Radial stability of a uniform-density star
= Radial stability of a uniform-density star
For the even polynomial family of degree $n\geq2$, the physical radial squared frequency is $[\gamma n(n+1)/2-4]\omega_d^2$. The fundamental $n=2$ mode is stable when $\gamma>4/3$ and marginal at $\gamma=4/3$. At angular degree zero the gradient of the <regular solid harmonic> vanishes, so the auxiliary displacement amplitude multiplying it is redundant.