Differential rotation and r-modes in magnetized neutron stars

Abstract

Rezzolla et al. [ApJ 531 (2000), L139; Phys. Rev. D 64 (2001), 104013; Phys. Rev. D 64 (2001), 104014] draw attention to the second order secular drift associated with r-modes and claimed that it should lead to magnetic field enhancement and suppression of r-mode instability in magnetized neutron stars. We critically revise these results. We present a particular second order r-mode solution with vanishing secular drift, thus refuting a widely believed statement that secular drift is an unavoidable feature of r-modes. This non-drifting solution is not affected by magnetic field $B$, if $B\ll B_{\mathrm{crit}}\approx 10^{17}(\nu /600\mathrm{Hz})$ G ($\nu$ is a spin frequency) and does not lead to secular evolution of magnetic field. For general second order r-mode solution the drift does not necessarily vanish, but the solution can be presented as a superposition of two solutions: one describes evolution of differential rotation in nonoscillating star (which describes secular drift; for nonmagnetized star it is arbitrary stationary rotation stratified on cylinders; for magnetized star differential rotation evolves on the Alfvén timescale and may lead to magnetic energy enhancement), and another one is non-drifting r-mode solution mentioned above. This representation allows us to conclude that enhancement of magnetic field energy is limited by initial energy of differential rotation, which is much less (for a factor $\propto {\alpha }^2$, where $\alpha$ is mode amplitude) than the total energy of r-mode. Hence, magnetic field enhancement by drift cannot suppress r-mode instability. Results can be generalized for any oscillation mode in any medium, if this mode has non-drifting solution for $B=0$.

8 pages, accepted for publication in MNRAS

References in corpus (5)

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• Spin Evolution of Accreting Neutron Stars: Nonlinear Development of the R-mode Instability
• New possible class of neutron stars: hot and fast non-accreting rotators
• Lagrangian perturbation theory for rotating magnetic stars
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Cited by in corpus (8)

• Rotating Stars in Relativity
• R-modes in neutron stars: Theory and observations
• Differential rotation of the unstable nonlinear r-modes
• Limits on Magnetic Field Amplification from the r-Mode Instability
• Evolution of newborn rapidly rotating magnetars: effects of r-mode and fall-back accretion
• Radiation driven instability of rapidly rotating relativistic stars: criterion and evolution equations via multipolar expansion of gravitational waves
• Long term evolution of CFS-unstable neutron stars and role of differential rotation on short time-scales
• Magnetic field amplification by the r-mode instability