# High-Order Multipole and Binary Love Number Universal Relations

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Abstract

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, , for several high-order multipoles (). We confirm the existence of a universal relation between the radius of the NS, and the reduced tidal parameter of the binary, , 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 , . We find that there is an optimal value of for every such that the uncertainty in the estimate of 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.