Triaxial galaxies containing massive black holes or central density cusps

The box orbits that form the backbone of a triaxial elliptical galaxy carry stars arbitrarily close to the centre. In this paper we investigate how these orbits are affected if either (i) a massive black hole lurks at the centre, or (ii) the stellar density becomes arbitrarily large near the centre. Elementary considerations show that a point mass at the centre will eventually disrupt the crucial box orbits by subjecting stars on these orbits to large-angle deflections. Numerical experiments show that the time-scale for disruption of box orbits by weaker encounters is comparable with the time for disruption by these hard encounters, and that the disruptive effect of the central mass can be modelled by a series of discrete scattering events. We argue that over a Hubble time a central black hole with 2 per cent of the core mass will disrupt most box orbits with apocentres interior to about 1 kpc. This may lead to an abrupt loss of triaxiality throughout the galaxy, but a simple calculation suggests that the loss of triaxiality will be confined to the centre. We calculate that a |10⁸ M_| black hole at the centre of a typical giant elliptical is currently disrupting stars at a rate | 4 10^-6 M_ \, yr^-1| if the galaxy is triaxial, and | 2 10^-7 M_ \, yr^-1| if it is axisymmetric. We show that regular box orbits persist in systems with singular central densities such as that implied by carrying the r1/4 law all the way to r = 0. Indeed, at low energies, Schwarzschild's model allows fewer box orbits than a model with the same axis ratios in which the central density diverges at the centre as in the standard r1/4 model.