José María Martí

Numerical Hydrodynamics in Special Relativity

This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results of a set of demanding test bench simulations obtained with different numerical SRHD methods are compared. Three applications (astrophysical jets, gamma-ray bursts and heavy ion collisions) of relativistic flows are discussed. An evaluation of various SRHD methods is presented, and future developments in SRHD are analyzed involving extension to general relativistic hydrodynamics and relativistic magneto-hydrodynamics. The review further provides FORTRAN programs to compute the exact solution of a 1D relativistic Riemann problem with zero and nonzero tangential velocities, and to simulate 1D relativistic flows in Cartesian Eulerian coordinates using the exact SRHD Riemann solver and PPM reconstruction.

Physical Parameters in the Hot Spots and Jets of Compact Symmetric Objects

We present a model to determine the physical parameters of jets and hot spots of a sample of compact symmetric objects (CSOs) under very basic assumptions like synchrotron emission and minimum energy conditions. Based on this model, we propose a simple evolutionary scenario for these sources assuming that they evolve in ram pressure equilibrium with the external medium and constant jet power. The parameters of our model are constrained from fits of observational data (radio luminosity, hot spot radius, and hot spot advance speed) versus projected linear size. From these plots we conclude that CSOs evolve self-similarly and that their radio luminosity increases with linear size along the first kiloparsec. Assuming that the jets feeding CSOs are relativistic from both kinematical and thermodynamical points of view, we use the values of the pressure and particle number density within the hot spots to estimate the fluxes of momentum (thrust), energy, and particles of these relativistic jets. The mean jet power obtained in this way is within an order of magnitude of that inferred for Fanaroff-Riley type 2 sources, which is consistent with CSOs being the possible precursors of large doubles. The inferred flux of particles corresponds to, for a barionic jet, about 10% of the mass accreted by a black hole of 108 M☉ at the Eddington limit, pointing toward a very efficient conversion of accretion flow into ejection or to a leptonic composition of jets. We have considered three different models (namely, models I, IIa, and IIb). Model I, assuming constant hot spot advance speed and increasing luminosity, can be ruled out on the grounds of its energy cost. However, models IIa and IIb seem to describe limiting behaviors of sources evolving at constant advance speed and decreasing luminosity (model IIa) and decreasing hot spot advance speed and increasing luminosity (model IIb). In all our models the slopes of the hot spot luminosity and advance speed with source linear size are governed by only one parameter, namely, the external density gradient. A short discussion on the validity of models IIa and IIb to describe the complete evolution of powerful radio sources from their CSO phase is also included.

On the deceleration of Fanaroff–Riley Class I jets: mass loading by stellar winds

Jets in low-luminosity radio galaxies are known to decelerate from relativistic speeds on parsec scales to mildly or sub-relativistic speeds on kiloparsec scales. Several mechanisms have been proposed to explain this effect, including strong reconfinement shocks and the growth of instabilities (both leading to boundary-layer entrainment) and mass loading from stellar winds or molecular clouds. We have performed a series of axisymmetric simulations of the early evolution of jets in a realistic ambient medium to probe the effects of mass loading from stellar winds using the code Ratpenat. We study the evolution of Fanaroff-Riley Class I (FRI) jets, with kinetic powers L_j sim 1.e41-1.e44 erg/s, within the first 2 kpc of their evolution, where deceleration by stellar mass loading should be most effective. Mass entrainment rates consistent with present models of stellar mass loss in elliptical galaxies produce deceleration and effective decollimation of weak FRI jets within the first kiloparsec. However, powerful FRI jets are not decelerated significantly. In those cases where the mass loading is important, the jets show larger opening angles and decollimate at smaller distances, but the overall structure and dynamics of the bow-shock are similar to those of unloaded jets with the same power and thrust. According to our results, the flaring observed on kpc scales is initiated by mass loading in the weaker FRI jets and by reconfinement shocks or the growth of instabilities in the more powerful jets. The final mechanism of decollimation and deceleration is always the development of disruptive pinching modes.

Intracluster Medium Reheating by Relativistic Jets

Galactic jets are powerful energy sources reheating the intracluster medium in galaxy clusters. Their crucial role in the cosmic puzzle, motivated by observations, has been established by a great number of numerical simulations excluding the relativistic nature of these jets. We present the first relativistic simulations of the very long-term evolution of realistic galactic jets. Unexpectedly, our results show no buoyant bubbles, but large cocoon regions compatible with the observed X-ray cavities. The reheating is more efficient and faster than in previous scenarios, and it is produced by the shock wave driven by the jet, that survives for several hundreds of Myr. Therefore, the X-ray cavities in clusters produced by powerful relativistic jets would remain confined by weak shocks for extremely long periods and their detection could be an observational challenge.

Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics

An overview of grid-based numerical methods used in relativistic hydrodynamics (RHD) and magnetohydrodynamics (RMHD) is presented. Special emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods. Results of a set of demanding test bench simulations obtained with different numerical methods are compared in an attempt to assess the present capabilities and limits of the various numerical strategies. Applications to three astrophysical phenomena are briefly discussed to motivate the need for and to demonstrate the success of RHD and RMHD simulations in their understanding. The review further provides FORTRAN programs to compute the exact solution of the Riemann problem in RMHD, and to simulate 1D RMHD flows in Cartesian coordinates.

Large-scale jets from active galactic nuclei as a source of intracluster medium heating: cavities and shocks

The evolution of powerful extragalactic jets is not only interesting by itself, but also for its impact on the evolution of the host galaxy and its surroundings. We have performed long-term axisymmetric numerical simulations of relativistic jets with different powers to study their evolution through an environment with a pressure and density gradient. Our results show key differences in the evolution of jets with different powers in terms of the spatial and temporal scales of energy deposition. According to our results, the observed morphology in X-ray cavities requires that an important fraction of the jet’s energetic budget is in the form of internal energy. Thus, light, lepton-dominated jets are favoured. In all cases, heating is mainly produced by shocks. Cavity overpressure is sustained by an important population of thermal particles. Our simulations reproduce the cool-core structure in projected, luminosity-weighted temperature. We have performed an additional simulation of a slow, massive jet and discuss the differences with its relativistic counterparts. Important qualitative and quantitative differences are found between the non-relativistic and the relativistic jets. Our conclusions point towards a dual-mode of AGN kinetic feedback, depending on the jet power.

On the convexity of relativistic hydrodynamics

The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 Relativistic Fluids and Magneto-Fluids (Cambridge: Cambridge University Press)). In this report, we derive the conditions for this system to be convex in terms of the fundamental derivative of the equation of state (Menikoff and Plohr1989 Rev. Mod. Phys. 61 75). The classical limit is recovered. Communicated by L Rezzolla

Magnetized, Relativistic Jets

Extragalactic relativistic jets are composed by charged particles and magnetic fields, as inferred from the synchrotron emission that we receive from them. The Larmor radii of the particles propagating along the magnetic field are much smaller than the scales of the problem, providing the necessary coherence to the system to treat is as a flow. We can thus study them using relativistic magnetohydrodynamics. As a first step, we have studied the structure of steady-state configurations of jets by using numerical simulations. We have used a helical field configuration and have changed different relevant parameters that control the way in which the energy flux is distributed in jets (namely, the proportion of the energy flux carried by internal, kinetic or magnetic energy). Our results show significant differences among the different kinds of jets. Finally, we also report on results based on synthetic maps of our simulated jets.

Radio mode feedback: Does relativity matter?

Radio mode feedback, associated with the propagation of powerful outflows in active galaxies, is a crucial ingredient in galaxy evolution. Extragalactic jets are well collimated and relativistic, both in terms of thermodynamics and kinematics. They generate strong shocks in the ambient medium, associated with observed hotspots, and carve cavities that are filled with the shocked jet flow. In this Letter, we compare the pressure evolution in the hotspot and the cavity generated by relativistic and classical jets. Our results show that the classical approach underestimates the cavity pressure by a factor larger or equal to 2 for a given shocked volume during the whole active phase. The tension between both approaches can only be alleviated by unrealistic jet flow densities or gigantic jet areas in the classical case. As a consequence, the efficiency of a relativistic jet heating the ambient is typically around 20% larger compared with a classical jet, and the heated volume is 2 to 10 times larger during the time evolution. This conflict translates into two substantially disparate manners, both spatially and temporal, of heating the ambient medium. These differences are expected to have relevant implications on the star formation rates of the host galaxies and their evolution.

Long-term simulations of extragalactic jets: cavities and feedback

We present long-term numerical simulations of powerful extragalactic relativistic jets in two dimensions. The jets are injected in a realistic atmosphere with powers 10 , 10 and 10 erg/s, during tens of Myrs. After this time, the jet injection is switched off. We follow the evolution of the jets and associated shocks from 1 kpc to hundreds of kiloparsecs during more than 100 Myrs. The 10 erg/s jet was simulated with leptonic and baryonic composition. Our results show that, for powerful jets, the main heating mechanisms are the driving shock-wave and mixing. We discuss the implications that these results have in the frame of cooling flows in clusters.