Hall cascade with fractional magnetic helicity in neutron star crusts
release_jzovg4g7zvbazp7xjvs7r2qp24
by
Axel Brandenburg
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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