Isothermal Magnetohydrodynamics Research Articles

Unveiling the Dynamics of Dense Cores in Cluster-forming Clumps: A 3D Magnetohydrodynamics Simulation Study of Angular Momentum and Magnetic Field Properties

We conducted isothermal magnetohydrodynamics simulations with self-gravity to investigate the properties of dense cores in cluster-forming clumps. Two different setups were explored: a single rotating clump and colliding clumps. We focused on determining the extent to which the rotation and magnetic field of the parental clump are inherited by the formed dense cores. Our statistical analysis revealed that the alignment between the angular momentum of dense cores, , and the rotational axis of the clump is influenced by the strength of turbulence and the simulation setup. In single rotating clumps, we found that tends to align with the clump’s rotational axis if the initial turbulence is weak. In colliding clumps, however, this alignment does not occur, regardless of the initial turbulence strength. This misalignment in colliding clumps is due to the induced turbulence from the collision and the isotropic gas inflow into dense cores. Our analysis of colliding clumps also revealed that the magnetic field globally bends along the shock-compressed layer, and the mean magnetic field of dense cores, , aligns with it. Both in single rotating clumps and colliding clumps, we found that the angle between and is generally random, regardless of the clump properties. We also analyzed the dynamical states of the formed cores and found a higher proportion of unbound cores in colliding clumps. In addition, the contribution of rotational energy was only approximately 5% of the gravitational energy, regardless of the model parameters for both single and colliding cases.

HOW-MHD: A High-order WENO-based Magnetohydrodynamic Code with a High-order Constrained Transport Algorithm for Astrophysical Applications

Due to the prevalence of magnetic fields in astrophysical environments, magnetohydrodynamic (MHD) simulation has become a basic tool for studying astrophysical fluid dynamics. To further advance the precision of MHD simulations, we have developed a new simulation code that solves ideal adiabatic or isothermal MHD equations with high-order accuracy. The code is based on the finite-difference weighted essentially nonoscillatory (WENO) scheme and the strong stability-preserving Runge–Kutta (SSPRK) method. Most of all, the code implements a newly developed, high-order constrained transport (CT) algorithm for the divergence-free constraint of magnetic fields, completing its high-order competence. In this paper, we present the version in Cartesian coordinates, which includes a fifth-order WENO and a fourth-order five-stage SSPRK, along with extensive tests. With the new CT algorithm, fifth-order accuracy is achieved in convergence tests involving the damping of MHD waves in 3D space. And substantially improved results are obtained in magnetic loop advection and magnetic reconnection tests, indicating a reduction in numerical diffusivity. In addition, the reliability and robustness of the code, along with its high accuracy, are demonstrated through several tests involving shocks and complex flows. Furthermore, tests of turbulent flows reveal the advantages of high-order accuracy and show that the adiabatic and isothermal codes have similar accuracy. With its high-order accuracy, our new code would provide a valuable tool for studying a wide range of astrophysical phenomena that involve MHD processes.

3D MHD analysis of prototypical manifold for liquid metal blankets

The water-cooled lead lithium (WCLL) and the dual-cooled lead lithium (DCLL) are two of the breeding blanket (BB) concepts that the EUROfusion consortium is pursuing in the framework of the development of the fusion reactor industrial demonstrator DEMO. Both involve the use of a liquid metal (LM) as working fluid, the lead-lithium eutectic alloy (PbLi), due to its excellent thermal properties and the possibility to serve as both the blanket coolant and tritium breeder and carrier. Unfortunately, due to the high electrical conductivity of LMs, their motion is influenced by the magnetic field used in the reactor to confine the plasma, generating a complex phenomenology which is studied by magnetohydrodynamics (MHD). In this work, a representative prototypical manifold of a BB bottom feeder is investigated for different configurations with the custom phiFoam solver, capable of simulating unsteady, incompressible and isothermal MHD flow. The aim of this study is to investigate which configuration minimizes the flow imbalance in the manifold for the WCLL or in the poloidal breeding zone channels for the DCLL. The distribution of the flow rate among the channels is strongly influenced by the position of the feeding pipe (FP) and by the development of the MHD internal layer near the expansion, which generates important jets close to the lower plate and the upper one, where the channels are attached. The channel aligned with the FP is the one carrying most of the flow, from 55% to 82%, while in the more distant one the flow is almost stagnant, carrying from 17% to 6% of the total flow rate. The total pressure loss is also estimated and its functional dependence on the manifold configuration is discussed.

A statistical study of the compressible energy cascade rate in solar wind turbulence: Parker solar probe observations

We investigated incompressible and compressible magnetohydrodynamic (MHD) energy cascade rates in the solar wind at different heliocentric distances. We used in situ magnetic field and plasma observations provided by the Parker Solar Probe mission and exact relations in fully developed turbulence. To estimate the compressible cascade rate, we applied two recent exact relations for compressible isothermal and polytropic MHD turbulence, respectively. Our observational results show a clear increase in the absolute value of the compressible and incompressible cascade rates as we get closer to the Sun. Moreover, we obtained an increase in both isothermal and polytropic cascade rates with respect to the incompressible case as compressibility increases in the plasma. Further discussion about the relation between the compressibility and the heliocentric distance is carried out. Furthermore, we compared both exact relations as compressibility increases in the solar wind, and although we note a slight trend to observe larger cascades using a polytropic closure, we obtained essentially the same cascade rate in the range of compressibility observed. Finally, we investigated the signed incompressible and compressible energy cascade rates and its connection with the real cascade rate.

The Effect of Shock-wave Duration on Star Formation and the Initial Condition of Massive Cluster Formation

Stars are born in dense molecular filaments irrespective of their mass. Compression of the interstellar medium by shocks causes filament formation in molecular clouds. Observations show that a massive star cluster formation occurs where the peak of gas column density in a cloud exceeds 1023 cm−2. In this study, we investigate the effect of the shock-compressed layer duration on filament/star formation and how the initial conditions of massive star formation are realized by performing three-dimensional isothermal magnetohydrodynamics simulations with gas inflow duration from the boundaries (i.e., shock-wave duration) as a controlling parameter. Filaments formed behind the shock expand after the duration time for short-shock-duration models, whereas long-duration models lead to star formation by forming massive supercritical filaments. Moreover, when the shock duration is longer than two postshock freefall times, the peak column density of the compressed layer exceeds 1023 cm−2, and the gravitational collapse of the layer causes the number of OB stars expected to be formed in the shock-compressed layer to reach the order of 10 (i.e., massive cluster formation).

CALLIOPE: Pseudospectral Shearing Magnetohydrodynamics Code with a Pencil Decomposition

Abstract The pseudospectral method is a highly accurate numerical scheme suitable for turbulence simulations. We have developed an open-source pseudospectral code, calliope, which adopts the P3DFFT library to perform a fast Fourier transform with the two-dimensional (pencil) decomposition of numerical grids. calliope can solve incompressible magnetohydrodynamics (MHD), isothermal compressible MHD, and rotational reduced MHD with parallel computation using very large numbers of cores (>105 cores for 20483 grids). The code can also solve for local magnetorotational turbulence in a shearing frame using the remapping method. calliope is currently the only pseudospectral code that can compute magnetorotational turbulence using pencil-domain decomposition. This paper presents the numerical scheme of calliope and the results of linear and nonlinear numerical tests, including compressible local magnetorotational turbulence with the largest grid number reported to date.

The Evolution of Compressible Solar Wind Turbulence in the Inner Heliosphere: PSP, THEMIS, and MAVEN Observations

Abstract The first computations of the compressible energy transfer rate from ∼0.2 up to ∼1.7 au is obtained using Parker Solar Probe (PSP), Time History of Events and Macroscale Interactions during Substorms (THEMIS), and Mars Atmosphere and Volatile EvolutioN (MAVEN) observations. Using a recently derived exact relation for isothermal magnetohydrodynamics turbulence, the compressible energy cascade rate, ε C , is computed for hundred of events at different heliocentric distances, for time intervals when the spacecrafts were in the pristine solar wind. The observational results show moderate increases of ε C with respect to the incompressible cascade rate, ε I . Depending on the level of compressibility in the plasma, which reaches up to 25% at PSP’s perihelion, the different terms in the exact compressible relation are shown to have different impacts on the total cascade rate, ε C . Finally, the observational results are connected with the local ion temperature and the solar wind heating problem.

Classification of Filament Formation Mechanisms in Magnetized Molecular Clouds

Abstract Recent observations of molecular clouds show that dense filaments are the sites of present-day star formation. Thus, it is necessary to understand the filament formation process because these filaments provide the initial condition for star formation. Theoretical research suggests that shock waves in molecular clouds trigger filament formation. Since several different mechanisms have been proposed for filament formation, the formation mechanism of the observed star-forming filaments requires clarification. In the present study, we perform a series of isothermal magnetohydrodynamics simulations of filament formation. We focus on the influences of shock velocity and turbulence on the formation mechanism and identified three different mechanisms for the filament formation. The results indicate that when the shock is fast, at shock velocity v sh ≃ 7 km s−1, the gas flows driven by the curved shock wave create filaments irrespective of the presence of turbulence and self-gravity. However, at a slow shock velocity v sh ≃ 2.5 km s−1, the compressive flow component involved in the initial turbulence induces filament formation. When both the shock velocities and turbulence are low, the self-gravity in the shock-compressed sheet becomes important for filament formation. Moreover, we analyzed the line-mass distribution of the filaments and showed that strong shock waves can naturally create high-line-mass filaments such as those observed in the massive star-forming regions in a short time. We conclude that the dominant filament formation mode changes with the velocity of the shock wave triggering the filament formation.

STARFORGE: the effects of protostellar outflows on the IMF

ABSTRACT The initial mass function (IMF) of stars is a key quantity affecting almost every field of astrophysics, yet it remains unclear what physical mechanisms determine it. We present the first runs of the STAR FORmation in Gaseous Environments project, using a new numerical framework to follow the formation of individual stars in giant molecular clouds (GMCs) using the gizmo code. Our suite includes runs with increasingly complex physics, starting with isothermal ideal magnetohydrodynamics (MHD) and then adding non-isothermal thermodynamics and protostellar outflows. We show that without protostellar outflows the resulting stellar masses are an order of magnitude too high, similar to the result in the base isothermal MHD run. Outflows disrupt the accretion flow around the protostar, allowing gas to fragment and additional stars to form, thereby lowering the mean stellar mass to a value similar to that observed. The effect of jets upon global cloud evolution is most pronounced for lower mass GMCs and dense clumps, so while jets can disrupt low-mass clouds, they are unable to regulate star formation in massive GMCs, as they would turn an order unity fraction of the mass into stars before unbinding the cloud. Jets are also unable to stop the runaway accretion of massive stars, which could ultimately lead to the formation of stars with masses ${\gt}500\, \mathrm{M}_{\rm \odot }$. Although we find that the mass scale set by jets is insensitive to most cloud parameters (i.e. surface density, virial parameter), it is strongly dependent on the momentum loading of the jets (which is poorly constrained by observations) as well as the temperature of the parent cloud, which predicts slightly larger IMF variations than observed. We conclude that protostellar jets play a vital role in setting the mass scale of stars, but additional physics are necessary to reproduce the observed IMF.

Engineering design and development of lead lithium loop for thermo-fluid MHD studies

In the frame of the design and development of Liquid breeder blankets, a number of R & D activities are in progress in the area of liquid metal technology development. In presence of strong plasma confining toroidal magnetic field, motion of electrically conducting liquid metal leads to Magneto Hydro Dynamic (MHD) phenomena, as a consequence of which liquid metal flow profile changes inside the flow channels of liquid breeder blankets and additional pressure drop occurs due to the flow opposing Lorentz force (J × B). For the design and development of liquid breeder blankets, 3D MHD flow needs to be studied for various flow configurations as present in the liquid breeder blankets. A lead lithium (Pb-Li) MHD loop is being developed at IPR to perform MHD experiments for Pb-Li flow in various flow geometry such as U-bend, transition zones, circular pipes, sudden expansion and contraction, etc. The test mock ups will be placed in a uniform magnetic field up to 1.4 T, produced by a C-shaped Iron core electromagnet with a pole gap of 370 mm. Both Isothermal and thermo-fluid MHD experiments are being planned for MHD database generation and code validation.

Compressible Magnetohydrodynamic Turbulence in the Earth's Magnetosheath: Estimation of the Energy Cascade Rate Using insitu Spacecraft Data.

The first estimation of the energy cascade rate |ε_{C}| of magnetosheath turbulence is obtained using the Cluster and THEMIS spacecraft data and an exact law of compressible isothermal magnetohydrodynamics turbulence. The mean value of |ε_{C}| is found to be close to 10^{-13} J m^{-3} s^{-1}, at least 2 orders of magnitude larger than its value in the solar wind (∼10^{-16} J m^{-3} s^{-1} in the fast wind). Two types of turbulence are evidenced and shown to be dominated either by incompressible Alfvénic or compressible magnetosoniclike fluctuations. Density fluctuations are shown to amplify the cascade rate and its spatial anisotropy in comparison with incompressible Alfvénic turbulence. Furthermore, for compressible magnetosonic fluctuations, large cascade rates are found to lie mostly near the linear kinetic instability of the mirror mode. New empirical power-laws relating |ε_{C}| to the turbulent Mach number and to the internal energy are evidenced. These new findings have potential applications in distant astrophysical plasmas that are not accessible to insitu measurements.

Alternative derivation of exact law for compressible and isothermal magnetohydrodynamics turbulence.

The exact law for fully developed homogeneous compressible magnetohydrodynamics (CMHD) turbulence is derived. For an isothermal plasma, without the assumption of isotropy, the exact law is expressed as a function of the plasma velocity field, the compressible Alfvén velocity, and the scalar density, instead of the Elsasser variables used in previous works. The theoretical results show four different types of terms that are involved in the nonlinear cascade of the total energy in the inertial range. Each category is examined in detail, in particular, those that can be written either as source or flux terms. Finally, the role of the background magnetic field B_{0} is highlighted and a comparison with the incompressible MHD (IMHD) model is discussed. This point is particularly important when testing this exact law on numerical simulations and in situ observations in space plasmas.

The formation of massive molecular filaments and massive stars triggered by a magnetohydrodynamic shock wave

Abstract Recent observations suggest an that intensive molecular cloud collision can trigger massive star/cluster formation. The most important physical process caused by the collision is a shock compression. In this paper, the influence of a shock wave on the evolution of a molecular cloud is studied numerically by using isothermal magnetohydrodynamics simulations with the effect of self-gravity. Adaptive mesh refinement and sink particle techniques are used to follow the long-time evolution of the shocked cloud. We find that the shock compression of a turbulent inhomogeneous molecular cloud creates massive filaments, which lie perpendicularly to the background magnetic field, as we have pointed out in a previous paper. The massive filament shows global collapse along the filament, which feeds a sink particle located at the collapse center. We observe a high accretion rate $\dot{M}_{\rm acc}> 10^{-4}\, M_{\odot }\:$yr−1 that is high enough to allow the formation of even O-type stars. The most massive sink particle achieves M > 50 M$_{\odot }$ in a few times 105 yr after the onset of the filament collapse.

Energy transfer in compressible magnetohydrodynamic turbulence

Magnetic fields, compressibility, and turbulence are important factors in many terrestrial and astrophysical processes. While energy dynamics, i.e., how energy is transferred within and between kinetic and magnetic reservoirs, has been previously studied in the context of incompressible magnetohydrodynamic (MHD) turbulence, we extend shell-to-shell energy transfer analysis to the compressible regime. We derive four new transfer functions specifically capturing compressibility effects in the kinetic and magnetic cascade, and capturing energy exchange via magnetic pressure. To illustrate their viability, we perform and analyze four simulations of driven isothermal MHD turbulence in the sub- and supersonic regime with two different codes. On the one hand, our analysis reveals robust characteristics across regime and numerical method. For example, energy transfer between individual scales is local and forward for both cascades with the magnetic cascade being stronger than the kinetic one. Magnetic tension and magnetic pressure related transfers are less local and weaker than the cascades. We find no evidence for significant nonlocal transfer. On the other hand, we show that certain functions, e.g., the compressive component of the magnetic energy cascade, exhibit a more complex behavior that varies both with regime and numerical method. Having established a basis for the analysis in the compressible regime, the method can now be applied to study a broader parameter space.

Magnetic reconnection during eruptive magnetic flux ropes

Aims. We perform a three-dimensional (3D) high resolution numerical simulation in isothermal magnetohydrodynamics to study the magnetic reconnection process in a current sheet (CS) formed during an eruption of a twisted magnetic flux rope (MFR). Because the twist distribution violates the Kruskal-Shafranov condition, the kink instability occurs, and the MFR is distorted. The centre part of the MFR loses its equilibrium and erupts upward, which leads to the formation of a 3D CS underneath it.Methods. In order to study the magnetic reconnection inside the CS in detail, mesh refinement has been used to reduce the numerical diffusion and we estimate a Lundquist number S = 104 in the vicinity of the CS.Results. The refined mesh allows us to resolve fine structures inside the 3D CS: a bifurcating sheet structure signaling the 3D generalization of Petschek slow shocks, some distorted-cylindrical substructures due to the tearing mode instabilities, and two turbulence regions near the upper and the lower tips of the CS. The topological characteristics of the MFR depend sensitively on the observer’s viewing angle: it presents as a sigmoid structure, an outwardly expanding MFR with helical distortion, or a flare-CS-coronal mass ejection symbiosis as in 2D flux-rope models when observed from the top, the front, or the side.

Energy Cascade Rate in Compressible Fast and Slow Solar Wind Turbulence

Abstract Estimation of the energy cascade rate in the inertial range of solar wind turbulence has been done so far mostly within incompressible magnetohydrodynamics (MHD) theory. Here, we go beyond that approximation to include plasma compressibility using a reduced form of a recently derived exact law for compressible, isothermal MHD turbulence. Using in situ data from the THEMIS/ARTEMIS spacecraft in the fast and slow solar wind, we investigate in detail the role of the compressible fluctuations in modifying the energy cascade rate with respect to the prediction of the incompressible MHD model. In particular, we found that the energy cascade rate (1) is amplified particularly in the slow solar wind; (2) exhibits weaker fluctuations in spatial scales, which leads to a broader inertial range than the previous reported ones; (3) has a power-law scaling with the turbulent Mach number; (4) has a lower level of spatial anisotropy. Other features of solar wind turbulence are discussed along with their comparison with previous studies that used incompressible or heuristic (nonexact) compressible MHD models.

SCALING OF COMPRESSIBLE MAGNETOHYDRODYNAMIC TURBULENCE IN THE FAST SOLAR WIND

ABSTRACT The role of compressible fluctuations in the energy cascade of fast solar wind turbulence is studied using a reduced form of an exact law derived recently for compressible isothermal magnetohydrodynamics and in situ observations from the THEMIS B/ARTEMIS P1 spacecraft. A statistical survey of the data revealed a turbulent energy cascade over a range of two decades of scales that is broader than the previous estimates made from an exact incompressible law. A term-by-term analysis of the compressible model reveals new insight into the role played by the compressible fluctuations in the energy cascade. The compressible fluctuations are shown to amplify by two to four times the turbulent cascade rate with respect to the incompressible model in of the analyzed samples. This new estimated cascade rate is shown to provide the adequate energy dissipation required to account for the local heating of the non-adiabatic solar wind.

General polytropic magnetohydrodynamic cylinder under self-gravity

Abstract Based on general polytropic (GP) magnetohydrodynamics (MHD), we offer a self-similar dynamic formalism for a magnetized, infinitely long, axially uniform cylinder of axisymmetry under self-gravity with radial and axial flows and with helical magnetic field. We identify two major classes of solution domains and obtain a few valuable MHD integrals in general. We focus on one class that has the freedom of prescribing a GP dynamic equation of state including the isothermal limit and derive analytic asymptotic solutions for illustration. In particular, we re-visit the isothermal MHD problem of Tilley & Pudritz (TP) and find that TP's main conclusion regarding the MHD solution behaviour for a strong ring magnetic field of constant toroidal flux-to-mass ratio Γφ to be incorrect. As this is important for conceptual scenarios, MHD cylinder models, testing numerical codes and potential observational diagnostics of magnetized filaments in various astrophysical contexts, we show comprehensive theoretical analysis and reasons as well as extensive numerical results to clarify pertinent points in this Letter. In short, for any given Γφ value be it small or large, the asymptotic radial scaling of the reduced mass density α(x) at sufficiently large x should always be ∼x−4 instead of ∼x−2 contrary to the major claim of TP.

Non-resonant magnetohydrodynamics streaming instability near magnetized relativistic shocks

We present in this paper both a linear study and numerical relativistic magnetohydrodynamic (MHD) simulations of the non-resonant streaming instability occurring in the precursor of relativistic shocks. In the shock front rest frame, we perform a linear analysis of this instability in a likely configuration for ultra-relativistic shock precursors. This considers magneto-acoustic waves having a wave vector perpendicular to the shock front and the large-scale magnetic field. Our linear analysis is achieved without any assumption on the shock velocity and is thus valid for all velocity regimes. In order to check our calculation, we also perform relativistic MHD simulations describing the propagation of the aforementioned magneto-acoustic waves through the shock precursor. The numerical calculations confirm our linear analysis, which predicts that the growth rate of the instability is maximal for ultra-relativistic shocks and exhibits a wavenumber dependence ∝ kx1/2. Our numerical simulations also depict the saturation regime of the instability where we show that the magnetic amplification is moderate but nevertheless significant (δB/B ≤ 10). This latter fact may explain the presence of strong turbulence in the vicinity of relativistic magnetized shocks. Our numerical approach also introduces a convenient means to handle isothermal (ultra-)relativistic MHD conditions.

Viscous Profiles for Shock Waves in Isothermal Magnetohydrodynamics

We prove existence of viscous profiles for slow and fast shock waves in isothermal magnetohydrodynamics with a general pressure law both using the Conley index and connection matrices.