Particle diffusion and localized acceleration in inhomogeneous AGN jets – II. Stochastic variation

We study the stochastic variation of blazar emission under a 2-D spatially resolved leptonic jet model we previously developed. Random events of particle acceleration and injection in small zones within the emission region are assumed to be responsible for flux variations. In addition to producing spectral energy distributions that d escribe the observed flux of Mrk 421, we further analyze the timing properties of the simulated light curves, such as the power spectral density (PSD) at different bands, flux-flux correlation s, as well as the cross-correlation function between X-rays and TeV γ-rays. We find spectral breaks in the PSD at a timescale comparable to the dominant characteristic time scale in the system, which is usually the predefined decay time scale of an acceleration event. Cooling im poses a delay, and so PSDs taken at lower energy bands in each emission component (synchrotron or inverse Compton) generally break at longer timescales. The flux-flux correlat ion between X-rays and TeVγ-rays can be either quadratic or linear, depending on whether or not there are large variation of the injection into the particle acceleration process. When the relationship is quadratic, the TeV flares lag the X-ray flares, and the optical & GeV flares are larg e enough to be comparable to the ones in X-ray. When the relationship is linear, the lags a re insignificant, and the optical & GeV flares are small.