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)=a R(M), with a_NS≈ a_SS ≈ 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.