Gravitational waves from a test particle scattered by a neutron star: Axial mode case

TL;DR

This paper investigates gravitational waves emitted by a test particle scattered by a relativistic star, revealing unique spectral features for ultracompact stars that could help distinguish them from normal neutron stars or black holes.

Contribution

It demonstrates that axial mode gravitational wave spectra contain distinctive resonant peaks for ultracompact stars, enabling their identification through spectral analysis.

Findings

Ultracompact stars exhibit additional resonant peaks due to axial quasinormal mode excitation.

Normal neutron stars show only a single peak related to orbital frequency.

Spectral differences can distinguish ultracompact stars from black holes or normal neutron stars.

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 an ultracompact star (the radius $R \lesssim 3M$), another type of resonant periodic peak appears in the spectrum. This is just because of an excitation by a scattered particle of axial quasinormal modes, which were found by Chandrasekhar and Ferrari. This excitation comes from the existence of the potential minimum inside of a star. We also find for an ultracompact 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 an ultracompact star and a normal neutron star (or a Schwarzschild black hole).