Blow-up Profile of Neutron Stars in the Chandrasekhar theory

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.