Hunting for wandering massive black holes with ngVLA
Kohei Inayoshi 1 , Tomonari Michiyama 1
1

Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, People s Republic of China
inayoshi@pku.edu.cn

Abstract
Supermassive black holes (SMBHs) are almost ubiquitously harbored in the nuclei of massive galaxies, whichwere assembled through galaxy mergers. As a natural outcome of frequent mergers, wandering massive BHs arelikely to be populated via ejection from the galactic nuclei through multi-body BH interactions and gravitational
wave recoils. Those wandering BHs are expected to plunge into diffuse and hot plasma (with an electron densityof ≃ 0.1 cm−3 and temperature of ≃ 107 K) and be fed with the gas at a rate of ≃ 10−7 − 10−6 ṀEdd , where
ṀEdd is the Eddington accretion rate. Radiation spectra from such radiatively inefficient accretion flows onto thewandering BH have a peak at the millimeter band, where the next-generation Very Large Array (ngVLA) has thehighest sensitivity. Therefore, future observations with ngVLA will enable us to hunt wandering BH populationand push the detection limit of wandering BH’s masses down to M• ≃ 5 × 106 M⊙ for massive nearby ellipticals,e.g., M87, and M• ≃ 3 × 104 M⊙ for Milky Way. With the capability of ngVLA, additional 8 nearby ellipticalgalaxies are interesting targets for hunting wandering BHs, assuming that those BHs are as massive as >∼ 1% of thenuclear SMBHs. The detection of wandering BHs is a key missing piece to understand the entire BH population andgive physical interpretations of off-nuclear BHs detected in dwarf galaxies, which may constrain BH seed formation
scenarios.
Key words: Accretion (14); Gravitational waves (678); Interstellar medium (847); Radio continuum emission(1340); Supermassive black holes (1663)

1.

Introduction

Galaxies were assembled out of smaller mass via halo andgalaxy mergers in the framework of hierarchical structure formation. As a natural result of frequent galaxy mergers, incoming massive BHs would sink toward the centers, form binary SMBHs at the galactic nuclei, and coalesce with gravitational wave (GW) emission, if the BHs would successfully decay their orbit via dynamical processes within a Hubble time
(Begelman et al. 1980; Yu 2002; Merritt 2013; Khan et al.
2016; Kelley et al. 2017). The GW emission associated with
their mergers will provide useful insights for us to understandthe population of massive binary BHs with future space-based
GW observatories (LISA, Tianqin, Taiji) and pulsar-timingarray experiments (PTAs) (Sesana et al. 2008; Inayoshi et al.
2018a; Bonetti et al. 2018a; Luo et al. 2016)
In giant ellipticals, which are the most massive objects inthe local universe and have experienced a large number of minor and dry mergers at low redshifts. In gas-poor environments, multiple BH encounters in the nuclei would be likely
to make the most massive two BHs coalesce but simultaneously to eject less massive ones from the nuclei (Bonetti
et al. 2018a; Ryu et al. 2018). Similarly, merger remnants
due to the successive BH interactions would be kicked by theanisotropic emission of GWs (or ‘gravitational recoil’) during the final BH coalescences (Bekenstein 1973; Campanelli
2005; Lousto et al. 2012). Those ejected BHs with a mass
range of M• ≃ 106 − 108 M⊙ at high velocities comparable
to the escape speed from the galactic cores are expected to orbit at the outskirts of galaxies as wandering BHs .
Wandering BHs would also be important candidates ofintermediate-mass BHs (IMBHs). In the Milky-Way galaxy
and low-mass dwarf galaxies, the existence of IMBHs (see a4
recent review by Greene et al. 2020) with M• >∼ 10 M⊙ hasbeen argued based on observations of high-velocity compact
clouds in the Galactic center (Oka et al. 2017) and off-nuclear
compact radio sources in dwarf galaxies (Reines et al. 2020).
Numerical simulations also predict that Milky Way-size halos
would host ∼ 10 IMBHs within their virial radii, and that theywould wandering within their host galaxies for several Gyr(Bellovary et al. 2010; Tremmel et al. 2018a). The detectionof IMBHs is a key missing piece to understand the entire BH
population (from stellar-mass to super-massive regimes) andthe properties of wandering BHs may constrain their seedingmechanisms (see a recent review by Inayoshi et al. 2020).
2. Radiation properties of wandering and accreting BHs
Wandering BHs in the outskirts of galaxies are likely tobe embedded in hot and diffuse plasma with density of ne ≃0.1 cm−3 and temperature of T ≃ 107 K (Russell et al. 2013)
and to be fed with the matter. Adopting the typical properties of the plasma, the canonical Bondi-Hoyle-Littleton (BHL)
mass accretion rate onto a moving BH with a mass of M• at a
speed of v∞ is given byṀBHL =

4πG2 M•2 ρ∞.
3
c∞ (1 + M2 )3/2

(1)

(Hoyle & Lyttleton 1939; Bondi 1952), where M ≡ v∞ /c∞ is
the Mach number, ρ∞ and c∞ are the density and sound speedof plasma. The accretion rate normalized by the Eddington rate
is given by2[Vol. ,

Fig. 1. Snapshots of accretion flows onto a moving BH at three different elapsed times.
From the left to the right, we show
the gas density, temperature, Mach number, radial velocity normalized by free-fall velocity, and azimuthal velocity normalized by the
Keplerian velocity.
The accretion flow is symmetric with respect in the early stage (top panels), forms a spiral structure owing to angular momentum supply (middle panels), and becomes highly turbulent in the late stage (bottom panels).
As a resultof turbulence, the BH feeding rate is limited to ∼ 10 − 20% of the BHL rate, which corresponds to ṁBHL ∼ O(10−7 ).

ṁBHL ≃ 1.5 × 10−6 (1 + M2 )−3/2()()( T )M•
ne×.
107 M⊙
0.1 cm−3
107 K

3. Detectability of wandering BHs(2)

At such low rates, the accreting matter does not cool but forms
a geometrically thick and hot disk; the so-called radiatively inefficient accretion flows (RIAFs) (Ichimaru 1977; Narayan &Yi 1994; Narayan & Yi 1995a; Narayan et al. 2000; Quataert &Gruzinov 2000; Blandford & Begelman 2004; Yuan & Narayan
2014).
Recently, Guo et al. (2020) studied the dynamics of accretion flows onto a wandering BH at such a low accretion rate
(RIAF regime), performing three-dimensional hydrodynamical
simulations (see Fig. 1). They found that a wandering BH is
fed with hot and diffuse plasma, and the accretion flow becomes turbulent. In the turbulent medium with a wide distribution of inflowing angular momentum, the mass accretion rate
is limited at ∼ 10 − 20% of the canonical BHL rate; namely,
the BH feeding rate corresponds to ṁBHL ≃ O(10−7 ) forM• ≃ 107 M⊙ . From the analogy of low-luminosity SMBHs
in the nearby universe, e.g., Sagittarius A⋆ , most of the radiation energy is released in the radio band (e.g., Yuan et al. 2004),
where the next generation VLA (ngVLA) has the highest sensitivity and spatial resolution. Therefore, ngVLA will be a powerful tool to hunt for a population of wandering BHs.

In this section, we calculate the radiation spectral energy
distribution (SED) of accretion flows onto a moving BH anddiscuss the detectability of wandering BHs in different typesof galaxies. Here, the mass accretion rate through the nuclear accretion disk, where most radiation is generated, is calculated from the hydrodynamical simulations, and the radiation spectra from the RIAF is obtained with a semi-analytical
two-temperature disk model (Manmoto et al. 1997; Yuan et al.
2004). In the following, we consider the radiation spectra fromwandering BHs that accrete gas at the outskirts of ellipticalgalaxies, the Milky Way, and dwarf galaxies and discuss theirdetectability by ngVLA.
3.1. Elliptical galaxies
First, as an example of a massive elliptical galaxy, we consider M87. Based on the Chandra observational data from
Russell et al. (2015), the properties of gas surrounding a wandering BH are given; the electron density ne ≃ 0.11 cm−3 andtemperature T ≃ 1.9 × 107 K at a distance of r ≃ 2 − 3 kpc
from the center. Here, the mass of the wandering BH is set toM• ≃ 107−8 M⊙ (Zivancev et al. 2020), which corresponds to≃ 0.1 − 1% of the mass of the central SMBH (≃ 6 × 109 M⊙ ;Event Horizon Telescope Collaboration et al. 2019), and theorbital velocity of the wandering BH is assumed to be ∼ cs ,No. ]

Fig. 2. Radiation spectra from a wandering BH that accretes hot
and diffuse plasma in the outskirt of the massive elliptical M87
galaxy. Each curve corresponds to the case with different BH
mass (107 ≤ M• /M⊙ ≤ 108 ).
The black curves show thengVLA sensitivity to continuum emission for 1 hour on-source integration (https://ngvla.nrao.edu/page/performance),
and the continuum sensitivity curves of VLA and ALMA under the same conditions.
Wandering BHs with masses of6M• >∼ 5 × 10 M⊙ , if any, could be detectable with ngVLA.

i.e., M ≃ 1.
Fig. 2 presents the radiation spectra with different BH
masses of M• = 107 , 3 × 107 , and 108 M⊙ . We also overlay
the sensitivity curve of ngVLA, VLA, and ALMA. For all thecases, the radiation spectra have peaks in the millimeter bandat νp ≃ 50−100 GHz. With the ongoing facilities such as VLA
and ALMA, only heavy wandering BHs (> 3 × 107 M⊙ ) could
be detectable. As the peak frequency is lowered for lower-mass
7
BHs, the emission from a wandering BHs with <∼ 10 M⊙
would peak in the band where ngVLA has the highest sensitivity. Within the design sensitivity curve of ngVLA, thedetection limit of wandering BH’s masses would be reduced
down to ≃ 5 × 106 M⊙ . Those less-massive BHs would be
more likely to be wandering BH populations according to BH
ejection through multi-body interactions in the galactic center(Zivancev et al. 2020).
We apply this argument to other nearby massive ellipticalgalaxies, assuming the existence of wandering BHs at theirgalaxy outskirts (listed in Table 1). Taking the observational
data (Russell et al. 2013; Russell et al. 2015; Inayoshi et al.
2020), we estimate the properties of gas surrounding those BHs
and calculate the radiation spectra shown in Fig. 3. The errors of density and temperature are given by the maximum andminimum values at distances of r ≃ 2 − 3 kpc from the centers. We assume the mass of the wandering BH to be 1% of thecentral SMBH mass, and we choose M = 0.5. As shown in
Fig. 3 and Table1, the radio fluxes at ν = 50 Hz are the ordersof 10−1.5 − 102 µJy. With the capability of ngVLA, therefore, BHs, if any, wandering at the galactic outskirts could be
detectable in 8 nearby elliptical galaxies in addition to M87.
In future, more detections of those wandering BHs in nearby
ellipticals will enable us to reveal the statistical properties of
those populations and to study the nature of BH merger events

3

Fig. 3. Radiation spectra from a wandering BH in several different local elliptical galaxies listed in Table 1. The mass of the wandering BH
is assumed to be 1% of the central SMBH mass. With the capabilityof ngVLA, therefore, BHs, if any, wandering at the galactic outskirts
could be detectable in 8 nearby elliptical galaxies in addition to M87.

associated with galaxy coalescences.
3.2.

Milky Way and dwarf galaxies

Next, we consider the same exercise as in §3.1 for wandering BHs with kpc-scale orbits within the Milky Way. To
model the properties of the hot gas surrounding the Milky
Way halo, we adopt the results of the Suzaku X-ray observations (Nakashima et al. 2018), which estimate a plasma
temperature of T ≃ 3 × 106 K and an emission measure of
EM ≃ (0.6 − 16.4) × 10−3 cm−6 pc. Based on these results,
we adopt ne = 0.01 cm−3 as the gas density around wandering
BHs. In Fig. 4, we show the radiation spectra of wandering
BHs with M• ≃ 3 × 104 − 3 × 105 M⊙ located at ∼ 10 kpc
from the Earth. The spectra in the millimeter band extend tolower frequencies, where (ng)VLA has the highest sensitivity.
4
We could detect IMBHs down to M• >∼ 3 × 10 M⊙ .
Recent radio observations of dwarf galaxies with the VLA
by Reines et al. (2020) reported a sample of wandering IMBH
candidates that are significantly offset from the optical centersof the host galaxies. Based on an empirical scaling relation between BH mass and total stellar mass, the authors argued thatthe candidate wandering BHs might have masses in the range
M• ≃ 104 − 106 M⊙ . The measurements of multi-band radio
spectra for those wandering BH candidates by a higher sensitivity of ngVLA will allow us to study the radiation mechanism
and reveal the origin of the emission. In future, more detectionsof wandering BHs in dwarf galaxies would constrain BH seed
formation scenarios.
References
Begelman, M. C., Blandford, R. D., & Rees, M. J. 1980, Nature, 287,307

4[Vol. ,
Name
(1)
M87
NGC 4472
NGC 4552
NGC 4374
NGC 5846
NGC 5813
NGC 507
NGC 4636
NGC 5044
NGC 1316

D (Mpc)
(2)
16.68
16.72
15.30
18.51
24.90
32.20
70.80
14.70
31.20
20.95

log (M• /M⊙ )(3)
9.789 ± 0.027
9.400 ± 0.100
8.920 ± 0.110
8.970 ± 0.050
8.820 ± 0.110
8.810 ± 0.110
9.210 ± 0.160
8.490 ± 0.080
8.710 ± 0.170
8.230 ± 0.080

ne (cm−3 )(4)0.114 ± 0.016
0.029 ± 0.010
0.018 ± 0.004
0.022 ± 0.005
0.042 ± 0.009
0.042 ± 0.009
0.029 ± 0.009
0.028 ± 0.011
0.050 ± 0.009
0.033 ± 0.007

T (keV)(5)
1.650 ± 0.050
0.785 ± 0.005
0.455 ± 0.035
0.595 ± 0.025
0.625 ± 0.015
0.585 ± 0.015
0.965 ± 0.015
0.485 ± 0.015
0.645 ± 0.015
0.620 ± 0.010

log ṁ
(6)-5.918 ± 0.104-6.418 ± 0.233-6.738 ± 0.257-6.778 ± 0.157-6.689 ± 0.210-6.661 ± 0.208-6.742 ± 0.288-7.029 ± 0.244-6.748 ± 0.254-7.385 ± 0.181

log (Fνp /µJy)(7)1.992 ± 0.096
1.065 ± 0.297
0.146 ± 0.339
0.021 ± 0.202-0.407 ± 0.304-0.633 ± 0.304-0.726 ± 0.465-0.731 ± 0.304-0.822 ± 0.431-1.803 ± 0.325

Table 1. Column 1: galaxy name; Column 2: distance; Column 3: mass of the central BH; Column 4 and 5: electron density and temperature at ∼ 2 − 3 kpc; Column 6: accretion rate normalized by the Eddington rate (ṁ ≡ Ṁ /ṀEdd ) by the scaling relation from thesimulation A1, assuming the wandering BH mass is 1% of the central BH mass and M = 0.5; Column 7: radiation flux density at
νp = 50 GHz, where the ngVLA sensitivity flux is ≃ 0.3 µJy. The distance and central BH mass are taken from Inayoshi et al. (2020).
The electron density and temperature are taken from Russell et al. (2015) for M87 galaxy and from Russell et al. (2013) for the others.

Fig. 4. Radiation spectra from BHs wandering in the outskirtsof the Milky Way. Each curve corresponds to the case withdifferent BH mass of 3 × 104 ≤ M• /M⊙ ≤ 3 × 105 .

Bekenstein, J. D. 1973, ApJ, 183, 657
Bellovary, J. M., Governato, F., Quinn, T. R., et al. 2010, ApJL, 721,
L148—. 2004, MNRAS, 349, 68
Bondi, H. 1952, MNRAS, 112, 195
Bonetti, M., Haardt, F., Sesana, A., & Barausse, E. 2018a, MNRAS,
477, 3910
Campanelli, M. 2005, Classical and Quantum Gravity, 22, S387
Event Horizon Telescope Collaboration, Akiyama, K., Alberdi, A.,et al. 2019, ApJ, 875, L1
Guo, M., Inayoshi, K., Michiyama, T., et al. 2020, ApJ, 901, 39
Greene, J. E., Strader, J., & Ho, L. C. 2020, ARA&A in press,
arXiv:1911.09678
Hoyle, F., & Lyttleton, R. A. 1939, Proceedings of the Cambridge
Philosophical Society, 35, 405
Ichimaru, S. 1977, ApJ, 214, 840
Inayoshi, K., Ichikawa, K., & Haiman, Z. 2018a, ApJL, 863, L36
Inayoshi, K., Ichikawa, K., & Ho, L. C. 2020, ApJ, 894, 141
Inayoshi, K., Ostriker, J. P., Haiman, Z., & Kuiper, R. 2018b,
MNRAS, 476, 1412
Inayoshi, K., Visbal, E., & Haiman, Z. 2020, ARA&A, 58, 27
Kelley, L. Z., Blecha, L., & Hernquist, L. 2017, MNRAS, 464, 3131

Khan, S., Husa, S., Hannam, M., et al. 2016, Phys. Rev. D, 93, 044007
Lousto, C. O., Zlochower, Y., Dotti, M., & Volonteri, M. 2012, Phys.
Rev. D, 85, 084015
Luo, J., Chen, L.-S., Duan, H.-Z., et al. 2016, Classical and Quantum
Gravity, 33, 035010
Manmoto, T., Mineshige, S., & Kusunose, M. 1997, ApJ, 489, 791
Merritt, D. 2013, Classical and Quantum Gravity, 30, 244005
Nakashima, S., Inoue, Y., Yamasaki, N., et al. 2018, ApJ, 862, 34
Narayan, R., Igumenshchev, I. V., & Abramowicz, M. A. 2000, ApJ,
539, 798
Narayan, R., & Yi, I. 1994, ApJL, 428, L13—. 1995a, ApJ, 444, 231
Oka, T., Tsujimoto, S., Iwata, Y., Nomura, M., & Takekawa, S. 2017,
Nature Astronomy, 1, 709
Quataert, E., & Gruzinov, A. 2000, ApJ, 539, 809
Reines, A. E., Condon, J. J., Darling, J., & Greene, J. E. 2020, ApJ,
888, 36
Russell, H. R., Fabian, A. C., McNamara, B. R., & Broderick, A. E.
2015, MNRAS, 451, 588
Russell, H. R., McNamara, B. R., Edge, A. C., et al. 2013, MNRAS,
432, 530
Ryan, B. R., Ressler, S. M., Dolence, J. C., et al. 2017, ApJL, 844,
L24
Ryu, T., Perna, R., Haiman, Z., Ostriker, J. P., & Stone, N. C. 2018,
MNRAS, 473, 3410
Sesana, A., Vecchio, A., & Colacino, C. N. 2008, MNRAS, 390, 192
Tremmel, M., Governato, F., Volonteri, M., Pontzen, A., & Quinn,
T. R. 2018a, ApJL, 857, L22
Yu, Q. 2002, MNRAS, 331, 935
Yuan, F., & Narayan, R. 2014, ARA&A, 52, 529
Yuan, F., Quataert, E., & Narayan, R. 2004, ApJ, 606, 894
Zivancev, C., Ostriker, J., & Kupper, A. H. W. 2020, MNRAS, 498,
3807