 16274 | 53.131080 |  $-$27.773108 | 2.220 | RL | $40.59\pm 0.03$ | $42.93\pm 0.06$ | $8.25\pm 0.27$ | $-2.13$ | SFG | $0.45$
GOODSS | 15901 | 53.193097 |  $-$27.775562 | 1.220 | RQ | $39.38\pm 0.06$ | $43.81\pm 0.04$ | $7.35\pm 0.11$ | $-0.35$ | SFG | $-0.28$
Table A2: Radio AGN sample used in the analysis for the fundamental plane (continued). [.5]()Survey | ID | R.A. | Decl. | $z$ | Type | $\log\left(\frac{L_{\rm R}}{{\rm erg}\ {\rm s}^{-1}}\right)$ | $\log\left(\frac{L_{\rm X}}{{\rm erg}\ {\rm s}^{-1}}\right)$ | $\log\left(\frac{M_{\rm BH}}{M_{\odot}}\right)$ | $\log\lambda_{\rm Edd}$ | Host galaxy | $\log\left(\frac{{\rm sSFR}}{{\rm Gyr}}\right)$
---|---|---|---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12)
GOODSS | 15381 | 53.180515 |  $-$27.779666 | 2.589 | RL | $40.35\pm 0.03$ | $42.26\pm 0.22$ | $7.96\pm 0.12$ | $-2.52$ | SFG | $0.42$
GOODSS | 14781 | 53.033328 |  $-$27.782575 | 2.612 | RQ | $40.30\pm 0.09$ | $44.15\pm 0.05$ | $8.40\pm 0.11$ | $-1.07$ | SFG | $-0.05$
GOODSS | 13729 | 53.036091 |  $-$27.792883 | 0.543 | RQ | $40.95\pm 0.00$ | $43.89\pm 0.01$ | $8.78\pm 0.12$ | $-1.71$ | SFG | $-0.92$
GOODSS | 12526 | 53.108340 |  $-$27.797645 | 1.897 | RL | $39.99\pm 0.11$ | $42.25\pm 0.19$ | $7.57\pm 0.14$ | $-2.14$ | SFG | $0.59$
GOODSS | 10578 | 53.165283 |  $-$27.814068 | 3.064 | RQ | $40.67\pm 0.02$ | $44.62\pm 0.03$ | $9.00\pm 0.20$ | $-1.19$ | QG | $-1.85$
GOODSS | 10497 | 53.181989 |  $-$27.814120 | 2.958 | RL | $40.63\pm 0.02$ | $42.69\pm 0.16$ | $8.26\pm 0.10$ | $-2.38$ | SFG | $-0.28$
GOODSS | 10348 | 53.066754 |  $-$27.816593 | 1.413 | RL | $39.86\pm 0.05$ | $41.71\pm 0.14$ | $8.33\pm 0.10$ | $-3.43$ | SFG | $-5.86$
GOODSS | 10014 | 53.058894 |  $-$27.819501 | 2.076 | RL | $40.60\pm 0.02$ | $42.53\pm 0.09$ | $7.70\pm 0.17$ | $-1.98$ | SFG | $0.45$
GOODSS | 8923 | 53.142844 |  $-$27.827890 | 0.366 | RL | $38.38\pm 0.05$ | $40.68\pm 0.14$ | $4.28\pm 0.36$ | $-0.42$ | SFG | $0.95$
GOODSS | 8833 | 53.030641 |  $-$27.828322 | 3.485 | RL | $40.80\pm 0.06$ | $43.13\pm 0.07$ | $7.00\pm 0.30$ | $-0.68$ | SFG | $0.00$
GOODSS | 8758 | 53.056171 |  $-$27.831346 | 0.731 | RL | $39.76\pm 0.02$ | $41.67\pm 0.13$ | $8.16\pm 0.10$ | $-3.31$ | QG | $-2.13$
GOODSS | 7551 | 53.131435 |  $-$27.841327 | 1.613 | RL | $40.20\pm 0.02$ | $42.47\pm 0.11$ | $8.82\pm 0.13$ | $-3.16$ | SFG | $-0.30$
GOODSS | 7442 | 53.141819 |  $-$27.841356 | 1.384 | RL | $39.69\pm 0.12$ | $40.62\pm 1.49$ | $8.10\pm 0.11$ | $-4.30$ | SFG | $0.06$
GOODSS | 7250 | 53.027374 |  $-$27.843922 | 0.339 | RL | $38.78\pm 0.11$ | $39.89\pm 0.57$ | $6.80\pm 0.14$ | $-3.73$ | SFG | $-0.05$
GOODSS | 7061 | 53.201811 |  $-$27.844133 | 2.661 | RL | $40.03\pm 0.13$ | $42.07\pm 0.20$ | $7.12\pm 0.31$ | $-1.87$ | SFG | $1.24$
GOODSS | 6752 | 53.076400 |  $-$27.848664 | 1.536 | RQ | $40.04\pm 0.04$ | $44.11\pm 0.04$ | $8.81\pm 0.13$ | $-1.51$ | QG | $-1.85$
GOODSS | 5893 | 53.195148 |  $-$27.855868 | 2.292 | RQ | $39.65\pm 0.04$ | $42.75\pm 0.09$ | $6.49\pm 0.16$ | $-0.56$ | SFG | $1.38$
GOODSS | 5479 | 53.078464 |  $-$27.859856 | 3.660 | RQ | $40.77\pm 0.05$ | $44.11\pm 0.09$ | $8.84\pm 0.13$ | $-1.54$ | SFG | $-0.30$
GOODSS | 4526 | 53.157342 |  $-$27.870087 | 1.603 | RQ | $40.33\pm 0.02$ | $44.35\pm 0.02$ | $9.09\pm 0.14$ | $-1.55$ | SFG | $-0.92$
GOODSS | 3973 | 53.139319 |  $-$27.874500 | 3.673 | RL | $41.14\pm 0.02$ | $43.34\pm 0.08$ | $8.58\pm 0.11$ | $-2.06$ | QG | $-5.86$
GOODSS | 3188 | 53.263706 |  $-$27.885171 | 1.346 | RL | $39.93\pm 0.09$ | $42.66\pm 0.19$ | $8.58\pm 0.11$ | $-2.74$ | SFG | $-1.85$
GOODSS | 1256 | 53.104830 |  $-$27.913926 | 1.090 | RQ | $39.90\pm 0.03$ | $43.33\pm 0.11$ | $8.73\pm 0.12$ | $-2.22$ | SFG | $-2.13$
GOODSS | 569 | 53.170144 |  $-$27.929655 | 3.350 | RQ | $40.13\pm 0.03$ | $44.76\pm 0.04$ | $6.72\pm 0.43$ | $1.22$ | SFG | $1.07$
GOODSS | 528 | 53.113470 |  $-$27.933294 | 1.089 | RL | $39.81\pm 0.07$ | $41.76\pm 0.20$ | $8.67\pm 0.12$ | $-3.72$ | SFG | $-1.85$
GOODSS | 135 | 53.142288 |  $-$27.944471 | 2.897 | RL | $41.39\pm 0.08$ | $43.76\pm 0.12$ | $8.51\pm 0.17$ | $-1.56$ | SFG | $0.87$
COSMOS | 552411 | 150.343730 | 2.140640 | 1.787 | RQ | $40.58\pm 0.03$ | $44.36\pm 0.03$ | $8.90\pm 0.14$ | $-1.36$ | SFG | $0.07$
COSMOS | 10002464 | 150.376620 | 1.717860 | 0.655 | RQ | $39.82\pm 0.03$ | $44.16\pm 0.04$ | $7.20\pm 0.12$ | $0.15$ | SFG | $0.07$
COSMOS | 10004014 | 150.671800 | 1.760100 | 1.175 | RQ | $40.29\pm 0.02$ | $43.95\pm 0.20$ | $8.67\pm 0.13$ | $-1.54$ | QG | $-0.21$
COSMOS | 10005234 | 150.478240 | 1.790330 | 0.702 | RQ | $39.66\pm 0.03$ | $43.45\pm 0.20$ | $8.36\pm 0.11$ | $-1.72$ | QG | $-0.54$
COSMOS | 10006773 | 150.661830 | 1.833660 | 1.574 | RL | $41.48\pm 0.02$ | $43.73\pm 0.20$ | $8.55\pm 0.12$ | $-1.64$ | QG | $-0.20$
COSMOS | 10009202 | 150.694850 | 1.886880 | 1.173 | RQ | $39.93\pm 0.04$ | $44.25\pm 0.20$ | $8.20\pm 0.11$ | $-0.76$ | SFG | $0.17$
COSMOS | 10009415 | 150.447070 | 1.882840 | 0.670 | RL | $40.71\pm 0.02$ | $42.74\pm 0.11$ | $9.46\pm 0.18$ | $-3.53$ | SFG | $-1.83$
COSMOS | 10012067 | 150.697430 | 1.933730 | 0.306 | RQ | $38.60\pm 0.04$ | $42.18\pm 0.20$ | $7.90\pm 0.11$ | $-2.54$ | QG | $-1.38$
COSMOS | 10012117 | 150.467640 | 1.935740 | 0.970 | RQ | $40.40\pm 0.03$ | $43.86\pm 0.08$ | $8.67\pm 0.13$ | $-1.63$ | SFG | $-0.16$
COSMOS | 10012366 | 150.607120 | 1.935110 | 0.680 | RQ | $40.15\pm 0.02$ | $43.20\pm 0.20$ | $8.66\pm 0.13$ | $-2.28$ | SFG | $-0.62$
COSMOS | 10014345 | 150.713940 | 1.972160 | 1.697 | RQ | $40.40\pm 0.03$ | $43.78\pm 0.20$ | $8.97\pm 0.14$ | $-2.00$ | SFG | $-0.19$
COSMOS | 10014743 | 150.574940 | 1.976770 | 0.863 | RL | $42.21\pm 0.02$ | $44.33\pm 0.20$ | $7.52\pm 0.11$ | $-0.00$ | SFG | $-0.04$
COSMOS | 10017028 | 150.060330 | 1.632690 | 0.554 | RQ | $39.60\pm 0.03$ | $43.94\pm 0.20$ | $8.73\pm 0.13$ | $-1.60$ | SFG | $-0.50$
COSMOS | 10018189 | 150.012040 | 1.652110 | 1.520 | RL | $41.28\pm 0.03$ | $43.52\pm 0.20$ | $8.16\pm 0.11$ | $-1.45$ | SFG | $1.25$
COSMOS | 10019570 | 150.100360 | 1.668190 | 0.620 | RL | $40.35\pm 0.02$ | $42.67\pm 0.20$ | $8.90\pm 0.14$ | $-3.04$ | QG | $-1.44$
COSMOS | 10020296 | 150.206940 | 1.680260 | 1.261 | RQ | $40.50\pm 0.03$ | $45.20\pm 0.06$ | $8.71\pm 0.13$ | $-0.33$ | SFG | $0.27$
COSMOS | 10023996 | 150.312400 | 1.730080 | 0.580 | RQ | $39.56\pm 0.03$ | $43.89\pm 0.10$ | $8.14\pm 0.11$ | $-1.07$ | SFG | $-0.23$
COSMOS | 10026655 | 150.180020 | 1.768870 | 0.350 | RL | $40.74\pm 0.06$ | $42.41\pm 0.07$ | $9.46\pm 0.18$ | $-3.86$ | QG | $-2.46$
COSMOS | 10027526 | 150.244130 | 1.782190 | 1.120 | RQ | $40.62\pm 0.02$ | $43.38\pm 0.06$ | $8.26\pm 0.11$ | $-1.70$ | SFG | $-0.38$
COSMOS | 10027888 | 150.128040 | 1.786460 | 1.574 | RQ | $40.39\pm 0.03$ | $43.78\pm 0.05$ | $8.87\pm 0.14$ | $-1.90$ | SFG | $-0.17$
COSMOS | 10038584 | 150.273380 | 1.934240 | 0.916 | RQ | $39.89\pm 0.04$ | $44.24\pm 0.02$ | $9.03\pm 0.15$ | $-1.61$ | SFG | $-0.55$
COSMOS | 10041613 | 149.842200 | 1.605160 | 1.285 | RQ | $40.53\pm 0.03$ | $44.48\pm 0.20$ | $8.51\pm 0.12$ | $-0.85$ | SFG | $0.05$
COSMOS | 10043686 | 149.559400 | 1.631030 | 0.901 | RL | $41.38\pm 0.02$ | $42.95\pm 0.20$ | $8.91\pm 0.14$ | $-2.78$ | SFG | $-1.14$
COSMOS | 10053489 | 149.592450 | 1.756740 | 1.970 | RQ | $40.85\pm 0.02$ | $45.08\pm 0.20$ | $9.18\pm 0.16$ | $-0.91$ | SFG | $-1.10$
COSMOS | 10053620 | 149.820140 | 1.761580 | 1.440 | RQ | $40.19\pm 0.03$ | $44.49\pm 0.07$ | $8.01\pm 0.11$ | $-0.33$ | QG | $0.46$
COSMOS | 10058534 | 149.564620 | 1.823090 | 1.510 | RQ | $40.99\pm 0.02$ | $45.18\pm 0.20$ | $7.90\pm 0.11$ | $0.46$ | SFG | $0.20$
COSMOS | 10061653 | 149.517180 | 1.863480 | 1.543 | RQ | $39.78\pm 0.07$ | $44.28\pm 0.08$ | $8.22\pm 0.11$ | $-0.76$ | SFG | $-0.12$
COSMOS | 10067794 | 149.781140 | 1.932180 | 1.778 | RL | $41.89\pm 0.02$ | $43.81\pm 0.13$ | $8.83\pm 0.14$ | $-1.84$ | QG | $-0.51$
COSMOS | 10074857 | 150.510680 | 2.029220 | 0.900 | RQ | $40.25\pm 0.03$ | $43.79\pm 0.04$ | $8.57\pm 0.12$ | $-1.60$ | SFG | $0.06$
COSMOS | 10076774 | 150.663700 | 2.060240 | 2.120 | RQ | $41.24\pm 0.02$ | $44.52\pm 0.20$ | $9.58\pm 0.19$ | $-1.87$ | SFG | $-0.76$
COSMOS | 10076991 | 150.447340 | 2.053940 | 0.333 | RL | $40.71\pm 0.02$ | $41.88\pm 0.12$ | $9.70\pm 0.20$ | $-4.63$ | QG | $-3.50$
COSMOS | 10084257 | 150.743420 | 2.170530 | 1.341 | RQ | $41.40\pm 0.02$ | $44.59\pm 0.20$ | $9.03\pm 0.15$ | $-1.26$ | SFG | $0.16$
COSMOS | 10084485 | 150.591320 | 2.176420 | 1.263 | RQ | $39.95\pm 0.05$ | $43.53\pm 0.20$ | $8.32\pm 0.11$ | $-1.60$ | SFG | $0.21$
COSMOS | 10084513 | 150.422270 | 2.175360 | 0.698 | RQ | $39.38\pm 0.04$ | $44.15\pm 0.02$ | $7.08\pm 0.13$ | $0.26$ | SFG | $0.57$
COSMOS | 10086247 | 150.472750 | 2.197960 | 0.404 | RL | $40.72\pm 0.02$ | $42.65\pm 0.03$ | $8.51\pm 0.12$ | $-2.68$ | QG | $-1.59$
COSMOS | 10089638 | 150.630870 | 2.255500 | 1.430 | RQ | $39.92\pm 0.05$ | $44.24\pm 0.20$ | $8.06\pm 0.11$ | $-0.64$ | SFG | $0.15$
COSMOS | 10093737 | 150.378070 | 2.318190 | 1.440 | RQ | $41.02\pm 0.02$ | $44.42\pm 0.08$ | $8.30\pm 0.11$ | $-0.70$ | SFG | $0.65$
COSMOS | 10094020 | 150.442750 | 2.322680 | 1.371 | RQ | $39.78\pm 0.06$ | $43.57\pm 0.06$ | $8.28\pm 0.11$ | $-1.52$ | SFG | $-0.00$
COSMOS | 10094905 | 150.595980 | 2.336060 | 1.090 | RQ | $40.11\pm 0.03$ | $43.87\pm 0.06$ | $8.29\pm 0.11$ | $-1.23$ | SFG | $0.15$
COSMOS | 10096301 | 150.604930 | 2.358700 | 2.694 | RQ | $40.96\pm 0.03$ | $44.14\pm 0.13$ | $8.14\pm 0.11$ | $-0.82$ | SFG | $0.88$
COSMOS | 10098600 | 150.403020 | 2.389870 | 1.267 | RQ | $40.57\pm 0.03$ | $43.87\pm 0.03$ | $8.58\pm 0.12$ | $-1.53$ | SFG | $-0.21$
COSMOS | 10100910 | 150.415700 | 2.430200 | 0.124 | RL | $38.80\pm 0.02$ | $41.01\pm 0.08$ | $9.17\pm 0.16$ | $-4.97$ | QG | $-2.88$
COSMOS | 10102594 | 150.401980 | 2.445030 | 0.120 | RQ | $37.96\pm 0.03$ | $40.92\pm 0.22$ | $8.74\pm 0.13$ | $-4.64$ | QG | $-2.89$
COSMOS | 10105342 | 150.106220 | 2.014390 | 1.954 | RL | $41.54\pm 0.03$ | $43.93\pm 0.10$ | $9.59\pm 0.19$ | $-2.47$ | SFG | $0.24$
COSMOS | 10106008 | 150.343410 | 2.019990 | 0.420 | RL | $41.22\pm 0.02$ | $42.50\pm 0.06$ | $8.77\pm 0.13$ | $-3.08$ | QG | $-1.72$
COSMOS | 10108227 | 150.266430 | 2.049850 | 0.960 | RQ | $39.96\pm 0.04$ | $43.31\pm 0.13$ | $9.19\pm 0.16$ | $-2.70$ | SFG | $-0.45$
Table A3: Radio AGN sample used in the analysis for the fundamental plane (continued). [.5]()Survey | ID | R.A. | Decl. | $z$ | Type | $\log\left(\frac{L_{\rm R}}{{\rm erg}\ {\rm s}^{-1}}\right)$ | $\log\left(\frac{L_{\rm X}}{{\rm erg}\ {\rm s}^{-1}}\right)$ | $\log\left(\frac{M_{\rm BH}}{M_{\odot}}\right)$ | $\log\lambda_{\rm Edd}$ | Host galaxy | $\log\left(\frac{{\rm sSFR}}{{\rm Gyr}}\right)$
---|---|---|---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12)
COSMOS | 10109081 | 150.042600 | 2.063280 | 1.465 | RQ | $40.13\pm 0.04$ | $44.66\pm 0.02$ | $7.93\pm 0.11$ | $-0.08$ | SFG | $0.41$
COSMOS | 10110759 | 150.208000 | 2.083340 | 0.758 | RQ | $39.96\pm 0.02$ | $44.77\pm 0.01$ | $8.18\pm 0.11$ | $-0.23$ | SFG | $-0.66$
COSMOS | 10111389 | 150.326900 | 2.094150 | 2.164 | RQ | $41.49\pm 0.02$ | $44.65\pm 0.03$ | $8.46\pm 0.12$ | $-0.63$ | SFG | $0.03$
COSMOS | 10113383 | 149.930920 | 2.118720 | 2.709 | RQ | $40.92\pm 0.03$ | $44.47\pm 0.04$ | $8.75\pm 0.13$ | $-1.10$ | SFG | $0.63$
COSMOS | 10113857 | 150.115700 | 2.126740 | 2.166 | RQ | $40.12\pm 0.07$ | $44.08\pm 0.11$ | $7.61\pm 0.11$ | $-0.35$ | SFG | $0.79$
COSMOS | 10120941 | 150.298770 | 2.214050 | 1.150 | RQ | $39.96\pm 0.04$ | $43.63\pm 0.06$ | $8.53\pm 0.12$ | $-1.71$ | SFG | $-0.04$
COSMOS | 10121043 | 149.953480 | 2.212480 | 0.474 | RL | $39.91\pm 0.02$ | $42.35\pm 0.09$ | $8.59\pm 0.12$ | $-3.06$ | QG | $-1.09$
COSMOS | 10121546 | 150.059140 | 2.219940 | 1.125 | RQ | $40.88\pm 0.02$ | $43.61\pm 0.05$ | $8.77\pm 0.13$ | $-1.97$ | SFG | $-0.22$
COSMOS | 10124490 | 150.002580 | 2.258650 | 1.555 | RL | $42.40\pm 0.02$ | $44.48\pm 0.04$ | $8.61\pm 0.13$ | $-0.94$ | SFG | $0.17$
COSMOS | 10125460 | 150.224060 | 2.270800 | 1.702 | RQ | $40.60\pm 0.03$ | $44.55\pm 0.06$ | $8.63\pm 0.13$ | $-0.90$ | SFG | $0.44$
COSMOS | 10125474 | 149.940340 | 2.269370 | 2.441 | RQ | $40.95\pm 0.03$ | $45.01\pm 0.07$ | $9.15\pm 0.16$ | $-0.96$ | SFG | $0.47$
COSMOS | 10130265 | 149.919800 | 2.327420 | 1.131 | RQ | $40.48\pm 0.03$ | $44.82\pm 0.01$ | $7.89\pm 0.11$ | $0.12$ | SFG | $0.69$
COSMOS | 10131028 | 150.171140 | 2.337050 | 1.260 | RQ | $39.59\pm 0.07$ | $44.10\pm 0.08$ | $8.05\pm 0.11$ | $-0.76$ | SFG | $-0.02$
COSMOS | 10131985 | 150.073650 | 2.346850 | 0.833 | RQ | $39.68\pm 0.03$ | $44.24\pm 0.03$ | $6.89\pm 0.14$ | $0.53$ | SFG | $0.62$
COSMOS | 10134934 | 150.288540 | 2.381910 | 1.581 | RQ | $40.96\pm 0.03$ | $43.72\pm 0.08$ | $9.09\pm 0.15$ | $-2.18$ | SFG | $0.50$
COSMOS | 10135522 | 150.058090 | 2.380430 | 0.350 | RL | $39.63\pm 0.02$ | $41.73\pm 0.08$ | $8.90\pm 0.14$ | $-3.98$ | QG | $-2.44$
COSMOS | 10136176 | 149.905940 | 2.396450 | 0.742 | RL | $41.01\pm 0.02$ | $42.89\pm 0.08$ | $8.40\pm 0.12$ | $-2.31$ | SFG | $-0.58$
COSMOS | 10136788 | 150.174000 | 2.402980 | 0.979 | RQ | $39.37\pm 0.07$ | $44.08\pm 0.02$ | $7.11\pm 0.13$ | $0.16$ | SFG | $0.55$
COSMOS | 10138319 | 150.181440 | 2.423420 | 0.727 | RL | $40.28\pm 0.02$ | $42.97\pm 0.08$ | $8.74\pm 0.13$ | $-2.58$ | QG | $-1.17$
COSMOS | 10144600 | 149.547800 | 2.033080 | 1.579 | RL | $41.10\pm 0.02$ | $43.36\pm 0.19$ | $8.01\pm 0.11$ | $-1.47$ | SFG | $0.44$
COSMOS | 10144923 | 149.419950 | 2.035540 | 0.734 | RQ | $39.74\pm 0.04$ | $44.66\pm 0.20$ | $6.83\pm 0.14$ | $1.02$ | SFG | $1.03$
COSMOS | 10145065 | 149.396200 | 2.034520 | 0.294 | RQ | $39.47\pm 0.03$ | $42.57\pm 0.20$ | $7.56\pm 0.11$ | $-1.80$ | SFG | $-0.07$
COSMOS | 10148505 | 149.673140 | 2.078660 | 1.773 | RQ | $40.50\pm 0.04$ | $45.13\pm 0.16$ | $9.01\pm 0.15$ | $-0.69$ | SFG | $0.14$
COSMOS | 10148583 | 149.497970 | 2.076670 | 1.757 | RQ | $40.03\pm 0.07$ | $44.58\pm 0.20$ | $8.25\pm 0.11$ | $-0.48$ | SFG | $0.01$
COSMOS | 10155880 | 149.827970 | 2.164330 | 0.889 | RQ | $40.98\pm 0.02$ | $45.07\pm 0.01$ | $7.62\pm 0.11$ | $0.63$ | SFG | $-0.13$
COSMOS | 10157147 | 149.885450 | 2.177170 | 0.660 | RQ | $40.16\pm 0.03$ | $43.52\pm 0.04$ | $8.83\pm 0.14$ | $-2.13$ | SFG | $-0.39$
COSMOS | 10159865 | 149.649640 | 2.209250 | 0.953 | RL | $41.24\pm 0.02$ | $42.96\pm 0.14$ | $9.03\pm 0.15$ | $-2.89$ | QG | $-1.17$
COSMOS | 10161631 | 149.648830 | 2.232750 | 0.670 | RQ | $40.16\pm 0.02$ | $43.10\pm 0.11$ | $9.03\pm 0.15$ | $-2.74$ | SFG | $-1.16$
COSMOS | 10163898 | 149.743930 | 2.249740 | 0.130 | RQ | $39.11\pm 0.02$ | $42.78\pm 0.01$ | $8.42\pm 0.12$ | $-2.46$ | SFG | $-1.61$
COSMOS | 10164140 | 149.572400 | 2.262690 | 0.706 | RQ | $41.07\pm 0.02$ | $44.33\pm 0.20$ | $8.70\pm 0.13$ | $-1.18$ | SFG | $-0.54$
COSMOS | 10164461 | 149.693280 | 2.267480 | 0.905 | RL | $41.52\pm 0.02$ | $43.31\pm 0.11$ | $8.01\pm 0.11$ | $-1.52$ | QG | $-0.21$
COSMOS | 10165881 | 149.891970 | 2.285120 | 2.937 | RQ | $40.99\pm 0.03$ | $45.17\pm 0.02$ | $9.49\pm 0.18$ | $-1.13$ | SFG | $-0.01$
COSMOS | 10166552 | 149.441480 | 2.287580 | 0.480 | RL | $40.84\pm 0.02$ | $43.37\pm 0.20$ | $8.67\pm 0.13$ | $-2.12$ | QG | $-0.97$
COSMOS | 10169163 | 149.761540 | 2.318430 | 0.350 | RQ | $38.88\pm 0.03$ | $44.11\pm 0.01$ | $7.49\pm 0.11$ | $-0.19$ | SFG | $-0.46$
COSMOS | 10169901 | 149.793800 | 2.327210 | 0.890 | RQ | $39.56\pm 0.04$ | $43.58\pm 0.06$ | $8.78\pm 0.13$ | $-2.02$ | SFG | $-0.64$
COSMOS | 10176857 | 149.839020 | 2.407780 | 0.730 | RQ | $39.95\pm 0.02$ | $42.77\pm 0.09$ | $9.33\pm 0.17$ | $-3.37$ | QG | $-1.27$
COSMOS | 10179656 | 149.597140 | 2.441240 | 1.170 | RQ | $40.14\pm 0.02$ | $43.40\pm 0.20$ | $7.82\pm 0.11$ | $-1.23$ | SFG | $0.54$
COSMOS | 10181467 | 150.639040 | 2.464400 | 0.800 | RQ | $39.79\pm 0.03$ | $44.14\pm 0.03$ | $8.71\pm 0.13$ | $-1.39$ | SFG | $-0.30$
COSMOS | 10183814 | 150.379800 | 2.490180 | 0.350 | RL | $40.61\pm 0.02$ | $42.35\pm 0.04$ | $8.98\pm 0.15$ | $-3.45$ | QG | $-2.13$
COSMOS | 10189778 | 150.683180 | 2.574640 | 0.573 | RQ | $39.19\pm 0.04$ | $43.54\pm 0.20$ | $8.79\pm 0.13$ | $-2.07$ | SFG | $-0.99$
COSMOS | 10192709 | 150.521000 | 2.625440 | 0.520 | RQ | $40.29\pm 0.02$ | $44.12\pm 0.20$ | $9.21\pm 0.16$ | $-1.90$ | SFG | $-1.70$
COSMOS | 10192764 | 150.705570 | 2.629600 | 1.767 | RL | $42.53\pm 0.02$ | $44.69\pm 0.20$ | $8.32\pm 0.11$ | $-0.44$ | SFG | $0.25$
COSMOS | 10195541 | 150.620060 | 2.671380 | 3.140 | RQ | $41.27\pm 0.03$ | $45.05\pm 0.20$ | $9.46\pm 0.18$ | $-1.22$ | SFG | $0.01$
COSMOS | 10195703 | 150.683720 | 2.672750 | 0.670 | RQ | $40.37\pm 0.02$ | $44.20\pm 0.20$ | $8.40\pm 0.12$ | $-1.01$ | SFG | $-1.02$
COSMOS | 10199183 | 150.426010 | 2.725190 | 1.661 | RQ | $41.08\pm 0.03$ | $43.88\pm 0.20$ | $9.62\pm 0.19$ | $-2.55$ | SFG | $-0.27$
COSMOS | 10200729 | 150.446880 | 2.749520 | 1.165 | RQ | $40.28\pm 0.03$ | $44.24\pm 0.20$ | $9.07\pm 0.15$ | $-1.65$ | QG | $-0.33$
COSMOS | 10201379 | 150.435960 | 2.758880 | 1.140 | RQ | $39.90\pm 0.04$ | $45.25\pm 0.20$ | $8.17\pm 0.11$ | $0.27$ | SFG | $0.05$
COSMOS | 10206501 | 150.130360 | 2.472150 | 0.926 | RQ | $39.62\pm 0.04$ | $43.55\pm 0.05$ | $8.74\pm 0.13$ | $-2.01$ | QG | $-0.84$
COSMOS | 10208978 | 149.977890 | 2.504240 | 1.171 | RL | $41.42\pm 0.02$ | $43.75\pm 0.10$ | $8.53\pm 0.12$ | $-1.59$ | QG | $-0.19$
COSMOS | 10210031 | 150.022420 | 2.516580 | 0.680 | RQ | $40.07\pm 0.02$ | $43.50\pm 0.03$ | $8.75\pm 0.13$ | $-2.07$ | QG | $-0.73$
COSMOS | 10210442 | 150.132320 | 2.523310 | 1.319 | RQ | $39.70\pm 0.06$ | $44.08\pm 0.07$ | $8.04\pm 0.11$ | $-0.77$ | SFG | $0.20$
COSMOS | 10210564 | 149.915730 | 2.521330 | 0.728 | RL | $40.12\pm 0.02$ | $42.80\pm 0.08$ | $9.03\pm 0.15$ | $-3.05$ | QG | $-1.04$
COSMOS | 10214987 | 150.333630 | 2.578830 | 3.751 | RL | $43.43\pm 0.02$ | $43.81\pm 0.20$ | $8.83\pm 0.14$ | $-1.83$ | SFG | $0.74$
COSMOS | 10215907 | 149.938320 | 2.577570 | 0.120 | RQ | $38.81\pm 0.02$ | $42.00\pm 0.09$ | $8.50\pm 0.12$ | $-3.31$ | QG | $-1.84$
COSMOS | 10220261 | 150.335130 | 2.642880 | 2.899 | RQ | $41.06\pm 0.03$ | $44.48\pm 0.20$ | $8.00\pm 0.11$ | $-0.33$ | SFG | $1.12$
COSMOS | 10221707 | 149.955170 | 2.657900 | 2.205 | RQ | $40.29\pm 0.05$ | $43.81\pm 0.14$ | $9.10\pm 0.15$ | $-2.10$ | SFG | $-0.24$
COSMOS | 10225941 | 150.042330 | 2.694830 | 0.248 | RL | $40.18\pm 0.02$ | $42.14\pm 0.11$ | $8.74\pm 0.13$ | $-3.42$ | QG | $-2.22$
COSMOS | 10226706 | 150.110410 | 2.708290 | 0.350 | RL | $40.49\pm 0.02$ | $41.88\pm 0.20$ | $9.07\pm 0.15$ | $-4.01$ | QG | $-2.11$
COSMOS | 10230501 | 149.998500 | 2.769160 | 0.170 | RL | $39.94\pm 0.02$ | $41.41\pm 0.20$ | $9.15\pm 0.16$ | $-4.56$ | QG | $-2.35$
COSMOS | 10231301 | 150.230470 | 2.778020 | 1.944 | RQ | $40.00\pm 0.07$ | $44.17\pm 0.20$ | $7.77\pm 0.11$ | $-0.41$ | SFG | $0.55$
COSMOS | 10232138 | 150.347530 | 2.788730 | 1.758 | RQ | $40.54\pm 0.03$ | $44.83\pm 0.20$ | $8.67\pm 0.13$ | $-0.66$ | SFG | $-0.04$
COSMOS | 10235445 | 149.659970 | 2.465100 | 1.010 | RQ | $40.16\pm 0.03$ | $43.78\pm 0.20$ | $9.25\pm 0.16$ | $-2.28$ | SFG | $-1.02$
COSMOS | 10241023 | 149.478880 | 2.521840 | 0.228 | RL | $39.44\pm 0.02$ | $41.20\pm 0.20$ | $8.26\pm 0.11$ | $-3.87$ | SFG | $-0.87$
COSMOS | 10253346 | 149.472720 | 2.687290 | 1.453 | RQ | $40.84\pm 0.02$ | $44.27\pm 0.20$ | $8.86\pm 0.14$ | $-1.41$ | SFG | $-0.20$
COSMOS | 10253580 | 149.734150 | 2.691090 | 0.910 | RL | $41.34\pm 0.02$ | $43.00\pm 0.20$ | $7.84\pm 0.11$ | $-1.65$ | SFG | $1.02$
COSMOS | 10257260 | 149.838840 | 2.736780 | 0.220 | RQ | $39.72\pm 0.02$ | $43.80\pm 0.06$ | $6.28\pm 0.18$ | $0.71$ | SFG | $0.21$
COSMOS | 10257734 | 149.525570 | 2.744430 | 0.899 | RQ | $39.52\pm 0.05$ | $44.37\pm 0.20$ | $8.46\pm 0.12$ | $-0.90$ | SFG | $-0.38$
COSMOS | 10260713 | 149.895980 | 2.783570 | 0.664 | RQ | $39.53\pm 0.03$ | $42.87\pm 0.20$ | $7.93\pm 0.11$ | $-1.88$ | SFG | $-0.30$
COSMOS | 10005564 | 150.657710 | 1.801750 | 2.464 | RQ | $41.18\pm 0.03$ | $44.38\pm 0.20$ | $8.95\pm 0.14$ | $-1.39$ | SFG | $0.43$
COSMOS | 10078654 | 150.496570 | 2.089290 | 1.150 | RQ | $40.11\pm 0.03$ | $43.86\pm 0.20$ | $8.70\pm 0.13$ | $-1.66$ | SFG | $-0.33$
COSMOS | 10078991 | 150.474720 | 2.094080 | 1.261 | RQ | $40.64\pm 0.03$ | $43.94\pm 0.20$ | $8.22\pm 0.11$ | $-1.09$ | SFG | $0.62$