Spin-Up of Hot Neutron Stars Just Born by the Subsequent Cooling

Abstract

A neutron star is formed in the central part of the collapsing supernova core as a result of the bounce and the successful explosion. The proto-neutron star at the bounce is expected to go very soon into the quasi hydrostatic stage; for example, its rapid contraction terminates within the first (0.1''-'1) sec after the bounce. l ) Here­ after we define a hot neutron star just born at this stage. In our preceding paper/) we showed that a neutron star at the birth have a fat density profile; relatively lower central density and larger radius, which originates from the stiffened equation of state (EOS) of supernova matter due to high lepton fraction and high temperature. Such a hot and fat neutron star, however, is cooled down by the diffusion of neutrinos and undergoes a gradual contraction in a time scale of (10~20) sec toward a usual cold neutron star. Then there arises a question to what extent the spin-up of hot neutron stars is possible in this subsequent cooling stage. The purpose of the present paper is to discuss this point, assuming the conservation o~ total angular momentum. We also discuss the case where cooled neutron stars contain pion condensation. For our purpose, it is indispensable to derive the EOS of supernova matter relevant to neutron stars at the birth era. Equation of state for hot neutron stars Supernova matter is characterized by almost constant entropy (estimated as S~ (1.0 ~ 1.5) per baryon)3) and also high and almost constant lepton fraction ( Yl ~ (0.3 ~ 004))3),4) throughout the density p. These are caused by the important effect of neutrino trapping 5 ),6) and are in contrast with. neutron star matter responsible for