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

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

Vertical angular momentum transfer from accretion discs and the formation of large-scale collimated jets

Invited conference 35th European Physical society on Plasma PhysicsInternational audienceIn this paper I present an overview of the favoured scenario explaining the presence of twin cylindrical astrophysical jets in the vicinity of accretion discs. These jets are made of plasma and host large-scale magnetic fields. The twin jets flow away from the accreting system in opposite directions, perpendicular to the plane of the accretion disc. In the scenario presented in this paper, the accretion disc interacts with the magnetic field in such a way that the disc angular momentum is removed from the disc and transported away along the magnetic field lines. Such a transport is the source of the jet phenomenon as the angular momentum is given back to a tiny amount of material extracted from the disc. This outflow is then powered by the disc rotation as the disc is able to enter an accretion motion where matter releases its gravitational energy. The angular momentum carried by the jet is actually present through the existence of an electric current. In the jet cylindrical geometry, the presence of this current is able to provide a collimating mechanism where the magnetic field pinches the plasma column. This mechanism is very close to the one acting in tokamak reactors. Apart from explaining how the plasma outflow is able to be self-confined by the magnetic field present in the flow, this scenario is also able to explain how jet mass can be accelerated thanks to the magnetohydrodynamics Poynting flux escaping from the disc. In this presentation I finally present the constraints arising from the scenario, in particular upon the turbulent transport coefficient required to get a steady structure

AMRVAC and Relativistic Hydrodynamic simulations for GRB afterglow phases

We apply a novel adaptive mesh refinement code, AMRVAC, to numerically investigate the various evolutionary phases in the interaction of a relativistic shell with its surrounding cold Interstellar Medium (ISM). We do this for both 1D isotropic as well as full 2D jetlike fireball models. This is relevant for Gamma Ray Bursts, and we demonstrate that, thanks to the AMR strategy, we resolve the internal structure of the shocked shell-ISM matter, which will leave its imprint on the GRB afterglow. We determine the deceleration from an initial Lorentz factor $\gamma=100$ up to the almost Newtonian $\gamma\sim{\cal O}(2)$ phase of the flow. We present axisymmetric 2D shell evolutions, with the 2D extent characterized by their initial opening angle. In such jetlike GRB models, we discuss the differences with the 1D isotropic GRB equivalents. These are mainly due to thermally induced sideways expansions of both the shocked shell and shocked ISM regions. We found that the propagating 2D ultrarelativistic shell does not accrete all the surrounding medium located within its initial opening angle. Part of this ISM matter gets pushed away laterally and forms a wide bow-shock configuration with swirling flow patterns trailing the thin shell. The resulting shell deceleration is quite different from that found in isotropic GRB models. As long as the lateral shell expansion is merely due to ballistic spreading of the shell, isotropic and 2D models agree perfectly. As thermally induced expansions eventually lead to significantly higher lateral speeds, the 2D shell interacts with comparably more ISM matter and decelerates earlier than its isotropic counterpart.Comment: 12 pages, accepted in MNRAS, 12/01/200

Formation and long-term evolution of 3D vortices in protoplanetary discs

In the context of planet formation, anticyclonic vortices have recently received lots of attention for the role they can play in planetesimals formation. Radial migration of intermediate size solids toward the central star may prevent their growth to larger solid grains. On the other hand, vortices can trap the dust and accelerate this growth, counteracting fast radial transport. Multiple effects have been shown to affect this scenario, such as vortex migration or decay. The aim of this paper is to study the formation of vortices by the Rossby wave instability and their long term evolution in a full three dimensional protoplanetary disc. We use a robust numerical scheme combined with adaptive mesh refinement in cylindrical coordinates, allowing to affordably compute long term 3D evolutions. We consider a full disc stratified both radially and vertically that is prone to formation of vortices by the Rossby wave instability. We show that the 3D Rossby vortices grow and survive over hundreds of years without migration. The localized overdensity which initiated the instability and vortex formation survives the growth of the Rossby wave instability for very long times. When the vortices are no longer sustained by the Rossby wave instability, their shape changes toward more elliptical vortices. This allows them to survive shear-driven destruction, but they may be prone to elliptical instability and slow decay. When the conditions for growing Rossby wave-related instabilities are maintained in the disc, large-scale vortices can survive over very long timescales and may be able to concentrate solids.Comment: Accepted for publication in A&

Time-dependent magnetohydrodynamic self-similar extragalactic jets

Extragalactic jets are visualized as dynamic erruptive events modelled by time-dependent magnetohydrodynamic (MHD) equations. The jet structure comes through the temporally self-similar solutions in two-dimensional axisymmetric spherical geometry. The two-dimensional magnetic field is solved in the finite plasma pressure regime, or finite $\beta$ regime, and it is described by an equation where plasma pressure plays the role of an eigenvalue. This allows a structure of magnetic lobes in space, among which the polar axis lobe is strongly peaked in intensity and collimated in angular spread comparing to the others. For this reason, the polar lobe overwhelmes the other lobes, and a jet structure arises in the polar direction naturally. Furthermore, within each magnetic lobe in space, there are small secondary regions with closed two-dimensional field lines embedded along this primary lobe. In these embedded magnetic toroids, plasma pressure and mass density are much higher accordingly. These are termed as secondary plasmoids. The magnetic field lines in these secondary plasmoids circle in alternating sequence such that adjacent plasmoids have opposite field lines. In particular, along the polar primary lobe, such periodic plasmoid structure happens to be compatible with radio observations where islands of high radio intensities are mapped

Two-flow magnetohydrodynamical jets around young stellar objects

We present the first-ever simulations of non-ideal magnetohydrodynamical (MHD) stellar winds coupled with disc-driven jets where the resistive and viscous accretion disc is self-consistently described. The transmagnetosonic, collimated MHD outflows are investigated numerically using the VAC code. Our simulations show that the inner outflow is accelerated from the central object hot corona thanks to both the thermal pressure and the Lorentz force. In our framework, the thermal acceleration is sustained by the heating produced by the dissipated magnetic energy due to the turbulence. Conversely, the outflow launched from the resistive accretion disc is mainly accelerated by the magneto-centrifugal force. We also show that when a dense inner stellar wind occurs, the resulting disc-driven jet have a different structure, namely a magnetic structure where poloidal magnetic field lines are more inclined because of the pressure caused by the stellar wind. This modification leads to both an enhanced mass ejection rate in the disc-driven jet and a larger radial extension which is in better agreement with the observations besides being more consistent.Comment: Accepted for publication in Astrophysics & Space Science. Referred proceeding of the fifth Mont Stromlo Symposium Dec. 1-8 2006, Canberra, Australia. 5 pages, 3 figures. For high resolution version of the paper, please click here http://www.apc.univ-paris7.fr/~fcasse/publications.htm

Magnetized Accretion-Ejection Structures: 2.5D MHD simulations of continuous Ideal Jet launching from resistive accretion disks

We present numerical magnetohydrodynamic (MHD) simulations of a magnetized accretion disk launching trans-Alfvenic jets. These simulations, performed in a 2.5 dimensional time-dependent polytropic resistive MHD framework, model a resistive accretion disk threaded by an initial vertical magnetic field. The resistivity is only important inside the disk, and is prescribed as eta = alpha_m V_AH exp(-2Z^2/H^2), where V_A stands for Alfven speed, H is the disk scale height and the coefficient alpha_m is smaller than unity. By performing the simulations over several tens of dynamical disk timescales, we show that the launching of a collimated outflow occurs self-consistently and the ejection of matter is continuous and quasi-stationary. These are the first ever simulations of resistive accretion disks launching non-transient ideal MHD jets. Roughly 15% of accreted mass is persistently ejected. This outflow is safely characterized as a jet since the flow becomes super-fastmagnetosonic, well-collimated and reaches a quasi-stationary state. We present a complete illustration and explanation of the `accretion-ejection' mechanism that leads to jet formation from a magnetized accretion disk. In particular, the magnetic torque inside the disk brakes the matter azimuthally and allows for accretion, while it is responsible for an effective magneto-centrifugal acceleration in the jet. As such, the magnetic field channels the disk angular momentum and powers the jet acceleration and collimation. The jet originates from the inner disk region where equipartition between thermal and magnetic forces is achieved. A hollow, super-fastmagnetosonic shell of dense material is the natural outcome of the inwards advection of a primordial field.Comment: ApJ (in press), 32 pages, Higher quality version available at http://www-laog.obs.ujf-grenoble.fr/~fcass

Magnetic Fields in Stellar Jets

Although several lines of evidence suggest that jets from young stars are driven magnetically from accretion disks, existing observations of field strengths in the bow shocks of these flows imply that magnetic fields play only a minor role in the dynamics at these locations. To investigate this apparent discrepancy we performed numerical simulations of expanding magnetized jets with stochastically variable input velocities with the AstroBEAR MHD code. Because the magnetic field B is proportional to the density n within compression and rarefaction regions, the magnetic signal speed drops in rarefactions and increases in the compressed areas of velocity-variable flows. In contrast, B ~ n^0.5 for a steady-state conical flow with a toroidal field, so the Alfven speed in that case is constant along the entire jet. The simulations show that the combined effects of shocks, rarefactions, and divergent flow cause magnetic fields to scale with density as an intermediate power 1 > p > 0.5. Because p > 0.5, the Alfven speed in rarefactions decreases on average as the jet propagates away from the star. This behavior is extremely important to the flow dynamics because it means that a typical Alfven velocity in the jet close to the star is significantly larger than it is in the rarefactions ahead of bow shocks at larger distances, the one place where the field is a measurable quantity. We find that the observed values of weak fields at large distances are consistent with strong fields required to drive the observed mass loss close to the star. For a typical stellar jet the crossover point inside which velocity perturbations of 30 - 40 km/s no longer produce shocks is ~ 300 AU from the source