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
4 Accretion onto quiescent black holes
Fig. 2.— Top panel: accretion rate, in solar masses per year, onto
a black hole in a stellar system with Mstellar= 103MBH. In each
set of curves the wind velocity varies from 100kms−1(bottom) to
50 kms−1(middle) to 10 kms−1(top). Solid curves: globular
clusters. Long-dashed curves: dwarf spheroidals.
curves: nuclear star clusters. Dotted curves: early-type galaxies.
Bottom panel: accretion radius for the same systems.
Fig. 3.— Top panel: accretion rate, in solar masses per year,
onto a black hole in a stellar system with Mstellar= 103MBH. In
each set of curves we vary the size of the stellar system. For glob-
ular clusters we assume Reff= 1 pc (top); Reff= 2 pc (middle);
Reff = 4 pc (bottom). For galaxies, the middle curve shows the
best fit Reff at a given stellar mass (Equations 4, 5 and 6), the
top curves assume that Reffis half the best fit value, the bottom
curves that Reff is twice the best fit value. The wind velocity is
fixed at 50 kms−1. Solid curves: globular clusters. Long-dashed
curves: dwarf spheroidals. Short-dashed curves: nuclear star clus-
ters. Dotted curves: early-type galaxies. Bottom panel: accretion
radius for the same systems.
vwind. The early type galaxies generate deeper potential
wells, never reaching the vwind≫ σ limit.
The bolometric luminosity of the massive black hole
can be written as:
Fig. 4.— Accretion rate, in Eddington units, of massive black
holes in different stellar systems. Top right: dwarf spheroidals;
bottom right=early type galaxies; bottom left=nuclear clusters;
top left=globular clusters.Gray filled triangles:
105M⊙; magenta stars=Mstellar
=Mstellar = 107M⊙; red empty triangles=Mstellar = 108M⊙;
blue dots=Mstellar= 109M⊙; green asterisks=Mstellar= 1010M⊙;
cyan squares=Mstellar= 1011M⊙. The mass-size relationship is
given by Equations 4, 5 and 6. We assume Reff= 2 for globular
clusters. The wind velocity is vwind= 50kms−1.
= 106M⊙; black pentagons
where ǫ represents the fraction of the accreted mass that
is radiated away. The nature of the accretion process,
and the consequent value of ǫ, is rather uncertain. AGNs
accrete through accretion discs with a high efficiency
(ǫ ∼ 0.1). Supermassive BHs at the centers of quiescent
galaxies, including the Milky Way, can have luminosities
as low as ∼ 10−9− 10−8of their Eddington values (e.g.
Loewenstein et al. (2001)), and well below the luminosity
one would estimate assuming ǫ ∼ 0.1.
Following Merloni & Heinz (2008) we define λ ≡
Lbol/LEdd, where Lbolis the bolometric luminosity and
LEdd = 4πGMBHmpc/σT ≃ 1.3 × 1038(MBH/M⊙) erg
s−1is the Eddington luminosity. We write the radia-
tive efficiency, ǫ, as a combination of the accretion effi-
ciency, η, that depends only on the location of the inner-
most stable circular orbit4, here assumed to be η = 0.1,
and of a term, ηacc, that depends on the properties of
the accretion flow itself: ǫ = η ηacc.
˙ m = η˙ Mc2/LEdd.
For ‘radiatively efficient’ accretion, ηacc = 1. To es-
timate the X–ray luminosity, we apply a simple bolo-
metric correction, and assume that the X-ray luminosity
is a fraction ηX of the bolometric luminosity. Ho et al.
(1999) suggest that for low-luminosity AGN, with Ed-
dington rates between 10−6and 10−3the luminosity on
the [0.5-10] keV band represents a fraction 0.06-0.33 of
the bolometric luminosity. We assume here ηX= 0.1, so
that LX= ηXǫ˙Mc2, where ǫ = η = 0.1. We refer to this
model as ‘radiatively efficient’.
We also define
4If the viscous torque vanishes at the innermost stable circular
orbit, then η is a function of BH spin only, ranging from η ≃
0.057 for Schwarzschild (non-spinning) black holes to η ≃ 0.42 for
maximally rotating Kerr black holes.
Volonteri et al.5
Fig. 5.— X–ray luminosity (top) of massive black holes in 29
nearby elliptical galaxies. Crosses and upper limits are from from
Pellegrini (2010), where we select only black holes with dynam-
ical mass measurement. Triangles: “radiatively efficient” model.
Squares: “radiatively inefficient” model.
Since the accretion rates we find are very sub-
Eddington, we assume, in a second model, that the ac-
cretion flow is optically thin and geometrically thick.
In this state the radiative power is strongly sup-
pressed (e.g., Narayan & Yi 1994; Abramowicz et al.
1988). Merloni & Heinz (2008) suggest that this tran-
sition occurs at ˙ m < ˙ mcr= 3 × 10−2, and that ηacc =
( ˙ m/ ˙ mcr), so that ǫ = η( ˙ m/ ˙ mcr). The X-ray luminosity
is therefore: LX= ηXǫ˙Mc2, where again ηX= 0.1. We
refer to this model as “radiatively inefficient”.
In Figure 4 we show the accretion rate, in Eddington
units, when we assume η = 0.1. Hereafter we vary the
mass of the massive black hole from 100M⊙to 104M⊙for
globular clusters, since there is no firm conclusion that
massive black holes’ masses scale with the mass of the
stellar component as MBH= 10−3Mstellar. For galaxies
we assume instead an upper limit to the massive black
hole mass corresponding to MBH = 2 × 10−2Mstellar, a
lower limit of 100M⊙for dSph and nuclear clusters and
a lower limit of 104M⊙for early type galaxies.
We complete the exercise by adding observational
results for a sample of 29 early type galaxies where
both dynamical black hole mass and X–ray luminos-
ity (Pellegrini 2010)5are available (see also Soria et al.
2006a; G¨ ultekin et al. 2009). 24 of these galaxies also
report the stellar mass of the bulge (Marconi & Hunt
2003). For those galaxies where the bulge mass is un-
available we derive stellar masses from B-band magni-
tudes. For these galaxies we also derive B-band lumi-
nosities directly from LV (G¨ ultekin et al. 2009), assum-
ing B −V = 1 (Coleman et al. 1980), and we check that
5The sample of Pellegrini (2010) comprises 112 galaxies with
measured X-ray luminosity. For systems that do not have dynam-
ical black hole mass measurement, Pellegrini (2010) derives black
hole masses from the M-σ relation. We limit our analysis to those
galaxies that have a direct black hole mass measurement to avoid
adding additional uncertainties, especially below MBH= 107M⊙,
where the M-σ relation is less secure. We note, however, that the
results we discuss hold for the whole sample.
our choice of a mass-to-light ratio of 5 agrees well with
this complementary technique to derive LB.
Figure 5 compares the luminosities we predict for these
galaxies to the measured X-ray luminosity of the galaxies
(or upper limits). In agreement with the conclusions of
Pellegrini (2005) and Soria et al. (2006b) the radiatively
inefficient case best fits the luminosity of most systems,
except the most luminous ones. Overall, even the radia-
tively inefficient case slightly overestimates the luminos-
ity, at least at the high mass end, and we find that, for
instance, ηX= 0.03 provides a much better fit. As dis-
cussed by Pellegrini (2010) there seems to be a smooth
transition between radiatively inefficient and radiatively
We also estimate the X–ray luminosities for Milky Way
dSphs with stellar mass > 105M⊙, where we use di-
rectly Rhalf and Mstellarfrom Walker et al. (2010). We
assume in one case that MBH= 10−3Mstellar, and in an-
other case that black holes have a fixed massive black
hole mass of 105M⊙, based on models presented in
Van Wassenhove et al. (2010). We note that in all these
cases the X–ray luminosities for massive black holes in
dwarf galaxies are below 1035ergs−1. Figure 6 summa-
rizes our primary results; predicted X-ray luminosities
for different stellar systems.
We have developed a simple model to estimate the
level of accretion fueled by recycled stellar winds on black
holes hosted in stellar systems of different types. Let us
examine the various assumptions of our models to ques-
tion if our approach is too conservative. To model the
accretion rate we need (1) a stellar density profile, (2)
physical size and mass of a system, (3) a total mass loss
from stars (which depends on their age and luminosity),
and (4) a velocity of stellar wind.
Regarding points (3) and (4), we note that our choice of
stellar ages and mass-to-light ratios are already quite op-
timistic (except for the case of globular clusters and early
type galaxies, but we note that our results for globulars
are consistent with the estimate of Miller & Hamilton
2002), and for most massive black holes in massive stel-
lar systems the wind velocity is not highly influential.
Regarding point (2), we can see from Fig. 3 that the re-
lationship between size and radius does not have a very
strong effect on our results. More interesting is point (1).
As long as the wind velocity is larger than the velocity
dispersion of a galaxy, the amount of available gas will
increase if the density profile is steeper. For instance,
an ideal density profile is an isothermal sphere (possibly
singular) where the velocity dispersion is constant while
the central density increases towards the center. In such
case the size of the accretion radius, and the accretion
rate, are maximized (see Equations 6 and 7).
One of our goals was to assess the detectability of pu-
tative massive black holes in Milky Way dSphs. If they
exist they provide valuable information on the process
that formed the seeds of the massive holes we detect in
much larger galaxies (Van Wassenhove et al. 2010). Fig-
ure 6 suggests that such black holes would be elusive, as
the expected luminosities are often even less than those
of X-ray binaries. Regarding the three points discussed
above, in the case of dSphs, the observed stellar density
profiles are very shallow and the central stellar densities