Fourier Analysis of Blazar Variability: Klein-Nishina Effects and the Jet Scattering Environment

TL;DR

This paper advances the theoretical understanding of blazar variability by incorporating the full Compton cross section into PSD and time lag models, enabling potential determination of external seed photon energies.

Contribution

It extends previous models by using accurate Compton emissivities, improving the analysis of blazar variability and electron cooling timescales.

Findings

Good agreement between δ-function and accurate PSD calculations for high-energy electrons.

Breaks in PSDs correspond to electron cooling timescales.

Time lags relate to differences in electron cooling timescales.

Abstract

The strong variability of blazars can be characterized by power spectral densities (PSDs) and Fourier frequency-dependent time lags. In previous work, we created a new theoretical formalism for describing the PSDs and time lags produced via a combination of stochastic particle injection and emission via the synchrotron, synchrotron self-Compton, and external Compton (EC) processes. This formalism used the Thomson cross section and simple $\delta$-function approximations to model the synchrotron and Compton emissivities. Here we expand upon this work, using the full Compton cross section and detailed and accurate emissivities. Our results indicate good agreement between the PSDs computed using the $\delta$-function approximations and those computed using the accurate expressions, provided the observed photons are produced primarily by electrons with energies exceeding the lower limit of the injected particle population. Breaks are found in the PSDs at frequencies corresponding to the cooling timescales of the electrons primarily responsible for the observed emission, and the associated time lags are related to the difference in electron cooling timescales between the two energy channels, as expected. If the electron cooling timescales can be determined from the observed time lags and/or the observed EC PSDs, then one could in principle use the method developed here to determine the energy of the external seed photon source for EC, which is an important unsolved problem in blazar physics.