Comparisons between theory and observation of active region tilts

Active regions in the Sun are generally tilted relative to the azimuthal direction, with the leading side being closer to the equator than the following side. This tilt is known to increase with latitude. Recently, theoretical calculations of the dynamics of emerging, initially toroidal active-region flux tubes have been done, showing that the observed tilts can be explained by the Coriolis force acting on a diverging flow field in emerging flux loops. The calculations of Fan, Fisher, & McClymont predict that α ∝ Φ^1/4B₀^-5/4 sin θ, where α is the tilt angle of the active region, B₀ is the magnetic field strength of the active-region flux tube near the base of the convection zone, and Φ is the amount of magnetic flux in the tube. We compare these theoretical predictions with the behavior of a sample of 24,701 sunspot groups observed at Mount Wilson over a period of 68 yr, using the polarity separation distance d as a proxy for Φ. Our major findings are: 1. The mean tilt of sunspot groups is an increasing function of both latitude θ and polarity separation d. If the data are fit to functions of the form α= A_γd^γ sin θ, where α is the mean tilt, then we find 0.1 < γ < 0.5. The theoretically predicted value of γ = 0.25 seems to be consistent with the observations, for which we find A_0.25 = 6.69 ± 0.27, with d given in Mm and Oα given in degrees. 2. When we compare the average tilts of large sunspot groups (d > 50 Mm) to the detailed numerical simulations of Fan, Fisher, & McClymont assuming Φ ≈ 10²² Mx, we find best agreement if B₀ ≈ 20-30 kG. 3. We find that the rms deviation Δ_αof spot-group tilts away from the mean tilt behavior obeys the approximate relation Δ_α 10° × (d/100)^-3/4 (where Δ_αis measured in degrees and d is measured in Mm) and does not seem to depend on latitude. The lack of a latitude dependence suggests that the range of B₀ for emerging flux loops is narrow. We propose that the source of the rms deviations is buffeting by convective motions, and we show how convection could produce a dependence of Δ_αon d similar to that observed.