Radiative Transfer Effects and Convective Collapse: Size-Strength Distribution for the Small-scale Solar Magnetic Flux Tubes

The effects of radiative energy exchange on the convective instability of a weak field magnetic structure, which lead to a prediction and a physical explanation of the magnetic flux dependent field strength, are examined in detail using a real model stratification for the photospheric and convection zone structure of the Sun. Adopting the generalised Eddington approximation for the radiative transfer, which is valid both in the optically thick and the thin limits, we model the lateral radiative energy exchange by the tube with the external medium with a self-consistent inclusion of vertical radiative losses.