Variable synchrotron emission from BL Lacertae objects. I. Shock-in-jet scenario

Abstract

This paper presents a modeling of the variable synchrotron emission in the BL Lacertae sources (BLLs). Flux variability is assumed to be a result of the interaction between a relativistic shock wave with a magnetized jet material. Long-term flares (of months to years durations) are modeled via the propagation of a plane relativistic shock wave though the emission zone of a cylindrical form with the radius R and length H. As for short-term bursts (lasting from days to weeks), they may result from shock passage through the jet inhomogeneities such as a shell of enhanced density downstream to a Mach disc, originated due to pressure imbalance between the jet and its ambient medium. Emitting particles (electrons) gain the energies, sufficient to produce synchrotron photons at optical—X-ray frequencies, via the first-order Fermi mechanism. Observation’s frequency is the main parameter determining a rate of the increase/ decay of the emission via the characteristic decay time of emitting electrons. The magnetic field, assumed to be turbulent with an average field constant throughout the entire emission zone, is another key parameter determining the slope of a lightcurve corresponding to the flare—the higher strength the magnetic field has, the steeper the lightcurve is. The rest input parameters (shock speed, jet viewing angle, maximum/minimum energies of the electrons, particles’ density etc.), as well the strength of average magnetic field, influence the energy output from a flare.