Time-dependent MHD Simulations Research Articles

Three-dimensional, Time-dependent MHD Simulation of Disk–Magnetosphere–Stellar Wind Interaction in a T Tauri, Protoplanetary System

We present a three-dimensional, time-dependent MHD simulation of the short-term interaction between a protoplanetary disk and the stellar corona in a T Tauri system. The simulation includes the stellar magnetic field, self-consistent coronal heating and stellar wind acceleration, and a disk rotating at sub-Keplerian velocity to induce accretion. We find that, initially, as the system relaxes from the assumed initial conditions, the inner part of the disk winds around and moves inward and close to the star as expected. However, the self-consistent coronal heating and stellar wind acceleration build up the original state after some time, significantly pushing the disk out beyond 10R ⋆. After this initial relaxation period, we do not find clear evidence of a strong, steady accretion flow funneled along coronal field lines, but only weak, sporadic accretion. We produce synthetic coronal X-ray line emission light curves, which show flare-like increases that are not correlated with accretion events nor with heating events. These variations in the line emission flux are the result of compression and expansion due to disk–corona pressure variations. Vertical disk evaporation evolves above and below the disk. However, the disk–stellar wind boundary stays quite stable, and any disk material that reaches the stellar wind region is advected out by the stellar wind.

Exoplanet Radio Transits as a Probe for Exoplanetary Magnetic Fields—Time-dependent MHD Simulations

We perform a series of time-dependent magnetohydrodynamic simulations of the HD 189733 star–planet system in order to predict radio transit modulations due to the interaction between the stellar wind and planetary magnetic field. The simulation combines a model for the stellar corona and wind with an exoplanet that is orbiting the star in a fully dynamic, time-dependent manner. Our simulations generate synthetic radio images that enable us to obtain synthetic radio light curves in different frequencies. We find a clear evidence for the planetary motion in the radio light curves. Moreover, we find specific repeated features in the light curves that are attributed to the passage of the planetary magnetosphere in front of the star during transit. More importantly, we find a clear dependence in magnitude and phase of these light-curve features on the strength of the planetary magnetic field. Our work demonstrates that if radio transits could be observed, they could indeed provide information about the magnetic field strength of the transiting exoplanet. Future work to parameterize these light-curve features and their dependence on the planetary field strength would provide tools to search for these features in radio observation data sets. As we only consider the thermal radio emission from the host star for our study, very sensitive radio interferometers are necessary to detect these kinds of planetary transits in radio.

Dynamical Coupling between Anomalous Cosmic Rays and Solar Wind in Outer Heliosphere

Voyager 2 (V2) observed that pickup ions (PUIs) and anomalous cosmic rays (ACRs) have a significant influence on the solar wind structures in the outer heliosphere. In particular, the maxima in energetic particle intensities often lagged behind the shock front, while the flow velocity in some cases featured a precursor in front of the shock. These two effects are believed to be caused by the cease of ACR injection from PUIs at large heliocentric distances, and the backward diffusion of ACRs, respectively. This paper investigates the dynamical coupling between the ACRs and the solar wind in the outer heliosphere by means of a time-dependent numerical MHD simulation, in which the ACRs are treated as a massless fluid that only contributes its pressure to the system. Two types of inner boundary conditions were used, namely a synthetic short-term shock event and an extended period of data-driven solar wind variability based on the OMNI database. The lag of the ACR pressure maximum relative to the shock front, and the extended shock precursor were reproduced by the numerical results. The increase rate of the lag is related to the corresponding diffusion coefficient and the injection efficiency from PUIs to ACRs. The model was also applied to the termination shock, where simulations likewise showed that the peak in the ACR distribution can be located a short distance downstream of the shock front, indicating that the time-dependent diffusive shock acceleration mechanism is a candidate to interpret the lag between the ACR pressure peak and the shock front observed by V2.

Stable compression of a spherical tokamak plasma

An analysis of toroidal plasma compression by a collapsing flux conserver reveals linearly stable scenarios of operation to high compression ratios. The resistive and ideal MHD stability is calculated in full toroidal geometry using the asymptotic matching method in realistic conditions. A time dependent MHD simulation of the compression is conducted to confirm the conservation principles used to calculate the equilibrium states for the analysis. The near edge current profile, controlled by toroidal field ramping during compression, is shown to be critical to stability due to coupling between poloidal components of the least stable mode. Two cases with slight differences in edge current are examined, one with a stable corridor to high compression and one without.

A new technique for observationally derived boundary conditions for space weather

Context. In recent years, space weather research has focused on developing modelling techniques to predict the arrival time and properties of coronal mass ejections (CMEs) at the Earth. The aim of this paper is to propose a new modelling technique suitable for the next generation of Space Weather predictive tools that is both efficient and accurate. The aim of the new approach is to provide interplanetary space weather forecasting models with accurate time dependent boundary conditions of erupting magnetic flux ropes in the upper solar corona. Methods. To produce boundary conditions, we couple two different modelling techniques, MHD simulations and a quasi-static non-potential evolution model. Both are applied on a spatial domain that covers the entire solar surface, although they extend over a different radial distance. The non-potential model uses a time series of observed synoptic magnetograms to drive the non-potential quasi-static evolution of the coronal magnetic field. This allows us to follow the formation and loss of equilibrium of magnetic flux ropes. Following this a MHD simulation captures the dynamic evolution of the erupting flux rope, when it is ejected into interplanetary space. Results.The present paper focuses on the MHD simulations that follow the ejection of magnetic flux ropes to 4 R⊙. We first propose a technique for specifying the pre-eruptive plasma properties in the corona. Next, time dependent MHD simulations describe the ejection of two magnetic flux ropes, that produce time dependent boundary conditions for the magnetic field and plasma at 4 R⊙ that in future may be applied to interplanetary space weather prediction models. Conclusions. In the present paper, we show that the dual use of quasi-static non-potential magnetic field simulations and full time dependent MHD simulations can produce realistic inhomogeneous boundary conditions for space weather forecasting tools. Before a fully operational model can be produced there are a number of technical and scientific challenges that still need to be addressed. Nevertheless, we illustrate that coupling quasi-static and MHD simulations in this way can significantly reduce the computational time required to produce realistic space weather boundary conditions.

An Empirically Driven Time-Dependent Model of the Solar Wind

We describe the development and application of a time-dependent model of the solar wind. The model is empirically driven, starting from magnetic maps created with the Air Force Data Assimilative Photospheric flux Transport (ADAPT) model at a daily cadence. Potential field solutions are used to model the coronal magnetic field, and an empirical specification is used to develop boundary conditions for an MHD model of the solar wind. The time-dependent MHD simulation shows classic features of stream structure in the interplanetary medium that are seen in steady-state models; it also shows time evolutionary features that do not appear in a steady-state approach. The model results compare reasonably well with 1 AU OMNI observations. Data gaps when SOLIS magnetograms were unavailable hinder the model performance. The reasonable comparisons with observations suggest that this modeling approach is suitable for driving long term models of the outer heliosphere. Improvements to the ingestion of magnetograms in flux transport models will be necessary to apply this approach in a time-dependent space weather model.

Numerical magnetohydrodynamic simulations of expanding flux ropes: Influence of boundary driving

The expansion dynamics of a magnetized, current-carrying plasma arch is studied by means of time-dependent ideal MHD simulations. Initial conditions model the setup used in recent laboratory experiments that in turn simulate coronal loops [J. Tenfelde et al., Phys. Plasmas 19, 072513 (2012); E. V. Stenson and P. M. Bellan, Plasma Phys. Controlled Fusion 54, 124017 (2012)]. Boundary conditions of the electric field at the “lower” boundary, intersected by the arch, are chosen such that poloidal magnetic flux is injected into the domain, either localized at the arch footpoints themselves or halfway between them. These conditions are motivated by the tangential electric field expected to exist in the laboratory experiments due to the external circuit that drives the plasma current. The boundary driving is found to systematically enhance the expansion velocity of the plasma arch. While perturbations at the arch footpoints also deform its legs and create characteristic elongated segments, a perturbation between the footpoints tends to push the entire structure upwards, retaining an ellipsoidal shape.

UNDERSTANDINGSDO/AIA OBSERVATIONS OF THE 2010 JUNE 13 EUV WAVE EVENT: DIRECT INSIGHT FROM A GLOBAL THERMODYNAMIC MHD SIMULATION

In this work, we present a comprehensive observation and modeling analysis of the 2010 June 13 extreme-ultraviolet (EUV) wave observed by the Atmospheric Imaging Assembly (AIA) aboard the Solar Dynamics Observatory (SDO). Due to extreme advances in cadence, resolution, and bandpass coverage in the EUV regime, the AIA instrument offers an unprecedented ability to observe the dynamics of large-scale coronal wave-like transients known as EUV waves. To provide a physical analysis and further complement observational insight, we conduct a three-dimensional, time-dependent thermodynamic MHD simulation of the eruption and associated EUV wave, and employ forward modeling of EUV observables to compare the results directly observations. We focus on two main aspects: (1) the interpretation of the stark thermodynamic signatures in the multi-filter AIA data within the propagating EUV wave front, and (2) an in-depth analysis of the simulation results and their implication with respect to EUV wave theories. Multiple aspects, including the relative phases of perturbed variables, suggest that the outer, propagating component of the EUV transient exhibits the behavior of a fast-mode wave. We also find that this component becomes decoupled from the evolving structures associated with the coronal mass ejection that are also visible, providing a clear distinction between wave and non-wave mechanisms at play.

Approximations for radiative cooling and heating in the solar chromosphere

Context. The radiative energy balance in the solar chromosphere is dominated by strong spectral lines that are formed out of LTE. It is computationally prohibitive to solve the full equations of radiative transfer and statistical equilibrium in 3D time dependent MHD simulations. Aims. To find simple recipes to compute the radiative energy balance in the dominant lines under solar chromospheric conditions. Methods. We use detailed calculations in time-dependent and 2D MHD snapshots to derive empirical formulae for the radiative cooling and heating. Results. The radiative cooling in neutral hydrogen lines and the Lyman continuum, the H and K and intrared triplet lines of singly ionized calcium and the h and k lines of singly ionized magnesium can be written as a product of an optically thin emission (dependent on temperature), an escape probability (dependent on column mass) and an ionization fraction (dependent on temperature). In the cool pockets of the chromosphere the same transitions contribute to the heating of the gas and similar formulae can be derived for these processes. We finally derive a simple recipe for the radiative heating of the chromosphere from incoming coronal radiation. We compare our recipes with the detailed results and comment on the accuracy and applicability of the recipes.

STUDY OF THE POYNTING FLUX IN ACTIVE REGION 10930 USING DATA-DRIVEN MAGNETOHYDRODYNAMIC SIMULATION

Powerful solar flares are closely related to the evolution of magnetic field configuration on the photosphere. We choose the Poynting flux as a parameter in the study of magnetic field changes. We use time-dependent multidimensional MHD simulations around a flare occurrence to generate the results, with the temporal variation of the bottom boundary conditions being deduced from the projected normal characteristic method. By this method, the photospheric magnetogram could be incorporated self-consistently as the bottom condition of data-driven simulations. The model is first applied to a simulation datum produced by an emerging magnetic flux rope as a test case. Then, the model is used to study NOAA AR 10930, which has an X3.4 flare, the data of which has been obtained by the Hinode/Solar Optical Telescope on 2006 December 13. We compute the magnitude of Poynting flux (S total), radial Poynting flux (Sz ), a proxy for ideal radial Poynting flux (S proxy), Poynting flux due to plasma surface motion (S sur), and Poynting flux due to plasma emergence (S emg) and analyze their extensive properties in four selected areas: the whole sunspot, the positive sunspot, the negative sunspot, and the strong-field polarity inversion line (SPIL) area. It is found that (1) the S total, Sz , and S proxy parameters show similar behaviors in the whole sunspot area and in the negative sunspot area. The evolutions of these three parameters in the positive area and the SPIL area are more volatile because of the effect of sunspot rotation and flux emergence. (2) The evolution of S sur is largely influenced by the process of sunspot rotation, especially in the positive sunspot. The evolution of S emg is greatly affected by flux emergence, especially in the SPIL area.

EFFECTS OF PHYSICAL FEATURES IN THE SOLAR ATMOSPHERE ON THE CORONAL MASS EJECTION EVOLUTION

Based on time-dependent MHD simulation, we investigate how physical features in the solar atmosphere affect the evolution of coronal mass ejections (CMEs). It is found that temperature and density play a crucial role in CME initiation. We argue that lower temperature facilitates the catastrophe's occurrence, and that the CMEs which initiate in low density could gain lower velocity. In our numerical experiment, by employing different values of beta, the resulting eruptions of either slow or fast events may be obtained.

Interaction between Adjacent Sheared Magnetic Arcades in the Solar Corona

Using an axisymmetric ideal-MHD model in spherical coordinates, we investigate the energy buildup of a multipole magnetic field due to photospheric shearing motions, with an emphasis on the interaction between adjacent sheared magnetic arcades. The coronal magnetic field to be sheared is a potential field that is symmetric with respect to the equator, consisting of four topologically disconnected magnetic arcades—a central arcade astride the equator, one arcade to either side of the central one, and an overlying arcade above them. Photospheric shearing is then introduced at the base of the central arcade, the flanking arcades, or both, and the associated force-free field solutions are obtained with time-dependent MHD simulations. It is found that if only one arcade is sheared, the magnetic energy of the sheared field is lower than that of the corresponding partly open field, in which the sheared arcade is fully open while the others remain closed and unsheared. This confirms a previous extension of the Aly conjecture from fully open force-free fields to partly open ones. When both the central and flanking arcades are sheared, they interact with each other: the critical azimuthal shear displacement for one arcade, at which it becomes open, depends on the shear state of the others. As a result, an arcade may become open either by virtue of an increase in its own shear or by changing the shear state of its adjacent arcades. Such an interaction may have implications for the triggering of large-scale active phenomena such as CMEs or sympathetic events that occur successively in different active regions of the Sun.

A Catastrophic Flux Rope in a Quadrupole Magnetic Field for Coronal Mass Ejections

We propose a flux-rope model for the initiation of flare-associated CMEs. The model triggers the eruption with a catastrophic loss of MHD equilibrium and then requires magnetic reconnection to sustain the eruption's acceleration. We carry out 2.5-dimensional time-dependent resistive MHD simulations, choosing the initial state such that a flux rope embedded in a quadrupole field is attached to the solar surface; we then increase the magnetic flux of the rope by two different amounts, thus obtaining two cases. One exhibits a gradual acceleration of the flux rope, whereas the other produces an immediate acceleration. In both cases, the maximum speed of the flux rope is representative of a fast CME. Thus, we conclude that the flux-rope dynamics depends on the intensity of the emergent magnetic flux. Our model does reproduce the three-component structure of CMEs.

Three-dimensional global simulation of multiple ICMEs’ interaction and propagation from the Sun to the heliosphere following the 25–28 October 2003 solar events

This study performs simulations of interplanetary coronal mass ejection (ICME) propagation in a realistic three-dimensional (3D) solar wind structure from the Sun to the Earth by using the newly developed hybrid code, HAFv.2+3DMHD. This model combines two simulation codes, Hakamada–Akasofu–Fry code version 2 (HAFv.2) and a fully 3D, time-dependent MHD simulation code. The solar wind structure is simulated out to 0.08 AU (18 Rs) from source surface maps using the HAFv.2 code. The outputs at 0.08 AU are then used to provide inputs for the lower boundary, at that location, of the 3D MHD code to calculate solar wind and its evolution to 1 AU and beyond. A dynamic disturbance, mimicking a particular flare’s energy output, is delivered to this non-uniform structure to model the evolution and interplanetary propagation of ICMEs (including their shocks). We then show the interaction between two ICMEs and the dynamic process during the overtaking of one shock by the other. The results show that both CMEs and heliosphere current sheet/plasma sheet were deformed by interacting with each other.

Slip-Running Reconnection in Quasi-Separatrix Layers

Using time dependent MHD simulations, we study the nature of three-dimensional magnetic reconnection in thin quasi-separatrix layers (QSLs), in the absence of null points. This process is believed to take place in the solar atmosphere, in many solar flares and possibly in coronal heating. We consider magnetic field configurations which have previously been weakly stressed by asymmetric line-tied twisting motions and whose potential fields already possessed thin QSLs. When the line-tied driving is suppressed, magnetic reconnection is solely due to the self-pinching and dissipation of narrow current layers previously formed along the QSLs. A generic property of this reconnection process is the continuous slippage of magnetic field lines along each other, while they pass through the current layers. This is contrary to standard null point reconnection, in which field lines clearly reconnect by pair and abruptly exchange their connectivities. For sufficiently thin QSLs and high resistivities, the field line footpoints slip-run at super-Alfvenic speeds along the intersection of the QSLs with the line-tied boundary, even though the plasma velocity and resistivity are there fixed to zero. The slip-running velocities of a given footpoint have a well-defined maximum when the field line crosses the thinnest regions of the QSLs. QSLs can then physically behave as true separatrices on MHD time scales, since magnetic field lines can change their connections on time scales far shorter than the travel-time of Alfven waves along them. Since particles accelerated in the diffusive regions travel along the field much faster than the Alfven speed, slip-running reconnection may also naturally account for the fast motion of hard X-ray sources along chromospheric ribbons, as observed during solar flares.

A New and Fast Way to Reconstruct a Nonlinear Force‐free Field in the Solar Corona

We reexamine the method of upward integration of a nonlinear force-free field (NFFF), which is, as is well known, an ill-posed problem. It can be modified to a well-posed one by the following means: instead of using finite difference to express partial derivatives, we use smooth continuous functions to approach magnetic field values, write down three field components consisting of amplitude functions multiplying morphology functions, and reduce four basic NFFF equations to ordinary differential ones. They are then solved in an asymptotic manner (zeroth-order, first-order, etc.). Considering the physical meaning of alpha, we found a self-consistent compatibility condition for the boundary values. Furthermore, a computation algorithm is proposed, similar to the usual time-dependent two-dimensional MHD simulation scheme. This algorithm is steady and robust against the noise in the magnetic field ( in particular, the transverse field) measurement and is able to deal with concentrated photospheric currents. The algorithm runs very fast on an ordinary PC and lasts only 6 minutes for the 80 x 60 (x x y) mesh up to a height of 80 (=216,000 km similar to 0.3 R-circle dot). So it provides a powerful tool for solar scientists to analyze the magnetic field properties of solar active regions and to make predictions of solar activity.

Three‐dimensional Simulations of Spherical Accretion Flows with Small‐Scale Magnetic Fields

Spherical (nonrotating) accretion flows with small-scale magnetic fields have been investigated using three-dimensional, time-dependent MHD simulations. These simulations have been designed to model high-resolution (quasi-) steady accretion flows in a wedge computational domain that represents a small fraction of the full spherical domain. Subsonic and supersonic (superfast-magnetosonic) accretion flows have been considered. Two accretion regimes have been studied: conservative, or radiatively inefficient; and nonconservative, in which the heat released in magnetic reconnections is completely lost. The flows in both regimes are turbulent. They show flattened radial density profiles and reduction of the accretion velocities and mass accretion rates in comparison with hydrodynamic Bondi flows. In the conservative regime, the turbulence is more intensive and supported mostly by thermal convection. In the nonconservative regime, the turbulence is less intensive and supported by magnetic buoyancy and various magnetic interactions. We have concluded that steady, supersonic spherical accretion cannot develop in the presence of small-scale magnetic fields.

Magnetohydrodynamic Simulations of the Solar Corona and Solar Wind Using a Boundary Treatment to Limit Solar Wind Mass Flux

Magnetohydrodynamic simulations of the solar corona and solar wind are sensitive to conditions in the sub-Alfv?nic plasma at the base of the solar corona because the structure of the simulated solar corona is determined by the pressure balance of the plasma and the magnetic field. Therefore, it is important to construct an adequate boundary treatment for the sub-Alfv?nic surface, and it is highly preferable to build the model from observation-based constraints and basic mathematical theories. We examine new boundary treatments based on the projected normal characteristic method for the MHD simulation of the trans-Alfv?nic solar wind and solar corona. Our new boundary treatment limits the mass flux escaping through the solar surface. This limit is set to match the solar wind mass flux Ulysses measured during its first fast-latitude scan of the heliosphere. In addition, combining the projected normal characteristic method and the mass flux limit, the model produces reasonable contrasts of the plasma temperature and density between the coronal hole and streamer. A two-dimensional version of the time-dependent MHD simulation with the new boundary treatment is tested using the axisymmetric dipole and quadrupole components of the solar magnetic field observed at solar minimum. The new boundary treatment can be characterized by the specific heat ratio on the surface, and we examined several cases. The solar wind computed with the new boundary treatment matches the Ulysses measurement at r > 1 AU quite well and simultaneously has good contrasts with coronal plasma parameters near the Sun.

Formation and Fragmentation of Gaseous Spurs in Spiral Galaxies

Intermediate-scale spurs are common in spiral galaxies, but perhaps most distinctively evident in a recent HST image of M51 (Scoville & Rector 2001). We investigate, using time-dependent numerical MHD simulations, how such spurs could form (and subsequently fragment) from the interaction of a gaseous ISM with a stellar spiral arm. We model the gaseous medium as a self-gravitating, magnetized, differentially-rotating, razor-thin disk. The basic flow shocks and compresses as it passes through a local segment of a tightly-wound, trailing stellar spiral arm, modeled as a rigidly-rotating gravitational potential. We first construct 1D profiles for flows with spiral shocks. When the post-shock Toomre parameter Q_sp is sufficiently small, self-gravity is too large for one-dimensional steady solutions to exist. The critical values of Q_sp are 0.8, 0.5, and 0.4 for our models with zero, sub-equipartition, and equipartition magnetic fields, respectively. We then study the growth of self-gravitating perturbations in fully 2D flows, and find that spur-like structures rapidly emerge in our magnetized models. We associate this gravitational instability with the magneto-Jeans mechanism, in which magnetic tension forces oppose the Coriolis forces. The shearing and expanding velocity field shapes the condensed material into spurs as it flows downstream from the arms. Although we find swing amplification can help form spurs when the arm-interarm contrast is moderate, unmagnetized systems that are quasi-axisymmetrically stable are generally also stable to nonaxisymmetric perturbations, suggesting that magnetic effects are essential. In nonlinear stages, the spurs in our models undergo fragmentation to form 4\times 10^6 solar mass clumps, which we suggest could evolve into bright arm/interarm HII regions as seen in spiral galaxies.

Prominence Magnetic Dips in Three-dimensional Sheared Arcades

We calculate the distribution of field-line dips in the three-dimensional sheared arcade model for prominence/filament magnetic fields. We consider both moderately and highly sheared configurations computed by fully time-dependent three-dimensional MHD simulations in which the field was relaxed to a static equilibrium end state. In agreement with previous low spatial resolution measurements of the magnetic field inside prominences, we find that for all configurations, the field in the great majority of the calculated dips exhibits inverse polarity. But for each configuration we also find well-defined narrow regions with stable dips of normal polarity. These tend to be located on the edges of the filament ends and at the top of the central part of the prominence. This distinctive mixture of normal/inverse polarity dips that we find in sheared arcades is not likely to be present in twisted flux rope prominence models. Therefore, our results provide a rigorous and unique observational test that can distinguish between the two classes of models, as well as new predictions for future high spatial resolution spectropolarimetric observations of filaments and prominences.