  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 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. 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 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.
