A Comprehensive Power Spectral Density Analysis of Astronomical Time Series. I. The Fermi-LAT Gamma-Ray Light Curves of Selected Blazars

Abstract

We present the results of the Fermi-Large Area Telescope 10 yr long light curve (LC) modeling of selected blazars: six flat-spectrum radio quasars (FSRQs) and five BL Lacertae (BL Lacs), examined in 7, 10, and 14 day binning. The LCs and power spectral densities (PSDs) were investigated with various methods: Fourier transform, Lomb–Scargle periodogram (LSP), wavelet scalogram, autoregressive moving average (ARMA) process, continuous-time ARMA (CARMA), Hurst exponent (H), and the plane. First, with extensive simulations we showed that parametric modeling returns unreliable parameters, with a high dispersion for different realizations of the same stochastic model. Hence, any such analysis should be supported with Monte Carlo simulations. For our blazar sample, we find that the power-law indices β calculated from the Fourier and LSP modeling mostly fall in the range 1 ≲ β ≲ 2. Using the wavelet scalograms, we confirm a quasi-periodic oscillation (QPO) in PKS 2155−304 at a 3σ significance level, but do not detect any QPOs in other objects. The ARMA fits reached higher orders for 7 day binned LCs and lower orders for 10 and 14 day binned LCs for the majority of blazars, suggesting there might exist a characteristic timescale for the perturbations in the jet and/or accretion disk to die out. ARMA and CARMA modeling revealed breaks in their PSDs at timescales of a few hundred days. The estimation of H was performed with several methods. We find that most blazars exhibit H > 0.5, indicating long-term memory. Finally, the FSRQ and BL Lac subclasses are clearly separated in the plane.

Periodicity Analysis of Mrk 501 and Mrk 421 in Gamma Rays

“…In order to determine whether Mrk 421 and 501 exhibit QPOs, we also employ other methods for periodicity analysis and PSD modeling. In the following e give a short overview of the methods that will be used in our publication, that are also described in Tarnopolski et al [20].…”

“…Unlike the Lomb-Scargle periodogram, which describes oscillations on the whole time-series as sine waves, Wavelet scalogram as described in Tarnopolski et al [20], models the time series as wavelets. Wavelets are short localized oscillations.…”

“…The A-T-plane first described in Tarnopolski [22] and further utilized in Tarnopolski et al [20], was introduced as a method to estimate the Hurst exponent. The A-T plane compares the number of turning points T to the Abbe value A.…”

Comprehensive power spectral density analysis of the Fermi-LAT $γ$-ray light curves of selected blazars

“…This proceedings is based on the [2] publication and the methodology is described there in details. [5,6] are methods to generate a global PSD for a given time series, to calculate indices, to check their relation to the coloured noise, and https://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/binned_likelihood_tutorial.html https://github.com/fermi-lat/Fermitools-conda/wiki https://fermipy.readthedocs.io/en/latest/ to investigate global components of the LCs, such as short-and long-lasting variations.…”

A Relativistic Orbit Model for Temporal Properties of AGN

“…This prominent outburst is explained by a black hole binary model, where a secondary black hole interacts with the accretion disk of a much more massive primary black hole [22][23][24][25][26][27]. A comprehensive analysis of PSDs of 11 blazars was carried out recently, using the Fermi-LAT gamma-ray 10-years-long light curves, where a QPO in PKS 2155-304 was confirmed [47].…”