The Entrainment-Limited Evolution of FR II Sources: Maximum Sizes and A
  Possible Connection to FR Is
  We construct a simple theoretical model to investigate how entrainment
gradually erodes high-speed FR II jets. This process is described by embedding
a mixing-layer model developed originally to describe FR I objects in a
self-similar model for the lobe structure of classical FR II sources. Following
the classical FR II models, we assume that the lobe is dominated by the
particles injected from the central jet. The entrainment produces a boundary
shear layer which acts at the interface between the dense central jet and the
less denser surrounding lobe, and the associated erosion of the jet places
interesting limits on the maximum size of FR II sources. The model shows that
this limit depends mainly on the initial bulk velocity of the relativistic jet
triggered. The bulk velocities of FR IIs suggested by our model are in good
agreement with that obtained from direct pc-scale observations on ordinary
radio galaxies and quasars. Finally, we discuss how FR IIs may evolve into FR
Is upon reaching their maximum, entrainment-limited sizes.
