Universality of the Acceleration Due to Gravity on the Surface of a Rapidly Rotating Neutron Star

Abstract

On the surface of a rapidly rotating neutron star, the effective centrifugal force decreases the effective acceleration due to gravity (as measured in the rotating frame) at the equator while increasing the acceleration at the poles due to the centrifugal flattening of the star into an oblate spheroid. We compute the effective gravitational acceleration for relativistic rapidly rotating neutron stars and show that for a star with mass $M$, equatorial radius $R_e$, and angular velocity $\Omega$, the deviations of the effective acceleration due to gravity from the nonrotating case take on a universal form that depends only on the compactness ratio $M/R_e$, the dimensionless square of the angular velocity $\Omega^2R_e^3/GM$, and the latitude on the star's surface. This dependence is universal, in that it has very little dependence on the neutron star's equation of state. The effective gravity is expanded in the slow rotation limit to show the dependence on the effective centrifugal force, oblate shape of the star and the quadrupole moment of the gravitational field. In addition, an empirical fit and simple formula for the effective gravity is found. We find that the increase in the acceleration due to gravity at the poles is of the same order of magnitude as the decrease in the effective acceleration due to gravity at the equator for all realistic value of mass, radius and spin. For neutron stars that spin with frequencies near 600 Hz the difference between the effective gravity at the poles and the equator is about 20%.