The Structure of Cooling Fronts in Accretion Disks

Recent work has shown that the speed of the cooling front in soft X-raytransients may be an important clue in understanding the nature of accretiondisk viscosity. In a previous paper (Vishniac and Wheeler 1996) we derived thescaling law for the cooling front speed. Here we derive a similarity solutionfor the hot inner part of disks undergoing cooling. This solution is exact inthe limit of a thin disk, power law opacities, and a minimum hot state columndensity which is an infinitesimal fraction of the maximum cold state density.For a disk of finite thickness the largest error is in the ratio of the massflow across the cooling front to the mass flow at small radii. Comparison tothe numerical simulations of Cannizzo et al. (1995) inidcates that the errorsin the other parameters do not exceed $(c_{sF}/r_F\Omega_F)^q$, that is, theratio of the sound speed at the disk midplane to its orbital velocity,evaluated at the cooling front, to the qth power. Here $q\approx 1/2$. Itsprecise value is determined by the relevant hot state opacity law and thefunctional form of the dimensionless viscosity.Comment: 13 pages, 1 figure, Astrophysical Journal (in press