Relativistic particle transport in extragalactic jets: I. Coupling MHD and kinetic theory

Multidimensional magneto-hydrodynamical (MHD) simulations coupled with stochastic differential equations (SDEs) adapted to test particle acceleration and transport in complex astrophysical flows are presented. The numerical scheme allows the investigation of shock acceleration, adiabatic and radiative losses as well as diffusive spatial transport in various diffusion regimes. The applicability of SDEs to astrophysics is first discussed in regards to the different regimes and the MHD code spatial resolution. The procedure is then applied to 2.5D MHD-SDE simulations of kilo-parsec scale extragalactic jets. The ability of SDE to reproduce analytical solutions of the diffusion-convection equation for electrons is tested through the incorporation of an increasing number of effects: shock acceleration, spatially dependent diffusion coefficients and synchrotron losses. The SDEs prove to be efficient in various shock configuration occurring in the inner jet during the development of the Kelvin-Helmholtz instability. The particle acceleration in snapshots of strong single and multiple shock acceleration including realistic spatial transport is treated. In chaotic magnetic diffusion regime, turbulence levels $\eta_T=/(B^2+)$ around $0.2-0.3$ are found to be the most efficient to enable particles to reach the highest energies. The spectrum, extending from 100 MeV to few TeV (or even 100 TeV for fast flows), does not exhibit a power-law shape due to transverse momentum dependent escapes. Out of this range, the confinement is not so efficient and the spectrum cut-off above few hundreds of GeV, questioning the Chandra observations of X-ray knots as being synchrotron radiation. The extension to full time dependent simulations to X-ray extragalactic jets is discussed.Comment: Astronomy & Astrophysics (in press), 18 page

Cosmic Ray propagation in sub-Alfvenic magnetohydrodynamic turbulence

This work has the main objective to provide a detailed investigation of cosmic ray propagation in magnetohydrodynamic turbulent fields generated by forcing the fluid velocity field at large scales. It provides a derivation of the particle mean free path dependences in terms of the turbulence level described by the Alfv\'enic Mach number and in terms of the particle rigidity. We use an upgrade version of the magnetohydrodynamic code {\tt RAMSES} which includes a forcing module and a kinetic module and solve the Lorentz equation for each particle. The simulations are performed using a 3 dimension periodical box in the test-particle and magnetostatic limits. The forcing module is implemented using an Ornstein-Uhlenbeck process. An ensemble average over a large number of particle trajectories is applied to reconstruct the particle mean free paths. We derive the cosmic ray mean free paths in terms of the Alfv\'enic Mach numbers and particle reduced rigidities in different turbulence forcing geometries. The reduced particle rigidity is $\rho=r_L/L$ where $r_L$ is the particle Larmor radius and $L$ is the simulation box length related to the turbulence coherence or injection scale $L_{inj}$ by $L \sim 5 L_{inj}$. We have investigated with a special attention compressible and solenoidal forcing geometries. We find that compressible forcing solutions are compatible with the quasi-linear theory or more advanced non-linear theories which predict a rigidity dependence as $\rho^{1/2}$ or $\rho^{1/3}$. Solenoidal forcing solutions at least at low or moderate Alfv\'enic numbers are not compatible with the above theoretical expectations and require more refined arguments to be interpreted. It appears especially for Alfv\'enic Mach numbers close to one that the wandering of field lines controls perpendicular mean free path solutions whatever the forcing geometry.Comment: 15 pages, 18 figures. Accepted for publication in section 2. Astrophysical processes of Astronomy and Astrophysic

MARCOS, a numerical tool for the simulation of multiple time-dependent non-linear diffusive shock acceleration

We present a new code aimed at the simulation of diffusive shock acceleration (DSA), and discuss various test cases which demonstrate its ability to study DSA in its full time-dependent and non-linear developments. We present the numerical methods implemented, coupling the hydrodynamical evolution of a parallel shock (in one space dimension) and the kinetic transport of the cosmic-rays (CR) distribution function (in one momentum dimension), as first done by Falle. Following Kang and Jones and collaborators, we show how the adaptive mesh refinement technique (AMR) greatly helps accommodating the extremely demanding numerical resolution requirements of realistic (Bohm-like) CR diffusion coefficients. We also present the paral lelization of the code, which allows us to run many successive shocks at the cost of a single shock, and thus to present the first direct numerical simulations of linear and non-linear multiple DSA, a mechanism of interest in various astrophysical environments such as superbubbles, galaxy clusters and early cosmological flows.Comment: accepted for publication in MNRAS by the Royal Astronomical Society and Blackwell Publishin

Non-resonant magnetohydrodynamics streaming instability near magnetized relativistic shocks

We present in this paper both a linear study and numerical relativistic MHD simulations of the non-resonant streaming instability occurring in the precursor of relativistic shocks. In the shock front restframe, we perform a linear analysis of this instability in a likely configuration for ultra-relativistic shock precursors. This considers magneto-acoustic waves having a wave vector perpendicular to the shock front and the large scale magnetic field. Our linear analysis is achieved without any assumption on the shock velocity and is thus valid for all velocity regimes. In order to check our calculation, we also perform relativistic MHD simulations describing the propagation of the aforementioned magneto-acoustic waves through the shock precursor. The numerical calculations confirm our linear analysis, which predicts that the growth rate of the instability is maximal for ultra-relativistic shocks and exhibits a wavenumber dependence $\propto k_x^{1/2}$. Our numerical simulations also depict the saturation regime of the instability where we show that the magnetic amplification is moderate but nevertheless significant ($\delta B/B\leq 10$). This latter fact may explain the presence of strong turbulence in the vicinity of relativistic magnetized shocks. Our numerical approach also introduces a convenient means to handle isothermal (ultra-)relativistic MHD conditions.Comment: 14 pages, 6 figures, MNRAS (in press

Transport of positrons in the interstellar medium

This work investigates some aspects of the transport of low-energy positrons in the interstellar medium (ISM). We consider resonance interactions with magnetohydrodynamic waves above the resonance threshold. Below the threshold, collisions take over and deflect positrons in their motion parallel to magnetic-field lines. Using Monte-Carlo simulations, we model the propagation and energy losses of positrons in the different phases of the ISM until they annihilate. We suggest that positrons produced in the disk by an old population of stars, with initial kinetic energies below 1 MeV, and propagating in the spiral magnetic field of the disk, can probably not penetrate the Galactic bulge.Comment: 4 pages, 3 figures, accepted for publication in the proceeding of the 6th INTEGRAL worksho

Radiation processes around accreting black holes

Accreting sources such as AGN, X-ray binaries or gamma-ray bursts are known to be strong, high energy emitters. The hard emission is though to originate from plasmas of thermal and/or non-thermal high energy particles. Not only does this emission allow to probe the unique properties of the matter in an extreme environment, but it also has a crucial backreaction on the energetics and the dynamics of the emitting medium itself. Understanding interactions between radiation and matter has become a key issue in the modelling of high energy sources. Although most cross sections are well known, they are quite complex and the way all processes couple non-linearly is still an open issue. We present a new code that solves the local, kinetic evolution equations for distributions of electrons, positrons and photons, interacting by radiation processes such as self-absorbed synchrotron and brems-strahlung radiation, Compton scattering, pair production/annihilation, and by Coulomb collisions. The code is very general and aimed to modelled various high energy sources. As an application, we study the spectral states of X-ray binaries, including thermalization by Coulomb collisions and synchrotron self-absorption. It is found that the low-hard and high-soft states can be modelled with different illumination but the same non-thermal acceleration mechanism.Comment: 4 pages, 2 figures, proceedings of the SF2A conference 200

Cosmic-ray acceleration and gamma-ray signals from radio supernovae

In this work the efficiency of particle acceleration at the forward shock right after the SN outburst for the particular case of the well-known SN 1993J is analyzed. Plasma instabilities driven by the energetic particles accelerated at the shock front grow over intraday timescales and drive a fast amplification of the magnetic field at the shock, that can explain the magnetic field strengths deduced from the radio monitoring of the source. The maximum particle energy is found to reach 1-10 PeV depending on the instability dominating the amplification process. We derive the time dependent particle spectra and the associated hadronic signatures of secondary particles arising from proton proton interactions. We find that the Cherenkov Telescope Array (CTA) should easily detect objects like SN 1993J in particular above 1 TeV, while current generation of Cherenkov telescopes such as H.E.S.S. could only marginally detect such events. The gamma-ray signal is found to be heavily absorbed by pair production process during the first week after the outburst. We predict a low neutrino flux above 10 TeV, implying a detectability horizon with a KM3NeT-type telescope of 1 Mpc only. We finally discuss the essential parameters that control the particle acceleration and gamma-ray emission in other type of SNe.Comment: 7 pages, 3 figures (Note: conflict of .sty file version explains the problems with journal title and the abstract, apologies for any inconvenience). Appears as Nuclear Physics B Proceedings Supplement 2014 Proceedings of the workshop "Cosmic Ray Origin beyond the standard models", San Vito (2014), ed. by O.Tibolla, L. Drur

Cosmic-ray acceleration in young protostars

The main signature of the interaction between cosmic rays and molecular clouds is the high ionisation degree. This decreases towards the densest parts of a cloud, where star formation is expected, because of energy losses and magnetic effects. However recent observations hint to high levels of ionisation in protostellar systems, therefore leading to an apparent contradiction that could be explained by the presence of energetic particles accelerated within young protostars. Our modelling consists of a set of conditions that has to be satisfied in order to have an efficient particle acceleration through the diffusive shock acceleration mechanism. We find that jet shocks can be strong accelerators of protons which can be boosted up to relativistic energies. Another possibly efficient acceleration site is located at protostellar surfaces, where shocks caused by impacting material during the collapse phase are strong enough to accelerate protons. Our results demonstrate the possibility of accelerating particles during the early phase of a proto-Solar-like system and can be used as an argument to support available observations. The existence of an internal source of energetic particles can have a strong and unforeseen impact on the star and planet formation process as well as on the formation of pre-biotic molecules.Comment: Accepted by Astronomy and Astrophysic

Shape and evolution of wind-blown bubbles of massive stars: on the effect of the interstellar magnetic field

The winds of massive stars create large (>10 pc) bubbles around their progenitors. As these bubbles expand they encounter the interstellar coherent magnetic field which, depending on its strength, can influence the shape of the bubble. We wish to investigate if, and how much, the interstellar magnetic field can contribute to the shape of an expanding circumstellar bubble around a massive star. We use the MPI-AMRVAC code to make magneto-hydrodynamical simulations of bubbles, using a single star model, combined with several different field strengths: B = 5, 10, and 20 muG for the interstellar magnetic field. This covers the typical field strengths of the interstellar magnetic fields found in the galactic disk and bulge. Furthermore, we present two simulations that include both a 5 muG interstellar magnetic field and a 10,000 K interstellar medium and two different ISM densities to demonstrate how the magnetic field can combine with other external factors to influence the morphology of the circumstellar bubbles. Our results show that low magnetic fields, as found in the galactic disk, inhibit the growth of the circumstellar bubbles in the direction perpendicular to the field. As a result, the bubbles become ovoid, rather than spherical. Strong interstellar fields, such as observed for the galactic bulge, can completely stop the expansion of the bubble in the direction perpendicular to the field, leading to the formation of a tube-like bubble. When combined with a warm, high-density ISM the bubble is greatly reduced in size, causing a dramatic change in the evolution of temporary features inside the bubble. The magnetic field of the interstellar medium can affect the shape of circumstellar bubbles. This effect may have consequences for the shape and evolution of circumstellar nebulae and supernova remnants, which are formed within the main wind-blown bubble.Comment: Proposed for acceptance for publication in Astronomy & Astrophysics. The published version will contain animations of each simulatio