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Multifractality Signatures in Quasars Time Series. I. 3C 273

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Multifractality Signatures in Quasars Time Series. I. 3C 273 MNRAS 000,1{12 (2017) Preprint 21 May 2018 Compiled using MNRAS LATEX style file v3.0 Multifractality Signatures in Quasars Time Series. I. 3C 273 A. Bewketu Belete,1? J. P. Bravo,1;2 B. L. Canto Martins,1;3 I. C. Le~ao,1 J. M. De Araujo,1 J. R. De Medeiros1 1Departamento de F´ısica Te´orica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, RN 59078-970, Brazil 2Instituto Federal de Educa¸c~ao, Ci^encia e Tecnologia do Rio Grande do Norte, Natal, RN 59015-000, Brazil 3Observatoire de Gen`eve, Universit´ede Gen`eve, Chemin des Maillettes 51, Sauverny, CH-1290, Switzerland Accepted 2018 May 15. Received 2018 May 15; in original form 2017 December 21 ABSTRACT The presence of multifractality in a time series shows different correlations for dif- ferent time scales as well as intermittent behaviour that cannot be captured by a single scaling exponent. The identification of a multifractal nature allows for a char- acterization of the dynamics and of the intermittency of the fluctuations in non-linear and complex systems. In this study, we search for a possible multifractal structure (multifractality signature) of the flux variability in the quasar 3C 273 time series for all electromagnetic wavebands at different observation points, and the origins for the observed multifractality. This study is intended to highlight how the scaling behaves across the different bands of the selected candidate which can be used as an addi- tional new technique to group quasars based on the fractal signature observed in their time series and determine whether quasars are non-linear physical systems or not. The Multifractal Detrended Moving Average algorithm (MFDMA) has been used to study the scaling in non-linear, complex and dynamic systems. To achieve this goal, we applied the backward (θ = 0) MFDMA method for one-dimensional signals. We observe weak multifractal (close to monofractal) behaviour in some of the time series of our candidate except in the mm, UV and X-ray bands. The non-linear temporal correlation is the main source of the observed multifractality in the time series whereas the heaviness of the distribution contributes less. Key words: methods: statistical { galaxies: active { (galaxies:) quasar: individual: 3C 273 1 INTRODUCTION among the most energetic and complex objects in the uni- verse. Variability is one of the main observational features Active galactic nucleus (AGN) is a very small fraction of a of AGNs noticed at the whole electromagnetic wavebands. galaxy whose luminosity outshines the entire galaxy - indi- Courvoisier et al.(1990) affirm that flux variation is a well- cating that the excess luminosity is not produced by stars. known property of AGNs. Quasars are a very luminous type arXiv:1805.07287v1 [astro-ph.GA] 18 May 2018 The luminosity observed almost in all the electromagnetic of AGNs which are roughly classified as radio loud and ra- (EM) spectrum further ensures that the energy production dio quiet. The variability observed in quasars light-curves mechanism in AGNs is completely different from the one at short and long time scale, from less than one hour up in stars. The exciting modern era of AGN studies begins to several decades, is one of the most important observed with the identification of the first high-luminosity AGNs characteristics of quasars. The physical features of quasars (Schmidt 1963). Even though the history of AGN research depend on several properties such as the mass of the central begun many years before, the science still remains with a black hole, the rate of gas accretion onto the black hole, the lot of open questions, such as understanding the energy pro- orientation of the accretion disk, the degree of obscuration duction mechanisms, determining the size of the broad line of the nucleus by dust, and the presence or absence of jets. region, and many others. As might be expected AGNs are The quasar 3C 273 is a non-extreme, but a very bright type of AGN (McHardy et al. 2007). The quasar 3C 273 ? E-mail: asnakew@fisica.ufrn.br has been extensively studied on diverse time scales across © 2017 The Authors 2 A. Bewketu et al. the entire EM spectrum, with measurements made in sin- (the so-called singularity spectrum) is needed. The multi- gle bands and often as well as in multi-bands (Fan et al. fractal analysis consists of determining whether some type 2014, 2009; Abdo et al. 2010; Pacciani et al. 2009; Dai et al. of power-law scaling exists for various statistical moments 2009; Soldi et al. 2008; McHardy et al. 2007; Chernyakova at different scales. The main feature of multifractals is that et al. 2007; Jester et al. 2006; Savolainen et al. 2006; At- the fractal dimension is not the same on all scales. In the tridge et al. 2005; Kataoka et al. 2002; Greve et al. 2002; case of a one-dimensional signal, the fractal dimension can Sambruna et al. 2001; Collmar et al. 2000; Mantovani et al. vary from unity to a dot. Thus, a fundamental character- 2000). Blazars show rapid flux variability across the com- istic of the multifractal structure is that the scaling prop- plete EM spectrum (Kalita et al. 2015). Fluctuations rang- erties may be different in different segments of the system ing from a few tens of minutes (and sometimes even more requiring more than one scaling exponent to be completely rapid) to less than a day is often known as intra-day vari- described. The multifractal spectrum effectively shows the ability (IDV) (Wagner & Witzel 1995). It has been reported distribution of scaling exponents for a signal and provides a by Courvoisier et al.(1990) that the flux variation across the measure of how much the local regularity of a signal varies spectra of 3C 273 shows no simple correlation. It was also in time. The presence of multifractality in a physical sys- noticed that, at higher frequencies, the strength of the flux tem indicates the non-linearity, inhomogeneity, complexity variations in 3C 273 are higher than in the lower frequencies of the system dynamics (Kantelhardt et al. 2002), the pres- (e.g. Fan et al. 2009). Fluctuation in the flux of astronomical ence of intermittency (Vio et al. 1991), and provides a way objects is an important and widespread phenomenon which to describe signals from a complex, non-linear and dynamic provides relevant information on the dynamics of the system systems. A multifractal analysis performed by Longo et al. that drives the fluctuation. The IDV in blazars is the least (1996) clearly indicated non-linear intermittent behaviour well-understood type of variations but it can provide an im- in the long term (1910 - 1991) B-band light curve of NGC portant tool for learning about structures on small spatial 4151. scales and it also provides us with a better understanding Several techniques have been proposed in the literature of the different radiation mechanisms that are important in to study the scaling and self-similarity or fractality prop- the emitting regions (e.g. Wagner & Witzel 1995). Any char- erties in the time series, such as Autocorrelation Function acteristic timescale of variability can effectively provide us (ACF), detrended fluctuation analysis (DFA), the multifrac- with information about the physical structure of the central tal detrended fluctuation analysis (MFDFA), rescaled range region and complex phenomena such as hot spots on accre- statistical (R/S) analysis that provide type of self-affinity for tion discs (e.g. Mangalam & Wiita 1993). It has been known stationary time series (Bashan et al. 2008), the periodogram that quasars are non-linear physical systems whose tempo- regression (GPH) method, the (m, k)-Zipf method, and the ral evolution is described by non-linear dynamical equations detrended moving average (DMA) analysis (Shao et al. 2012; and their light-curves cannot be analysed only by means of Carbone et al. 2004). The simplest type of multifractal anal- the classical method (e.g., PS, SF, and covariance analyses) ysis is based upon the standard partition function multi- which are suitable only for dealing the signals of a linear fractal formalism, which has been developed for the multi- system (Vio et al. 1991). The presence of non-linearity in a fractal characterization of normalized, stationary measure- time series leaves open the possibility that the time series is ments (Peitgen et al. 2004; Bacry et al. 2001; Barab´asi & produced by a chaotic system. However, as indicated by Vio Vicsek 1991; Feder 1988). However, this standard formal- et al.(1992), non-linearity is a necessary, but not sufficient, ism does not give correct results for non-stationary time condition for a light curve to be produced by a chaotic sys- series that are affected by trends or that cannot be nor- tem. There are a number of real-world signals from complex malized. Therefore, an improved multifractal formalism was systems that exhibit self-similarity and non-linear power-law developed known as wavelet transform modulus maxima behaviour that depends on higher-order moments and scale, (WTMM) method (Muzy et al. 1991), which is based on which is the signature of a fractal signature in the system the wavelet analysis and involves tracing the maxima lines (Feder 1988). in the continuous wavelet transform over all scales. This To study the variability seen in quasars light-curves, as- method has been widely used in diverse fields of solar ac- tronomers have been working on the time-frequency analysis tivities to the earth science (e.g. Geology, DNA sequences, using different approaches to unveil the physics behind the neuron spiking, heart rate dynamics, economic time series observed physical characteristics.
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