Differential rotation of the unstable nonlinear r-modes

Abstract

At second order in perturbation theory, the $r$-modes of uniformly rotating stars include an axisymmetric part that can be identified with differential rotation of the background star. If one does not include radiation-reaction, the differential rotation is constant in time and has been computed by Sá. It has a gauge dependence associated with the family of time-independent perturbations that add differential rotation to the unperturbed equilibrium star: For stars with a barotropic equation of state, one can add to the time-independent second-order solution arbitrary differential rotation that is stratified on cylinders (that is a function of distance $\varpi$ to the axis of rotation). We show here that the gravitational radiation-reaction force that drives the $r$-mode instability removes this gauge freedom: The expontially growing differential rotation of the unstable second-order $r$-mode is unique. We derive a general expression for this rotation law for Newtonian models and evaluate it explicitly for slowly rotating models with polytropic equations of state.

Published (2016) version, but with two updated references

References in corpus (4)

• Spinning down newborn neutron stars: nonlinear development of the r-mode instability
• Spin Evolution of Accreting Neutron Stars: Nonlinear Development of the R-mode Instability
• Lagrangian perturbation theory for rotating magnetic stars
• Differential rotation and r-modes in magnetized neutron stars

Cited by in corpus (9)

• Rotating Stars in Relativity
• Searches for continuous gravitational waves from neutron stars: A twenty-year retrospective
• R-modes and neutron star recycling scenario
• X-ray bounds on the r-mode amplitude in millisecond pulsars
• Electromagnetic fields in the exterior of an oscillating relativistic star -- II. Electromagnetic damping
• Limits on Magnetic Field Amplification from the r-Mode Instability
• Long term evolution of CFS-unstable neutron stars and role of differential rotation on short time-scales
• Magnetic amplification in premerger neutron stars through resonance-induced magnetorotational instabilities
• Magnetic field amplification by the r-mode instability