A key factor to the spin parameter of uniformly rotating compact stars: crust structure

We study the key factor to determine the dimensionless spin parameter $j\equiv cJ/(GM^2)$ of different kinds of uniformly rotating compact stars, including the traditional neutron stars, hyperonic neutron stars, and hybrid stars, and check the reliability of the results on various types of equations of state of dense matter. The equations of state from the relativistic mean field theory and the MIT bag model are adopted to simulate compact stars. Numerical calculations of rigidly rotating neutron stars are performed using the RNS code in the framework of general relativity by solving the Einstein equations for stationary axis-symmetric spacetime. The crust structure of compact stars is found to be a key factor to determine the maximum value of the spin parameter $j_{\rm max}$. For the stars with inclusion of the crust, $j_{\rm max}\sim 0.7$ is sustained for various kinds of compact stars with $M>0.5 M_{\odot}$, and is found to be insensitive to the mass of star and selected equations of state. For the traditional neutron stars, hyperonic neutron stars and hybrid stars without crust structure, the value $j_{\rm max}$ lies in the range of $[0.7, 1.0]$. Thus, not $j>0.7$ but $j>1$ could be treated as the candidate criterion to distinguish the strange quark stars from the other kinds of compact stars. Furthermore, a universal formula $j=0.48(f/f_K)^3-0.42(f/f_K)^2+0.63(f/f_K)$ is suggested to calculate the spin parameter at any rotational frequency for all kinds of compact stars with crust structure and $M>0.5M_{\odot}$.