Effects of Massive Central Black Holes on Dense Stellar Systems

We discuss some dynamical and astrophysical consequences of the presence of a massive black hole, of mass Mh in a dense stellar system, applying our results to the cores of globular clusters and to galactic nuclei. The black hole would dominate the dynamics of stars out to a radius |rₕ\, \, GMₕ/c\, ^2, \, ₂| being the velocity dispersion in the core. Within rh, the stellar velocity dispersion is proportional to r–1/2 and the stellar density n (r) may be enhanced. A quasisteady state can be established, involving a steady influx of stars which are swallowed or disrupted near the hole. We define and calculate a ‘critical radius’ rcrit such that most stars on orbits with |r\, \, rcrit| diffuse into lowangular momentum ‘loss-cone ’ orbits (and are swallowed) in the ‘reference time ’ tR; whereas outside rcrit, loss-cone effects are negligible and a typical star diffuses inward into a more tightly-bound orbit on a time scale | tR (r/rcrit) |⁠. The density profile in the cusp is |n (r) \, \, r^-7/4\, for\, r₂ₑ₈ₓ\, \, r\, \, rₕ;| and somewhat flatter inside rcrit. Generally rcrit is larger than either the tidal radius rT of the hole or the ‘collision radius ’ rcoll at which |GMₕ/rcoll| equals the binding energy per unit mass of a typical star: indeed, in some cases |rcrit\, \, rₕ. | The swallowing or disruption rate of stars varies as M4/3 when |rcrit\, \, rₕ, |M61/27 when |rₕ\, \, rcrit\, rcoll| and M3 when |rcrit\, \, rcoll. | We discuss some consequences of stellar disruption and tidal capture by black holes of |10^3-\, 10^4\, M_| in globular clusters: X-ray emission, possible optical or ultraviolet ‘flares ’, and the likelihood of there being a captured star in orbit near rT. Finally, we briefly apply our considerations to Hills' quasar model, which invokes |\, 10^7\, M_| black holes in galactic nuclei.