A Magnetohydrodynamic Model of The M87 Jet. II. Self-consistent
  Quad-shock Jet Model for Optical Relativistic Motions and Particle
  Acceleration
  We describe a new paradigm for understanding both relativistic motions and
particle acceleration in the M87 jet: a magnetically dominated relativistic
flow that naturally produces four relativistic magnetohydrodynamic (MHD) shocks
(forward/reverse fast and slow modes). We apply this model to a set of optical
super- and subluminal motions discovered by Biretta and coworkers with the {\em
Hubble Space Telescope} during 1994 -- 1998. The model concept consists of
ejection of a {\em single} relativistic Poynting jet, which possesses a
coherent helical (poloidal + toroidal) magnetic component, at the remarkably
flaring point HST-1. We are able to reproduce quantitatively proper motions of
components seen in the {\em optical} observations of HST-1 with the same model
we used previously to describe similar features in radio VLBI observations in
2005 -- 2006. This indicates that the quad relativistic MHD shock model can be
applied generally to recurring pairs of super/subluminal knots ejected from the
upstream edge of the HST-1 complex as observed from radio to optical
wavelengths, with forward/reverse fast-mode MHD shocks then responsible for
observed moving features. Moreover, we identify such intrinsic properties as
the shock compression ratio, degree of magnetization, and magnetic obliquity
and show that they are suitable to mediate diffusive shock acceleration of
relativistic particles via the first-order Fermi process. We suggest that
relativistic MHD shocks in Poynting-flux dominated helical jets may play a role
in explaining observed emission and proper motions in many AGNs.
