 Thermal timescale of an accretion disk

The thermal timescale compares the internal energy stored in a disc annulus with its local heating or cooling. In a gas-pressure-supported alpha disk, $t_{\mathrm{th}}\sim (\alpha {\Omega }_K{)}^{-1}$, whereas the viscous timescale is longer by approximately $(R/H{)}^2$. A local thermal perturbation is therefore studied at fixed surface density of a disk, rather than fixed steady-state mass accretion rate.