#  Observable signatures of stellar-mass black holes in active galactic nuclei

Hiromichi Tagawa11affiliationmark:  22affiliationmark:  , Shigeo S
Kimura22affiliationmark:  33affiliationmark:  , Zoltán
Haiman11affiliationmark:  44affiliationmark:  , Rosalba
Perna55affiliationmark:  66affiliationmark:  , Imre Bartos77affiliationmark:
11affiliationmark:  Department of Astronomy, Columbia University, 550 W. 120th
St., New York, NY, 10027, USA
22affiliationmark:  Astronomical Institute, Graduate School of Science, Tohoku
University, Aoba, Sendai 980-8578, Japan
33affiliationmark:  Frontier Research Institute for Interdisciplinary
Sciences, Tohoku University, Sendai 980-8578, Japan
44affiliationmark:  Department of Physics, Columbia University, 550 W. 120th
St., New York, NY, 10027, USA
55affiliationmark:  Department of Physics and Astronomy, Stony Brook
University, Stony Brook, NY 11794-3800, USA
66affiliationmark:  Center for Computational Astrophysics, Flatiron Institute,
New York, NY 10010, USA
77affiliationmark:  Department of Physics, University of Florida, PO Box
118440, Gainesville, FL 32611, USA
E-mail<EMAIL_ADDRESS>
###### Abstract

Stellar-mass black holes (BHs) are predicted to be embedded in the disks of
active galactic nuclei (AGN) due to gravitational drag and in-situ star
formation. However, clear evidence for AGN disk-embedded BHs is currently
lacking. Here, as possible electromagnetic signatures of these BHs, we
investigate breakout emission from shocks emerging around Blandford-Znajek
jets launched from accreting BHs in AGN disks. We assume that the majority of
the highly super-Eddington flow reaches the BH, produces a strong jet, and the
jet produces feedback that shuts off accretion and thus leads to episodic
flaring. While these assumptions are highly uncertain at present, they predict
a breakout emission characterized by luminous thermal emission in the X-ray
bands, and bright, broadband non-thermal emission from the infrared to the
gamma-ray bands. The flare duration depends on the BH’s distance $r$ from the
central supermassive BH, varying between $10^{3}-10^{6}$ s for $r\sim 0.01-1$
pc. This emission can be discovered by current and future infrared, optical,
and X-ray wide-field surveys and monitoring campaigns of nearby AGNs.

###### Subject headings:

gravitational waves – stars: black holes – galaxies: active

##  1\. Introduction

It is a common belief that stars and compact objects (COs), including stellar-
mass black holes (BHs), are embedded in the disks of active galactic nuclei
(AGNs) due to capture via dynamical interactions between the nuclear star
cluster (NSC) and the AGN disk (Ostriker, 1983; Syer et al., 1991), and in-
situ star formation (Levin & Beloborodov, 2003; Goodman & Tan, 2004; Thompson
et al., 2005; Levin, 2007). There are several observations supporting this
picture. The high metallicity of quasars is presumably related to frequent
explosive phenomena of COs and stars in AGN disks (Artymowicz et al., 1993;
Wang et al., 2010; Xu et al., 2018; Wang et al., 2021c; Toyouchi et al.,
2021). The existence of young stars (Genzel et al., 2003; Levin & Beloborodov,
2003) and clusters (Milosavljević & Loeb, 2004) around Sgr A*, as well as the
high metallicity component of NSCs (Antonini et al., 2015; Do et al., 2020;
Neumayer et al., 2020; Fahrion et al., 2021) imply that stars, and hence COs,
form in-situ in AGN disks. Furthermore, the spatial distribution of low-mass
X-ray binaries discovered in the Galactic center (Hailey et al., 2018; Mori et
al., 2021) is consistent with the evolution of COs and stars in an AGN disk
(Tagawa et al., 2020b).

AGN disks are plausible environments for BH-BH (e.g. Bartos et al., 2017;
Stone et al., 2017; McKernan et al., 2018; Yang et al., 2019; Tagawa et al.,
2020b) and BH-neutron star (NS) mergers (McKernan et al., 2020; Tagawa et al.,
2021b; Yang et al., 2020a) reported as gravitational wave (GW) events by the
LIGO (Aasi et al., 2015), Virgo (Acernese et al., 2015) and KAGRA (Akutsu et
al., 2021) detectors (Venumadhav et al., 2019; Abbott et al., 2020a; The LIGO
Scientific Collaboration et al., 2021). This pathway can explain the
distributions of masses, mass ratios (Yang et al., 2020b; Gayathri et al.,
2021), spin vectors (Tagawa et al., 2020a), and correlation between the masses
and spin magnitudes (Tagawa et al., 2021a) for the bulk of merging events.
Furthermore, AGN disks are promising environments to explain the
characteristic properties, high mass (Tagawa et al., 2021b), possible high
eccentricity (Samsing et al., 2020; Tagawa et al., 2021c; Romero-Shaw et al.,
2020; Gayathri et al., 2022), and hypothesized electromagnetic (EM)
counterpart, ZTF19abanrhr (Graham et al., 2020), of the unexpected GW event
GW190521 (Abbott et al., 2020b). In addition, the first GW event, GW150914
(Abbott et al., 2016), might be associated with a bright gamma-ray event,
GW150914-GBM (Connaughton et al. 2016, 2018, but see Greiner et al. 2016;
Xiong 2016; Savchenko et al. 2016), which may imply a merger in a gas-rich
environment.

Recently, several studies have investigated emission from transients emerging
from AGN disks. Zhu et al. (2021c), Zhu et al. (2021a), Perna et al. (2021a),
Yuan et al. (2021), Wang et al. (2022), and Lazzati et al. (2022) estimated
the emission from gamma-ray bursts, and Perna et al. (2021b) and Zhu et al.
(2021b) discussed the electromagnetic signatures expected from accretion
induced collapse of neutron stars and white dwarfs. Yang et al. (2021) studied
the properties of tidal disruption of stars by stellar-mass BHs, while Grishin
et al. (2021) investigated supernova explosions, and Bartos et al. (2017) and
Stone et al. (2017) estimated the electromagnetic emission produced by thermal
radiation and/or outflows from circum-BH disks in AGN disks. There are several
studies which investigated possible transients from merging BHs in AGN disks,
focusing on the association of the optical flare, ZTF19abanrhr, with the BH
merger. McKernan et al. (2019) discussed emission from shocks caused by
collision between gas bound to the merged remnant and unbound gas after recoil
kicks due to anisotropic radiation of GWs. Graham et al. (2020) assessed the
net luminosity and timescales for gas accretion induced by recoil kicks. de
Mink & King (2017) considered flares emerging from shocks in a circum-BH disk
due to recoil kicks. Kimura et al. (2021a) and Wang et al. (2021a, b),
respectively, considered thermal and non-thermal emission from bubbles around
BHs due to strong outflows considering continuous and episodic super-Eddington
accretion, and Wang et al. (2021a) further considered emission from shocks
emerging due to interactions of Blandford-Znajek (BZ) jets (Blandford &
Znajek, 1977) launched from accreting BHs to the broad line regions. Tagawa et
al. (2022) (hereafter Paper I) estimated the structure of the cavity created
by the BZ jet and dynamical evolution of gas around the BHs. Tagawa et al.
(2023) (hereafter Paper II) investigated the properties of emission from
shocks emerging around jets launched from a BH merger remnant.

In this paper, we apply the method developed in Paper II, and evaluate
properties and observabilities of thermal and non-thermal emission from shocks
emerging around jets launched by accreting solitary BHs due to the BZ effect
(Fig. 1). We find that thermal emission is bright in X-ray bands, while non-
thermal emission is bright in infrared to gamma-ray bands. This emission is
predicted to be discoverable by current and future optical and X-ray
telescopes, that is the Zwicky Transient Facility (ZTF), Vera Rubin, XMM-
Newton, HiZ-GUNDAM, Einstein Probe, NuSTAR, FORCE, XRT, Chandra, JWST, and
WISE.

Figure 1.—  Schematic picture of quiescent phases (left) and the breakout
emission from the head of a jet launched from a solitary BH (right) embedded
in an AGN disk.

##  2\. Emission

In this section we describe the method for calculating the properties of the
breakout emission produced from solitary BHs in AGN disks. More details on
this computation are provided in Paper II.

###  2.1. Mechanisms for breakout emission

Here we highlight the physical mechanisms responsible for producing the
breakout emission from solitary BHs in AGN disks (see Fig. 1 for a schematic
representation). In these disks, isolated BHs are surrounded by circum-BH
disks, since the gas captured by BHs from the AGN disk has enough angular
momentum to circularize around the BHs (Tanigawa et al., 2012). When the
circum-BH disk is advection dominated, as expected here, a magnetically
dominated state can be realized (e.g. Meier, 2001; Kimura et al., 2021b) owing
to the accumulation of the magnetic flux in the vicinity of the BH (Cao,
2011). Even if the magnetic flux is initially weak, the outflow from the disk
converts the toroidal magnetic field generated by the shear motion into a
poloidal field (Liska et al., 2020). In these cases, jets from spinning BHs
can be launched through the BZ process (Blandford & Znajek, 1977). The jet
power ($L_{\rm j}$) is proportional to the mass accretion rate onto the BH
(${\dot{m}}$),

$\displaystyle L_{\rm j}=\eta_{\rm j}{\dot{m}}c^{2},$ (1)

where $\eta_{\rm j}$ is the conversion efficiency from rest mass to jet power,
which is approximated by $\eta_{\rm j}\sim a_{\rm BH}^{2}$ for a magnetically
dominated jet (e.g. Tchekhovskoy et al., 2010; Narayan et al., 2021), $a_{\rm
BH}$ is the dimensionless spin of the BH (see § 2.2 for its choice), and $c$
is the speed of light. Since the power of a shock emerging around the jet and
the luminosity of radiation emitted from the shock are roughly proportional to
the jet power, the accretion rate onto the BH is a key quantity to determine
the observed luminosity from the system.

The accretion rate onto a circum-BH disk in the AGN disk is often evaluated
via a modified Bondi-Hoyle-Lyttleton (BHL) rate, as given by Eq. (1) of Paper
I. To consider a possible reduction from the BHL rate, we parameterized the
fraction of the accretion rate onto the BH (${\dot{m}}$) over the Bondi-Hoyle-
Lyttleton rate (${\dot{m}}_{\rm BHL}$) as $f_{\rm
acc}={\dot{m}}/{\dot{m}}_{\rm BHL}$. For example, low $f_{\rm acc}$ may be
predicted due to winds from an accretion disk with a super-Eddington rate,
although recent simulations suggest that the conversion to wind is moderate
(Kitaki et al., 2021) for accretion flows in which the circularization radius
(where gas is circularized after being captured by a BH) is much larger than
the trapping radius (within which photons are advected to a BH without
escaping), as is the case for BHs embedded in an AGN disk. In addition, the
accretion rate onto a BH in a cavity during the active phases is estimated to
be lower by a factor of a few compared to that without a cavity (Tagawa et
al., 2022). As a fiducial value, we simply adopt $f_{\rm acc}=1$.

Once the jet collides with the AGN gas, a cocoon of shocked gas forms around
the jet. Due to the high pressure of the cocoon, AGN gas around the BH,
together with the outer regions of the circum-BH disk, are quickly evacuated.
The BH keeps accreting and the jet remains active until the inner remnant
regions of the truncated circum-BH disk are consumed by the accretion.
Subsequently, the BH is quiescent and the cavity begins to fill in gradually.
Finally, AGN gas is recaptured by the BH, and the cocoon reopens a cavity. We
predicted in Paper I that such a cycle repeats many times until the
dissipation of the AGN disk.

As the jet collides with unshocked gas in the AGN disk, strong shocks form.
During the early phases, photons in the shocked medium cannot escape from the
system because they are surrounded by the optically thick AGN disk. As the
shock approaches the surface of the AGN disk, thermal photons in the shocks
begin escaping from the system, and non-thermal electrons begin to be
accelerated due to the formation of collisionless shocks, leading to luminous
thermal and non-thermal emission. As non-thermal emission, we take into
account synchrotron radiation, synchrotron-self Compton scattering, and
second-order inverse Compton scattering. Because of the high density of AGN
gas, we need to consider synchrotron self-absorption.

In Paper II we predicted the properties of the breakout emission emerging from
merger remnant BHs, and the same formulae can be applied to the emission from
solitary BHs. Hence here, by applying the models constructed in Paper II, we
discuss the properties and the observability of the breakout emission from
solitary BHs.

###  2.2. Numerical choices

In the fiducial model we adopt the same parameter values as in Paper I. More
specifically: the BH mass is $m=10\,{\rm M}_{\odot}$, the radial distance of
the BH from the central SMBH is $R_{\rm BH}=1\,{\rm pc}$, the mass of the SMBH
is $M=10^{6}\,{\rm M}_{\odot}$, the gas inflow rate from the outer boundary
($R_{\rm out}=5\,{\rm pc}$) of the AGN disk is ${\dot{M}}_{\rm in}=1~{}L_{\rm
Edd}/c^{2}$, where $L_{\rm Edd}$ is the Eddington luminosity of the SMBH, the
angular momentum transfer parameter in the outer AGN disk is $m_{\rm AM}=0.15$
(Thompson et al., 2005), the viscous parameter in the inner disk is
$\alpha_{\rm AGN}=0.1$ (King et al., 2007; Martin et al., 2019), and the
opening angle of the injected jet is $\theta_{0}=0.2$ (e.g. Pushkarev et al.,
2009; Hada et al., 2013, 2018; Berger, 2014).

We set the jet energy conversion efficiency to $\eta_{\rm j}=0.1$ considering
that spin-up by accretion and spin-down by the BZ jet may be roughly equal at
around $a_{\rm BH}\lesssim 0.3$111 The spin magnitude of the BHs in the AGN
disk is assumed to be lower than that observed for typical X-ray binaries
(Reynolds, 2021). This is because the former keeps powering a BZ jet while
accreting, while the other does not in soft states. The fiducial choice is
conservative, and the breakout emission becomes brighter if the spin magnitude
is higher.  (e.g., Fig. 10 of Narayan et al. 2021), the fraction of postshock
energy carried by the post shock magnetic field and by electrons to
$\epsilon_{\rm B}=0.03$ (e.g., Panaitescu & Kumar 2001; Uchiyama et al. 2007;
Santana et al. 2014) and $\epsilon_{\rm e}=0.1$ (e.g., Waxman & Loeb 1999;
Panaitescu & Kumar 2001; Sironi et al. 2013; Santana et al. 2014),
respectively, and the power-law slope for injected electrons accelerated by
the first-order Fermi process to $p=2.5$.

Figure 2.—  The luminosity and duration as a function of the distance from the
SMBH ($R$) for emission from breakout of shocks produced around solitary BHs
in the fiducial model. (a) The shock kinetic (solid black), breakout (dashed
black), and non-thermal (solid orange) luminosity. (b) The duration of
emission, $t_{\rm duration}$. The BH locations adopted in the fiducial model
are indicated with filled circles superposed on the black solid lines.  Figure
3.—  The spectral energy distribution for non-thermal (thick solid black) and
thermal (thick solid brown) emission in the fiducial model (§ 2.2) at
$R=1~{}{\rm pc}$. The left, middle, and right components in black lines
represent synchrotron emission, synchrotron-self Compton (SSC), and second-
order inverse Compton (IC) scattering, respectively. Blue and dashed blue
lines represent emission from the host AGN and its variability, respectively.
Dotted cyan, green, red, purple, gray, gold, pink, and orange lines indicate
the sensitivities of ZTF, Vera Rubin and Roman space telescope, Chandra and
XMM-Newton, HiZ-GUNDAM and Einstein Probe, BAT and XRT, NuSTAR and FORCE,
WISE, and JWST, respectively. The results are also shown for models with lower
accretion rate onto BH ($f_{\rm acc}=0.1$, thin solid lines), or lower
efficiencies of electron acceleration ($\epsilon_{\rm e}=0.01$, thin dashed)
in panel (a), or lower magnetic field amplification ($\epsilon_{\rm
B}=10^{-5}$, thin dotted), or a higher jet efficiency ($\eta_{\rm j}=1$, thin
dashed-dotted) in panel b.  Figure 4.—  Same as Fig. 3, but for BH sources at
$R=0.01~{}{\rm pc}$.

##  3\. Properties of breakout emission

In the following we discuss the properties of the breakout emission (see Paper
II for computational methods).

###  3.1. Properties of breakout emission from solitary BHs

In the outer regions of $R\gtrsim 0.1~{}{\rm pc}$ for the fiducial model,
since the aspect ratio ($H_{\rm AGN}/R$) of the AGN disk is large due to
intense star formation to stabilize the disk (Thompson et al., 2005), the
accretion rates onto BHs, and accordingly the breakout luminosity $L_{\rm
breakout}$, are low (Fig.2 a). In the inner regions of $R\lesssim
10^{-2}~{}{\rm pc}$, $L_{\rm breakout}$ is low since gaps form in these
regions, which reduce the accretion rates onto BHs. The accretion rates onto
BHs at $R=1$ and $10^{-2}~{}{\rm pc}$ are, respectively, $3\times
10^{-4}~{}{\rm M}_{\odot}~{}{\rm yr^{-1}}$ and $3\times 10^{-3}~{}{\rm
M}_{\odot}~{}{\rm yr^{-1}}$, corresponding to $\sim 10^{4}$ and $10^{5}$ times
the Eddington rate. Despite the fact that the accretion rate and the duration
of accretion are, respectively, much lower and longer than for gamma-ray
bursts, the range of values for the plasma parameters ($\epsilon_{\rm e}$,
$\epsilon_{\rm B}$) can be reasonably adopted from observations of afterglow
emission of gamma-ray bursts (e.g. Panaitescu & Kumar, 2001; Santana et al.,
2014). This is motivated by the consideration that the basic physics of the
radiation processes in the two contexts is similar, since in both cases the
emission is produced by the interaction of a relativistic jet with the
surrounding medium. However, we do note that the jet production physics may be
different (e.g. Bromberg & Tchekhovskoy, 2016; Liu et al., 2017), the
compositions of the jets may be different (e.g. Beloborodov, 2003; Kimura et
al., 2022; Chen et al., 2022), the duration and the accretion rate are
different, and the contribution of synchrotron self-absorption to emission is
different due to the difference in the density of the ambient material. The
above differences may result in significantly different distributions of the
plasma parameters between the jets from BHs in AGN disks and those in gamma-
ray bursts.

It is predicted that BHs tend to reside in the outer regions with
$R\gtrsim{\rm pc}$ since the Type I migration timescale is long, as well as in
the inner regions with $R\lesssim 10^{-2}~{}{\rm pc}$ as annular gaps are
predicted to form where migration is slow causing BHs to accumulate (e.g.
Tagawa et al., 2020b; Gilbaum & Stone, 2021; Perna et al., 2021b). Therefore,
below we consider the two cases with BHs at $1~{}{\rm pc}$ and at
$10^{-2}~{}{\rm pc}$ as representative examples.

The spectral energy distributions for emission from BHs at $R=1~{}{\rm pc}$
and $R=0.01~{}{\rm pc}$ in the fiducial model are shown in Figs. 3 and 4,
respectively. In this model, the thermal emission is computed under the
assumption that the radiation energy in the shock is released once the shock
becomes optically thin (e.g. Levinson & Nakar, 2020). Non-thermal emission is
produced from electrons accelerated at collisionless shocks by synchrotron
radiation, synchrotron-self Compton scattering, and second-order inverse
Compton scattering.

The non-thermal emission is bright from the infrared to the gamma-ray bands
(solid black lines). The three peaks are contributed by synchrotron radiation,
synchrotron-self Compton scattering, and second-order inverse Compton
scattering, while the lower cutoff in non-thermal emission is due to
synchrotron self-absorption. The thermal emission is mostly bright in X-rays
(solid brown lines), and it has a much higher luminosity than the non-thermal
emission (due to the reduction by a factor of $\epsilon_{\rm e}$ compared to
the total energy).

In Paper I we evaluated the breakout of shocks around a jet produced from a
solitary BH and found it to be episodic. Emission phases last for the
consumption timescale of the circum-BH disk with $t_{\rm cons}\sim 300~{}{\rm
yr}$, followed by quiescent phases lasting for the resupply timescale of
$t_{\rm re}\sim 10^{4}~{}{\rm yr}$ at $R\sim{\rm pc}$, with the cycle
repeating. At $R\sim 10^{-2}~{}{\rm pc}$, $t_{\rm cons}\sim 1~{}{\rm yr}$ and
$t_{\rm re}\sim 10~{}{\rm yr}$. By using the duration of emission (solid black
line in Fig. 2 b), which is $t_{\rm duration}\sim 2\times 10^{6}~{}{\rm s}$ at
$R\sim{\rm pc}$ and $\sim 200~{}{\rm s}$ at $R\sim 0.01~{}{\rm pc}$, the total
duration for breakout emission to be released from one BH over the AGN
lifetime time is estimated to be $f_{\rm active}\sim t_{\rm duration}/t_{\rm
re}\sim 10^{-5}$–$10^{-6}$. Here, note that the duration is reduced for the
model with $\eta_{\rm j}=1$ to $7\times 10^{5}~{}{\rm s}$ at $R=1~{}{\rm pc}$
and $300~{}{\rm s}$ at $R=0.01~{}{\rm pc}$, and enhanced for the model with
$f_{\rm acc}=0.1$ to $3\times 10^{6}~{}{\rm s}$ at $R=1~{}{\rm pc}$ and
$6\times 10^{3}~{}{\rm s}$ at $R=0.01~{}{\rm pc}$. As discussed in Paper I,
the number of AGN disk-embedded BHs is $\sim 300~{}({\dot{M}}_{\rm
in}/1~{}L_{\rm Edd}c^{2})^{1/2}$. Using the predicted mass distribution of
$dN_{\rm BH}/dR\propto R^{\gamma_{\rho}}$ with $-0.5~{}\hbox
to0.0pt{$<$\hss}{\lower 4.30554pt\hbox{$\sim$}}\gamma_{\rho}~{}\hbox
to0.0pt{$<$\hss}{\lower 4.30554pt\hbox{$\sim$}}0$ (Freitag et al., 2006;
Hopman & Alexander, 2006; Alexander et al., 2007), we tentatively assume that
$N_{\rm BH}\sim 200$ and $\sim 30$ BHs are embedded at $R\sim{\rm pc}$ and
$\sim 10^{-2}~{}{\rm pc}$, respectively. Note that these numbers evolve with
time and are highly uncertain. With these, the time interval between flares in
one AGN is $t_{\rm interval}\sim t_{\rm re}/N_{\rm BH}\sim 50~{}{\rm yr}$ and
$\sim 0.3~{}{\rm yr}$ at $R\sim{\rm pc}$ and $R\sim 10^{-2}~{}{\rm pc}$,
respectively. From solitary BHs at $R\sim{\rm pc}$, thermal emission with
luminosity of $\sim 2\times 10^{42}~{}{\rm erg/s}$ in X-ray bands (brown line
in Fig. 3) and non-thermal emission with $\sim 10^{39}$–$10^{41}~{}{\rm
erg/s}$ in infrared to gamma-ray bands (black line in Fig. 3) are predicted
with duration of $t_{\rm duration}\sim 0.1~{}{\rm yr}$ (solid black line in
Fig. 2 b) by observing one AGN for $t_{\rm interval}\sim 50~{}{\rm yr}$. From
solitary BHs at $R\sim 10^{-2}~{}{\rm pc}$, thermal emission with luminosity
of $\sim 4\times 10^{43}~{}{\rm erg/s}$ in hard X-ray bands (brown line in
Fig. 4) and non-thermal emission with luminosity of $\sim
10^{41}$–$10^{42}~{}{\rm erg/s}$ in optical to gamma-ray bands (black line in
Fig. 4) are predicted with duration of $\lesssim 10^{3}~{}{\rm s}$ by
observing an AGN for $\sim 0.3~{}{\rm yr}$.

Here, the luminosity from the host AGN in the relevant energy range is

$\displaystyle\nu L_{\rm AGN}(\nu)\sim 10^{42}~{}{\rm erg/s}(M/10^{6}~{}{\rm
M}_{\odot})$ $\displaystyle({\dot{M}}c^{2}/1~{}L_{\rm Edd})(f_{\rm
bol}/10)^{-1}\,.$ (2)

where $f_{\rm bol}$ is the bolometric correction at the given frequency. As
depicted by the blue lines in Figs. 3 and 4, we assume that $f_{\rm bol}\sim
5$ at $c/\nu=4400~{}$Å and extrapolate the luminosity for $10^{12}~{}{\rm
Hz}\lesssim\nu\lesssim 10^{15}~{}{\rm Hz}$ using the cyan or blue points in
Fig. 7 of Ho (2008) depending on the assumed Eddington rate, and $f_{\rm
bol}\sim 10$ in $0.1~{}{\rm keV}\leq h\nu$ (Ho, 2008; Trakhtenbrot et al.,
2017; Duras et al., 2020) with the upper exponential cut off at $300~{}{\rm
keV}$ (e.g. Ricci et al., 2018). We also assume that the fraction of the
variable luminosity compared to the average luminosity ($f_{\rm var}$) in
optical bands with $t_{\rm duration}\lesssim 0.1~{}{\rm yr}$ is $f_{\rm
var}\lesssim 0.1$ (Kozłowski, 2016) and that in X-ray bands is $f_{\rm
var}\sim 0.3$ (Soldi et al. 2014; Maughan & Reiprich 2019, dashed blue lines).

In the optical, X-ray, and gamma-ray bands, the luminosity for non-thermal
emission at $R=0.01~{}{\rm pc}$ exceeds the variable luminosity (solid black
and dashed blue lines in Fig. 4). Additionally, the variability of AGNs is
typically stronger at shorter wavelengths (Arévalo et al., 2008), while non-
thermal emission for $R=0.01~{}{\rm pc}$ is brighter at longer wavelengths in
the optical bands. This unusual trend can help distinguish the breakout
emission from a solitary BH from stochastic AGN variability. Also, the thermal
X-ray luminosity clearly exceeds the AGN luminosity at both $R=1~{}{\rm pc}$
and $0.01~{}{\rm pc}$ (blue and brown lines in Figs. 3 and 4). Hence, non-
thermal emission from BHs at $R=0.01~{}{\rm pc}$ and thermal emission at
$R=0.01~{}{\rm pc}$ and $R=1~{}{\rm pc}$ can be recognized as unusual
variability of AGNs due to their luminosity and color.

However, we do note that the properties of emission are significantly
influenced by uncertainties in the model parameters, namely $f_{\rm acc}$,
$\epsilon_{\rm e}$, $\epsilon_{\rm B}$, and $\eta_{\rm j}$. Since
$\epsilon_{\rm e}$ and $\epsilon_{\rm B}$ are respectively found to vary
within the ranges $\sim 0.01$–$0.3$ and $\sim 10^{-5}$–$0.1$ from GRB
afterglow observations (Panaitescu & Kumar, 2001; Santana et al., 2014), and
$\eta_{\rm j}$ can typically range between $0.1$–$1$ as discussed above, in
Figs. 3 and 4 we also show emission models with $\epsilon_{\rm e}=0.01$ (thin
dashed lines in panel a), $\epsilon_{\rm B}=10^{-5}$ (thin dotted lines in
panel b), and $\eta_{\rm j}=1$ (thin dashed-dotted lines in panel b). Given
that $f_{\rm acc}$ is also highly uncertain, we additionally present a model
with $f_{\rm acc}=0.1$ (thin solid lines in panel a) as a representative
example. Figs. 3 and 4 show that non-thermal emission at $R=0.01~{}{\rm pc}$
can be dimmer than the AGN variability if the values of the model parameters
are in their lower range. On the other hand, thermal emission is relatively
less affected by these parameters. If we assume that $\eta_{\rm j}$ is well
constrained by numerical simulations (e.g. Narayan et al., 2021), then thermal
emission is almost solely influenced by the accretion rate onto the BHs. Thus,
by observing the thermal emission, we can improve our understanding of the
accretion processes in super-Eddington regimes.

As an additional point in relation to observations, we note that the estimates
above suggest that we need to wait a long time to come across breakout
emission by monitoring a single AGN. A more viable strategy would be that of
observing many AGNs and check whether there is variability in various bands,
as discussed in $\S~{}\ref{sec:observability_solitary}$.

###  3.2. Differences with respect to the emission from merging remnants

While the basic physical emission mechanisms are the same for solitary BHs and
the post-merger BHs discussed in Paper II, there are some important
quantitative differences between the two cases, which we highlight below. (1)
Merger remnants tend to be massive compared to isolated BHs. (2) Merger
remnants have higher BH spin magnitude, and hence higher conversion efficiency
$\eta_{\rm j}$ of mass to jet power. (3) An enhancement of the accretion rate
(compared to the solitary BH case) is expected for merger remnants due to
shocks emerging in circum-BH disks by GW recoil kicks. (4) The flares from
merger remnants are correlated with GW events. Due to (1)–(3), the luminosity
of the breakout emission is higher in the case of a post-merger BH, and due to
(4) the transients are easier to discover when produced by merger remnants and
the associated GW source has already been detected. The above suggests that
the emission from solitary BHs is more difficult to observe compared to that
from merger remnants; therefore, the search for emission from solitary BHs
needs to be strategized, as discussed in the next section.

###  3.3. Observability of breakout emission

Here, we consider whether emission from solitary BHs can be discovered by
current and future observing facilities.

The luminosity from non-thermal emission from solitary BHs at $R=0.01~{}{\rm
pc}$ exceeds the sensitivity limit by ZTF, Vera Rubin, XRT, Chandra, XMM-
Newton, WISE, and JWST at $d_{\rm L}=30~{}{\rm Mpc}$ (solid black, dashed
cyan, dashed green, dashed gray, dashed red, and dashed pink, and dashed
orange lines in Fig. 4). Here, the typical variable luminosity of AGNs with
duration of $\lesssim 0.1~{}{\rm yr}$ is (Kozłowski, 2016)

$\displaystyle\nu L_{\rm AGN,vari}(\nu)\sim 2\times 10^{40}~{}{\rm
erg/s}(M/10^{6}~{}{\rm M}_{\odot})$
$\displaystyle({\dot{M}}c^{2}/0.01~{}L_{\rm Edd})(f_{\rm bol}/5)^{-1}(f_{\rm
var}/0.1),$ (3)

which is generally lower than the luminosity of breakout emission $L_{\rm
flare}\sim f_{\rm acc}(10^{41}$–$10^{42})~{}{\rm erg/s}$, unless the reduction
in the accretion rate from the Bondi-Hoyle-Lyttleton rate is $f_{\rm
acc}~{}\hbox to0.0pt{$<$\hss}{\lower 4.30554pt\hbox{$\sim$}}0.1$.
Additionally, non-thermal emission for $R=0.01~{}{\rm pc}$ is redder around
the optical bands as mentioned in $\S\,$3.1. Thus, we can identify the
breakout emission by the magnitude of its luminosity as well as by the color
of the flare. Here, note that the luminosity of the breakout emission is
roughly proportional to the accretion rate onto the SMBH (e.g. Paper I).
Hence, it reduces the influence of both the AGN accretion rate ${\dot{M}}_{\rm
in}$ and mass $M$ on the detectability of the breakout emission, since the AGN
luminosity is also proportional to the accretion rate onto the SMBH. However,
in pessimistic cases in which the accretion rate onto BHs is lower than
assumed in the fiducial model, or the efficiencies of electron acceleration or
magnetic field amplification are lower, then non-thermal emission is dimmer
than the typical variability of AGNs, and hence it would be difficult to
observe.

On the other hand, thermal emission from solitary BHs at $R=0.01~{}{\rm pc}$
and $R=1~{}{\rm pc}$ can most likely be discovered by several X-ray telescopes
(Figs. 3 and 4), unless the accretion rate onto BHs is significantly lower
than assumed in our fiducial model. For emission from $R=1~{}{\rm pc}$, since
the flare is as rare as $t_{\rm interval}\sim 50~{}{\rm yr}$ per AGN, many
($\sim t_{\rm interval}/t_{\rm obs}\sim 50(t_{\rm interval}/50~{}{\rm
yr})(t_{\rm obs}/{\rm yr})^{-1}$) AGNs need to be simultaneously observed to
be discovered within the observational timescale ($t_{\rm obs}$). This
requires wide field surveys, such as HiZ-GUNDAM/Einstein Probe (Table 1).
Multi-wavelength observations are likely to be key to identifying the breakout
emission. This is because in the solitary BH model, flares occur
simultaneously over a broad range of bands (infrared, optical, and X-ray),
while for AGN variability the evolution is delayed depending on the frequency.
The actual false-alarm probability for the detection of the breakout emission
should be quantified in future work, using observed multi-band AGN light-
curves.

We also estimate observability when the BH spin magnitude is maximal ($a_{\rm
BH}\sim 1$), and so is the jet energy conversion efficiency ($\eta_{\rm j}\sim
1$, Narayan et al. 2021), as an upper limit (dotted lines in panels b of Figs.
3 and 4). In this case the luminosity of the breakout emission is enhanced by
an order of magnitude compared to that in the fiducial model. Additionally,
the shock velocity is higher by a factor of $\sim 1.6$ (Bromberg et al.,
2011), and the frequency of the emission is enhanced accordingly. Then, the
non-thermal emission from the BH at $R=0.01~{}{\rm pc}$ would be detectable by
ZTF and the HiZ-GUNDAM/Einstein Probe. Additionally, the non-thermal emission
for $R=1~{}{\rm pc}$ can be identified by wide-field surveys in radio bands,
such as the Atacama Cosmology Telescope (Naess et al., 2021) and the Large
Submillimeter Telescope (Kawabe et al., 2016). Therefore, in this optimistic
case, the emission could be easily discovered by several instruments at
various wavelengths.

More generally, in the fiducial model non-thermal emission from solitary BHs
at $R\sim 10^{-2}~{}{\rm pc}$ can be discovered by ZTF, Vera Rubin, XRT,
Chandra, XMM-Newton, JWST, and WISE as unusually intense and red-colored
variability, while thermal emission from solitary BHs at $R\sim 1~{}{\rm pc}$
can be discovered by HiZ-GUNDAM and Einstein Probe.

##  4\. Conclusions

In this paper we have evaluated the properties of breakout emission from
shocks emerging around jets launched from accreting and spinning solitary BHs
embedded in AGN disks, and discussed the observability of such emission. In
our model, accretion, and hence jet formation, is episodic, since gas around
the BHs is evacuated by the jets; once gas is resupplied, the jet is expected
to collide with the gas. Due to the formation of shocks at collision, thermal
emission produced by the shocked gas and non-thermal emission produced by
accelerated electrons are expected. Our main results are summarized as
follows:

  1. 1.

Thermal and non-thermal emission are bright in X-ray bands and in infrared to
gamma-ray bands, respectively.

  2. 2.

Breakout-emission from solitary BHs is harder to observe than from merger
remnants because (1) the non-thermal and thermal emission are not as bright,
and (2) the burst is rare and there is no GW trigger. Hence, catching it
requires monitoring a large number of AGNs. However, we can still identify
breakout emission from solitary BHs as peculiar flares in nearby AGNs,
characterized by broad-band non thermal emission (from the $\gamma$-rays to
the IR), with superimposed thermal emission and duration that depends on the
distance of the BH from the central SMBH, varying between $10^{3}-10^{6}$ s
for distances $R\sim 0.01-1$ pc.

  3. 3.

Non-thermal emission from solitary BHs at $R~{}\sim~{}0.01~{}{\rm pc}$ from
the SMBH with duration of $\sim 10^{3}~{}{\rm s}$ can be discovered by
infrared, optical, and X-ray telescopes as unusually red-colored variability
of less luminous AGNs. Additionally, thermal emission from solitary BHs at
$R\sim 1~{}{\rm pc}$ with duration of $\sim 10^{6}~{}{\rm s}$ can be
discovered by current and future X-ray telescopes.

We find that the observability of the breakout emission from solitary BHs in
AGN disks is strongly influenced by accretion processes in super-Eddington
regimes. To discover signatures from the solitary BHs, the accretion processes
and plasma physics should be better understood through numerical simulations.
Conversely, if the emission is discovered but their properties are different
from what we predict, this would improve our understanding of the underlying
accretion processes and plasma physics.

This work was financially supported by Japan Society for the Promotion of
Science (JSPS) KAKENHI grant Number JP21J00794 (HT) and 22K14028 (S.S.K.).
S.S.K. was supported by the Tohoku Initiative for Fostering Global Researchers
for Interdisciplinary Sciences (TI-FRIS) of MEXT’s Strategic Professional
Development Program for Young Researchers. Z.H. was supported by NASA grant
NNX15AB19G and NSF grants AST-2006176 and AST-1715661. R.P. acknowledges
support by NSF award AST-2006839. I.B. acknowledges the support of the Alfred
P. Sloan Foundation and NSF grants PHY-1911796 and PHY-2110060.

## Telescopes

We list the name and properties of telescopes in Table 1.

Table 1The name and properties of telescopes appropriate for detecting electromagnetic signatures from solitary BHs in AGN disks. Telescope name | Photon energy | Sensitivity $[{\rm erg/s/cm^{2}}]$ | Field of view$[{\rm sr}]$ | Operation
---|---|---|---|---
JWST |  $\sim 0.04$–$2~{}[{\rm eV}]$ |  $\sim 10^{-17}$–$10^{-15}$ for $t_{\rm int}\sim 10^{4}~{}{\rm s}$ | $\sim 10^{-6}$ | pointing telescope
WISE |  $\sim 0.05$–$0.4~{}[{\rm eV}]$ |  $\sim 10^{-13}$–$10^{-12}$ for $t_{\rm int}\sim 10^{4}~{}{\rm s}$ | $\sim 10^{-4}$ | pointing telescope
Roman space telescope (Spergel et al., 2015) |  $\sim 0.6$–$1~{}[{\rm eV}]$ |  $\sim 4\times 10^{-16}$ for $t_{\rm int}\sim 10^{4}~{}{\rm s}$ | $\sim 0.6$ | wide-field survey
ZTF (Bellm et al., 2018) |  $\sim 1.4$–$3.1~{}[{\rm eV}]$ |  $\sim 10^{-13}$ for $t_{\rm int}\sim 30~{}{\rm s}$ | 0.01 | wide-field survey
Vera Rubin (Ivezić et al., 2019) |  $\sim 1.2$–$3.9~{}[{\rm eV}]$ |  $\sim 10^{-15}$ for $t_{\rm int}\sim 40~{}{\rm s}$ | 0.003 | wide-field survey
Subaru/HSC (Aihara et al., 2018) |  $\sim 1$–$3~{}[{\rm eV}]$ |  $\sim 10^{-16}$–$10^{-15}$ for $t_{\rm int}\sim 10^{3}~{}{\rm s}$ | 0.0005 | pointing telescope
Tomo-e Gozen (Sako et al., 2018) |  $\sim 1.7$–$3.4~{}[{\rm eV}]$ |  $\sim 2\times 10^{-13}$ for $t_{\rm int}\sim 100~{}{\rm s}$ | 0.006 | wide-field survey
Chandra |  $\sim 0.2$–$10~{}[{\rm keV}]$ |  $\sim 10^{-14}$ for $t_{\rm int}\sim 2\times 10^{4}~{}{\rm s}$ | $6\times 10^{-5}$ | pointing telescope
XMM-Newton (Jansen et al., 2001) |  $\sim 0.4$–$3~{}[{\rm keV}]$ |  $\sim 10^{-14}$ for $t_{\rm int}\sim 10^{4}~{}{\rm s}$ | $8\times 10^{-5}$ | pointing telescope
HiZ-GUNDAM (Yonetoku et al., 2020) |  $\sim 0.4$–$4~{}[{\rm keV}]$ |  $\sim 10^{-11}$ for $t_{\rm int}\sim 10^{4}~{}{\rm s}$ | 1.2 | wide-field survey
Einstein Probe (Yuan et al., 2015) |  $\sim 0.5$–$4~{}[{\rm keV}]$ |  $\sim 3\times 10^{-11}$ for $t_{\rm int}\sim 10^{3}~{}{\rm s}$ | 1.0 | wide-field survey
MAXI (Matsuoka et al., 2009) |  $\sim 2$–$30~{}[{\rm keV}]$ |  $\sim 7\times 10^{-11}$ for $t_{\rm int}\sim 6\times 10^{5}~{}{\rm s}$ | 0.07 | wide-field survey
NuSTAR (Harrison et al., 2013) |  $\sim 10$–$30~{}[{\rm keV}]$ |  $\sim 10^{-14}$ for $t_{\rm int}\sim 10^{6}~{}{\rm s}$ | $3\times 10^{-5}$ | pointing telescope
FORCE (Mori et al., 2016) |  $\sim 1$–$80~{}[{\rm keV}]$ | $\sim 10^{-14}(t_{\rm int}/10^{5}~{}{\rm s})^{-1}$ | $10^{-5}$ | pointing telescope
Swift X-ray telescope (XRT) (Burrows et al., 2005) |  $\sim 0.2$–$10~{}[{\rm keV}]$ | $\sim 2\times 10^{-14}(t_{\rm int}/10^{4}~{}{\rm s})^{-1}$ | $5\times 10^{-5}$ | pointing telescope
Swift BAT (Barthelmy et al., 2005) |  $\sim 15$–$150~{}[{\rm keV}]$ | $\sim 10^{-8}(t_{\rm int}/1~{}{\rm s})^{-1/2}$ | 1.4 | wide-field survey
Fermi GBM (Meegan et al., 2009) |  $\sim 8$–$4000~{}[{\rm keV}]$ |  $\sim 10^{-8}$–$10^{-6}$ for $t_{\rm int}\sim 1~{}{\rm s}$ | $\sim 4\pi$ | wide-field survey
INTEGRAL SPI-ACS (Winkler et al., 2003) |  $\sim 75$–$2000~{}[{\rm keV}]$ |  $\sim 10^{-7}$–$10^{-6}$ for $t_{\rm int}\sim 1~{}{\rm s}$ | $\sim 4\pi$ | wide-field survey

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