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.

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

A series of simulated maps showing the appearance in total intensity of flows computed using a recently developed relativistic hydrodynamic code (Duncan \& Hughes 1994: ApJ, 436, L119) are presented. The radiation transfer calculations were performed by assuming the flow is permeated by a magnetic field and fast particle distribution in energy equipartition, with energy density proportional to the hydrodynamic energy density (i.e., pressure). We find that relativistic flows subject to strong perturbations exhibit a density structure consisting of a series of nested bow shocks, and that this structure is evident in the intensity maps for large viewing angles. However, for viewing angles $<30^{\circ}$, differential Doppler boosting leads to a series of axial knots of emission, similar to the pattern exhibited by many VLBI sources. The appearance of VLBI knots is determined primarily by the Doppler boosting of parts of a more extended flow. To study the evolution of a perturbed jet, a time series of maps was produced and an integrated flux light curve created. The light curve shows features characteristic of a radio loud AGN: small amplitude variations and a large outburst. We find that in the absence of perturbations, jets with a modest Lorentz factor ($\sim 5$) exhibit complex intensity maps, while faster jets (Lorentz factor $\sim 10$) are largely featureless. We also study the appearance of kiloparsec jet-counterjet pairs by producing simulated maps at relatively large viewing angles; we conclude that observed hot spot emission is more likely to be associated with the Mach disk than with the outer, bow shock.

https://arxiv.org/pdf/astro-ph/9606004.pdf

Simulated VLBI Images From Relativistic Hydrodynamic Jet Models

Numerical simulations of jets

Simulations of Jets from Active Galactic Nuclei and Gamma-Ray Bursts

The enormous sizes and variability of emission of radio-loud AGNs arise from the relativistic flows of plasma along two oppositely directed jets. We use the Athena hydrodynamics code to simulate an extensive suite of 54 propagating three-dimensional relativistic jets with wide ranges of input jet velocities and jet-to-ambient matter density ratios. We determine which parameter sets yield unstable jets that produce jet dominated FR I type radio galaxy morphologies and which tend to produce stable jets with hot-spots and FR II morphologies. Nearly all our simulations involve jets with internal pressures matched to those of the ambient medium but we also consider over-pressured jets and discuss differences from the standard ones. We also show that the results are not strongly dependent on the adiabatic index of the fluid. We focus on simulations that remain stable for extended distances (60-240) times the initial jet radius. Scaled to the much smaller sizes probed by VLBI observations, the fluctuations in such simulated flows yield variability in observed emissivity on timescales from months. Adopting results for the densities, pressures and velocities from these simulations we estimate normalized rest frame synchrotron emissivities from individual cells in the jets. The observed emission from each cell is strongly dependent upon its variable Doppler boosting factor. We sum the fluxes from thousands of zones around the primary reconfinement shock. The light curves an power-spectra, with red-noise slopes between -2.1 and -2.5, so produced are similar to those observed from blazars.

D. R. Rayburn

Papers

A search for redshifted hydrogen absorption in the BL Lacertae object PKS 0735+178.