Does the Sun Shrink with Increasing Magnetic Activity?

Abstract

We have analyzed the full set of Solar and Heliospheric Observatory (SOHO) Michelson Doppler Imager (MDI) f- and p-mode oscillation frequencies from 1996 to date in a search for evidence of solar radius evolution during the rising phase of the current activity cycle. Just as Antia et al. in 2000, we find that a significant fraction of the f-mode frequency changes scale with frequency and that if these are interpreted in terms of a radius change, it implies a shrinking Sun. Our inferred rate of shrinkage is about 1.5 km yr-1, which is somewhat smaller than found by Antia et al. We argue that this rate does not refer to the surface but, rather, to a layer extending roughly from 4 to 8 Mm beneath the visible surface. The rate of shrinking may be accounted for by an increasing radial component of the rms random magnetic field at a rate that depends on its radial distribution. If it were uniform, the required field would be ~7 kG. However, if it were inwardly increasing, then a 1 kG field at 8 Mm would suffice. To assess contribution to the solar radius change arising above 4 Mm, we analyzed the p-mode data. The evolution of the p-mode frequencies may be explained by a magnetic field growing with activity. Our finding here is very similar to that of Goldreich et al. (1991). If the change were isotropic, then a 0.2 kG increase, from activity minimum to maximum, is required at the photosphere, which would grow to about 1 kG at 1 Mm. If only the radial component of the field were to increase, then the requirement for the photospheric field increase is reduced to a modest 60-90 G. A relative decrease in temperature of the order of 10-3 in the subphotospheric layers, or an equivalent decrease in the turbulent energy, would have a similar effect to the required inward growth of magnetic field change. The implications of the near-surface magnetic field changes depend on the anisotropy of the random magnetic field. If the field change is predominantly radial, then we infer an additional shrinking at a rate between 1.1 and 1.3 km yr-1 at the photosphere. If, on the other hand, the increase is isotropic, we find a competing expansion at a rate of 2.3 km yr-1. In any case, variations in the Sun's radius in the activity cycle are at the level of 10-5 or less and, hence, have a negligible contribution to the irradiance variations.