The Effects of Convection Zone Turbulence on the Tilt Angles of Magnetic Bipoles

Bipolar magnetic regions are believed to form when flux originating below the solar convection zone rises to the surface in the form of long thin loops. Numerical models of rising flux tubes have been able to explain many observed features of these bipoles, including their angle of tilt relative to the east-west direction. Observations reveal that the mean tilt angle, α, varies with both latitude of emergence and with flux, in agreement with simulations. However, observed bipoles also exhibit a considerable fluctuation, Δα, about the mean tilt angle. Here we show that tilt angle fluctuations can arise in model calculations from interactions with hydrodynamic turbulence during the tube's rise. Numerical simulations indicate that both the magnitude of these fluctuations, and their scaling with footpoint separation (Δα ∼d⁻¹), are consistent with observations. Best agreement with observations occurs for flux tubes whose magnetic field strength is similar to those used in other numerical investigations, B₀ ∼ 30 kG. Furthermore, the agreement with observation suggests that turbulent velocities throughout the convection zone are consistent with those derived from mixing-length convection models.