A Necessary Condition for the Submergence of Proto–Neutron Star Magnetic Fields by Supernova Fallback

Central compact objects (CCOs) are a subclass of neutron stars (NSs) with a dipole magnetic field strength considerably weaker than those of radio pulsars and magnetars. One possible explanation for such weak magnetic fields in the CCOs is the hidden magnetic field scenario, in which supernova fallback submerges the magnetosphere of a proto-NS (PNS) beneath a newly formed crust. However, the fallback mass and timescale required for this submergence process remain uncertain. We perform one-dimensional general relativistic magnetohydrodynamic simulations of the supernova fallback onto a magnetized PNS, while considering neutrino cooling. In our simulations, the infalling material compresses the magnetic field and drives a strong shock. The shock initially expands outward, but eventually stalls and recedes as neutrino cooling becomes significant. After the shock stalls, the gas density above the magnetosphere increases rapidly, potentially leading to the formation of a new crust. To understand the shock dynamics, we develop semianalytic models that describe the resulting magnetospheric and shock radii when the shock stalls. By comparing the fallback timescale with the shock stalling timescale, corresponding to the waiting time for the new crust formation, we derive a necessary condition for the submergence of the PNS's magnetic field. Our results will provide guidance for investigating the diversity of young isolated NSs through multidimensional simulations.