Relativistic Jet Propagation: Its Evolution and Linear Size Cosmic Dilation

Relativistic jets are ubiquitous in astrophysical systems that contain central cores. They transport large amounts of energy to large distances from the source and their interaction with the ambient medium has a crucial effect on the evolution of the system. Furthermore, the radio luminosity exhibited by these jets are merely an indirect measure of the energy transported through the jets from the central engine which is not easily interpretable. The mechanism(s) responsible for these jet phenomena is still a subject of debate. In this work, we use both statistical and analytical methods to obtain a mathematical relation that may explain the observed physical processes in the evolution of astrophysical jets. We first obtain measured observable parameters characterizing these jets, and then carry out linear regressions of these parameters against each other to obtain a statistical relation. We also use analytical method to obtain a relation which in conjunction with the statistical relation yields a new relation that may explain how these jets interact with the ambient medium through which they propagate. Result shows that radio jet velocity () depends on the radio source energy density (u) and ambient particle number density () according to the relation, . This relation suggestively indicates that jet velocity has a direct power-law relationship with the source energy density and an inverse power-law relationship with the ambient particle number density.