Chaotic and stochastic processes in the accretion flows of the black hole X-ray binaries revealed by recurrence analysis

Abstract

Aims. Both the well known microquasar GRS 1915+105, as well as its recently discovered analogue, IGR J17091-3624, exhibit variability that is characteristic of a deterministic chaotic system. Their specific kind of quasi-periodic flares that are observed in some states is intrinsically connected with the global structure of the accretion flow, which are governed by the nonlinear hydrodynamics. One plausible mechanism that is proposed to explain this kind of variability is the thermal-viscous instability that operates in the accretion disk. The purely stochastic variability that occurs because of turbulent conditions in the plasma, is quantified by the power density spectra and appears in practically all types of sources and their spectral states. Methods. We pose a question as to whether these two microquasars are one of a kind, or if the traces of deterministic chaos, and hence the accretion disk instability, may also be hidden in the observed variability of other sources. We focus on the black hole X-ray binaries that accrete at a high rate and are, therefore, theoretically prone to the development of radiation pressure-induced instability. To study the nonlinear behaviour of the X-ray sources and distinguish between the chaotic and stochastic nature of their emission, we propose a novel method, which is based on recurrence analysis. Widely known in other fields of physics, this powerful method is used here for the first time in an astrophysical context. We estimate the indications of deterministic chaos quantitatively, such as the Rényi's entropy for the observed time series, and we compare them with surrogate data. Results. Using the observational data collected by the RXTE satellite, we reveal the oscillations pattern and the observable properties of six black hole systems. For five of them, we confirm the signatures of deterministic chaos being the driver of their observed variability. Conclusions. We test the method and confirm the deterministic nature of variability in the microquasars GRS 1915+105 and IGR J17091-3624. Furthermore, we also find significant traces of nonlinear dynamics in three other sources: GX 339-4, XTE J1550-564 and GRO J1655-40, particularly in the disk-dominated soft state, as well as in the intermediate states at the rising and declining phase of the outburst. Only for the source XTE J1650-500 no observation with such variability pattern was found. This is possibly due to the global accretion rate in this source being too small for the limit-cycle instability to develop.

Modified viscosity in accretion disks

“…Furthermore, a sample of sources proposed in Janiuk & Czerny (2011) suggested to undergo luminosity oscillations, possibly induced by the non-linear dynamics of the emitting gas. This suggestion was confirmed by the recurrence analysis of the observed time series, presented in Suková et al (2016). One possible driver of the non-linear process in the accretion disk is its thermal and viscous oscillation induced by the radiation pressure term; it can be dominant for high enough accretion rates in the innermost regions of the accretion disk, which are the hottest.…”

The chaotic long-term X-ray variability of 4U 1705–44

“…The recurrence analysis tool introduced by Eckmann et al (1987) and further developed by Marwan et al (2007) has been used in time series analysis of various experimental data sets for the purpose of distinguishing recurrent phenomena not easily extrapolated by other correlation methods. Recurrence analysis was recently used to characterise deterministic versus stochastic structure in the light curves of black hole X-ray binaries (Grzedzielski et al 2015, Suková et al 2016. The production of a recurrence plot (RP) is similar to the Close Returns method used in Sec.…”

Recurrence network measures for hypothesis testing using surrogate data: Application to black hole light curves

“…The complete light curves have been presented in [22], where all the light curves have been analyzed using D 2 and K 2 and classified based on a dynamical perspective and the nature of the noise content. This classification is mostly confirmed by a recurrence plot analysis [43] and very recently by a machine learning software analysis [44], where the authors developed a set of automated schemes based on supervised machine learning tools to efficiently Table 1 Variation of the K-L measure obtained by comparing the probability distributions of local CC of the RNs for successive embedding dimensions for time series from Lorenz attractor, white noise and the light curves from all GRS states. The last column indicates the embedding dimension at which the measure saturates in each case.…”