Limits on magnetic field amplification from the r mode instability
Abstract
At second order in perturbation theory, the unstable r mode of a rotating star includes growing differential rotation whose form and growth rate are determined by gravitationalradiation reaction. With no magnetic field, the angular velocity of a fluid element grows exponentially until the mode reaches its nonlinear saturation amplitude and remains nonzero after saturation. With a background magnetic field, the differential rotation winds up and amplifies the field, and previous work where large mode amplitudes were considered [L. Rezzolla, F. K. Lamb, and S. L. Shapiro, Astrophys. J. 531, L139 (2000)., 10.1086/312539], suggests that the amplification may damp out the instability. A background magnetic field, however, turns the saturated timeindependent perturbations corresponding to adding differential rotation into perturbations whose characteristic frequencies are of order the Alfvén frequency. As found in previous studies, we argue that magneticfield growth is sharply limited by the saturation amplitude of an unstable mode. In contrast to previous work, however, we show that if the amplitude is small, i.e., ≲10^{4} , then the limit on the magneticfield growth is stringent enough to prevent the loss of energy to the magnetic field from damping or significantly altering an unstable r mode in nascent neutron stars with normal interiors and in cold stars whose interiors are type II superconductors. We show this result first for a toy model, and we then obtain an analogous upper limit on magneticfield growth using a more realistic model of a rotating neutron star. Our analysis depends on the assumption that there are no marginally unstable perturbations, and this may not hold when differential rotation leads to a magnetorotational instability.
 Publication:

Physical Review D
 Pub Date:
 December 2017
 DOI:
 10.1103/PhysRevD.96.124008
 arXiv:
 arXiv:1707.09419
 Bibcode:
 2017PhRvD..96l4008F
 Keywords:

 Astrophysics  High Energy Astrophysical Phenomena;
 General Relativity and Quantum Cosmology
 EPrint:
 This is essentially the published version