Solar irradiance variations and nonlinear mean field dynamo

By using a nonlinear model of an axisymmetricα – Ω dynamo, an analytical expression which gives the magnitude of the mean magnetic field as a function of rotation and other parameters for a solar-type convective zone is obtained. The mean magnetic field varies as the\(\frac{3}{4}\) power of the rotation rate. The resulting theoretical relationship of the X-ray luminosity as a function of the angular velocity is in agreement with observations by Fleming, Gioia, and Maccacaro (1989).