= Isothermal transonic accretion in the Paczyński-Wiita potential
{title2=$r_c=\frac{GM}{4c_s^2}(1+\beta/2+\sqrt{1+\beta})$}
For $\beta=16c_s^2/c^2$, the exterior <sonic point> of the <barotropic spherical accretion equation> lies outside $r_G=2GM/c^2$. Its <mass density> is $\rho_c=\rho_\infty\exp[4/(1+\sqrt{1+\beta})-1/2]$. The selected smooth transonic accretion rate is $4\pi r_c^2\rho_cc_s$. Subsonic formal solutions are not assigned this rate without transonic selection.
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