The Gravitational Radius of an Irradiated Disk

Abstract

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_o)/(T₀/10⁴ K) AU. The value of 1.4 AU 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.