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Properties of non-rotating and rapidly rotating protoneutron stars

Properties of non-rotating and rapidly rotating protoneutron stars and neutron stars are investigated. Protoneutron stars are hot, lepton rich neutron stars which are formed in Type-II supernovae. The hot dense matter is described by a realistic equation of state which is obtained by extending a recent approach of Myers and Swiatecki to the nuclear mass formula. We investigate the properties of protoneutron stars and neutron stars at different evolutionary stages in order to emphasize the differences between very young and old neutron stars. The numerical calculations are performed by means of an exact description of rapid, uniform rotation in the framework of general relativity. We show that the minimal marginally stable protoneutron star mass is much higher than the corresponding minimum mass of a cold neutron star. The minimum gravitational (baryonic) mass of 0.89 - 1.13 M_{\sun} (0.95 - 1.29 M_{\sun}) of a neutron star is therefore determined at the earliest stages of its evolution. We also show that the use of different temperature profiles in the envelope as well as different shapes of the neutrino sphere change the properties of protoneutron stars and hot neutron stars by up to 20 %. A preliminary analysis indicates that even the most massive protoneutron stars rotating with Kepler frequency are secularly stable. Under the assumption of conserved angular momentum and baryonic mass, the maximum rotational frequency of an evolved neutron star is determined by the Kepler frequency of the protoneutron star. We can thus derive a lower limit, P_min ~ 1.56 - 2.22 ms, to the rotational period of young neutron stars with a canonical gravitational mass of 1.35 M_{\sun}. This result furtherly supports the assumption that millisecond pulsars are accelerated due to accretion onto a cold neutron star.