# Extended I-Love relations for slowly rotating neutron stars

### Abstract

Observations of gravitational waves from inspiralling neutron star binaries—such as GW170817—can be used to constrain the nuclear equation of state by placing bounds on stellar tidal deformability. For slowly rotating neutron stars, the response to a weak quadrupolar tidal field is characterized by four internal-structure-dependent constants called “Love numbers”. The tidal Love numbers $k_2^\text{el}$ and $k_2^\text{mag}$ measure the tides raised by the gravitoelectric and gravitomagnetic components of the applied field, and the \emph{rotational-tidal} Love numbers $\mathfrak{f}^\text{o}$ and $\mathfrak{k}^\text{o}$ measure those raised by couplings between the applied field and the neutron star spin. In this work we compute these four Love numbers for perfect fluid neutron stars with realistic equations of state. We discover (nearly) equation-of-state independent relations between the rotational-tidal Love numbers and the moment of inertia, thereby extending the scope of $I$-Love-$Q$ universality. We find that similar relations hold among the tidal and rotational-tidal Love numbers. These relations extend the applications of $I$-Love universality in gravitational-wave astronomy. As our findings differ from those reported in the literature, we derive general formulas for the rotational-tidal Love numbers in post-Newtonian theory and confirm numerically that they agree with our general-relativistic computations in the weak-field limit.

Publication
Phys. Rev. D 97, 064042
##### Stephen R. Green
###### Nottingham Research Fellow

I am a theoretical physicist studying gravitational waves, based at the University of Nottingham. My main interests are in black hole perturbation theory and applying probabilistic machine-learning methods to analyze LIGO data.