Radiative transfer effects and the dynamics of small-scale magnetic structures on the Sun

The dynamical consequences of radiative energy transport on the evolution of gas confined to small-scale magnetic structures on the Sun are studied. Convective collapse, which transforms weak-field structures into intense structures of field strengths in the 1-2 kG range on the photosphere, is strongly in influenced by radiative heating from the surroundings and cooling due to losses in the vertical direction. We first present analytic results in the quasi-adiabatic approximation to attempt a qualitative understanding of the influence of radiative effects on the convective stability of Bur tubes. We demonstrate the destabilizing action of vertical radiative losses, that tend to enhance convective collapse and produce strong tubes at a relatively smaller horizontal scale than those expected from calculations based solely on horizontal radiative energy transport. Our calculations clearly point to an asymmetry between upflow and downflow perturbations-only the latter are amplified in the presence of vertical radiative transport. Using a realistic model of the solar atmospheric structure and treating radiative transfer in the diffusion and Eddington approximations, we next perform numerical stability analyses and produce size (flux)strength relations for solar flux tubes. Our results provide a physical explanation for the observed flux-dependent (equivalently size-dependent) field strengths of the solar small-scale magnetic structures in the form of weak intranetwork and strong network components.