Slowly rotating neutron stars with small differential rotation: equilibrium models and oscillations in the Cowling approximation

TL;DR

This paper develops a new formalism for modeling slowly rotating, differentially rotating neutron stars with small differential rotation, analyzing their equilibrium and oscillation modes, and examining the impact on gravitational wave emission.

Contribution

It introduces a novel approach to model differential rotation in neutron stars under the slow rotation approximation, enabling variable separation in Einstein's equations.

Findings

Differential rotation slightly suppresses gravitational radiation from f-modes.

The formalism allows decoupling of frame-dragging equations into three ODEs.

Differential rotation influences neutron star oscillation modes.

Abstract

Newly born neutron stars can present differential rotation, even if later it should be suppressed by viscosity or a sufficiently strong magnetic field. And in this early stage of its life, a neutron star is expected to have a strong emission of gravitational waves, which could be influenced by the differential rotation. We present here a new formalism for modelling differentially rotating neutron stars: working on the slow rotation approximation and assuming a small degree of differential rotation, we show that it is possible to separate variables in the Einstein field equations. The dragging of inertial frames is determined by solving three decoupled ODEs. After we establish our equilibrium model, we explore the influence of the differential rotation on the f and r-modes of oscillation of the neutron star in the Cowling approximation, and we also analyze an effect of the differential rotation on the emission of gravitational radiation from the f-modes. We see that the gravitational radiation from the f-modes is slightly suppressed by introducing differential rotation to the equilibrium stars.