  We consider a 3D quantum system of $N$ identical bosons in a trapping
potential $|x|^p$, with $p\geq0$, interacting via a Newton potential with an
attractive interaction strength $a_{N}$. For a fixed large $N$ and the coupling
constant $a_{N}$ smaller than a critical value $a_{*}$ (Chandrasekhar limit
mass), in an appropriate sense, the many-body system admits a ground state. We
investigate the blow-up behavior of the ground state energy as well as the
ground states when $a_{N}$ approaches $a_{*}$ sufficiently slowly in the limit
$N\to\infty$. The blow-up profile is given by the Gagliardo-Nirenberg
solutions.
