Gaussian and q-Gaussian Functions for the Decomposition of J1022+1001 Pulsar Profiles

The pulsar profiles are profiles obtained by pulse sequences averaged on several cycles. The mean profiles are usually decomposed in Gaussian components, but decompositions in von Mises functions have been proposed too. The Gaussian decompositions can be based on the central limit theorem (CLT), so that a Gaussian component can be regarded as an attractor in the space of distributions with finite variance. Well-known non-Gaussian attractors exist and are the Lévy distributions. Other proposed attractors are the q-Gaussian functions, which are generalizing the Gaussians in the Tsallis q-statistics. These functions have power-law tails. For parameter q equal to 1, the q-Gaussians become the standard Gaussian distributions. In this framework of Gaussian and non-Gaussian attractors, we propose decompositions of pulsar profiles both in Gaussian and q-Gaussian functions. Our investigation is aiming to compare the decompositions to highlight possible differences and dependences on q-parameters. Here we consider, in particular, the intensity profiles given by the EPN Database of Pulsar Profiles, of J1022+1001 at several frequencies. Power-law behaviors of the leading edges have been observed.