RAPID UNIFORM ROTATION OF PROTONEUTRON STARS

Rapid uniform rotation of newborn neutron stars (protoneutron stars) i s studied for a range of internal temperatures and entropies per baryo n predicted by the existing numerical simulations. Calculations are pe rformed using general relativistic equations of hydrostatic equilibriu m of rotating, axially symmetric stars. Stability of rotating configur ations with respect to mass shedding and the axially symmetric perturb ations is studied. Numerical calculations are performed for a realisti c dense matter equation of state, under various assumptions concerning neutron star interior (large trapped lepton number, no trapped lepton number, isentropic, isothermal). For configurations with baryon mass well below the maximum one for the non-rotating models, the mass shedd ing limit depends quite sensitively on the position of the ''neutrinos phere'' (which has a deformed, spheroidal shape); this dependence weak ens with increasing baryon mass. The absolute upper limit on rotation frequency is, to a good approximation. obtained for the maximum baryon mass of rotating configurations. Empirical formula for the maximum ro tation frequency of uniformly rotating protoneutron stars is shown to be quite precise; it actually coincides with that used for cold neutro n stars. Evolutionary sequences at fixed baryon mass and angular momen tum, which correspond to evolution of protoneutron stars into cold neu tron stars are studied, and resulting constraints on the maximum rotat ion frequency of solitary pulsars are discussed.