Studies of the Jet in BL Lacertae I. Recollimation Shock and Moving
  Emission Features
  Parsec-scale VLBA images of BL Lac at 15 GHz show that the jet contains a
permanent quasi-stationary emission feature 0.26 mas (0.34 pc projected) from
the core, along with numerous moving features. In projection, the tracks of the
moving features cluster around an axis at position angle -166.6 deg that
connects the core with the standing feature. The moving features appear to
emanate from the standing feature in a manner strikingly similar to the results
of numerical 2-D relativistic magneto-hydrodynamic (RMHD) simulations in which
moving shocks are generated at a recollimation shock. Because of this, and the
close analogy to the jet feature HST-1 in M87, we identify the standing feature
in BL Lac as a recollimation shock. We assume that the magnetic field dominates
the dynamics in the jet, and that the field is predominantly toroidal. From
this we suggest that the moving features are compressions established by slow
and fast mode magneto-acoustic MHD waves. We illustrate the situation with a
simple model in which the slowest moving feature is a slow-mode wave, and the
fastest feature is a fast-mode wave. In the model the beam has Lorentz factor
about 3.5 in the frame of the host galaxy, and the fast mode wave has Lorentz
factor about 1.6 in the frame of the beam. This gives a maximum apparent speed
for the moving features 10c. In this model the Lorentz factor of the pattern in
the galaxy frame is approximately 3 times larger than that of the beam itself.
