INTERPRETATION OF VLBI KINEMATIC AND POLARIZATION DATA - APPLICATION TO 3C-345

We present a new method of extracting kinematic information from multi epoch VLBI observations that relaxes the usual assumption that the jet is straight. Analyzing multiple observations of the quasar 3C 345 mad e by ourselves and by the Caltech group, we find that components C2 an d C3 move along a common path and that their proper motions are consis tent with a single constant pattern speed. With this assumption, we ca n then reconstruct the full three-dimensional trajectory of the jet. W e find that the trajectory makes an initial angle theta similar or equ al to 2 degrees 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 constrai nts with the polarization information for component C3 and for the und erlying jet obtained by VLBI polarimetry (Brown, Roberts, and Wardle 1 994). We show that component 3C can be interpreted as a shock in a flu id jet with an ultrarelativistic equation of state. We explore the sho ck parameters that are consistent with the observations and determine the ranges of shock strength, thickness of the shocked region, upstrea m 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 th e 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 ap art from that due to adiabatic compression. This fast shock is in cont rast to that required for the BL Lacertae object OJ 287, where the pol arization, kinematic, and X-ray data show that the shock is slower tha n the underlying jet (Cawthorne and Wardle 1988). This difference may account in part for the slower superluminal speeds observed in BL Lace rtae objects.