Pressure-truncated singular isothermal gas sphere
= Pressure-truncated singular isothermal gas sphere
For $p=a_T^2\rho$, spherical <hydrostatic equilibrium> admits $\rho=a_T^2/(2\pi Gr^2)$ with $M(r)=2a_T^2r/G$. Matching an external <pressure> $p_0$ fixes $r_s=a_T^2/\sqrt{2\pi Gp_0}$. The central <density> is singular although the enclosed <mass> tends to zero; this is one branch, not every finite-centred isothermal cloud.