We present results of 3D magnetohydrodynamic simulations of the magnetic tearing instability of a coronal current sheet in both line-tied and periodic systems. We perform a parameter study of the current-sheet height in the line-tied guide-field direction, to mimic the effects of photospheric boundary driving on coronal reconnection. For short sheets (in the guide-field direction), magnetic tension resulting from the line-tied boundaries provides a restoring force on the magnetic field that resists the movement created by reconnection outflows to the point of shutting down significant energy conversion. For taller sheets, this effect is minimized. Thus, the current-sheet height, and the manner in which the sheet is tethered to the photosphere, affect the onset of magnetic reconnection in the solar corona. We also briefly address the effects of line tying in the direction of the reconnecting field component.

Solar eruptions arise from instabilities or loss of equilibria in the solar atmosphere, but routinely inferring the precise magnetic and plasma properties that lead to eruptions is not currently practical using synoptic solar observations. Data-driven simulations offer an appealing alternative. We test our boundary data-driven magnetohydrodynamic (MHD) approach, based on the method of characteristics, on a simulation that includes full MHD, a stratified atmosphere, and the emergence of a model solar magnetic active region, from the photosphere upward. The data-driven simulation is tested against a larger, ab initio "Ground Truth" simulation that extends downward into the convection zone. Our data-driven simulation accurately reproduces the dynamic emergence of the active region above the photosphere, the formation of key topological features throughout the corona, and the subsequent eruption of mass and magnetic field. The total emerged energy matches to better than one percent, the ratio of emerged to eruptive energy is approximate to 2%, and the actual values of each energy term agree to within 10% between the two cases. Crucially, the data injection cadence, when properly scaled, matches the cadence of synoptic observations of the Sun's surface magnetic field, and is 3-4 orders of magnitude longer than the inherent CFL time step of the simulations. The stability of the code and fidelity of the results over an entire active region lifetime, from emergence to eruption, strongly suggest that our method will produce reliable results when driven using solar synoptic observations from existing and anticipated ground- and spaced-based observatories.

Many proxies for assessing the eruptive activity of solar active regions (ARs) have been suggested, mostly based on measurements of the photospheric magnetic field. Here we test the usefulness of DC/RC (ratio of photospheric direct to return current) for assessing the ability of ARs to produce CMEs, and compare it with the amount of shear along the eruptive section of the polarity inversion line (PIL). We find that all source regions of eruptive flares have DC/RC > 1.63 and PIL shear > 45° (3.2 and 68° on average), tending to be larger for stronger events. Both quantities are on average smaller for source regions of confined flares (2.2 and 46°), albeit with substantial overlap. Many source regions, especially those of eruptive X-class flares, exhibit elongated direct currents (EDCs) bracketing the eruptive PIL segment, typically coinciding with areas of continuous PIL shear > 45°. However, a small subset of confined flares have DC/RC close to unity, very low PIL shear (< 38°), and no clear EDC signatures, rendering such regions less likely to produce a CME. A simple quantitative analysis reveals that DC/RC and PIL shear are almost equally good proxies for assessing CME-productivity, and comparable to other proxies suggested in the literature. We also demonstrate that an inadequate selection of the current-integration area typically yields a substantial underestimation of DC/RC.

Recent observations of the solar atmosphere in cool extreme-ultraviolet lines have reported the prevalence of coronal rain falling from coronal cloud filaments that are associated with the magnetic dips of coronal X-point structures. These filaments mysteriously appear as clouds of mass in the corona that subsequently shrink and disappear due to mass losses that drain as coronal rain along arced field lines. Using a two-and-a-half-dimensional magnetohydrodynamic model, we investigated evaporation-condensation as the formation mechanism of the subset of coronal cloud filaments that form above coronal X-points. Our simulation included the effects of field-aligned thermal conduction and optically thin radiation, and used the state-of-the-art transition region adaptive conduction (TRAC) method to model the formation, maintenance, and mass loss of a filament above a coronal X-point. This paper presents a physical model that demonstrates magnetic reconnection as a filament loss mechanism, producing hybrid filament/coronal rain via mass losses through the X-point. A detailed analysis of how the mass of the filament forces the field to reconnect is also presented, revealing three phases that characterize the evolution of the reconnecting current sheet and associated mass losses. We conclude that the formation of certain coronal cloud filaments and subsequent mass losses via coronal rain can be explained by the evaporation-condensation model combined with filament mass losses forced by magnetic reconnection. We also report that rebound shocks generated by the impact of coronal rain condensations on the chromosphere together with retractive upflows can cause upward-propagating condensations to form through a dynamic thermal runaway process.

The energy that heats the magnetically closed solar corona originates in the complex motions of the massive photosphere. Turbulent photospheric convection slowly displaces the footpoints of coronal field lines, causing them to become twisted and tangled. Magnetic stresses gradually build until reaching a breaking point when the field reconnects and releases a sudden burst of energy. We simulate this basic picture of nanoflares using a high-fidelity, three-dimensional, multi-stranded magnetohydrodynamic simulation that starts with a fully stratified atmosphere. This simulation includes the effects of field-aligned thermal conduction and optically thin radiation and uses the state-of-the-art Transition Region Adaptive Conduction (TRAC) method to capture the response of the plasma to the nanoflare heating. We find that our physical model supports a unified explanation for both the diffuse emission observed in active regions and the bright coronal loops. Specifically, our results suggest that the diffuse emission originates from spatially and temporally uncorrelated nanoflares, whereas coherent clusters of nanoflares - nanoflare storms - are responsible for the formation of bright coronal loops. Quantitative comparisons between the simulated emission and observed characteristics of coronal loops show that key observed properties - such as loop widths, lifetimes and cross sections - are reasonably well reproduced by the model. The idea that avalanche spread naturally leads to circular cross sections in coronal loops is strongly supported. Our results also suggest that phase differences in heating and cooling events across neighboring magnetic flux strands are a plausible explanation for the anomalous cross-field motions of coronal loops that were recently reported in high-resolution observations.

We present our implementation of non-reflecting boundary conditions in the magnetohydrodynamics (MHD) code LaRe3D. This implementation couples a characteristics-based boundary condition with a Lagrangian remap code, demonstrating the generality and flexibility of such non-reflecting boundary conditions for use with arbitrary grid-based MHD schemes. To test this implementation for perturbations on a background state, we present simulations of a hot sphere in an angled magnetic field. We then examine a series of simulations where we advect a spheromak through a non-reflecting boundary condition at four speeds related to the fast and slow magnetosonic speeds and the Alfvén speed. We compare the behavior of these simulations to ground truth simulations run from the same initial condition on an extended grid that keeps the spheromak in the simulation volume at all times. We find that the non-reflecting boundary condition can lead to severe, physical differences developing between a simulation using a non-reflecting boundary and a ground truth simulation using a larger simulation volume. We conclude by discussing the origins of these differences.

We develop a general description of how information propagates through a magnetohydrodynamic (MHD) system based on the method of characteristics and use that to formulate numerical boundary conditions that are intrinsically consistent with the MHD equations. Our formulation includes two major advances for simulations of the Sun. First, we derive data-driven boundary conditions that optimally match the state of the plasma inferred from a time series of observations of a boundary (e.g., the solar photosphere). Second, our method directly handles random noise and systematic bias in the observations, and finds a solution for the boundary evolution that is strictly consistent with MHD and maximally consistent with the observations. We validate the method against a Ground Truth (GT) simulation of an expanding spheromak. The data-driven simulation can reproduce the GT simulation above the photosphere with high fidelity when driven at high cadence. Errors progressively increase for lower driving cadence until a threshold cadence is reached and the driven simulation can no longer accurately reproduce the GT simulation. However, our characteristic formulation of the boundary conditions still requires adherence of the boundary evolution to the MHD equations even when the driven solution departs from the true solution in the driving layer. That increasing departure clearly indicates when additional information at the boundary is needed to fully specify the correct evolution of the system. The method functions even when no information about the evolution of some variables on the lower boundary is available, albeit with a further decrease in fidelity.

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 two-dimensional (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. (2014) as the initial condition and drive our simulations by imposing boundary conditions extracted from a flux-emergence simulation by Leake et al. (2013). We identify three mechanisms that determine the evolution of the system: (i) reconnection displacing foot points 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 pre-existing and newly emerging flux systems. The relative contributions and effects of these mechanisms depend on the properties of the pre-existing 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.

We report on a study of the Multiview Observatory for Solar Terrestrial Science (MOST) mission that will provide comprehensive imagery and time series data needed to understand the magnetic connection between the solar interior and the solar atmosphere/inner heliosphere. MOST will build upon the successes of SOHO and STEREO missions with new views of the Sun and enhanced instrument capabilities. This article is based on a study conducted at NASA Goddard Space Flight Center that determined the required instrument refinement, spacecraft accommodation, launch configuration, and flight dynamics for mission success. MOST is envisioned as the next generation great observatory positioned to obtain three-dimensional information of large-scale heliospheric structures such as coronal mass ejections, stream interaction regions, and the solar wind itself. The MOST mission consists of 2 pairs of spacecraft located in the vicinity of Sun-Earth Lagrange points L4 (MOST1, MOST3) and L5 (MOST2 and MOST4). The spacecraft stationed at L4 (MOST1) and L5 (MOST2) will each carry seven remote-sensing and three in-situ instrument suites, including a novel radio package known as the Faraday Effect Tracker of Coronal and Heliospheric structures (FETCH). MOST3 and MOST4 will carry only the FETCH instruments and are positioned at variable locations along the Earth orbit up to 20° ahead of L4 and 20° behind L5, respectively. FETCH will have polarized radio transmitters and receivers on all four spacecraft to measure the magnetic content of solar wind structures propagating from the Sun to Earth using the Faraday rotation technique. The MOST mission will be able to sample the magnetized plasma throughout the Sun-Earth connected space during the mission lifetime over a solar cycle.

We present the first results of three-dimensional (3D) numerical magnetohydrodynamic (MHD) simulations of the onset of magnetic reconnection via the tearing instability in dynamically thinning current sheets in the solar corona. In all our simulations, the onset of the non-linear tearing instability, which leads to the break-up of the thinning current sheet, does not occur until after the instability growth time becomes faster than the dynamic thinning time. Furthermore, as in previous 3D MHD simulations of static current sheets in the corona, for some parameters, the amount of magnetic shear is a fundamental switch-on parameter, which has consequences for coronal heating models. These results open up the possibility of using observable quantities of coronal current sheets to predict when they will break-up and release magnetic energy to power various energetic phenomena and/or heat the atmosphere.

It has been suggested that the ratio of photospheric direct to return current, ∣DC/RC∣, may be a better proxy for assessing the ability of solar active regions to produce a coronal mass ejection (CME) than others such as the amount of shear along the polarity inversion line (PIL). To test this conjecture, we measure both quantities prior to eruptive and confined flares of varying magnitude. We find that eruptive-flare source regions have ∣DC/RC∣ > 1.63 and PIL shear above 45° (average values of 3.°2 and 68°, respectively), tending to be larger for stronger events, while both quantities are on average smaller for confined-flare source regions (2.°2 and 68°, respectively), albeit with substantial overlap. Many source regions, especially those of eruptive X-class flares, exhibit elongated direct currents (EDCs) bracketing the eruptive PIL segment, which typically coincide with areas of continuous PIL shear above 45°. However, a small subset of confined-flare source regions have ∣DC/RC∣ close to unity, very low PIL shear (<38°), and no clear EDC signatures, rendering such regions less likely to produce a CME. A simple quantitative analysis reveals that ∣DC/RC∣ and PIL shear are almost equally good proxies for assessing CME-productivity, comparable to other proxies suggested in the literature. We also show that an inadequate selection of the current-integration area typically yields a substantial underestimation of ∣DC/RC∣, discuss specific cases that require careful consideration for ∣DC/RC∣ calculation and interpretation of the results, and suggest improving photospheric CME-productivity proxies by incorporating coronal measures such as the decay index.

We present a report of recent progress on the topic of understanding solar coronal mass ejection (CME) onset from both modeling and observational viewpoints, as carried out from 2019 to the present by the NASA Living with a Star Focused Science Topic team on "Understanding the Onset of Major Solar Eruptions." Following the typical Focused Science Topic paradigm, a number of research groups were selected and joined together to tackle this problem. The work being carried out by this team explores the role of topology and of helicity transport in creating an environment favorable to CME eruption and in then providing the energy required for CME onset. The team investigated CME energization and initiation via photospheric shearing, via flux rope formation, and via magnetic flux emergence. This article will highlight recent progress made by six American research groups working in these areas. We do not intend to present an exhaustive review of these topics, but rather summarize the ideas from these research groups regarding ongoing and upcoming challenges to the questions of how, when, and why coronal mass ejections erupt from the sun.

Cutting edge research of the region between the solar photosphere and Alfvén surface, where the solar wind disconnects from the solar surface, increasingly relies on largescale computational modeling.This is true not just for numerical experiments that only involve simulations, but also for interpreting the ever-more-intricate observations coming out of new facilities.A paradigm shift is currently underway in the field, away from ad hoc and ab initio models of the atmosphere and towards simulations that are directly driven by observations.While this topic is currently at the level of basic research into the techniques, the intent is for it to serve both basic research and operational space-weather needs.We must advance data driven simulations and their supporting infrastructure to the point where community members can use time dependent dynamic models on a regular basis as a tool to interpret observations and test physical theories.Because of the complexity of the task, the immense computational resources required, and the required longevity of such a project, we argue that this effort should be strategically funded.Such an effort is required to make the most out of current and upcoming multi-mission, multi-instrument, heterogeneous observational data.

The thickness of current sheets is extremely important, especially as it relates to the onset of fast magnetic reconnection. Onset determines how much magnetic free energy can build up in a field before it is explosively released. This has implications for many phenomena on the Sun and throughout the universe, including the heating of the solar corona. Significant effort has been devoted to the question of whether equilibrium current sheets in realistic geometries have finite or zero thickness. Using a simple force balance analysis, we show why current sheets without a guide field (2D) and with a guide field that is invariant in the guide field direction (2.5D) cannot be in equilibrium if they have both finite thickness and finite length. We then estimate the conditions under which the tension of a curved line-tied guide field can facilitate equilibrium in 3D sheets that are finite in all dimensions. Finally, we argue that some quasi-statically evolving current sheets undergoing slow stressing (e.g., when the coronal magnetic field is subjected to photospheric boundary driving) may reach a critical shear, at which point they lose equilibrium, spontaneously collapse, and reconnect. The critical shear is generally consistent with the heating requirements of solar active regions.

We present a strategy for answering the question of how the magnetically closed corona is heated. Pursuing this strategy will lead to important new knowledge about fundamental physical processes such as magnetic reconnection and the role of coupling between disparate spatial scales. The strategy is focused on the goal of constructing physics-based models that can nowcast and eventually forecast the solar spectral irradiance at an accuracy that is useful for space weather operations. Such models will also be invaluable for studying the spectral irradiance from other stars and its effect on the development of life and the habitability of planets. We recommend investments that are needed for ultimate success, including a dedicated modeling program and a mission to observe the corona at ultra-high spatial resolution.

Results from 2.5D and 3D studies of the onset and development of the tearing instability are presented, using high fidelity resistive MHD simulations. A limited parameter study of the strength of the reconnecting field (or shear angle) was performed. An initially simple 1D equilibrium was used, consisting of a modified force-free current sheet, with periodic boundary conditions in all directions. In all cases, the linear and non-linear evolution led to a primary current sheet between two large flux ropes. The global reconnection rate during this later stage was analyzed in all simulations. It was found that in 2.5D the primary current sheet fragmented due to plasmoids, and as expected, the global reconnection rate, calculated using multiple methods, increases with the strength of the reconnecting field due to a stronger Alfvén speed. In 3D, the presence of interacting oblique modes of the tearing instability complicates the simple 2.5D picture, entangling the magnetic field of the inflow and introducing a negative effect on the reconnection rate. The two competing effects of stronger Alfvén speed and entangling, which both increase with the strength of the reconnecting field, resulted in a decrease in the reconnection rate with increasing reconnecting field. For all simulations, the 3D rates were less than in 2.5D, but suggest that as one goes to weak reconnecting field (or strong guide field), the system becomes more 2.5D like and the 2.5D and 3D rates converge. These results have relevance to situations like nano-flare heating and flare current sheets in the corona.

Solar eruptive events such as coronal mass ejections and eruptive flares are frequently associated with the emergence of magnetic flux from the convection zone into the corona. We use three-dimensional magnetohydrodynamic numerical simulations to study the interaction of coronal magnetic fields with emerging flux and determine the conditions that lead to eruptive activity. A simple parameter study is performed, varying the relative angle between emerging magnetic flux and a preexisting coronal dipole field. We find that in all cases the emergence results in a sheared magnetic arcade that transitions to a twisted coronal flux rope via low-lying magnetic reconnection. This structure, however, is constrained by its own outer field and so is noneruptive in the absence of reconnection with the overlying coronal field. The amount of this overlying reconnection is determined by the relative angle between the emerged and preexisting fields. The reconnection between emerging and preexisting fields is necessary to generate sufficient expansion of the emerging structure so that flare-like reconnection below the coronal flux rope becomes strong enough to trigger its release. Our results imply that the relative angle is the key parameter in determining whether the resultant active regions exhibit eruptive behavior and is thus a potentially useful candidate for predicting eruptions in newly emerging active regions. More generally, our results demonstrate that the detailed interaction between the convection zone/photosphere and the corona must be calculated self-consistently in order to model solar eruptions accurately.

This article presents results that challenge the paradigms that (1) the convection zone is the source of the radial magnetic field in the photosphere and (2) that coronal currents are neutralized from the perspective of the photosphere. We demonstrate, using a new analysis tool applied to simulations and observations, that bare or partially dressed current channels are supported by the solar corona and that fingerprints of these coronal current systems can be detected in the photosphere. These coronal current channels can be a significant source of the radial component of the magnetic field in the photosphere. The roots of these coronal current channels in the photosphere are the source of the magnetic field component parallel to the polarity inversion line in active region NOAA 12673. These analyses and observations transform our theoretical understanding of coronal evolution and argue for a reexamination of the present paradigm in which the convection zone is the sole source of the photospheric magnetic field.

The role of twist in the emergence of magnetic flux ropes into the solar atmosphere has remained unclear for some time. Although many studies have investigated how the photospheric properties of active regions resulting from the simulated emergence of magnetic flux ropes from the convection zone with different twists compare to the observed properties of active regions, these simulations have a wide range of magnetic flux rope radii, depths, and initial configurations, making it challenging to form a complete picture of the role of any one variable in the emergence process. Twist, in particular, has been difficult to analyze because isothermally buoyant magnetic flux ropes with different twists also experience different accelerations. In this paper, we develop an analytical model of a toroidal magnetic flux rope in approximate vertical force balance in the convection zone. We numerically implement this model in a stratified atmosphere, and then subtract off a twist-independent density to make magnetic flux ropes buoyant in a twist-independent way, ensuring that the initial acceleration of each magnetic flux rope is approximately the same. We perform numerical simulations to obtain a parameter study of toroidal magnetic flux ropes with different twist rising at the same speed. We analyze the photospheric and coronal properties of the active regions resulting from the emergence of these magnetic flux ropes, and argue that the Parker instability is responsible for many of the features observed in the simulations.

Magnetic flux ropes (MFRs) rising buoyantly through the Sun’s convection zone are thought to be subject to viscous forces preventing them from rising coherently. Numerous studies have suggested that MFRs require a minimum twist in order to remain coherent during their rise. Furthermore, even MFRs that get to the photosphere may be unable to successfully emerge into the corona unless they are at least moderately twisted, since the magnetic pressure gradient needs to overcome the weight of the photospheric plasma. To date, however, no lower limit has been placed on the critical minimum twist required for an MFR to rise coherently through the convection zone or emerge through the photosphere. In this paper, we simulate an untwisted toroidal MFR that is able to rise from the convection zone and emerge through the photosphere as an active region that resembles those observed on the Sun. We show that untwisted MFRs can remain coherent during their rise and then pile up near the photosphere, triggering undular instability, allowing the MFR to emerge through the photosphere. We propose that the toroidal geometry of our MFR is critical for its coherent rise. Upon emergence, a pair of lobes rises into the corona. The two lobes then interact and reconnect, resulting in a localized high speed jet. The resulting photospheric magnetogram displays the characteristic salt-and-pepper structure often seen in observations. Our major result is that MFRs need not be twisted to rise coherently through the convection zone and emerge through the photosphere.