Abstract
We discuss the 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 (2000–2001) 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.
Highlights
Neutron stars contain matter which is denser than that in atomic nuclei
We show that magnetic windup cannot suppress the r-mode instability if the nonlinear saturation amplitude is low, as predicted by current theoretical models, e.g. [30, 31, 32]
Before nonlinear saturation is achieved [i.e., at the stage of exponentially growing α(t)], the magnetic energy growth rate is a factor of α2(t) smaller than the r-mode energy growth rate by radiation reaction
Summary
Neutron stars contain matter which is denser than that in atomic nuclei. Because cold matter at such densities cannot be produced in terrestrial laboratories, neutron stars provide a unique opportunity to study the properties of super-dense matter by comparing observations of these stars with theoretical models. 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).
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