Evolution of Global Properties of Powerful Radio Sources. I. Hydrodynamical Simulations in a Constant Density Atmosphere and Comparison with Self-similar Models

We have carried out two-dimensional axisymmetric numerical simulations of light, supersonic jets propagating into constant density atmospheres over a broad range of parameter space. We examine the evolution of the global properties of the sources as a function of source size, for a range of Mach numbers, density contrast, and jet power. We also compare our results with the expectations of current analytical self-similar models. The derived global parameters are not sensitive to small changes in input parameters. The material content of the relativistic jet does affect its propagation and the overall structure and energetics (see Paper II) of the source. The jet in case 1 (pressure dominated by relativistic electrons) propagates faster, the cocoon has a smaller aspect ratio and maintains higher pressure, and the bow shock expands at higher lateral velocity than case 2 jets (pressure dominated by relativistic electrons and protons). However, these differences generally become less important as the jet Lorentz factor increases. We have confirmed the suggestion of Wilson & Falle that the location of the first shock in the jet depends linearly on the jet radius and Mach number. We show that the result is largely independent of density contrast and that over a wide range in Mach number the relation can be used to make a crude estimate of the jet Mach number. We find that the pressure in the cocoon and the bow-shocked region varies both along and across the source axis. The degree to which the cocoon comes into pressure balance with the ambient medium depends on the jet Mach number, with intermediate-M jets having cocoons that are in pressure balance with the ambient medium over much of the length of the source, while high- or low-M jets have cocoons that are overpressured or underpressured, respectively. The bow shock lateral expansion decelerates quickly behind the jet head, but the velocity remains at least somewhat supersonic. On the other hand, the cocoon lateral expansion velocity quickly drops behind the jet head and becomes subsonic with respect to the post-bow shock gas. The strong time dependence of the cocoon and bow shock pressure and lateral expansion speed is expected to influence the properties of the emission-line nebula associated with the radio source. The slow expansion of the cocoon and bow shock over most of their length will limit the maximum velocity to which ambient clouds can be accelerated. The behavior of the time evolution of the source size (zh ∝ tm) is in general more complex than the predictions of the self-similar models. The time dependence of the source size exhibits up to three phases whose relative length depends on the jet Mach number. The radius of the jet head is a weak function of density ratio and a stronger function of Mach number, with higher Mach number jets tending to have smaller jet heads. The advance speed of the jet head depends on the head radius in agreement with the expectations of ram pressure balance. As a result of the dependence of the growth rate of the jet head with Mach number, the advance speed of the head decreases slowly for low Mach number and remains roughly constant for high Mach number. The volume of the region enclosed by the bow shock increases with time at a rate that is close, but not identical to, the predictions of the constant velocity self-similar models. The bow shock expansion rate seems to increase with time for small Mach number but is relatively stable at high Mach number. The cocoon volume generally increases more slowly than the volume of the region enclosed by the bow shock. In low Mach number jets, the dissipation of energy through internal shocks is able to disrupt the jets and turn off the supply of energy to the cocoon. At this stage, the bow shock propagates as a sound wave and the morphology of the inferred radio-emitting material becomes faint and diffuse. Thus, we suggest that low Mach number jets may be able to transition between FR II- and FR I-type radio morphologies.