Axisymmetric pulsations of rotating neutron stars can be excited in several scenarios, such as core collapse, crust‐ and core‐quakes or binary mergers, and could become detectable in either gravitational waves or high‐energy radiation. Here, we present a comprehensive study of all low‐order axisymmetric modes of uniformly and rapidly rotating relativistic stars. Initial stationary configurations are appropriately perturbed and are numerically evolved using an axisymmetric, non‐linear relativistic hydrodynamics code, assuming time‐independence of the gravitational field (Cowling approximation). The simulations are performed using a high‐resolution shock‐capturing finite‐difference scheme accurate enough to maintain the initial rotation law for a large number of rotational periods, even for stars at the mass‐shedding limit. Through Fourier transforms of the time evolution of selected fluid variables, we compute the frequencies of quasi‐radial and non‐radial modes with spherical harmonic indices l=0, 1, 2 and 3, for a sequence of rotating stars from the non‐rotating limit to the mass‐shedding limit. The frequencies of the axisymmetric modes are affected significantly by rotation only when the rotation rate exceeds about 50 per cent of the maximum allowed. As expected, at large rotation rates, apparent mode crossings between different modes appear. In addition to the above modes, several axisymmetric inertial modes are also excited in our numerical evolutions.
We study gravitational waves from a hierarchical three-body system up to first-order post-Newtonian approximation. Under certain conditions, the existence of a nearby third body can cause periodic exchange between eccentricity of an inner binary and relative inclination, known as Kozai-Lidov oscillations. We analyze features of the waveform from the inner binary system undergoing such oscillations. We find that variation caused due to the tertiary companion can be observed in the gravitational waveforms and energy spectra, which should be compared with those from isolated binaries and coplanar three-body system. The detections from future space-based interferometers will make possible the investigation of gravitational wave spectrum in mHz range and may fetch signals by sources addressed.
We study a hierarchical triple system with the Kozai-Lidov mechanism, and analyse the cumulative shift of periastron time of a binary pulsar by the emission of gravitational waves. Time evolution of the osculating orbital elements of the triple system is calculated by directly integrating the first-order post-Newtonian equations of motion. The Kozai-Lidov mechanism will bend the evolution curve of the cumulative shift when the eccentricity becomes large. We also investigate the parameter range of mass and semi-major axis of the third companion with which the bending of the cumulative-shift curve could occur within 100 years.
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