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

7. ARE MDOs TOO BLACK TO BE BLACK HOLES?

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 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 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 M_BH / v_w² 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 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 / 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 M₈^2.33 n₄^1.60 [ ² / (100 km ^s-1)² ]^-2.88 m_*^1.06 r_*^0.40 y^-1. (3)

Here M₈ = M_BH / (10⁸ M), n₄ is the stellar density at the cusp radius r_cusp 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), r_cusp 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 r_t = 2.3 x 10¹³ M₈^1/3 m_*^-1/3 r_* cm. The Schwarzschild radius of the BH is r_S = 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 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 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).