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Aims. We use observations of solar activity to constrain parameters relating to the α effect in stochastic nonlinear dynamo models. Methods. Thisis achieved through performing a comprehensive statistical comparison by computing probabilitydistribution functions (PDFs) of solar activity from observations and from our simulation of α − Ω mean field dynamo model. The observational data that are used are the time history of solar activity inferred for C14 data in the past 11000 years on a long time scale and direct observations of the sun spot numbers obtained in recent years 1795−1995 on a short time scale. Monte Carlo simulations are performed on these data to obtain probability distribution functions (PDFs) of the solar activity on both long and short time scales. These PDFs are then compared with predicted PDFs from numerical simulation of our α − Ω dynamo model, where α is assumed to have both mean α0 and fluctuating α  parts. Results. By varying the correlation time τα of fluctuating α  , the ratio of the amplitude of the fluctuating to mean alpha αR =  α 2 /α 2 (where angular brackets  denote ensemble average), and the ratio of poloidal to toroidal magnetic fields, we show that the results from our stochastic dynamo model can match the PDFs of solar activity when τα ∈ [22,44] years with αR ∈ [0.21,0.24].

Determining the temporal dynamics of the solarαeffect