On the twist of emerging flux loops in the solar convection zone

We perform numerical simulations of emerging flux loops in the solar convec tive envelope based on a weakly twisted thin flux tube model recently deriv ed by Longcope and Klapper, generalizing the original formulation for the d ynamics of untwisted thin flux tubes by Spruit. The generalized formulation includes the description of torsional Alfven waves and takes into account the coupling of the writhing motion of the tube axis to the change in the f lux tube twist based on the requirement of global helicity conservation of the closed thin flux tube. In this model, the twist of the thin flux tube i s described by a quantity q defined as the angular rate of field-line rotat ion about the tube axis per unit length of the tube. We examine the evoluti on of twist along Omega-shaped emerging flux loops which are formed as a re sult of the non-linear growth of the Parker instability of toroidal magneti c flux tubes at the base of the solar convection zone. We find that: (1) In the northern hemisphere, a left-handed twist is generated in the flux tube s as a result of the right-handed tilt or writhe of the emerging loops indu ced by the Coriolis force. The generated twist increases with the latitude of emergence over the range from 0 degrees to about 38 degrees latitude, bu t then decreases when the emerging latitude exceeds 38 degrees, because of a change in the preferred eruption pattern. The magnitude of the generated twist q is very small, less than or similar to 2x10(-4) rad Mm(-1), more th an an order of magnitude smaller than the observed amplitude of twist (simi lar to 0.01 rad Mm(-1)) in solar active regions. (2) For a toroidal flux ri ng with a uniform initial twist q(0) along the ring, the twist amplitude |q | at the apex of the emerging loop decrease by a factor of about 0.67 becau se of the stretching of the loop, as it rises from the base of the convecti on zone to about 20 Mm below the photosphere, at which depth the flux tube can no longer be considered thin. However, because of the more rapid increa se of the tube cross-sectional radius a with height, |qa|, which correspond s to the ratio between the azimuthal field to the axial field B-theta/B-l o f the tube, increases by a factor of about 2.5 at the apex of the loop, as it rises over the same distance. (3) Because of the effect of the Coriolis force, the distribution of twist along the emerging loop is asymmetric betw een the leading (in the direction of rotation) and the following sides of t he loop. Both |q| and |qa| are greater at the following side than the leadi ng at any depth. Based on the evolution of twist along emerging flux loops, we discuss possible constraints on the twist q(0) of initial toroidal flux tubes at the base of the convection zone.