Non-linear oscillator models for the X-ray bursting of the microquasar GRS 1915+105

TL;DR

This paper introduces a non-linear differential equation model based on Fitzhugh-Nagumo equations to simulate the light curves and energy lags observed in the rho-state of the microquasar GRS 1915+105, linking accretion rate to state transitions.

Contribution

It provides a simple mathematical framework using non-linear equations to predict the bursting behavior and energy variations in GRS 1915+105, connecting accretion rate dynamics to observed states.

Findings

Model reproduces rho-class burst profiles

Energy modulation similar to observed data

Outer accretion rate influences state transitions

Abstract

The microquasar GRS 1915+105, exhibits a large variety of characteristic states, according to its luminosity, spectral state, and variability. The most interesting one is the so-called rho-state, whose light curve shows recurrent bursts. This paper presents a model based on Fitzhugh-Nagumo equations containing two variables: x, linked to the source photon luminosity L detected by the MECS, and y related to the mean photon energy. We aim at providing a simple mathematical framework composed by non-linear differential equations useful to predict the observed light curve and the energy lags for the rho-state and possibly other classes of the source. We studied the equilibrium state and the stability conditions of this system that includes one external parameter, J, that can be considered a function of the disk accretion rate. Our work is based on observations performed with the MECS on board BeppoSAX when the source was in rho and nu mode, respectively. The evolution of the mean count rate and photon energy were derived from a study of the trajectories in the count rate - photon energy plane. Assuming J constant, we found a solution that reproduces the x profile of the rho class bursts and, unexpectedly, we found that y exhibited a time modulation similar to that of the mean energy. Moreover, assuming a slowly modulated J the solutions for x quite similar to those observed in the nu class light curves is reproduced. According these results, the outer mass accretion rate is probably responsible for the state transitions, but within the rho-class it is constant. This finding makes stronger the heuristic meaning of the non-linear model and suggests a simple relation between the variable x and y. However, how a system of dynamical equations can be derived from the complex mathematical apparatus of accretion disks remains to be furtherly explored.