Solar radius and luminosity variations induced by the internal dynamo magnetic fields

Although the occurrence of solar irradiance variations induced by magnetic surface features (e.g., sunspots, faculae, magnetic network) is generally accepted, the existence of intrinsic luminosity changes due to the internal magnetic fields is still controversial. This additional contribution is expected to be accompanied by radius variations and occurs on timescales not limited to that of the 11-year cycle, and thus to be potentially significant for the climate of the Earth. We aim to constrain theoretically the radius and luminosity variations of the Sun that are due to the effect of the variable magnetic fields in its interior associated with the dynamo cycle. We have extended a one-dimensional stellar evolution code to include several effects of the magnetic fields on the interior structure, such as the contributions to the hydrostatic equilibrium equation and to the energy conservation equation, the impact on the density and the equation of state, and the inhibition of convective energy transport. We investigate different magnetic configurations, based on both observational constraints and on the output of state-of-the-art mean field dynamo models. We explore both step-like and simply periodic time dependences of the magnetic field peak strength. We find that magnetic models have decreased luminosity and increased radii with respect to their nonmagnetic counterparts. In other words, the luminosity and radius variations are in anti-phase and in phase, respectively, with the magnetic field strength. For peak magnetic field strengths of the order of tens of kilogauss, luminosity variations ranging between 10^-6 and 10^-3 (in modulus) and radius variations between 10^-6 and 10^-5 are obtained. Modest but significant radius variations (up to 10^-5 in relative terms) are obtained for magnetic fields of realistic strength and geometry, providing a potentially observable signature of the intrinsic variations. Establishing their existence in addition to the accepted surface effects would have very important implications for the understanding of solar-induced long-term trends on climate.