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.