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_⊙) ^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 f_K(M) holds within a few percent for neutron stars with realistic EOSs, provided 0.5 M_⊙ < 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_⊙ < 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_⊙ < 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) = α R(M), with α_NS ≈ a_ss ≈ 1.44. The value of α_ss is very weakly dependent on the mass of the crust of the strange star. Both α values are smaller than the analytic value α_Roche =1.5 from the relativistic Roche model.