Constraints on the Magnetic Field Geometry of Magnetars
H. Sotani, A. Colaiuda, and K. D. Kokkotas

TL;DR
This paper investigates how different magnetic field geometries affect the oscillation spectra of magnetized stars, revealing that magnetic fields must permeate the entire star to match observational data.
Contribution
It provides new insights into the influence of magnetic field geometry on magnetar oscillations, emphasizing the necessity of a star-wide magnetic field.
Findings
Toroidal magnetic fields do not significantly affect crustal torsional oscillations.
Magnetic fields confined to the crust alter the oscillation spectrum drastically.
Observations exclude crust-confined magnetic fields, implying fields permeate the whole star.
Abstract
We study the effect of the magnetic field geometry on the oscillation spectra of strongly magnetized stars. The magnetic field distributions include both toroidal and poloidal contributions. We observe that the toroidal contribution does not influence significantly the torsional oscillations of the crust. Moreover, in the case that the core is a type I supercontactor and the magnetic fields are confined in the crust, the torsional oscillation spectrum is drastically affected by the presence of the strong magnetic fields. Comparison with results and estimations for the magnetic field strength, from observations, exclude the possibility that magnetars will have a magnetic field solely confined in the crust i.e. our results suggest that the magnetic field in whatever geometry has to permeate the whole star.
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