Polytrope of index zero
= Polytrope of index zero
{title2=$\theta(\xi)=1-\xi^2/6$}
The regular $n=0$ solution of the <Lane-Emden equation> is $\theta=1-\xi^2/6$, with first zero $\sqrt6$. Its interior density is constant and its pressure varies as $\theta$. This is the structural incompressible limit; $P=K\rho^{1+1/n}$ itself is singular at $n=0$, and does not assign the perturbative <stellar adiabatic exponent> of a thermally stratified ideal-gas model.