Oscillations of rapidly rotating relativistic stars

Abstract

Nonaxisymmetric oscillations of rapidly rotating relativistic stars are studied using the Cowling approximation. The oscillation spectra have been estimated by Fourier transforming the evolution equations describing the perturbations. This is the first study of its kind and provides information on the effect of fast rotation on the oscillation spectra while it offers the possibility of studying the complete problem by including space-time perturbations. Our study includes both axisymmetric and nonaxisymmetric perturbations and provides limits for the onset of the secular bar mode rotational instability. We also present approximate formulas for the dependence of the oscillation spectrum from rotation. The results suggest that it is possible to extract the relativistic star's parameters from the observed gravitational wave spectrum

Relativistic g-modes in rapidly rotating neutron stars

“…The basic formulation of this work was already drafted in a previous article by the authors, see [26] (abbreviated GK08 in the remainder of this paper) for the case of barotropic oscillations. Here, we will shortly summarize the fundamental points and the extensions that were made in order to handle stratified stars.…”

“…The slow rotation approximation assumes that the star is rotating at such a rate that the effects of rotation on the shape of the star can be neglected. Only in the last five years or so it became possible to study fast rotating stars in the general relativistic framework either using a linearized form of relativistic perturbation equations [24,25,26] or by evolving the non-linear hydrodynamical equations in the relativistic framework [27,28,29].…”

Oscillation modes of rapidly rotating neutron stars in scalar-tensor theories of gravity

“…For example, rapidly rotating neutron stars were constructed only in a few alternative theories of gravity [36][37][38][39][40] because deriving analytically the reduced field equations and solving them numerically in very involved. Studying oscillation modes of rapidly rotating stars, especially the nonaxisymmetric ones, on the other hand is also a very complicated problem even in pure GR that was addressed only recently [3,4,27,29]. Our goal will be to combine these two and perform the first study of oscillating rapidly rotating neutron stars in alternative theories of gravity determining the qualitative behavior of the oscillation frequencies and the possible deviations from general relativity.…”

“…Therefore, the studies of quasinormal modes of neutron stars in the static limit are a very important first step to understand the problem and make some qualitative estimations, but in order to be able to study realistic scenarios for the gravitational wave emission by CFS unstable f -modes, one has to go to rapid rotation. The first studies of f -mode oscillations of rapidly rotating neutron stars were performed in the axisymmetric case in [26] and for nonaxisymmetric modes in [3,4,[27][28][29][30][31]. Only the non-axisymmetric modes, though, are prone to CFS instability.…”

“…Only the non-axisymmetric modes, though, are prone to CFS instability. Because of the complexity of the problem, most of the studies in this case were performed in the linear regime employing the Cowling approximation [3,4,27,29,30,32], where the spacetime degrees of freedom are neglected and only the fluid variables are evolved in time. The only exceptions are the studies in the conformal flatness approximation [26,31] where a few exemplary sequences with polytropic equation of state where examined, and the full general relativistic nonlinear results in [28].…”