THE SPEED OF COOLING FRONTS AND THE FUNCTIONAL FORM OF THE DIMENSIONLESS VISCOSITY IN ACCRETION DISKS

We examine the speed of inward-traveling cooling fronts in accretion d isks. We show that their speed is determined by the rarefaction wave t hat precedes them and is approximately alpha(F)c(F)(H/r)(q), where <al pha(F) is the dimensionless viscosity, c(F) is the sound speed, r is t he radial coordinate, H is the disk thickness, and all quantities are evaluated at the cooling front. The scaling exponent q lies in the int erval [0, 1], depending on the slope of the (T, Sigma) relation in the hot state. For a Kramer's law opacity and alpha proportional to (H/r) (n), where n is of order unity, we find that q similar to 1/2. This su pports the numerical work of Cannizzo, Chen, & Livio and their conclus ion that n approximate to 3/2 is necessary to reproduce the exponentia l decay of luminosity in black hole X-ray binary systems. Our results are insensitive to the structure of the disk outside of the radius whe re rapid cooling sets in. In particular, the width of the rapid coolin g zone is a consequence of the cooling front speed rather than its cau se. We conclude that the exponential luminosity decay of cooling disks is probably compatible with the wave-driven dynamo model. It is not c ompatible with models with separate, constant values of alpha for the hot and cold states.