Blazar Variability: A Study of Nonstationarity and the Flux–Rms Relation

Abstract

We analyze X-ray light curves of the blazars Mrk 421, PKS 2155−304, and 3C 273 using observations by the Soft X-ray Telescope on board AstroSat and archival XMM-Newton data. We use light curves of length 30–90 ks from three to four epochs for all three blazars. We apply the autoregressive integrated moving average model, which indicates the variability is consistent with short memory processes for most of the epochs. We show that the power spectral density (PSDs) of the X-ray variabilities of the individual blazars are consistent within uncertainties across the epochs. This implies that the construction of broadband PSD using light curves from different epochs is accurate. However, using certain properties of the variance of the light curves and its segments, we show that the blazars exhibit hints of nonstationarity beyond that due to their characteristic red-noise nature in some of those observations. We find a linear relationship between the root-mean-squared amplitude of variability at shorter timescales and the mean flux level at longer timescales for light curves of Mrk 421 across epochs separated by decades as well as light curves spanning 5 days and ∼10 yr. The presence of a flux–rms relation over very different timescales may imply that, similar to the X-ray binaries and Seyfert galaxies, longer and shorter timescale variabilities are connected in blazars.

Short-Term X-ray Variability during Different Activity Phases of Blazars S5 0716+714 and PKS 2155-304

“…Test of stationarity using ADF and KPSS shows that the variability is highly non-stationary both in normal and logarithmic space (see Table 2) except probably for S5 0716+714 where the KPSS test suggests trend-stationarity. In fact, short-term X-ray variability of blazars has been normally found to be non-stationarity, (e.g., [5,6,8]). This suggests that using Fourier methods to investigate variability can result in erroneous inferences.…”

“…This suggests that using Fourier methods to investigate variability can result in erroneous inferences. However, the difference light curve derived by subtracting the previous value from the next makes all the light curves stationary except IDs 0411780501 and 0411780601 of PKS 2155-304, indicating the auto-regressive integrated moving average (ARIMA) method for timing studies as more appropriate (e.g., [8]).…”

“…Earlier and even now, optical bands have been primarily leading the IDV studies as photon statistic at higher energies has prohibited such studies in the past. However, with the continuous advancement in detector technologies, such sub-day studies have now been possible at X-ray, (e.g., [5][6][7][8]), gamma-ray, (e.g., [9,10]), and very high energies VHEs [11,12], albeit still for bright flares. These studies have also reported sub-hours to a few minutes variability-implying a compact, highly luminous emission region, still optically thin to pair production.…”

“…The renewed focus and targeted campaigns of blazars with good cadence observations, especially after the launch of the Fermi observatory that continuously surveys the sky at MeV-GeV energies have made such studies now possible, over both long and short timescales, (e.g., [1,16]). Attempts have been made to connect the short-and long-term behavior, (e.g., [8,17]) and compare these properties to those of other AGNs. Though they can provide a general idea, inferring any time scale by comparing long-and short-term trends are fraught with uncertainties as the short-term behavior is not yet widely established.…”

“…The short-term variability being primarily a result of competition between particle acceleration and cooling provides not only a key to study these two but the statistical behavior can be used to test a few models of blazars as well a comparative study with the well-established properties of AGNs. In this sense, long-term properties of variability have been explored fairly well, (e.g., [1,16,[18][19][20][21]) but the short-term detailed studies are still few, (e.g., [5,6,8,22,23]), especially at high energies due to fewer long exposure observations during such occurrences. Interestingly, literature refers to blazars as extreme AGNs with emission dominated almost entirely by the relativistic jet, in stark contrast with a majority of AGNs.…”