1998A&A...330.1005G

Models of differentially rotating protoneutron stars are calculated, using realistic equations of state of dense hot matter. Various conditions within the stellar interior, corresponding to different stages of protoneutron star evolution, are considered. Numerical calculations are performed within the approximation of stationary equilibrium, using general relativistic equations of stationary motion of differentially rotating, axially symmetric stars and using a numerical code based on spectral methods. Families of differentially rotating models of a given baryon mass are calculated, using a two-parameter formula describing the angular velocity profile within a rotating protoneutron star. Apart from the usual ``mass shedding limit'', we introduce an additional ``minimal mass limit'' for differentially rotating protoneutron stars resulting from a type II supernovae. Maximum angular momentum, which can be accommodated by a protoneutron star within these limits is calculated, for various thermal conditions in stellar interior, for a baryon mass of 1.5M_☉. In the case of a thermally homogeneous (isentropic or isothermal) neutrino-opaque interior this maximum angular momentum turns out to be somewhat higher than that of a cold neutron star of the same baryon mass, rotating uniformly at the mass shedding angular velocity. However, if the protoneutron star has a thermal structure characteristic of initial state, with a low entropy (unshocked) core, and a high entropy (shocked) outer half of baryon mass, the maximum angular momentum is significantly lower. This leads to a minimum period of uniform rotation of cold neutron stars of baryon mass ∼1.5M_☉, formed directly (i.e. without a subsequent significant accretion of mass) from protoneutron stars with shocked envelope, of about 1.7ms and strengthens the hypothesis that millisecond pulsars are accretion accelerated neutron stars.