Implications of a Fast Pulsar for the Equation of State

The recent observation of a sub-millisecond pulsar 1] in the remnant of SN1987A with period P = 0:508 ms is very exciting because the possibility exists of pinning down the equation of state (EOS) of supra-nuclear density matter, if the pulsations are due to rotation. The neutrinos detected by Kamioka 2] and IMB, 3], although basically connrming the standard theoretical models of neutron star birth, did not give an accurate enough estimate of the neutron star's binding energy or mass to constrain the EOS. The maximum rotation rate of a star must be less than or equal to the Keplerian rate, K , at which the equatorial surface velocity equals the orbital velocity of a particle at the equator. Recent general relativistic instability analyses 4] demonstrate that the maximum rotation rate cannot be less than about 0:99 K. If there exist physical mechanisms for increasing the neutrino uxes of young neutron stars, such as quarks or meson condensates, the maximum rotation rate becomes nearly equal to K. In general, K is larger for more compact neutron stars with higher central densities. Thus, the maximum rotation rate is an increasing function of the \softness" of the EOS. The observed period of 0.508 ms, if due to rotation, sets one limit to the EOS. In addition, the masses (1.44 M and 1.38 M) of the components of the binary pulsar PSR 1913+16 5] set a lower limit to the maximum mass of a neutron star. The maximum mass is a decreasing function of the \softness" of the EOS, and therefore establishes a second constraint. These two constraints will restrict the EOS to lie in a narrow range. The calculations of the maximum rotation rate and the maximum mass permitted by a given EOS has to be done with full general relativity. It has been shown, however, that an approximate formula 6] for the Keplerianrotation rate in terms of the maximum mass properties of the non-rotating star is extremely accurate 7]. It is The subscripts \max" refer to the maximum mass non-rotating star of a given equation of state. This formula is, in fact, accurate to within 4% for all equations of state we have tested, except that of a completely incompressible uid (for which the coeecient 7.7 is 9.6). In addition, the general relativistic calculations of Friedman, Ipser and Parker 8] follow this formula to within the same accuracy. The challenge for …