The spin parameter of uniformly rotating compact stars

We study the dimensionless spin parameter $j (= c J/ (G M^2))$ of uniformly rotating neutron stars and quark stars in general relativity. We show numerically that the maximum value of the spin parameter of a neutron star rotating at the Keplerian frequency is $j_{\rm max} \sim 0.7$ for a wide class of realistic equations of state. This upper bound is insensitive to the mass of the neutron star if the mass of the star is larger than about $1 M_\odot$. On the other hand, the spin parameter of a quark star modeled by the MIT bag model can be larger than unity and does not have a universal upper bound. Its value also depends strongly on the bag constant and the mass of the star. Astrophysical implications of our finding will be discussed.