Complex variability of Kepler AGN revealed by recurrence analysis

Abstract

The advent of new time domain surveys and the imminent increase in astronomical data expose the shortcomings of traditional time series analysis (such as power spectra analysis) in characterising the abundantly varied, complex and stochastic light curves of Active Galactic Nuclei (AGN). Recent applications of novel methods from non-linear dynamics have shown promise in characterising higher modes of variability and time-scales in AGN. Recurrence analysis in particular can provide complementary information about characteristic time-scales revealed by other methods, as well as probe the nature of the underlying physics in these objects. Recurrence analysis was developed to study dynamical trajectories in phase space, which can be constructed from one-dimensional time series such as light curves. We apply the methods of recurrence analysis to two optical light curves of Kepler-monitored AGN. We confirm the detection and period of an optical quasi-periodic oscillation in one AGN, and confirm multiple other time-scales recovered from other methods ranging from 5 days to 60 days in both objects. We detect regions in the light curves that deviate from regularity, provide evidence of determinism and non-linearity in the mechanisms underlying one light curve (KIC 9650712), and determine realizations of a linear stochastic process describe the dominant variability in the other light curve (Zwicky 229–015). We discuss possible underlying processes driving the dynamics of the light curves and their diverse classes of variability.

A ring accelerator? Unusual jet dynamics in the IceCube candidate PKS 1502+106

“…During the analysis, the connection between the radio and 𝛾-ray light curves was found since the RPs of both light curves in Fig. 15 show very similar structures at the Recurrence Rate (RR) = 30 per cent as also used in Phillipson et al (2020).…”

Investigating non-linear and stochastic hard X-ray variability of active galactic nuclei using recurrence analysis

“…Measures that quantify the structures present in RPs were introduced by Webber & Zbilut (1994), collectively called Recurrence Quantification Analysis (RQA), and subsequently applied to various fields including Mathematics, Geology, and Physiology (Gao & Cai 2000;Marwan et al 2002;Zbilut et al 2002) and others. RQA has been utilized in the study of the stability of terrestrial planets (Asghari et al 2004), in the distinction of chaotic and stochastic behavior in the X-ray variability of microquasars (Suková et al 2016), and in the confirmation of a quasi-periodic oscillation and the distinction of deterministic versus stochastic behavior in two Kepler -monitored AGN (Phillipson et al 2020). For an extensive overview of the history of RPs, RQA, and their applications, see the seminal review by Marwan et al (2007).…”

“…We use the time delay method in this study (discussed in Sec. 3; a detailed discussion of the method can be found in Phillipson et al 2020). As a rule of thumb, should not exceed approximately 10 percent the maximum phase space diameter (Zbilut & Webber 1992).…”

“…Lmax is a proxy for the K2 entropy, which is related to the maximum Lyapunov exponent that describes the rate of decay of nearby initial conditions for the geometric object (attractor) manifested from a set of differential equations. This measure has been used as a first-pass indication of nonlinearity, approximating results from calculating the K2 entropy outright in AGN monitored by Kepler (Phillipson et al 2020), when compared against the IAAFT surrogates, and as a probe of nonlinearity in XRBs (Suková et al 2016). When significant against the phase or IAAFT surrogates, Lmax gives an indication that higher-order moments beyond the second-order metrics contained in a PSD are responsible for the observed nonlinearity.…”

“…Recent work in the study of the optical light curves of AGN exemplifies how methods from nonlinear time series analysis can recover the same variability information as contained in the PSD and additionally probe traces of nonlinear structure (Phillipson et al 2020). Applications of the same method have been used to study the stochastic and nonlinear modes of Galactic X-ray binaries (Suková et al 2016;Phillipson et al 2018) and suggests that we test for similar behavior in the long-term monitoring of AGN.…”