J. M. Marti

Hydrodynamical Models of Superluminal Sources

We present numerical simulations of the generation, evolution, and radio emission of superluminal components in relativistic jets. We perform the fluid dynamical calculations using a relativistic time-dependent code based on a high-resolution shock-capturing scheme, and then we calculate the radio emission by integrating the transfer equations for synchrotron radiation. These simulations show that a temporary increase in the flow velocity at the base of the jet produces a moving perturbation that contains both a forward and a reverse shock and is trailed by a rarefaction. The perturbation appears in the simulated maps as a region of enhanced emission moving downstream at a superluminal apparent velocity. Interactions of the perturbation with the underlying steady jet result in changes in the internal brightness distribution of the superluminal component, which are manifested as low-level fluctuations about the long-term evolution of both the apparent velocity and the exponential decay of the light curves.

GENESIS: A High-Resolution Code for Three-dimensional Relativistic Hydrodynamics

The main features of a three-dimensional, high-resolution special relativistic hydro code based on relativistic Riemann solvers are described. The capabilities and performance of the code are discussed. In particular, we present the results of extensive test calculations that demonstrate that the code can accurately and efficiently handle strong shocks in three spatial dimensions. Results of the performance of the code on single and multiprocessor machines are given. Simulations (in double precision) with ≤7×106 computational cells require less than 1 Gbyte of RAM memory and ≈ 7×10-5 CPU s per zone and time step (on a SCI Cray-Origin 2000 with a R10000 processor). Currently, a version of the numerical code is under development, which is suited for massively parallel computers with distributed memory architecture (such as, e.g., Cray T3E).

Jet Stability and the Generation of Superluminal and Stationary Components

We present a numerical simulation of the response of an expanding relativistic jet to the ejection of a superluminal component. The simulation has been performed with a relativistic time-dependent hydrodynamical code from which simulated radio maps are computed by integrating the transfer equations for synchrotron radiation. The interaction of the superluminal component with the underlying jet results in the formation of multiple conical shocks behind the main perturbation. These trailing components can be easily distinguished because they appear to be released from the primary superluminal component instead of being ejected from the core. Their oblique nature should also result in distinct polarization properties. Those appearing closer to the core show small apparent motions and a very slow secular decrease in brightness and could be identified as stationary components. Those appearing farther downstream are weaker and can reach superluminal apparent motions. The existence of these trailing components indicates that not all observed components necessarily represent major perturbations at the jet inlet; rather, multiple emission components can be generated by a single disturbance in the jet. While the superluminal component associated with the primary perturbation exhibits a rather stable pattern speed, trailing components have velocities that increase with distance from the core but move at less than the jet speed. The trailing components exhibit motion and structure consistent with the triggering of pinch modes by the superluminal component. The increase in velocity of the trailing components is an indirect consequence of the acceleration of the expanding fluid, which is assumed to be relativistically hot; if observed, such accelerations would therefore favor an electron-positron (as opposed to proton rest mass) dominated jet.

A numerical simulation of the evolution and fate of a Fanaroff–Riley type I jet. The case of 3C 31

The evolution of FRI jets has been long studied in the framework of the FRI-FRII dichotomy. The present paradigm consists of the expansion of overpressured jets in the ambient medium and the generation of standing recollimation shocks, follo wed by mass entrainment from the external medium that decelerates the jets to subsonic sp eeds. In this paper, we test the present theoretical and observational models via a relativ istic numerical simulation of the jets in the radio galaxy 3C 31. We use the parameters derived from the modelling presented by Laing & Bridle (2002a,b) as input parameters for the simulation of the evolution of the source, thus assuming that they have not varied over the life time of the source. We simulate about 10 % of the total lifetime of the jets in 3C 31. Realistic density and pressure gradients for the atmosphere are used. The simulation includes an equation of state for a two-component relativistic gas that allows a separate treatment of lepton ic and baryonic matter. We compare our results with the modelling of the observational data of t he source. Our results show that the bow shock evolves self-similarly at a quasi-constant sp eed, with slight deceleration by the end of the simulation, in agreement with recent X-ray observations that show the presence of bow shocks in FRI sources. The jet expands until it becomes underpressured with respect to the ambient medium, and then recollimates. Subsequent oscillations around pressure equilibrium and generation of standing shocks lead to the mass loading and disruption of the jet flow. We derive an estimate for the minimum age of the source of t> 1:10 8 yrs, which may imply continuous activity of 3C 31 since the triggering of it s activity. The simulation shows that weak CSS sources may be the young counterparts of FRIs. We conclude that the observed properties of the jets in 3C 31 are basically recovered by the standing shock scenario.

SPECTRAL EVOLUTION OF SUPERLUMINAL COMPONENTS IN PARSEC-SCALE JETS

We present numerical simulations of the spectral evolution and emission of radio components in relativistic jets. We compute jet models by means of a relativistic hydrodynamics code. We have developed an algorithm (SPEV) for the transport of a population of nonthermal electrons including radiative losses. For large values of the ratio of gas pressure to magnetic field energy density, αB ~ 6 × 104, quiescent jet models show substantial spectral evolution, with observational consequences only above radio frequencies. Larger values of the magnetic field (αB ~ 6 × 102), such that synchrotron losses are moderately important at radio frequencies, present a larger ratio of shocked-to-unshocked regions brightness than the models without radiative losses, despite the fact that they correspond to the same underlying hydrodynamic structure. We also show that jets with a positive photon spectral index result if the lower limit γmin of the nonthermal particle energy distribution is large enough. A temporary increase of the Lorentz factor at the jet inlet produces a traveling perturbation that appears in the synthetic maps as a superluminal component. We show that trailing components can be originated not only in pressure matched jets, but also in overpressured ones, where the existence of recollimation shocks does not allow for a direct identification of such features as Kelvin-Helmholtz modes, and its observational imprint depends on the observing frequency. If the magnetic field is large (αB ~ 6 × 102), the spectral index in the rarefaction trailing the traveling perturbation does not change much with respect to the same model without any hydrodynamic perturbation. If the synchrotron losses are considered the spectral index displays a smaller value than in the corresponding region of the quiescent jet model.

Does the plasma composition affect the long-term evolution of relativistic jets?

We study the influence of the matter content of extragalactic jets on their morphology, dynamics and emission properties. For this purpose we consider jets of extremely different compositions, including pure leptonic and baryonic plasmas. Our work is based on two-dimensional relativistic hydrodynamic simulations of the long-term evolution of powerful extragalactic jets propagating into a homogeneous environment. The equation of state used in the simulations accounts for an arbitrary mixture of electrons, protons and electron–positron pairs. Using the hydrodynamic models, we have also computed synthetic radio maps and the thermal bremsstrahlung X-ray emission from their cavities. Although there is a difference of about three orders of magnitude in the temperatures of the cavities inflated by the simulated jets, we find that both the morphology and the dynamic behaviour are almost independent of the assumed composition of the jets. Their evolution proceeds in two distinct epochs. During the first one, multidimensional effects are unimportant and the jets propagate ballistically. The second epoch starts when the first larger vortices are produced near the jet head, causing the beam cross-section to increase and the jet to decelerate. The evolution of the cocoon and cavity is in agreement with a simple theoretical model. The beam velocities are relativistic (Γ≃4) at kiloparsec scales, supporting the idea that the X-ray emission of several extragalactic jets may be due to relativistically boosted CMB photons. The radio emission of all models is dominated by the contribution of the hotspots. All models exhibit a depression in the X-rays surface brightness of the cavity interior, in agreement with recent observations.

Radio Emission from Three-dimensional Relativistic Hydrodynamic Jets: Observational Evidence of Jet Stratification

We present the first radio emission simulations from high-resolution three-dimensional relativistic hydrodynamic jets; these simulations allow us to study the observational implications of the interaction between the jet and the external medium. This interaction gives rise to a stratification of the jet in which a fast spine is surrounded by a slow high-energy shear layer. The stratification (in particular, the large specific internal energy and slow flow in the shear layer) largely determines the emission from the jet. If the magnetic field in the shear layer becomes helical (e.g., resulting from an initial toroidal field and an aligned field component generated by shear), the emission shows a cross section asymmetry, in which either the top or the bottom of the jet dominates the emission. This, as well as limb or spine brightening, is a function of the viewing angle and flow velocity, and the top/bottom jet emission predominance can be reversed if the jet changes direction with respect to the observer or if it presents a change in velocity. The asymmetry is more prominent in the polarized flux because of field cancellation (or amplification) along the line of sight. Recent observations of jet cross section emission asymmetries in the blazar 1055+018 can be explained by assuming the existence of a shear layer with a helical magnetic field.

Nonlinear stability of relativistic sheared planar jets

The linear and non-linear stability of sheared, relativistic planar jets is studied by means of linear stability analysis and numerical hydrodynamical simulations. Our results extend the previous Kelvin-Hemlholtz stability studies for relativistic, planar jets in the vortex sheet approximation performed by Perucho et al. (2004a,b) by including a shear layer between the jet and the external medium and more general perturbations. The models considered span a wide range of Lorentz factors (2.5 20) and internal energies (0.08c 2 60c 2 ) and are classified into three classes according to the main characteristics of their long-term, non-linear evolution. We observe a clear separation of these three groups in a relativistic Mach-number Lorentz-factor plane. Jets with a low Lorentz factor and small relativistic Mach number are disrupted after saturation. Those with a large Lorentz factor and large relativistic Mach number are the stablest, due to the appearance of short wavelength resonant modes which generate local mixing and heating in the shear layer around a fast, unmixed core, giving a plausible solution for the problem of the long-term stability of relativistic jets. A third group is present between them, including jets with intermediate values of Lorentz factor and relativistic Mach number, which are disrupted by a slow process of mixing favored by an efficient and continuous conversion ofkinetic into internal energy. In the long term, all the models develop a distinct transversal structure (shear/transition layers) as a consequence of KH perturbation growth, depending on the class they belong to. The properties of these shear layers are analyzed in connection with the parameters of the original jet models.

Stability of hydrodynamical relativistic planar jets. I. Linear evolution and saturation of Kelvin-Helmholtz modes

The effects of relativistic dynamics and thermodynamics in the development of Kelvin-Helmholtz instabilities in planar, relativistic jets along the early phases (namely linear and saturation phases) of evolution has been studied by a combi- nation of linear stability analysis and high-resolution numerical simulations for the most unstable first reflection modes in the temporal approach. Three different values of the jet Lorentz factor (5, 10 and 20) and a few different values of specific internal energy of the jet matter (from 0.08 to 60.0c 2 ) have been considered. Figures illustrating the evolution of the perturbations are also shown. Our simulations reproduce the linear regime of evolution of the excited eigenmodes of the different models with a high accuracy. In all the cases the longitudinal velocity perturbation is the first quantity that departs from the linear growth when it reaches a value close to the speed of light in the jet reference frame. The saturation phase extends from the end of the linear phase up to the saturation of the transversal velocity perturbation (at approximately 0.5c in the jet reference frame). The saturation times for the different numerical models are explained from elementary considerations, i.e. from properties of linear modes provided by the linear stability analysis and from the limitation of the transversal perturbation velocity. The limitation of the components of the velocity perturbation at the end of the linear and saturation phases allows us to conclude that the relativistic nature of the flow appears to be responsible for the departure of the system from linear evolution. The high accuracy of our simulations in describing the early stages of evolution of the KH instability (as derived from the agreement between the computed and expected linear growth rates and the consistency of the saturation times) establishes a solid basis to study the fully nonlinear regime, to be done elsewhere. The present paper also sets the theoretical and numerical background for these further studies.

Stability of three-dimensional relativistic jets: implications for jet collimation

Context. The stable propagation of jets in FRII sources is remarkable if one takes into account that large-scale jets are subjected to potentially highly disruptive three-dimensional (3D) Kelvin-Helmholtz instabilities. Aims. Numerical simulations can address this problem and help clarify the causes of this remarkable stability. Following previous studies of the stability of relativistic flows in two dimensions (2D), it is our aim to test and extend the conclusions of such works to three dimensions. Methods. We present numerical simulations for the study of the stability properties of 3D, sheared, relativistic flows. This work uses a fully parallelized code (Ratpenat) that solves equations of relativistic hydrodynamics in 3D. Results. The results of the present simulations confirm those in 2D. We conclude that the growth of resonant modes in sheared relativistic flows could be important in explaining the long-term collimation of extragalactic jets.