RADIATIVE HEATING AND THE BUOYANT RISE OF MAGNETIC-FLUX TUBES IN THE SOLAR INTERIOR

We study the effect of radiative heating on the evolution of thin magn etic flux tubes in the solar interior and on the eruption of magnetic flux loops to the surface. Magnetic flux tubes experience radiative he ating because (1) the mean temperature gradient in the lower convectio n zone and the overshoot region deviates substantially from that of ra diative equilibrium, and hence there is a non-zero divergence of radia tive heat flux; and (2) the magnetic pressure of the flux tube causes a small change of the thermodynamic properties within the tube relativ e to the surrounding field-free fluid, resulting in an additional dive rgence of radiative heat flux. Our calculations show that the former c onstitutes the dominant source of radiative heating experienced by the flux tube. In the overshoot region, the radiative heating is found to cause a quasi-static rising of the toroidal flux tubes with an upward drift velocity similar to 10(-3) \delta\(-1) cm s(-1), where delta dr op del(c) - del(ad) < 0 describes the subadiabaticity in the overshoot layer. The upward drift velocity does not depend sensitively on the f ield strength of the flux tubes. Thus in order to store toroidal flux tubes in the overshoot region for a period comparable to the length of the solar cycle, the magnitude of the subadiabaticity delta(< 0) in t he overshoot region must be as large as similar to 3 x 10(-4). We disc uss the possibilities for increasing the magnitude of delta and for re ducing the rate of radiative heating of the flux tubes in the overshoo t region. Using numerical simulations we study the formation of 'Omega '-shaped emerging loops from toroidal flux tubes in the overshoot regi on as a result of radiative heating. The initial toroidal tube is assu med to be non-uniform in its thermodynamic properties along the tube a nd lies at varying depths beneath the base of the convection zone. The tube is initially in a state of neutral buoyancy with the internal de nsity of the tube plasma equal to the local external density. We find from our numerical simulations that such a toroidal tube rises quasi-s tatically due to radiative heating. The top portion of the nonuniform tube first enters the convection zone and may be brought to an unstabl e configuration which eventually leads to the eruption of an anchored flux loop to the surface. Assuming reasonable initial parameters, our numerical calculations yield fairly short rise times (2-4 months) for the development of the emerging flux loops. This suggests that radiati ve heating is an effective way of causing the eruption of magnetic flu x loops, leading to the formation of active regions at the surface.