Figure 5
Figure 5: Top: Fitting curves (solid curve) and numerical results (points) of the universal I-Love (left) and Q-Love (right) relations for various equations of state, normalized as I¯= I ∕M 3NS, ¯λ (tid) = λ(tid)∕M 5NS and Q¯ = − Q(rot)∕[M 3NS(S∕M N2S )2], MNS is the neutron-star mass, λ(tid) is the tidal Love number, Q(rot) is the rotation-induced quadrupole moment, and S is the magnitude of the neutron-star spin angular momentum. The neutron-star central density is the parameter varied along each curve, or equivalently the neutron-star compactness. The top axis shows the neutron star mass for the APR equation of state, with the vertical dashed line showing MNS = 1M ⊙. Bottom: Relative fractional errors between the fitting curve and the numerical results. Observe that these relations are essentially independent of the equation of state, with loss of universality at the 1% level. Image reproduced by permission from [452], copyright by APS.