A numerical simulation of the evolution and fate of a FRI jet. The case of 3C 31

The evolution of FRI jets has been long studied in the framework of the FRI-FRII dichotomy. In this paper, we test the present theoretical and observational models via a relativistic numerical simulation of the jets in the radio galaxy 3C 31. We use the parameters derived from the modelling presented by \cite{lb02a,lb02b} as input parameters for the simulation of the evolution of the source, thus assuming that they have not varied over the lifetime 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 leptonic and baryonic matter. We compare our results with the modelling of the observational data of the source. Our results show that the bow shock evolves self-similarly at a quasi-constant speed, 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 $t>1. 10^8 \rm{yrs}$, which may imply continuous activity of 3C 31 since the triggering of its 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.Comment: Accepted for publication in MNRAS. For better quality figures, please check http://www.mpifr-bonn.mpg.de/staff/mperucho/Research.htm

Simulations of the relativistic parsec-scale jet in 3C273

We present a hydrodynamical 3D simulation of the relativistic jet in 3C273, in comparison to previous linear perturbation analysis of Kelvin-Helmholtz instability developing in the jet. Our aim is to assess advantages and limitations of both analytical and numerical approaches and to identify spatial and temporal scales on which the linear regime of Kelvin-Helmholtz instability can be applied in studies of morphology and kinematics of parsec-scale jets.Comment: 4 pages, 3 figures; to be published in Proceedings of the workshop "Multiband Approach to AGN", held on Sep.30-Oct.2 in Bonn. Publication: Memorie della Societa Astronomica Italiana, v. 26, No.1 (2005). Reduced figure resolution! Version with original figures is availavble at http://www.mpifr-bonn.mpg.de/bonn04/proceedings/perucho.pd

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

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. 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. 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. 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.Comment: Accepted for publication in A&

On the nature of an ejection event in the jet of 3C111

We present a possible scenario for the ejection of a superluminal component in the jet of the Broad Line Radio Galaxy 3C111 in early 1996. VLBI observations at 15 GHz discovered the presence of two jet features on scales smaller than one parsec. The first component evolves downstream, whereas the second one fades out after 1 parsec. We propose the injection of a perturbation of dense material followed by a decrease in the injection rate of material in the jet as a plausible explanation. This scenario is supported by 1D relativistic hydrodynamics and emission simulations. The perturbation is modeled as an increase in the jet density, without modifying the original Lorentz factor in the initial conditions. We show that an increase of the Lorentz factor in the material of the perturbation fails to reproduce the observed evolution of this flare. We are able to estimate the lifetime of the ejection event in 3C111 to be 36\pm7 days.Comment: Accepted for publication in Astronomy & Astrophysics Letter

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 ($0.08 c^2-60 c^2$) 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 of kinetic 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.Comment: accepted for publication in A&A (in press). High resolution plots, figures and Appendices of the paper will be found in the online version of the paper in A&A, and on request to [email protected]

The Entrainment-Limited Evolution of FR II Sources: Maximum Sizes and A Possible Connection to FR Is

We construct a simple theoretical model to investigate how entrainment gradually erodes high-speed FR II jets. This process is described by embedding a mixing-layer model developed originally to describe FR I objects in a self-similar model for the lobe structure of classical FR II sources. Following the classical FR II models, we assume that the lobe is dominated by the particles injected from the central jet. The entrainment produces a boundary shear layer which acts at the interface between the dense central jet and the less denser surrounding lobe, and the associated erosion of the jet places interesting limits on the maximum size of FR II sources. The model shows that this limit depends mainly on the initial bulk velocity of the relativistic jet triggered. The bulk velocities of FR IIs suggested by our model are in good agreement with that obtained from direct pc-scale observations on ordinary radio galaxies and quasars. Finally, we discuss how FR IIs may evolve into FR Is upon reaching their maximum, entrainment-limited sizes.Comment: 9 pages, 5 figures, accepted for publication in MNRA

Stability of hydrodynamical relativistic planar jets. II. Long-term nonlinear evolution

In this paper we continue our study of the Kelvin-Helmholtz (KH) instability in relativistic planar jets following the long-term evolution of the numerical simulations which were introduced in Paper I. The models have been classified into four classes (I to IV) with regard to their evolution in the nonlinear phase, characterized by the process of jet/ambient mixing and momentum transfer. Models undergoing qualitatively different non-linear evolution are clearly grouped in well-separated regions in a jet Lorentz factor/jet-to-ambient enthalpy diagram. Jets with a low Lorentz factor and small enthalpy ratio are disrupted by a strong shock after saturation. Those with a large Lorentz factor and enthalpy ratio are unstable although the process of mixing and momentum exchange proceeds to a longer time scale due to a steady conversion of kinetic to internal energy in the jet. In these cases, the high value of the initial Lorentz seems to prevent transversal velocity from growing far enough to generate the strong shock that breaks the slower jets. Finally, jets with either high Lorentz factors and small enthalpy ratios or low Lorentz factors and large enthalpy ratios appear as the most stable.Comment: Paper II, 16 pages. Accepted for publication in Astronomy & Astrophysics. Due to arXiv limits, figures have low quality. Better quality ones will be available in the published paper or on request to [email protected]