Magnetic Cycles in the Sun: Modeling the Changes in Radius, Luminosity, andp‐Mode Frequencies

Abstract

We report on the results obtained with a stellar evolution code in which cyclic magnetic fields are imposed in the convection zone of a 1.0 M☉ star. Magnetic effects are incorporated in two ways: (1) the field pressure and energy density are included in the equations of hydrostatic equilibrium and conservation of energy; and (2) the field inhibits the onset of convection according to a prescription derived by Gough & Tayler (1966). Inserting magnetic fields into the convection zone with strengths comparable to the observed global fields in the Sun, and assuming a simple depth dependence for the field strength, we find differences in luminosity and radius between nonmagnetic and magnetic models that are consistent in amplitude with the observed activity-related changes in the Sun. Using the same magnetic fields, and computing p-mode frequencies for nonmagnetic and magnetic models, we find that the frequencies in a magnetic model are larger than those for a nonmagnetic model. The frequency differences between nonmagnetic and magnetic models agree in sign, and overlap in magnitude and frequency dependence, with the shifts in frequency which have been observed in the Sun between solar minimum and solar maximum. We find that the luminosity variations are out of phase with the magnetic variations: in order to help reconcile this result with empirical solar data, we note that the global (poloidal) fields in the Sun are observed to pass through minimum values at times that correspond roughly with times of maximum toroidal fields.