Non-extensivity of the X-ray binary systems

Systems in stationary states or in quasi-stationary states that cannot be consistently approached by classical Boltzmann and Gibbs Thermostatistics are non-additive. On the other hand, objects whose gravitational forces display a long-range gravitational reach are parts of so-called Self-Gravitating Systems (SGS). For both cases, the Generalized Thermostatistical formalism (GTS) proposed by Tsallis is a possible tool to be applied in replacement of classical Thermostatistics. X-Ray Binary Systems (XRBS) are SGS objects that present quasi-stationary states features. If one knows their emission values of light curves it is possible measuring their probability density distributions. The obtained results presented as the best fitting $q$-Gaussian distributions. For the present paper the research tasks analyzed 136 curves relating to time series evolution of X-Ray emission
values of XRBS. Some nonlinear Fokker-Planck equations present as solution to the steady-states $q$-Gaussian distributions. We recall that it was in good accordance to the data provided by the X-Ray Rossi satellite. The results showed accuracy with respect to the original data, by means of analysis of variance (ANOVA), with $F_{Value} = 140297$ and $ Prob > F = 0$. In all analyzes the $q$-Gaussian distribution proved better fit to the points regarding the Gaussian distribution, demonstrating the non-extensive character of the behavior of the X-Rays emissions arising from XRBS.