Author: Qian Xia and Valentina Zharkova at Northumbria University, Newcastle.

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Introduction

Coronal mass ejections (CMEs) are explosive solar events that involve enormous ejections of plasma and magnetic flux, which drive interplanetary dynamics. CMEs are often associated with a filament channel, in the form of a twisted flux rope or sheared arcade, that stores the required large amount of free magnetic energy. The structures can be destabilised by reconnection or by an ideal process (e.g., torus or kink instability) leading to consequent eruption.

In the magnetic breakout model [1], the energy buildup in the filament channel deforms a coronal nullpoint above the system. It forms the breakout current sheet (CS), as shown in Fig. (1). This CS eventually reconnects, removing the flux overlaying the filament channel, disrupting the force balance, and triggering the eruption onset. A generic vertical flare CS forms beneath the erupting filament and reconnects and drives explosive CME acceleration.

Observations show that a significant fraction of the total released magnetic energy is transferred to high-energy electrons and ions. Energetic electrons in flares can be observed through bremsstrahlung hard X-ray, as illustrated in Fig. (2), and gyrosynchrotron microwave emission from the solar corona and chromosphere. At the same time, a fraction of energetic particles escapes to interplanetary space as solar energetic particles that can be detected by in situ observations. The strong particle energisation during solar flares may be driven by various mechanisms associated with a magnetic reconnection process [3]. By studying particle energisation in different breakout and flare CSs occurring during a CME’s evolution, we can understand the energy release by magnetic field restructuring in these events and the energy transfer to energetic particles, and, thus, determine the properties of the high-energy particles produced.

Numerical approaches

Current computing power is unable to resolve the particle characteristic scale (e.g., proton gyroradius ~ 10² m) in an observable hydrodynamic domain (flare current sheets ~ 10⁶m) [3]. Due to the kinetic effects of particle acceleration, many kinetic simulation codes have been developed, such as hybrid and particle-in-cell approaches. The simulation domains are simplified and restricted to the most interesting area, such as the magnetic reconnection sites or the shock fronts, targeting a single specific process. On the other hand, the test-particle approach implements passively moving particles into magnetohydrodynamic (MHD) simulations (their motion would not change the electromagnetic fields). It allows scientists to access the larger hydrodynamic scale. In this nugget, we outline recent progress with this method, which explores multiple particle acceleration regions simultaneously in a single CME eruption model.

Results and discussion

The ideal MHD code, ARMS, is adaptively refined. The non-uniform grid size becomes smaller near the discontinuities (such as current sheets, shocks) due to the steeper gradients (Fig. 3). This ultra-high-resolution code can produce fine structures, such as magnetic islands in the breakout and flare current sheets.

A large number of test particles are initialised randomly in the green regions of Fig. 4 [5]. The particle acceleration sites identified by the most accelerated particles include the single X-nullpoint, the magnetic islands, and the flare loop-top regions, which are consistent with previous localised kinetic studies. Furthermore, particle re-acceleration in different regions (the blue line in Fig. 4 (3) and (6)) is shown for the first time.

When we look at the particle distributions, we first notice that the protons and electrons are ejected from the X-nullpoint asymmetrically, consistent with the previous kinetic (particle-in-cell) results [6]. After the particles are accelerated, the flare current sheets are more efficient at accelerating particles than the breakout current sheets. What is the reason behind them? Can they contribute to different acceleration mechanisms?

To answer these questions, we adopt the particle drift equations and the fluid description of magnetic field energy changes. These analyses ignore the single-particle motions and instead, focus on the macro scale. For example, the betatron acceleration is related to the change of magnetic field strength, and the first-order Fermi acceleration is related to the shortening of magnetic field lines. The results indicate that different mechanisms dominate different acceleration sites (e.g., 1st-order Fermi acceleration is important in the magnetic islands, the compression of the magnetic field does the trick in the flare loop top, etc.). The amplitudes of the energisation terms explain the different efficiency of acceleration sources. If we look into the change of particle energy distributions, we find that the peak of the distribution starts higher than the loop top and then moves downwards to the flare loop. The transition is consistent with the hard X-ray emissions in the impulsive phase of an X8.2 (a giant explosion) flare event matching the standard CME eruption model. On the other hand, the decrease of particle acceleration efficiency in the decaying phase of the flare is accompanied by the fading of the magnetic guiding field after the impulsive phase.

The numerical studies presented have calculated particle acceleration for a “realistic” CME eruption system rather than a preassumed current sheet. The combination of MHD and test-particle simulation assists the prediction of maximum energy gains of particles in different magnetic configurations, and different phases of the flares. Our model could distinguish the different particle energization mechanisms operating on these macro-scales.

References

• [1] Antiochos, S. K., Dahlburg, R. B., & Klimchuk, J. A. 1994, ApJL, 420, L41
• [2] Karpen, J. T., Antiochos, S. K., & DeVore, C. R. 2012, ApJ, 760, 81
• [3] Zharkova, V. V., Arzner, K., Benz, A. O., et al. 2011, SSRv, 159, 357
• [4] Masson, S., Antiochos, S. K., DeVore, C.R. 2013, ApJ, 771, 82
• [5] Xia, Q., Dahlin, J. T., Zharkova, V. V., Antiochos, S. K. 2020, ApJ, 894, 2
• [6] Siversky, T. V., & Zharkova, V. V. 2009, J. Plasma Phys., 75, 619

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Author: Allan Macneil, Mathew Owens, Mike Lockwood, Matthew Lang, Sarah Bentley (University of Reading) and Robert Wicks (University of Northumbria)

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Introduction

Local inversions in the heliospheric magnetic field (HMF) are observed at a range of solar distances and latitudes by in situ solar wind spacecraft. Figure 1 shows a schematic example of inverted and uninverted magnetic field.

Recent observations of numerous rapid, Alfvénic inversions (known as ‘switchbacks’) by the new Parker Solar Probe (PSP) mission at distances down to 0.16 au have led to renewed interest in this phenomenon [2, 3]. Finding the origins of these inversions, and specifically whether they are formed at the Sun or through in-transit processes, is of particular interest. Knowledge of some solar origin for these inversions could help to reveal processes occurring in the corona which contribute to the production of the solar wind, such as jets and interchange reconnection [4, 5]. In this nugget, we describe results which put constraints on the origins of HMF inversions by quantifying the change in inversion occurrence as a function of distance r, as measured by the Helios 1 spacecraft.

Helios Observations of Inverted Field

Helios 1 observed the low-latitude solar wind and HMF over distances of 0.3 to 1 au, over several orbits from 1974 to 1981. For this data set, we classify 40 s cadence magnetic field samples as corresponding to either inverted or uninverted HMF. This is done by combining the magnetic field polarity (defined relative to the nominal Parker spiral direction) with the beam direction of the suprathermal electron strahl (which traces an anti-sunward path along the field). Once all valid data has been classified, we bin the samples into bins of r for analysis.

Evolution of Relative Inverted Field Occurrence

For our binned data, we calculate the fractions of all valid samples which correspond to inverted and uninverted HMF. These results are plotted against r in Figure 2.

The occurrence of inverted HMF increases between 0.3 and 1 au, at the expense of uninverted HMF. The relative number of inverted HMF samples increases by a factor of around 4. This result implies that inverted HMF over this distance range is primarily created through some driving process in the heliosphere. If most inversions formed at the Sun, then we would expect inverted HMF occurrence to instead drop-off with r, as the inversions gradually decay.

Direction of Magnetic Field Deflection

Field and plasma properties associated with inversions can provide evidence as to what mechanisms are driving the creation of inverted HMF. We calculate the azimuthal ‘deflection angle’, Δϕ_P, of each sampled magnetic field vector away from the nominal Parker spiral direction. The strahl beam direction is used again to remove magnetic sector dependence, such that |Δϕ_P| is 0° when the field is unperturbed, and |Δϕ_P| > 90° indicates that the field has been deflected to the point of inversion.

Figure 3 shows that the distribution of Δϕ_P gradually broadens with r. This supports the above interpretation that the increase in inverted HMF is driven by the gradual deflection of the field away from the nominal Parker spiral direction, as more samples exceed |Δϕ_P| = 90°.

Generation of Inversions

In Figure 4 we show some simple schematics of possible processes, adapted from suggestions in [6], which could generate inverted magnetic fields in the heliosphere.

Panels a to c show that the action of convecting plasma in the solar wind can drive inversions into the field. The angle between the background Parker spiral field and the radial propagation of these elements means that inversions can only be generated through a deflection in the positive Δϕ_P direction. Meanwhile, inversions created by waves and turbulence can result from deflection of the field in either direction. Comparison of the wings of the distributions in Figure 3 at the positive and negative extremes reveals that there is no strong bias towards inversion through either clockwise or anti-clockwise deflection. Thus, of the presented processes, only waves and turbulence are consistent with our observations. We note that the schematics here do not account for more complex possible effects, such as the interaction between stream shears and turbulence [7] or the expansion of inverted structures [8].

Conclusions

We have shown that the occurrence of inverted HMF gradually increases over the distance range 0.3 to 1 au. This indicates that most of these inversions are being actively driven into the HMF, instead of being a remnant of some process at the Sun. Analysis of the azimuthal deflection angle of inverted HMF suggests that waves and turbulence may be the dominant process in creating these inversions. While these results demonstrate that in situ driving of inversions takes place, they do not rule out that inversions may also be generated by processes at the Sun. This is particularly true for the frequent near-Sun switchbacks observed by PSP. These results raise an interesting question: as the switchbacks which dominate the PSP encounters become common on approaching the Sun, at what distance does the occurrence of inverted HMF start to (presumably) increase?

References

• [1] Macneil, A. R., et al., MNRAS 494 3 (2020)
• [2] Bale, S. D., et al., Nature 576 7786 (2019)
• [3] Kasper, J. C., et al., Nature 576 7786 (2019)
• [4] Horbury, T. S., Matteini, L., and Stansby, D., MNRAS 478 2 (2018)
• [5] Crooker, N. U., et al. JGR: Space Phys 109 A3 (2004)
• [6] Lockwood, M., Owens, M. J., and Macneil, A. R., Sol Phys 294 6 (2019)
• [7] Landi, S., Hellinger, P., and Velli, M., GRL 33 14 (2006)
• [8] Jokipii,i J. R., Kota, J., GRL 16 L1 (1989)

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Author: Hugh Hudson, Nicolina Chrysaphi, and Norman Gray at the University of Glasgow.

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Introduction

A “Grand Archive of Solar Flare Cartoons” has long existed on the Web [1], but without updates within the past decade because of the unfortunate loss of a password, and because the original quite primitive HTML made it hard to access new items. Now, announced here for the first time, a brand-new Archive [2] at last replaces it! The new version contains almost 400 entries (see Figure 1 for some examples), each with a new or good-as-new refurbished descriptive blurb, usually containing links that let the user hop around seeking that exactly perfect concept (which almost never exists, alas). The blurb links to the original source.

Note that some mission creep has occurred: originally inspired only by the venerable and too-often-cited CSHKP model, the Archive has gone far beyond that in an effort to capture lateral thinking and more physically relevant items. Note please that we capitalize Archive in an effort to clothe our pretty lightweight subject with some gravitas. We would not describe these toons as funny ha-ha, at least not by intent.

Often the inspiration for an important bit of science appears first as a sketch on a bit of crumpled paper, perhaps in a bar somewhere like the Eagle Pub in Cambridge (UK). We think that a good cartoon represents a sort of intuitive interpolation formula, in that it captures some crucial new aspect of the science and allows extrapolations of that idea into some useful further direction or other. Note that many of the cartoons in the Archive do not actually do that very well. These often suggest the possibility (probability?) of obsolescence as a matter of course. In fact, one could argue that perpetuating even the most brilliant cartoon may actually serve to stifle innovation and lead to a stale cartoon-chasing style of research.

Of what use is such an Archive?

Does the Archive really serve any useful purpose, or does it merely ossify outdated concepts of little generality? Both, we think. We offer this Archive mainly as an educational matter for the benefit of the Archivist really, but many eager users of the old Archive [1] have (if faintly) praised it. The typical comment notes last-minute deadline pressure for writing a presentation or a proposal. The Archivist has in fact sometimes sat glumly through seminar presentations that seemed to consist mainly of cartoons, and has no statistical basis for judging the success rate for any of the proposal efforts.

Access to the Archive

A recent example (shown in Figure 2) shows how a cartoon can neatly suggest a specific physical mechanism within a global structure. This one also pops up in the segment of the thumbnails view of the Archive shown in Figure 1, clickable in its direct form though not here. In addition to this thumbnails view, the Archive also offers various list options; the chronological list view starts in 1905. The Archive embraces half a dozen varieties of cartoon, but tries to avoid snapshots of numerical simulations wherever possible. Though, of course, a good simulation really just fleshes out somebody’s idea of the important physics.

Contributions

The Archive continues to grow gradually as further brilliant ideas appear (or sometimes, just as the graphics get better). A successful new entry must satisfy at least one basic requirement: it needs to have appeared in a regular journal with a better-than-average impact factor. If you have a really new and interesting cartoon in such a state that does not currently appear on the Archive, please email the Archive Accessions Department directly. Note again that the Archive does not presently include intentionally funny items.

References

• [1] The old Archive
• [2] The Grand Archive of Flare/CME Cartoons (new!)
• [3] CME-driven Shock and Type II Solar Radio Burst Band Splitting, Chrysaphi, Kontar, Holman, Temmer ApJ 822, 2 (2018)

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Author: Norbert Magyar and Valery M. Nakariakov at the University of Warwick.

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Introduction

In solar physics, coronal loops have long been in the spotlight. As building blocks of the closed solar corona, understanding their structure and evolution is akin to understanding the coronal heating problem. Moreover, oscillations detected in loops can serve as natural diagnostic probes of their physical properties through coronal seismology, a field in which the properties of coronal plasmas are inferred from observed wave properties and wave theory. Since the first observation of kink oscillations of coronal loops and the first application of coronal seismology [2], models have continuously improved to account for effects such as loop curvature, density stratification, loop cross-sectional variations, cooling, elliptic cross-sections, and so on. A frequently observed property of loops is non-planarity, i.e. exhibiting a helical or sigmoid shape [3]. The effects of coronal loop helicity on their standing kink oscillations were previously investigated analytically, but only through their effect on the local stratified equilibrium density [4]. Here, for the first time, we simulate kink oscillations of sigmoid coronal loops and investigate the ability of coronal seismology to assess the sigmoidity.

Numerical model

Our 3D numerical model consists of a background coronal plasma in a hydrostatic equilibrium in which we embed a coronal loop of higher density. The magnetic field is a force-free dipole with constant ⍺ parameter, adapted from [5]. The ⍺ parameter controls the helicity of the field lines (according to ∇ X B = ⍺B ). We add a higher density loop by tracing a single magnetic field line, and then using it as a central axis to construct a tube. The origin of this single field line, which varies depending on ⍺, is chosen in order to maximise the sigmoidity of the resulting loop while keeping it in the simulation domain. See Figure 1 for an example of a sigmoid flux tube.

The pulse is a horizontally polarised velocity perturbation varying sinusoidally along the loop, which aims to excite a fundamental standing kink mode. However, note that this initial perturbation probably does not coincide with the eigenfunction of the fundamental kink, which is not known. Therefore, while preferentially exciting the fundamental kink mode, other modes are also excited to a small degree, including leaky waves. The resulting kink oscillation of the loop is shown in Figure 2.

The ideal MHD equations are solved in a 3D rectangular domain using MPI-AMRVAC 2.0 [6], with a finite-volume approach. We applied a splitting strategy for the magnetic field, with the time-independent force-free magnetic field considered as a background field. Thus we only solve for the (nonlinear) perturbed magnetic field components. For this, we used the newly-implemented HLLD solver adapted for magnetic field decomposition described in [7].

Results

Analysis of the oscillation properties is based on synthetic 171 Å intensity and Doppler shift images with the lines of sight corresponding to the coordinate axes. After measuring the oscillation properties, we proceed to infer magnetic field estimates seismologically by calculating the theoretical kink period. We do this using the WKB approximation, as the kink speed varies along the loop. From this the magnetic field intensity is determined using the measured oscillation period, loop length, and estimations of the density.

The results are shown in Figure 3. We have considered a range of an order of magnitude for the precision to which the average internal density can be determined, while the density ratio (internal to external density) is taken to range from 1.5 to 10. In the simulation, the average density ratio is close to 2. Here we assume that the measurements of the length of the loop and of the oscillation period are exact.

For the simulation with no sigmoidity, despite the measured and theoretically calculated periods being close to each other, the seismologically predicted magnetic field value is lower than the average value. This can be understood in the following way: as the displacement amplitude of the fundamental mode has a maximum near the apex, the oscillation period is more sensitive to the weaker magnetic field near the apex rather than near footpoints. With increasing sigmoidity however, the predicted magnetic field shows an increasing trend with respect to the average value. This observation might allow for the seismological determination of the sigmoidity of a coronal loop, if some other method to determine the average magnetic field is available, such as force-free extrapolations. In this sense, the free magnetic energy in a coronal loop could be estimated seismologically.

Conclusions

We propose that the dependence of the magnetic field estimate on the loop sigmoidity could be exploited seismologically in order to measure the non-potentiality, i.e. the free magnetic energy in coronal loops. However, for this method to work, the determination of the average magnetic field along the loop is needed, as well as an accurate measurement of the density along the loop. The external/internal density ratio only weakly impacts the results. On the other hand, we demonstrated the robustness of the seismological method, even when applied to non-planar or sigmoid coronal loops. For all values of sigmoidity considered, the estimation of the magnetic field is within the extremal magnetic field values measured in the loop, despite considering an order of magnitude accuracy for the average density determination.

References

• [1] Magyar, N. & Nakariakov, V. M., ApJL 894 L23 (2020)
• [2] Nakariakov, V. M. & Ofman, L., A&A, 372, L53 (2001)
• [3] Aschwanden, M. J. et al., ApJ, 756, 124 (2012)
• [4] Ruderman, M. S. & Scott, A., A&A, 529, A33 (2011)
• [5] Cuperman, S. et al., A&A, 216, 265 (1989)
• [6] Xia, C. et al., ApJS, 234, 30 (2018)
• [7] Guo, X. et al., JCP, 327, 543 (2016)

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Author: Sargam M. Mulay (now University of Glasgow) Giulio Del Zanna, and Helen Mason at the University of Cambridge.

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Introduction

Solar jets are small scale energetic events that eject collimated plasma in the solar atmosphere. The appearance of jets in different magnetic environments (quiet sun, active region, and coronal holes) and their association with various explosive solar events (surges, nonthermal type-III radio burst, hard X-ray emission, and solar flares, etc.) make them most interesting candidates for space-weather studies.

Due to the dynamic nature of jets, they are difficult to observe simultaneously using imaging instruments and spectrographs. We were fortunate to find a simultaneous observation in the existing database. We carried out a comprehensive analysis of the cool (log T [K] < 5.7 (0.5 MK)) and hot (log T [K] > 6.0 (1.3 MK)) components of recurring active region jets (AR jets) using both spectroscopic observations from the Interface Region Imaging Spectrograph (IRIS; [3]) and imaging observations from the slit-jaw imager (IRIS/SJI), the Solar Dynamics Observatory Atmospheric Imaging Assembly (AIA; [8]) and the Hinode X-ray Telescope (XRT; [7]). A direct comparison of cool and hot plasma in AR jets has been carried out for the first time and the study provided important clues about their thermal structure.

Overview and kinematics

The homologous and recurrent AR jets were observed on July 10, 2015 (from 07:29 to 08:35 UT). They originated from the eastern boundary of active region NOAA 12381 and the footpoint of the jet was embedded in the penumbra of the trailing sunspot. A fine, multi-threaded structure of the jet “spire” was observed in multithermal AIA and SJI channels (see the movie in Fig. 1). Here, we measured the physical parameters for the AR jet-4 (observed during 08:19:07 – 08:30:27 UT) using Si IV 1402.77 Å and O IV 1401.16 Å lines.

The wavelength calibration was carried out using the photospheric O I 1355.6 Å line. Non-Gaussian Si IV line profiles (with a narrow core and broad wings) were seen at various pixels and the intensities were calculated by summing the total intensity under the line profile. An intensity raster map was created (see panel (a) of Fig. 2) and the Doppler velocities were obtained for the spire (green boxed region, -32±6 km/s, blue-shift) and footpoint region of the jet (yellow boxed region, 13±4 km/s, red-shift) (see panel (b) of Fig. 2). By considering that a single Gaussian is a good approximation for the core of the line, the Si IV line was fitted with single Gaussian and the nonthermal velocities (see panel (c) of Fig. 2) were measured at similar locations (spire – 69±6 and footpoint – 53±14 km/s).

Temperature structure of the jet

The temperature of the jet spire and footpoint regions (green and yellow boxed regions) was obtained by performing differential emission measure (DEM) analysis in the temperature interval 4.1<log T [K]<7.0. In order to combine the spectra from the IRIS (Si IV (log T [K] = 4.9) and O IV (log T [K] = 5.15) lines) and the images from the AIA (94, 131, 171, 193, 211, and 335 Å channels) in the DEM analysis, we substantially modified the xrt_dem_iterative2.pro routine [12]. This is the first time that such an analysis has been carried out, and the IRIS lines provided a better constraint on the lower temperatures (log T [K] < 5.4) for the DEMs.

The coalignment of AIA images with IRIS raster images was tricky for a number of reasons such as different exposure times, the sensitivity of the AIA channels to a broad range of temperatures, the temporal and spatial resolution of the IRIS slit, etc. The coalignment method given by [4] was followed and the time-averaged images for each AIA channel were obtained (see panels (a)-(d) of Fig. 3). The CHIANTI atomic database ([2], [6]), contribution functions of the Si IV and O IV lines, electron number densities from O IV lines (spire – 2.0×10¹⁰ and footpoint – 7.6×10¹⁰ cm^-3) and the photospheric abundances by [1] were used in this analysis.

A best-fit DEM for the footpoint is shown in panel (e) of Fig. 3. By randomly varying the input intensities by 20%, the uncertainties on the DEM were obtained and they are plotted as 50% (blue), 80% (red), and 95% (yellow) of the solutions closest to best-fit DEM. The DEM curve shows strong cool emission in the footpoint along with hot emission which peaked at log T [K] = 6.5 with peak DEM of 7×10²¹ cm^-5 K^-1. The total EM (9.7×10³¹ cm^-5) was obtained by integrating DEM over the temperature interval, 4.1 < log T [K] < 7.0. Further, we compared this AIA+IRIS DEM with the DEM that we obtained using only AIA EUV images (see panel (f) of Fig. 3). Because of the lower sensitivity of AIA EUV channels for log T [K] < 5.2, the DEMs were calculated for the temperature interval, 5.2 < log T [K] < 7.0. The DEM curve shows a similar peak temperature log T [K] = 6.5 as that obtained for AIA+IRIS DEM but a slightly higher peak DEM of 1.1×10²² cm^-5 K^-1 was obtained for the AIA DEM. The total EM (3.1×10²⁸ cm^-5) calculated for the AIA DEM in the temperature range 5.2 < log T [K] < 7.0 was found to be almost three orders of magnitude lower than that obtained for AIA+IRIS DEM. Both DEM curves fall sharply as there is no constraint on the higher temperatures (log T [K] > 6.6) of DEMs.

In order to get a reliable estimate of higher temperatures (log T [K] > 6.2), we estimated Fe XVIII 93.932 Å emission (see panels (f) of Fig. 2 and (d) of Fig. 3) from the AIA 94 Å channel using the empirical formula (I(Fe XVIII (93.93 Å)) = I(94 Å) – I(211 Å)/120 – I(171 Å)/450) given by [5]. The images show a clear indication of Fe XVIII emission at the footpoint and their comparison with simultaneous SJI images show the existence of cool plasma (log T [K] = 4.9-5.1) at the same location (see panels (d)-(f) of Fig.… continue to the full article

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Author: Gerry Doyle (Armagh); Abhishek Srivastava, Sudheer Mishra, Bhola Dwivedi & Dipankar Banerjee (India), Petr Jelı́nek & Pradeep Kayshap (Czech Republic); Tanmoy Samanta & Hui Tian (China); Vaibhav Pant (Belgium)

Introduction

Magnetic reconnection is a physical process that may yield various phenomena in astrophysical and laboratory plasma, e.g., energetic flares, geomagnetic substorms, tokamak disruptions, controlled fusion experiments, etc [1,2]. In the high temperature astrophysical plasmas of solar and stellar coronae, it is basically defined as the self-organization and relaxation of complex and twisted magnetic fields leading to the liberation of stored magnetic energy [2]. In the magnetically dominated solar corona, magnetic reconnection is one of the key physical processes to heat its atmosphere, and also to generate various space weather candidates (e.g., flares, prominence eruption, and coronal mass ejections), which may influence the Earth’s outer atmosphere, its satellite and communication systems, power systems etc [3,4,5,6]. The variety of exact physical conditions of the magnetic reconnection region are still poorly known despite several novel discoveries both in theory and observations in the astrophysical and laboratory plasmas. Some known burning issues that need to be explored in a more deterministic manner are the formation of current sheets and their morphology, appropriate reconnection rate, establishment of natural diffusion regions and their physical properties, etc to understand exactly the role of reconnection in various exotic plasma processes.

Forced Reconnection is Unveiled in the Large-Scale Solar Corona

Using multi-wavelength observations of the solar corona from the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) on 12 May 2012, we establish directly that forced reconnection at a considerably high rate occur locally in its magnetized plasma (Fig. 1; [7]). It was triggered in the corona when two oppositely directed magnetic field lines forming an X-point are perturbed by an external disturbance (prominence motion in the present case). This type of reconnection has only been reported in theory [8,9], and has never been directly observed in the Sun’s large-scale corona.

Figure 1 displays SDO/AIA imaging observations on 3rd May 2012 at 14:10:08 UT, which show the formation of a temporary X-point and a forced reconnection region. In the righthand panel (“a”) we have the composite image of AIA 171Å, 304Å showing the off-limb region. In the top middle panel (“b”) we have a zoomed view of the region of interest as shown by the dotted-black box in panel “a”. In the top left panel (“c”) we have the difference image map of AIA 171Å, which clearly display the formation of the temporary X-point and the set of the inflowing and outflowing plasma in the large-scale corona exhibiting the reconnection. This is forced reconnection which is driven externally by an impulse generated by a prominence.

The Differential Emission Measure (DEM) map for coronal temperature (shown in the bottom left panel “d”) display the formation of the current sheet and an instance of the ongoing forced reconnection. The modelling of current sheet initialized by the observed initial conditions of the forced reconnection (shown in the middle bottom panel “e”) exhibits an important result that the implementation of the external driver increases the rate of the reconnection even when the resistivity required for creating a normal diffusion region decreases. The detailed description of these first observational results are published in the Astrophysical Journal [7].

Conclusion

In conclusion, the dynamical corona may be episodically subjected to the rapid forced reconnection driven by external perturbations. It can help significantly in the energy release and in the evolution of the eruptive phenomena. These first observational clues to the forced reconnection can also be extended to the laboratory plasma, where it can be employed to constrain the behaviour of the diffusive plasma, and to generate the energy.

References

• [1] Yamada, M., Kulsrud, R. & Ji, H., Magnetic reconnection, Rev. Mod. Phys. 82, 603-664 (2010)
• [2] Priest, E.R. & Forbes, T.G. Reconnection of Magnetic Fields: Magnetohydrodynamics and Collision less Theory and Observations (Cambridge Univ. Press, 2007).
• [3] Cargill, P.J. & Klimchuk, J.A. Nano-flare heating of the corona revisited. Astrophys. J. 605, 911-920 (2004).
• [4] Klimchuk, J.A. Key aspects of coronal heating. Phil. Trans. R. Soc. A. 373, 20140256 (2015). 11.
• [5] Shibata, K. & Magara, T. 2011, Solar Flares: Magnetohydrodynamic Processes; Living Reviews in Solar Physics, 8, 6.
• [6] Schwenn, R. Space weather: The solar perspective. Liv. Rev. Sol. Phys. 3, article id. 2, 72 pp (2006).
• [7] Srivastava, A.K., Mishra, Sudheer K., Jelinek, P., Samanta, T., Tian, H.; Pant, Vaibhav, Kayshap, P., Banerjee,D., Doyle, J.G., Dwivedi, B.N., On the observations of the forced reconnection in the solar corona, 2019, ApJ 887 2.
• [8] Jain, R., Browning, P. & Kusano, K., Solar coronal heating by forced magnetic reconnection: Multiple reconnection events. Phys. Plasmas 12, 012904-012904-12 (2005).
• [9] Potter, M., Browning, P., & Gordovskyy, M., Forced magnetic reconnection and plasmoid coalescence. I. Magnetohydrodynamic simulations, Astro. Astrophys. 623, A 15(2018).

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Author: Farhad Allian, Rekha Jain (The University of Sheffield) and Bradley W. Hindman (University of Colorado Boulder)

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Introduction & Motivation

Amongst the most fascinating features of the dynamic solar atmosphere lie the complex curved loops of illuminatingly hot plasma that are traced by the magnetic field lines. These loops form waveguides that support various magnetohydrodynamic waves and are typically observed to undulate back and forth in the plane-of-the-sky. Distinctively, oscillations generated by impulsive events, such as solar flares, have displacement amplitudes that suddenly grow and diminish within a few wave-periods [1]. Conversely, oscillations in the absence of an obvious driver are observed to oscillate for longer without any significant decay, and with displacement amplitudes on the order of SDO/AIA’s pixel size.

Alongside appropriate mathematical models, coronal loop oscillations remain an indispensable tool to indirectly probe the solar atmosphere. However, such seismological inversions rely on time-series analyses of a clear oscillating loop with well-defined amplitude boundaries. This leads to the unavoidable question: how can we analyse EUV images of coronal loop oscillations with a poor background contrast?

Observations

Utilising the high spatial and temporal resolutions of SDO/AIA, we examined EUV imagery of coronal loop oscillations embedded within a complex arcade on 27th January 2014 [2]. This arcade belonged to a multi-polar active region, which exhibited two consecutive M-class flares prior to the initiation of large-amplitude oscillations. Surprisingly, despite the flaring activities being situated next to each other, the second flare did not restart any additional large-amplitude oscillations.

In association with the first flare, we observed a small wavefront propagating away from the solar limb and throughout the arcade. By carefully tracking the wavefront, we estimated an initial projected speed of about 40 km/s. After its initial stage of propagation, the wavefront was obscured by a bundle of loops in the line-of-sight and so further tracking was not possible. This coincidence with the wavefront and the first flare proved difficult to distinctively determine the likely exciter for these large-amplitude oscillations.

Moreover, we investigated the oscillations manifested along two slits placed perpendicular to the apparent arcade, as shown in Figure 1. The bright loop featured in the time-distance image of Slit 1 undergoes a clear decaying large-amplitude oscillation with a periodicity of approximately 13 minutes. However, within this slit and even more so in Slit 2, exists the presence of an overlapping multitude of faint oscillations, perhaps with different periodicities. In such cases, the oscillatory parameters cannot be estimated with fidelity.

The 2D Autocorrelation Function: Observed & Synthetic Signals

The regularly sampled intensity variations recorded by AIA allows us to use our newly developed analysis procedure which employs spatio-temporal autocorrelations. The main benefit of our procedure is that it reveals the periodicities that remain hidden in the traditional time–distance analysis. In general, the autocorrelation describes the degree of similarity of a given input with itself and as a result, this transformation reveals any periodic structure that is already present in the data. For applications to complex loop systems viewed in time-distance images, as in Figure 1, our procedure simply requires a temporal high-pass filter in order to sharpen the oscillatory features. Thereafter, we generate the autocorrelation as a function of time lag (minutes) and spatial offset (Mm) for our two slits.

The autocorrelation function for the time-distance image of Slit 1 is shown in Figure 2. The maximum correlation occurs at the zero lag and offset as expected, which is used as the reference point of recurring structures. Noticeably, the focal points of this image are a series of X-like structures in addition to the near-vertical streaks. In order to understand these structures, we generated synthetic signals that consist of a bright oscillating loop embedded in a background of faint, dispersed oscillations, shown in Figure 3. We immediately see that the X-like features are due to the bright oscillating loop correlating with itself. Moreover, the slopes passing through the centers of the Xs arise due to a time shift of the faint background loops along the slit, possibly due to a moving driver or the observed wavefront. The bottom panel of Figure 3 demonstrates the dependency on the relative brightness contrast between the bright loop and the faint phase-shifted background within the autocorrelation. As a result, for time-distance images wherein a bright loop is not distinguished well, the 2D autocorrelation still reveals the dominant periodic structures as a series of strongly correlated slopes.

Conclusions

We have introduced and developed a novel image analysis procedure based on 2D autocorrelations that can be utilised in complex loop systems to reveal the periodicity of the faint background.

We have demonstrated that the autocorrelation of a bright loop is revealed as a series of Xs, whereas the faint background oscillations are revealed as a series of phase-shifted slopes. From our observations, we have successfully extracted the dominant periodicity of the bright loop at 13 minutes, as well as the periodicity of the background at 10 minutes. Moreover, the gradient of the background within the 2D autocorrelation corresponds to the group velocity of the wavefield across the slit.

Importantly, our method has the salutary feature that it can be successfully applied to coronal arcades for which a typical time-series fitting method would fail due to the poor image contrast, for example, in complex loop systems or when seeking for small-amplitude oscillations. As a result, our procedure can be used to constrain the seismological inversions that are necessary to understand the local plasma conditions of solar coronal arcades.

Acknowledgments

F.A. acknowledges the STFC (UK) studentship. We are grateful for the use of SDO/AIA and GOES data. This research has made use of SunPy, an open-source and free community-developed solar data analysis Python package [3].

References

• [1] Jain et al 2015 ApJL 804 L19
• [2] Allian et al, 2019, ApJ, 880, 3
• [3] SunPy Community, Mumford, S. J., Christe, S., et al. 2015, CS&D, 8, 014009

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Author: Deborah Baker, Lidia van Driel-Gesztelyi, David Long (UCL-MSSL, UK) and David H. Brooks (George Mason University, USA).

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Introduction

The elemental composition of astrophysical plasma and its variations are crucial to our understanding of the physical conditions and processes occurring within the plasma. Elemental abundance variations of solar and stellar coronae have mainly been linked to the surface temperatures of stars [1] and recent EUV spectroscopic observations of the Sun demonstrate that magnetic activity also has a major role to play [e.g. 2-5].

Coronae of the Sun and solar-type stars are over-abundant in elements with low first ionization potential (FIP effect), while cooler M dwarfs, which have large starspots and produce giant flares, have coronae either depleted of such elements or enhanced in high-FIP elements (inverse FIP or IFIP effect). Plasma fractionation takes place in stellar chromospheres where low-FIP elements are ionized and high-FIP elements are neutral.

For the first time, Hinode/EIS observed the IFIP effect on the Sun in highly localized patches near large sunspots during flares [6]. Since then, IFIP plasma has been observed in only eight active regions. In this nugget, we feature the most striking Hinode/EIS observations showing the spatial distribution and temporal evolution of IFIP plasma in AR 11429 during the decay phase of an M-class flare. This work was published in [7].

Hinode/EIS Observations

Hinode/EIS observed AR 11429 when operating in an autonomous observing mode during a Major Flare Watch campaign on 6 March 2012. The M2.2 flare triggered a high cadence response study and Hinode/EIS rastered the active region from the time of the flare’s peak to the end of the decay phase (Figure 1).

We have selected a series of observations that highlight the rapid and extreme evolution of plasma composition. Figure 2 is composed of Ar XIV intensity maps (top panel) and line ratio composition maps of high-FIP Ar XIV to low-FIP Ca XIV (bottom panel). When the flare is at peak intensity (12:38 UT), only FIP effect is evident throughout the active region. Minutes into the decay phase (12:47 UT and 12:56 UT), IFIP plasma appears at the footpoints of bright flare loops within the active region while the loop tops exhibit enhanced FIP composition. By the time the soft X-ray intensity has returned to preflare levels (13:23 UT), the plasma at the eastern footpoints has evolved to photospheric plasma (ratio ~1) whereas IFIP composition still persists at the western footpoints. At the same time, the FIP effect has weakened along the loops. Hinode/EIS observed these extremes in plasma evolution in less than one hour after the decay phase of the flare. Seven hours later there was no IFIP plasma detected within the active region.

What is special about the location of the IFIP patches?

Distinct IFIP patches occurred at very particular locations within the unusually complex magnetic configuration of AR 11429. Figure 3 displays an SDO/HMI continuum image during the flare’s decay phase at 12:47 UT overplotted with contours of IFIP plasma (green) and flare ribbons (orange). The IFIP patches are located in the highly sheared emerging flux over coalescing umbrae that are crossed by flare ribbons as indicated by the intersection of the contours. When the active region first rotated onto the solar disk, it was a mature sunspot group containing several common penumbra. For several days, major flux emergence of highly sheared field took place with 2–3 major bipoles still in emergence at the time of the Hinode/EIS observations on 6 March.

During the evolution of the active region, flux approached and collided with a pre-existing spot, forcing the coalescence of the smaller flux fragments into a growing, strongly coherent umbra surrounded by a common penumbra. Such field represents different strands of highly sheared field – evidenced by the presence of magnetic tongues [8] – that are converging towards each other to form sunspots, and therefore meet below the photosphere/chromosphere in the location of the coalescing umbrae. This is highly suggestive of subsurface/sub-chromospheric magnetic reconnection. Such reconnection leads to increased fast-mode wave flux from below the region of plasma fractionation in the chromosphere.

Our interpretation of the observations is consistent with the ponderomotive fractionation model for the creation of IFIP plasma [9]. The model invokes the ponderomotive force exerted by Alfvén waves when they refract from the high density gradient in the chromosphere. This gives rise to ion–neutral separation in the chromospheres of the Sun and other stars. The direction of the ponderomotive force determines whether low FIP elements become enhanced or depleted in stellar coronae. Alfvén waves originating in the corona produce the FIP effect and waves of sub-chromospheric origin create the IFIP effect. Sunspots are preferential locations for upward traveling acoustic waves to mode convert as the plasma β = 1 layer occurs at lower heights within the photosphere. Therefore the increased wave flux generated by the subsurface reconnection at coalescing umbrae will in turn preferentially create IFIP plasma above the umbrae. The IFIP plasma is only observed when the flare ribbons cross the umbrae and the IFIP plasma is evaporated into the flare loops. The flare reveals the IFIP plasma but does not create it.

Conclusions

We have shown that IFIP plasma is observed for a short time during the decay phase of a moderate flare in very particular locations within the unusually complex magnetic configuration of AR 11429. These highly localized regions of IFIP plasma appear over coalescing umbrae crossed by flare ribbons. We argue that the highly unusual plasma composition was created by increased fast mode wave flux that was generated by subsurface reconnection of the coalescing umbrae. According to the Laming fractionation model, fast mode waves coming from below the fractionation region of the chromosphere means that the ponderomotive force is directed downward so that low-FIP elements are depleted from the chromospheric plasma. The plasma is then evaporated into the corona in the flaring loops where it is observed by Hinode/EIS. This has implications for understanding the coronal composition of M dwarfs. The spatially resolved observations on the Sun may provide clues to the processes on M-stars which have IFIP-dominated coronae all the time, not only during large flares.… continue to the full article

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Author: Adam J. Finley, Sean P. Matt and Victor See, University of Exeter.

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Introduction

There have only been a few of attempts to quantify the rate at which angular momentum is lost from the Sun due to the solar wind. In this nugget, we bring to light two methods, one using in-situ observations of the solar wind, coupled with recent stellar wind modelling, and the other based on studying the rotation rates of other Sun-like stars.

The rotation rates of Sun-like stars are observed to decrease with age due to angular momentum loss through their magnetised stellar winds. There are models that describe this rotation period evolution (e.g. [1]), which show us how stellar wind torques evolve over 100Myr to Gyr timescales, independently of our understating of the physical mechanism governing the wind torques. When applied to the Sun, these models predict a near-single value of 6.2×10³⁰erg for the solar wind torque, which is insensitive to the Sun’s previous rotation history (see Fig. 1). This is due to the observed convergence of rotation periods and the dependence of wind torques on rotation rates [2]. This is our first method, which we will compare to our recent magnetohydrodynamic (MHD) simulations results for the current solar angular momentum loss rate [3].

Previous Measurements

Here we draw attention to two previous estimates for the solar wind torque which utilise in-situ observations (see Fig. 2, upper panel); using the Helios spacecraft [4], and data from Ulysses [5].  The direct measurement of the solar angular momentum flow by [4] should be the most accurate method, however this work required assuming very significant spacecraft pointing corrections. Therefore, it is not clear how robust this measurement was. Both measurements are displayed in Fig. 2 with coloured dots.

Magnetohydrodynamic Modelling of Stellar Winds

We have considered two semi-analytic approaches to calculating the solar wind angular momentum loss. These semi-analytic prescriptions for the angular momentum loss rate are available [6,7], and are based on over 160 stellar wind simulations using the PLUTO MHD code [8]. The MHD simulations are performed using axisymmetric magnetic geometries combined with polytropic Parker-like wind solutions, which are relaxed to a steady state. The first semi-analytic description of the braking process is formulated using the surface dipole, quadrupole and octupole magnetic field components along with the mass loss rate of the wind. It is further shown that the large scale magnetic field (i.e. the dipole) is the most significant in controlling the angular momentum loss rate of stellar winds. A second semi-analytic formula is available which parameterises the solar wind torque using the open magnetic flux in the wind. The simplicity of the semi-analytic derivation for the open-flux torque formulation (see [9]) suggests that this method produces the most reliable torque. This method is shown to be insensitive to surface geometry and any details of how the field is opened [10].

The Sun’s Variable Angular Momentum Loss Rate

Both semi-analytic formulae are applied to the solar wind in [3]. We use remote observations of the surface magnetic field from SOHO/MDI and SDO/HMI (pySHTOOLS is used to decompose the field into components), and estimates of the mass loss rate and open magnetic flux from in-situ measurements taken by the ACE satellite. The solar wind torque is recovered over the last 20 years, and is shown to vary with the solar cycle using both formulae. However, the surface field formula produces a much smaller value for the solar wind torque than the open flux formula. The reason for this discrepancy may relate (in part) to the “open flux problem” where models of the solar wind often fail to predict the correct amount of open magnetic flux at 1au (based on solar magnetogram observations). Here we present the result from the open flux formulation in Fig. 2, compared with previous estimates  [4,5]. The sunspot cycle is shown in the lower panel of Fig. 2, which appears correlated with the angular momentum loss rate. The average value of the solar wind torque is 2.3×10³⁰erg, which is smaller than required by considering the observed rotation period evolution of Sun-like stars (6.2×10³⁰erg). It remains unclear why the MHD wind torques do not agree with rotation evolution torques.

Conclusions

Using semi-analytic formulae (based on MHD simulations), we show the angular momentum loss rate of the Sun varies in phase with the solar spot cycle. The average value of the solar wind torque is discrepant depending on whether we use observations of the surface magnetic field, or the open magnetic flux in the wind as our input variables. Both of our MHD-based torques are found to be systematically lower than torques derived from rotation evolution models. This also appears to be true for other Sun-like stars [11], and even if we consider millennial-scale variability of the Sun by using indirect proxies of solar activity [12]. This implies that there are some fundamental issues with current stellar wind models and/or observations, which have yet to be understood.

References

• [1] Matt, S. P., Brun, A. S., Baraffe, I., Bouvier, J., & Chabrier, G. 2015, ApJL, 799, L23
• [2] Skumanich, A. 1972, ApJ, 171, 565
• [3] Finley, A. J., Matt, S. P., & See, V. 2018, ApJ, 864, 125
• [4] Pizzo, V., Schwenn, R., Marsch, E., et al. 1983, ApJ, 271, 335
• [5] Li, J. 1999, MNRAS, 302, 203
• [6] Finley, A. J., & Matt, S. P. 2017, ApJ, 845, 46
• [7] Finley, A. J., & Matt, S. P. 2018, ApJ, 854, 78
• [8] Pantolmos, G., & Matt, S. P. 2017, ApJ, 849, 83
• [9] Mignone, A., Bodo, G., Massaglia, S., et al. 2007, ApJS, 170, 228
• [10] Réville, V., Brun, A. S., Matt, S. P., Strugarek, A., & Pinto, R. F. 2015, ApJ, 798, 116
• [11] Finley, A. J., See, V., & Matt, S. P. 2019, ApJ, 876, 44
• [12] Finley, A. J., Deshmukh, S., Matt, S. P., Owens, M., & Wu, C. J. 2019, ApJ, 883, 67

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Author: Petros Syntelis and Vasilis Archontis at the University of St Andrews, and Kanaris Tsinganos at the University of Athens.

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Introduction

Coronal mass ejections (CMEs) are large scale eruptive events responsible for the sudden expulsion of magnetised plasma from the solar corona into the interplanetary medium. These eruptive events are commonly associated with the destabilisation of a pre-existing magnetic flux rope (MFR). Most of the time, they are also associated with the sudden release of energy in the form of a flare arcade that remains rooted in the solar surface at the location of origin of the CME. The kinetic energy content of CMEs ranges from 10²⁶-10³² erg [1], with the bulk of the eruptive events characterized as CMEs to have energies of 10²⁸-10³¹ erg.

Solar eruptive events appear also at smaller scales than traditional CMEs. Such events are usually referred to as nano-, mini-, or micro-CMEs [2-4], and they appear to be miniature versions of the larger scale CMEs, with similar morphology and dynamics such as e.g. small-scale sigmoids, eruption of small filaments and less energetic flares. Recently, solar coronal jets (E_kin~10²⁶-10²⁷ erg), a seemingly different energetic expulsion of plasma, have also been associated with eruptions of small scale filaments, indicating connections between jets and CMEs [5-9].

We have recently developed flux emergence numerical models for small scale eruptions and studied their formation and triggering mechanism [10]. By increasing the energy budget below the photosphere, we studied eruptions with kinetic energies spanning two orders of magnitude [11]. In this nugget, we present these models and their connection to explaining the multi-scale nature of solar eruptions.

Model

We use the Lare3D code, which solves the 3D time-dependent, resistive, compressible MHD equations, to simulate the partial emergence of a twisted flux tube into a stratified solar atmosphere. The atmosphere consists of a sub-photospheric layer, an isothermal layer mimicking the photosphere/chromosphere, a thin layer representing the transition region and an isothermal layer mimicking the corona. The flux tube is initially placed under the photosphere. A density deficit is introduced in the flux tube, making its central part buoyant. The magnetic field of this central part partially emerges into the solar atmosphere, resulting in the formation of a bipolar region at the photosphere. The corona is initially field free, so there is no external reconnection between an atmospheric ambient field and the emerging field. We perform a parametric study by varying the energy content of the flux tube to produce eruptions of different scales.

Formation and triggering of the small scale eruptions

We first describe the eruption associated with the flux tube with the lowest energy content.
The upper part of the subphotospheric flux tube emerges above the photosphere forming a bipolar region (Fig. 1), while its axis remains below/at the photosphere. Shearing, rotational and converging motions develop self-consistently (arrows and red contours), injecting free energy into the atmosphere. A sheared arcade (blue lines, panel a) is formed near the polarity inversion line (PIL) which eventually adopts a J-shaped loops morphology (b). Reconnection between the sheared lines at a low-lying current sheet (purple isosurface) initially form long loops (c) and eventually result in a MFR that exists prior to the eruption (yellow lines, panel c).

The height-time profile of the MFR and the torus index at the height of the MFR is shown in Fig. 2a (upper and lower panels). The torus index (n = – dlnB/dlnz) is a metric of the decrease of the magnetic field strength with height, and a MFR is expected to be destabilized by torus instability when its located in regions of n between 1 and 2. Although the MFR is located inside a high torus-index region from the very early stages of its evolution (e.g. n > 1.5 for t > 57 min), the exponential rise associated with the eruption is not triggered by the torus instability. Only the initial accelerations of the flux rope (first vertical line and insert) could be attributed to torus instability. During the initial acceleration, the MFR moves upwards and stretched the envelope field above it (red lines, panel 2b).

The fast ejection of the MFR (second vertical line, panel 2a) occurs when the envelope field lines are stretched to the point that they reconnect underneath the MFR with other envelope field lines. Then, the MFR becomes eruptive and the reconnected flux (red lines, panel 2c) is injected towards the centre of the erupting field via a fast (right panel, 2d), hot (middle panel, 2d) and dense (left panel, 2d) reconnection flow, while a flare arcade is formed underneath the flare current sheet (cyan lines, 2c). The density and temperature profiles of the erupting field are similar to the large scale CME eruption. The kinetic energy of the eruption is 10²⁶ erg and the physical size is ~40Mm, therefore the eruption is a small scale CME-like eruption (mini/nano-CME).

Multi-scale eruptions

To study eruptions on multiple scales, we increase the initial magnetic energy content of the subphotospheric flux tube, and increase the physical size of the numerical domain (from 65³ Mm to 153³ Mm). The kinetic and the magnetic energy of the resulting eruptions against the photospheric flux are shown in Fig. 3. The energies of the eruptions follow a power law distribution. The kinetic energies are 10²⁶ to 10²⁸, ranging from small scale mini/nano-CME eruptions to small CMEs. Extrapolating for a typical AR flux of 10²¹ Mx, we predict energies of 4 × 10³⁰ – 3 × 10³³ erg, which are typical energies of CMEs.

Conclusions

Using a self-consistent model with different initial magnetic energy contents, we study eruptions of multiple scales [10,11], with energies ranging from that of small scale eruptions and jets (10²⁶ erg) up to small CMEs (10²⁸ erg). A power law is predicted between the energies of the eruptions and the photospheric flux. Testing whether such scaling laws exist between the observed small scale eruption, jets and the larger scale CMEs would be a strong indication for the jet-CME connection and the multi-scale self-similar nature of eruptions.… continue to the full article

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