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

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.

v3: 1 figure added, minor typos corrected, 12 pages, 12 figures, final version to appear in PRD

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• Fundamental oscillation modes of neutron stars: validity of universal relations
• Thermal emission of neutron stars with internal heaters
• R-mode frequencies of rapidly and differentially rotating relativistic neutron stars
• The effect of magnetic fields on the r-modes of slowly rotating relativistic neutron stars
• Four-Hair Relations for Differentially Rotating Neutron Stars in the Weak-Field Limit
• Differential rotation and r-modes in magnetized neutron stars
• $M/R$ estimates for two neutron stars in LMXBs with possible r-mode frequencies detected
• Long term evolution of CFS-unstable neutron stars and role of differential rotation on short time-scales