The Bulk Flow Velocity and Acceleration of the Inner Jet in M\,87 (2106.13886v1)

Abstract: A high sensitivity, 7mm Very Long Baseline Array image of M\,87 is analyzed in order to estimate the jet velocity within 0.65 mas of the point of origin. The image captured a high signal to noise, double-ridged, counter-jet extending $\sim 1$ mas from the nucleus. After defining conditions and requirements that justify approximate time averaged bilateral symmetry, a continuous set of Lorentz transformations are found that map the double-ridged counter-jet intensity profile into the double-ridged jet intensity profile. The mapping is realized by a uniformly accelerating flow with intrinsic velocity of $\sim 0.27$c at 0.4 mas (a de-projected distance of 0.38 lt-yrs) to $0.38$c at 0.65 mas (a de-projected distance of 0.61 lt-yrs) from the nucleus. Since the velocity field is derived from the global surface brightness profile and does not depend on the motion of enhanced features, it is most likely a bulk flow velocity as opposed to a pattern velocity. This interpretation is corroborated by the fact that the distribution of the apparent velocities of previously identified individual features (from the literature) within 0.65 mas of the nucleus are consistent with local hydrodynamic shocks being advected with the local bulk flow velocity. The bulk flow velocity of the visible inner jet is a constraint that can potentially break degeneracies between numerical simulations that are designed to replicate both the annulus that was imaged by the Event Horizon Telescope as well as the base of the inner jet.