MHD Shock Research Articles

PRIME‐SH: A Data‐Driven Probabilistic Model of Earth's Magnetosheath

AbstractA data‐driven model of Earth's magnetosheath is developed by training a recurrent neural network (RNN) with probabilistic outputs to reproduce Magnetospheric MultiScale (MMS) measurements of the magnetosheath plasma and magnetic field using measurements from the Wind spacecraft upstream of Earth at the first Earth‐Sun Lagrange point (L1). This model, called Probabilistic Regressor for Input to the Magnetosphere Estimation‐magnetosheath (PRIME‐SH) in reference to its progenitor algorithm PRIME, is shown to predict spacecraft observations of magnetosheath conditions accurately in a statistical sense with a continuous rank probability score of 0.227σ (dimensionless standard deviation units). PRIME‐SH is shown to be more accurate than many current analytical models of the magnetosheath. Furthermore, PRIME‐SH is shown to reproduce physics not explicitly enforced during training, such as field line draping, the dayside plasma depletion layer, the magnetosheath flow stagnation point, and the Rankine‐Hugoniot MHD shock jump conditions. PRIME‐SH has the additional benefits of being computationally inexpensive relative to global MHD simulations, being capable of reproducing difficult‐to‐model physics such as temperature anisotropy, and being capable of reliably estimating its own uncertainty to within 3.5%.

Near-Earth Interplanetary Coronal Mass Ejections and Their Association with DH Type II Radio Bursts During Solar Cycles 23 and 24

We analyse the characteristics of interplanetary coronal mass ejections (ICMEs) during Solar Cycles 23 and 24. The present analysis is primarily based on the near-Earth ICME catalogue (Richardson and Cane, 2010). An important aspect of this study is to understand the near-Earth and geoeffective aspects of ICMEs in terms of their association (type II ICMEs) versus absence (non-type II ICMEs) of decameter-hectometer (DH) type II radio bursts, detected by Wind/WAVES and STEREOS/WAVES. Notably, DH type II radio bursts driven by a CME indicate powerful MHD shocks leaving the inner corona and entering the interplanetary medium. We find a drastic reduction in the occurrence of ICMEs by 56% in Solar Cycle 24 compared to the previous cycle (64 versus 147 events). Interestingly, despite a significant decrease in ICME/CME counts, both cycles contain almost the same fraction of type II ICMEs (~47%). Our analysis reveals that, even at a large distance of 1 AU, type II CMEs maintain significantly higher speeds compared to non-type II events (523 km/s versus 440 km/s). While there is an obvious trend of decrease in ICME transit times with increase in the CME initial speed, there also exists a noticeable wide range of transit times for a given CME speed. Contextually, Cycle 23 exhibits 10 events with shorter transit times ranging between 20-40 hours of predominantly type II categories while, interestingly, Cycle 24 almost completely lacks such "fast" events. We find a significant reduction in the parameter $V_{ICME} \times B_{z}$, the dawn to dusk electric field, by 39% during Solar Cycle 24 in comparison with the previous cycle. Further, $V_{ICME} \times B_{z}$ shows a strong correlation with Dst index, which even surpasses the consideration of $B_{z}$ and $V_{ICME}$ alone. The above results imply the crucial role of $V_{ICME} \times B_{z}$ toward effectively modulating the geoeffectiveness of ICMEs.

Reflections by Bengt Ulf Östen Sonnerup

First, I will tell readers about memories of my graduate student days at Cornell. I will highlight some of my experiences there, and what I learned, and didn’t learn from them. Then I will then discuss a few of the research topics I have been working on over the years, including data interpretation and the tools for it, with special emphasis on the magnetopause. Aspects of MHD shocks and other structures, including boundary layers, are among those topics. I will mention a few people with whom I have worked closely and a few famous individuals, who influenced me in a significant way. The presentation contains material of potential interest to new, as well as more seasoned workers in the field. It will not always be in time order.

High-resolution observations with ARTEMIS/JLS and the NRH

Context.Narrowband bursts (spikes) are very small duration and bandwidth bursts which appear on dynamic spectra from microwave to decametric frequencies. They are believed to be manifestations of small-scale energy release through magnetic reconnection.Aims.We study the position of the spike-like structures relative to the front of type-II bursts and their role in the burst emission.Methods.We used high-sensitivity, low-noise dynamic spectra obtained with the acousto-optic analyzer (SAO) of the ARTEMIS-JLS solar radiospectrograph, in conjunction with high-time-resolution images from the Nançay Radioheliograph (NRH) in order to study spike-like bursts near the front of a type-II radio burst recorded at the west limb during the November 3, 2003 extreme solar event. The spike-like emission in the dynamic spectrum was enhanced by means of high-pass-time filtering.Results.We identified a number of spikes in the NRH images. Due to the lower temporal resolution of the NRH, multiple spikes detected in the dynamic spectrum appeared as single structures in the images. These spikes had an average size of ≈200″ and their observed brightness temperature was 1.4 to 5.6 × 109K, providing a significant contribution to the emission of the type-II burst front. At variance with a previous study on the type-IV associated spikes, we found no systematic displacement between the spike emission and the emission between spikes. At 327.0 MHz, the type II emission was located about 0.3R⊙above the pre-existing continuum emission, which, in turn, was located 0.1R⊙above the western limb.Conclusions.This study, combined with our previous results, indicates that the spike-like chains aligned along the type II burst MHD shock front are not a perturbation of the type II emission, as in the case of type IV spikes, but a manifestation of the type II emission itself. The preponderance of these chains, together with the lack of isolated structures or irregular clusters, points towards some form of small-scale magnetic reconnection, organized along the type-II propagating front.

Wind of a young massive star colliding with a supernova remnant shell

The fast stellar winds of massive stars, along with supernovae, determine the dynamics within the star-forming regions. Within a compact star cluster, counterpropagating supersonic MHD shock flows associated with winds and supernova remnants can provide favorable conditions for efficient Fermi I particle acceleration up to energies > 10 PeV over a short timescale of several hundred years. To model the nonthermal spectra of such systems it is necessary to know the complex structure of colliding supersonic flows. In this paper using the PLUTO code we study on a subparsec scale a 2D MHD model of the collision of a core-collapse supernova remnant with a magnetized wind of a hot rotating O-star. As a result the detailed high resolution (~ 10−4 pc) maps of density, magnetic field, and temperature during the the wind - supernova shell interaction are presented.

Conversion and Smoothing of MHD Shocks in Atmospheres with Open and Closed Magnetic Field and Neutral Points

Planar acoustically dominated magneto\-hydro\-dynamic waves are initiated at the high-$\beta$ base of a simulated 2D isothermal stratified atmosphere with potential magnetic field exhibiting both open and closed field regions as well as neutral points. They shock on their way upward toward the Alfv\'en-acoustic equipartition surface $a=c$, where $a$ and $c$ are the Alfv\'en and sound speeds respectively. Expanding on recent 1.5D findings that such shocks mode-convert to fast shocks and slow smoothed waves on passing through $a=c$, we explore the implications for these more complex magnetic geometries. It is found that the 1.5D behaviour carries over to the more complex case, with the fast shocks strongly attracted to neutral points, which are disrupted producing extensive fine structure. It is also observed that shocks moving in the opposite direction, from $a>c$ to $a<c$, split into fast and slow components too, and that again it is the slow component that is smoothed.

Transverse bifurcation of viscous slow MHD shocks

We study by a combination of analytical and numerical Evans function techniques multi-D viscous and inviscid stability and associated transverse bifurcation of planar slow Lax MHD shocks in a channel with periodic boundary conditions. Notably, this includes the first multi-D numerical Evans function study for viscous MHD. Our results suggest that, rather than a planar shock, a nonplanar traveling wave with the same normal velocity is the typical mode of propagation in the slow Lax mode. Moreover, viscous and inviscid stability transitions appear to agree, answering (for this particular model and setting) an open question of Zumbrun and Serre.

The debye region in astrophysical plasmas: a new access to the problem

We study the consequences of defining the Debye region in astrophysical plasmas as that region where purely stochastic Poissonian density fluctuations must be perturbed by the appearance of unscreened electric Coulomb forces. Here by we test a new definition of the charge screening length requiring that purely statistical density fluctuations in sub-volumes of the system can only be expected, if particle residence probabilities in those volumes are uncorrelated. We find that within Debye spheres where electric micro fields appear, this can evidently not anymore be guaranteed. We introduce a new definition of the charge-screening length based on this requirement. It turns out that the newly defined charge screening length increases compared to its classical Debye value proportional to the so-called Debye number, i.e. the number of particles in the Debye sphere, while the classical Debye length delivers one unique result independent on the Debye number. We discuss the astrophysical relevance of this new definition which has the consequence that the effective screening length increases with the square of the temperature and decreases inversely proportional to the density, instead of with their square roots as in classic representations. Based on this revised Debye concept we furthermore study the general dispersion relation for electrostatic waves and show, that these waves when propagating into the direction of increasing electron temperatures will grow nonlinear and thus dissipate their excess energy to the electrons, with the consequence of heating them further up. This naturally explains the occurence of observed electron temperature increases at space plasma passages over MHD shocks. Furthermore we study the radiowave scattering in a plasma environment due to density-fluctuations which induce dielectricity fluctuations exciting secondary dipolar radio waves which latter serve as a valuable diagnostic tool for plasma investigations.

Heliophysics: from observations to models and applications

Study of the physical phenomena and processes on the Sun and in the heliosphere, a natural plasma laboratory, is based on near-earth and space-based observations and building models which help to obtain a general view of how the Sun was made and how it works, while allowing one to address the practical problems of solar activity influencing space weather and its impact on various areas of human activity. In this paper a brief outline is given of the models of trigger mechanisms driving the most powerful manifestations of solar activity — solar flares and mass ejections, the wave mechanism of solar corona heating. Also, analytical solutions are presented for MHD shock waves in solar wind collisionless plasma with heat fluxes.

Laboratory Study of Bilateral Supernova Remnants and Continuous MHD Shocks

Abstract Many supernova remnants (SNRs), such as G296.5+10.0, exhibit an axisymmetric or barrel shape. Such morphologies have previously been linked to the direction of the Galactic magnetic field, although this remains uncertain. These SNRs generate magnetohydrodynamic shocks in the interstellar medium, modifying its physical and chemical properties. The ability to study these shocks through observations is difficult due to the small spatial scales involved. In order to answer these questions, we perform a scaled laboratory experiment in which a laser-generated blast wave expands under the influence of a uniform magnetic field. The blast wave exhibits a spheroidal shape, whose major axis is aligned with the magnetic field, in addition to a more continuous shock front. The implications of our results are discussed in the context of astrophysical systems.

Propagation of an exponential shock wave in a rotational axisymmetric isothermal or adiabatic flow of a self-gravitating non-ideal gas under the influence of axial or azimuthal magnetic field

Abstract In this paper, we consider a quasilinear hyperbolic system of partial differential equations (PDEs) governing unsteady cylindrically symmetric motion of an inviscid, perfectly conducting and non-ideal gas in which the effects of magnetic field as well as gravitational field are significant. The ambient medium is assumed to have radial, azimuthal and axial components of fluid velocity. The fluid velocities and the initial magnetic field of the ambient medium are assumed to be varying and obeying exponential laws. The density of the ambient medium is assumed to be constant. Solutions are obtained for self-gravitating MHD shock in a rotating medium with the vorticity vector and its components in one-dimensional flow case. The numerical solutions are obtained using Runge-Kutta method of the fourth order. The effects of variation of the non-idealness parameter of the gas, gravitational parameter, the Shock Cowling number, and the adiabatic exponent of the gas are are worked out in detail. Further, a comparison between the solutions obtained in the case of isothermal and adiabatic flows is done. It is manifested that the non-idealness parameter of gas, presence of magnetic field (axial or azimuthal), and the adiabatic exponent of the gas have decaying effect on the shock wave however increase in the value of gravitational parameter has reverse effect on the shock strength. Further, it is shown that the consideration of isothermal flow or the presence of azimuthal magnetic field removes the singularity in the density distribution, the magnetic field distribution and the non-dimensional axial component of the vorticity vector distribution which arises in the case of adiabatic flow. It is investigated that the self-gravitation reduces the effects of the non-idealness of the gas. The obtained results are found in good agreement with the existing results.

On the shock induced instabilities in collisionless plasma

Firehose, mirror and ion-acoustic instabilities behind MHD shock waves are discussed for collisionless anisotropic plasma with heat fluxes. For the parallel shock wave it has been demonstrated that initially stable plasma can be destabilized by the shock which leads to turbulence generation in the downstream flow. Upstream parameter domains are determined where such destabilization occurs.

MHD-shock structures of astrospheres: λ Cephei -like astrospheres

ABSTRACT The interpretation of recent observations of bow shocks around O-stars and the creation of corresponding models require a detailed understanding of the associated (magneto-)hydrodynamic structures. We base our study on 3D numerical (magneto-)hydrodynamical models, which are analysed using the dynamically relevant parameters, in particular, the (magneto)sonic Mach numbers. The analytic Rankine–Hugoniot relation for HD and MHD are compared with those obtained by the numerical model. In that context, we also show that the only distance which can be approximately determined is that of the termination shock, if it is an HD shock. For MHD shocks, the stagnation point does not, in general, lie on the inflow line, which is the line parallel to the inflow vector and passing through the star. Thus an estimate via the Bernoulli equation as in the HD case is, in general, not possible. We also show that in O-star astrospheres, distinct regions exist in which the fast, slow, Alfvénic, and sonic Mach numbers become lower than one, implying subslow magnetosonic as well as subfast and subsonic flows. Nevertheless, the analytic MHD Rankine–Hugoniot relations can be used for further studies of turbulence and cosmic ray modulation.

A computational study of the properties of the quasi-perpendicular fast forward shock event during solar maximum

MHD shock waves and discontinuities are often observed in the solar wind. We studied a strong shock wave event on 7 June 2014, during a solar maximum. The properties of forward shock are investigated and all physical parameters of interplanetary shock are analyzed. The upstream parameters, such as Alfven velocity and sound speed are calculated, and the angle ( $${\theta }$$ ) between the upstream magnetic field direction and the shock normal is estimated. To determine the propagation speed of the shock, a full numerical solution of shock adiabatic equation is carried out. The thermal pressure for electrons and ions are calculated and also the pressure ratio and the entropy change across the shock are estimated. The results show that the shock strength is about 3.88 with $${\theta }\approx \text{72 }^{\circ }$$ (a quasi-perpendicular case), and shock propagation velocity is about 678 km/s. The increase in the specific entropy is also evaluated.

Propagation of shock wave in a rotational axisymmetric ideal gas with density varying exponentially and azimuthal magnetic field: isothermal flow

In the present paper, the non-similarity solution for unsteady isothermal flow behind the cylindrical shock wave in a rotational axisymmetric perfect gas in the presence of azimuthal magnetic field is investigated. The ambient medium is assumed to have axial, azimuthal and radial components of fluid velocity. Solutions are obtained for MHD shock in a rotating medium with the vorticity vector and its components in one-dimensional flow case. The numerical solutions are obtained using Mathematica software and Runge–Kutta method of the fourth order. The Alfven Mach number, time and adiabatic exponent effects are worked out in detail. It is obtained that in the presence of magnetic field at the piston (inner expanding surface), the pressure and density vanish and hence a vacuum is formed at the line of symmetry, which is an excellent conformity with conditions to produce the shock wave in laboratory. Also, without magnetic field, the shock strength increases with an increase in time, whereas time has reverse affects on the shock strength in the presence of magnetic field. Our solutions are valid for arbitrary values of time. A comparison is also made between the behavior of non-rotating and rotating medium solutions in the presence or absence of magnetic field.

Interstellar Plunging Waves: ALMA Resolves the Physical Structure of Nonstationary MHD Shocks

Abstract Magnetohydrodynamic (MHD) shocks are violent events that inject large amounts of energy in the interstellar medium dramatically modifying its physical properties and chemical composition. Indirect evidence for the presence of such shocks has been reported from the especial chemistry detected toward a variety of astrophysical shocked environments. However, the internal physical structure of these shocks remains unresolved since their expected spatial scales are too small to be measured with current instrumentation. Here we report the first detection of a fully spatially resolved, MHD shock toward the infrared dark cloud (IRDC) G034.77-00.55. The shock, probed by silicon monoxide (SiO) and observed with the Atacama Large Millimeter/submillimeter Array (ALMA), is associated with the collision between the dense molecular gas of the cloud and a molecular gas flow pushed toward the IRDC by the nearby supernova remnant (SNR) W44. The interaction is occurring on subparsec spatial scales thanks to the enhanced magnetic field of the SNR, making the dissipation region of the MHD shock large enough to be resolved with ALMA. Our observations suggest that molecular flow–flow collisions can be triggered by stellar feedback, inducing shocked molecular gas densities compatible with those required for massive star formation.

Smoothing of MHD Shocks in Mode Conversion

Abstract Shock waves are simulated passing through the Alfvén-acoustic equipartition layer in a stratified isothermal magneto-atmosphere. The recent ray-theoretic calculations of Núñez predicted smoothing of the shock through this layer, causing both the fast and slow components to emerge as continuous waves. However, it is found that the partial mode conversion expected from linear theory for oblique incidence of the shock on the magnetic field is accompanied by a smoothing of the slow shock only, while the fast shock persists. Explanations are presented based on magnetohydrodynamic mode conversion and shock theory.

High-order magnetohydrodynamics for astrophysics with an adaptive mesh refinement discontinuous Galerkin scheme

Modern astrophysical simulations aim to accurately model an ever-growing array of physical processes, including the interaction of fluids with magnetic fields, under increasingly stringent performance and scalability requirements driven by present-day trends in computing architectures. Discontinuous Galerkin methods have recently gained some traction in astrophysics, because of their arbitrarily high order and controllable numerical diffusion, combined with attractive characteristics for high performance computing. In this paper, we describe and test our implementation of a discontinuous Galerkin (DG) scheme for ideal magnetohydrodynamics in the AREPO-DG code. Our DG-MHD scheme relies on a modal expansion of the solution on Legendre polynomials inside the cells of an Eulerian octree-based AMR grid. The divergence-free constraint of the magnetic field is enforced using one out of two distinct cell-centred schemes: either a Powell-type scheme based on nonconservative source terms, or a hyperbolic divergence cleaning method. The Powell scheme relies on a basis of locally divergence-free vector polynomials inside each cell to represent the magnetic field. Limiting prescriptions are implemented to ensure non-oscillatory and positive solutions. We show that the resulting scheme is accurate and robust: it can achieve high-order and low numerical diffusion, as well as accurately capture strong MHD shocks. In addition, we show that our scheme exhibits a number of attractive properties for astrophysical simulations, such as lower advection errors and better Galilean invariance at reduced resolution, together with more accurate capturing of barely resolved flow features. We discuss the prospects of our implementation, and DG methods in general, for scalable astrophysical simulations.

The challenges of modelling microphysics: ambipolar diffusion, chemistry, and cosmic rays in MHD shocks

From molecular clouds to protoplanetary disks, non-ideal magnetic effects are important in many astrophysical environments. Indeed, in star and disk formation processes, it has become clear that these effects are critical to the evolution of the system. The efficacy of non-ideal effects are, however, determined by the complex interplay between magnetic fields, ionising radiation, cosmic rays, microphysics, and chemistry. In order to understand these key microphysical parameters, we present a one-dimensional non-ideal magnetohydrodynamics code and apply it to a model of a time-dependent, oblique, magnetic shock wave. By varying the microphysical ingredients of the model, we find that cosmic rays and dust play a major role, and that, despite the uncertainties, the inclusion of microphysics is essential to obtain a realistic outcome in magnetic astrophysical simulations.

Perpendicular relativistic shocks in magnetized pair plasma

Perpendicular relativistic ($\gamma_0=10$) shocks in magnetized pair plasmas are investigated using two dimensional Particle-in-Cell simulations. A systematic survey, from unmagnetized to strongly magnetized shocks, is presented accurately capturing the transition from Weibel-mediated to magnetic-reflection-shaped shocks. This transition is found to occur for upstream flow magnetizations $10^{-3}<\sigma<10^{-2}$ at which a strong perpendicular net current is observed in the precursor, driving the so-called current-filamentation instability. The global structure of the shock and shock formation time are discussed. The MHD shock jump conditions are found in good agreement with the numerical results, except for $10^{-4} < \sigma < 10^{-2}$ where a deviation up to 10\% is observed. The particle precursor length converges toward the Larmor radius of particles injected in the upstream magnetic field at intermediate magnetizations. For $\sigma>10^{-2}$, it leaves place to a purely electromagnetic precursor following from the strong emission of electromagnetic waves at the shock front. Particle acceleration is found to be efficient in weakly magnetized perpendicular shocks in agreement with previous works, and is fully suppressed for $\sigma > 10^{-2}$. Diffusive Shock Acceleration is observed only in weakly magnetized shocks, while a dominant contribution of Shock Drift Acceleration is evidenced at intermediate magnetizations. The spatial diffusion coefficients are extracted from the simulations allowing for a deeper insight into the self-consistent particle kinematics and scale with the square of the particle energy in weakly magnetized shocks. These results have implications for particle acceleration in the internal shocks of AGN jets and in the termination shocks of Pulsar Wind Nebulae.