Tidal Deformability and Electromagnetic Love Numbers of Magnetars

Finite-size effects, such as the tidal deformability of stellar bodies, are an excellent avenue to expand our understanding of both gravitational and nuclear physics. Information about the internal physics of stars is imprinted in gravitational wave signals, and knowledge about tidal effects is crucial for such studies. Perturbative models of neutron stars with electromagnetic fields, motivated by magnetars, have been extensively studied without tidal interactions. Thus, studying how these electromagnetic fields interact with tidal fields is worthwhile. We build on recent work that constructed a perturbative model of magnetized, tidally-deformed neutron stars by considering perturbations to the Maxwell field due to tidal interactions. We also extend the model by adding slow-rotation perturbations, which induce an electric field. This allows us to find modifications to the gravitational Love number of the star as well as a new electromagnetic field Love number. Both Love numbers vanish for Reissner-Nordström black holes, but the presence of matter in the neutron star case leads to interesting non-trivial results. These interactions between the tidal and electromagnetic fields can lead to measurable effects in double magnetar systems that may be observed using gravitational waves.