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 alpha infinity PHI1/4B0-5/4 sin theta, where alpha 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 PHI 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 PHI. Our major findings are: 1. The mean tilt of sunspot groups is an increasing function of both latitude theta and polarity separation d. If the data are fit to functions of the form alphaBAR = A(y) d(y) sin theta, where alphaBAR is the mean tilt, then we find 0.1 < y < 0.5. The theoretically predicted value of y = 0.25 seems to be consistent with the observations, for which we find A0.25 = 6.69 +/- 0.27, with d given in Mn and alphaBAR 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 PHI almost-equal-to 10(22) Mx, we find best agreement if B0 almost-equal-to 20-30 kG. 3. We find that the rms deviation DELTAalpha of spot-group tilts away from the mean tiltt behavior obeys the approximate relation DELTAalpha almost-equal-to 10-degrees x (d/100)-3/4 (where DELTAalpha is 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 DELTAalpha on d similar to that observed.