Variability constraints on blazar magnetic fields

Synchrotron self-Compton (SSC), external Compton, and hadronic models of blazar emission all invoke particle acceleration at relativistic shocks as the dissipation mechanism seeding their non-thermal X-ray and gamma-ray emission. Studies of diffusive acceleration at such relativistic shocks are more sparse than those pertaining to their non-relativistic counterparts. This paper presents acceleration time results from the theory of relativistic shock acceleration that are pertinent to AGN observations. This temporal information interfaces critically with the observed rapid variability of blazars. Very recent theoretical results are presented, where it is determined that acceleration times can never become arbitrarily short in relativistic shocks, but are dominated by diffusion in the downstream region and couple to the particle's gyroperiod. This fundamental bound links to the variability timescale to generate a firm lower bound to the environmental magnetic field of blazars such as Mrk 421. Consistency of such a bound with SSC spectral models and flare decay times is discussed.