## Appendix: calculation of the recombination curvesIn the absence of energetic radiative sources and assuming that local collisional processes are too weak to produce substantial hydrogen ionization the equation governing the decoupled time-dependent recombination of the gas can be easily found combining the standard continuity equations for the total and electron densities (see, e.g., Osterbrock 1989) through . The final equation for the ionization fraction in this simple case reads: where is the substantial time derivative, with the flow speed, and is the recombination coefficient valid in Case B (Hummer & Storey 1987). We assume that in the recollimated portion of the jet the gas flows on average along a set of axisymmetric nested flow surfaces, which in a cylindrical coordinate system and in the proper frame of the source are described by the equations , where is the axial coordinate, and is the local radius of the jet channel. The parameter labels the different surfaces, the axis being identified by and the external boundary of the jet, by . We neglect azimuthal motions, and take a constant value of the axial velocity all over the flow. Variations of the quantities with time can therefore be described as variations along the spatial coordinate . It is easily shown that in these conditions the total density of a fluid particle behaves as: , where and are the hydrogen density and the channel radius at the arbitrarily chosen initial point of the integration . Here we will assume for simplicity that the flow surfaces are shaped as nested cones, so that , where is the average opening angle of the jet (which is positive for diverging jets and negative for converging ones). Coherently with the spectral read-out we adopted, we shall limit ourselves to the study of the fluid particles located on the axis of the flow, assigning to each of them the average physical properties of the jet section the particle belongs to. Under these assumptions, and expressing variables and coordinates through quantities directly related to observations, the solution of equation (2) can be written as: where where © European Southern Observatory (ESO) 1999 Online publication: February 23, 1999 |