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 timeindependent perturbations that add differential rotation to the unperturbed equilibrium star: For stars with a barotropic equation of state, one can add to the timeindependent secondorder solution arbitrary differential rotation that is stratified on cylinders (that is a function of distance ϖ to the axis of rotation). We show here that the gravitational radiationreaction force that drives the r mode instability removes this gauge freedom; the exponentially growing differential rotation of the unstable secondorder 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.
 Publication:

Physical Review D
 Pub Date:
 January 2016
 DOI:
 10.1103/PhysRevD.93.024023
 arXiv:
 arXiv:1503.08864
 Bibcode:
 2016PhRvD..93b4023F
 Keywords:

 Astrophysics  High Energy Astrophysical Phenomena;
 General Relativity and Quantum Cosmology
 EPrint:
 Published (2016) version, but with two updated references