Sunspot group tilt angles and the strength of the solar cycle

¹ Max-Planck-Institut für Sonnensystemforschung, Max-Planck-Str. 2, 37191 Katlenburg-Lindau, Germany e-mail: dasi@mps.mpg.de
² School of Space Research, Kyung Hee University, Yongin, Gyeonggi, 446-701, Korea
³ Astronomical institute of the St. Petersburg State University, Universitetsky prospekt, 28, 198504, Peterhof, St. Petersburg, Russia
⁴ European Southern Observatory, ESO, Karl-Schwarzschild-Strasse 2, 85748, Garching bei Mnchen, Germany

Received: 22 February 2010
Accepted: 7 May 2010

Abstract

Context. It is well known that the tilt angles of active regions increase with their latitude (Joy's law). It has never been checked before, however, whether the average tilt angles change from one cycle to the next. Flux transport models show the importance of tilt angles for the reversal and build up of magnetic flux at the poles, which is in turn correlated to the strength of the next cycle.

Aims. Here we analyse time series of tilt angle measurements and look for a possible relationship of the tilt angles with other solar cycle parameters, in order to glean information on the solar dynamo and to estimate their potential for predicting solar activity.

Methods. We employed tilt angle data from Mount Wilson and Kodaikanal observatories covering solar cycles 15 to 21. We analyse the latitudinal distribution of the tilt angles (Joy's law), their variation from cycle to cycle, and their relationship to other solar cycle parameters, such as the strength (or total area covered by sunspots in a cycle), amplitude, and length.

Results. The two main results of our analysis follow. 1. We find an anti-correlation between the mean normalised tilt angle of a given cycle and the strength (or amplitude) of that cycle, with a correlation coefficient of r_c = –0.95 (99.9% confidence level) and r_c = –0.93 (99.76% confidence level) for Mount Wilson and Kodaikanal data, respectively. 2. The product of the cycle's averaged tilt angle and the strength of the same cycle displays a significant correlation with the strength of the next cycle (r_c = 0.65 at 89% confidence level and r_c = 0.70 at 92% confidence level for Mount Wilson and Kodaikanal data, respectively). An even better correlation is obtained between the source term of the poloidal flux in Babcock-Leighton-type dynamos (which contains the tilt angle) and the amplitude of the next cycle. Further we confirm the linear relationship (Joy's law) between the tilt angle and latitude with slopes of 0.26 and 0.28 for Mount Wilson and Kodaikanal data, respectively. In addition, we obtain good positive correlations between the normalised-area-weighted tilt angle and the length of the following cycle, whereas the strength or the amplitude of the next cycle does not appear to be correlated to the tilt angles of the current cycle alone.

Conclusions. The results of this study indicate that, in combination with the cycle strength, the active region tilt angles play an important role in building up the polar fields at cycle minimum.