Simulations Of Flux Emergence Research Articles

Convective Magnetic Flux Emergence Simulations from the Deep Solar Interior to the Photosphere: Comprehensive Study of Flux Tube Twist

The emergence of magnetic flux from the deep convection zone plays an important role in solar magnetism, such as the generation of active regions and triggering of various eruptive phenomena, including jets, flares, and coronal mass ejections. To investigate the effects of magnetic twist on flux emergence, we performed numerical simulations of flux tube emergence using the radiative magnetohydrodynamic code R2D2 and conducted a systematic survey on the initial twist. Specifically, we varied the twist of the initial tube both positively and negatively from zero to twice the critical value for kink instability. As a result, regardless of the initial twist, the flux tube was lifted by the convective upflow and reached the photosphere to create sunspots. However, when the twist was too weak, the photospheric flux was quickly diffused and not retained long as coherent sunspots. The degree of magnetic twist measured in the photosphere conserved the original twist relatively well and was comparable to actual solar observations. Even in the untwisted case, a finite amount of magnetic helicity was injected into the upper atmosphere because the background turbulence added helicity. However, when the initial twist exceeded the critical value for kink instability, the magnetic helicity normalized by the total magnetic flux was found to be unreasonably larger than the observations, indicating that the kink instability of the emerging flux tube may not be a likely scenario for the formation of flare-productive active regions.

Energy and helicity evolution in a flux emergence simulation

Aims. The main aim of this work is to study the evolution of the recently introduced relative helicity of the magnetic polarity inversion line (PIL) in a magnetohydrodynamics simulation. Methods. The simulation used is a typical flux emergence simulation in which there is additionally an oblique, pre-existing magnetic field. The interaction of the emerging and ambient fields produces intense coronal activity, with four jets standing out. The 3D magnetic field allows us to compute various energies and helicities, and to study their evolution during the simulation, especially around the identified jets. We examine the evolution of all quantities in three different regions: in the whole volume, in three separate subvolumes of the whole volume, and in a 2D region around the PIL on the photosphere. Results. We find that the helicities are in general more responsive to the jets, followed by the free energy. The eruptivity index, the ratio of the current-carrying helicity to the relative helicity, does not show the typical behaviour it has in other cases, as its variations do not follow the production of the jets. By considering the subvolumes we find that the magnetic field gets more potential and less helical with height. The PIL relative helicity confirms the recent results it showed in observed active regions, exhibiting stronger variations during the jets compared to the standard relative helicity. Moreover, the current-carrying helicity around the PIL has a similar behaviour to the PIL relative helicity, and so this quantity could be equally useful in solar eruptivity studies.

Small-scale magnetic flux emergence preceding a chain of energetic solar atmospheric events

Context.Advancements in instrumentation have revealed a multitude of small-scale extreme-ultraviolet (EUV) events in the solar atmosphere and considerable effort is currently undergoing to unravel them.Aims.Our aim is to employ high-resolution and high-sensitivity magnetograms to gain a detailed understanding of the magnetic origin of such phenomena.Methods.We used coordinated observations from the Swedish 1-m Solar Telescope (SST), the Interface Region Imaging Spectrograph (IRIS), and the Solar Dynamics Observatory (SDO) to analyze an ephemeral magnetic flux emergence episode and the following chain of small-scale energetic events. These unique observations clearly link these phenomena together.Results.The high-resolution (0.″057 pixel−1) magnetograms obtained with SST/CRISP allowed us to reliably measure the magnetic field at the photosphere and to detect the emerging bipole that caused the subsequent eruptive atmospheric events. Notably, this small-scale emergence episode remains indiscernible in the lower resolution SDO/HMI magnetograms (0.″5 pixel−1). We report the appearance of a dark bubble in Ca IIK 3933 Å related to the emerging bipole, a sign of the canonical expanding magnetic dome predicted in flux emergence simulations. Evidence of reconnection are also found, first through an Ellerman bomb and later by the launch of a surge next to a UV burst. The UV burst exhibits a weak EUV counterpart in the coronal SDO/AIA channels. By calculating the differential emission measure (DEM), its plasma is shown to reach a temperature beyond 1 MK and to have densities between the upper chromosphere and transition region.Conclusions.Our study showcases the importance of high-resolution magnetograms in revealing the mechanisms that trigger phenomena such as EBs, UV bursts, and surges. This could hold implications for small-scale events similar to those recently reported in the EUV using Solar Orbiter. The finding of temperatures beyond 1 MK in the UV burst plasma strongly suggests that we are examining analogous features. Therefore, we recommend caution when drawing conclusions from full-disk magnetograms that lack the necessary resolution to reveal their true magnetic origin.

On the ambipolar diffusion formulation for ion-neutral drifts in the non-negligible drift velocity limit.

The ambipolar diffusion approximation is used to model partially ionized plasma dynamics in a single-fluid setting. To correctly apply the commonly used version of ambipolar diffusion, a set of criteria should be satisfied including the requirement that the difference in velocity between charges and neutral species (known as drift velocity) is much smaller than the thermal velocity, otherwise the drift velocity will drive a non-negligible level of further collisions between the two species. In this paper, we explore the consequences of relaxing this assumption. We show that a new induction equation can be formulated without this assumption. This formulation reduces to the ambipolar induction equation in the case the drift velocity is small. In the large drift velocity limit, the feedback of the drift velocity on the collision frequency results in decreased diffusion of the magnetic field compared with the standard ambipolar diffusion approximation for the same parameters. This has a natural consequence of reducing the frictional heating that can occur. Applying this to results from flux emergence simulations where the expansion of the magnetic field leads to strong adiabatic cooling of the partially ionized chromosphere resulted in a noticeable reduction in the magnitude of the predicted drift velocities. This article is part of the theme issue 'Partially ionized plasma of the solar atmosphere: recent advances and future pathways'.

Solar Eruptions Triggered by Flux Emergence below or near a Coronal Flux Rope

Observations have shown a clear association of filament/prominence eruptions with the emergence of magnetic flux in or near filament channels. Magnetohydrodynamic (MHD) simulations have been employed to systematically study the conditions under which such eruptions occur. These simulations to date have modeled filament channels as 2D flux ropes or 3D uniformly sheared arcades. Here we present MHD simulations of flux emergence into a more realistic configuration consisting of a bipolar active region containing a line-tied 3D flux rope. We use the coronal flux-rope model of Titov et al. as the initial condition and drive our simulations by imposing boundary conditions extracted from a flux emergence simulation by Leake et al. We identify three mechanisms that determine the evolution of the system: (i) reconnection displacing footpoints of field lines overlying the coronal flux rope, (ii) changes of the ambient field due to the intrusion of new flux at the boundary, and (iii) interaction of the (axial) electric currents in the preexisting and newly emerging flux systems. The relative contributions and effects of these mechanisms depend on the properties of the preexisting and emerging flux systems. Here we focus on the location and orientation of the emerging flux relative to the coronal flux rope. Varying these parameters, we investigate under which conditions an eruption of the latter is triggered.

Flux emergence simulation and coronal response at ephemeral region scale

AbstractFlux emergence at different spatial scales and with different amounts of flux has been studied using radiative magnetohydrodynamics (rMHD) simulations. We use the radiative MHD code MURaM to simulate the emergence of an untwisted magnetic flux tube of ephemeral region scale with a density nonuniformity into a background atmosphere with a small unipolar open field. We find that the tube rises to the photosphere, forming complex loop structures seen in synthetic Atmospheric Imaging Assembly(AIA) 171 Å images. The atmosphere reaches 105K at 3Mm above the surface. Our simulation provides a reference example of a less twisted ephemeral region emergence and the atmospheric response.

Photospheric signatures of retraction and reconnection in realistic magnetohydrodynamic simulations

Context. Magnetic flux emergence and cancelling in the quiet Sun is a frequently observed phenomenon. The two possible physical flux-removal mechanisms involved in this cancelling process are retraction and reconnection. Aims. We seek to find distinct observational signatures characterising retraction and reconnection. Methods. We carried out three-dimensional non-grey radiative magnetohydrodynamic (MHD) simulations of convection near the solar surface and the solar photosphere using the STAGGER code, and employing different initial conditions: (1) mixed-polarity simulations with alternating horizontal stripes of opposite vertical magnetic field and separated by a zero field stripe, and (2) flux emergence simulations with continuous injection of magnetic flux from the lower boundary. These initial conditions are meant to represent two different situations in the solar photosphere, namely magnetic flux cancelling in the absence or presence of magnetic flux emergence, respectively. Results. We analyse the observational signatures of magnetic flux-removal processes for flux emergence as well as for mixed-polarity MHD simulations. In the flux emergence simulation, we are able to identify ubiquitous reconnection events anywhere from the solar surface to the upper photosphere. For a few of those reconnection events, we can identify supersonic upflow velocities in the upper photosphere as well as strong temperature enhancements. We also see strong electric currents very close to the locations where reconnection takes place, as well as supersonic horizontal velocities leading to sideways plasma compression. In the mixed-polarity simulations, we only detect observational signatures of magnetic field retraction related to large downflow velocities that appear in between regions where opposing horizontal velocities converge. These horizontal velocities are often supersonic, leading to heating due to shock dissipation. We do not see clear signatures of magnetic reconnection in these mixed-polarity simulations. Conclusions. We suggest that, in the emerging flux regions of the quiet Sun, the main flux-removal process is reconnection, while in regions without flux emergence, retraction is the dominant flux-removal process.

Flux emergence and generation of flare-productive active regions

Solar flares and coronal mass ejections are among the most prominent manifestations of the magnetic activity of the Sun. The strongest events of them tend to occur in active regions (ARs) that are large, complex, and dynamically evolving. However, it is not clear what the key observational features of such ARs are, and how these features are produced. This article answers these fundamental questions based on morphological and magnetic characteristics of flare-productive ARs and their evolutionary processes, i.e., large-scale flux emergence and subsequent AR formation, which have been revealed in observational and theoretical studies. We also present the latest modeling of flare-productive ARs achieved using the most realistic flux emergence simulations in a very deep computational domain. Finally, this review discusses the future perspective pertaining to relationships of flaring solar ARs with the global-scale dynamo and stellar superflares.

Testing a Data-driven Active Region Evolution Model with Boundary Data at Different Heights from a Solar Magnetic Flux Emergence Simulation

Abstract A data-driven active region evolution (DARE) model has been developed to study the complex structures and dynamics of solar coronal magnetic fields. The model is configured with a typical coronal environment of tenuous gas governed by strong magnetic field, and thus its lower boundary is set at the base of the corona, but driven by magnetic fields observed in the photosphere. A previous assessment of the model using data from a flux emergence simulation (FES) showed that the DARE failed to reproduce the coronal magnetic field in the FES, which is attributed to the fact that the photospheric data in the FES has a very strong Lorentz force and therefore spurious flows are generated in the DARE model. Here we further test the DARE by using three sets of data from the FES sliced at incremental heights, which correspond to the photosphere, the chromosphere, and the base of the corona. It is found that the key difference in the three sets of data is the extent of the Lorentz force, which makes the data-driven model perform very differently. At the two higher levels above the photosphere, the Lorentz force decreases substantially, and the DARE model attains results in much better agreement with the FES, confirming that the Lorentz force in the boundary data is a key issue affecting the results of the DARE model. However, unlike the FES data, the photospheric field from SDO/HMI observations has recently been found to be very close to force-free. Therefore, we suggest that it is still reasonable to use the photospheric magnetic field as an approximation of the field at the coronal base to drive the DARE model.

On the Lorentz Force and Torque of Solar Photospheric Emerging Magnetic Fields

Abstract Magnetic flux generated and intensified by the solar dynamo emerges into the solar atmosphere, forming active regions (ARs) including sunspots. Existing theories of flux emergence suggest that the magnetic flux can rise buoyantly through the convection zone but is trapped at the photosphere, while its further rising into the atmosphere resorts to the Parker buoyancy instability. To trigger such an instability, the Lorentz force in the photosphere needs to be as large as the gas pressure gradient to hold up an extra amount of mass against gravity. This naturally results in a strongly non-force-free photosphere, which is indeed shown in typical idealized numerical simulations of flux tube buoyancy from below the photosphere into the corona. Here we conduct a statistical study of the extents of normalized Lorentz forces and torques in the emerging photospheric magnetic field with a substantially large sample of Solar Dynamics Observatory/Helioseismic and Magnetic Imager vector magnetograms. We found that the photospheric field has a rather small Lorentz force and torque on average, and thus is very close to a force-free state, which is not consistent with theories as well as idealized simulations of flux emergence. Furthermore, the small extents of forces and torques seem not to be influenced by the emerging AR’s size, the emergence rate, or the nonpotentiality of the field. This result puts an important constraint on future development of theories and simulations of flux emergence.

On rising magnetic flux tube and formation of sunspots in a deep domain

ABSTRACT We investigate the rising flux tube and the formation of sunspots in an unprecedentedly deep computational domain that covers the whole convection zone with a radiative magnetohydrodynamics simulation. Previous calculations had shallow computational boxes (<30 Mm) and convection zones at a depth of 200 Mm. By using our new numerical code Radition and RSST for Deep Dynamics(r2d2), we succeed in covering the whole convection zone and reproduce the formation of the sunspot from a simple horizontal flux tube because of the turbulent thermal convection. The main findings are as follows. (1) The rising speed of the flux tube is larger than the upward convection velocity because of the low density caused by the magnetic pressure and the suppression of the mixing. (2) The rising speed of the flux tube exceeds 250 m s−1 at a depth of 18 Mm, while we do not see any clear evidence of the divergent flow 3 h before the emergence at the solar surface. (3) Initially, the root of the flux tube is filled with the downflows, and then the upflow fills the centre of the flux tube during the formation of the sunspot. (4) The essential mechanisms for the formation of the sunspot are the coherent inflow and the turbulent transport. (5) The low-temperature region is extended to a depth of at least 40 Mm in the matured sunspot, with the high-temperature region in the centre of the flux tube. Some of the findings indicate the importance of the deep computational domain for the flux emergence simulations.

Comparative Study of Data-driven Solar Coronal Field Models Using a Flux Emergence Simulation as a Ground-truth Data Set

Abstract For a better understanding of the magnetic field in the solar corona and dynamic activities such as flares and coronal mass ejections, it is crucial to measure the time-evolving coronal field and accurately estimate the magnetic energy. Recently, a new modeling technique called the data-driven coronal field model, in which the time evolution of magnetic field is driven by a sequence of photospheric magnetic and velocity field maps, has been developed and revealed the dynamics of flare-productive active regions. Here we report on the first qualitative and quantitative assessment of different data-driven models using a magnetic flux emergence simulation as a ground-truth (GT) data set. We compare the GT field with those reconstructed from the GT photospheric field by four data-driven algorithms. It is found that, at minimum, the flux rope structure is reproduced in all coronal field models. Quantitatively, however, the results show a certain degree of model dependence. In most cases, the magnetic energies and relative magnetic helicity are comparable to or at most twice of the GT values. The reproduced flux ropes have a sigmoidal shape (consistent with GT) of various sizes, a vertically standing magnetic torus, or a packed structure. The observed discrepancies can be attributed to the highly non-force-free input photospheric field, from which the coronal field is reconstructed, and to the modeling constraints such as the treatment of background atmosphere, the bottom boundary setting, and the spatial resolution.

Numerical Simulations of Flare-productive Active Regions: δ-sunspots, Sheared Polarity Inversion Lines, Energy Storage, and Predictions

Abstract Solar active regions (ARs) that produce strong flares and coronal mass ejections (CMEs) are known to have a relatively high non-potentiality and are characterized by δ-sunspots and sheared magnetic structures. In this study, we conduct a series of flux emergence simulations from the convection zone to the corona and model four types of active regions that have been observationally suggested to cause strong flares, namely the spot–spot, spot–satellite, quadrupole, and inter-AR cases. As a result, we confirm that δ-spot formation is due to the complex geometry and interaction of emerging magnetic fields, and we find that the strong-field, high-gradient, highly sheared polarity inversion line (PIL) is created by the combined effect of the advection, stretching, and compression of magnetic fields. We show that free magnetic energy builds up in the form of a current sheet above the PIL. It is also revealed that photospheric magnetic parameters that predict flare eruptions reflect the stored free energy with high accuracy, while CME-predicting parameters indicate the magnetic relationship between flaring zones and entire ARs.

THE CONTRIBUTION OF CORONAL JETS TO THE SOLAR WIND

ABSTRACT Transient collimated plasma eruptions in the solar corona, commonly known as coronal (or X-ray) jets, are among the most interesting manifestations of solar activity. It has been suggested that these events contribute to the mass and energy content of the corona and solar wind, but the extent of these contributions remains uncertain. We have recently modeled the formation and evolution of coronal jets using a three-dimensional (3D) magnetohydrodynamic (MHD) code with thermodynamics in a large spherical domain that includes the solar wind. Our model is coupled to 3D MHD flux-emergence simulations, i.e., we use boundary conditions provided by such simulations to drive a time-dependent coronal evolution. The model includes parametric coronal heating, radiative losses, and thermal conduction, which enables us to simulate the dynamics and plasma properties of coronal jets in a more realistic manner than done so far. Here, we employ these simulations to calculate the amount of mass and energy transported by coronal jets into the outer corona and inner heliosphere. Based on observed jet-occurrence rates, we then estimate the total contribution of coronal jets to the mass and energy content of the solar wind to (0.4–3.0)% and (0.3–1.0)%, respectively. Our results are largely consistent with the few previous rough estimates obtained from observations, supporting the conjecture that coronal jets provide only a small amount of mass and energy to the solar wind. We emphasize, however, that more advanced observations and simulations (including parametric studies) are needed to substantiate this conjecture.

STATISTICAL ANALYSIS OF THE HORIZONTAL DIVERGENT FLOW IN EMERGING SOLAR ACTIVE REGIONS

Solar active regions (ARs) are thought to be formed by magnetic fields from the convection zone. Our flux emergence simulations revealed that a strong horizontal divergent flow (HDF) of unmagnetized plasma appears at the photosphere before the flux begins to emerge. In our earlier study, we analyzed HMI data for a single AR and confirmed presence of this precursor plasma flow in the actual Sun. In this paper, as an extension of our earlier study, we conducted a statistical analysis of the HDFs to further investigate their characteristics and better determine the properties. From SDO/HMI data, we picked up 23 flux emergence events over a period of 14 months, the total flux of which ranges from 10^{20} to 10^{22} Mx. Out of 23 selected events, 6 clear HDFs were detected by the method we developed in our earlier study, and 7 HDFs detected by visual inspection were added to this statistic analysis. We found that the duration of the HDF is on average 61 minutes and the maximum HDF speed is on average 3.1 km s^{-1}. We also estimated the rising speed of the subsurface magnetic flux to be 0.6-1.4 km s^{-1}. These values are highly consistent with our previous one-event analysis as well as our simulation results. The observation results lead us to the conclusion that the HDF is rather a common feature in the earliest phase of AR emergence. Moreover, our HDF analysis has capability of determining the subsurface properties of emerging fields that cannot be directly measured.

Formation of a Flare-Productive Active Region: Observation and Numerical Simulation of NOAA AR 11158

We present a comparison of the Solar Dynamics Observatory (SDO) analysis of NOAA Active Region (AR) 11158 and numerical simulations of flux-tube emergence, aiming to investigate the formation process of this flare-productive AR. First, we use SDO/Helioseismic and Magnetic Imager (HMI) magnetograms to investigate the photospheric evolution and Atmospheric Imaging Assembly (AIA) data to analyze the relevant coronal structures. Key features of this quadrupolar region are a long sheared polarity inversion line (PIL) in the central δ-sunspots and a coronal arcade above the PIL. We find that these features are responsible for the production of intense flares, including an X2.2-class event. Based on the observations, we then propose two possible models for the creation of AR 11158 and conduct flux-emergence simulations of the two cases to reproduce this AR. Case 1 is the emergence of a single flux tube, which is split into two in the convection zone and emerges at two locations, while Case 2 is the emergence of two isolated but neighboring tubes. We find that, in Case 1, a sheared PIL and a coronal arcade are created in the middle of the region, which agrees with the AR 11158 observation. However, Case 2 never builds a clear PIL, which deviates from the observation. Therefore, we conclude that the flare-productive AR 11158 is, between the two cases, more likely to be created from a single split emerging flux than from two independent flux bundles.

On magnetic reconnection and flux rope topology in solar flux emergence

We present an analysis of the formation of atmospheric flux ropes in a magnetohydrodynamic (MHD) solar flux emergence simulation. The simulation domain ranges from the top of the solar interior to the low corona. A twisted magnetic flux tube emerges from the solar interior and into the atmosphere where it interacts with the ambient magnetic field. By studying the connectivity of the evolving magnetic field, we are able to better understand the process of flux rope formation in the solar atmosphere. In the simulation, two flux ropes are produced as a result of flux emergence. Each has a different evolution resulting in different topological structures. These are determined by plasma flows and magnetic reconnection. As the flux rope is the basic structure of the coronal mass ejection (CME), we discuss the implications of our findings for solar eruptions.

NONLINEAR FORCE-FREE EXTRAPOLATION OF THE CORONAL MAGNETIC FIELD BASED ON THE MAGNETOHYDRODYNAMIC RELAXATION METHOD

We develop a nonlinear force-free field (NLFFF) extrapolation code based on the magnetohydrodynamic (MHD) relaxation method. We extend the classical MHD relaxation method in two important ways. First, we introduce an algorithm initially proposed by cite{2002JCoPh.175..645D} to effectively clean the numerical errors associated with $nabla cdot vec{B}$. Second, the multi-grid type method is implemented in our NLFFF to perform direct analysis of the high-resolution magnetogram data. As a result of these two implementations, we successfully extrapolated the high resolution force-free field introduced by cite{1990ApJ...352..343L} with better accuracy in a drastically shorter time. We also applied our extrapolation method to the MHD solution obtained from the flux-emergence simulation by cite{2012ApJ...748...53M}. We found that NLFFF extrapolation may be less effective for reproducing areas higher than a half-domain, where some magnetic loops are found in a state of continuous upward expansion. However, an inverse S shaped structure consisting of the sheared and twisted loops formed in the lower region can be captured well through our NLFFF extrapolation method. We further discuss how well these sheared and twisted fields are reconstructed by estimating the magnetic topology and twist quantitatively.

When the Sun Erupts

Solar Physics Coronal mass ejections (CMEs) are large-scale clouds of plasma that erupt from the solar atmosphere and travel into interplanetary space. They represent the most energetic events in the solar system and can be harmful to satellites in space, Earth-based power grids, and even to humans if they are in space or on airplanes, particularly on polar routes. CMEs are common, occurring four to five times a day during periods of maximum solar activity, but they weren't detected until the early 1970s when satellites were launched to study the Sun. After four decades of research, however, there is still no complete understanding of the physical mechanisms behind CMEs. Roussev et al. describe state-of-the art computer simulations that couple a detailed magnetic flux emergence simulation extending from the interior of the Sun to its atmosphere with a global model of the solar atmosphere and the solar wind. The results reproduce x-ray observations of CMEs and show how the injection of magnetic flux leads to a catastrophic evolution of the solar atmosphere. To better understand collisions of CMEs as they travel in interplanetary space, Shen et al. analyzed observations of two CMEs that erupted from the Sun on 2 November 2008. The two structures collided as though they were solidlike objects and likely experienced a superelastic collision (i.e., a collision in which the linear kinetic energy of the colliding system increases). Nat. Phys. 10.1038/nphys2427; 10.1038/nphys2440 (2012).

BUILDUP OF MAGNETIC SHEAR AND FREE ENERGY DURING FLUX EMERGENCE AND CANCELLATION

We examine a simulation of flux emergence and cancellation, which shows a complex sequence of processes that accumulate free magnetic energy in the solar corona essential for the eruptive events such as coronal mass ejections (CMEs), filament eruptions and flares. The flow velocity at the surface and in the corona shows a consistent shearing pattern along the polarity inversion line (PIL), which together with the rotation of the magnetic polarities, builds up the magnetic shear. Tether-cutting reconnection above the PIL then produces longer sheared magnetic field lines that extend higher into the corona, where a sigmoidal structure forms. Most significantly, reconnection and upward energy-flux transfer are found to occur even as magnetic flux is submerging and appears to cancel at the photosphere. A comparison of the simulated coronal field with the corresponding coronal potential field graphically shows the development of nonpotential fields during the emergence of the magnetic flux and formation of sunspots.