Detectability of axisymmetric magnetic fields from the core to the surface of oscillating post-main-sequence stars

Recently, asteroseismic estimates of radial magnetic field amplitudes were obtained for 24 red giants (RGs) in the hydrogen-burning shell (H-shell) phase by measuring frequency splittings in their power spectra. Using general Lorentz-stress (magnetic) kernels, we investigated the potential for detectability of near-surface magnetism in a 1.3 M⊙ star as it evolves from a mid subgiant (SG) to a late SG and into an RG. Based on these sensitivity kernels, we decompose an RG into three zones — deep core, H-shell, and near-surface. The SGs instead required decomposition into an inner core, an outer core, and a near-surface layer. Additionally, we find that for a low-frequency g-dominated l=1 mode in a typical stable magnetic field, ~25% of the frequency shift comes from the H-shell and the remaining from deeper layers. The ratio of the subsurface tangential field to the radial field in the H-shell determines if subsurface fields may be potentially detectable. For p-dominated l=1 modes close to 𝜈_max, this ratio is around two orders of magnitude smaller in the SG phase than in the corresponding RG phase. Furthermore, with the availability of magnetic kernels, we propose lower limits for field strengths in crucial layers of our stellar model during its evolutionary phases. The theoretical prescription we have used provides the first formal way to devise inverse problems for stellar magnetism and can be seamlessly employed for slow rotators.