THE STRUCTURE OF COOLING FRONTS IN ACCRETION DISKS

Recent work has shown that the speed of the cooling front in soft X-ra y transients may be an important clue in understanding the nature of a ccretion disk viscosity. In a previous paper (Vishniac & Wheeler), we derived the scaling law for the cooling front speed. Here we derive a similarity solution for the hot inner part of disks undergoing cooling . This solution is exact in the limit of a thin disk, power-law opacit ies, and a minimum hot state column density, which is an infinitesimal fraction of the maximum cold state density. For a disk of finite thic kness, the largest error is in the ratio of the mass how across the co oling front to the mass how at small radii. Comparison to the numerica l simulations of Cannizzo et al. indicates that the errors in other pa rameters do not exceed (c(sF)/r(F) Omega(F))(q), that is, the ratio of the sound speed at the disk midplane to its orbital velocity, evaluat ed at the cooling front, to the qth power. Here q approximate to 1/2. Its precise value is determined by the relevant hot state opacity law and the functional form of the dimensionless viscosity.