Doris Folini

The energetics of relativistic magnetic reconnection: ion-electron repartition and particle distribution hardness

Collisionless magnetic reconnection is a prime candidate to account for flare-like or steady emission, outflow launching, or plasma heating, in a variety of high-energy astrophysical objects, including ones with relativistic ion-electron plasmas. But the fate of the initial magnetic energy in a reconnection event remains poorly known. What are the amounts assigned to kinetic energy, the ion and electron distribution, and the hardness of the particle distributions? We explored these questions with 2D particle-in-cell simulations of ion-electron plasmas. We find that 45 to 75% of the total initial magnetic energy ends up in kinetic energy, this fraction increasing with the inflow magnetization. Depending on the guide field strength, ions get from 30% to 60% of the total kinetic energy. Particles can be separated into two populations that mix only weakly: (i) particles initially in the current sheet heated by its initial tearing and subsequent contraction of the islands, and (ii) particles from the background plasma that primarily gain energy via the reconnection electric field when passing near the X-point. Particles of (ii) tend to form a power law with an index p = dlogn( )=dlog that depends mostly on the inflow Alfven speed VA and magnetization s of species s. For electrons p = 5 to 1.2 for increasing e. The highest particle Lorentz factor for ions or electrons increases roughly linearly with time for all the relativistic simulations. This is faster, and the spectra can be harder, than for collisionless shock acceleration. We discuss applications to microquasar and AGN coronae, to extragalactic jets, and to radio lobes. We point out situations where e ects, such as Compton drag or pair creation, are important.

Apar-T: code, validation, and physical interpretation of particle-in-cell results

We present the parallel particle-in-cell (PIC) code Apar-T and, more importantly, address the fundamental question of the relations between the PIC model, the Vlasov-Maxwell theory, and real plasmas. First, we present four validation tests: spectra from simulations of thermal plasmas, linear growth rates of the relativistic tearing instability and of the filamentation instability, and nonlinear filamentation merging phase. For the filamentation instability we show that the effective growth rates measured on the total energy can differ by more than 50% from the linear cold predictions and from the fastest modes of the simulation. We link these discrepancies to the superparticle number per cell and to the level of field fluctuations. Second, we detail a new method for initial loading of Maxwell-Juttner particle distributions with relativistic bulk velocity and relativistic temperature, and explain why the traditional method with individual particle boosting fails. The formulation of the relativistic Harris equilibrium is generalized to arbitrary temperature and mass ratios. Both are required for the tearing instability setup. Third, we turn to the key point of this paper and scrutinize the question of what description of (weakly coupled) physical plasmas is obtained by PIC models. These models rely on two building blocks: coarse-graining, i.e., grouping of the order of p ∼ 10 10 real particles into a single computer superparticle, and field storage on a grid with its subsequent finite superparticle size. We introduce the notion of coarse-graining dependent quantities, i.e., quantities depending on p. They derive from the PIC plasma parameter Λ PIC , which we show to behave as Λ PIC ∝ 1/p. We explore two important implications. One is that PIC collision- and fluctuation-induced thermalization times are expected to scale with the number of superparticles per grid cell, and thus to be a factor p ∼ 10 10 smaller than in real plasmas, a fact that we confirm with simulations. The other is that the level of electric field fluctuations scales as 1/Λ PIC ∝ p. We provide a corresponding exact expression, taking into account the finite superparticle size. We confirm both expectations with simulations. Fourth, we compare the Vlasov-Maxwell theory, often used for code benchmarking, to the PIC model. The former describes a phase-space fluid with Λ=+ ∞ and no correlations, while the PIC plasma features a small Λ and a high level of correlations when compared to a real plasma. These differences have to be kept in mind when interpreting and validating PIC results against the Vlasov-Maxwell theory and when modeling real physical plasmas.

A Jacobian-free Newton-Krylov method for time-implicit multidimensional hydrodynamics

This work is a continuation of our efforts to develop an efficient implicit solver for multidimensional hydrodynamics for the purpose of studying important physical processes in stellar interiors, such as turbulent convection and overshooting. We present an implicit solver that results from the combination of a Jacobian-Free Newton-Krylov method and a preconditioning technique tailored to the inviscid, compressible equations of stellar hydrodynamics. We assess the accuracy and performance of the solver for both 2D and 3D problems for Mach numbers down to

Structuring and support by Alfvén waves around prestellar cores

10^{-6}

Multi-dimensional structure of accreting young stars

. Although our applications concern flows in stellar interiors, the method can be applied to general advection and/or diffusion-dominated flows. The method presented in this paper opens up new avenues in 3D modeling of realistic stellar interiors allowing the study of important problems in stellar structure and evolution.

Circumstellar medium around rotating massive stars at solar metallicity

Observations of molecular clouds show the existence of starless, dense cores, threaded by magnetic fields. Observed line widths indicate these dense condensates to be embedded in a supersonically turbulent environment. Under these conditions, the generation of magnetic waves is inevitable. In this paper, we study the structure and support of a 1D plane-parallel, self-gravitating slab, as a monochromatic, circularly polarized Alfven wave is injected in its central plane. Dimensional analysis shows that the solution must depend on three dimensionless parameters. To study the nonlinear, turbulent evolution of such a slab, we use 1D high resolution numerical simulations. For a parameter range inspired by molecular cloud observations, we find the following. 1) A single source of energy injection is sufficient to force persistent supersonic turbulence over several hydrostatic scale heights. 2) The time averaged spatial extension of the slab is comparable to the extension of the stationary, analytical WKB solution. Deviations, as well as the density substructure of the slab, depend on the wave-length of the injected wave. 3) Energy losses are dominated by loss of Poynting-flux and increase with increasing plasma beta. 4) Good spatial resolution is mandatory, making similar simulations in 3D currently prohibitively expensive.

THE FORMATION OF KNOTS AND FILAMENTS IN SHOCKS

This work is the first attempt to describe the multi-dimensional structure of accreting young stars based on fully compressible time implicit multi-dimensional hydrodynamics simulations. One major motivation is to analyse the validity of accretion treatment used in previous 1D stellar evolution studies. We analyse the effect of accretion on the structure of a realistic stellar model of the young Sun. Our work is inspired by the numerical work of Kley \& Lin (1996, ApJ, 461, 933) devoted to the structure of the boundary layer in accretion disks. We analyse the redistribution of accreted material with a range of values of specific entropy relative to the bulk specific entropy of the material in the accreting objects convective envelope. A primary goal is to understand whether and how accreted energy deposited onto a stellar surface is redistributed in the interior. This study focusses on the high accretion rates characteristic of FU Ori systems. We find that the highest entropy cases produce a distinctive behaviour in the mass redistribution, rms velocities, and enthalpy flux in the convective envelope. This change in behaviour is characterised by the formation of a hot layer on the surface of the accreting object, which tends to suppress convection in the envelope. We analyse the long-term effect of such a hot buffer zone on the structure and evolution of the accreting object with 1D stellar evolution calculations. We study the relevance of the assumption of redistribution of accreted energy into the stellar interior used in the literature. One conclusion is that, for a given amount of accreted energy transferred to the accreting object, a treatment assuming accretion energy redistribution throughout the stellar interior could significantly overestimate the effects on the stellar structure, in particular, on the resulting expansion.

Supersonic turbulence in 3D isothermal flow collision

Aims. Observations show nebulae around some massive stars but not around others. If observed, their chemical composition is far from homogeneous. Our goal is to put these observational features into the context of the evolution of massive stars and their circumstellar medium (CSM) and, more generally, to quantify the role of massive stars for the chemical and dynamical evolution of the ISM. Methods. Using the A-MAZE code, we perform 2d-axisymmetric hydrodynamical simulations of the evolution of the CSM, shaped by stellar winds, for a whole grid of massive stellar models from 15 to 120 M and following the stellar evolution from the zero-age main-sequence to the time of supernova explosion. In addition to the usual quantities, we also follow five chemical species: H, He, C, N, and O. Results. We show how various quantities evolve as a function of time: size of the bubble, position of the wind termination shock, chemical composition of the bubble, etc. The chemical composition of the bubble changes considerably compared to the initial composition, particularly during the red-supergiant (RSG) and Wolf-Rayet (WR) phases. In some extreme cases, the inner region of the bubble can be completely depleted in hydrogen and nitrogen, and is mainly composed of carbon, helium, and oxygen. We argue why the bubble typically expands at a lower rate than predicted by self-similarity theory. In particular, the size of the bubble is very sensitive to the density of the ISM, decreasing by a factor of 2.5 for each additional dex in ISM density. The bubble size also decreases with the metallicity of the central star, because low-metallicity stars have weaker winds. Our models qualitatively fit the observations of WR ejecta nebulae.

Spherical-shell boundaries for two-dimensional compressible convection in a star

We present a survey of different kinds of instabilities in the context of radiative colliding flows which greatly contribute to structure formation. In particular, this includes analytical results for different kinds of thin shell instabilities (DI, NDI, NTSI). New numerical results for the non-linear evolution of such instabilities in two dimensions, and their coupling with the thermal cooling instability are presented. The astrophysical implications are briefly outlined, in particular the formation of knots and filaments.

Emergence of MHD structures in a collisionless PIC simulation plasma

Large scale supersonic bulk flows are present in a wide range of astrophysical objects, from O-star winds to molecular clouds, galactic sheets, accretion, or γ-ray bursts. Associated flow collisions shape observable properties and internal physics alike. Our goal is to shed light on the interplay between large scale aspects of such collision zones and the characteristics of the compressible turbulence they harbor. Our model setup is as simple as can be: 3D hydrodynamical simulations of two head-on colliding, isothermal, and homogeneous flows with identical upstream (subscript u) flow parameters and Mach numbers 2 < Mu < 43. The turbulence in the collision zone is driven by the upstream flows, whose kinetic energy is partly dissipated and spatially modulated by the shocks confining the zone. Numerical results are in line with expectations from self-similarity arguments. The spatial scale of modulation grows with the collision zone. The fraction of energy dissipated at the confining shocks decreases with increasing Mu. The mean density is ρm ≈ 20ρu, independent of Mu. The root mean square Mach number is Mrms ≈ 0.25Mu. Deviations toward weaker turbulence are found as the collision zone thickens and for small Mu. The density probability function is not log-normal. The turbulence is inhomogeneous, weaker in the center of the zone than close to the confining shocks. It is also anisotropic: transverse to the upstream flows Mrms is always subsonic. We argue that uniform, head-on colliding flows generally disfavor turbulence that is at the same time isothermal, supersonic, and isotropic. The anisotropy carries over to other quantities like the density variance – Mach number relation. Line-of-sight effects thus exist. Structure functions differ depending on whether they are computed along a line-of-sight perpendicular or parallel to the upstream flow. Turbulence characteristics generally deviate markedly from those found for uniformly driven, supersonic, isothermal turbulence in 3D periodic box simulations. We suggest that this should be kept in mind when interpreting turbulence characteristics derived from observations. Our simulations show that even a simple model setup results in a richly structured interaction zone. The robustness of our findings toward more realistic setups remains to be tested.