3D MHD Model Research Articles

Coronal magnetic field and emission properties of small-scale bright and faint loops in the quiet Sun

Context. The present study provides statistical information on the coronal magnetic field and intensity properties of small-scale bright and faint loops in the quiet Sun. Aims. We aim to quantitatively investigate the morphological and topological properties of the coronal magnetic field in bright and faint small-scale loops, with the former known as coronal bright points (CBPs). Methods. We analyse 126 small-scale loops of all sizes using quasi-temporal imaging and line-of-sight magnetic field observations. These observations are taken by the Atmospheric Imaging Assembly (AIA) in the Fe XII 193 Å channel and the Helioseismic Magnetic Imager (HMI) on board the Solar Dynamics Observatory. We employ a recently developed automatic tool that uses a linear magneto-hydro-static (LMHS) model to compute the magnetic field in the solar atmosphere and automatically match individual magnetic field lines with small-scale loops. Results. For most of the loops, we automatically obtain an excellent agreement of the magnetic field lines from the LMHS model and the loops seen in the AIA 193 Å channel. One stand-out result is that the magnetic field is non-potential. We obtain the typical ranges of loop heights, lengths, intensities, mean magnetic field strength along the loops and at loop tops, and magnetic field strength at loop footpoints. We investigate the relationship between all those parameters. We find that loops below the classic chromospheric height of 1.5 Mm are flatter, suggesting that non-magnetic forces (one of which is the plasma pressure) play an important role below this height. We find a strong correlation (Pearson coefficient of 0.9) between loop heights and lengths. An anti-correlation is found between the magnetic field strength at loop tops and loop heights and lengths. The average intensity along the loops correlates stronger with the average magnetic field along the loops than with the field strength at loop tops. Conclusions. The latter correlation indicates that the energy release in the loops is more likely linked to the average magnetic field along the loops than the field strength on the loop tops. In other words, the energy is probably released all along the loops, but not just at the loop top. This result is consistent with a recent benchmarking radiative 3D MHD model.

Modelling non-radially propagating coronal mass ejections and forecasting the time of their arrival at Earth

We present the study of two solar eruptive events observed on December 7 2020 and October 28 2021. Both events were associated with full halo coronal mass ejections (CMEs) and flares. These events were chosen because they show a strong non-radial direction of propagation in the low corona and their main propagation direction observed in the inner heliosphere is not fully aligned with the Sun-Earth line. This characteristic makes them suitable for our study, which aims to inspect how the non-radial direction of propagation in the low corona affects the time of CMEs’ arrival at Earth. We reconstructed the CMEs using SOHO/LASCO and STEREO/COR observations and modelled them with the 3D MHD model EUHFORIA and the cone model for CMEs. In order to compare the accuracy of forecasting the CME and the CME-driven shock arrival time at Earth obtained from different methods, we also used so-called type II bursts, radio signatures of associated shocks, to find the velocities of the CME-driven shocks and forecast the time of their arrival at Earth. Additionally, we estimated the CME arrival time using the 2D CME velocity obtained from the white light images. Our results show that the lowest accuracy of estimated CME Earth arrival times is found when the 2D CME velocity is used (time difference between observed and modelled arrival time, Δt ≈ −29 h and −39 h, for the two studied events, respectively). The velocity of the type II radio bursts provides somewhat better – but still not very accurate – results (Δt ≈ +21 h and −29 h, for the two studied events, respectively). Employing, as an input to EUHFORIA, the CME parameters obtained from the graduated cylindrical shell (GCS) fittings at consequently increasing heights, results in a strongly improved accuracy of the modelled CME and shock arrival time; Δt changes from 20 h to 10 min in the case of the first event, and from 12 h to 30 min in the case of the second one. This improvement shows that when we increased the heights of the GCS reconstruction we accounted for the change in the propagation direction of the studied CMEs, which allowed us to accurately model the CME flank encounter at Earth. Our results show the great importance of the change in the direction of propagation of the CME in the low corona when modelling CMEs and estimating the time of their arrival at Earth.

Modeling the Propagation of Slow Magnetoacoustic Waves in a Multistranded Coronal Loop

We study the propagation properties of slow magnetoacoustic waves in a multithermal coronal loop using a 3D MHD model, for the first time. A bundle of 33 vertical cylinders, each of 100 km radius, randomly distributed over a circular region of radius 1 Mm, is considered to represent the coronal loop. The slow waves are driven by perturbing the vertical velocity (v z ) at the base of the loop. We apply forward modeling to the simulation results to generate synthetic images in the coronal channels of the Solar Dynamics Observatory/Atmospheric Imaging Assembly. Furthermore, we add appropriate data noise to enable direct comparison with the real observations. It is found that the synthetic images at the instrument resolution show noncospatial features in different temperature channels in agreement with previous observations. Time–distance maps are constructed from the synthetic data to study the propagation properties. The results indicate that the oscillations are only visible in specific channels, depending on the temperature range of the plasma existing within the loop. Additionally, the propagation speed of slow waves is also found to be sensitive to the available temperature range. Overall, we propose that the cross-field thermal properties of coronal structures can be inferred using a combination of numerical simulations and observations of slow magnetoacoustic waves.

Three-dimensional GRMHD simulations of rapidly rotating stellar core collapse

ABSTRACT We present results from fully general relativistic (GR), three-dimensional (3D), neutrino-radiation magneto-hydrodynamic (MHD) simulations of stellar core collapse of a 20 M⊙ star with spectral neutrino transport. Our focus is to study the gravitational-wave (GW) signatures from the magnetorotationally (MR)-driven models. By parametrically changing the initial angular velocity and the strength of the magnetic fields in the core, we compute four models. Among our models, only those with cores having an initial magnetic field strength of 1012 G and rotation rates of 1 or 2 rad s−1 produce MHD jets. Seen from the direction perpendicular to the rotational axis, a characteristic waveform is obtained exhibiting a monotonic time increase in the wave amplitude. As previously identified, this stems from the propagating MHD outflows along the axis. We show that the GW amplitude from anisotropic neutrino emission becomes more than one order-of-magnitude bigger than that from the matter contribution, whereas seen from the rotational axis, both of the two components are in the same order-of-magnitudes. Due to the memory effect, the frequency of the neutrino GW from our full-fledged 3D-MHD models is in the range less than ∼10 Hz. Toward the future GW detection for a Galactic core-collapse supernova, if driven by the MR mechanism, the planned next-generation detector as DECIGO is urgently needed to catch the low-frequency signals.

CMEs evolve in the interplanetary medium to double their predicted geo-effectiveness

Context. We explore the impact of interactions between coronal mass ejections (CMEs) – known as CME–CME interactions – on Earth using remote-sensing and in situ observations and estimate the amplification of the geo-effectiveness of the individual CMEs by a factor of ∼2 due to CME–CME interactions. Aims. We present 3D reconstructions of interacting CMEs, which provide essential information on the orientation and interaction of the events. Additionally, we analysed coronal evolution of CMEs and their in situ characteristics at 1 AU to explore the impact of interactions between CMEs on their geo-effectiveness. Methods. We analysed CME interaction using white light data from LASCO and STEREO COR-A. The reported CMEs were reconstructed using the gradual cylindrical shell (GCS) model and simulated self-consistently with the physics-based 3D MHD model EUHFORIA (EUropean Heliosphere FORecasting Information Asset). By running different simulations, we estimated the geo-effectiveness of both individual and interacting CMEs using an empirical relationship method for the disturbance storm index. Results. The SOHO/LASCO spacecraft observed three CMEs erupting from the Sun within an interval of 10 h during a very active period in early November 2021. There were two partial halo CMEs that occurred on 1 Nov. 2021 at 19:00 UT and 22:00 UT, respectively, from the active region 12887 (S28W58), and a third halo CME occurred from AR 12891 (N17E03) on 2 Nov. 2021 at 02:48 UT. By combining remote observations close to the Sun, in situ data at 1 AU, and further numerical analyses of each individual CME, we are able to identify the initial and interplanetary evolution of the CMEs. Conclusions. (i) White light observations and a 3D reconstruction of the CMEs show cannibalism by CME-2 on CME-1 and a flank interaction of CME-3 with the merged CME-1 and CME-2 at 45–50 Rs. (ii) Interacting CMEs exhibit an increase in geo-effectiveness compared to an individual CME.

Evidence of Kelvin-Helmholtz and tearing mode instabilities at the magnetopause during space weather events

Introduction: Kelvin-Helmholtz (KH) and tearing mode (TM) instabilities are one of the most important mechanisms of solar wind energy, momentum and plasma transport within the magnetosphere.Methods: To investigate the conditions under which KHTM instabilities occur in the Earth environment it is fundamental to combine simultaneous multipoint in situ measurements and MHD simulations. We analyzed data from the THEMIS and Cluster spacecraft considering two Space Weather (SWE) events starting with an M2.0 flare event (hereafter Case-1) that occurred on 21 June 2015 and the most-intensive flare (X9.3) of solar cycle 24 that occurred on 6 September 2017 (hereafter Case-2).Results: Our analysis utilized a 2D MHD model for incompressible and viscous flow. The results from Case-1 indicate the presence of KH and TM instabilities, suggesting existence of observed low-amplitude oscillations at the nose of the magnetopause. However, the MHD simulations for Case-2 did not show any evidence of KH vortices, but did reveal the presence of “magnetic island” structures during a low-shear condition. The reconnection rate derived from the observations is compared with the computed one in the presence of developed instabilities inside the Earth’s magnetopause.

Simulating Wind-Blown Nebulae from Single and Binary Massive Stars

Winds from massive stars expand supersonically into their surroundings, creating dynamic and fascinating nebulae that can give us insight into physical processes in interstellar plasma, and into the evolutionary history of the stars. Around single stars, parsec-scale bubbles such as bow shocks and ring nebulae are formed, whereas in colliding-wind binary (CWB) systems the high wind density produces intense time- and space-dependent emission across the electromagnetic spectrum from radio to gamma-rays. This contribution summarizes some recent results from 3D MHD modelling of bow shocks around runaway stars such as ζ Oph, and of the wind-collision zone of the CWB systems WR140 and WR21a. A resolution study of 3D simulations of bow shocks shows that X-ray emission from the shocked wind is time-variable and that converged results can be obtained once the Kelvin-Helmholtz instability at the contact discontinuity is resolved. Simulations of the CWB system WR140 show that inverse-Compton cooling of the shocked plasma can trigger runaway cooling when the orbit is near periastron, producing strong compression and dynamical instabilities. This sharply reduces the hard-X-ray emission around periastron, in agreement with observations. Scaling tests of the simulation software pion are also presented for a model of the CWB system WR21a run on up to 8192 cores using the HPC system Karolina.

Non-thermal broadening of coronal lines in a 3D MHD loop model

ABSTRACT Observed spectral profiles of emission lines from the corona are found to have widths exceeding the thermal line width. To investigate the physical mechanism, we run a 3D magnetohydrodynamics model of a single, straightened loop in which we partially resolve turbulent motions that form in response to the driving by self-consistently evolving magneto-convection in the photosphere. The convective motions shear and twist the magnetic field lines, leading to heating. From the model, we synthesize spectral profiles of emission lines forming at temperatures around and above 1 MK. The coronal heating process generates a range of velocity amplitudes and directions structured on a scale much smaller than the resolving power of current instruments, leading to a broadening of the spectral lines. Our model includes the mass exchange between corona and chromosphere, thus we also capture flows parallel to the loop axis. We find that the spectral lines show a non-thermal line broadening roughly consistent with observations for a viewing angle perpendicular to the axis. The broadening through field-parallel flows is comparable, although slightly smaller. The line broadening is independent of the instrument resolution for a perpendicular line of sight (LOS). We can connect the non-thermal line broadening to heating events and flows. While small-scale velocities along the LOS are mainly responsible for the broadening observed perpendicular to the loop, chromospheric evaporation is important for the line broadening observed along the loop. The model reproduces observed values for non-thermal line widths. In the model, these result from continuous driving by magnetoconvection, without imposing driving motions or starting from an already braided field.

Global Alfvénic modes excitation in ohmic tokamak plasmas following magnetic reconnection events

A possible triggering mechanism of Alfvén waves (AWs) in tokamak plasmas, based on localized perturbations induced by magnetic reconnection events, is discussed in the framework of nonlinear viscoresistive 3D magnetohydrodynamics (MHD) modeling. Numerical simulations are performed with the SpeCyl code (Cappello and Biskamp 1996 Nucl. Fusion 36 571) that solves the equations of the viscoresistive MHD model in cylindrical geometry. We investigate a ohmic tokamak configuration where the m = 1, n = 1 internal kink mode (m is the poloidal mode number and n is the toroidal mode number) undergoes a complete reconnection process. An in-depth investigation of the process shows a spatio-temporal correlation between the velocity perturbations associated with the reconnection and the excitation of the shear AW in the core region and the global Alfvén eigenmodes, both with dominant m = 1, n = 0 periodicity. In particular they are observed to emanate from the outflow cones of the reconnection layer associated with the internal kink. The excitation mechanism described in this paper could explain the observations of Alfvénic fluctuations in the absence of energetic ions in several tokamak experiments documented in the literature and could contribute to AWs excitation in general, even in the presence of fast particles. This result shares similarities with analogous study in reversed-field pinch (RFP) configuration (Kryzhanovskyy et al 2022 Nucl. Fusion 62 086019) where AWs were found to be excited by the RFP sawtoothing.

О проявлении коротирующих областей взаимодействия солнечного ветра в вариациях интенсивности ГКЛ

The regions of interaction between solar wind streams of different speed, known as corotating interaction regions, form an almost constantly existing structure of the inner heliosphere. Using observational data on the main characteristics of the heliosphere, important for GCR modulation, and the results of 3D MHD modeling of corotating interaction regions, and Monte Carlo simulation of recurrent GCR variations, we analyze the importance of the corotating interaction regions for longitude-averaged characteristics of the heliosphere and GCR propagation, and possible ways for simulating long-term GCR intensity variations with respect to the corotating interaction regions.

О проявлении коротирующих областей взаимодействия солнечного ветра в вариациях интенсивности ГКЛ

The regions of interaction between solar wind streams of different speed, known as corotating interaction regions, form an almost constantly existing structure of the inner heliosphere. Using observational data on the main characteristics of the heliosphere, important for GCR modulation, and the results of 3D MHD modeling of corotating interaction regions, and Monte Carlo simulation of recurrent GCR variations, we analyze the importance of the corotating interaction regions for longitude-averaged characteristics of the heliosphere and GCR propagation, and possible ways for simulating long-term GCR intensity variations with respect to the corotating interaction regions.

Nonlinear Fast Magnetosonic Waves in Solar Prominence Pillars

We investigate the properties of nonlinear fast magnetosonic (NFM) waves in a solar prominence, motivated by recent high-resolution and high-cadence Hinode/Solar Optical Telescope (SOT) observations of small-scale oscillations in a prominence pillar. As an example, we analyze the details of the 2012 February 14 Hinode/SOT observations of quasi-periodic propagating features consistent with NFM waves, imaged in emission in Ca ii and in the far blue wing of Hα. We perform wavelet analysis and find oscillations in the 1–3 minutes period range. Guided by these observations, we model the NFM waves with a three-dimensional magnetohydrodynamics (3D MHD) model, extending previous 2.5D MHD studies. The new model includes the structure of the high-density, low-temperature material of the prominence pillar embedded in the hot corona, in both potential and non-force-free sheared magnetic field configurations. The nonlinear model demonstrates the effects of mode coupling and the propagating density compressions associated with linear and NFM waves. The guided fast magnetosonic waves, together with density compressions and currents, are reproduced in the 3D pillar structure. We demonstrate for the first time the dynamic effects of the Lorentz force due to the magnetic shear in the non-force-free field on the pillar structure and on the propagation of the waves. The insights gained from the 3D MHD modeling are useful for improving the coronal seismology of prominence structures that exhibit fast MHD wave activity.

Slow wind belt in the quiet solar corona

The slow solar wind belt in the quiet corona, observed with the Metis coronagraph on board Solar Orbiter on May 15, 2020, during the activity minimum of the cycle 24, in a field of view extending from 3.8 R⊙ to 7.0 R⊙, is formed by a slow and dense wind stream running along the coronal current sheet, accelerating in the radial direction and reaching at 6.8 R⊙ a speed within 150 and 190 km s−1, depending on the assumptions on the velocity distribution of the neutral hydrogen atoms in the coronal plasma. The slow stream is separated by thin regions of high velocity shear from faster streams, almost symmetric relative to the current sheet, with peak velocity within 175 and 230 km s−1 at the same coronal level. The density–velocity structure of the slow wind zone is discussed in terms of the expansion factor of the open magnetic field lines that is known to be related to the speed of the quasi-steady solar wind, and in relation to the presence of a web of quasi-separatrix layers, S-web, the potential sites of reconnection that release coronal plasma into the wind. The parameters characterizing the coronal magnetic field lines are derived from 3D MHD model calculations. The S-web is found to coincide with the latitudinal region where the slow wind is observed in the outer corona and is surrounded by thin layers of open field lines expanding in a non-monotonic way.

Large deviation principle for a class of stochastic hydrodynamical type systems driven by multiplicative Lévy noises

This article is devoted to the large deviation principle for a wide class of stochastic hydrodynamical systems driven by multiplicative Lévy noise. The model covers many equations arising form fluid dynamics such as 2D Navier-Stokes equations, 2D MHD models and the 2D magnetic Bénard problem and also shell models of turbulence. The main difficulty in proving the large deviation principle for the system is overcame by using the weak convergence method introduced by Budhiraja, Dupuis and Maroulas (Ann. Probab. 36: 1390–1420, 2008 and Annales De L Institut Henri Poincare. 47: 725–747, 2011).

Extracting the Heliographic Coordinates of Coronal Rays Using Images from WISPR/Parker Solar Probe

The Wide-field Imager for Solar Probe (WISPR) onboard Parker Solar Probe (PSP), observing in white light, has a fixed angular field of view, extending from 13.5 degree to 108 degree from the Sun and approximately 50 degree in the transverse direction. In January 2021, on its seventh orbit, PSP crossed the heliospheric current sheet (HCS) near perihelion at a distance of 20 solar radii. At this time, WISPR observed a broad band of highly variable solar wind and multiple coronal rays. For six days around perihelion, PSP was moving with an angular velocity exceeding that of the Sun. During this period, WISPR was able to image coronal rays as PSP approached and then passed under or over them. We have developed a technique for using the multiple viewpoints of the coronal rays to determine their location (longitude and latitude) in a heliocentric coordinate system and used the technique to determine the coordinates of three coronal rays. The technique was validated by comparing the results to observations of the coronal rays from Solar and Heliophysics Observatory (SOHO) / Large Angle and Spectrometric COronagraph (LASCO)/C3 and Solar Terrestrial Relations Observatory (STEREO)-A/COR2. Comparison of the rays' locations were also made with the HCS predicted by a 3D MHD model. In the future, results from this technique can be used to validate dynamic models of the corona.

JOREK3D: An extension of the JOREK nonlinear MHD code to stellarators

Although the basic concept of a stellarator was known since the early days of fusion research, advances in computational technology have enabled the modeling of increasingly complicated devices, leading up to the construction of Wendelstein 7-X, which has recently shown promising results. This recent success has revived interest in the nonlinear 3D MHD modeling of stellarators in order to better understand their performance and operational limits. This study reports on the extension of the JOREK code to 3D geometries and on the first stellarator simulations carried out with it. The first simple simulations shown here address the classic Wendelstein 7-A stellarator using a reduced MHD model previously derived by us. The results demonstrate that stable full MHD equilibria are preserved in the reduced model: the flux surfaces do not move throughout the simulation and closely match the flux surfaces of the full MHD equilibrium. Furthermore, both tearing and ballooning modes were simulated, and the linear growth rates measured in JOREK are in reasonable agreement with the growth rates from the CASTOR3D linear MHD code.

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.

Global Regularity for the 2D MHD and Tropical Climate Model with Horizontal Dissipation

Global Regularity for the 2D MHD and Tropical Climate Model with Horizontal Dissipation

Linking computational models to follow the evolution of heated coronal plasma

ABSTRACT A ‘proof of principle’ is presented, whereby the Ohmic and viscous heating determined by a three-dimensional (3D) MHD model of a coronal avalanche are used as the coronal heating input for a series of field-aligned, one-dimensional (1D) hydrodynamic models. Three-dimensional coronal MHD models require large computational resources. For current numerical parameters, it is difficult to model both the magnetic field evolution and the energy transport along field lines for coronal temperatures much hotter than $1\, \mathrm{MK}$, because of severe constraints on the time step from parallel thermal conduction. Using the 3D MHD heating derived from a simulation and evaluated on a single field line, the 1D models give coronal temperatures of $1\, \mathrm{MK}$ and densities $10^{14}\textrm {--}10^{15}\, \mathrm{m}^{-3}$ for a coronal loop length of $80\, \mathrm{Mm}$. While the temperatures and densities vary smoothly along the field lines, the heating function leads to strong asymmetries in the plasma flows. The magnitudes of the velocities in the 1D model are comparable with those seen in 3D reconnection jets in our earlier work. Advantages and drawbacks of this approach for coronal modelling are discussed.

New unexpected flow patterns in the problem of the stellar wind interaction with the interstellar medium: stationary ideal-MHD solutions

ABSTRACT The astropause (heliopause for the Sun) is the tangential discontinuity separating the stellar wind from the interstellar plasma. The global shape of the heliopause is a matter of debates. Two types of the shape are under discussion: comet-like and tube-like. In the second type, the two-jets oriented towards the stellar rotation axis are formed by the action of azimuthal component of the stellar magnetic field. We explore a simplified global astrosphere in which (1) the surrounding and moving with respect to the star circumstellar medium is fully ionized, (2) the interstellar magnetic field is neglected, (3) the radial component of the stellar magnetic field is neglected as compared with the azimuthal component, and (4) the stellar wind outflow is spherically symmetric and supersonic. We present the results of numerical 3D MHD modelling and explore how the global structure depends on the gas-dynamic Mach number of the interstellar flow, M∞, and the Alfvenic Mach number in the stellar wind. It is shown that the astropause has a tube-like shape for small values of M∞. The wings of the tube are distorted towards the tail as larger as larger the Mach number is. The new (to our knowledge) result is the reverse interstellar flow in the vicinity of the astropause in the tail. The larger the interstellar Mach number is the narrower the reverse flow is. At some values of the Mach number, the stellar wind overcomes the reverse interstellar flow and moves out in downwind. In this regime, the astropause changes its topology from tube-like to sheet-like.