We present AGILE, a GPU-enabled adaptive mesh refinement (AMR) framework for the solution of (near-) conservation laws which occur in astro- and solar-physical applications. AGILE is written in modern fortran 2003, inherits a part of its modules and mesh handling from MPI-AMRVAC, and achieves excellent GPU performance via OpenACC offloading. We here discuss the design decisions which enable AGILE to perform cost-efficient and scalable deeply nested AMR simulations with moderate block sizes of e.g. 16^3 cells. AGILE currently implements several physics modules, ie. hydrodynamics, frozen-field hydrodynamics, magnetohydrodynamics and special-relativistic hydrodynamics and can easily be extended further through its modular design. Besides strong scaling tests to up to 2048 GPUs and standard benchmarks which show consistent performance across a large range of devices and problem sizes, we demonstrate AGILE's capabilities by means of state-of-the art science applications with all currently available physics modules.

Solar filament eruptions are central to coronal mass ejections and space weather, yet their triggering mechanisms remain a fundamental open question. In particular, the early-stage that drives a magnetic flux rope toward instability and its observable signatures are poorly understood. Here, combining multi-instrument observations, we report successive coronal jets impacting a filament, causing its gradual rise and oscillations with growing amplitude and period. When the filament reaches the height where the decay index exceeds the torus instability threshold, the rapid filament eruption commences. This filament eruption is reproduced by magnetohydrodynamic simulations, in which successive thermal jets disturb a stable filament in a magnetic flux rope and excite oscillations together with the eruption of the filament. As the filament rises to erupt, the restoring forces for the oscillation progressively weaken, which naturally leads to an increase of the oscillation amplitude and period. Our results demonstrate the growing oscillations as one of the observable precursors for filament eruptions, enhancing our ability to predict solar eruptions.

Solar prominences usually have a horizontally elongated body with many feet extending to the solar surface, resembling a multi-arch bridge with many bridge piers. The basic mechanism by which solar prominences acquire these common structures during their evolution, however, remains an unresolved question. For the first time, our three-dimensional magneto-frictional simulation, driven by supergranular motions, self-consistently replicates the commonly observed multi-arch bridge morphology and its characteristic structures of solar quiescent prominences in a magnetic flux rope. In comparison with traditional views, our simulations demonstrate that the spine, feet, and voids (bubbles) are inherent prominence structures spontaneously forming as the flux rope evolves to a mature state. The voids mainly consist of legs of sheared magnetic loops caused by unbalanced supergranular flows, and prominence feet settle at the bottom of helical field lines piled up from the photosphere to the spine. Similarities between the simulated prominences and observed real prominences by the Chinese Hα Solar Explorer, the New Vacuum Solar Telescope, and NASA's Solar Dynamics Observatory suggest the high validity of our model. This work corroborates the pivotal role of photospheric supergranulation as a helicity injection source in the formation and shaping of quiescent prominence structures within the solar atmosphere, thereby paving a new avenue for future investigations into their fine dynamics and stability.

Utilizing multi-wavelength data from the Solar Dynamics Observatory, we report the first imaging detection of reconnection jets driven by the footpoint drift of an erupting hot-channel flux rope (HFR) during an X1.6-class solar flare. Our results demonstrate that these jets are inherent byproducts of the HFR eruption, exhibiting strong spatiotemporal coupling with the HFR footpoint drift and the morphological evolution of the associated flare ribbon hooks. Unlike standard coronal jets, these ejections lack an inverted-Y morphology and show no association with underlying photospheric flux cancellation or emergence. They manifest as clusters of small-scale, collimated ejecta (180-200 km s^-1) featuring co-existing cool and hot emission components visible in both cool (304 and 171 Angstrom) and hot (94 Angstrom) EUV channels. The imaging observations reveal that these jets are triggered by successive 3D arcade-flux rope (ar-rf) reconnection as the expanding HFR interacts with the ambient coronal side arcades. The morphological and dynamic complexity of these observed jets implies that the ongoing ar-rf reconnection in solar eruptions is episodic and bursty in nature. Our estimates show that a decrease of approximately 9 G in localized magnetic field strength is required to power these individual jets. As direct signatures of 3D magnetic reconnection, these observed jets pinpoint the exact site and characterize the nature of the process, providing new observational insight into 3D numerical simulation extensions of the standard flare model. Further observational case studies of these jets are required to fully understand their prevalence across solar eruptions.

GPUs and other accelerators are increasingly used for scientific computing. In the future, we want to add GPU support to parallel adaptive mesh refinement (AMR) codes written in Fortran. To understand which changes are necessary to obtain good performance we have developed foap4, an AMR framework implemented in Fortran that uses OpenACC, MPI, and the p4est library. We discuss the design and implementation of the framework. Several benchmark problems are considered, in which Euler's equations of gas dynamics are solved using explicit time integration. These benchmarks are performed in both 2D and 3D, using static and adaptive meshes, for varying problem sizes on different hardware. Our results show that AMR simulations can be carried out efficiently on GPUs with OpenACC and MPI, even when using relatively small grid blocks of 8^3 or 16^3 cells.

Solar prominences are very spectacular structures embedded in the tenuous and hot solar corona. Counterstreaming flows, a common feature in solar quiescent prominences, have been discovered for more than 20 yr. However, the mechanism driving the counterstreaming flows is still elusive. To unveil the nature of this phenomenon, we analyzed data of a quiescent prominence observed by the New Vacuum Solar Telescope, the Interface Region Imaging Spectrograph, and the Solar Dynamical Observatory. It is found that there is a distinct longitudinal oscillation of prominence plasma along the higher part of the prominence spine in H α observations. The oscillation period is approximately 83 minutes and the amplitude is about 32 Mm. The counterstreaming flows are dominant in the middle part of the prominence spine. The velocities of the counterstreaming flows range from about 4 to 11 km s ^−1 . Moreover, intermittent mass flows with upward plumes from the top of the bubbles and tornado-like barbs are observed to be injected into the lower part of the prominence spine from the lower atmosphere. The velocities of these injected mass flows range from about 3 to 30 km s ^−1 . Some injected mass flows exhibit redshifted Doppler signals, while others exhibit blueshifted signals. Based on these high-resolution observations, it is found that different parts of the prominence spine exhibit different dynamic characteristics. These results further advance the understanding of the ubiquitous counterstreaming flows in solar quiescent prominences.

Filaments are special plasma phenomena embedded in the solar atmosphere, characterized by unique thermodynamic properties and magnetic structures. Magnetohydrodynamic (MHD) simulations are useful to investigate the eruption mechanisms of filaments. We conduct a data-constrained zero- β MHD simulation in spherical coordinates to investigate a C3.5 class flare triggered by an eruptive filament on 2022 August 15 in the decaying weak active region 13079. We reconstruct the three-dimensional coronal magnetic field using vector magnetograms and synoptic maps from the Solar Dynamics Observatory/Helioseismic and Magnetic Imager. We transform the vector magnetic field into Stonyhurst heliographic spherical coordinates combined with a synoptic map and construct a potential field source surface model with a magnetic flux rope embedded using the regularized Biot–Savart laws. Subsequently, we conduct a spherical zero- β MHD simulation using the message-passing interface adaptive mesh refinement versatile advection code (MPI-AMRVAC) and replicate the entire dynamic process of the filament eruption consistent with observations. With the calculation of the time–distance profile, quasi-separatrix layers, and synthetic radiation from simulated current density, we find a good agreement between our simulation and observations in terms of dynamics and magnetic topology. Technically, we provide a useful method of advanced data-constrained simulation of weak active regions in spherical coordinates. Scientifically, the model allows us to quantitatively describe and diagnose the entire process of filament eruption.

We investigate the acceleration and transport of electrons in the highly fine-structured current sheet that develops during magnetic flux rope (MFR) eruptions. Our work combines ultraresolved magnetohydrodynamic (MHD) simulations of MFR eruption, with test-particle studies performed using the guiding center approximation. Our grid-adaptive, fully 3D, high-resolution MHD simulations model MFR eruptions that form complex current-sheet topologies, serving as background electromagnetic fields for particle acceleration. Within the current sheet, tearing-mode instabilities give rise to mini flux ropes. Electrons become temporarily trapped within these elongated structures, undergoing acceleration and transport processes that significantly differ from those observed in 2D or 2.5D simulations. Our findings reveal that these fine-scale structures act as efficient particle accelerators, surpassing the acceleration efficiency of single X-line reconnection events, and are capable of energizing electrons to energies exceeding 100 keV. High-energy electrons accelerated in different mini flux ropes follow distinct trajectories, due to spatially varying magnetic field connectivity, ultimately precipitating onto opposite sides of flare ribbons. Remarkably, double electron sources at the flare ribbons originate from different small-flux-rope acceleration regions, rather than from the same reconnecting field line, as previously suggested. Distinct small flux ropes possess opposite magnetic helicity, to accelerate electrons to source regions with different magnetic polarities, establishing a novel conjugate double-source configuration. Furthermore, electrons escaping from the lower regions exhibit a broken-power-law energy spectrum. This spectral break arises from electrons accelerated in disparate mini flux ropes, each exhibiting magnetic reconnection rates and acceleration efficiencies, which reflect the varying local reconnection conditions.

3D magnetic reconnection is a fundamental plasma process crucial for heating the solar corona and generating the solar wind, but resolving and characterizing it for the Sun remain challenging. Using high-quality data from the Chinese New Vacuum Solar Telescope, the Solar Dynamics Observatory, and the Interface Region Imaging Spectrograph, this work presents highly suggestive direct imaging evidence of magnetic reconnection during the untangling of braided magnetic structures above a sunspot. These magnetic structures, visible as bright superpenumbral threads in extreme-ultraviolet passbands, initially bridge opposite-polarity magnetic fluxes and then gradually tangle in their middle section. Magnetic extrapolation reveals the fibrils to form a small flux rope that is twisted and braided, possibly created by persistent and complex photospheric motions. During untangling, repetitive reconnection events occur inside the flux rope, accompanied by transient plasma heating, bidirectional outflowing blobs, and signatures of nanojets. An emission analysis reveals that the outflowing blobs are multithermal structures with temperatures well below 1 MK, undergoing rapid cooling and leaving emission imprints in H α images. The measured reconnection angles indicate that 16%–22% of the magnetic field along each thread is antiparallel, with the remaining field acting as a guide field. The estimated energy released during these reconnection events is comparable to nanoflares, which can be powered by up to 6% of the magnetic energy stored in the antiparallel field. This work presents a textbook example of magnetic flux rope reconnection in the solar atmosphere, providing new insights into fine-scale energy release processes within sunspot superpenumbral fibrils.

Utilizing high-resolution imaging and spectroscopic observations from the New Vacuum Solar Telescope, the Interface Region Imaging Spectrograph, and the Solar Dynamics Observatory, we investigated the nature and origin of counterstreaming flows within a forming active region filament. The ever-present counterstreaming flows observed within the filament are identified as interleaved unidirectional mass flows in opposing directions occurring in neighboring threads. Multiwavelength observations corroborate the multithermal nature of these counterstreaming flows: the cool H alpha component flows at about 10-20 km s-1, while the warm ultraviolet and extreme-ultraviolet components reach 40-70 km s-1. The Si iv 1400 & Aring; line reveals significant microturbulence in the filament's counterstreaming flows, with a nonthermal velocity width of similar to 40 km s-1. These multithermal flows emanate from compact brightenings at the filament's ends, manifesting as small-scale, collimated upflows at their nascent phase. They continuously inject both chromospheric and transition region plasma into the filament channel, thereby feeding the counterstreaming flows. At their base, the Si iv and C ii spectral lines show pronounced line broadening and intensity enhancements, indicating significant localized chromospheric heating. Additionally, numerous small-scale photospheric flux emergence and cancellation events, with a magnitude of similar to 1017 Mx, are detected near their base. We suggest that such weak magnetic-field activities, possibly associated with unresolved magnetic reconnection events, drive these persistent upflows and localized footpoint heating. This work elucidates the multithermal origin of counterstreaming flows within a forming filament and provides evidence of localized chromospheric heating at the filament footpoints.

The eruption of a solar prominence can eject substantial mass and magnetic field into interplanetary space and cause geomagnetic storms. However, various questions about prominences and their eruption mechanism remain unclear. In particular, what causes the intriguing Doppler bullseye pattern in prominences has not yet been solved, despite some preliminary studies proposing that they are probably associated with counterstreaming mass flows. Previous studies are mainly based on single-angle and short-timescale observations, making it difficult to determine the physical origin of Doppler bullseye patterns in prominences. Here, taking advantage of stereoscopic observations taken by the Solar Dynamics Observatory and the Solar Terrestrial Relations Observatory and a three-dimensional numerical simulation, we investigate the origin of the prominence Doppler bullseye pattern by tracing a long-lived transequatorial filament/prominence from 2012 July 23 to August 4. We find that the Doppler bullseye pattern can be launched by repeated coronal jets at one end of the prominence. It is evidenced in our observations and simulation that during the forward traveling of jet plasma along the helical magnetic field structure of the prominence, part of the ejecting plasma can not pass through the apex of the prominence due to the insufficient kinetic energy and therefore forms a backward-moving mass flow along the same or neighboring magnetic field lines. This process finally forms counterstreaming mass flows in on-disk filaments. When the on-disk filament rotates to the solar limb to be a prominence, the counterstreaming mass flows are naturally observed as a Doppler bullseye pattern.

Magnetic flux emergence is traditionally considered to be a key trigger of solar filament eruptions, yet its role in suppressing filament eruptions remains less understood. Using multiwavelength observations from the Solar Dynamics Observatory, this study investigates a unique case of flux emergence below a quiescent filament from 2016 January 3 to 5, where the newly emerging magnetic flux suppressed rather than promoted the eruption of the filament. It is found that the emerging magnetic bipole within the filament channel directly interacted and reconnected with the overlying filament magnetic field and produced a series of two-sided coronal jets along the filament axis. Instead of eruption, the filament kept stable but broke into two segments at the reconnection site. Further magnetic cancellation or recession of the emerged bipole allowed the filament to recover its original structure. Our analysis results revealed that the flux emergence suppressed the filament eruption by reducing the upward net force. The formation and evolution of the filament fine structures (such as filament threads) are closely linked to the reconnection processes between the emerging bipole and the filament's horizontal magnetic field. This study provides direct observational evidence for accounting for the stabilization of solar filaments driven by flux emergence, offering new insights into magnetic emergence's dual role in triggering and suppressing solar eruptions.

We review major achievements in our understanding of multiphase coronal plasma, where cool-dense and hot-tenuous matter coexists, brought about by advances in modeling and theory, inspired by observations. We give an overview of models that self-consistently form solar (or stellar) prominences and filaments, or (postflare) coronal rain, and clarify how these different phenomena share a common physical origin, relating radiative losses and coronal heating. While we do not fully understand the coronal heating, multi-dimensional models of solar prominence and rain formation demonstrate how thermal instability triggers condensations, and how their morphology may reveal aspects of the applied heating at play. We emphasize how the many pathways to linear instability due to combined ingredients of heat-loss, gravity, flows, and magnetic topologies are all involved in the resulting nonlinear magnetohydrodynamics. We provide some challenges to future model efforts, especially concerning prominence fine structure, internal dynamics, and their overall lifecycle.

Filament eruptions are magnetically driven violent explosions commonly observed on the Sun and late-type stars, sometimes leading to monster coronal mass ejections that directly affect the nearby planets' environments. More than a century of research on solar filaments suggests that the slow evolution of photospheric magnetic fields plays a decisive role in initiating filament eruptions, but the underlying mechanism remains unclear. Using high-resolution observations from the Chinese Hα Solar Explorer, the Solar Upper Transition Region Imager, and the Solar Dynamics Observatory, we present direct evidence that a giant solar filament eruption is triggered by a series of minifilament eruptions occurring beneath it. These minifilaments, which are homologous to the giant filament but on a smaller tempo-spatial scale, sequently form and erupt due to extremely weak mutual flux disappearance of opposite-polarity photospheric magnetic fields. Through multi-fold magnetic interactions, these erupting minifilaments act as the last straw to break the force balance of the overlying giant filament and initiate its ultimate eruption. The results unveil a possible novel pathway for small-scale magnetic activities near the stellar surface to initiate spectacular filament eruptions, and provide new insight into the magnetic coupling of filament eruptions across different tempo-spatial scales.

Solar prominences (or filaments) are cooler and denser plasma suspended in the much hotter and rarefied solar corona. When viewed on the solar disk, filament barbs or feet protrude laterally from the filament spine. When observed at the limb of the Sun, they reach into the chromosphere or even further down. For a long time, the magnetic field orientation of barbs has remained a mystery due to the paradox that the barbs possess vertical fine structures and flows but are likely to be supported in a horizontal magnetic field. Here we present unambiguous observations of a magnetic dip in a quiescent prominence foot with an upward-curved field. That is indicated by the horizontal bidirectional outflows probably produced by magnetic reconnection between the fields of a tiny erupting filament and those in a prominence foot. The altitude at the bottom of the dip is ∼30 Mm. At the edge of the prominence foot, the angle between the dip field and the local horizontal is ∼4°. Additionally, the curvature radius of the dip bottom is estimated to be around 73 Mm. We also conduct magnetofrictional simulation to self-consistently form a large-scale magnetic flux rope with magnetic dips resembling the spine and feet of the quiescent prominence. The observations shed light on the field structure of prominences, which is crucial for the instability that accounts for the eruption of prominences and coronal mass ejections.

Understanding the early evolution of coronal mass ejections (CMEs), in particular their initiation, is the key to forecasting solar eruptions and induced disastrous space weather. Although many initiation mechanisms have been proposed, a full understanding of CME initiation, which is identified as a slow rise of CME progenitors in kinematics before impulsive acceleration, remains elusive. Here, with a state-of-the-art thermal magnetohydrodynamics simulation, we determine a complete CME initiation route in which multiple mainstream mechanisms occur in sequence yet are tightly coupled. The slow rise is first triggered and driven by the developing hyperbolic flux tube (HFT) reconnection. Subsequently, the slow rise continues as driven by the coupling of the HFT reconnection and the early development of torus instability. The end of the slow rise, i.e., the onset of the impulsive acceleration, is induced by the start of the fast magnetic reconnection coupled with the torus instability. These results unveil that CME initiation is a complicated process involving multiple physical mechanisms, thus being hardly resolved by a single initiation mechanism.

Magnetic flux ropes are a bundle of twisted magnetic field lines produced by internal electric currents, which are responsible for solar eruptions and are the major drivers of geomagnetic storms. As such, it is crucial to develop a numerical model that can capture the entire evolution of a flux rope, from its birth to death, in order to predict whether adverse space weather events might occur or not. In this paper, we develop a data-driven modeling that combines a time-dependent magnetofrictional approach with a thermodynamic magnetohydrodynamic model. Our numerical modeling successfully reproduces the formation and confined eruption of an observed flux rope, and unveils the physical details behind the observations. Regarding the long-term evolution of the active region, our simulation results indicate that the flux cancellation due to collisional shearing plays a critical role in the formation of the flux rope, corresponding to a substantial increase in magnetic free energy and helicity. Regarding the eruption stage, the deformation of the flux rope during its eruption can cause an increase in the downward tension force, which suppresses it from further rising. This finding may shed light on why some torus-unstable flux ropes lead to failed eruptions after large-angle rotations. Moreover, we find that twisted fluxes can accumulate during confined eruptions, which would breed the subsequent eruptive flares.

Solar eruptive activities, such as flares, coronal mass ejections (CMEs), and prominence or filament eruptions, pose both scientific and practical challenges to human beings. To understand and predict these phenomena in the future, we have to combine observations, theoretical, and numerical models closely. Data-driven and data-constrained magnetohydrodynamic (MHD) simulations provide a promising tool to utilize observational data and incorporate relevant physics in the solar atmosphere. They employ magnetic field, along with density and temperature observations, as the initial and boundary conditions. Since there are still difficulties in observing the coronal magnetic field routinely and accurately, we have to rely on magnetic field models in most cases. We introduce some frequently used flux rope models, including the Gibson–Low, Titov–Démoulin, regularized Biot–Savart laws, nonlinear force-free field, and magnetohydrostatic models. In some studies, the static flux rope models constrained by multi-wavelength observations are used. We discuss many suggested techniques for setting the initial and boundary conditions from both observation and theory, and recent successful applications of the data-driven and data-constrained MHD simulations. We find that data-driven and data-constrained MHD simulations could provide new insights into the physical mechanisms of flux rope formation and eruption, CME structure, and MHD waves.

To understand the magnetic fields of the polar crown filaments (PCFs) at high latitudes near polar regions of the Sun, we perform magnetofrictional numerical simulations on the long-term magnetic evolution of bipolar fields with roughly east-west polarity inversion lines (PILs) in a three-dimensional (3D) spherical wedge domain near polar regions. The Coriolis effect induced vortical motions at the boundaries of several supergranular cells inject magnetic helicity from the photospheric boundary into the solar atmosphere. Supergranular-scale helicity injection, transfer, and condensation produce strongly sheared magnetic fields. Magnetic reconnections at footpoints of the sheared fields produce magnetic flux ropes (MFRs) with helicity signs consistent with the observed Hemispheric Helicity Rule (HHR). The cross-sectional area of MFRs exhibits an uneven distribution, resembling a "foot-node-foot" periodic configuration. Experiments with different tilt directions of PILs indicate that the PCFs preferably form along PILs with the western end close to the polar region. The bending of PILs caused by supergranular flows, forming S-shape (Z-shape) PIL segments, promotes the formation of dextral (sinistral) MFRs. The realistic magnetic models we got can serve as starting points for the study of the plasma formation and eruption of PCFs.

The periodic coronal rain and in-phase radiative intensity pulsations have been observed in multiple wavelengths in recent years. However, due to the lack of three-dimensional coronal magnetic fields and thermodynamic data in observations, it remains challenging to quantify the coronal heating rate that drives the mass cycles. In this work, based on the MURaM code, we conduct a three-dimensional radiative magnetohydrodynamic simulation spanning from the convective zone to the corona, where the solar atmosphere is heated self-consistently through dissipation resulting from magnetoconvection. For the first time, we model the periodic coronal rain in an active region. With a high spatial resolution, the simulation well resembles the observational features across different extreme-ultraviolet wavelengths. These include the realistic interweaving coronal loops, periodic coronal rain, and periodic intensity pulsations, with two periods of 3.0 hr and 3.7 hr identified within one loop system. Moreover, the simulation allows for a detailed three-dimensional depiction of coronal rain on small scales, revealing adjacent shower-like rain clumps ∼500 km in width and showcasing their multithermal internal structures. We further reveal that these periodic variations essentially reflect the cyclic energy evolution of the coronal loop under thermal nonequilibrium state. Importantly, as the driver of the mass circulation, the self-consistent coronal heating rate is considerably complex in time and space, with hour-level variations in 1 order of magnitude, minute-level bursts, and varying asymmetry reaching ten times between footpoints. This provides an instructive template for the ad hoc heating function and further enhances our understanding of the coronal heating process.