Dynamical Analysis of the Structure of Neutron Star Critical Collapses

Jin et al reported that axisymmetric simulations of NS-like objects with polytropic EOS undergo critical gravitational collapse. As the critical collapse observed via fine-tuning of the adiabatic index $\mathrm{\Gamma }$, they conjecture that critical phenomena may occur in realistic astrophysical scenarios. To clarify the implications this numerical observation has on realistic astrophysical scenarios, here, we perform dynamical analysis on the structure of the critical collapse observed in the former work. We report the time scales and oscillation frequencies exhibited by the critical solution and compare these results with values obtained from analytic perturbative mode analysis of equilibrium TOV configurations. We also establish the universality of the critical solution with respect to a 1-parameter family of initial data as well as the phase space manifold of the critical collapse.