Quadrupole Moments of Rotating Neutron Stars

Numerical models of rotating neutron stars are constructed for four equations of state using the computer code RNS written by Stergioulas. For each equation of state the star's angular momentum is varied from J=0 to the Keplerian limit J=J_{max}, but the gravitational mass is kept fixed to 1.4 solar masses. For each neutron-star configuration we compute Q, the quadrupole moment of the mass distribution. We show that for a given value of J, |Q| increases with the stiffness of the equation of state. For a given equation of state, the dependence on J is well reproduced with a simple quadratic fit, Q \\simeq - aJ^2/M c^2, where c is the speed of light, and a is a parameter of order unity depending on the equation of state.

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