Blazars are a subclass of active galactic nuclei (AGN) whose relativistic jets are pointing towards the observer. As AGN, they consist of a supermassive black hole (SMBH), a luminous accretion disk, gas clouds (broad- and narrow-line regions), a dusty torus, and radio jets. Due to their relativistic nature, superluminal motion is observed in the jets. Blazars exhibit flux variability on a wide range of timescales, from minutes up to decades. In some instances, the variability can be attributed to a second SMBH crossing the accretion disk of the first one (OJ 287). In many cases, though, the source of variability is not well-known, and it seems to originate from complex stochastic processes governing the matter–radiation interaction in AGN. The simplest continuous-time stochastic model is the Ornstein-Uhlenbeck process (its discrete version being the first order autoregressive process, AR(1)). However, some blazars exhibit power spectral densities (PSDs) that are better described by a higher order autoregressive moving average (ARMA) process, and its continuous-time analog, the CARMA model. Both modelling and theoretical explanations of such spectra are a hot topic nowadays.

Figure 1. (a) An illustrative example of a blazar LC, and (b) its PSD which exhibits two power law regions with a change of index at a break frequency, a peak signifying a quasiperiodic oscillation, and a plateau down to a Poisson noise level (coming from the uncertainties of individual observations) at high frequencies. (c) A high-energy spectral energy distribution of the blazar PKS 1222+21, extending into the very high-energy regime. (d) The Fermi-LAT gamma-ray LC of the blazar 3C 279 below the threshold (horizontal red line) exhibits different dynamics than above it. A threshold ARMA model was fitted. (e) The unambiguous separation of FSRQs (cold colours) and BL Lacs (warm colors) in the A—T plane. Differently sampled LCs (7, 10, and 14d binnings) behave consistently.

Blazars are further divided into subclasses (flat spectrum radio quasars, FSRQs, and BL Lacertae objects, BL Lacs) which are usually discerned based on their characteristics visible in the optical spectra: FSRQs possess prominent emission lines, whereas BL Lacs exhibit featureless continua or weak emission lines only. These two blazar types appear to reside in different regions of the A—T plane. The latter relies only on the light curves, hence is particularly useful when spectroscopy is not feasible. This finding is therefore of particular importance since it hints that the variability patterns (not only in the optical band, but in the gamma rays as well) stem from different emission mechanisms.

Figure 2. Blazar candidates observed in the optical range by OGLE follow the subclass separation in the A—T plane, although the separation is not as sharp as in the gamma-rays. This might be due to a misclassification, or hint at subtly different emission mechanisms in different wavebands.

In my research I explore other ways to describe the variability patterns, e.g., the Hurst exponent or stochastic threshold models. The latter are composed of ARMA processes of different orders dependent on the flux threshold. They constitute a promising opportunity as they can provide means to distinguish quiescent states from flares, which is of importance when it comes to modelling the emission. Characterising single sources is not enough, though, hence a population analysis is desired to quantify the nature of flares globally. Such an approach, when applied to a handful of blazars (Wang et al. 2020), showed that the spectral energy distributions (SEDs) during flares can become softer, harder, or remain the same compared to quiescent states. Therefore, a careful comparison of the performance of different emission models, applied to a vast data set in unison with the threshold models for the light curves, can be expected to give unprecedented insight into the physical processes at play. Combined with multivariate stochastic modelling of (possibly multiwavelength) light curves, PSDs, and SEDs, it is expected it will allow, eventually, to put constraints on the interconnections between the underlying processes, and a thorough interpretation in light of the numerous physical theories.