Annu. Rev. Astron. Astrophys. 1995. 33:
581-624 Copyright © 1995 by Annual Reviews. 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 (109 L)-1 y-1 of gas (Faber & Gallagher 1976). For example, gas shed by the bulge of M31 (L = 6 x 109 L), if accreted at a steady rate onto a BH at 10% efficiency (0.1 1), would provide a luminosity of 1011 L. Just the stars that are gravitationally bound to the BH (i.e., at r 6 pc) already generate 108 0.1L. 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 vw 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 1043 0.1 erg s-1 1010 0.1 L. The luminosity of Sgr A* is tremendously uncertain but unlikely to be larger than 1040 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 103 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 MBH / vw2 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 MBH (1 to 2) x 106 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 1053 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 / tr, where tr is the half-mass relaxation time and N is the number of stars bound to the BH (that is, with r < rcusp GMBH / 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:
Here M8 = MBH / (108
M),
n4 is the stellar density at the cusp
radius rcusp in units of 104
pc-3, and m* and r* are the
typical stellar mass and radius in solar units.
Applying these equations to M31, for M8 = 0.3
(Table 1), rcusp
6 pc, and n4
= 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 rt = 2.3 x 1013
M81/3 m*-1/3
r* cm. The Schwarzschild radius of the BH is
rS = 3.0 x 1013 M8 cm. So for
M8 < 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
rt, 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 104 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).