Upper limit of the angular velocity of neutron stars

The maximum angular velocity of uniformly rotating neutron stars is investigated. If we consider a hot neutron star stage after its birth from supernova explosions, an upper limit of the angular velocity for uniformly rotating neutron stars becomes a little smaller than that obtained by the equation of state for cold neutron matter. Since the equatorial radius of hot neutron stars becomes large, the angular velocity for such configurations cannot become so large. Therefore the hot neutron star stage sets the limit to the angular velocity of uniformly rotating cold neutron stars if we consider an evolution without losing the angular momentum during the cooling stage. We have studied cold and hot neutron stars whose temperature ranges from 0.75 MeV to 9 MeV. We assume hot neutron stars to be isothermal and in hydrostatic equilibrium. Using some equations of state of the hot neutron gas and the two-dimensional numerical code to get equilibrium structures of rapidly rotating relativistic stars, we have solved sequences of rotating neutron stars up to the mass-shedding state. For hot neutron stars of temperature of 9 MeV with a very soft equation of state, we get a stable model in a critical state with the angular velocity of 8.0 × 10³ s^-1, which corresponds to a neutron star with a rotational period of 0.8 ms and a gravitational mass of 1.6 M_⊙. If this neutron star cools down to a cold neutron star of 0.75 MeV without losing its angular momentum, the angular velocity becomes 7.0 × 10³ s^-1. It corresponds to the rotational period of 0.9 ms. We conclude that 1 ms is a rough lower limit of the rotational period of neutron stars born from the explosion of massive stars (M > 10 M_⊙).