THE ACCRETION DISK LIMIT-CYCLE INSTABILITY IN BLACK-HOLE X-RAY BINARIES

We investigate the operation of the limit cycle mechanism in accretion disks around similar to 10 M. black holes. We explore a regime of parameter space relevant to these systems, and delineate a range of possible behaviors by testing the response of our one-dimensional, time-dependent, hydrodynamic model to variations in each of the control parameters in the theory. These parameters are the number of radial grid points N, the accretor mass M(1), the inner disk radius r(inner), the outer disk radius r(outer), the mass transfer rate into the outer disk from the secondary star M(T), and the accretion disk viscosity parameter alpha-parameterized in separate computations both in terms of radius (including a step function between low and high states) and in terms of local aspect ratio h/r. For the class of models in which alpha is taken to vary in a step function between the two stable branches of accretion, we find a tendency for the outbursts to exhibit faster-than-exponential decays, in contrast to the observations. This behavior cannot be substantially affected by taking alpha to vary with radius-alpha proportional to r(epsilon)-as in previous works, nor is it affected by the numerical resolution. Models in which alpha is a function of the local aspect ratio h/r can produce robustly exponential decays as observed if alpha proportional to (h/r)(n), where n = 1.5. This critical value for n is independent of the primary mass, unlike the critical epsilon value in the r(epsilon) scaling. Numerically, we find that the transition front width is equal to the geometric average of h and r. (It is this fact that leads to the critical value n = 1.5 for exponential decay.) Previous studies have lacked the numerical resolution to make this determination, and in fact the specific results presented in earlier papers were probably severely compromised by grid spacing limitations. Finally, for models in which the decay is produced by accretion onto the central object rather than by the action of a cooling front, we require n = -2 for exponential decays.