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

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.

References in corpus (1)

• On the limit cycle instability in magnetized accretion discs

Cited by in corpus (10)

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• AstroSat view of IGR J17091-3624 and GRS 1915+105: decoding the 'pulse' in the 'Heartbeat State'
• Revisiting Evidence of Chaos in X-ray Light Curves: The Case of GRS 1915+105
• A non-linear mathematical model for the X-ray variability classes of the microquasar GRS 1915+105 -- II: transition and swaying classes
• Disc-corona interaction in the heartbeat state of GRS 1915+105
• A non-linear mathematical model for the X-ray variability classes of the microquasar GRS 1915+105 -- I: quiescent, spiking states and QPOs
• Correlating nonlinear time series and spectral properties of IGR J17091-3624: Is it similar to GRS 1915+105?
• Lyapunov functions for a non-linear model of the X-ray bursting of the microquasar GRS 1915+105
• Similarities and Differences in Accretion Flow Properties between GRS 1915+105 and IGR J17091-3624: a Case Study
• Recurrent Instability in LMXB Accretion Disks: How Strange is GRS 1915+105?