Radial pulsations and stability of protoneutron stars

Radial pulsations of newborn neutron stars (protoneutron stars) are studied for a range of internal temperatures and entropies per baryon predicted by the existing numerical simulations. Protoneutron star models are constructed using a realistic equation of state of hot dense matter, and under various assumptions concerning stellar interior (large trapped lepton number, zero trapped lepton number, isentropic, isothermal). Under prevailing conditions, linear oscillations of a protoneutron star can be treated as adiabatic, and evolutionary effects can be neglected on dynamic timescale. The dynamic behavior is governed by the adiabatic index, which in turn depends on the physical state of the stellar interior. The eigenfrequencies of the lowest radial modes of linear, adiabatic pulsations are calculated. Stability of protoneutron stars with respect to small radial perturbations is studied, and the validity of the static stability criteria is discussed.