Cosmic rays transport equation solution and wavelets analysis: A case of pulsar source

Our purpose is to analyse time dependence of the cosmic ray particles density as a function of a modelled pulsar source variability using Morlet wavelets.Unlike the conventional spectral analysis the wavelet transform is a suitable tool for description of non-stationary processes containing multiscale features detection of singularities and analysis of transient phenomena. Methods such as wavelet should be very suitable; thus it can be applied to the problem under consideration. We have proceeded for the Morlet reconstructions to detect and predict new period details or singularities hidden behind the original spectra describing galactic cosmic ray density modulations as a response to a certain source.Wavelet coefficients calculated by the wavelet transform represent changes in the time series at a particular resolution. Thus it should be possible to filter out noise by looking at the time series in various resolutions.We present in this work semi-analytical solutions of cosmic rays transport equation for two cases of sources: time dependant discrete source and a pulsar source.When studying the case with time dependant source, a maximum for the Morlet decomposition coefficients was detected for a period of 4–5 years around the time of injection. For the same period the CR particles density presents a maximum and describes the two phenomena corresponding to creation and losses of particles.The observed characteristics of pulsars and the manner with which they would affect cosmic rays as sources of this radiation have been considered.We chose RP J0737-3039 A pulsar as a model of source. We used the Morlet wavelets to describe the oscillations of pulsar source to analyse the CR particles density.The description of the pulsar modelled source with a single Morlet wavelet shows characteristic periods of 23 ms, 2–5, 8, and 20 s for different scale parameter values. The analysis of CR density as a response to this source reveals periods of 20, 8, 220–250 s.A more realistic description is given, modelling the source oscillations by a sum of Morlet wavelets. The CR density response to this source has mainly changed in paces showing more realistic behaviour. Informations contained in Morlet decompositions and reconstructions show essentially periods of 250, 300 and 25 s.This analysis of cosmic rays particle density and propagation through the Morlet wavelets provides us a detailed zoom of hidden periods and structures for CR particles density and generally variations versus time and energy in vicinity and far from the CR sources.