Inside-out collapse of a singular isothermal sphere
= Inside-out collapse of a singular isothermal sphere
A collapse front propagates out through an initially singular isothermal envelope at $r_f=a_Tt$. The only steady accretion scale is $\dot M\propto a_T^3/G\propto T^{3/2}$ for fixed mean particle <mass>. The front sweeps original <mass> at $2a_T^3/G$, but the exact central accretion coefficient requires the dynamical similarity solution and cannot be identified with front sweeping alone.