Critical adiabatic exponent for spherical power-law flow
= Critical adiabatic exponent for spherical power-law flow
{title2=$\gamma_{\rm crit}=(4+\beta)/(4-\beta)\quad(0<\beta<4)$}
For $0<\beta<4$, a nondegenerate <transonic spherical flow in a power-law potential> connected to infinity requires $\gamma<(4+\beta)/(4-\beta)$. For $\beta\geq4$, every finite $\gamma>1$ satisfies the local crossing condition; there is no finite upper bound. The uniformly valid inequality is $2\beta-(4-\beta)(\gamma-1)>0$.