STOCHASTIC RESONANCE, THE RAYLEIGH TEST, AND IDENTIFICATION OF THE 25-DAY PERIODICITY IN THE SOLAR-ACTIVITY

We consider the problem of extracting a periodic signal from a noisy e nvironment using the stochastic resonance effect, The solution of this problem Involves the analysis of stochastic series of discrete events for periodicity, which is performed by means of the Rayleigh test. A relation is established between the parameters of the Fourier spectra of the flux intensity of discrete events and the Rayleigh power spectr a of realizations of such a flow. It is shown that, in the cases where the flux intensity can be expanded in a series of the form m(t) = (a( 0)/2) [1 + Sigma A(k)cos(omega(k)t+phi(k))], the expected mean Rayleig h power spectrum of a realization of such a flux of events {t(j)},j = 1,..., N has certain characteristic features provided the length of th e realization Delta t approximate to t(N) - t(1) much greater than 2 p i/omega(k): (1) the spectrum consists of peaks at frequencies omega(k) ; (2) the amplitudes of spectral peaks proportional to 1 + 0.25(N - 1) A(k)(2), and (3) the widths of spectral peaks proportional to Delta t( -1). The results obtained were used to analyze the X-ray measurements in the 1-8 Angstrom range performed from 1968 to 1974 and 1986 to 1992 . In our previous works (Alibegov 1994; Alibegov and Katyushina 1995) we showed that these series contain periodic components at the frequen cies of harmonics of the usual solar rotation and at harmonics of the frequency 463 nHz (period approximate to 25 days). In view of our resu lts, the identification of such periodicities can be considered to be an application of the stochastic resonance effect to the detection of periodic modulations in the solar flare activity.