Gravitational waves from a test particle scattered by a nuetron star : axial mode case
Abstract
Using a metric perturbation method, we study gravitational waves from a test particle scattered by a spherically symmetric relativistic star. We calculate the energy spectrum and the waveform of gravitational waves for axial modes. Since metric perturbations in axial modes do not couple to the matter fluid of the star, emitted waves for a normal neutron star show only one peak in the spectrum, which corresponds to the orbital frequency at the turning point, where the gravitational field is strongest. However, for a ultra compact star (the radius $R \lesssim 3M$), another types of resonant periodic peaks appear in the spectrum. This is just because of an excitation by a scattered particle of axial quasinormal modes, which are found by Chandrasekhar and Ferrari. This excitation comes from the existence of the potential minimum inside of a star. We also find for a ultra compact star many small periodic peaks at the frequency region beyond the maximum of the potential, which would be due to a resonance of two waves reflected by two potential barriers (Regge-Wheeler type and one at the center of the star). Such resonant peaks appear neither for a normal neutron star nor for a Schwarzschild black hole. Consequently, even if we analyze the energy spectrum of gravitational waves only for axial modes, it would be possible to distinguish between a ultra compact star and a normal neutron star (or a Schwarzschild black hole).Keywords
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