Regularity conditions for toroidal magnetic-field perturbations at the stellar center

Resolve the failure of the extended central regularity conditions in the ACOR oscillation framework to ensure regularity of magnetic-field perturbations for confined axisymmetric toroidal magnetic fields, thereby allowing magnetic configurations that do not require strong decay near the stellar center.

Background

The extended ACOR formulation introduces magnetic perturbation variables and corresponding central regularity conditions for oscillations in stars containing confined, axisymmetric toroidal magnetic fields. The authors report that the chosen system of equations does not yield regular magnetic-field perturbations at the center when these conditions are applied.

To avoid the numerical or analytical difficulty, the present implementation restricts the magnetic field to configurations with strong decay near the center, leaving the innermost stellar layers effectively unaffected. Developing a treatment that removes or relaxes this restriction is identified as work for a future study.

References

However, this approach failed to ensure the regularity of the magnetic field perturbation, despite having tested various sets of equations. To overcome this issue, which is related to the chosen set of equations and not to the underlying assumptions, we decided to consider only magnetic fields with a strong decay close to the center so that the innermost layers remain unaffected by the magnetic field. We shall tackle this issue in a future study.

— Probing magnetic fields in stars: A 2D oscillation framework including rotation and magnetism  (2608.28290 - Fort et al., 28 Aug 2026) in Section 3, subsection “Boundary conditions” (label: subsec:BC)