On the Relationship between BL-Lacertae Objects and FRI Radio Galaxies

The idea that Fanaroff-Riley Class~I Radio Galaxies contain core jets with Lorentz factors of the order of a few and are the parent population for BL~Lac Objects is examined, with particular reference to the data on two FRI Radio Galaxies, NGC~315 and NGC~6251. Conservation laws for an entraining relativistic jet are derived and are used to determine a relationship between Mach number and velocity for initially relativistic jets. One immediate consequence of this relationship is that, if an initially relativistic jet is decelerated to a transonic Mach number between, say 0.5 and 1.5, then its velocity at this point is between 0.3 and 0.7 times the speed of light. Analysis of the milliarcsecond and arcsecond data on NGC~315 and NGC~6251 shows that the Lorentz factors of the core jets in these galaxies can be as high as 2-4 provided that the jet pressures are not much more than an order of magnitude higher than the minimum pressures. Such Lorentz factors are more plausible if the jets are inclined at $\sim 30$ degrees to the line of sight, although larger angles would also be possible. For core Lorentz factors in the range 2-4, the jets are mildly relativistic on the large scale and their velocities are consistent with the jet brightness asymmetries being caused by Doppler beaming. The Lorentz factors required for significant beaming of core jets may be reconciled with subluminal motions of knots in the core if these are reverse shocks advected by the jet. Moderate jet Lorentz factors are possible if the shocks are normal and higher Lorentz factors are possible if the shocks are oblique. This paper provides support for the idea that the transition from two-sided to one-sided jets across the FRI/II break is due to the transition from