A comparison of the acceleration mechanisms in young stellar objects and active galactic nuclei jets

We examine the hypothesis that there exists a simple scaling between the observed velocities of jets found in Young Stellar Objects (YSOs) and jets found in Active Galactic Nuclei (AGN). We employ a very simplified physical model of the jet acceleration process. We use time-dependent, spherically symmetric wind models in Newtonian and relativistic gravitational fields to ask whether the energy input rates required to produce the jet velocities observed in YSOs (of about 2 $\times$ the escape velocity from the central object) can also produce AGN jet velocities (Lorentz factors of $\gamma \sim$ 10). Such a scaling would be expected if there is a common production mechanism for such jets. We demonstrate that such a scaling does exist, provided that the energy input process takes place sufficiently deep in the gravitational potential well, enabling physical use to be made of the speed of light as a limiting velocity, and provided that the energy released in the accretion process is imparted to a small fraction of the available accreting material.