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Hall cascade with fractional magnetic helicity in neutron star crusts
- Source :
- Astrophys. J. 901, 18 (2020)
- Publication Year :
- 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 $t$: $\propto t^{-2/5}$ instead of $\propto t^{-2/3}$ 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 $10^{14}\,$G, the large-scale magnetic field might only be $10^{11}\,$G, while still producing magnetic dissipation of $10^{33}\,$erg$\,$s$^{-1}$ 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.<br />Comment: 14 pages, 17 figures, 5 tables, ApJ, in press
- Subjects :
- Astrophysics - High Energy Astrophysical Phenomena
Physics - Fluid Dynamics
Subjects
Details
- Database :
- arXiv
- Journal :
- Astrophys. J. 901, 18 (2020)
- Publication Type :
- Report
- Accession number :
- edsarx.2006.12984
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.3847/1538-4357/abad92