Magnetized Proto-Neutron Stars: Structure and Stability

We investigate the evolution of magnetized protoneutron stars (PNSs) through four schematic stages: neutrino trapped, deleptonization, neutrino transparent, and the final cold, catalyzed neutron star (NS). Using a quasi static approximation on the Kelvin Helmholtz timescale, we construct strongly magnetized configurations (magnetic field strengths up to 1e17 G) with the axisymmetric XNS 4.0 code, employing equations of state derived from relativistic mean field theory calibrated with the DDME2 parameter set. We analyze the evolution of the gravitational mass, equatorial radius, stellar deformation, magnetic flux, and the ratio of magnetic to gravitational binding energy as functions of thermodynamic and compositional changes. We find that increasing entropy per baryon and decreasing lepton fraction lead to higher core temperatures, which enhance magnetic deformation, flux confinement, and the magnetic to binding energy ratio. Magnetic field dissipation is most efficient during the deleptonization and neutrino transparent stages, and this process largely determines the observable magnetic field strength of the mature neutron star. This work provides the first general relativistic characterization of how the thermal and compositional evolution of protoneutron stars reshapes magnetic field deformation and energetics across poloidal, toroidal, and mixed field configurations at fixed baryonic mass.