Keplerian frequency of uniformly rotating neutron stars and strange stars

Aims. 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, f(K), proposed by Lattimer & Prakash, f(K)(M) = C (M/M-circle dot)(1/2)(R/10 km)(-3/2), where M is the (gravitational) mass of the 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 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. 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-circle dot < M < 0.9 M-max(stat), where M-max(stat) is the maximum allowable mass of non-rotating neutron stars for an EOS, and C = C-NS = 1.08 kHz. Similar precision is obtained for strange stars with 0.5 M-circle dot < M < 0.9 M-max(stat). For maximal crust masses we obtain C-SS = 1.15 kHz, and the value of C-SS is not very sensitive to the crust mass. All our Cs are significantly larger than the analytic value from the relativistic Roche model, C-Roche = 1.00 kHz. For 0.5 M-circle dot < M < 0.9 M-max(stat), the equatorial radius of the Keplerian configuration of mass M, R-K(M), is, to a very good approximation, proportional to the radius of the non-rotating star of the same mass, R-K(M) = a R(M), with a(NS) approximate to a(SS) approximate to 1.44. The value of a(SS) is very weakly dependent on the mass of the crust of the strange star. Both a values are smaller than the analytic value a(Roche) = 1.5 from the relativistic Roche model.