Hall cascade with fractional magnetic helicity in neutron star crusts release_jzovg4g7zvbazp7xjvs7r2qp24

by Axel Brandenburg

Released as a report .

2020  

Abstract

The ohmic decay of magnetic fields in the crusts of neutron stars is generally believed to be governed by Hall drift which leads to what is known as a Hall cascade. Here we show that helical and fractionally helical magnetic fields undergo strong inverse cascading like in magnetohydrodynamics (MHD), but the magnetic energy decays more slowly with time t: ∝ t^-2/5 instead of ∝ t^-2/3 in MHD. Even for a nonhelical magnetic field there is a certain degree of inverse cascading for sufficiently strong magnetic fields. The inertial range scaling with wavenumber k is compatible with earlier findings for the forced Hall cascade, i.e., proportional to k^-7/3, but in the decaying cases, the subinertial range spectrum steepens to a novel k^5 slope instead of the k^4 slope in MHD. The energy of the large-scale magnetic field can increase quadratically in time through inverse cascading. For helical fields, the energy dissipation is found to be inversely proportional to the large-scale magnetic field and proportional to the fifth power of the root-mean square (rms) magnetic field. For neutron star conditions with an rms magnetic field of a few times 10^14G, the large-scale magnetic field might only be 10^11G, while still producing magnetic dissipation of 10^33ergs^-1 for thousands of years, which could manifest itself through X-ray emission. Finally, it is shown that the conclusions from local unstratified models agree rather well with those from stratified models with boundaries.
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Type  report
Stage   submitted
Date   2020-08-03
Version   v4
Language   en ?
Number  NORDITA-2020-063
arXiv  2006.12984v4
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