How well does surface magnetism represent deep Sun-like star dynamo action?

For Sun-like stars, the generation of toroidal magnetic field from poloidal magnetic field is an essential piece of the dynamo mechanism powering their magnetism. Previous authors have estimated the net toroidal flux generated in each hemisphere of the Sun by exploiting its conservative nature. This only requires observations of the surface magnetic field and differential rotation. We explore this approach using a 3D magnetohydrodynamic dynamo simulation of a cool star, for which the magnetic field generation is known throughout the entire star. Changes to the net toroidal flux in each hemisphere were evaluated using a closed line integral bounding the cross-sectional area of each hemisphere, following the application of Stokes-theorem to the induction equation; the individual line segments corresponded to the stellar surface, base, equator, and rotation axis. The influence of the large-scale flows, the fluctuating flows, and magnetic diffusion to each of the line segments was evaluated, along with their depth-dependence. In the simulation, changes to the net toroidal flux via the surface line segment typically dominate the total line integral surrounding each hemisphere, with smaller contributions from the equator and rotation axis. The bulk of the toroidal flux is generated deep inside the convection zone, with the surface observables capturing this due to the conservative nature of the net flux. Surface magnetism and rotation can therefore be used to estimate the net toroidal flux generated in each hemisphere, allowing us to constrain the reservoir of magnetic flux for the next magnetic cycle. However, this methodology cannot identify the physical origin, nor the location, of the toroidal flux generation. In addition, not all dynamo mechanisms depend on the net toroidal field produced in each hemisphere, meaning this method may not be able to characterise every magnetic cycle.