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### abstract

• 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).

### publication date

• January 1, 1994