Radiative transfer effects and convective collapse: Size(flux)-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.