Derivation of stochastic differential equations for sunspot activity

Abstract

Aims. A system of stochastic differential equations (SDEs) is derived for sunspot activity. Methods. The SDE derivation relies on basic assumptions about a cyclic but randomly varying source of sunspots and on an average lifetime for sunspots. The SDE model parameters are fit to sunspot data for three different 11-year sunspot cycles. Results of calculations for the SDE system are compared with the data for each of the three sunspot cycles. Results. Certain characteristics are shared by both the SDE model and the data. In particular, the second and third moments about the mean divided by the mean are similar for the SDE system and for the data and appear to be approximately constant over the cycle. © 2010 ESO.