Keplerian frequency of uniformly rotating neutron stars and strange stars

Abstract

<i>Aims. <i/>We calculate Keplerian (mass shedding) configurations of rigidly rotating neutron stars and strange stars with crusts. We check the validity of the empirical formula for Keplerian frequency, <i>f<i/><sub>K<sub/>, proposed by Lattimer & Prakash, , where <i>M<i/> is the (gravitational) mass of the Keplerian configuration, <i>R<i/> is the (circumferential) radius of the non-rotating configuration of the same gravitational mass, and kHz.<i>Methods. <i/>Numerical calculations are performed using precise 2D codes based on the multi-domain spectral methods. We use a representative set of equations of state (EOSs) of neutron stars and quark stars.<i>Results. <i/>We show that the empirical formula for holds within a few percent for neutron stars with realistic EOSs, provided , where is the maximum allowable mass of non-rotating neutron stars for an EOS, and kHz. Similar precision is obtained for strange stars with . For maximal crust masses we obtain kHz, and the value of <i>C<i/><sub>SS<sub/> is not very sensitive to the crust mass. All our <i>C<i/>s are significantly larger than the analytic value from the relativistic Roche model, kHz. For , the equatorial radius of the Keplerian configuration of mass <i>M<i/>, , is, to a very good approximation, proportional to the radius of the non-rotating star of the same mass, , with . The value of <i>a<i/><sub>SS<sub/> is very weakly dependent on the mass of the crust of the strange star. Both <i>a<i/> values are smaller than the analytic value from the relativistic Roche model.