Modelling the shape of sunspot cycle using a modified Maxwell-Boltzmann probability distribution function

Abstract

Abstract

The 11 year sunspot number cycle has been a fascinating phenomenon for many scientists in the last three centuries.  Various mathematical functions have been used for modelling the 11 year sunspot number cycles. In this paper, we present a new model, which is derived from the well known Maxwell-Boltzmann probability distribution function. A modification has been carried out by introducing a new parameter, called area parameter to model sunspot number cycle using Maxwell-Boltzmann probability distribution function. This parameter removes the normality condition possessed by probability density function, and fits an arbitrary sunspot cycle of any magnitude. The new model has been fitted in the actual monthly averaged sunspot cycles and it is found that, the Hathaway-Wilson-Reichmann measure, goodness of fit is high. The estimated parameters of the sunspot number cycles 1 to 24 has been presented in this paper. A Monte Carlo based simple random search is used for nonlinear parameter estimation. Prediction has been carried out for  the next sunspot number cycles 25 through a model by  averaging of recent cycle’s model parameters. This prediction can be used for simulating a more realistic sunspot cycle profile. Through extensive Monte Carlo simulations, large number of sunspot cycle profile could be generated and these can be used in the orbital dynamics studies.