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Let $M(r)$ be the enclosed mass. A spherical shell of thickness $dr$ has inward gravitational acceleration $GM(r)/r^2$, so hydrostatic equilibrium requiresWith $\rho =A{r}^{2}P$, these equations reduce toFor a regular central value $P(0)=P_c>0$, the first equation integrates toThe exponential function is strictly positive at every finite $r$, so the pressure and density cannot reach zero at a finite stellar surface. The equations may describe an atmosphere whose density decreases at large radius, but they admit no nontrivial hydrostatic star of finite radius. Therefore

With the travelling wave coordinate $\xi =x-ct$, the reaction–diffusion system becomesAt the advancing leading edge the healthy-tissue density is small. Put $f(\xi )\sim e^{-\lambda \xi }$ with $\lambda >0$. The linearization at $f=0$ givesso a nonoscillatory decaying front requires real positive roots,The pulled travelling front selects the Fisher-KPP minimum wave speed, and therefore

For the initial wound $0<x<W$, two mirror-image fronts enter from its endpoints. The left front moves right from $x=0$ and the right front moves left from $x=W$, each with speed approximately $c_{\min }$. A sequence of sketches would show the initial rectangular depression becoming two smooth monotone transition layers, the zero-density plateau shrinking, and the two layers meeting near $x=W/2$ before the profile relaxes to $S=1$. Their meeting time isThere is an additional local relaxation time of order $1/r$ if “close to one” is assigned a fixed numerical tolerance, so the displayed estimate is the dominant healing time when $W$ is large compared with the front width $\sqrt{D/r}$.