The measurement of solar differential rotation from proper motion of individual sunspots

Abstract

The differential rotation is the result of the interaction between rotation and convection and causes dynamo circulation that affect the cycle of solar activity. Tracer method using features in the photosphere such as sunspot is a simple method to measure the differential rotation. In this study, 98 individual sunspots on January 8-22, 2013 and August 25-September 7, 2013 were used to measure the differential rotation of the Sun. The Sun's continuum images were obtained from HMI (Helioseismic Magnetic Imager) instrument at SDO (Solar Dynamic Observatory). Coordinate and area of sunspot were measured using ImageJ software and converted to Carrington coordinates. From the measurement, we derived the differential rotation equation, the relation of velocity and area of sunspot, and the relation of sunspot's velocity and Zurich classification. The differential rotation equation obtained in this study is ω (B) = (14.376 ± 0.04) + (0.6 ± 0.38) sin2B (°/day). For the relation between velocity and area of sunspot, we got the sidereal rotation rate of sunspots with area < 100 pixels2 is about 0.8% higher than sunspots with area > 100 pixels2.