Supersonic turbulence in 3D isothermal flow collision

Colliding supersonic bulk flows shape observable properties and internal physics of various astrophysical objects, like O-star winds, molecular clouds, galactic sheets, binaries, or gamma-ray bursts. Using numerical simulations, we show that the bulk flows leave a clear imprint on the collision zone, its mean properties and the turbulence it naturally develops. Our model setup consists of 3D head-on colliding isothermal hydrodynamical flows with Mach numbers between 2 and 43. Simulation results are in line with expectations from self-similarity: root mean square Mach numbers (Mrms) scale linearly with upstream Mach numbers, mean densities remain limited to a few times the upstream density. The density PDF is not log-normal. The turbulence is inhomogeneous: weaker in the zone center than close to the confining shocks. It is anisotropic: while Mrms is generally supersonic, Mrms transverse to the upstream flow is always subsonic. We argue that uniform, isothermal, head-on colliding flows generally disfavor isotropic, supersonic turbulence. The anisotropy carries over to other quantities like the density variance - Mach number relation. Structure functions differ depending on whether they are computed along a line-of-sight perpendicular or parallel to the upstream flow. We suggest that such line-of-sight effects should be kept in mind when interpreting turbulence characteristics derived from observations.Comment: 20 pages, 14 figures, 4 tables, accepted by Astronomy and Astrophysic

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 is the amount given to kinetic energy, the ion/electron repartition, and the hardness of the particle distributions? We explore 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 only weakly mix: (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 (ii) tend to form a power-law with an index $p=-d\log n(\gamma)/d\log\gamma$, that depends mostly on the inflow Alfv\'en speed $V_A$ and magnetization $\sigma_s$ of species $s$, with for electrons $p=5$ to $1.2$ for increasing $\sigma_e$. 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 effects such as Compton drag or pair creation are important.Comment: 15 pages, submitted to A&

Lithium depletion in solar-like stars: effect of overshooting based on realistic multi-dimensional simulations

We study lithium depletion in low-mass and solar-like stars as a function of time, using a new diffusion coefficient describing extra-mixing taking place at the bottom of a convective envelope. This new form is motivated by multi-dimensional fully compressible, time implicit hydrodynamic simulations performed with the MUSIC code. Intermittent convective mixing at the convective boundary in a star can be modeled using extreme value theory, a statistical analysis frequently used for finance, meteorology, and environmental science. In this letter, we implement this statistical diffusion coefficient in a one-dimensional stellar evolution code, using parameters calibrated from multi-dimensional hydrodynamic simulations of a young low-mass star. We propose a new scenario that can explain observations of the surface abundance of lithium in the Sun and in clusters covering a wide range of ages, from $\sim$ 50 Myr to $\sim$ 4 Gyr. Because it relies on our physical model of convective penetration, this scenario has a limited number of assumptions. It can explain the observed trend between rotation and depletion, based on a single additional assumption, namely that rotation affects the mixing efficiency at the convective boundary. We suggest the existence of a threshold in stellar rotation rate above which rotation strongly prevents the vertical penetration of plumes and below which rotation has small effects. In addition to providing a possible explanation for the long standing problem of lithium depletion in pre-main sequence and main sequence stars, the strength of our scenario is that its basic assumptions can be tested by future hydrodynamic simulations.Comment: 7 pages, 3 figures, Accepted for publication in ApJ Letter

Relativistic magnetic reconnection in collisionless ion-electron plasmas explored with particle-in-cell simulations

Magnetic reconnection is a leading mechanism for magnetic energy conversion and high-energy non-thermal particle production in a variety of high-energy astrophysical objects, including ones with relativistic ion-electron plasmas (e.g., microquasars or AGNs) - a regime where first principle studies are scarce. We present 2D particle-in-cell (PIC) simulations of low $\beta$ ion-electron plasmas under relativistic conditions, i.e., with inflow magnetic energy exceeding the plasma rest-mass energy. We identify outstanding properties: (i) For relativistic inflow magnetizations (here $10 < \sigma_e < 360$), the reconnection outflows are dominated by thermal agitation instead of bulk kinetic energy. (ii) At large inflow electron magnetization ($\sigma_e > 80$), the reconnection electric field is sustained more by bulk inertia than by thermal inertia. It challenges the thermal-inertia-paradigm and its implications. (iii) The inflows feature sharp transitions at the entrance of the diffusion zones. These are not shocks but results from particle ballistic motions, all bouncing at the same location, provided that the thermal velocity in the inflow is far smaller than the inflow E cross B bulk velocity. (iv) Island centers are magnetically isolated from the rest of the flow, and can present a density depletion at their center. (v) The reconnection rates are slightly larger than in non-relativistic studies. They are best normalized by the inflow relativistic Alfv\'en speed projected in the outflow direction, which then leads to rates in a close range (0.14-0.25) thus allowing for an easy estimation of the reconnection electric field.Comment: Submitted to A&

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 non-linear 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. Second, we detail a new method for initial loading of Maxwell-J\"uttner particle distributions with relativistic bulk velocity and relativistic temperature, and explain why the traditional method with individual particle boosting fails. Third, we scrutinize the question of what description of 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 Lambda^{PIC}, which we show to scale as 1/p. We explore two 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. The other is that the level of electric field fluctuations scales as 1/Lambda^{PIC} ~ p. We provide a corresponding exact expression. Fourth, we compare the Vlasov-Maxwell theory, which describes a phase-space fluid with infinite Lambda, to the PIC model and its relatively small Lambda.Comment: 24 pages, 14 figures, accepted in Astronomy & Astrophysic

An ensemble-based approach to climate reconstructions

Data assimilation is a promising approach to obtain climate reconstructions that are both consistent with observations of the past and with our understanding of the physics of the climate system as represented in the climate model used. Here, we investigate the use of ensemble square root filtering (EnSRF) – a technique used in weather forecasting – for climate reconstructions. We constrain an ensemble of 29 simulations from an atmosphere-only general circulation model (GCM) with 37 pseudo-proxy temperature time series. Assimilating spatially sparse information with low temporal resolution (semi-annual) improves the representation of not only temperature, but also other surface properties, such as precipitation and even upper air features such as the intensity of the northern stratospheric polar vortex or the strength of the northern subtropical jet. Given the sparsity of the assimilated information and the limited size of the ensemble used, a localisation procedure is crucial to reduce "overcorrection" of climate variables far away from the assimilated information

Benchmarking the Multi-dimensional Stellar Implicit Code MUSIC

11 pages, 11 figures, accepted for publication in A&AWe present the results of a numerical benchmark study for the MUlti-dimensional Stellar Implicit Code (MUSIC) based on widely applicable two- and three-dimensional compressible hydrodynamics problems relevant to stellar interiors. MUSIC is an implicit large eddy simulation code that uses implicit time integration, implemented as a Jacobian-free Newton Krylov method. A physics based preconditioning technique which can be adjusted to target varying physics is used to improve the performance of the solver. The problems used for this benchmark study include the Rayleigh-Taylor and Kelvin-Helmholtz instabilities, and the decay of the Taylor-Green vortex. Additionally we show a test of hydrostatic equilibrium, in a stellar environment which is dominated by radiative effects. In this setting the flexibility of the preconditioning technique is demonstrated. This work aims to bridge the gap between the hydrodynamic test problems typically used during development of numerical methods and the complex flows of stellar interiors. A series of multi-dimensional tests are performed and analysed. Each of these test cases is analysed with a simple, scalar diagnostic, with the aim of enabling direct code comparisons. As the tests performed do not have analytic solutions we verify MUSIC by comparing to established codes including ATHENA and the PENCIL code. MUSIC is able to both reproduce behaviour from established and widely-used codes as well as results expected from theoretical predictions. This benchmarking study concludes a series of papers describing the development of the MUSIC code and provides confidence in the future applications.This project has received funding from the European Unions Seventh Framework Programme for research, technological development and demonstration under grant agreement no 320478. The calculations for this paper were performed on the DiRAC Complexity machine, jointly funded by STFC and the Large Facilities Capital Fund of BIS, and the University of Exeter Super- computer, a DiRAC Facility jointly funded by STFC, the Large Facilities Capital Fund of BIS and the University of Exeter. We are very thankful to Colin McNally for providing his results for the Kelvin-Helmholtz test