Magnetic Relaxation and the Landscape of Stable Magnetic Equilibria in Stellar Interiors

Magnetic fields can persist as long-lived, stable configurations in stellar interiors. In non-degenerate stars, internal fields are promising agents of angular momentum redistribution; in neutron stars, they can heat the interior, power quiescent luminosity, and couple to the crust to drive surface activity. At the same time, astroseismology is beginning to provide indirect probes of these hidden fields. Despite this growing observational relevance, we still lack a systematic theory for the space of magnetic equilibria in stellar interiors and how these equilibria depend on their dynamo-generated initial conditions.

In this talk, I frame the formation of stable magnetic configurations as a relaxation problem constrained by magnetic helicity and stable stratification. This motivates a compact ‘phase space’ of magnetic equilibria described by four quantities: (i) the fractional helicity, (ii) the ratio of Brunt–Väisälä to Alfvén frequencies, (iii) the toroidal-to-poloidal magnetic energy ratio, and (iv) a characteristic length scale of the magnetic field. I discuss candidate theories for stratified MHD relaxation that predict how these quantities evolve from initial to final states. I then present results from numerical experiments where I test these theories by solving the equations of MHD in global, three-dimensional geometry of the star using Dedalus. By independent control over all four parameters characterizing the initial conditions, including magnetic helicity, our numerical setup enables a systematic study of stable magnetic structures in stars, and their implications for stellar evolution and astroseismic observations.