Hall cascade with fractional magnetic helicity in neutron star crusts

by Axel Brandenburg (Nordita)

Wednesday 26 Aug 2020, 13:30 → 14:15 Europe/Stockholm

https://stockholmuniversity.zoom.us/j/530682073

https://arxiv.org/abs/2006.12984

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 k5 slope instead of the k4 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 1014G, the large-scale magnetic field might only be 1011G, while still producing magnetic dissipation of 1033ergs−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.