Nonradial oscillations of slowly and differentially rotating compact stars

TL;DR

This paper derives equations for nonradial oscillations in differentially rotating relativistic stars using a slow rotation approximation, revealing new coupling effects and validating results against nonlinear studies.

Contribution

It introduces a perturbative approach to model oscillations in differentially rotating stars, incorporating differential rotation effects with high accuracy.

Findings

Perturbative equations match nonlinear results within a few percent.

Differential rotation introduces new coupling terms in oscillation equations.

Spectral properties of oscillations are consistent with nonlinear hydrodynamical studies.

Abstract

The equations describing nonradial adiabatic oscillations of differentially rotating relativistic stars are derived in relativistic slow rotation approximation. The differentially rotating configuration is described by a perturbative version of the relativistic j-constant rotation law. Focusing on the oscillation properties of the stellar fluid, the adiabatic nonradial perturbations are studied in the Cowling approximation with a system of five partial differential equations. In these equations, differential rotation introduces new coupling terms between the perturbative quantites with respect to the uniformly rotating stars. In particular, we investigate the axisymmetric and barotropic oscillations and compare their spectral properties with those obtained in nonlinear hydrodynamical studies. The perturbative description of the differentially rotating background and the oscillation spectrum agree within a few percent with those of the nonlinear studies.