Magnetic field amplification by the r-mode instability

Abstract

We discuss magnetic field enhancement by unstable r-modes (driven by the gravitational radiation reaction force) in rotating stars. In the absence of a magnetic field, gravitational radiation exponentially increases the r-mode amplitude α, and accelerates differential rotation (secular motion of fluid elements). For a magnetized star, differential rotation enhances the magnetic field energy. Rezzolla et al. (2000 argued that if the magnetic energy grows faster than the gravitational radiation reaction force pumps energy into the r-modes, then the r-mode instability is suppressed. Chugunov (2015) demonstrated that without gravitational radiation, differential rotation can be treated as a degree of freedom decoupled from the r-modes and controlled by the back reaction of the magnetic field. In particular, the magnetic field windup does not damp r-modes. Here we discuss the effect of the back reaction of the magnetic field on differential rotation of unstable r-modes, and show that it limits the generated magnetic field and the magnetic energy growth rate preventing suppression of the r-mode instability by magnetic windup at low saturation amplitudes, α ≪ 1, predicted by current models.

Long-term evolution of CFS-unstable neutron stars and the role of differential rotation on short time-scales

“…Analysis is performed within generalized toy model by Friedman et al (2017) and shows that differential rotation can affect apparent spin down rate for growing (unsaturated) and, in some cases, saturated rmodes (corresponding criteria are suggested). In Subsection 4.3 I discuss r-mode instability in magnetized perfect fluid star, applying the results by Friedman et al (2017) (see Chugunov et al (2017b) for short summary). They demonstrate that magnetic field suppresses differential motion of fluid elements.…”