A non-linear mathematical model for the X-ray variability classes of the microquasar GRS 1915+105 – I. Quiescent, spiking states, and quasi-periodic oscillations. Issue 1 (26th April 2020) - Massaro, E; Capitanio, F; Feroci, M; Mineo, T; Ardito, A; Ricciardi, P
ABSTRACT: The microquasar GRS 1915+105 is known to exhibit a very variable X-ray emission on different time-scales and patterns. We propose a system of two ordinary differential equations, adapted from the Hindmarsh–Rose model, with two dynamical variables x ( t ), y ( t ), and an input constant parameter J 0, to which we added a random white noise, whose solutions for the x ( t ) variable reproduce consistently the X-ray light curves of several variability classes as well as the development of low-frequency quasi-periodic oscillations (QPO). We show that changing only the value of J 0, the system moves from stable to unstable solutions and the resulting light curves reproduce those of the quiescent classes like ϕ and χ, the δ class and the spiking ρ class. Moreover, we found that increasing the values of J 0 the system induces high-frequency oscillations that evolve into QPO when it moves into another stable region. This system of differential equations gives then a unified view of the variability of GRS 1915+105 in term of transitions between stable and unstable states driven by a single input function J 0 . We also present the results of a stability analysis of the equilibrium points and some considerations on the existence of periodic solutions.