A non-linear mathematical model for the X-ray variability classes of the microquasar GRS 1915+105 -- II: transition and swaying classes

TL;DR

This paper extends a non-linear differential equation model to reproduce and classify the complex X-ray variability patterns of GRS 1915+105, revealing three main types of behavior linked to equilibrium states.

Contribution

It introduces an extended mathematical model with variable input to accurately reproduce multiple variability classes and their transitions in GRS 1915+105.

Findings

Most classes can be categorized into stable, unstable, or transition patterns.

Transitions involve slow changes, spikes, dips, and red noise.

The model offers a physical interpretation aligned with slim disc theory.

Abstract

The complex time evolution in the X-ray light curves of the peculiar black hole binary GRS 1915+105 can be obtained as solutions of a non-linear system of ordinary differential equations derived form the Hindmarsch-Rose model and modified introducing an input function depending on time. In the first paper,assuming a constant input with a superposed white noise, we reproduced light curves of the classes rho, chi, and delta. We use this mathematical model to reproduce light curves, including some interesting details, of other eight GRS 1915+105 variability classes either considering a variable input function or with small changes of the equation parameters. On the basis of this extended model and its equilibrium states, we can arrange most of the classes in three main types: i) stable equilibrium patterns: (classes phi, chi, alpha'', theta, xi, and omega) whose light curve modulation follows the same time scale of the input function, because changes occur around stable equilibrium points; ii) unstable equilibrium patterns: characterised by series of spikes (class rho) originated by a limit cycle around an unstable equilibrium point; iii) transition pattern: (classes delta, gamma, lambda, kappa and alpha'), in which random changes of the input function induce transitions from stable to unstable regions originating either slow changes or spiking, and the occurrence of dips and red noise. We present a possible physical interpretation of the model based on the similarity between an equilibrium curve and literature results obtained by numerical integrations of a slim disc equations.