Keplerian frequency of uniformly rotating neutron stars and quark stars

Aims. We calculate Keplerian (mass shedding) configurations of rigidly rotating neutron stars and quark stars with crusts. We check the validity of empirical formula for Keplerian frequency, fK, proposed by Lattimer & Prakash, fK(M) = C (M/M⊙) (R/10 km) , where M is the (gravitational) mass of Keplerian configuration, R is the (circumferential) radius of the non-rotating configuration of the same gravitational mass, and C = 1.04 kHz. Methods. Numerical calculations are performed using precise 2-D codes based on the multi-domain spectral methods. We use a representative set of equations of state (EOSs) of neutron stars and quark stars. Results. We show that the empirical formula for fK(M) holds within a few percent for neutron stars with realistic EOSs, provided 0.5 M⊙ < M < 0.9 M stat max, where M stat max is the maximum allowable mass of non-rotating neutron stars for an EOS, and C = CNS = 1.08 kHz. Similar precision is obtained for quark stars with 0.5 M⊙ < M < 0.9 M stat max. For maximal crust masses we obtain CQS = 1.15 kHz, and the value of CQS is not very sensitive to the crust mass. All our C’s are significantly larger than the analytic value from the relativistic Roche model, CRoche = 1.00 kHz. For 0.5 M⊙ < M < 0.9 M stat max, the equatorial radius of Keplerian configuration of mass M , RK(M), is, to a very good approximation, proportional to the radius of the non-rotating star of the same mass, RK(M) = a R(M), with aNS ≈ aQS ≈ 1.44. The value of aQS is very weakly dependent on the mass of the crust of the quark star. Both a’s are smaller than the analytic value aRoche = 1.5 from the relativistic Roche model.