Interpretation of VLBI kinematic and polarization data: Application to 3C 345

Abstract

We present a new method of extracting kinematic information from multiepoch VLBI observations that relaxes the usual assumption that the jet is straight. Analyzing multiple observations of the quasar 3C 345 made by ourselves and by the Caltech group, we find that components C2 and C3 move along a common path and that their proper motions are consistent with a single constant pattern speed. With this assumption, we can then reconstruct the full three-dimensional trajectory of the jet. We find that the trajectory makes an initial angle θ~ 2^deg^ with the line of sight and is gently curving away from it. The Lorentz factor of the pattern speed is at least 11.8 h^-1^ (H_0_ = 100 h km s^-1^ Mpc^-1^). We then combine these kinematic constraints with the polarization information for component C3 and for the underlying jet obtained by VLBI polarimetry (Brown, Roberts, & Wardle 1994). We show that component 3C can be interpreted as a shock in a fluid jet with an ultrarelativistic equation of state. We explore the shock parameters that are consistent with the observations and determine the ranges of shock strength, thickness of the shocked region, upstream and downstream fluid velocities, and degree of order of the magnetic field in the underlying jet. We find that the shock speed is greater than that of the underlying jet (i.e., the fluid velocity is toward the nucleus in the frame of the shock) and that the shock must be rather weak. Also, there can be little particle acceleration in the shock apart from that due to adiabatic compression. This fast shock is in contrast to that required for the BL Lacertae object OJ 287, where the polarization, kinematic, and X-ray data show that the shock is slower than the underlying jet (Cawthorne & Wardle 1988). This difference may account in part for the slower superluminal speeds observed in BL Lacertae objects.