Annu. Rev. Astron. Astrophys. 1995. 33:
581-624
Copyright © 1995 by Annual Reviews Inc. All rights reserved |

If massive dark objects are black holes, they should accrete nearby matter and radiate some of its binding energy. This insight provides a test of the presence of BHs.

An old stellar population produces 0.015 *M*_{} (10^{9}
*L*_{})^{-1} y^{-1} of gas (Faber &
Gallagher 1976). For example, gas shed by the bulge
of M31 (*L* = 6 x 10^{9} *L*_{}), if accreted at a steady rate onto
a BH at 10% efficiency (_{0.1}
1), would provide a
luminosity of 10^{11} *L*_{}. Just the stars that are gravitationally bound
to the BH (i.e., at *r* 6 pc) already generate
10^{8} _{0.1}*L*_{}. This greatly exceeds the luminosity of either nucleus.

The situation looks worse in our Galaxy. Geballe *et al.* (1987,
and references therein) estimate that IRS 16 emits a wind with velocity
*v*_{w} 700 km
s^{-1} and mass flow rate ~ 4 x 10^{-3}
*M*_{}
y^{-1}. If all of it were
accreted onto a BH, its luminosity would be 10^{43} _{0.1}
erg s^{-1}
10^{10} _{0.1} *L*_{}. The luminosity of
Sgr A* is tremendously uncertain but unlikely to be larger than
10^{40} erg s^{-1} (Genzel *et al.* 1994). This
estimate considerably exceeds any output
actually observed, but it falls short of the expected accretion
luminosity by a factor of 10^{3} _{0.1}. On the other hand, Melia (1992a, 1994) and
Melia *et al.* (1992) argue that only part of the wind is accreted,
i.e., the
gas that passes within *r* 2 *G M*_{BH} /
*v*_{w}^{2} of the BH. Then the
accretion rate is ~ 10^{-4} *M*_{} y^{-1}. Melia
calculates the
resulting spectrum; it agrees with observations over 11 decades in frequency
provided that *M*_{BH} (1 to 2) x 10^{6} *M*_{}. The model has
problems - it predicts a radio source size that is three times larger than the
observed limit at 3 mm (Section 4.6) -
but it is reasonably successful. A
different model is proposed by Falcke *et al.* (1993a,b), Falcke
(1994), and
Falcke & Heinrich (1994). They suggest that a dense accretion disk currently
accumulates most of the above inflow; then the BH accretion rate is only
10^{-7} to 10^{-8.5} *M*_{} y^{-1}. However,
their disk radiates more
efficiently, so it also fits the observed spectrum. Similar models fit M31
(Melia 1994b; Falcke & Heinrich 1994). So: the accretion physics is still
being debated, but there is no clear luminosity problem.

The Falcke model illustrates the easy escape from any BH luminosity problem: we can hypothesize non-steady accretion. It is possible that normal nuclei cycle between an accreting, low-level AGN state and a non-accreting, normal state.

A second fuel source for nuclear BHs is accretion of stars (e.g., Lacy
*et al.* 1982; Rees 1988; Goodman & Lee 1989; Phinney 1989; Evans &
Kochanek
1989; Rees 1990, 1993, 1994). A BH will tidally disrupt main-sequence stars on
relativistic orbits. For sufficiently low-mass BHs, tidal disruption occurs
outside the Schwarzschild radius. Half of the stellar mass is likely to be
accreted, with an energy output of 10^{53} *m*_{*}
_{0.1} erg.
Stars that are initially on doomed orbits will be destroyed within an
orbital timescale of
the formation of the BH. Later, stars are destroyed at the rate at which these
orbits are repopulated.

The rate of repopulation of the ``loss cone'' (actually more nearly a
cylinder) by two-body gravitational interactions is a well studied but very
complicated subject originally motivated by the expectation that BHs form in
globular clusters. There are two regimes: 1. Sufficiently close to the hole,
stars scatter into or out of the loss cone on timescales that are longer than
the orbital time. Stars scattered into the cone die almost instantly and the
loss cone is empty. In this case, the calculation of the disruption rate is
complicated by the necessity to treat this empty part of phase space as a
boundary condition on the evolution of the phase space density of stars. 2.
Farther from the hole, the timescale for small changes in rms angular momentum
is short compared to an orbital time, so the loss cone is populated. Estimates
of stellar disruption are complicated by the likelihood that stars will scatter
out of the loss cone before reaching the perilous environs of the BH.
In either
case, it is clear on dimensional grounds that the stellar destruction rate is
bounded from above by *d N / d t* = *N / t*_{r}, where
*t*_{r} is the half-mass relaxation
time and *N* is the number of stars bound to the BH (that is, with
*r* < *r*_{cusp} *GM*_{BH} / ^{2}). Improving on this limit is difficult. The
reader is referred to a very lucid review by Shapiro (1985) and to Cohn &
Kulsrud (1978), particularly their Equation 66:

*d N/ d t* = 0.018 M_{8}^{2.33}
*n*_{4}^{1.60} [ ^{2} / (100 km
^{s}-1)^{2} ]^{-2.88}
*m*_{*}^{1.06} *r*_{*}^{0.40}
y^{-1}.

Here *M*_{8} = *M*_{BH} / (10^{8}
*M*_{}),
*n*_{4} is the stellar density at the cusp
radius *r*_{cusp} in units of 10^{4}
pc^{-3}, and *m*_{*} and *r*_{*} are the
typical stellar mass and radius in solar units.

Applying these equations to M31, for *M*_{8} = 0.3
(Table 1), *r*_{cusp}
6 pc, and *n*_{4}
= 1 (Lauer *et al.* 1993), we find a stellar disruption
rate of 10^{-4} y^{-1}. This is consistent with Rees (1988) and
with Goodman & Lee (1989). What happens to the shattered star? Tidal breakup
occurs at a radius *r*_{t} = 2.3 x 10^{13}
*M*_{8}^{1/3} *m*_{*}^{-1/3}
*r*_{*} cm. The Schwarzschild radius of the BH is
*r*_{S} = 3.0 x 10^{13} *M*_{8} cm. So for
*M*_{8} < 1, solar-mass main-sequence stars are disrupted
outside the Schwarzschild radius and the fireworks should be
visible. Note that the rate of
breakup flashes could be greatly enhanced over the above estimate by the
accretion of a second BH or even of a secondary nucleus. Since one or both of
these things may be happening in M31, the current rate of stellar breakup
flashes could be much larger than the above estimate.

The least certain aspect of this problem is the duration and spectrum of a
flash. The stream of bound debris from the shattered star will self-intersect
within months. The gas should shock and transfer angular momentum efficiently.
Rapid relativistic perhelion precession probably precludes the formation of an
elliptical disk, so the timescale for the event is likely to be 1 y.
On the other hand, Cannizzo *et al.* (1990) note that at late times
there is a
self-similar disk accretion solution that may preserve a power-law decay for
many years. If they are correct, then the inactivity of M31 is a
serious argument against a nuclear BH.

We are unaware of any calculation of the spectrum of the flashes. If the
debris forms dust rapidly and becomes optically thick, then the radiation will
be reprocessed in a region significantly larger than
*r*_{t}, and most of the
signal will emerge in the infrared (as emphasized by Rees). If, on the other
hand, the stellar orbital angular momentum is aligned with that of the BH, or
if the BH has negligible angular momentum, then the debris may orbit in a plane
and the luminosity may be dominated by the inner edge of the accretion disk.
Then the temperature could be 500,000 *K*. The resulting spectrum would
peak in the extreme ultraviolet or soft x-ray band (Sembay & West 1993). Given
a large sample with diverse angular momenta, x-ray and infrared flashes
both probably occur.

If one considers the possibly short duty cycle and its uncertainties, the
absence of activity in M31 or in any other BH candidate is not terribly
disturbing. Some low level AGNs noted by Filippenko & Sargent (1985,
1987) may
even be powered by stellar breakup flashes. A key test of the BH paradigm is
nevertheless implied. A survey of 10^{4} galaxies should yield
one stellar breakup flash per year at luminosities exceeding those of
supernovae. Periodic
imaging of a set of clusters of galaxies should be informative very quickly
(Rees 1994). It is even possible that several hundred x-ray flashes have
already been detected in the *ROSAT* all-sky survey (Sembay & West 1993).