Simple Calculation of Critical Parameters of Neutron Stars

The instability of neutron stars comes about because of the softening of the equation of state for densities p (1-4) x 1015 g cm -3. For soft equations of state, such as the independent- particle model, this happens when y(p) = pdP/Pdp falls below yca 4/3, the critical value in Newtonian gravitational theory: the equation of state softens where the neutrons become special- relativistic. For stiffer equations of state, general relativity leads to instability at ca values somewhat greater than 4/3; nevertheless, the softening of the equation of state, for causality reasons or otherwise, is what brings y(p) down below yca. Particularly for relatively stiff equations of state, once y(p) is approximately known in the region of densities about p 1015 g , the relativistic polytrope model considered in the preceding paper permits a quick slide-rule estimate of the mass and of the radius and critical density to an accuracy of about 5-10 and 10-20 percent respectively. Subject headings: equation of state - interiors, stellar - neutron stars - relativity