2015ApJ...803....3C

We study the kinematics of ridge lines on the parsec-scale jet of the active galactic nucleus BL Lacertae. We show that the ridge lines display transverse patterns that move superluminally downstream, and that the moving patterns are analogous to waves on a whip. Their apparent speeds β_app(units of c) range from 3.9 to 13.5, corresponding to β_wave^gal = 0. 981 - 0.998 in the galaxy frame. We show that the magnetic field in the jet is well ordered with a strong transverse component, and assume that it is helical and that the transverse patterns are Alfvén waves propagating downstream on the longitudinal component of the magnetic field. The wave-induced transverse speed of the jet is non-relativistic (β_tr^gal ≲ 0.09). In 2010 the wave activity subsided and the jet then displayed a mild wiggle that had a complex oscillatory behavior. The Alfvén waves appear to be excited by changes in the position angle of the recollimation shock, in analogy to exciting a wave on a whip by shaking the handle. A simple model of the system with plasma sound speed β_s= 0.3 and apparent speed of a slow MHD wave β_app, S_= 4 yields Lorentz factor of the beam Γ_beam∼ 4.5, pitch angle of the helix (in the beam frame) α ∼ 67°, Alfvén speed β_A∼ 0.64, and magnetosonic Mach number M_ms∼ 4.7. This describes a plasma in which the magnetic field is dominant and in a rather tight helix, and Alfvén waves are responsible for the moving transverse patterns.