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Minifilaments are widespread small-scale structures in the solar atmosphere. To better understand their formation and eruption mechanisms, we investigate the entire life of a sigmoidal minifilament located below a large quiescent filament observed by Big Bear Solar Observatory/Goode Solar Telescope on 2015 August 3. The H α structure initially appears as a group of arched threads, then transforms into two J-shaped arcades, and finally forms a sigmoidal shape. Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly observations in 171 Å show that two coronal jets occur around the southern footpoint of the minifilament before the minifilament eruption. The minifilament eruption starts from the southern footpoint, then interacts with the overlying filament and fails. The aforementioned observational changes correspond to three episodes of flux cancellations observed by SDO/Helioseismic and Magnetic Imager. Unlike previous studies, the flux cancellation occurs between the polarity where the southern footpoint of the minifilament is rooted and an external polarity. We construct two magnetic field models before the eruption using the flux rope insertion method and find a hyperbolic flux tube above the flux cancellation site. The observation and modeling results suggest that the eruption is triggered by the external magnetic reconnection between the core field of the minifilament and the external fields due to flux cancellations. This study reveals a new triggering mechanism for minifilament eruptions and a new relationship between minifilament eruptions and coronal jets. [ABSTRACT FROM AUTHOR]

We investigate a quiescent filament that erupted on 2013 August 2; the eruption was observed in EUV and H α by the Solar Dynamics Observatory and GONG. After a B9.7 flare in the nearby active region, the dark filament materials near its eastern footpoint start to move in the direction of eruption, and are followed by a counterclockwise rotation identified as the motion of a combination of dark and bright filament materials. Then the entire filament rises up and keeps rotating in a clockwise direction during the eruption. More interestingly, the filament exhibits an unusual two-helix structure near its western footpoint during the eruption, which indicates the existence of a highly twisted flux rope. This hypothesis is confirmed by magnetic field modeling using the flux rope insertion method. In the best-fit unstable model, the lower limits of the estimated maximum and average twist numbers of the erupting flux rope reach 7.5 π and 4 π, which suggests that kink instability plays an important role in the eruption. During these magnetically coupled sympathetic eruptions, the highly twisted filament under the western lobe of a pseudo-streamer-like structure becomes unstable and erupts due to the removal of confinement by magnetic reconnection at the overlying hyperbolic flux tube, which is initiated by the B9.7 flare in the nearby active region. The initial filament motion occurs at the more unstable eastern footpoint, where the surrounding fields are weaker and decrease with height more rapidly. [ABSTRACT FROM AUTHOR]

Similar to the cases of anemone jets, two-sided loop solar jets can also be produced by either flux emergence from the solar interior or small-scale filament eruptions. Using high-quality data from the Solar Dynamics Observatory, we have analyzed a two-sided loop solar jet triggered by the eruption of a small filament. The jet occurred in a pre-existing big filament channel. The detailed processes involved in the eruption of the small filament, the interaction between the erupted filament and the big filament channel, and the launch of the two-sided loop jet are presented. The observations further revealed notable asymmetry between the two branches of the jet spire: the northeastern branch is narrow and short, while the southern branch is wide and long and accompanied by discernible untwisting motions. We explored the unique appearance of the jet by employing the method of local potential field extrapolation to calculate the coronal magnetic field configuration around the jet. The photospheric magnetic flux below the small filament underwent cancellation for approximately 7 hr before the filament eruption, and the negative flux near the southern footpoint of the filament decreased by about 56% during this interval. Therefore, we propose that the primary photospheric driver of the filament eruption and the associated two-sided loop jet in this event is flux cancellation rather than flux emergence. [ABSTRACT FROM AUTHOR]

We consider small-scale jetlike events that might make the solar wind, as has been suggested in recent studies. We show that the events referred to as "coronal jets" and as "jetlets" both fall on a power-law distribution that also includes large-scale eruptions and spicule-sized features; all of the jetlike events could contribute to the solar wind. Based on imaging and magnetic field data, it is plausible that many or most of these events might form by the same mechanism: Magnetic flux cancelation produces small-scale flux ropes, often containing a cool-material minifilament. This minifilament/flux rope erupts and reconnects with adjacent open coronal field, along which "plasma jets" flow and contribute to the solar wind. The erupting flux ropes can contain twist that is transferred to the open field, and these become Alfvénic pulses that form magnetic switchbacks, providing an intrinsic connection between switchbacks and the production of the solar wind. [ABSTRACT FROM AUTHOR]

We perform a data-constrained simulation with the zero- β assumption to study the mechanisms of strong rotation and failed eruption of a filament in active region 11474 on 2012 May 5 observed by Solar Dynamics Observatory and Solar Terrestrial Relations Observatory. The initial magnetic field is provided by nonlinear force-free field extrapolation, which is reconstructed by the regularized Biot–Savart laws and magnetofrictional method. Our simulation reproduces most observational features very well, e.g., the filament large-angle rotation of about 130°, the confined eruption, and the flare ribbons, allowing us to analyze the underlying physical processes behind observations. We discover two flux ropes in the sigmoid system, an upper flux rope (MFR1) and a lower flux rope (MFR2), which correspond to the filament and hot channel in observations, respectively. Both flux ropes undergo confined eruptions. MFR2 grows by tether-cutting reconnection during the eruption. The rotation of MFR1 is related to the shear-field component along the axis. The toroidal field tension force and the nonaxisymmetry forces confine the eruption of MFR1. We also suggest that the mutual interaction between MFR1 and MFR2 contributes to the large-angle rotation and the eruption failure. In addition, we calculate the temporal evolution of the twist and writhe of MFR1, which is a hint of probable reversal rotation. [ABSTRACT FROM AUTHOR]

The coronal magnetic topology significantly affects the outcome of magnetic flux rope (MFR) eruptions. The recently reported nested double null magnetic system remains unclear as to how it affects MFR eruptions. Using observations from the New Vacuum Solar Telescope and the Solar Dynamics Observatory, we studied the formation and successful eruption of a hot channel MFR from NOAA active region AR 12173 on 2014 September 28. We observed that a hot channel MFR formed and erupted as a coronal mass ejection (CME), and the magnetic field of the source region was a nested double null magnetic system in which an inner magnetic null point system was nested by an outer fan–spine magnetic system. Observational analysis suggests that the origin of the MFR was due to magnetic reconnection at the inner null point, which was triggered by the photospheric swirling motions. The long-term shearing motion in the source region throughout around 26 hr might accumulate enough energy to power the eruption. Since previous studies showed that MFR eruptions from nested double null magnetic systems often result in weak jets and stalled or failed eruptions, it is hard to understand the generation of the large-scale CME in our case. A detailed comparison with previous studies reveals that the birth location of the MFR relative to the inner null point might be the critical physical factor for determining whether an MFR can erupt successfully or not in such a particular nested double null magnetic system.

The eruption of solar filaments, also known as prominences appearing off limb, is a common phenomenon in the solar atmosphere. It ejects massive plasma and high-energy particles into interplanetary space, disturbing the solar-terrestrial environment. It is vital to obtain the three-dimensional velocity fields of erupting filaments for space-weather predictions. We derive the three-dimensional kinematics of an off-limb prominence and an on-disk filament, respectively, using the full-disk spectral and imaging data detected by the Chinese H α Solar Explorer (CHASE). It is found that both the prominence and the filament experience a fast semicircle-shaped expansion at first. The prominence keeps propagating outward with an increasing velocity until escaping successfully, with the south leg of the prominence finally moving back to the Sun in a swirling manner. For the filament, the internal plasma falls back to the Sun in a counterclockwise rotation in the late ejection, matching the failed eruption without a coronal mass ejection. During the eruptions, both the prominence and the filament show material splitting along the line-of-sight direction, revealed by the bimodal H α spectral profiles. For the prominence, the splitting begins at the top and gradually spreads to almost the whole prominence with a fast blueshift component and a slow redshift component. The material splitting in the filament is more fragmental. As shown by the present results, the CHASE full-disk spectroscopic observations make it possible to systematically study the three-dimensional kinematics of solar filament eruptions.

To understand its evolution and the effects of its eruptive events, the Sun is permanently monitored by multiple satellite missions. The optically thin emission of the solar plasma and the limited number of viewpoints make it challenging to reconstruct the geometry and structure of the solar atmosphere; however, this information is the missing link to understand the Sun as it is: a 3D evolving star. We present a method that enables a complete 3D representation of the uppermost solar layer (corona) observed in extreme ultraviolet (EUV) light. We use a deep-learning approach for 3D scene representation that accounts for radiative transfer to map the entire solar atmosphere from three simultaneous observations. We demonstrate that our approach provides unprecedented reconstructions of the solar poles and directly enables height estimates of coronal structures, solar filaments, coronal hole profiles, and coronal mass ejections. We validate the approach using model-generated synthetic EUV images, finding that our method accurately captures the 3D geometry of the Sun even from a limited number of 32 ecliptic viewpoints (∣latitude∣ ≤ 7°). We quantify the uncertainties of our model using an ensemble approach that allows us to estimate the model performance in the absence of a ground truth. Our method enables a novel view of our closest star and is a breakthrough technology for the efficient use of multi-instrument data sets, which paves the way for future cluster missions.

We report a failed solar filament eruption that involves external magnetic reconnection in a quadrupolar magnetic configuration. The evolution exhibits three phases of kinematic evolution: a slow rise, an acceleration, and a deceleration. In the early slow rise, extreme-ultraviolet brightenings appear at the expected null point above the filament and are connected to the outer polarities by the hot loops, indicating the occurrence of a breakout reconnection. Subsequently, the filament is accelerated outward, accompanied by the formation of low-lying high-temperature post-flare loops (>15 MK), complying with the standard flare model. However, after 2–3 minutes, the erupting filament starts to decelerate and is finally confined in the corona. The important finding is that the confinement is closely related to an external reconnection as evidenced by the formation of high-lying large-scale hot loops (>10 MK) with their brightened footpoints at the outer polarities, the fragmentation and subsequent falling of the filament along the newly formed large-scale loops, as well as a hard X-ray source close to one of the outer footpoint brightenings. We propose that, even though the initial breakout reconnection and subsequent flare reconnection commence and accelerate the filament eruption, the following external reconnection between the erupting flux rope and overlying field, as driven by the upward filament eruption, causes the eruption to finally fail, as validated by the numerical simulation of a failed flux rope eruption. [ABSTRACT FROM AUTHOR]

The eruption of magnetic flux ropes (MFRs), often taking filaments together, leads to coronal mass ejections (CMEs). Theoretical studies propose that both the resistive magnetic reconnection and the ideal instability of an MFR system can release magnetic-free energy and accelerate CMEs (i.e., MFRs or filaments) during eruptions. Observations find that the full kinematic evolution of CMEs usually undergoes three phases: the initiation phase, impulsive acceleration phase, and propagation phase. The impulsive acceleration phase often starts and ceases simultaneously with the flare onset time and peak time, respectively. This synchronization can be explained by the positive feedback relationship between the acceleration of CMEs and flare magnetic reconnection, and suggests that the reconnection has the dominant contribution to the acceleration of CMEs. It is rare to see strong evidence that supports the dominant contribution of ideal instability to the acceleration. In this paper, we report an intriguing filament eruption that occurred on 2011 May 11. Its complete acceleration is well recorded by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. The kinematic analysis shows that the impulsive acceleration phase starts and ceases obviously earlier than the flare onset time and peak time, respectively, which means a complete asynchronization between the impulsive acceleration phase and flare rise phase, and strongly supports that the ideal instability plays a dominant role in this impulsive acceleration. Furthermore, the accompanied flare is a B-class one, also implying that the contribution of reconnection is negligible in the energy release process. [ABSTRACT FROM AUTHOR]

Although the magnetic field structures of solar filaments have been studied for several decades, the detailed evolution of the structure around a filament prior to its eruption is rarely observed. On 2021 October 28 in AR 12887, a major solar flare (X1.0 class) occurred at 15:35 UT. Based on the Solar Dynamics Observatory high-spatial-resolution observations, we find this flare is associated with the eruption of two filaments, namely F1 and F2. The two filaments are initially independent. The western leg (WLEG) of F1 approaches the northern leg of F2, due to the continuous movement and rotation of the magnetic field in which the WLEG roots in. We find first that there are some threads wrapping the WLEG. Brightening and bidirectionally plasmoid flows that originate from a brightening are detected in these threads, then the threads disappear, and the two filaments connect. NLFFF extrapolation reveals that there is a toroidal magnetic structure enveloping the WLEG and corresponding spatially to the threads. It is expected that a filament is enveloped by toroidal magnetic fields. According to the observations and extrapolation, we suggest that these threads represent the toroidal magnetic fields wrapping the WLEG. This paper provides new details about the dynamics of the toroidal magnetic fields. Magnetic reconnection takes place in the toroidal fields and thus destroys the fields, then F1 and F2 connect, and subsequently, the two filaments erupt and the flare occurs. [ABSTRACT FROM AUTHOR]

We report an M9.3 flare and filaments activities from NOAA Active Region 11261 that are strongly modulated by the 3D magnetic skeleton. Magnetic field extrapolation from the vector magnetic field suggests complex magnetic connectivity and the existence of a high coronal null point southeast of the active region. A small filament over the inversed V-shaped polarity inversion line erupted and resulted in the M9.3 flare associated with a weak ejection in the EUV hot channel and the formation of a relatively large filament. Both the weak ejection and the eruption of the large filament were toward the southeast. Comparative analyses have disclosed the following new facts. First, the trajectory of looptop hard X-ray emission provides solid evidence that the magnetic reconnection site propagated up toward the coronal null point as the flare and filaments erupted. Second, the EVU observations show coronal mass ejection-like eruption features in the ejection region of the magnetic skeleton. Third, the closed fan confined the west end of the large filament and the corresponding flare ribbons. We demonstrate a spatiotemporal relationship between the magnetic skeleton and the flare filament activity. We conclude that the magnetic skeleton can modulate and determine almost all the characteristics of the studied activity in the corresponding scale.

Solar filaments can undergo eruptions that result in the formation of coronal mass ejections, which can significantly impact planetary space environments. Observations of eruptions involving polar crown filaments, situated in the polar regions of the Sun, are limited. In this study, we report a polar crown filament eruption (SOL2023-06-12), characterized by fast downflows below the filament. The downflows appear instantly after the onset of the filament eruption and persist for approximately 2 hr, exhibiting plane-of-sky velocities ranging between 92 and 144 km s ^−1 . They originate from the leading edge of the filament, and no clear acceleration is observed. Intriguingly, these downflows appear at two distinct sites, symmetrically positioned at the opposite ends of the conjugate flare ribbons. Based on the observations, we propose that the filament might be supported by a magnetic flux rope (MFR), and these downflows possibly occur along the legs of the MFR. The downflows likely result from continuous reconnections between the MFR and the overlying magnetic field structures and could either be reconnection outflows or redirected filament materials. We also observed horizontal drifting of the locations of downflows, which might correspond to the MFR’s footpoint drifting. This type of downflow can potentially be utilized to track the footpoints of MFRs during eruptions.

Minifilament eruptions producing small jets and microflares have mostly been studied based on coronal observations at extreme-ultraviolet and X-ray wavelengths. This study presents chromospheric plasma diagnostics of a quiet-Sun minifilament of size ∼ 2″ × 5″ with a sigmoidal shape and an associated microflare observed on 2021 August 7 17:00 UT using high temporal and spatial resolution spectroscopy from the Fast Imaging Solar Spectrograph (FISS) and high-resolution magnetograms from the Near InfraRed Imaging Spectropolarimeter (NIRIS) installed on the 1.6 m Goode Solar Telescope at Big Bear Solar Observatory. Using FISS H α and Ca ii 8542 Å line spectra at the time of the minifilament activation we determined a temperature of 8600 K and a nonthermal speed of 7.9 km s ^−1 . During the eruption, the minifilament was no longer visible in the Ca ii 8542 Å line, and only the H α line spectra were used to find the temperature of the minifilament, which reached 1.2 × 10 ^4 K and decreased afterward. We estimated thermal energy of 3.6 × 10 ^24 erg from the maximum temperature and kinetic energy of 2.6 × 10 ^24 erg from the rising speed (18 km s ^−1 ) of the minifilament. From the NIRIS magnetograms we found small-scale flux emergence and cancellation coincident with the minifilament eruption, and the magnetic energy change across the conjugate footpoints reaches 7.2 × 10 ^25 erg. Such spectroscopic diagnostics of the chromospheric minifilament complement earlier studies of minifilament eruptions made using coronal images.

Prominence bubbles, the dark arch-shaped voids below quiescent prominences, are generally believed to be caused by the interaction between the prominences and the slowly emerging or quasi-stable underlying magnetic loops. However, this scenario could not explain some short-lived bubbles with extremely dynamic properties of evolution. Based on high-resolution H α observations, here we propose that bubbles should be classified into two categories according to their dynamic properties: quasi-steady Type-I bubbles and transient Type-II bubbles. Type-I bubbles could remain relatively stable and last for several hours, indicating the existence of a quasi-stable magnetic topology, while Type-II bubbles grow and collapse quickly within 1 hr without stability duration, which are usually associated with erupting minifilaments. Analysis of several typical Type-II bubbles from different views, especially including an on-disk event, reveals that Type-II bubbles quickly appear and expand at a velocity of ∼5–25 km s ^−1 accompanied by an erupting minifilament below. The minifilament’s rising velocity is slightly larger than that of the Type-II bubbles’ boundary, which will lead to the collision with each other in a short time, subsequent collapse of Type-II bubbles, and formation of a large plume into the above prominence. We also speculate that only if the angle between the axis of the erupting minifilament and the line of sight is large enough, the interaction between the erupting minifilament and the overlying prominence could trigger a Type-II bubble with a typical arch-shaped but quickly expanding bright boundary.

Minifilaments are widespread small-scale structures in the solar atmosphere. To better understand their formation and eruption mechanisms, we investigate the entire life of a sigmoidal minifilament located below a large quiescent filament observed by Big Bear Solar Observatory/Goode Solar Telescope on 2015 August 3. The H α structure initially appears as a group of arched threads, then transforms into two J-shaped arcades, and finally forms a sigmoidal shape. Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly observations in 171 Å show that two coronal jets occur around the southern footpoint of the minifilament before the minifilament eruption. The minifilament eruption starts from the southern footpoint, then interacts with the overlying filament and fails. The aforementioned observational changes correspond to three episodes of flux cancellations observed by SDO/Helioseismic and Magnetic Imager. Unlike previous studies, the flux cancellation occurs between the polarity where the southern footpoint of the minifilament is rooted and an external polarity. We construct two magnetic field models before the eruption using the flux rope insertion method and find a hyperbolic flux tube above the flux cancellation site. The observation and modeling results suggest that the eruption is triggered by the external magnetic reconnection between the core field of the minifilament and the external fields due to flux cancellations. This study reveals a new triggering mechanism for minifilament eruptions and a new relationship between minifilament eruptions and coronal jets.

Solar quiet- and coronal-hole region coronal jets frequently clearly originate from erupting minifilaments, but active-region jets often lack an obvious erupting-minifilament source. We observe a coronal-jet-productive active region (AR), AR 12824, over 2021 May 22 0–8 UT, primarily using Solar Dynamics Observatory (SDO) Atmospheric Imaging Array (AIA) EUV images and SDO/Helioseismic and Magnetic Imager magnetograms. Jets were concentrated in two locations in the AR: on the south side and on the northwest side of the AR’s lone large sunspot. The south-location jets are oriented so that we have a clear view of the jets’ origin low in the atmosphere: their source is clearly minifilaments erupting from locations showing magnetic flux changes/cancelations. After erupting a projected distance ≲5″ away from their origin site, the minifilaments erupt outward onto far-reaching field as part of the jet’s spire, quickly losing their minifilament character. In contrast, the northwest-location jets show no clear erupting minifilament, but the source site of those jets are obscured along our line of sight by absorbing chromospheric material. EUV and magnetic data indicate that the likely source sites were ≳15″ from where the we first see the jet spire; thus, an erupting minifilament would likely lose its minifilament character before we first see the spire. We conclude that such AR jets could work like non-AR jets, but the erupting-minifilament jet source is often hidden by obscuring material. Another factor is that magnetic eruptions making some AR jets carry only a harder-to-detect comparatively thin (∼1″–2″) minifilament “strand.”

We investigate a quiescent filament that erupted on 2013 August 2; the eruption was observed in EUV and H α by the Solar Dynamics Observatory and GONG. After a B9.7 flare in the nearby active region, the dark filament materials near its eastern footpoint start to move in the direction of eruption, and are followed by a counterclockwise rotation identified as the motion of a combination of dark and bright filament materials. Then the entire filament rises up and keeps rotating in a clockwise direction during the eruption. More interestingly, the filament exhibits an unusual two-helix structure near its western footpoint during the eruption, which indicates the existence of a highly twisted flux rope. This hypothesis is confirmed by magnetic field modeling using the flux rope insertion method. In the best-fit unstable model, the lower limits of the estimated maximum and average twist numbers of the erupting flux rope reach 7.5 π and 4 π , which suggests that kink instability plays an important role in the eruption. During these magnetically coupled sympathetic eruptions, the highly twisted filament under the western lobe of a pseudo-streamer-like structure becomes unstable and erupts due to the removal of confinement by magnetic reconnection at the overlying hyperbolic flux tube, which is initiated by the B9.7 flare in the nearby active region. The initial filament motion occurs at the more unstable eastern footpoint, where the surrounding fields are weaker and decrease with height more rapidly.

When and where the magnetic field energy is released and converted in eruptive solar flares remains an outstanding topic in solar physics. To shed light on this question, here we report multiwavelength observations of a C9.4-class eruptive limb flare that occurred on 2017 August 20. The flare, accompanied by a magnetic flux rope eruption and a white light coronal mass ejection, features three post-impulsive X-ray and microwave bursts immediately following its main impulsive phase. For each burst, both microwave and X-ray imaging suggest that the nonthermal electrons are located in the above-the-loop-top region. Interestingly, contrary to many other flares, the peak flux of the three post-impulsive microwave and X-ray bursts shows an increase for later bursts. Spectral analysis reveals that the sources have a hardening spectral index, suggesting a more efficient electron acceleration into the later post-impulsive bursts. We observe a positive correlation between the acceleration of the magnetic flux rope and the nonthermal energy release during the post-impulsive bursts in the same event. Intriguingly, different from some other eruptive events, this correlation does not hold for the main impulse phase of this event, which we interpret as energy release due to the tether-cutting reconnection before the primary flux rope acceleration occurs. In addition, using footpoint brightenings at conjugate flare ribbons, a weakening reconnection guide field is inferred, which may also contribute to the hardening of the nonthermal electrons during the post-impulsive phase.

Double-decker filaments and their eruptions have been widely observed in recent years, but their physical formation mechanism is still unclear. Using high spatiotemporal resolution, multi-wavelength observations taken by the New Vacuum Solar Telescope and the Solar Dynamics Observatory, we show the formation of a double-decker pair of flux rope system by two successive tether-cutting eruptions in a bipolar active region. Due to the combined effect of photospheric shearing and convergence motions around the active region’s polarity inversion line (PIL), the arms of two overlapping inverse-S-shaped short filaments reconnected at their intersection, which created a simultaneous upward-moving magnetic flux rope (MFR) and a downward-moving post-flare-loop (PFL) system striding the PIL. Meanwhile, four bright flare ribbons appeared at the footpoints of the newly formed MFR and the PFL. As the MFR rose, two elongated flare ribbons connected by a relatively larger PFL appeared on either side of the PIL. After a few minutes, another MFR formed in the same way at the same location and then erupted in the same direction as the first one. Detailed observational results suggest that the eruption of the first MFR might experienced a short pause before its successful eruption, while the second MFR was a failed eruption. This implies that the two newly formed MFRs might reach a new equilibrium at relatively higher heights for a while, which can be regarded as a transient double-decker flux rope system. The observations can well be explained by the tether-cutting model, and we propose that two successive confined tether-cutting eruptions can naturally produce a double-decker flux rope system, especially when the background coronal magnetic field has a saddle-like distribution of magnetic decay index profile in height.

This paper presents a multiwavelength Sun-as-a-star analysis of the M8.7 flare on 2022 October 2, which was associated with a filament eruption and the subsequent coronal mass ejection. The Sun-as-a-star analysis was performed using H α data taken by Solar Dynamics Doppler Imager on board the Solar Magnetic Activity Research Telescope at Hida Observatory, Kyoto University, and full-disk integrated extreme ultraviolet (EUV) spectra taken by the Extreme ultraviolet Variability Experiment (EVE) on board the Solar Dynamics Observatory. The Sun-as-a-star H α spectra showed blueshifted absorption corresponding to the filament eruption. Furthermore, the EVE O v 629.7 Å spectra showed blueshifted brightening, which can also be attributed to the filament eruption. Even when the blueshifted absorption became almost invisible in the Sun-as-a-star H α spectra, the O v blueshifted brightening up to −400 km s ^−1 was still clearly visible. This result indicates that even when the shifted components—which are expected to originate from stellar eruptions—become almost invisible in the spatially integrated stellar H α spectra, the erupting materials may still be present and observable in EUV spectra. Additionally, the Sun-as-a-star H α and O v spectra exhibited redshifted absorption and brightening, respectively, during the decay phase of the flare. These components probably originate from the post-flare loops, providing clues to the multitemperature nature of the post-flare loops in the spatially integrated observation. Our Sun-as-a-star results suggest that the combination of H α and EUV lines allows the investigation of the multitemperature structure and temporal development of stellar active phenomena even in spatially integrated spectra.

Similar to the cases of anemone jets, two-sided loop solar jets can also be produced by either flux emergence from the solar interior or small-scale filament eruptions. Using high-quality data from the Solar Dynamics Observatory, we have analyzed a two-sided loop solar jet triggered by the eruption of a small filament. The jet occurred in a pre-existing big filament channel. The detailed processes involved in the eruption of the small filament, the interaction between the erupted filament and the big filament channel, and the launch of the two-sided loop jet are presented. The observations further revealed notable asymmetry between the two branches of the jet spire: the northeastern branch is narrow and short, while the southern branch is wide and long and accompanied by discernible untwisting motions. We explored the unique appearance of the jet by employing the method of local potential field extrapolation to calculate the coronal magnetic field configuration around the jet. The photospheric magnetic flux below the small filament underwent cancellation for approximately 7 hr before the filament eruption, and the negative flux near the southern footpoint of the filament decreased by about 56% during this interval. Therefore, we propose that the primary photospheric driver of the filament eruption and the associated two-sided loop jet in this event is flux cancellation rather than flux emergence.

On 2022 February 15, an impressive filament eruption was observed off the solar eastern limb from three remote-sensing viewpoints, namely, Earth, STEREO-A, and Solar Orbiter. In addition to representing the most-distant observed filament at extreme ultraviolet wavelengths—captured by Solar Orbiter's field of view extending to above 6 R _⊙ —this event was also associated with the release of a fast (∼2200 km s ^−1 ) coronal mass ejection (CME) that was directed toward BepiColombo and Parker Solar Probe. These two probes were separated by 2° in latitude, 4° in longitude, and 0.03 au in radial distance around the time of the CME-driven shock arrival in situ. The relative proximity of the two probes to each other and the Sun (∼0.35 au) allows us to study the mesoscale structure of CMEs at Mercury's orbit for the first time. We analyze similarities and differences in the main CME-related structures measured at the two locations, namely, the interplanetary shock, the sheath region, and the magnetic ejecta. We find that, despite the separation between the two spacecraft being well within the typical uncertainties associated with determination of CME geometric parameters from remote-sensing observations, the two sets of in situ measurements display some profound differences that make understanding the overall 3D CME structure particularly challenging. Finally, we discuss our findings within the context of space weather at Mercury's distance and in terms of the need to investigate solar transients via spacecraft constellations with small separations, which has been gaining significant attention during recent years.

Flares are intense explosions on the solar and stellar surfaces, and solar flares are sometimes accompanied by filament or prominence eruptions. Recently, a large filament eruption associated with a superflare on a solar-type star EK Dra was discovered for the first time. The absorption of the H α spectrum initially exhibited a blueshift with the velocity of 510 km s ^−1 , and decelerated in time probably due to gravity. Stellar coronal mass ejections (CMEs) were thought to occur, although the filament eruption did not exceed the escape velocity under the surface gravity. To investigate how such a filament eruption can occur and whether CMEs are associated with the filament eruption or not, we perform a one-dimensional hydrodynamic simulation of the flow along an expanding magnetic loop emulating a filament eruption under adiabatic and unsteady conditions. The loop configuration and expanding velocity normal to the loop are specified in the configuration parameters, and we calculate the line-of-sight velocity of the filament eruption using the velocities along and normal to the loop. We find that (i) the temporal variations of the H α spectrum for EK Dra can be explained by a falling filament eruption in the loop with longer time and larger spatial scales than that of the Sun, and (ii) the stellar CMEs are also thought to be associated with the filament eruption from the superflare on EK Dra, because the rarefied loop unobserved in the H α spectrum needs to expand faster than the escape velocity, whereas the observed filament eruption does not exceed the escape velocity.

We consider small-scale jetlike events that might make the solar wind, as has been suggested in recent studies. We show that the events referred to as “coronal jets” and as “jetlets” both fall on a power-law distribution that also includes large-scale eruptions and spicule-sized features; all of the jetlike events could contribute to the solar wind. Based on imaging and magnetic field data, it is plausible that many or most of these events might form by the same mechanism: Magnetic flux cancelation produces small-scale flux ropes, often containing a cool-material minifilament. This minifilament/flux rope erupts and reconnects with adjacent open coronal field, along which “plasma jets” flow and contribute to the solar wind. The erupting flux ropes can contain twist that is transferred to the open field, and these become Alfvénic pulses that form magnetic switchbacks, providing an intrinsic connection between switchbacks and the production of the solar wind.

We perform a data-constrained simulation with the zero- β assumption to study the mechanisms of strong rotation and failed eruption of a filament in active region 11474 on 2012 May 5 observed by Solar Dynamics Observatory and Solar Terrestrial Relations Observatory. The initial magnetic field is provided by nonlinear force-free field extrapolation, which is reconstructed by the regularized Biot–Savart laws and magnetofrictional method. Our simulation reproduces most observational features very well, e.g., the filament large-angle rotation of about 130°, the confined eruption, and the flare ribbons, allowing us to analyze the underlying physical processes behind observations. We discover two flux ropes in the sigmoid system, an upper flux rope (MFR1) and a lower flux rope (MFR2), which correspond to the filament and hot channel in observations, respectively. Both flux ropes undergo confined eruptions. MFR2 grows by tether-cutting reconnection during the eruption. The rotation of MFR1 is related to the shear-field component along the axis. The toroidal field tension force and the nonaxisymmetry forces confine the eruption of MFR1. We also suggest that the mutual interaction between MFR1 and MFR2 contributes to the large-angle rotation and the eruption failure. In addition, we calculate the temporal evolution of the twist and writhe of MFR1, which is a hint of probable reversal rotation.

Young solar-type stars frequently produce superflares, serving as a unique window into the young Sun-Earth environments. Large solar flares are closely linked to coronal mass ejections (CMEs) associated with filament/prominence eruptions, but observational evidence for stellar superflares remains scarce. Here, we present a 12-day, multiwavelength campaign observation of young solar-type star EK Draconis (G1.5V, 50–120 Myr age) utilizing the Transiting Exoplanet Survey Satellite, the Neutron star Interior Composition ExploreR, and the Seimei telescope. The star has previously exhibited blueshifted H α absorptions as evidence for a filament eruption associated with a superflare. Our simultaneous optical and X-ray observations identified three superflares of 1.5 × 10 ^33 –1.2 × 10 ^34 erg. We report the first discovery of two prominence eruptions on a solar-type star, observed as blueshifted H α emissions at speeds of 690 and 430 km s ^−1 and masses of 1.1 × 10 ^19 and 3.2 × 10 ^17 g, respectively. The faster, massive event shows a candidate of post-flare X-ray dimming with the amplitude of up to ∼10%. Several observational aspects consistently point to the occurrence of a fast CME associated with this event. The comparative analysis of the estimated length scales of flare loops, prominences, possible dimming region, and starspots provides the overall picture of the eruptive phenomena. Furthermore, the energy partition of the observed superflares in the optical and X-ray bands is consistent with flares from the Sun, M-dwarfs, and close binaries, yielding the unified empirical relations. These discoveries provide profound implications of the impact of these eruptive events on early Venus, Earth, and Mars and young exoplanets.

Solar coronal jets are frequently occurring collimated ejections of solar plasma, originating from magnetically mixed polarity locations on the Sun of size scale comparable to that of a supergranule. Many, if not most, coronal jets are produced by eruptions of small-scale filaments, or minifilaments, whose magnetic field reconnects both with itself and also with surrounding coronal field. There is evidence that minifilament eruptions are a scaled-down version of typical filament eruptions that produce solar flares and coronal mass ejections (CMEs). Moreover, the magnetic processes building up to and triggering minifilament eruptions, which is often flux cancelation, might similarly build up and trigger the larger filaments to erupt. Thus, detailed study of coronal jets will inform us of the physics leading to, triggering, and driving the larger eruptions. Additionally, such studies potentially can inform us of smaller-scale coronal-jet-like features, such as jetlets and perhaps some spicules, that might work the same way as coronal jets. We propose a high-resolution (∼0″. 1 pixels), high-cadence (∼5 s) EUV-solar-imaging mission for the upcoming decades, that would be dedicated to observations of features of the coronal-jet size scale, and smaller-scale solar features produced by similar physics. Such a mission could provide invaluable insight into the operation of larger features such as CMEs that produce significant Space Weather disturbances, and also smaller-scale features that could be important for coronal heating, solar wind acceleration, and heliospheric features such as the magnetic switchbacks that are frequently observed in the solar wind.

We report a failed solar filament eruption that involves external magnetic reconnection in a quadrupolar magnetic configuration. The evolution exhibits three phases of kinematic evolution: a slow rise, an acceleration, and a deceleration. In the early slow rise, extreme-ultraviolet brightenings appear at the expected null point above the filament and are connected to the outer polarities by the hot loops, indicating the occurrence of a breakout reconnection. Subsequently, the filament is accelerated outward, accompanied by the formation of low-lying high-temperature post-flare loops (>15 MK), complying with the standard flare model. However, after 2–3 minutes, the erupting filament starts to decelerate and is finally confined in the corona. The important finding is that the confinement is closely related to an external reconnection as evidenced by the formation of high-lying large-scale hot loops (>10 MK) with their brightened footpoints at the outer polarities, the fragmentation and subsequent falling of the filament along the newly formed large-scale loops, as well as a hard X-ray source close to one of the outer footpoint brightenings. We propose that, even though the initial breakout reconnection and subsequent flare reconnection commence and accelerate the filament eruption, the following external reconnection between the erupting flux rope and overlying field, as driven by the upward filament eruption, causes the eruption to finally fail, as validated by the numerical simulation of a failed flux rope eruption.

The eruption of magnetic flux ropes (MFRs), often taking filaments together, leads to coronal mass ejections (CMEs). Theoretical studies propose that both the resistive magnetic reconnection and the ideal instability of an MFR system can release magnetic-free energy and accelerate CMEs (i.e., MFRs or filaments) during eruptions. Observations find that the full kinematic evolution of CMEs usually undergoes three phases: the initiation phase, impulsive acceleration phase, and propagation phase. The impulsive acceleration phase often starts and ceases simultaneously with the flare onset time and peak time, respectively. This synchronization can be explained by the positive feedback relationship between the acceleration of CMEs and flare magnetic reconnection, and suggests that the reconnection has the dominant contribution to the acceleration of CMEs. It is rare to see strong evidence that supports the dominant contribution of ideal instability to the acceleration. In this paper, we report an intriguing filament eruption that occurred on 2011 May 11. Its complete acceleration is well recorded by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. The kinematic analysis shows that the impulsive acceleration phase starts and ceases obviously earlier than the flare onset time and peak time, respectively, which means a complete asynchronization between the impulsive acceleration phase and flare rise phase, and strongly supports that the ideal instability plays a dominant role in this impulsive acceleration. Furthermore, the accompanied flare is a B-class one, also implying that the contribution of reconnection is negligible in the energy release process.

Although the magnetic field structures of solar filaments have been studied for several decades, the detailed evolution of the structure around a filament prior to its eruption is rarely observed. On 2021 October 28 in AR 12887, a major solar flare (X1.0 class) occurred at 15:35 UT. Based on the Solar Dynamics Observatory high-spatial-resolution observations, we find this flare is associated with the eruption of two filaments, namely F1 and F2. The two filaments are initially independent. The western leg (WLEG) of F1 approaches the northern leg of F2, due to the continuous movement and rotation of the magnetic field in which the WLEG roots in. We find first that there are some threads wrapping the WLEG. Brightening and bidirectionally plasmoid flows that originate from a brightening are detected in these threads, then the threads disappear, and the two filaments connect. NLFFF extrapolation reveals that there is a toroidal magnetic structure enveloping the WLEG and corresponding spatially to the threads. It is expected that a filament is enveloped by toroidal magnetic fields. According to the observations and extrapolation, we suggest that these threads represent the toroidal magnetic fields wrapping the WLEG. This paper provides new details about the dynamics of the toroidal magnetic fields. Magnetic reconnection takes place in the toroidal fields and thus destroys the fields, then F1 and F2 connect, and subsequently, the two filaments erupt and the flare occurs.

Type II radio bursts are often associated with coronal shocks that are typically driven by coronal mass ejections (CMEs) from the Sun. Here we conduct a case study of a type II radio burst that is associated with a C4.5-class flare and a blowout jet, but without the presence of a CME. The blowout jet is observed near the solar disk center in the extreme-ultraviolet (EUV) passbands with different characteristic temperatures. Its evolution involves an initial phase and an ejection phase with a velocity of 560 ± 87 km s ^−1 . Ahead of the jet front, an EUV wave propagates at a projected velocity of ∼403 ± 84 km s ^−1 in the initial stage. The velocity of the type II radio burst is estimated to be ∼641 km s ^−1 , which corresponds to the shock velocity against the coronal density gradient. The EUV wave and the type II radio burst are closely related to the ejection of the blowout jet, suggesting that both are likely the manifestation of a coronal shock driven by the ejection of the blowout jet. The type II radio burst likely starts lower than those associated with CMEs. The combination of the velocities of the radio burst and the EUV wave yields a modified shock velocity at ∼757 km s ^−1 . The Alfvén Mach number is in the range of 1.09–1.18, implying that the shock velocity is 10%–20% larger than the local Alfvén velocity.

Coronal mass ejections (CMEs) are violent ejections of magnetized plasma from the Sun that can trigger geomagnetic storms, endanger satellite operations, and destroy electrical infrastructures on the Earth. After systematically searching Sun-as-a-star spectra observed by the Extreme Ultraviolet Variability Experiment on board the Solar Dynamics Observatory (SDO) from 2010 May to 2022 May, we identified eight CMEs associated with flares and filament eruptions by analyzing the blue-wing asymmetry of the O iii 52.58 nm line profiles. Combined with images simultaneously taken by the 30.4 nm channel of the Atmospheric Imaging Assembly on board SDO, the full velocity and propagation direction for each of the eight CMEs are derived. We find a strong correlation between geomagnetic indices ( Kp and Dst) and the angle between the CME propagation direction and the Sun–Earth line, suggesting that Sun-as-a-star spectroscopic observations at extreme-ultraviolet wavelengths can potentially help to improve the prediction accuracy of the geoeffectiveness of CMEs. Moreover, an analysis of synthesized long-exposure Sun-as-a-star spectra implies that it is possible to detect CMEs from other stars through blue-wing asymmetries or blueshifts of spectral lines.

We present the first results of the hybrid data-driven magnetofrictional (MF) and data-constrained magnetohydrodynamic (MHD) simulations of solar active region NOAA 11158, which produced an X-class flare and coronal mass ejection on 2011 February 15. First, we apply the MF approach to build the coronal magnetic configuration corresponding to the SDO/HMI photospheric magnetograms by using the JSOC PDFI_SS electric field inversions at the bottom boundary of the simulation domain. We then use the preeruptive MF state at about 1.5 hr before the observed X-class flare as the initial state for the MHD simulation, assuming a stratified polytropic solar corona. The MHD run shows that the initial magnetic configuration containing twisted magnetic fluxes and a three-dimensional (3D) magnetic null point is out of equilibrium. We find the eruption of a complex magnetic structure consisting of two magnetic flux ropes, as well as the development of flare ribbons, with their morphology being in good agreement with observations. We conclude that the combination of the data-driven MF and data-constrained MHD simulations is a useful practical tool for understanding the 3D magnetic structures of real solar ARs that are unobservable otherwise.

Coronal mass ejections (CMEs) that originate from pseudostreamers, which separate coronal holes of the same magnetic polarity, are characterized by a narrow (∼5°–30°), fan-shaped appearance in white-light coronagraph images. Despite this striking morphological similarity, a wide variety of underlying eruptions are observed, including not only coronal jets, but also larger-scale filament eruptions, footpoint flares, and even extreme-ultraviolet (EUV) waves that reflect off the coronal hole boundaries. Using EUV images recorded by the Solar Dynamics Observatory during the early rising phase of cycle 25 (2020–2022), we describe examples of the different kinds of underlying eruptions and identify the corresponding fan-like ejections in Large Angle and Spectrometric Coronagraph images. We attribute the narrowness of the white-light CMEs to lateral confinement by the like-polarity open flux surrounding the pseudostreamer and point out that, although the multipolar topology facilitates the “breakout” of material through the cusp region, it also tends to inhibit the eruption of the pseudostreamer as a whole. We also note that the self-similar “continuum” formed by the pseudostreamer mass ejections does not include the larger, more space-weather-effective CMEs associated with helmet streamers, which are surrounded by open flux of opposite polarity and undergo much greater lateral expansion.

We use observations taken with a novel solar telescope spectroheliograph to investigate the association between the early filament rise and coronal mass ejections (CMEs). The instrument allows the H _α full line profile to be registered in each pixel of the solar disk with a time cadence of about 1 minute. We analyze observations of three eruptive filaments in 2021 and show that patrol telescope measurements of the H _α line profile with a spectral resolution R = 40,000 can be used to detect precursors of filament eruptions with an advance of several hours and to estimate the initial acceleration of CMEs. Our limited case study also suggests that while detecting an early filament rise may serve as an indicator of a possible eruption, the filament ascent alone is not a definite sign of a CME.

Different from the classical emerging-flux model for solar jets, recent studies proposed that the great majority of solar coronal jets are triggered by minifilament eruptions and two magnetic reconnection processes should take place during the course, named as external reconnection (breakout reconnection) and internal reconnection (flare reconnection). With the excellent data of the Solar Dynamics Observatory, we present the observational signatures of these two magnetic reconnection processes during a solar coronal jet that occurred in a huge coronal hole of northern hemisphere. The jet was triggered by the eruption of a minifilament that located at a coronal bright point in the coronal hole. Weak bidirectional outflows were observed when the erupting minifilament approached the ambient open field, ejecting along the triggered jet spire and the jet base simultaneously. In addition, a flare current sheet occurred after the eruption of the minifilament, connecting the jet spire and the jet bright point (or flare). We suggest the occurrence of the weak bidirectional outflows and the flare current sheet correspond to the external and the internal reconnections, respectively. Prior to the eruption of the minifilament and the jet, photospheric magnetic flux cancellation maintained for more than 7 hr in the source region, and the positive flux decreased for about 28.6% during this period. So, consistent with the recent observations, the trigger mechanism of the minifilament eruption and the following jet in this event may be flux cancellation rather than flux emergence.

To better understand the physical connections in sympathetic solar eruptions, we investigated the interaction between two nearby filaments and their successive partial eruptions in the active region (AR) NOAA 12866 on 2021 September 9 by using data from the Solar Dynamics Observatory and the New Vacuum Solar Telescope. Based on H α and extreme ultraviolet observations, we found that the right part of one filament (F1) became active first and experienced an obvious rolling motion. Then the whole body of the filament became wider and expanded toward another filament (F2). They collided with each other, and the interaction between them was accompanied by the brightening and bidirectional flows that appeared between them. This implies that magnetic reconnection occurred between the threads of two filaments. The interaction resulted in a rightward motion of F2 at first, and then its activation, and finally part of it erupted. Furthermore, when the erupted F2 deflected rapidly toward the middle part of F1, the left part of F1 erupted with its overlying magnetic fields pushed by F2. These observational results imply that these successive eruptions within a short time are physically linked, and this was caused by the interaction of the filaments. Nonlinear force-free field extrapolation reveals that the magnetic structure of the filament F1 was composed of several magnetic flux ropes with different twists. These results further advance our understanding of partial filament eruptions and sympathetic solar eruptions.

We often find spectral signatures of chromospheric cold plasma ejections accompanied by flares in a wide range of spatial scales in the solar and stellar atmospheres. However, the relationship between physical quantities (such as mass, kinetic energy, and velocity) of cold ejecta and flare energy has not been investigated in a unified manner for the entire range of flare energies to date. This study analyzed the spectra of cold plasma ejections associated with small-scale flares and solar flares (energy 10 ^25 –10 ^29 erg) to supply smaller energy samples. We performed H α imaging spectroscopy observation by the Solar Dynamics Doppler Imager on the Solar Magnetic Activity Research Telescope. We determined the physical quantities of the ejecta by cloud model fitting to the H α spectrum. We determined the flare energy by differential emission measure analysis using the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory for small-scale flares and by estimating the bolometric energy for large-scale flares. As a result, we found that the ejection mass M and the total flare energy E _tot follow a relation of $M\propto {E}_{\mathrm{tot}}^{2/3}$ . We show that the scaling law derived from a simple physical model explains the solar and stellar observations with a coronal magnetic field strength as a free parameter. We also found that the kinetic energy and velocity of the ejecta correlate with the flare energy. These results suggest a common mechanism driven by magnetic fields to cause cold plasma ejections with flares on the Sun and stars.

We report a detailed analysis of a failed eruption and flare in active region 12018 on 2014 April 3 using multiwavelength observations from the Solar Dynamics Observatory/Atmospheric Imaging Assembly, IRIS, STEREO, and Hinode/Solar Optical Telescope. At least four jets were observed to emanate from the cusp of this small active region (large bright point) with a null-point topology during the 2 hr prior to the slow rise of a filament. During the filament slow rise multiple plasma blobs were seen, most likely formed in a null-point current sheet near the cusp. The subsequent filament eruption, which was outside the IRIS field of view, was accompanied by a flare but remained confined. During the explosive flare reconnection phase, additional blobs appeared repetitively and moved bidirectionally within the flaring region below the erupting filament. The filament kinked, rotated, and underwent leg–leg reconnection as it rose, yet it failed to produce a coronal mass ejection. Tiny jet-like features in the fan loops were detected during the filament slow rise/preflare phase. We interpret them as signatures of reconnection between the ambient magnetic field and the plasmoids leaving the null-point sheet and streaming along the fan loops. We contrast our interpretation of these tiny jets, which occur within the large-scale context of a failed filament eruption, with the local nanoflare-heating scenario proposed by Antolin et al.

Coronal jets are short-lived eruptive features commonly observed in polar coronal holes and are thought to play a key role in the transfer of mass and energy into the solar corona. We describe unique contemporaneous observations of a coronal blowout jet seen by the Extreme Ultraviolet Imager (EUI) on board the Solar Orbiter (SO) spacecraft and the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). The coronal jet erupted from the south polar coronal hole, and was observed with high spatial and temporal resolution by both instruments. This enabled identification of the different stages of a breakout reconnection process producing the observed jet. We find bulk plasma flow kinematics of ∼100–200 km s ^−1 across the lifetime of its observed propagation, with a distinct kink in the jet where it impacted and was subsequently guided by a nearby polar plume. We also identify a faint faster feature ahead of the bulk plasma motion propagating with a velocity of ∼715 km s ^−1 , which we attribute to untwisting of newly reconnected field lines during the eruption. A differential emission measure (DEM) analysis using the SDO/AIA observations revealed a very weak jet signal, indicating that the erupting material was likely much cooler than the coronal passbands used to derive the DEM. This is consistent with the very bright appearance of the jet in the Ly α passband observed by SO/EUI. The DEM was used to estimate the radiative thermal energy of the source region of the coronal jet, finding a value of ∼2 × 10 ^24 erg, comparable to the energy of a nanoflare.

Solar filament eruptions often show complex and dramatic geometric deformation that is highly relevant to the underlying physical mechanism triggering the eruptions. It is well known that the writhe of filament axes is a key parameter characterizing its global geometric deformation, but a quantitative investigation of the development of writhe during its eruption is still lacking. Here we introduce the Writhe Application Toolkit, which can be used to characterize accurately the topology of filament axes. This characterization is achieved based on the reconstruction and writhe number computation of three-dimensional paths of the filament axes from dual-perspective observations. We apply this toolkit to four dextral filaments located in the northern hemisphere with a counterclockwise (CCW) rotation during their eruptions. Initially, all these filaments possess a small writhe number (≤0.20) indicating a weak helical deformation of the axes. As the CCW rotation kicks in, their writhe numbers begin to decrease and reach large negative values. Combined with the extended Călugăreanu theorem, the absolute value of twist is deduced to decrease during the rotation. Such a quantitative analysis strongly indicates a consequence of the conversion of twist into writhe for the studied events.