Modeling the Subsurface Evolution of Active Region Flux Tubes

I present results from a set of 3D spherical-shell MHD simulations of the buoyant rise of active region flux tubes in the solar interior which put new constraints on the initial twist of the subsurface tubes in order for them to emerge with tilt angles consistent with the observed Joy's law for the mean tilt of solar active regions. Due to the asymmetric stretching of the $\Omega$-shaped tube by the Coriolis force, a field strength asymmetry develops with the leading side having a greater field strength and thus being more cohesive compared to the following side. Furthermore, the magnetic flux in the leading leg shows more coherent values of local twist $\alpha \equiv {\bf J} \cdot {\bf B} / B^2$, whereas the values in the following leg show large fluctuations and are of mixed signs.