Transonic spherical flow in a power-law potential
= Transonic spherical flow in a power-law potential
A smooth <transonic branch> in a <power-law gravitational potential> has $u_*^2=c_*^2=A\beta/(2r_*^\beta)$ at its <sonic point>. Substitution into the <Bernoulli function> gives $\mathcal B=c_*^2[1/(\gamma-1)+1/2-2/\beta]$. The local <sonic-point slope discriminant> distinguishes a genuine crossing from a degenerate everywhere-sonic scaling solution.