 Cooling-controlled planetary envelope growth

Gravitational binding is necessary but not sufficient for gas capture. A hydrostatic envelope contracts by losing energy on a Kelvin-Helmholtz scale $t_{\mathrm{KH}}\sim |E|/L$. Solid accretion heats it, while radiative transport depends on opacity and convection carries energy when the radiative gradient is unstable. The disk supply and outer tidal/thermal boundaries also matter.