The Gravitational Radius of an Irradiated Disk

We derive an updated, analytic formula for the gravitational radius, r_g, of an irradiated, thin disk. For such a disk, the region outside the gravitational radius will produce a thermal wind, while the region interior to the gravitational radius will be stable. We find that r_g ~ 1.4 (M_*/M_solar)/(T₀/10⁴K)AU. The value of 1.4AU is approximately one fifth of currently used values. The analysis uses the adiabatic approximation. We argue that the same formula applies for the non-adiabatic, isothermal case.