A non-linear mathematical model for the X-ray variability classes of the microquasar GRS 1915+105 -- I: quiescent, spiking states and QPOs

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 phi and chi, the delta class and the spiking rho class. Moreover, we found that increasing the values of J_0 the system induces high frequency oscillations that evolve to 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.