Gravitational signals emitted by a point mass orbiting a neutron star: A perturbative approach

We compute the energy spectra of the gravitational signals emitted when a pointlike mass moves on a closed orbit around a nonrotating neutron star, inducing a perturbation of its gravitational field and its internal structure. The Einstein equations and the hydrodynamical equations are perturbed and numerically integrated in the frequency domain. The results are compared with the energy spectra computed by the quadrupole formalism which assumes that both masses are pointlike, and accounts only for the radiation emitted because the orbital motion produces a time dependent quadrupole moment. The results of our perturbative approach show that, in general, the quadrupole formalism overestimates the amount of emitted radiation, especially when the two masses are close. However, if the pointlike mass is allowed to move on an orbit so tight that the Keplerian orbital frequency resonates with the frequency of the fundamental quasinormal mode of the star $(2\mathrm{}{\omega }_K={\omega }_f),$ this mode can be excited and the emitted radiation can be considerably larger than that computed by the quadrupole approach.