Prediction of solar active longitudes

Abstract

Context. After considering the solar surface differential rotation, it was found that two persistent active longitudes of sunspots and of solar X-ray flares, separated by about 180 degrees, exist on the sun. Aims. According to the migration rule of the active longitudes on the Sun, we predict the central positions of the solar active longitudes in Carrington frame. Methods. The migration, M, of an active longitude on the kth day of the ith Carrington rotation in Carrington frame can be described as M = T c Σ Ni i= (Ω i - Ω c ) + k(Ω i - Ω c ), where Ω ι , (sidereal) is the angular velocity of the active longitude in the ith Carrington rotation, Ωc (sidereal), the angular velocity of Carrington frame, and T c , the Carrington rotation period. Solar active longitudes rotate in agreement with solar surface differential rotation law, which can be simply described as Ω ι , = Ω 0 - Bsin 2 (Φ ι ), where Ω 0 is the equatorial angular velocity, B the differential rotation rate, and Φι, the mean latitude of solar activity in the ith rotation. Parameters, Ω 0 and B, can be obtained from observations. If the latitude in the (i + 1)th rotation is approximately that of the ith rotation, the expected angular velocity of an active longitude in the (i + 1)th rotation can be described as Ω(ι+1) p = Ω0- B sin 2 (Φ ι ). The central positions of active longitude, Δ(ι+1)kp, can be expected as well. Results. We predict active longitudes of solar X-ray flares qualitatively between 1997-2006. Active longitudes with half width of 20°-30° cover 80% of C-flares during the minimum of solar activities and X-flares during the maximum. Conclusions. Solar active longitudes can be predicted by differential rotation parameters and latitude of solar activity.