Probing fossil magnetic field effects in the core of evolved low-mass stars using mixed-mode frequencies

The recent discovery of the moderate differential rotation between the core and the envelope of intermediate-mass (IM) main-sequence and evolved stars, and the population of IM red giants presenting a surprisingly low-amplitude of their mixed modes (i.e. modes that behave as acoustic modes in their external envelope and as gravity modes in their core) could both be the signature of a strong magnetic field trapped inside the radiative regions of IM stars. Indeed, stars more massive than 1.1 solar mass are known to develop a convective core during their main sequence. The field generated by the dynamo triggered by this convection could be the progenitor of a strong fossil magnetic field trapped inside the core of the star for the rest of its evolution. In this context, the mixed modes observed thanks to space-based asteroseismology can constitute an excellent probe of the deepest layers in IM evolved stars: such magnetic fields may impact their propagation inside the core of these stars, and these perturbations should be visible in asteroseismic data. To unravel which constraints can be obtained from these observations, we theoretically investigate the effects of a plausible mixed magnetic field with various amplitudes on the mixed-mode frequencies of red giants. Applying a perturbative method, we estimate the magnetic splitting of the frequencies of simulated mixed dipolar modes that depends on the magnetic field strength and its configuration. A complete asymptotic analysis is derived, showing the potential of asteroseismology to probe the magnetism at each depth as this is done for stellar rotation. The effects of the mass and the metallicity of the stars are also explored. Finally, we infer an upper limit for the strength of the field and the associated lower limit for the timescale of its action to redistribute angular momentum in stellar interiors.