Estimates of the maximum angular velocity of rotating neutron stars

The instabilities that limit the rotation rate of neutron stars are driven by gravitational radiation reaction and moderated by viscosity. This paper estimates the angular velocities where these instabilities set in. These estimates improve on previous work in two ways: (1) by approximating the influence of the dissipative mechanisms on the locations of the critical angular velocities, and (2) by using fully relativistic calculations of some of the relevant frequencies and time scales. This analysis indicates that the influence of gravitational radiation is somewhat greater than had been anticipated in earlier work, and as a result that an m = 4 or 5 (rather than m = 3 or 4) instability is probably responsible for limiting the angular velocity of rapidly rotating neutron stars. The minimum rotation periods are computed here for a sample of eight different equations of state for the nuclear matter, for a range of different viscosities, and for the allowed range of neutron star masses. These calculations show that the critical rotation periods are very insensitive to the value of the viscosity but depend stronly on the equation of state of the nuclear matter and on the mass of the neutron star.