2011ApJ...729..104K

High energy emission from blazars is thought to arise in a relativistic jet launched by a supermassive black hole. The emission site must be far from the hole and the jet relativistic, in order to avoid absorption of the photons. In extreme cases, rapid variability of the emission suggests that structures of length scale smaller than the gravitational radius of the central black hole are imprinted on the jet as it is launched and modulate the radiation released after it has been accelerated to high Lorentz factor. We propose a mechanism which can account for the acceleration of the jet, and for the rapid variability of the radiation, based on the propagation characteristics of large-amplitude waves in charge-starved, polar jets. Using a two-fluid (e ^±) description, we find that the outflows exhibit a delayed acceleration phase that starts when the inertia associated with the wave currents becomes important. The fluids propagate with the wave at approximately the sonic speed, corresponding to a bulk Lorentz factor γ~10^4 Δt_{100}^{1/3}κ_{rg}^{–1/3}L{46}^{1/6}M9^{-1/3} out to radius r_1~Δt_{100}^{1/3} κ_{rg}^{2/3}L{46}^{1/6}M9^{2/3}  pc, after which the wave Lorentz factor accelerates as γ_w∝ r, and that of the fluids as γ ∝ r ². (Δt₁₀₀ is the variability time in units of 100 s, κ_{rg} is the pair multiplicity at one gravitational radius, L₄₆ is the "4π-luminosity" of the jet in units of 10⁴⁶ erg/s, and M₉ is the black hole mass in units of 10⁹ M_☉) The time structure imprinted on the jet at launch modulates photons produced by the accelerating jet provided κ_{rg}<14  Δt_{100} L_{46}{1/8}M_{9}^{-1}, suggesting that very rapid variability is confined to sources in which the electromagnetic cascade in the black hole magnetosphere is not prolific.