arXiv subjects

Pak Shing Li

Publications and source records attributed to Pak Shing Li.

At least 37 records · Page 2Linked to original sources

arXiv2022

Magnetic fields in the formation of the first stars.--II Results

Beginning with cosmological initial conditions at z=100, we simulate the effects of magnetic fields on the formation of Population III stars and compare our results with the predictions of Paper I. We use Gadget-2 to follow the evolution of the system while the field is weak. We introduce a new method for treating kinematic fields by tracking the evolution of the deformation tensor. The growth rate in this stage of the simulation is lower than expected for diffuse astrophysical plasmas, which have a very low resistivity (high magnetic Prandtl number); we attribute this to the large numerical resistivity in simulations, corresponding to a magnetic Prandtl number of order unity. When the magnetic field begins to be dynamically significant in the core of the minihalo at z=27, we map it onto a uniform grid and follow the evolution in an adaptive mesh refinement, MHD simulation in Orion2. The nonlinear evolution of the field in the Orion2 simulation violates flux-freezing and is consistent with the theory proposed by Xu & Lazarian. The fields approach equipartition with kinetic energy at densities ~ 10^10 - 10^12 cm^-3. When the same calculation is carried out in Orion2 with no magnetic fields, several protostars form, ranging in mass from ~ 1 to 30 M_sol with magnetic fields, only a single ~ 30 M_sol protostar forms by the end of the simulation. Magnetic fields thus suppress the formation of low-mass Pop III stars, yielding a top-heavy Pop III IMF and contributing to the absence of observed Pop III stars.

astro-ph.CO↗

arXiv2021

Mapping the magnetic field in the Taurus/B211 filamentary cloud with SOFIA HAWC+ and comparing with simulation

Optical and infrared polarization mapping and recent Planck observations of the filamentary cloud L1495 in Taurus show that the large-scale magnetic field is approximately perpendicular to the long axis of the cloud. We use the HAWC+ polarimeter on SOFIA to probe the complex magnetic field in the B211 part of the cloud. Our results reveal a dispersion of polarization angles of $36^\circ$, about five times that measured on a larger scale by Planck. Applying the Davis-Chandrasekhar-Fermi (DCF) method with velocity information obtained from IRAM 30m C$^{18}$O(1-0) observations, we find two distinct sub-regions with magnetic field strengths differing by more than a factor 3. The quieter sub-region is magnetically critical and sub-Alfvénic; the field is comparable to the average field measured in molecular clumps based on Zeeman observations. The more chaotic, super-Alfvénic sub-region shows at least three velocity components, indicating interaction among multiple substructures. Its field is much less than the average Zeeman field in molecular clumps, suggesting that the DCF value of the field there may be an underestimate. Numerical simulation of filamentary cloud formation shows that filamentary substructures can strongly perturb the magnetic field. DCF and true field values in the simulation are compared. Pre-stellar cores are observed in B211 and are seen in our simulation. The appendices give a derivation of the standard DCF method that allows for a dispersion in polarization angles that is not small, present an alternate derivation of the structure function version of the DCF method, and treat fragmentation of filaments.

astro-ph.GA↗

arXiv2020

Magnetic Fields in the Formation of the First Stars. I. Theory vs. Simulation

While magnetic fields are important in contemporary star formation, their role in primordial star formation is unknown. Magnetic fields of order 10^-16 G are produced by the Biermann battery due to the curved shocks and turbulence associated with the infall of gas into the dark matter minihalos that are the sites of formation of the first stars. These fields are rapidly amplified by a small-scale dynamo until they saturate at or near equipartition with the turbulence in the central region of the gas. Analytic results are given for the outcome of the dynamo, including the effect of compression in the collapsing gas. The mass-to-flux ratio in this gas is 2-3 times the critical value, comparable to that in contemporary star formation. Predictions of the outcomes of simulations using smooth particle hydrodynamics (SPH) and grid-based adaptive mesh refinement (AMR) are given. Because the numerical viscosity and resistivity for the standard resolution of 64 cells per Jeans length are several orders of magnitude greater than the physical values, dynamically significant magnetic fields affect a much smaller fraction of the mass in simulations than in reality. An appendix gives an analytic treatment of free-fall collapse, including that in a constant density background. Another appendix presents a new method of estimating the numerical viscosity; results are given for both SPH and grid-based codes.

astro-ph.GA↗

arXiv2019

The Formation and Evolution of Wide-Orbit Stellar Multiples In Magnetized Clouds

Stars rarely form in isolation. Nearly half of the stars in the Milky Way have a companion, and this fraction increases in star-forming regions. However, why some dense cores and filaments form bound pairs while others form single stars remains unclear. We present a set of three-dimensional, gravo-magnetohydrodynamic simulations of turbulent star-forming clouds, aimed at understanding the formation and evolution of multiple-star systems formed through large scale (>~$10^3$ AU) turbulent fragmentation. We investigate three global magnetic field strengths, with global mass-to-flux ratios of $μ_ϕ$=2, 8, and 32. The initial separations of protostars in multiples depends on the global magnetic field strength, with stronger magnetic fields (e.g., $μ_ϕ$=2) suppressing fragmentation on smaller scales. The overall multiplicity fraction (MF) is between 0.4-0.6 for our strong and intermediate magnetic field strengths, which is in agreement with observations. The weak field case has a lower fraction. The MF is relatively constant throughout the simulations, even though stellar densities increase as collapse continues. While the MF rarely exceeds 60% in all three simulations, over 80% of all protostars are part of a binary system at some point. We additionally find that the distribution of binary spin mis-alignment angles is consistent with a randomized distribution. In all three simulations, several binaries originate with wide separations and dynamically evolve to <~ $10^2$ AU separations. We show that a simple model of mass accretion and dynamical friction with the gas can explain this orbital evolution.

astro-ph.GA↗

arXiv2019

Massive Star Formation via the Collapse of Subvirial and Virialized Turbulent Massive Cores

Similar to their low-mass counterparts, massive stars likely form via the collapse of pre-stellar molecular cores. Recent observations suggest that most massive cores are subvirial (i.e., not supported by turbulence) and therefore are likely unstable to gravitational collapse. Here we perform radiation hydrodynamic simulations to follow the collapse of turbulent massive pre-stellar cores with subvirial and virialized initial conditions to explore how their dynamic state affects the formation of massive stars and core fragmentation into companion stars. We find that subvirial cores undergo rapid monolithic collapse resulting in higher accretion rates at early times as compared to the collapse of virialized cores that have the same physical properties. In contrast, we find that virialized cores undergo a slower, gradual collapse and significant turbulent fragmentation at early times resulting in numerous companion stars. In the absence of strong magnetic fields and protostellar outflows we find that the faster growth rate of massive stars that are born out of subvirial cores leads to an increase in the radiative heating of the core thereby further suppressing fragmentation at early times when turbulent fragmentation occurs for virialized cores. Regardless of initial condition, we find that the massive accretion disks that form around massive stars dominant the accretion flow onto the star at late times and eventually become gravitationally unstable and fragment to form companion stars at late times.

astro-ph.SR↗

arXiv2019

Magnetic fields in the infrared dark cloud G34.43+0.24

We present the B-fields mapped in IRDC G34.43+0.24 using 850\,$μ$m polarized dust emission observed with the POL-2 instrument at JCMT. We examine the magnetic field geometries and strengths in the northern, central, and southern regions of the filament. The overall field geometry is ordered and aligned closely perpendicular to the filament's main axis, particularly in regions containing the central clumps MM1 and MM2, whereas MM3 in the north has field orientations aligned with its major axis. The overall field orientations are uniform at large (POL-2 at 14$\arcsec$ and SHARP at 10$\arcsec$) to small scales (TADPOL at 2.5$\arcsec$ and SMA at 1.5$\arcsec$) in the MM1 and MM2 regions. SHARP/CSO observations in MM3 at 350\,$μ$m from Tang et al. show a similar trend as seen in our POL-2 observations. TADPOL observations demonstrate a well-defined field geometry in MM1/MM2 consistent with MHD simulations of accreting filaments. We obtained a plane-of-sky magnetic field strength of 470$\pm$190\,$μ$G, 100$\pm$40\,$μ$G, and 60$\pm$34\,$μ$G in the central, northern and southern regions of G34, respectively, using the updated Davis-Chandrasekhar-Fermi relation. The estimated value of field strength, combined with column density and velocity dispersion values available in the literature, suggests G34 to be marginally critical with criticality parameter $\rm λ$ values 0.8$\pm$0.4, 1.1$\pm$0.8, and 0.9$\pm$0.5 in the central, northern, and southern regions, respectively. The turbulent motions in G34 are sub-Alfvénic with Alfvénic Mach numbers of 0.34$\pm$0.13, 0.53$\pm$0.30, and 0.49$\pm$0.26 in the three regions. The observed aligned B-fields in G34.43+0.24 are consistent with theoretical models suggesting that B-fields play an important role in guiding the contraction of the cloud driven by gravity.

astro-ph.GA↗

arXiv2019

Magnetized interstellar molecular clouds: II. The Large-Scale Structure and Dynamics of Filamentary Molecular Clouds

We perform ideal MHD high resolution AMR simulations with driven turbulence and self-gravity and find that long filamentary molecular clouds are formed at the converging locations of large-scale turbulence flows and the filaments are bounded by gravity. The magnetic field helps shape and reinforce the long filamentary structures. The main filamentary cloud has a length of ~4.4 pc. Instead of a monolithic cylindrical structure, the main cloud is shown to be a collection of fiber/web-like sub-structures similar to filamentary clouds such as L1495. Unless the line-of-sight is close to the mean field direction, the large-scale magnetic field and striations in the simulation are found roughly perpendicular to the long axis of the main cloud, similar to 1495. This provides strong support for a large-scale moderately strong magnetic field surrounding L1495. We find that the projection effect from observations can lead to incorrect interpretations of the true three-dimensional physical shape, size, and velocity structure of the clouds. Helical magnetic field structures found around filamentary clouds that are interpreted from Zeeman observations can be explained by a simple bending of the magnetic field that pierces through the cloud. We demonstrate that two dark clouds form a T-shape configuration which are strikingly similar to the Infrared dark cloud SDC13 leading to the interpretation that SDC13 results from a collision of two long filamentary clouds. We show that a moderately strong magnetic field (M_A ~ 1) is crucial for maintaining a long and slender filamentary cloud for a long period of time ~0.5 million years.

astro-ph.GA↗

arXiv2018

Compressed magnetic field in the magnetically-regulated global collapsing clump of G9.62+0.19

How stellar feedback from high-mass stars (e.g., H{\sc ii} regions) influences the surrounding interstellar medium and regulates new star formation is still unclear. To address this question, we observed the G9.62+0.19 complex in 850 $μ$m continuum with the JCMT/POL-2 polarimeter. An ordered magnetic field has been discovered in its youngest clump, the G9.62 clump. The magnetic field strength is determined to be $\sim$1 mG. Magnetic field plays a larger role than turbulence in supporting the clump. However, the G9.62 clump is still unstable against gravitational collapse even if thermal, turbulent, and magnetic field support are taken into account all together. The magnetic field segments in the outskirts of the G9.62 clump seem to point toward the clump center, resembling a dragged-in morphology, indicating that the clump is likely undergoing magnetically-regulated global collapse. However, The magnetic field in its central region is aligned with the shells of the photodissociation regions (PDRs) and is approximately parallel to the ionization (or shock) front, indicating that the magnetic field therein is likely compressed by the expanding H{\sc ii} regions that formed in the same complex.

astro-ph.SR↗

arXiv2018

A holistic perspective on the dynamics of G035.39-00.33: the interplay between gas and magnetic fields

Magnetic field is one of the key agents that play a crucial role in shaping molecular clouds and regulating star formation, yet the complete information on the magnetic field is not well constrained due to the limitations in observations. We study the magnetic field in the massive infrared dark cloud G035.39-00.33 from dust continuum polarization observations at 850 $\micron$ with SCUBA-2/POL-2 at JCMT. The magnetic field tends to be perpendicular to the densest part of the main filament (F$_{M}$), whereas it has a less defined relative orientation in the rest of the structure, where it tends to be parallel to some diffuse regions. A mean plane-of-the-sky magnetic field strength of $\sim$50 $μ$G for F$_{M}$ is obtained using Davis-Chandrasekhar-Fermi method. Based on $^{13}$CO (1-0) line observations, we suggest a formation scenario of F$_{M}$ due to large-scale ($\sim$10 pc) cloud-cloud collision. Using additional NH$_3$ line data, we estimate that F$_{M}$ will be gravitationally unstable if it is only supported by thermal pressure and turbulence. The northern part of F$_{M}$, however, can be stabilized by a modest additional support from the local magnetic field. The middle and southern parts of F$_{M}$ are likely unstable even if the magnetic field support is taken into account. We claim that the clumps in F$_{M}$ may be supported by turbulence and magnetic fields against gravitational collapse. Finally, we identified for the first time a massive ($\sim$200 M$_{\sun}$), collapsing starless clump candidate, "c8", in G035.39-00.33. The magnetic field surrounding "c8" is likely pinched, hinting at an accretion flow along the filament.

astro-ph.GA↗

arXiv2018

The TOP-SCOPE survey of PGCCs: PMO and SCUBA-2 observations of 64 PGCCs in the 2nd Galactic Quadrant

In order to understand the initial conditions and early evolution of star formation in a wide range of Galactic environments, we carried out an investigation of 64 \textit{Planck} Galactic Cold Clumps (PGCCs) in the second quadrant of the Milky Way. Using the $^{13}$CO and C$^{18}$O $J = 1 - 0$ lines, and 850\,$μ$m continuum observations, we investigated cloud fragmentation and evolution associated with star formation. We extracted 468 clumps and 117 cores from the $^{13}$CO line and 850\,$μ$m continuum maps, respectively. We make use of the Bayesian Distance Calculator and derived the distances of all 64 PGCCs. We found that in general, the mass-size plane follows a relation of $m\sim r^{1.67}$. At a given scale, the masses of our objects are around 1/10 of that of typical Galactic massive star-forming regions. Analysis of the clump and core masses, virial parameters, densities, and mass-size relation suggests that the PGCCs in our sample have a low core formation efficiency ($\sim$3.0\%), and most PGCCs are likely low-mass star-forming candidates. Statistical study indicates that the 850\,$μ$m cores are more turbulent, more optically thick, and denser than the $^{13}$CO clumps for star formation candidates, suggesting that the 850\,$μ$m cores are likely more appropriate future star-formation candidates than the $^{13}$CO clumps.

astro-ph.GA↗

arXiv2017

ALMA reveals sequential high-mass star formation in the G9.62+0.19 complex

Stellar feedback from high-mass stars (e.g., H{\sc ii} regions) can strongly influence the surrounding interstellar medium and regulate star formation. Our new ALMA observations reveal sequential high-mass star formation taking place within one sub-virial filamentary clump (the G9.62 clump) in the G9.62+0.19 complex. The 12 dense cores (MM 1-12) detected by ALMA are at very different evolutionary stages, from starless core phase to UC H{\sc ii} region phase. Three dense cores (MM6, MM7/G, MM8/F) are associated with outflows. The mass-velocity diagrams of outflows associated with MM7/G and MM8/F can be well fitted with broken power laws. The mass-velocity diagram of SiO outflow associated with MM8/F breaks much earlier than other outflow tracers (e.g., CO, SO, CS, HCN), suggesting that SiO traces newly shocked gas, while the other molecular lines (e.g., CO, SO, CS, HCN) mainly trace the ambient gas continuously entrained by outflow jets. Five cores (MM1, MM3, MM5, MM9, MM10) are massive starless core candidates whose masses are estimated to be larger than 25 M$_{\sun}$, assuming a dust temperature of $\leq$ 20 K. The shocks from the expanding H{\sc ii} regions ("B" \& "C") to the west may have great impact on the G9.62 clump through compressing it into a filament and inducing core collapse successively, leading to sequential star formation. Our findings suggest that stellar feedback from H{\sc ii} regions may enhance the star formation efficiency and suppress the low-mass star formation in adjacent pre-existing massive clumps.

astro-ph.GA↗

arXiv2017

The Formation of Stellar Clusters in Magnetized, Filamentary Infrared Dark Clouds

Star formation in a filamentary infrared dark cloud (IRDC) is simulated over a dynamic range of 4.2 pc to 28 au for a period of $3.5\times 10^5$ yr, including magnetic fields and both radiative and outflow feedback from the protostars. At the end of the simulation, the star formation efficiency is 4.3 per cent and the star formation rate per free fall time is $ε_{\rm ff}\simeq 0.04$, within the range of observed values (Krumholz et al. 2012a). The total stellar mass increases as $\sim\,t^2$, whereas the number of protostars increases as $\sim\,t^{1.5}$. We find that the density profile around most of the simulated protostars is $\sim\,ρ\propto r^{-1.5}$, as predicted by Murray & Chang (2015). At the end of the simulation, the protostellar mass function approaches the Chabrier (2005) stellar initial mass function. We infer that the time to form a star of median mass $0.2\,M_\odot$ is about $1.4\times 10^5$~yr from the median mass accretion rate. We find good agreement among the protostellar luminosities observed in the large sample of Dunham et al. (2013), our simulation, and a theoretical estimate, and conclude that the classical protostellar luminosity problem Kenyon et al. (1990) is resolved. The multiplicity of the stellar systems in the simulation agrees to within a factor 2 of observations of Class I young stellar objects; most of the simulated multiple systems are unbound. Bipolar protostellar outflows are launched using a sub-grid model, and extend up to 1 pc from their host star. The mass-velocity relation of the simulated outflows is consistent with both observation and theory.

astro-ph.GA↗

arXiv2015

The CH+ Abundance in Turbulent, Diffuse Molecular Clouds

The intermittent dissipation of interstellar turbulence is an important energy source in the diffuse ISM. Though on average smaller than the heating rates due to cosmic rays and the photoelectric effect on dust grains, the turbulent cascade can channel large amounts of energy into a relatively small fraction of the gas that consequently undergoes significant heating and chemical enrichment. In particular, this mechanism has been proposed as a solution to the long-standing problem of the high abundance of CH+ along diffuse molecular sight lines, which steady-state, low temperature models under-produce by over an order of magnitude. While much work has been done on the structure and chemistry of these small-scale dissipation zones, comparatively little attention has been paid to relating these zones to the properties of the large-scale turbulence. In this paper, we attempt to bridge this gap by estimating the temperature and CH+ column density along diffuse molecular sight-lines by post-processing 3-dimensional MHD turbulence simulations. Assuming reasonable values for the cloud density (30 / cm^3), size (20 pc), and velocity dispersion (2.3 km / s), we find that our computed abundances compare well with CH+ column density observations, as well as with observations of emission lines from rotationally excited H2 molecules.

astro-ph.GA↗

arXiv2015

Magnetized Interstellar Molecular Clouds. I. Comparison Between Simulations and Zeeman Observations

The most accurate measurements of magnetic fields in star-forming gas are based on the Zeeman observations analyzed by Crutcher et al. (2010). We show that their finding that the 3D magnetic field scales approximately as density$^{0.65}$ can also be obtained from analysis of the observed line-of-sight fields. We present two large-scale AMR MHD simulations of several thousand $M_\odot$ of turbulent, isothermal, self-gravitating gas, one with a strong initial magnetic field (Alfven Mach number $M_{A,0}= 1$) and one with a weak initial field ($M_{A,0}=10$). We construct samples of the 100 most massive clumps in each simulation and show that they exhibit a power-law relation between field strength and density in excellent agreement with the observed one. Our results imply that the average field in molecular clumps in the interstellar medium is $ \sim 42 n_{H,4}^{0.65} μ$G. Furthermore, the median value of the ratio of the line-of-sight field to density$^{0.65}$ in the simulations is within a factor of about (1.3, 1.7) of the observed value for the strong and weak field cases, respectively. The median value of the mass-to-flux ratio, normalized to the critical value, is 70% of the line-of-sight value. This is larger than the 50% usually cited for spherical clouds because the actual mass-to-flux ratio depends on the volume-weighted field, whereas the observed one depends on the mass-weighted field. Our results indicate that the typical molecular clump in the ISM is significantly supercritical (~ factor of 3). The results of our strong-field model are in very good quantitative agreement with the observations of Li et al. (2009), which show a strong correlation in field orientation between small and large scales. Because there is a negligible correlation in the weak-field model, we conclude that molecular clouds form from strongly magnetized (although magnetically supercritical) gas.

astro-ph.GA↗

arXiv2012

Ambipolar Diffusion Heating in Turbulent Systems

The temperature of the gas in molecular clouds is a key determinant of the characteristic mass of star formation. Ambipolar diffusion (AD) is considered one of the most important heating mechanisms in weakly ionized molecular clouds. In this work, we study the AD heating rate using 2-fluid turbulence simulations and compare it with the overall heating rate due to turbulent dissipation. We find that for observed molecular clouds, which typically have Alfven Mach numbers of ~1 (Crutcher 1999) and AD Reynolds numbers of ~20 (McKee et al. 2010), about 70% of the total turbulent dissipation is in the form of AD heating. AD has an important effect on the length scale where energy is dissipated: when AD heating is strong, most of the energy in the cascade is removed by ion-neutral drift, with a comparatively small amount of energy making it down to small scales. We derive a relation for the AD heating rate that describes the results of our simulations to within a factor of two. Turbulent dissipation, including AD heating, is generally less important that cosmic-ray heating in molecular clouds, although there is substantial scatter in both.

astro-ph.SR↗

arXiv2011

A Stable, Accurate Methodology for High Mach Number, Strong Magnetic Field MHD Turbulence with Adaptive Mesh Refinement: Resolution and Refinement Studies

Performing a stable, long duration simulation of driven MHD turbulence with a high thermal Mach number and a strong initial magnetic field is a challenge to high-order Godunov ideal MHD schemes because of the difficulty in guaranteeing positivity of the density and pressure. We have implemented a robust combination of reconstruction schemes, Riemann solvers, limiters, and Constrained Transport EMF averaging schemes that can meet this challenge, and using this strategy, we have developed a new Adaptive Mesh Refinement (AMR) MHD module of the ORION2 code. We investigate the effects of AMR on several statistical properties of a turbulent ideal MHD system with a thermal Mach number of 10 and a plasma $β_0$ of 0.1 as initial conditions; our code is shown to be stable for simulations with higher Mach numbers ($M_rms = 17.3$) and smaller plasma beta ($β_0 = 0.0067$) as well. Our results show that the quality of the turbulence simulation is generally related to the volume-averaged refinement. Our AMR simulations show that the turbulent dissipation coefficient for supersonic MHD turbulence is about 0.5, in agreement with unigrid simulations.

astro-ph.IM↗

arXiv2011

Sub-Alfvenic Non-Ideal MHD Turbulence Simulations with Ambipolar Diffusion: III. Implications for Observations and Turbulent Enhancement

Ambipolar diffusion (AD) is believed to be a crucial process for redistributing magnetic flux in the dense molecular gas that occurs in regions of star formation. We carry out numerical simulations of this process in regions of low ionization using the heavy ion approximation. The simulations are for regions of strong field (plasma β=0.1) and mildly supersonic turbulence (M=3, corresponding to an Alfven mach number of 0.67). The velocity power spectrum of the neutral gas changes from an Iroshnikov-Kraichnan spectrum in the case of ideal MHD to a Burgers spectrum in the case of a shock-dominated hydrodynamic system. The magnetic power spectrum shows a similar behavior. We use a 1D radiative transfer code to post-process our simulation results; the simulated emission from the CS J=2-1 and H13CO+ J=1-0 lines shows that the effects of AD are observable in principle. Linewidths of ions are observed to be less than those of neutrals, and we confirm previous suggestions that this is due to AD. We show that AD is unlikely to affect the Chandrasekhar-Fermi method for inferring field strengths unless the AD is stronger than generally observed. Finally, we present the first fully 3D study of the enhancement of AD by turbulence, finding that AD is accelerated by factor 2-4.5 for non self-gravitating systems with the level of turbulence we consider.

astro-ph.SR↗

arXiv2011

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.

astro-ph.SR↗