arXiv:1011.4311v2 [astro-ph.GA] 10 Feb 2011
Draft version February 11, 2011
Preprint typeset using LATEX style emulateapj v. 11/10/09
MASSIVE BLACK HOLES IN STELLAR SYSTEMS: ‘QUIESCENT’ ACCRETION AND LUMINOSITY
M. Volonteri1, M. Dotti2, D. Campbell1& M. Mateo1,
Draft version February 11, 2011
Only a small fraction of local galaxies harbor an accreting black hole, classified as an active galactic
nucleus (AGN). However, many stellar systems are plausibly expected to host black holes, from
globular clusters to nuclear star clusters, to massive galaxies. The mere presence of stars in the
vicinity of a black hole provides a source of fuel via mass loss of evolved stars. In this paper we assess
the expected luminosities of black holes embedded in stellar systems of different sizes and properties,
spanning a large range of masses. We model the distribution of stars and derive the amount of gas
available to a central black hole through a geometrical model. We estimate the luminosity of the black
holes under simple, but physically grounded, assumptions on the accretion flow. Finally we discuss
the detectability of ‘quiescent’ black holes in the local Universe.
Dynamical evidence indicates that massive black holes
with masses in the range MBH ∼ 106− 109M⊙ or-
dinarily dwell in the centers of most nearby galax-
ies (Ferrarese & Ford 2005).
larly compelling in the case of our own galaxy, host-
ing a central black hole with mass ≃ 4 × 106M⊙ (e.g.,
Sch¨ odel et al. 2003; Ghez et al. 2005).
holes with smaller masses exist as well. For example, the
Seyfert galaxies, POX 52 and NGC 4395, are thought
to contain massive black holes with mass ∼ 105M⊙
(Barth et al. 2004; Peterson et al. 2005). Low mass black
holes might also exist in dwarf galaxies, for instance in
Milky Way satellites. If these black holes exist they can
help us understand the process that formed the seeds
of the massive holes we detect in much larger galaxies
(Van Wassenhove et al. 2010).
galaxies have a high probability that the central black
hole is not “pristine”, that is, it has increased its mass
by accretion or mergers. Dwarf galaxies undergo instead
a quieter merger history, and as a result, if they host
black holes, they still retain some “memory” of the orig-
inal seed mass distribution (Volonteri et al. 2008).
The dynamical-mass estimates indicate that, across
a wide range, central black hole mass are about 0.1%
of the spheroidal component of the host galaxy, with
a possible mild dependence on mass (Magorrian et al.
1998; Marconi & Hunt 2003; H¨ aring & Rix 2004).
tight correlation is also observed between the massive
black hole mass and the stellar velocity dispersion of the
hot stellar component (“M-σ”, Ferrarese & Merritt 2000;
Gebhardt et al. 2000; Tremaine et al. 2002; Graham
2008;G¨ ultekin et al.2009).
suggest that atleast some
break down at the largest galaxy and black hole
masses (but see Bernardi et al. 2007; Tundo et al.
2007; Graham 2008). One unanswered question is
whether this symbiosis extends down to the low-
est galaxyand black hole
The evidence is particu-
Black holes in massive
Lauer et al.
masses(Greene et al.
1University of Michigan, Astronomy Department, Ann Arbor,
2Max Planck Institute for Astrophysics, Karl-Schwarzschild-
Str. 1, 85741 Garching, Germany
2008), due to changes in the accretion properties
(Mathur & Grupe 2005), dynamical effects (Volonteri
2007), or a cosmic bias (Volonteri & Natarajan 2009;
Van Wassenhove et al. 2010).
It has also been proposed (e.g., Portegies Zwart et al.
2004; G¨ urkan et al. 2004) that black holes of intermedi-
ate mass (between the stellar mass range, ∼ few tens
M⊙, and the supermassive black hole range,∼
can form in the center of dense young star clusters. It
is proposed that the formation of the black hole is fos-
tered by the tendency of the most massive stars to con-
centrate into the cluster core through mass segregation.
The merging of main-sequence stars via direct physical
collisions can enter into a runaway phase, forming a very
massive star, which can then collapse to form a black
hole (Begelman & Rees 1978; Ebisuzaki et al. 2001;
Miller & Hamilton 2002; Portegies Zwart & McMillan
2002; Portegies Zwart et al. 2004; Freitag et al. 2006b,a;
G¨ urkan et al. 2004, 2006). Observational evidences for
intermediate mass black holes in globular clusters are
scant (e.g., van der Marel & Anderson 2010; Pasquato
2010, and references therein).
ments are hampered by the small size of the sphere
of influence of these black holes, and only four candi-
dates have currently been identified, in M15, M54, G1
and ω Centauri (Gerssen et al. 2002; Ibata et al. 2009;
Gebhardt et al. 2005; Noyola et al. 2008). The radio and
X-ray emission detected from G1 make this cluster the
strongest candidate, although alternative explanations,
such as an X-ray binary are possible (Ulvestad et al.
2007; Pooley & Rappaport 2006).
‘Massive’ black holes (more massive than stellar mass
black holes) are therefore expected to be widespread in
stellar systems, from those of the lowest to highest mass.
Only a small fraction of these massive black holes are
active at levels that are expected for AGNs, and, indeed,
most massive black holes at the present day are ‘quies-
cent’. However, because MBHs are embedded in stellar
systems, they are unlikely to ever become completely in-
active. A massive black hole surrounded by stars could
be accreting material, either stripped from a compan-
ion star or available as recycled material via mass loss of
evolved stars. (Ciotti & Ostriker 1997). Quataert (2004)
2Accretion onto quiescent black holes
model the gas supply in the central parsec of the Galac-
tic center due to the latter process. Winds from massive
stars can provide ∼ 10−3M⊙yr−1of gas, with a few per-
cent, ∼ 10−5M⊙yr−1, of the gas flowing in toward the
central massive black hole. Quataert (2004) shows that
the observed luminosity from Sgr A* can indeed be ex-
plained by relatively inefficient accretion of gas originat-
ing from stellar winds.
Elliptical galaxies with quiescent massive black holes,
systems for which we have both accurate massive black
hole masses and data about their surroundings, hint
that stellar winds may be a significant source of fuel
for the massive black hole. The hot gas of the inter-
stellar medium, lending itself to X-ray observations, can-
not be the sole source of fuel for at least some massive
black holes. In particular, some massive black holes are
brighter than one would expect for inefficient accretion,
but significantly less bright than for normal accretion
(Soria et al. 2006a). The X-ray luminosity can vary by
∼ 3 orders of magnitude displaying no relationship be-
tween massive black hole mass or the Bondi accretion
rate (Pellegrini 2005). It is likely that warm gas that
has not yet been thermalized or virialized originating
from stellar winds and supernovae from near the mas-
sive black hole provides a significant amount of material
for accretion, possibly an order of magnitude larger than
the Bondi accretion rate of hot interstellar medium gas
alone (Soria et al. 2006b).
We attempt in this paper a simple estimate of how
much recycled gas is available for accretion onto a mas-
sive black hole in different stellar systems, from globu-
lar clusters to galaxies, including dwarf spheroidals, nu-
clear star clusters in the cores of late type galaxies and
early type normal galaxies. We show that the amount
of fuel available to massive black holes through stellar
winds in quiescent galaxies is indeed meager, and unless
extreme conditions are met, X-ray detection of massive
black holes in globular clusters and low-mass galaxies is
expected to be uncommon.
2.1. Stellar models
To model the accretion rate, we must choose 3-
dimensional stellar distributions for the various stellar
systems we consider here.
dwarf spheroidals we assume the stars to be distributed
following a Plummer profile:
For globular clusters and
where a = Reff is the core radius.
Early type galaxies and nuclear clusters are modeled
as Hernquist spheres:
r(r + rh)3, (2)
where the scale length rh≈ Reff/1.81. To fully define the
stellar systems we have only to relate the stellar mass,
Mstellar, to the effective radius, Reff.
For globular clusters, we recall that simulations by
Baumgardt et al. (2005, 2004) suggest that globular clus-
ters with massive black holes have relatively large cores
a ∼ 1 − 3 pc (see also Trenti et al. 2007).
sistent results were found using Monte Carlo simula-
tions (Umbreit et al. 2009) and in analytical models
(Heggie et al. 2007). The core radii (where measured)
of globular clusters hosting intermediate mass black hole
candidates, are roughly consistent with the values we
considered, ranging from approx 0.5 pc in M15 (Gerssen
et al. 2002, core radius from the catalog presented in
Harris et al. 20103), up to few pc in omega Centauri
(Noyola et al. 2008).
For early type galaxies, we adopt the fits by Shen et al.
(2003) for stellar-mass vs effective radius in Sloan Digital
Sky Survey galaxies:
4 × 1010M⊙
The scatter is roughly 0.2 dex for stellar masses be-
tween 108M⊙ and 1010M⊙: σlnR = 0.34 + 0.13/[1 +
(Mstellar/4 × 1010M⊙)].
We note that for 5 galaxies (NGC 4697, NGC 3377,
NGC 4564, NGC 5845, NGC 821) where measurements
of the effective radius are available (along with stel-
lar masses, black hole masses, and gas density- see
Soria et al. (2006a) and Marconi & Hunt (2003)) the fits
derived by Shen et al. (2003) provide values of the effec-
tive radius roughly 55% times larger than the measured
value. This is likely due to Shen et al. (2003) definition
of effective radius as the radius enclosing 50 per cent of
the Petrosian flux. This definition differs from the stan-
dard definition of projected radius enclosing half of the
total luminosity. We therefore scale the fit for early type
galaxies by a factor of 0.55 for consistency. As shown
below (Fig. 3) this small correction does not influence
the accretion rate we derive.
For dwarf spheroidals, we fit the data presented in
Walker et al. (2009, 2010). We assume a constant mass-
to-light ratio of two for the visible component, and derive
stellar masses from the total luminosities:
where the uncertainties in the slope and in the normal-
ization are 0.06 and 0.2 dex respectively. Finally for nu-
clear clusters we fit the stellar mass vs effective radius
data presented in Seth et al. (2008), leading to:
Reff= 7.9 × 10−3
where the uncertainties in the slope and in the normal-
ization are 0.05 and 0.3 dex respectively. These scalings
are shown in Figure 1.
2.2. Geometrical model
We develop here a simple geometrical model to es-
timate the accretion rate onto a massive black hole
in a stellar system, fueled by mass loss from stars
(Quataert et al. 1999).If a star is located at a dis-
tance r from the massive black hole, and if it produces
an isotropic wind, with velocity vwind, only the fraction
Volonteri et al.3
Fig. 1.— Relationship between half-mass radii and stellar mass
for different galaxy morphological types.
and nuclear clusters we show the data along with our best fit. For
elliptical galaxies we show the effective radii of 5 galaxies from
Soria et al. (2006a), along with Shen et al. (2003) fit and a cor-
rection of a factor 0.55. We include as a shaded area the range in
half-mass radii and stellar mass adopted for globular clusters.
For dwarf spheroidals
of gas which passes within the accretion radius of the
massive black hole,
wind+ σ2+ c2
can be accreted (ignoring gravitational focusing). Here
σ2= GMstellar/(2.66rh) is the velocity dispersion of the
stellar system at the half-mass radius. For a Hernquist
profile, where the density in the inner region ρ ∝ r−1,
the velocity dispersion decreases towards the center. Es-
timating σ at the half mass radius gives a conservative
lower limit to the accretion radius, and hence the accre-
tion rate. Following Miller & Hamilton (2002), we as-
sume that in equation 6 the sound speed cs= 10kms−1,
and, vwind= 50kms−1as reference values, although we
study the effect that a different vwindhas on our model
(see Figure 2).
If σ ≫ vwind, Racc depends only on the proper-
ties of the potential well of the stellar distribution,
not on the wind properties.
MBHReff/Mstellar ≃ 10−3Reff if Mstellar = 103MBH.
Note that, at fixed black hole mass, the more massive
the galaxy, the smaller Raccis, as the scaling of Reffwith
Mstellaris a power law with exponent less than one (see,
e.g., equation 3). On the other hand, if σ ≪ vwind, Racc
depends only on the wind velocity. These two limits are
apparent in Figures 2 and 3, and they will be discussed
in the next section.
Geometrical considerations suggest that, for r > Racc:
In particular, Racc ≃
star lies within Racc, we consider ˙Macc,∗= ˙M∗. Eq. (7)
implicitly assumes that the stars have a spherically sim-
metric distribution and that their velocity field (and, as
˙M∗ is the mass loss rate from the star. If the
a consequence, the velocity field of the wind) is isotropic.
In a rotating stellar system, the presence of net angular
momentum of the gas can change the accretion rate onto
the black hole (e.g., Cuadra et al. 2008). A study of the
dependence of the accretion rate on the degree of rota-
tional support of the stellar distribution is beyond the
scope of this paper.
The total contribution from all stars is found by inte-
grating over the density profile of the stellar system:
where ?m∗? is the mean stellar mass and ρ is given by
eq. (1) and (2). The normalization in eq. (8) is given
by the cumulative mass loss rate of all the stars in the
stellar structure, that we estimate following Ciotti et al.
˙Mgal= 1.5 × 10−11M⊙yr−1LB
where t∗is the age of the stellar population, and LB is
the total luminosity of the stellar system. We set t∗= 5
Gyr for dSphs and nuclear star clusters, and t∗ = 12
Gyr for early type galaxies and globular clusters. We
derive B-band luminosities from stellar masses assuming
a mass-to-light ratio of 5 in the B-band.
We obtain an upper limit of the luminosity of the mas-
sive black hole by assuming that the whole˙Maccis indeed
accreted by the massive black hole.
2.3. Accretion rate and luminosity
Figure 2 shows the resulting accretion rate for a cen-
tral massive black hole in different stellar systems, where
we assume that the massive black hole mass scales with
the mass of stellar component, MBH = 10−3Mstellar
(Marconi & Hunt 2003; H¨ aring & Rix 2004), and we
have considered vwind a free parameter.
sumed that Reffscales exactly with Mstellarfollowing the
relationships discussed above. Note that for high values
of the stellar masses in early-type galaxies and nuclear
star clusters, the accretion rate and Raccdo not depend
on the wind velocities. In these cases σ ≫ vwind, and
the accretion rate depends only on the properties of the
host stellar structure and on the black hole mass (see the
discussion of Equation 6 above).
In Figure 3 we instead fix vwind, and allow for a scat-
ter in the mass-size relationship. For globular clusters
we assume Reff= 1 pc; Reff= 2 pc and Reff= 4 pc. For
galaxies, the middle curve shows the best fit Reff for a
given stellar mass value (Equations 1, 2 and 3), the top
curves assume that Reffis half the best fit value, and the
bottom curves assume that Reffis twice the best fit value.
We have assumed Mstellar = 105− 107M⊙ for globular
clusters, Mstellar = 105− 108M⊙ for dwarf spheroidals
and nuclear star clusters, and Mstellar= 108− 1011M⊙
for early type galaxies, limiting our investigation to the
mass ranges probed by Shen et al. (2003); Walker et al.
(2009); Seth et al. (2008). In this plot the vwind ≫ σ
limit of Equation 6 becomes evident:
masses, for every type of stellar distribution but for the
early type galaxies, Racc does not depend on Reff, and
it is determined only by the BH mass and the assumed
We have as-
at low stellar