Multi-wavelength Variability Signatures of Relativistic Shocks in Blazar Jets

Mildly relativistic shocks that are embedded in colliding magnetohydrodynamic flows are prime sites for relativistic particle acceleration and the production of strongly variable, polarized multi-wavelength emission from relativistic jet sources such as blazars and gamma-ray bursts. The principal energization mechanisms at these shocks are diffusive shock acceleration and shock drift acceleration. In recent work, we had self-consistently coupled shock acceleration and radiation transfer simulations in blazar jets in a basic one-zone scenario. These one-zone models revealed that the observed spectral energy distributions (SEDs) of blazars strongly constrain the nature of the hydromagnetic turbulence in the shock layer. In this paper, we expand our previous work by including full time dependence and treating two zones, one being the site of acceleration and the other a larger emission zone. This construction is applied to multi-wavelength flares of the flat-spectrum radio quasar (FSRQ) 3C.279, fitting snapshot SEDs and generating light curves that are consistent with observed variability timescales. We also present a generic study for the typical flaring behavior of the BL Lac object Mrk 501. The model predicts correlated variability across all wavebands, but cross-band time lags depending on the type of blazar (FSRQ versus BL Lac), as well as distinctive spectral hysteresis patterns in all wavelength bands, from millimeter radio waves to gamma-rays. These evolutionary signatures serve to provide diagnostics on the competition between acceleration and radiative cooling.