G. Comer Duncan

Simulations of relativistic extragalactic jets

We describe a method for the numerical solution of the relativistic Euler equations which we have found to be both robust and efficient, and which has enabled us to simulate relativistic jets. The technique employs a solver of the Godunov-type, with approximate solution of the local Riemann problems, applied to laboratory frame variables. Lorentz transformations provide the rest frame quantities needed for the estimation of wave speeds, etc. This is applied within the framework of an adaptive mesh refinement algorithm, allowing us to perform high-resolution, 2-D simulations with modest computing resources. We present the results of nonrelativistic, and relativistic (

A Comparison of the Morphology and Stability of Relativistic and Nonrelativistic Jets

\gamma=5

Three-dimensional Hydrodynamic Simulations of Relativistic Extragalactic Jets

and

Time-dependent Structure of Perturbed Relativistic Jets

10

Simulated VLBI Images From Relativistic Hydrodynamic Jet Models

) runs, for adiabatic indices of

Scaling of curvature in subcritical gravitational collapse

5/3

Numerical evolution of Brill waves

and

A microscopic model for the heteromolecular theory of nucleation

4/3

Evolution of discrete coagulation equation

. We find the same gross morphology in all cases, but the relativistic runs exhibit little instability and less well-defined structure internal to the jet: this might explain the difference between (relatively slow) BL~Lacs and (faster) QSOs. We find that the choice of adiabatic index makes a small but discernible difference to the structure of the shocked jet and ambient media.

A Comparison of the Morphology and Stability of Relativistic and

We compare results from a relativistic and a nonrelativistic set of two-dimensional axisymmetric jet simulations. For a set of five relativistic simulations that either increase the Lorentz factor or decrease the adiabatic index, we compute nonrelativistic simulations with equally useful power or thrust. We examine these simulations for morphological and dynamical differences, focusing on the velocity field, the width of the cocoon, the age of the jets, and the internal structure of the jet itself. The primary result of these comparisons is that the velocity field of nonrelativistic jet simulations cannot be scaled up to give the spatial distribution of Lorentz factors seen in relativistic simulations. Since the local Lorentz factor plays a major role in determining the total intensity for parsec-scale extragalactic jets, this suggests that a nonrelativistic simulation cannot yield the proper intensity distribution for a relativistic jet. Another general result is that each relativistic jet and its nonrelativistic equivalents have similar ages (in dynamical time units, ≡R/aa, where R is the initial radius of a cylindrical jet and aa is the sound speed in the ambient medium). Also, jets with a larger Lorentz factor have a smaller cocoon size. In addition to these comparisons, we have completed four new relativistic simulations to investigate the effect of varying thermal pressure on relativistic jets. The simulations confirm that faster (larger Lorentz factor) and colder jets are more stable, with smaller amplitude and longer wavelength internal variations. However, an exception to this occurs for the hottest jets, which appear the most stable. The apparent stability of these jets does not follow from linear normal mode analysis, which suggests that there are available growing Kelvin-Helmholtz modes. However, these modes are not excited because of a lack of perturbations able to couple to them. As an example of how these simulations can be applied to the interpretation of observations, we use our results to estimate some parameters of Cygnus A. Although none of these estimates alone can determine if the jets in Cyg A are relativistic or nonrelativistic, estimates for the age and the jet to ambient density ratio confirm values for these parameters estimated by other means.