  We study the Chandrasekhar variational model for neutron stars, with or
without an external potential. We prove the existence of minimizers when the
attractive interaction strength $\tau$ is strictly smaller than the
Chandrasekhar limit $\tau_c$ and investigate the blow-up phenomenon in the
limit $\tau\uparrow \tau_{c}$. We show that the blow-up profile of the
minimizer(s) is given by the Lane-Emden solution.
