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 par ameter space relevant to these systems, and delineate a range of possi ble behaviors by testing the response of our one-dimensional, time-dep endent, hydrodynamic model to variations in each of the control parame ters in the theory. These parameters are the number of radial grid poi nts N, the accretor mass M(1), the inner disk radius r(inner), the out er disk radius r(outer), the mass transfer rate into the outer disk fr om 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 o f local aspect ratio h/r. For the class of models in which alpha is ta ken to vary in a step function between the two stable branches of accr etion, we find a tendency for the outbursts to exhibit faster-than-exp onential decays, in contrast to the observations. This behavior cannot be substantially affected by taking alpha to vary with radius-alpha p roportional to r(epsilon)-as in previous works, nor is it affected by the numerical resolution. Models in which alpha is a function of the l ocal aspect ratio h/r can produce robustly exponential decays as obser ved if alpha proportional to (h/r)(n), where n = 1.5. This critical va lue for n is independent of the primary mass, unlike the critical epsi lon value in the r(epsilon) scaling. Numerically, we find that the tra nsition 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 earl ier papers were probably severely compromised by grid spacing limitati ons. Finally, for models in which the decay is produced by accretion o nto the central object rather than by the action of a cooling front, w e require n = -2 for exponential decays.