An HLLC Solver for Relativistic Flows -- II. Magnetohydrodynamics

An approximate Riemann solver for the equations of relativistic magnetohydrodynamics (RMHD) is derived. The HLLC solver, originally developed by Toro, Spruce and Spears, generalizes the algorithm described in a previous paper (Mignone & Bodo 2004) to the case where magnetic fields are present. The solution to the Riemann problem is approximated by two constant states bounded by two fast shocks and separated by a tangential wave. The scheme is Jacobian-free, in the sense that it avoids the expensive characteristic decomposition of the RMHD equations and it improves over the HLL scheme by restoring the missing contact wave. Multidimensional integration proceeds via the single step, corner transport upwind (CTU) method of Colella, combined with the contrained tranport (CT) algorithm to preserve divergence-free magnetic fields. The resulting numerical scheme is simple to implement, efficient and suitable for a general equation of state. The robustness of the new algorithm is validated against one and two dimensional numerical test problems.Comment: 17 pages, 12 figure

Low-mass planets in nearly inviscid disks: Numerical treatment

Embedded planets disturb the density structure of the ambient disk and gravitational back-reaction will induce possibly a change in the planet's orbital elements. The accurate determination of the forces acting on the planet requires careful numerical analysis. Recently, the validity of the often used fast orbital advection algorithm (FARGO) has been put into question, and special numerical resolution and stability requirements have been suggested. In this paper we study the process of planet-disk interaction for small mass planets of a few Earth masses, and reanalyze the numerical requirements to obtain converged and stable results. One focus lies on the applicability of the FARGO-algorithm. Additionally, we study the difference of two and three-dimensional simulations, compare global with local setups, as well as isothermal and adiabatic conditions. We study the influence of the planet on the disk through two- and three-dimensional hydrodynamical simulations. To strengthen our conclusions we perform a detailed numerical comparison where several upwind and Riemann-solver based codes are used with and without the FARGO-algorithm. With respect to the wake structure and the torque density acting on the planet we demonstrate that the FARGO-algorithm yields correct results, and that at a fraction of the regular cpu-time. We find that the resolution requirements for achieving convergent results in unshocked regions are rather modest and depend on the pressure scale height of the disk. By comparing the torque densities of 2D and 3D simulations we show that a suitable vertical averaging procedure for the force gives an excellent agreement between the two. We show that isothermal and adiabatic runs can differ considerably, even for adiabatic indices very close to unity.Comment: accepted by Astronomy & Astrophysic

STAble: A novel approach to de novo assembly of RNA-seq data and its application in a metabolic model network based metatranscriptomic workflow

Background: De novo assembly of RNA-seq data allows the study of transcriptome in absence of a reference genome either if data is obtained from a single organism or from a mixed sample as in metatranscriptomics studies. Given the high number of sequences obtained from NGS approaches, a critical step in any analysis workflow is the assembly of reads to reconstruct transcripts thus reducing the complexity of the analysis. Despite many available tools show a good sensitivity, there is a high percentage of false positives due to the high number of assemblies considered and it is likely that the high frequency of false positive is underestimated by currently used benchmarks. The reconstruction of not existing transcripts may false the biological interpretation of results as - for example - may overestimate the identification of "novel" transcripts. Moreover, benchmarks performed are usually based on RNA-seq data from annotated genomes and assembled transcripts are compared to annotations and genomes to identify putative good and wrong reconstructions, but these tests alone may lead to accept a particular type of false positive as true, as better described below. Results: Here we present a novel methodology of de novo assembly, implemented in a software named STAble (Short-reads Transcriptome Assembler). The novel concept of this assembler is that the whole reads are used to determine possible alignments instead of using smaller k-mers, with the aim of reducing the number of chimeras produced. Furthermore, we applied a new set of benchmarks based on simulated data to better define the performance of assembly method and carefully identifying true reconstructions. STAble was also used to build a prototype workflow to analyse metatranscriptomics data in connection to a steady state metabolic modelling algorithm. This algorithm was used to produce high quality metabolic interpretations of small gene expression sets obtained from already published RNA-seq data that we assembled with STAble. Conclusions: The presented results, albeit preliminary, clearly suggest that with this approach is possible to identify informative reactions not directly revealed by raw transcriptomic data

Resistive jet simulations extending radially self-similar magnetohydrodynamic models

Numerical simulations with self-similar initial and boundary conditions provide a link between theoretical and numerical investigations of jet dynamics. We perform axisymmetric resistive magnetohydrodynamic (MHD) simulations for a generalised solution of the Blandford & Payne type, and compare them with the corresponding analytical and numerical ideal-MHD solutions. We disentangle the effects of the numerical and physical diffusivity. The latter could occur in outflows above an accretion disk, being transferred from the underlying disk into the disk corona by MHD turbulence (anomalous turbulent diffusivity), or as a result of ambipolar diffusion in partially ionized flows. We conclude that while the classical magnetic Reynolds number $R_{\rm m}$ measures the importance of resistive effects in the induction equation, a new introduced number, \rbeta=(\beta/2)R_{\rm m} with $\beta$ the plasma beta, measures the importance of the resistive effects in the energy equation. Thus, in magnetised jets with $\beta<2$, when \rbeta \la 1 resistive effects are non-negligible and affect mostly the energy equation. The presented simulations indeed show that for a range of magnetic diffusivities corresponding to \rbeta \ga 1 the flow remains close to the ideal-MHD self-similar solution.Comment: Accepted for publication in MNRA

Large scale magnetic fields in viscous resistive accretion disks. I. Ejection from weakly magnetized disks

Cold steady-state disk wind theory from near Keplerian accretion disks requires a large scale magnetic field at near equipartition strength. However the minimum magnetization has never been tested. We investigate the time evolution of an accretion disk threaded by a weak vertical magnetic field. The strength of the field is such that the disk magnetization falls off rapidly with radius. Four 2.5D numerical simulations of viscous resistive accretion disk are performed using the magnetohydrodynamic code PLUTO. In these simulations, a mean field approach is used and turbulence is assumed to give rise to anomalous transport coefficients (alpha prescription). The large scale magnetic field introduces only a small perturbation to the disk structure, with accretion driven by the dominant viscous torque. A super fast magnetosonic jet is observed to be launched from the innermost regions and remains stationary over more than 953 Keplerian orbits. The self-confined jet is launched from a finite radial zone in the disk which remains constant over time. Ejection is made possible because the magnetization reaches unity at the disk surface, due to the steep density decrease. However, no ejection is reported when the midplane magnetization becomes too small. The asymptotic jet velocity remains nevertheless too low to explain observed jets due to the negligible power carried away by the jet. Astrophysical disks with superheated surface layers could drive analogous outflows even if their midplane magnetization is low. Sufficient angular momentum would be extracted by the turbulent viscosity to allow the accretion process to continue. The magnetized outflows would be no more than byproducts, rather than a fundamental driver of accretion. However, if the midplane magnetization increases towards the center, a natural transition to an inner jet dominated disk could be achieved.Comment: Accepted by Astronomy and Astrophysic

Magnetic field structure of relativistic jets without current sheets

We present an analytical class of equilibrium solutions for the structure of relativistic sheared and rotating magnetized jets that contain no boundary current sheets. We demonstrate the overall dynamical stability of these solutions and, most importantly, a better numerical resistive stability than the commonly employed force-free structures which inevitably require the presence of dissipative surface currents. The jet is volumetrically confined by the external pressure, with no pressure gradient on the surface. We calculate the expected observed properties of such jets. Given the simplicity of these solution we suggest them as useful initial conditions for relativistic jet simulations.Comment: 13 pages, 13 figures, Accepted by MNRA

A Two-dimensional HLLC Riemann Solver for Conservation Laws : Application to Euler and MHD Flows

In this paper we present a genuinely two-dimensional HLLC Riemann solver. On logically rectangular meshes, it accepts four input states that come together at an edge and outputs the multi-dimensionally upwinded fluxes in both directions. This work builds on, and improves, our prior work on two-dimensional HLL Riemann solvers. The HLL Riemann solver presented here achieves its stabilization by introducing a constant state in the region of strong interaction, where four one-dimensional Riemann problems interact vigorously with one another. A robust version of the HLL Riemann solver is presented here along with a strategy for introducing sub-structure in the strongly-interacting state. Introducing sub-structure turns the two-dimensional HLL Riemann solver into a two-dimensional HLLC Riemann solver. The sub-structure that we introduce represents a contact discontinuity which can be oriented in any direction relative to the mesh. The Riemann solver presented here is general and can work with any system of conservation laws. We also present a second order accurate Godunov scheme that works in three dimensions and is entirely based on the present multidimensional HLLC Riemann solver technology. The methods presented are cost-competitive with traditional higher order Godunov schemes

Local Simulations of Instabilities in Relativistic Jets I: Morphology and Energetics of the Current-Driven Instability

We present the results of a numerical investigation of current-driven instability in magnetized jets. Utilizing the well-tested, relativistic magnetohydrodynamic code Athena, we construct an ensemble of local, co-moving plasma columns in which initial radial force balance is achieved through various combinations of magnetic, pressure, and rotational forces. We then examine the resulting flow morphologies and energetics to determine the degree to which these systems become disrupted, the amount of kinetic energy amplification attained, and the non-linear saturation behaviors. Our most significant finding is that the details of initial force balance have a pronounced effect on the resulting flow morphology. Models in which the initial magnetic field is force-free deform, but do not become disrupted. Systems that achieve initial equilibrium by balancing pressure gradients and/or rotation against magnetic forces, however, tend to shred, mix, and develop turbulence. In all cases, the linear growth of current-driven instabilities is well-represented by analytic models. CDI-driven kinetic energy amplification is slower and saturates at a lower value in force-free models than in those that feature pressure gradients and/or rotation. In rotating columns, we find that magnetized regions undergoing rotational shear are driven toward equipartition between kinetic and magnetic energies. We show that these results are applicable for a large variety of physical parameters, but we caution that algorithmic decisions (such as choice of Riemann solver) can affect the evolution of these systems more than physically motivated parameters.Comment: 18 pages, 23 figures. Accepted to MNRAS and in press, with only minor revisions from original submitted versio

Extragalactic jets with helical magnetic fields: relativistic MHD simulations

Extragalactic jets are inferred to harbor dynamically important, organized magnetic fields which presumably aid in the collimation of the relativistic jet flows. We here explore by means of grid-adaptive, high resolution numerical simulations the morphology of AGN jets pervaded by helical field and flow topologies. 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 overdense external medium. We use the AMRVAC code, employing a novel hybrid block-based AMR strategy, to compute ideal plasma dynamics in special relativity. The helicity of the beam magnetic field is effectively transported down the beam, with compression zones in between diagonal internal cross-shocks showing stronger toroidal field regions. In comparison with equivalent low-relativistic jets which get surrounded by cocoons with vortical backflows filled by mainly toroidal field, the high speed jets demonstrate only localized, strong toroidal field zones within the backflow vortical structures. We find evidence for 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 transferred. For the high speed reference jet considered here, significant jet deceleration only occurs beyond distances exceeding ${\cal O}(100 R_j)$, as the axial flow can reaccelerate downstream to the internal cross-shocks. This reacceleration is magnetically aided, due to field compression across the internal shocks which pinch the flow.Comment: 16 pages, Astronomy and Astrophysics accepted for publicatio

Comparing Numerical Methods for Isothermal Magnetized Supersonic Turbulence

We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss convergence of various characteristics for the turbulence decay test and impacts of various components of numerical schemes on the accuracy of solutions. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the magnetic field using the constrained transport method, and using little to no explicit artificial viscosity. Codes which fall short in one or more of these areas are still useful, but they must compensate higher numerical dissipation with higher numerical resolution. This paper is the largest, most comprehensive MHD code comparison on an application-like test problem to date. We hope this work will help developers improve their numerical algorithms while helping users to make informed choices in picking optimal applications for their specific astrophysical problems.Comment: 17 pages, 5 color figures, revised version to appear in ApJ, 735, July 201