Zakaria Meliani

Parallel, grid-adaptive approaches for relativistic hydro and magnetohydrodynamics

Relativistic hydro and magnetohydrodynamics provide continuum fluid descriptions for gas and plasma dynamics throughout the visible universe. We present an overview of state-of-the-art modeling in special relativistic regimes, targeting strong shock-dominated flows with speeds approaching the speed of light. Significant progress in its numerical modeling emerged in the last two decades, and we highlight specifically the need for grid-adaptive, shock-capturing treatments found in several contemporary codes in active use and development. Our discussion highlights one such code, MPI-AMRVAC (Message-Passing Interface-Adaptive Mesh Refinement Versatile Advection Code), but includes generic strategies for allowing massively parallel, block-tree adaptive simulations in any dimensionality. We provide implementation details reflecting the underlying data structures as used in MPI-AMRVAC. Parallelization strategies and scaling efficiencies are discussed for representative applications, along with guidelines for data formats suitable for parallel I/O. Refinement strategies available in MPI-AMRVAC are presented, which cover error estimators in use in many modern AMR frameworks. A test suite for relativistic hydro and magnetohydrodynamics is provided, chosen to cover all aspects encountered in high-resolution, shock-governed astrophysical applications. This test suite provides ample examples highlighting the advantages of AMR in relativistic flow problems.

Computing the Dust Distribution in the Bow Shock of a Fast-moving, Evolved Star

We study the hydrodynamical behavior occurring in the turbulent interaction zone of a fast-moving red supergiant star, where the circumstellar and interstellar material collide. In this wind-interstellar-medium collision, the familiar bow shock, contact discontinuity, and wind termination shock morphology form, with localized instability development. Our model includes a detailed treatment of dust grains in the stellar wind and takes into account the drag forces between dust and gas. The dust is treated as pressureless gas components binned per grain size, for which we use 10 representative grain size bins. Our simulations allow us to deduce how dust grains of varying sizes become distributed throughout the circumstellar medium. We show that smaller dust grains (radius <0.045 μm) tend to be strongly bound to the gas and therefore follow the gas density distribution closely, with intricate fine structure due to essentially hydrodynamical instabilities at the wind-related contact discontinuity. Larger grains which are more resistant to drag forces are shown to have their own unique dust distribution, with progressive deviations from the gas morphology. Specifically, small dust grains stay entirely within the zone bound by shocked wind material. The large grains are capable of leaving the shocked wind layer and can penetrate into the shocked or even unshocked interstellar medium. Depending on how the number of dust grains varies with grain size, this should leave a clear imprint in infrared observations of bow shocks of red supergiants and other evolved stars.

Gamma‐ray burst afterglows from transrelativistic blast wave simulations

We present a study of the intermediate regime between ultrarelativistic and non-relativistic flow for gamma-ray burst afterglows. The hydrodynamics of spherically symmetric blast waves is numerically calculated using the amrvac adaptive mesh refinement code. Spectra and light curves are calculated using a separate radiation code that, for the first time, links a parametrization of the microphysics of shock acceleration, synchrotron self-absorption and electron cooling to a high-performance hydrodynamic simulation. For the dynamics, we find that the transition to the non-relativistic regime generally occurs later than expected, the Sedov-Taylor solution overpredicts the late-time blast wave radius and the analytical formula for the blast wave velocity from Huang, Dai & Lu overpredicts the late-time velocity by a factor of 4/3. Also, we find that the lab frame density directly behind the shock front divided by the fluid Lorentz factor squared remains very close to four times the unshocked density, while the effective adiabatic index of the shock changes from relativistic to non-relativistic. For the radiation, we find that the flux may differ up to an order of magnitude depending on the equation of state that is used for the fluid and that the counterjet leads to a clear rebrightening at late times for hard-edged jets. Simulating GRB 030329 using predictions for its physical parameters from the literature leads to spectra and light curves that may differ significantly from the actual data, emphasizing the need for very accurate modelling. Predicted light curves at low radio frequencies for a hard-edged jet model of GRB 030329 with opening angle 22 degrees show typically two distinct peaks, due to the combined effect of jet break, non-relativistic break and counterjet. Spatially resolved afterglow images show a ring-like structure.

A multidimensional grid-adaptive relativistic magnetofluid code

A robust second order, shock-capturing numerical scheme for multidimensional special relativistic magnetohydrodynamics on computational domains with adaptive mesh refinement is presented. The base solver is a total variation diminishing Lax-Friedrichs scheme in a finite volume setting and is combined with a diffusive approach for controlling magnetic monopole errors. The consistency between the primitive and conservative variables is ensured at all limited reconstructions and the spatial part of the four velocity is used as a primitive variable. Demonstrative relativistic examples are shown to validate the implementation. We recover known exact solutions to relativistic MHD Riemann problems, and simulate the shock-dominated long term evolution of Lorentz factor 7 vortical flows distorting magnetic island chains

Extragalactic jets with helical magnetic fields: relativistic MHD simulations

Context. Extragalactic jets are judged to harbor dynamically important, organized magnetic fields that presumably aid in the collimation of the relativistic jet flows. Aims. We here explore the morphology of AGN jets pervaded by helical field and flow topologies by means of grid-adaptive, high-resolution numerical simulations. We concentrate on morphological features of the bow shock and the jet beam behind the Mach disk, for various jet Lorentz factors and magnetic field helicities. We investigate the influence of helical magnetic fields on jet beam propagation in an overdense external medium. We adopt a special relativistic magnetohydrodynamic (MHD) viewpoint on the shock-dominated AGN jet evolution. Due to the adaptive mesh refinement (AMR), we can concentrate on the long-term evolution of kinetic energy-dominated jets, with beam-averaged Lorentz factor Gamma similar or equal to 7, as they penetrate denser clouds. These jets have near-equipartition magnetic fields (with the thermal energy) and radially varying Gamma(R) profiles within the jet radius R < R-j maximally reaching Gamma similar to 22. Methods. We used the AMRVAC code, with a novel hybrid block-based AMR strategy, to compute ideal plasma dynamics in special relativity. We combined this with a robust second-order shock-capturing scheme and a diffusive approach to controlling magnetic monopole errors. Results. We find that the propagation speed of the bow shock systematically exceeds the value expected from estimates using beam-average parameters, in accordance with the centrally-peaked Gamma(R) variation. The helicity of the beam magnetic field is effectively transported down the beam, with compression zones between the diagonal internal cross-shocks showing stronger toroidal field regions. In comparison with equivalent low-relativistic jets ( Gamma similar or equal to 1.15), which get surrounded by cocoons with vortical backflows filled by mainly toroidal field, the high speed jets only demonstrate localized, strong toroidal field zones within the backflow vortical structures. These structures are ring-like due to our axisymmetry assumption and may further cascade to a smaller scale in 3D. We find evidence of a more poloidal, straight field layer, compressed between jet beam and backflows. This layer decreases the destabilizing influence of the backflow on the jet beam. In all cases, the jet beam contains rich cross-shock patterns, across which part of the kinetic energy gets transfered. For the high-speed reference jet considered here, significant jet deceleration only occurs beyond distances exceeding O(100R(j)), as the axial flow can reaccelerate downstream to the internal cross shocks. This reacceleration is magnetically aided by field compression across the internal shocks that pinch the flow.

DECELERATING RELATIVISTIC TWO-COMPONENT JETS

Transverse stratification is a common intrinsic feature of astrophysical jets. There is growing evidence that jets in radio galaxies consist of a fast low-density outflow at the jet axis, surrounded by a slower, denser, extended jet. The inner and outer jet components then have a different origin and launching mechanism, making their effective inertia, magnetization, associated energy flux, and angular momentum content different as well. Their interface will develop differential rotation, where disruptions may occur. Here we investigate the stability of rotating, two-component relativistic outflows typical for jets in radio galaxies. For this purpose, we parametrically explore the long-term evolution of a transverse cross section of radially stratified jets numerically, extending our previous study where a single, purely hydrodynamic evolution was considered. We include cases with poloidally magnetized jet components, covering hydro and magnetohydrodynamic (MHD) models. With grid-adaptive relativistic MHD simulations, augmented with approximate linear stability analysis, we revisit the interaction between the two jet components. We study the influence of dynamically important poloidal magnetic fields, with varying contributions of the inner component jet to the total kinetic energy flux of the jet, on their non-linear azimuthal stability. We demonstrate that two-component jets with high kinetic energy flux and inner jet effective inertia which is higher than the outer jet effective inertia are subject to the development of a relativistically enhanced, rotation-induced Rayleigh-Taylor-type instability. This instability plays a major role in decelerating the inner jet and the overall jet decollimation. This novel deceleration scenario can partly explain the radio source dichotomy, relating it directly to the efficiency of the central engine in launching the inner jet component. The FRII/FRI transition could then occur when the relative kinetic energy flux of the inner to the outer jet grows beyond a certain threshold.

Faranoff-Riley type I jet deceleration at density discontinuities - Relativistic hydrodynamics with a realistic equation of state

Aims. We propose a model that could explain the sudden jet deceleration in active galactic nuclei, thereby invoking density discontinuities. Motivated particularly by recent indications from HYbrid MOrphology Radio Sources (HYMORS) that Fanaroff-Riley classification is induced in some cases by variations in the density of the external medium. We explore how one-sided jet deceleration and a transition to FR I type can occur in HYMORS, which start as FR II (and remain so on the other side). Methods. We implemented the Synge-type equation of state introduced in the general polytropic case by Meliani et al. (2004, A&A, 425, 773) into the relativistic hydrodynamic grid-adaptive AMRVAC code. To demonstrate its accuracy, we set up various test problems in an appendix, which we compare to exact solutions that we calculate as well. We use the code to analyse the deceleration of jets in FR II/FR I radio galaxies, following them at high resolution across several hundred jet beam radii. Results. We present results for 10 model computations that vary the inlet Lorentz factor from 10 to 20, include uniform or decreasing density profiles, and allow for cylindrical versus conical jet models. As long as the jet propagates through uniform media, we find that the density contrast sets most of the propagation characteristics, fully consistent with previous modelling efforts. When the jet runs into a denser medium, we find a clear distinction in the decelaration of high-energy jets depending on the encountered density jump. For fairly high-density contrast, the jet becomes destabilised and compressed, decelerates strongly (up to subrelativistic speeds), and can form knots. If the density contrast is too weak, the high-energy jets continue with FR II characteristics. The trend is similar for the low-energy jet models, which start as underdense jets from the outset, and decelerate by entrainment into the lower region as well. We point out differences that are found between cylindrical and conical jet models, together with dynamical details like the Richtmyer-Meshkov instabilities developing at the original contact interface.

Numerical Modeling of the Initiation of Coronal Mass Ejections in Active Region NOAA 9415

Coronal mass ejections (CMEs) and solar flares are the main drivers of weather in space. Understanding how these events occur and what conditions might lead to eruptive events is of crucial importance for up to date and reliable space weather forecasting. The aim of this paper is to present a numerical magnetohydrodynamic (MHD) data-inspired model suitable for the simulation of the CME initiation and their early evolution. Starting from a potential magnetic field extrapolation of the active region (AR) NOAA 9415, we solve the full set of ideal MHD equations in a non-zero plasma-β environment. As a consequence of the applied twisting motions, a force-free-magnetic field configuration is obtained, which has the same chirality as the investigated AR. We investigate the response of the solar corona when photospheric motions resembling the ones observed for AR 9415 are applied at the inner boundary. As a response to the converging shearing motions, a flux rope is formed that quickly propagates outward, carrying away the plasma confined inside the flux rope against the gravitational attraction by the Sun. Moreover, a compressed leading edge propagating at a speed of about 550 km s–1 and preceding the CME is formed. The presented simulation shows that both the initial magnetic field configuration and the plasma-magnetic-field interaction are relevant for a more comprehensive understanding of the CME initiation and early evolution phenomenon.

No visible optical variability from a relativistic blast wave encountering a wind termination shock

Gamma-ray burst afterglow flares and rebrightenings of the optical and X-ray light curves have been attributed to both late-time inner engine activity and density changes in the medium surrounding the burster. To test the latter, we study the encounter between the relativistic blast wave from a gamma-ray burster and a stellar wind termination shock. The blast wave is simulated using a high-performance adaptive mesh relativistic hydrodynamic code, amrvac, and the synchrotron emission is analysed in detail with a separate radiation code. We find no bump in the resulting light curve, not even for very high density jumps. Furthermore, by analysing the contributions from the different shock wave regions we are able to establish that it is essential to resolve the blast wave structure in order to make qualitatively correct predictions on the observed output and that the contribution from the reverse shock region will not stand out, even when the magnetic field is increased in this region by repeated shocks. This study resolves a controversy in the recent literature.

Thin shell morphology in the circumstellar medium of massive binaries

Context. In massive binaries, the powerful stellar winds of the two stars collide, leading to the formation of shock-dominated environments that can be modeled only in 3D. Aims. We investigate the morphology of the collision-front shell between the stellar winds of binary components in two long-period binary systems, one consisting of a hydrogen-rich Wolf-Rayet star (WNL) and an O-star and the other of a luminous blue variable (LBV) and an O-star. We follow the development and evolution of instabilities due to both the wind interaction and the orbital motion, that form in this shell if it is sufficiently compressed. Methods. We use MPI-AMRVAC to time-integrate the equations of hydrodynamics, combined with optically thin radiative cooling, on an adaptive mesh 3D grid. Using parameters for generic binary systems, we simulate the interaction between the winds of the two stars. Results. The WNL + O star binary represent a typical example of an adiabatic wind collision. The resulting shell is thick and smooth, showing no instabilities. On the other hand, the shell created by the collision of the O star wind with the LBV wind, as well as the orbital motion of the binary components, is susceptible to thin shell instabilities, which create a highly structured morphology. We identify the instabilities as both linear and non-linear thin-shell instabilities, there being distinct differences between the leading and the trailing parts of the collision front. We also find that for binaries containing a star with a (relatively) slow wind, the global shape of the shell is determined more by the slow wind velocity and the orbital motion of the binary, than the ram pressure balance between the two winds. Conclusions. Additional parametric studies of the interaction between the massive binary winds are needed to identify the role and dynamical importance of multiple instabilities at the collision front, as shown here for an LBV + O star system.