High-Order Multipole and Binary Love Number Universal Relations

Daniel A. Godzieba, David Radice.


Using a data set of approximately 2 million phenomenological equations of state consistent with observational constraints, we construct new equation-of-state-insensitive universal relations that exist between the multipolar tidal deformability parameters of neutron stars, \Lambda_l, for several high-order multipoles (l = 5,6,7,8). We confirm the existence of a universal relation between the radius of the 1.4 M_\odot NS, R_{1.4} and the reduced tidal parameter of the binary, \tilde{\Lambda}, and the chirp mass. We extend this relation to a large number of chirp masses and to the radii of isolated NSs of different mass M, R_M. We find that there is an optimal value of M for every \mathcal{M} such that the uncertainty in the estimate of R_M is minimized when using the relation. We discuss the utility and implications of these relations for the upcoming LIGO O4 run and third-generation detectors.