Tidal deformability and gravitational-wave phase evolution of magnetised compact-star binaries

The evolution of the gravitational-wave phase in the signal produced by inspiralling binaries of compact stars is modified by the nonzero deformability of the two stars. Hence, the measurement of these corrections has the potential of providing important information on the equation of state of nuclear matter. Extensive work has been carried out over the last decade to quantify these corrections, but it has so far been restricted to stars with zero intrinsic magnetic fields. While the corrections introduced by the magnetic tension and magnetic pressure are expected to be subdominant, it is nevertheless useful to determine the precise conditions under which these corrections become important. To address this question, we have carried out a second-order perturbative analysis of the tidal deformability of magnetised compact stars under a variety of magnetic-field strengths and equations of state describing either neutron stars or quark stars. Overall, we find that magnetically induced corrections to the tidal deformability will produce changes in the gravitational-wave phase evolution that are unlikely to be detected for realistic magnetic field i.e., $B\sim 10^{10} - 10^{12}\,{\rm G}$. At the same time, if the magnetic field is unrealistically large, i.e., $B\sim 10^{16}\,{\rm G}$, these corrections would produce a sizeable contribution to the phase evolution, especially for quark stars. In the latter case, the induced phase differences would represent a unique tool to measure the properties of the magnetic fields, providing information that is otherwise hard to quantify.