Solar differential rotation coefficients fitted from synoptic magnetic maps

Abstract

ABSTRACT Based on the consecutive synoptic magnetic maps, we devise a new method to calculate the solar differential rotation coefficients. This method is very easy to implement and has a high accuracy. Firstly, based on the two-term or three-term differential rotation formula, we simulate a synoptic map CR$_{n}$ evolves one Carrington Rotation (CR) time only under the effect of the differential rotation, and thereby a stretched synoptic map CR$_{n*}$ is obtained. Then, through searching the maximum covariance between the maps CR$_{n*}$ and CR$_{n+1}$ by the grid search method, the rotation coefficients can be determined. Based on the synoptic maps of CRs 1625 to 2278 (during the years 1975–2023), the two-term coefficients A and B for latitude region between $\pm 40^{\circ }$ are calculated. The rotation coefficient B shows an obvious 11-yr period. From the time series of B, we find that the Sun usually rotates more differentially in the rising phases of the sunspot cycles than in the falling phases. Moreover, the strong magnetic field corresponds to an increasing of B (note that B has a negative sign) or decreasing of differential. The evolutionary trend of B also indicates that there are several years until the maximum value of B will be reached in solar cycle 25, and the coefficient B will be still in the rising phase in the few coming years. The two-term rotation coefficients for the two hemispheres are also calculated separately, and in the studied time-scale, the largest N–S asymmetry of the rotation rate appeared in October 2007.