Superluminal Motion as a Lower Bound: Lorentz Factors and Viewing Angles for Fast Jet Components

This paper addresses a single accounting question in the physics of relativistic jets: what an observed apparent transverse speed, by itself and without any flux information, forces the true Lorentz factor and viewing angle of a jet component to be. Using published apparent speeds from six to twenty-six times the speed of light for seven well-tracked components, the calculation derives new bounds and budgets from standard synchrotron and special-relativistic relations, with every number produced by the deposited compute script. The headline results are: gamma min max = 26, gamma min min = 6.08, theta max for fastest = 2.2. Even the slowest component in the set requires a Lorentz factor above six, and the fastest requires a value above twenty-six with a viewing angle below about two degrees. The study is a computation from stated assumptions and published inputs; it is simulated, not measured, and its conclusions are stated at the precision those inputs support.