Time dependent simulations of multiwavelength variability of the blazar Mrk 421 with a Monte Carlo multi-zone code

(abridged) We present a new time-dependent multi-zone radiative transfer code and its application to study the SSC emission of Mrk 421. The code couples Fokker-Planck and Monte Carlo methods, in a 2D geometry. For the first time all the light travel time effects (LCTE) are fully considered, along with a proper treatment of Compton cooling, which depends on them. We study a set of simple scenarios where the variability is produced by injection of relativistic electrons as a `shock front' crosses the emission region. We consider emission from two components, with the second one either being pre-existing and co-spatial and participating in the evolution of the active region, or spatially separated and independent, only diluting the observed variability. Temporal and spectral results of the simulation are compared to the multiwavelength observations of Mrk 421 in March 2001. We find parameters that can adequately fit the observed SEDs and multiwavelength light curves and correlations. There remain however a few open issues, most notably: i) systematic soft intra-band X-ray lags. ii) The quadratic correlation between the TeV and X-ray flux during the flare decay has not been reproduced. These features are among those affected by the spatial extent and geometry of the source. The difficulty of producing hard X-ray lags is exacerbated by a bias towards soft lags caused by the combination of energy dependent radiative cooling time-scales and LCTE. About the second emission component, our results strongly favor the scenario where it is co-spatial and it participates in the flare evolution, suggesting that different phases of activity may occur in the same region. The cases presented in this paper represent only an initial study, and despite their limited scope they make a strong case for the need of true time-dependent and multi-zone modeling.

Comments: Accepted for publication in MNRAS, 20 pages, 9 figures

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