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Session 76 - Cataclysmic Variables and Accretion Disks.
Display session, Wednesday, January 15
We examine the speed of inward traveling cooling fronts in accretion disks and the structure of the hot phase of the disk inside the cooling front. We show that the cooling front speed is determined by the rarefaction wave that precedes it and is approximately \alpha_F c_F (H/r)^q, where \alpha_F is the dimensionless viscosity, c_F is the sound speed, r is the radial coordinate, H is the disk thickness, and all quantities are evaluated at the cooling front. The scaling exponent q lies in the interval [0,1], depending on the slope of the (T,\Sigma) relation in the hot state. For a Kramers law opacity and \alpha\propto (H/r)^n, where n is of order unity, we find that q\sim 1/2. In addition, we derive a similarity solution which is exact in the limit of a thin disk with power law opacities and allows us to predict the coefficient in the cooling front speed scaling law. Our results support the numerical work of Cannizzo, Chen, and Livio (1995) and their conclusion that n\approx 3/2 is necessary to reproduce the exponential decay of luminosity in black hole X-ray binary systems. Our results are insensitive to the structure of the disk outside the radius where rapid cooling sets in. In particular, the width of the rapid cooling zone is a consequence of the cooling front speed rather than its cause. This implies that our conclusions depend only on the structure of the hot phase of the disk, which is relatively well understood. We discuss the implications of this result for theoretical models of disk viscosity.
Program listing for Wednesday