Eruptive-Impulsive Homologous M-class Flares Associated with Double-Decker Flux Rope Configuration in Mini-Sigmoid of NOAA 12673
Prabir K. Mitra, Bhuwan Joshi, Astrid M. Veronig, Ramesh Chandra, K. Dissauer, Thomas Wiegelmann
DDraft version July 24, 2020
Typeset using L A TEX default style in AASTeX61
ERUPTIVE-IMPULSIVE HOMOLOGOUS M-CLASS FLARES ASSOCIATED WITH DOUBLE-DECKER FLUXROPE CONFIGURATION IN MINI-SIGMOID OF NOAA 12673
Prabir K. Mitra,
1, 2
Bhuwan Joshi, Astrid M. Veronig, Ramesh Chandra, K. Dissauer,
3, 5 andThomas Wiegelmann Udaipur Solar Observatory, Physical Research Laboratory, Udaipur 313 001, India Department of Physics, Gujarat University, Ahmedabad 380 009, India Institute of Physics & Kanzelh¨ohe Observatory, University of Graz, Universit¨atsplatz 5, A-8010 Graz, Austria Department of Physics, DSB Campus, Kumaun University, Nainital 263 002, India NorthWest Research Associates, 3380 Mitchell Lane, Boulder CO, 80301, USA Max-Planck-Institut f¨ur Sonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077 G¨ottingen, Germany
ABSTRACTWe present a multiwavelength analysis of two homologous, short lived, impulsive flares of GOES class M1.4 and M7.3,that occurred from a very localized mini-sigmoid region within the active region NOAA 12673 on 2017 September 7.Both flares were associated with initial jet-like plasma ejection which for a brief amount of time moved toward east ina collimated manner before drastically changing direction toward southwest. Non-linear force-free field extrapolationreveals the presence of a compact double-decker flux rope configuration in the mini-sigmoid region prior to the flares. Aset of open field lines originating near the active region which were most likely responsible for the anomalous dynamicsof the erupted plasma, gave the earliest indication of an emerging coronal hole near the active region. The horizontalfield distribution suggests a rapid decay of the field above the active region, implying high proneness of the flux ropesystem toward eruption. In view of the low coronal double-decker flux ropes and compact extreme ultra-violet (EUV)brightening beneath the filament along with associated photospheric magnetic field changes, our analysis supports thecombination of initial tether-cutting reconnection and subsequent torus instability for driving the eruption.
Keywords:
Sun: activity — Sun: corona — Sun: filaments, prominences — Sun: flares — Sun: X-rays,gamma rays
Corresponding author: Prabir K. [email protected] a r X i v : . [ a s t r o - ph . S R ] J u l Mitra et al. INTRODUCTIONFlares are transient activities occurring in the solar atmosphere in which a huge amount of energy is released withina short time i.e., few minutes to few hours. Earth-directed coronal mass ejections (CMEs) along with their associatederuptive flares are known to produce hazardous effects in the near-Earth environment and drive geomagnetic storms.Magnetic reconnection, a topological reconfiguration of magnetic field in a plasma medium (Priest & Forbes 2000),is widely accepted to be the fundamental energy release process during solar transient activities. In the process ofreconnection, magnetic energy is rapidly converted into plasma heating, bulk motions and kinetic energy of non-thermalparticles (Priest & Forbes 2002; Shibata & Magara 2011). Eruptive flares and their associated CMEs are, therefore,responsible for large-scale changes in the magnetic structure of the solar atmosphere. With a complex mechanisminvolving large-scale magnetic fields and its direct consequences on the Earth’s atmosphere, flares and CMEs havebeen widely studied over the years and still is a prominent field of interest (e.g., reviews by Fletcher et al. 2011; Benz2017; Green et al. 2018).The ‘Standard Flare Model’, also known as the CSHKP model (Carmichael 1964; Sturrock 1966; Hirayama 1974;Kopp & Pneuman 1976), considers the existence of a prominence as a pre-requisite for the initiation of eruptive flares.Theoretical models suggests that the basic structure of a prominence/filament is composed of magnetic flux rope(MFR) defined as a set of twisted magnetic field lines wrapped around its central axis more than once (Gibson & Fan2006). Further, the MFR is identified as the dark cavity in the 3-part structure of CMEs (e.g., Riley et al. 2008).Once the MFR is dynamically activated by an external triggering or by some kind of instabilities and it is set into aneruptive motion, magnetic reconnection begins in a vertical current sheet formed beneath the MFR causing intenseflare emission. The CSHKP model successfully incorporates several key features of eruptive flares: flare ribbons;looptop and footpoint sources; hot cusp; post-flare loop arcade; etc. However, the processes that are responsible forthe formation of MFR and triggering mechanisms for the eruptive flares are still important and debatable in solarphysics. Also, in many eruptive flares, the spatial evolution of looptop sources and flare ribbons during the earlyphases exhibit significant deviation from the classical scenario described in the CSHKP model which point toward amuch complicated energy release process in complex magnetic configuration (e.g., Veronig et al. 2006; Joshi et al. 2009;Dalmasse et al. 2015; Joshi et al. 2017a; Gou et al. 2017, see also review by Joshi et al. 2012).It is essential to note that the CSHKP model is a 2D model, and therefore, it is not designed to accommodate the 3Dstructures and configurations e.g., sheared arcades, J-shaped flare ribbons, flux ropes, complex flare loops, etc., whichare important in the understanding of solar flares. To implement these features in a general flare model, the CSHKPmodel has been extended to three dimensions on the basis of a series of numerical simulations (Aulanier et al. 2012,2013; Janvier et al. 2013, 2014). These MHD simulation results suggest that in the highly sheared preflare magneticconfiguration, small-scale current sheets could be generated in the regions of high magnetic gradients i.e., quasi-separatrix layers (QSLs; Titov et al. 2002). Reconnections in these current sheets are responsible for the formation ofMFRs from the sheared arcades as well as its destabilization. During the eruption of the MFRs, the inner legs of thesheared arcades which envelop the MFR, straighten vertically beneath the erupting MFR and eventually reconnectresulting in the formation of postflare arcades.The successful eruption of an MFR is essential for generating a CME. There are two basic groups of models describingthe activation and eruption of an MFR from its stable state: models invoking ideal MHD instabilities and modelsinvoking magnetic reconnection (see e.g., reviews by Priest & Forbes 2002; Aulanier 2014; Green et al. 2018). Inthe ideal instability model, a pre-existing MFR can erupt if the background magnetic field displays a rapid decaywith height (torus instability; Kliem & T¨or¨ok 2006), or the rope’s twist number increases beyond a critical value(kink instability; T¨or¨ok et al. 2004). Two representative reconnection models, namely, tether-cutting and magneticbreakout, use different preflare magnetic configurations of the active region (AR) while describing the eruption of anMFR. The tether-cutting model requires a bipolar magnetic field configuration, with the earliest reconnection (i.e.,triggering process) taking place deep in the sheared core fields (Moore & Roumeliotis 1992; Moore et al. 2001). Thebreakout model involves a multipolar topology, containing one or more pre-existing coronal null points (Karpen et al.2012). In this case, the CME onset is triggered by reconnection occurring well above the core region which reduces thetension of the overlying field (Antiochos et al. 1999). Irrespective of the triggering mechanism, once the MFR attainseruptive motion, standard flare reconnection sets in beneath the erupting MFR and this scenario is common to all themodels of eruptive flares (e.g., see Vrˇsnak et al. 2004; Veronig et al. 2006; Liu et al. 2008; Joshi et al. 2013; Vrˇsnak2016; Joshi et al. 2016; Veronig et al. 2018; Mitra & Joshi 2019; Sahu et al. 2020). mpulsive-eruptive homologous flares from mini-sigmoid α surges,EUV and H α macrospicules etc. (see e.g., Moore et al. 1977; Schmieder et al. 1995; Jiang et al. 2007). Moore et al.(2010) proposed a dichotomy in solar jets: standard and blowout. In the standard jet scenario, reconnection betweena pre-existing open field and a newly emerging magnetic field of opposite polarity, is responsible for guiding the hotplasma along the post reconnection open field resulting in a narrow, long jet-spire. On the other hand, the blowoutcategory of jets involve eruption of the jet’s base-arch that contains a mini- flux rope, resulting in a broader andapparently untwisting jet-spire and a CME (see also, Archontis & Hood 2013; Joshi et al. 2016; Chandra et al. 2017;Joshi et al. 2017b).During 2017, when the Sun was moving toward the minimum phase of the solar cycle 24, a simple α -type ARNOAA 12673 emerged on the eastern limb of the Sun on 2017 August 28. It gradually became complex with time andturned into a βγδ -type sunspot on 2017 September 5. Before disappearing over the western limb of the Sun on 2017September 10, it produced 4 X-class and 27 M-class flares along with numerous C-class flares making it one of themost powerful ARs of solar cycle 24. Notably, it produced the two biggest flares of solar cycle 24, namely the X9.3event on 2017 September 6 and the X8.2 flare on 2017 September 10, which were subject to numerous studies (e.g.,Yang et al. 2017; Seaton & Darnel 2018; Romano et al. 2018; Verma 2018; Guo et al. 2018; Liu et al. 2018c; Hou et al.2018; Gary et al. 2018; Liu et al. 2018a; Veronig et al. 2018; Mitra et al. 2018; Romano et al. 2019; Moraitis et al.2019; Liu et al. 2019; Duan et al. 2019; Chen et al. 2020). Most of the flaring activity from the AR occurred from thecentral region where the sunspot group arranged into ‘ δ ’-configuration (K¨unzel 1960). This region was characterizedby a sharp polarity inversion line (PIL) exhibiting high magnetic gradient across the PIL; for example, Mitra et al.(2018) noted a magnetic gradient of 2.4 kG Mm − in the line of sight (LOS) magnetic field across the PIL, prior tothe X-flares flares of 2017 September 6.In this article, we present a comprehensive multiwavelength analysis of two impulsive flares of classes M1.4 and M7.3,which occurred on 2017 September 7 in a very localized region situated near the edge of the main sunspot group of AR12673. Both events were accompanied with highly collimated eruptions, a characteristic of coronal jet. The jet-flareevents initiated from an unusually small coronal sigmoid which we explore in detail by (E)UV imaging and coronalmagnetic field modeling; thanks to the high resolution data from the Solar Dynamics Observatory ( SDO ; Pesnell et al.2012). An important aspect of this study lies in the early dynamics of the eruptions during the flares. Section 2provides a brief account of the observational data and analysis techniques. In Section 3, we derive the observationalresults on the basis of measurements taken at photospheric, chromospheric and coronal levels. In Section 4, we comparethe chromospheric and coronal observations of different flare-associated features with the modeled coronal magneticconfigurations. We discuss and interpret our results in Section 5. OBSERVATIONAL DATA AND ANALYSIS TECHNIQUESFor imaging the solar atmosphere, we used observations from the Atmospheric Imaging Assembly (AIA; Lemenet al. 2012) on board
SDO . AIA produces 4096 × . (cid:48)(cid:48) . (cid:48)(cid:48) log ( T ) = 6 .
8) and 335 ˚A (Fe XVI; log ( T ) = 6 .
4) filters along with the193 ˚A (Fe XII, XXIV; log ( T ) = 6 . , .
3) channel were used for investigation of coronal activities associated with theflares. For imaging of the lower atmospheric layers, we have extensively used 12 s cadence observations in the 304 ˚A(He II; log ( T ) = 4 .
7) and 24 s cadence observations in the 1600 ˚A (C IV & continuum; log ( T ) = 5 & 3 .
4) channels.
Reuven Ramaty High Energy Solar Spectroscopic Imager ( RHESSI ; Lin et al. 2002) observed the second (M7.3)flare almost completely and the interval between the two homologous flares while it missed the first (M1.4) event
Mitra et al. due to the spacecraft’s passage through the South Atlantic Anomaly (SAA ). RHESSI observed the full Sun withan unprecedented combination of angular (spatial) resolution (as fine as ≈ . (cid:48)(cid:48)
3) and energy resolution (1–5 keV) inthe energy range 3 keV–17 MeV. The image reconstruction is done with the CLEAN algorithm (Hurford et al. 2002)using only front detector segments with an integration time of 12 s and pixel scale of 2 . (cid:48)(cid:48)
0. Out of 9 detector segments,segment 2 was excluded for imaging at 6–12, 12–25, 25–50, and 50–100 keV, while segments 2 and 7 were excluded for3–6 keV imaging.Photospheric structures associated with the AR NOAA 12673 were observed from full disk 4096 × SDO at a spatial resolution of 1 . (cid:48)(cid:48) . (cid:48)(cid:48) ; Wang & Sheeley1992) and a non-linear force-free field (NLFFF) model (Wiegelmann & Inhester 2010; Wiegelmann et al. 2012). Asboundary condition for the NLFFF modeling, we used photospheric vector magnetograms of 2017 September 07 09:46UT from the ‘hmi.sharp cea 720s’ series of SDO /HMI at a reduced resolution of 0 . ◦
06 and a temporal cadence of 720s. The NLFFF extrapolations were done in a Cartesian volume of dimensions 344 × ×
224 pixels which correspondsto a physical size of ≈ × ×
160 Mm in the solar atmosphere. The NLFFF field lines were visualized using theVisualization and Analysis Platform for Ocean, Atmosphere, and Solar Researchers (VAPOR ; Clyne et al. 2007)software which produces an interactive 3D visualization environment.We calculated the magnetic decay index in the NLFFF extrapolation volume using the results of potential fieldextrapolation obtained by solving a Green’s function method (Seehafer 1978). The magnetic decay index ( n ) is givenby the equation: n = − log ( B ex ( z )) log ( z ) , where B ex ( z ) is the horizontal component of the external field above the AR and z is height (Bateman 1978; Kliem & T¨or¨ok 2006).The CME that originated from the filament eruption was observed by the C2 and C3 instruments of the Large Angleand Spectrometric Coronagraph (LASCO; Brueckner et al. 1995) on board the Solar and Heliospheric Observatory ( SOHO ; Domingo et al. 1995). C2 and C3 are white-light coronagraphs that image the solar corona from 1.5–6 R (cid:12) and from 3.7–30 R (cid:12) , respectively. MUTIWAVELENGTHS OBSERVATIONS AND ANALYSIS3.1.
Event overview
We present observations of AR NOAA 12673 on 2017 September 7 from 09:45 UT to 10:30 UT. During this period,the AR produced two GOES M-class flares . The temporal evolution of the M-class flares is represented by the softX-ray (SXR) flux variation in the 1–8 ˚A channel of GOES in Figure 1(a) (shown by the red curve). The first M-classflare (M1.4; indicated by an arrow in Figure 1(a)) initiated at ≈ ≈ ≈ ≈ ≈ ≈ ≈ RHESSI observed the AR from 2017 September 7 ≈ ≈ RHESSI observations, we divided the entireduration (09:45 UT–10:30 UT) into three periods: periods I and III cover the M1.4 flare and the M7.3 flares with theassociated eruptions, respectively, whereas period II covers the rather quiet phase in between the two M-class flares(Figure 1(a)).The AIA (E)UV lightcurves from the AR during this time (Figure 1(c)) show a general agreement with the GOESSXR flux variation signifying that the disk-integrated GOES measurement was largely influenced by the coronal activityof the AR NOAA 12673. The intensity variations in all the AIA channels suggest the initiation of the M1.4 flare at https://heasarc.gsfc.nasa.gov/docs/rosat/gallery/misc_saad.html mpulsive-eruptive homologous flares from mini-sigmoid Figure 1.
Panel (a): GOES SXR flux in the of 1–8 ˚A (red curve) and 0.5–4 ˚A (blue curve) bands on 2017 September 7 from09:45 UT to 10:30 UT covering the two M-class flares under study. Panel (b):
RHESSI
X-ray fluxes normalized by factors of , , , and for 12–25 keV, 25–50 keV, 50–100 keV, and 100–300 keV energy bands, respectively. The horizontal red,green, and blue bars in panel (b) indicate the RHESSI attenuator states (A0, A1, and A3, respectively). The orange and bluehorizontal bars in panel (b) indicate the durations missed by
RHESSI due to SAA and ‘
RHESSI -night’, respectively. Panel(c): AIA (E)UV lightcurves. For clear visualization, AIA lightcurves in the channels 171 ˚A and 94 ˚A are scaled by and ,respectively. Mitra et al.
Table 1.
Chronology of events during the two M-class flares occurred on 2017 September 7Sr. Evolutionary ObservingNo. stages Time instrument/ wavelength Remarks1 Preflare phase 09:45 UT AIA (E)UV & HMI A very localized inverted ‘S’ structured brightening wasobserved in AIA 304 and other AIA coronal images inthe AR. We call it “mini-sigmoid”.2 Initiation of the M1.4 flare 09:49 UT GOES 1–8 ˚A3 Initiation of plasma ejectionduring the M1.4 flare 09:53 UT AIA 94 ˚A and 304 ˚A Collimated ejection of plasma from the core of themini-sigmoid toward east.4 End of the M1.4 flare 09:58 UT GOES 1–8 ˚A A small filament appeared in the mini-sigmoid region.
RHESSI observation started at ≈ RHESSI sources of energiesup to ≈
100 keV were found from the mini-sigmoidregion.7 Initiation of the secondphase of plasma ejectionduring the M7.3 flare 10:16 UT AIA 304 ˚A The southern end of the filament erupted ejectingplasma toward south.8 Merging of the plasmaejected in the first phasewith plasma ejected in thesecond phase 10:22 UT AIA 335 ˚A Plasma ejected toward east during the M7.3 flarestrangely changed direction from east to south-westand merged with the plasma ejected in the secondphase during the M7.3 flare.9 End of the M7.3 flare 10:18 UT GOES 1–8 ˚A10 Detection of CME 10:24 UT LASCO C2 CME propagated along the central PA of 254 ◦ andangular width of 32 ◦ with a linear speed of 470 km s − . ≈ ≈ mpulsive-eruptive homologous flares from mini-sigmoid Figure 2.
Panel (a): HMI white light image of AR 12673 on 2017 September 7 09:44 UT. Panel (b): Co-temporal HMImagnetogram. Panels (c)–(e): AIA EUV images of the AR in 94 ˚A, 335 ˚A, and 304 ˚A respectively, showing the morphology ofthe active region in the corona and chromosphere. Panel (f): AIA UV image of the active region in 1600 ˚A . The dashed boxesin panels (a) and (b) indicate the photospheric region associated with the two M-class flares. The boxes in panels (c) and (e)indicate the field of view of the AR plotted in Figures 3, 5, and 6. Arrows in panels (c)–(e) indicate the mini-sigmoid regionwhereas the arrows in panel (f) indicate brightenings at the location of the mini-sigmoid.
Mitra et al.
Period I: Evolution of the M1.4 flare
Figure 3 displays a series of AIA 94 ˚A (Figures 3(a)–(i)) and AIA 304 ˚A (Figures 3(j)–(r)) images showing themorphological evolution of the region shown inside the boxes in Figures 2(c) and (e) during the M1.4 flare and theassociated jet-like plasma eruption. As discussed in Section 3.1, before the flare onset, the northern part of the ARcontained a mini-sigmoid. In terms of sharpness of the observed feature and its relative brightness in comparison tothe ambient medium, the mini-sigmoid was apparently more prominent in the hot, coronal AIA 94 ˚A channel than therelatively cooler AIA 304 ˚A filter. In Figure 3(a), we outline the mini-sigmoid by a black dashed line which brightenedup after 09:50 UT, marking the onset of the M1.4 flare. After 09:53 UT, we observe a localized kernel-like brighteningin the western leg of the mini-sigmoid (shown by the blue arrow in Figure 3(c)). Further, looking at the spatial extentas well as the relative intensity, this localized brightening was observed to be more prominent in the 304 ˚A than in the94 ˚A observations (cf. Figures 3(c) and (l)) which suggests that the early energy release during the initiation of M1.4flare occurred in lower i.e., chromospheric heights (cf. Figures 3(c) and (l)). At the same time we observe the ejectionof plasma from the middle of the mini-sigmoid (shown by the white arrow in Figure 3(c)). The ejected plasma followeda very narrow and collimated path (i.e., a jet-like eruption) toward the east for a distance of ≈
40 arcsec and thenabruptly changed its direction. The progress of the ejected plasma is indicated by the white arrows in Figures 3(c)–(h)and (l)–(q). Here, we note that the ejecting plasma was observed more clearly in AIA 304 ˚A images than in AIA 94˚A images. This is indicative of cooler plasma being ejected from lower layers in the solar atmosphere (presumablyfilament material), and partially being heated during the ejection process. At the peak phase of the flare, the easternleg of the mini-sigmoid became the brightest location in the entire AR as observed in the AIA 94 ˚A images (Figure3(e); shown by the yellow arrow). The decay phase of the M1.4 flare was characterized by the appearance of a smallfilament structure observed in AIA 304 ˚A images (shown by the black arrow in Figure 3(r)).3.3.
Period II: Quiet phase between the two M-class flares
A small filament started to appear during the late phase of the M1.4 flare along the axis of the mini-sigmoid (Section3.2). After the M1.4 flare, i.e., in ‘Period II’ of the study (see Figure 1), this filament became prominent. Notably,after missing Period I due to the SAA,
RHESSI started observing in period II, with high sensitivity at low energies(no attenuator in place, state A0). In Figure 4, we show a series of AIA 304 ˚A images overplotted with contours of
RHESSI
X-ray sources in the energy ranges 3–6 keV (shown by sky contours) and 6–12 keV (shown by blue contours).We readily find emission in the 6–12 keV range to have peak intensity along the axis of the mini-sigmoid (Figure 4(a)).We also note that the X-ray emission in the 3–6 keV energy range at 10:00 UT displayed two distinct sources on eithersides of the filament. At ≈ Period III: Evolution of the M7.3 flare and associated filament eruption
The M7.3 flare was initiated at ≈ ≈ ≈ ∼ ≈ ≈
100 keV was observed from the mini-sigmoid region by
RHESSI during this flare. In Figure 5, weplot contours of
RHESSI
X-ray emission in different energy channels and find X-ray sources to be co-spatial with theEUV brightenings. AIA 304 ˚A images of the region displayed an interesting feature during this time. The southernpart of the filament kept rising and slowly developed into a cusp-like structure at ≈ ≈ mpulsive-eruptive homologous flares from mini-sigmoid Figure 3.
Series of AIA 94 ˚A (panels (a)–(i)) and 304 ˚A (panels (j)–(r)) images showing the time evolution of the M1.4 flare.The mini-sigmoid structure identified in the preflare phase is outlined by the dashed black dotted curve in panel (a). The whitearrows in different panels indicate the ejected jet-like plasma. The blue arrows in panels (c) and (l) indicate a newly emergedbrightening in the western end of the mini-sigmoid which led to the flare onset. The yellow arrows in panels (e) and (n) indicatethe brightening in the eastern end of the mini-sigmoid during the peak phase of the M1.4 flare. The black arrow in panel (r)indicate a newly formed filament structure during the decaying phase of the M1.4 flare. Mitra et al.
Figure 4.
Series of AIA 304 ˚A images of the flaring region during the relatively quiet period between the two M-class flares.Contours of
RHESSI mpulsive-eruptive homologous flares from mini-sigmoid ≈ Development of the CME from the erupting filament
As discussed in Sections 3.2 and 3.4, both the M-class flares were associated with plasma ejections. Interestingly,plasma ejection signatures during the M1.4 flare became too weak to be observed few minutes after its first appearancewithin AIA field of view (FOV). Erupting plasma during the M7.3 flare, however, was distinctly observed to produce aCME by SOHO/LASCO. In this Section, we focus on the motion of the ejected plasma during the M7.3 flare (Figure 7)and the corresponding CME (Figure 8). The plasma ejection was initiated in a collimated manner toward east (shownby the red arrow in Figures 7(b) and (c)) and then dramatically changed its direction toward south-west. In Figure7(e), we have approximately outlined the changing direction of erupting plasma. A second phase of plasma ejectioninitiated from the western end of the mini-sigmoid region after ≈ (Yashiro et al. 2004), C2 detected the CME at 10:24 UT at ≈ (cid:12) andit was observed in the field of view of C3 until 16:18 UT when the leading edge of the CME reached ≈ (cid:12) . Thenarrow CME (angular width being only 32 ◦ ) propagated along the position angle 254 ◦ with a linear speed of ≈ km s − . 3.6. Structure and evolution of the magnetic configuration of AR 12673
The distribution and configuration of the photospheric magnetic flux of AR 12673 (Figure 9(a)) remained withoutany major changes during our observing period. However, it experienced consistent changes in the magnetic fieldstrength. In Figure 9(b), we plot the photospheric LOS magnetic flux variation associated with the flaring regionshown by the dashed box in Figure 9(a) on 2017 September 07 from 08:00 UT to 10:30 UT. Notably, this regionwas associated with the formation and eruption of the filament in the mini-sigmoid. We find that, the negativeflux underwent a monotonic decrease during the preflare period from ≈ ≈ ≈ × Mx s − . On the other hand, the positive flux underwent a gradual enhancement during the preflare periodwith two distinguishable phases of flux decrease ( ≈ ≈ . MAGNETIC FIELD MODELING4.1.
Large-scale magnetic field configuration
Large-scale magnetic field configurations, such as open magnetic field lines represented by coronal holes (CHs;Cranmer 2009), may strongly influence the early propagation of CMEs, and may cause significant deflections of their https://cdaw.gsfc.nasa.gov/CME_list/UNIVERSAL/2017_09/yht/20170907.102406.w032n.v0470.p244g.yht During the impulsive phases of WLFs, sudden changes in the LOS photospheric fields have been observed by several earlier studies(see e.g., Zhao et al. 2009; Maurya & Ambastha 2009; Maurya et al. 2012; Kushwaha et al. 2014). The sudden transient changes observedin LOS magnetograms can be interpreted in terms of the theoretical calculations of Ding et al. (2002) that show the field reversal duringstrong flares could be an observational artifact that is locally induced by bombardment of energetic electron beams at the photosphere. Mitra et al.
Figure 5.
Series of AIA 94 ˚A (panels (a)–(i)) and 304 ˚A (panels (j)–(r)) images showing the time evolution of the M7.3 flare.The brown and blue arrows in different panels indicate the development of the filament. The yellow arrows in panels (d)–(g)indicate the first phase of plasma ejection during the M7.3 flare. The black arrows in panel (n) indicate a second phase of theeruption during the flare. The white boxes in panels (o), (p) and (q) indicate post flare arcade observed from an edge-on view.Contours of
RHESSI mpulsive-eruptive homologous flares from mini-sigmoid Figure 6.
Series of AIA 335 ˚A (panels (a)–(i)) and 1600 ˚A (panels (j)–(r)) images showing the time evolution of the M7.3 flare.Brown arrows in panels (a)–(d) indicate emergence of a small filament structure in the preflare phase. Yellow arrows in panels(c)–(e) indicate the ejecting plasma. Black arrow in panel (f) indicate the direction a second stream of ejecting plasma. The redarrows in panels (j)–(l) indicate flare ribbon like structures formed during the M7.3 flare. The blue arrow in panel (o) indicatea subtle brightening occurred in the decay phase of the flare which, most probably, was responsible for the small enhancementin the GOES SXR lightcurves (see Figure 1). Mitra et al.
Figure 7.
Series of AIA 335 ˚A images showing large scale eruption of plasma from active region NOAA 12673 during the M7.3flare reported in this paper. The red arrows in panels (b) and (c) indicate the initial phases of the ejecting plasma movingtoward east. The curve in panel (e) outlines the unusual turning of the ejecting plasma from east to south-west. The ejectedplasma during the M7.3 flare resulted in a CME of medium speed and small angular width. original direction of motion (Gopalswamy et al. 2009; Heinemann et al. 2019). In order to check if the direction of theCME was influenced by the open field configuration associated with a nearby coronal hole, we extrapolated the globalmagnetic field using PFSS and looked for observational signatures of coronal holes in the AIA EUV images (Figure10). Figure 10(b) shows a global PFSS extrapolation concentrating around the AR NOAA 12673 (the AR is indicatedby a black arrow in Figure 10(b)), where open and closed field lines are shown in grey and blue, respectively. From mpulsive-eruptive homologous flares from mini-sigmoid
Non-linear force-free field (NLFFF) extrapolation
Optimization based NLFFF extrapolation technique
To understand the coronal magnetic field configuration associated with the AR NOAA 12673, we applied an opti-mization technique (Wheatland et al. 2000; Wiegelmann 2004) to compute the NLFFF-equilibrium. Here we used anadvanced version of this code, which takes care of measurement errors in the magnetogram (Wiegelmann & Inhester2010) and has been optimized for use with data from
SDO /HMI (Wiegelmann et al. 2012). In the optimizationapproach, L is minimized (Wiegelmann & Inhester 2010), where L = (cid:90) V (cid:32) ω f | ( ∇ × (cid:126)B ) × (cid:126)B | B + ω d | ∇ · (cid:126)B | (cid:33) dv + ν (cid:90) S ( (cid:126)B − (cid:126)B obs ) · W · ( (cid:126)B − (cid:126)B obs ) d(cid:126)S. (1)Here, ω f , ω d , and ν are weighting functions while W is a diagonal error matrix with the elements w los , w trans , and w trans ; ‘ los ’ and ‘ trans ’ being the line-of-sight and transverse components, respectively. The NLFFF code used in thisarticle, calculates ω f , ω d (in the code, ω f and ω d are chosen to be identical i.e., ω f = ω d ). and allows ν , w los , and w trans as free parameters (i.e., these parameters can be explicitly defined upon calling of the preprocessing/optimization).Since the photosphere is not force-free, the photospheric mangetograms used as the input boundary conditions, needto be pre-processed (Wiegelmann et al. 2006). In Equation 1, (cid:126)B obs denotes the preprocessed magnetic field. For thepurpose of preprocessing, a second functional L is defined as L = µ L + µ L + µ L + µ L (2)where L = (cid:16)(cid:88) B x B z (cid:17) + (cid:16)(cid:88) B y B z (cid:17) + (cid:16)(cid:88) B z − B x − B y (cid:17) L = (cid:16)(cid:88) x ( B z − B x − B y ) (cid:17) + (cid:16)(cid:88) y ( B z − B x − B y ) (cid:17) + (cid:16)(cid:88) yB x B z − xB y B z (cid:17) L = (cid:88) ( B x − B x,obs ) + (cid:88) ( B y − B y,obs ) + (cid:88) ( B z − B z,obs ) L = (cid:88) (cid:0) (∆ B x ) + (∆ B y ) + (∆ B z ) (cid:1) Here, the summations are done over all the grid nodes of the bottom boundary. The values of µ , µ , µ , and µ arefree parameters and therefore, user defined.In this article, for pre-processing the input photospheric magnetogram, we used the values of free parameters asfollows: ν = 0 . w los = 1; w trans = B trans max ( B trans ) ; µ = µ = 1; µ = 0 . µ = 0 .
01 (3)In Table 2, we compare the values of dimensionless flux, dimensionless force and dimensionless torque before and afterpre-processing, which can be used to assess the degree of force-freeness of the input processed magnetograms. With theextrapolated magnetic field, the following parameters were calculated which can be considered as the quantification offorce and divergence freeness of the extrapolated magnetic field:
F ractional f lux ratio ( < | f i | > ) = 5 . × − ; | (cid:126)J × (cid:126)B | = 3 . × − ; weighted angle between (cid:126)J and (cid:126)B = 6 . ◦ (4) See DeRosa et al. (2015). Mitra et al.
Figure 8.
LASCO observations of the CME that developed from the plasma ejection during the M7.3 flare. Panels (a)–(b)present observations from C2 coronagraph (1.5–6 R (cid:12) ) while panel (c) shows observation from C3 coronagraph (3.7–30 R (cid:12) ).The CME is indicated by the black arrow in panel (c). The CME was first observed by LASCO at 10:24 UT and was observeduntil 16:18 UT. mpulsive-eruptive homologous flares from mini-sigmoid Table 2.
Values of different parameters before and after pre-processingParameter Before AfterFlux balance − . × − − . × − Dimensionless force 0.29 4.18 × − Dimensionless torque 0.31 1.05 × − In this context, it is noteworthy that at the time of extrapolation i.e., 2017 September 07 09:46 UT, the AR NOAA12673 was centered at the heliographic position ∼ S07W46 . A detailed study by Allen Gary & Hagyard (1990) onthe implications of the Sun’s curvature on the magnetogram observations, suggest that full spherical geometry mustbe taken into account for off-center regions for angles > ◦ . During the extrapolations, we used ‘cylindrical equalarea (CEA; Allen Gary & Hagyard 1990)’ projected magnetograms which do not produce results as accurate as fullspherical geometry does, but considering that we were interested in particularly the northeastern area of the AR whichlies well within 50 ◦ , CEA projection can be accepted to be decently reliable.4.2.2. Extrapolation results
In Figure 11(a), we show a LOS magnetogram of the AR during the preflare phase. We specify a small part of theAR (shown inside the blue box in Figure 11(a)) for plotting the NLFFF extrapolated field lines. The region inside thebox represents a complex distribution of magnetic polarities in a largely bipolar configuration of major positive andnegative fields in the western and eastern parts, respectively (the regions inside the blue box in Figure 11(a)). In thenorthern part of the box, we find a small positive polarity region surrounded by negative polarity regions from threesides (the region inside the green box in Figure 11(a)). In the north-western side of the AR, we find many dispersebut strong negative polarity patches. For computation of the modeled magnetic field lines, we assume that the regionshowing flare associated brightenings (which also includes a filament) contains part of flux rope which underwentmagnetic reconnection (i.e., relevant field lines).NLFFF extrapolation results reveal the presence of two small MFRs along the PIL of the mini-sigmoid region (shownby blue and green lines in Figure 11(b)). The two MFRs were intertwined with each other forming a “double-deckerflux rope system”. We plot only the intertwined MFRs in Figure 11(c) for better visualization. Further, NLFFFextrapolation also suggests the presence of relatively large-scale closed magnetic field lines connecting the centralpositive and northern negative polarity regions (shown by the yellow lines in Figure 11(b)).4.3.
Distribution of magnetic decay index and twist number
To explore, how the strength of the coronal magnetic field of AR 12673 varied with height, we calculated the magneticdecay index in the whole AR volume (i.e., 344 × ×
244 pixels; see Section 2). In Figures 11(d), we show the variationof the magnetic decay index with height in a plane above the flux rope axis. For this purpose, we considered anapproximate shape of the axis of the double-decker flux rope system which is shown by the red curves in Figures 11(a)and (c). The approximated PIL was then projected onto the 2D lower boundary and the decay index was computedin a plane vertically above that approximate path. This process is similar to the technique undertaken by Liu et al.(2015). We plot two contours on the vertical surface with levels n =1.0 and 1.5. The approximate height of thedouble-decker system is indicated by the yellow dashed-dotted line in Figure 11(d). We find that a few segments ofthe double-decker flux ropes system were associated with a magnetic decay index as high as ≈ ≈ ≈ ≈ ≈ ≈ Mitra et al.
Figure 9.
Panel (a): HMI Magnetogram of AR 12673 on 2017 September 7 09:45 UT. Time evolution of photospheric magneticflux of the whole AR and inside the selected region within the dotted box in panel (a) are plotted in panel (b). The dashed linesin panel (b) mark the starting and ending time of the M1.4 flare as observed by GOES and the dashed-dotted lines in thesemark the starting and ending time of the M7.3 flare as observed by GOES.
In order to explore the possibility of kink instability as the triggering mechanism of the eruption of the flux rope,we calculated the twist number ( T w ) in the flaring region, defined as (Berger & Prior 2006) T w = (cid:90) L ( ∇ × (cid:126)B ) · (cid:126)B πB dl (5)where L is the length of the flux rope. Our calculations reveal that the double-decker system was associated withnegative twist. The average value of | T w | associated with the double-decker system was found to be ≈ DISCUSSIONIn this paper, we present a multiwavelengths analysis of two M-class flares from the AR NOAA 12673 on 2017September 7 that resulted in the successive activation of a filament and subsequent narrow CME. As indicated inFigure 1, both M-class flares were very impulsive with the respective impulsive phases lasting for ≈ ≈ mpulsive-eruptive homologous flares from mini-sigmoid Figure 10.
PFSS extrapolation of the global magnetic field (panel b) together with AIA 193 ˚A images during the events understudy (panel a) and one solar rotation later on October 4, 2017 (panel (c)). Grey and blue field lines indicate closed and openmagnetic field lines, respectively. The open field lines originating to the north and west side of the flaring active region, areobserved as the signature of a coronal hole, one solar rotation later (indicated by the white arrow). Mitra et al. within the boxes in Figures 2(c) and (e)). AIA 94 ˚A images sampling hot coronal plasma, clearly revealed an inverted‘S’-shaped structure lying in east-west orientation at the same location (Figure 3(a)). Such coronal ‘S’ (or, inverted‘S’) shaped structures are known as ‘coronal sigmoids’ (see, Manoharan et al. 1996; Rust & Kumar 1996). However,while usually coronal sigmoids are observed to have lengths of ∼ ∼
20 Mm ( ≈ (cid:48)(cid:48) ). In view of the much smaller length-scales, we can be justifiably term it as ‘mini-sigmoid’.During different phases of the two M-class flares, we clearly observed the formation and activation of a small filamentfrom the sigmoidal region and associated jet-like plasma ejection (Figures 3 and 5).Sigmoids are associated with twisted or helical magnetic structures i.e., MFRs or filament channels (Gibson et al.2002). MFRs are complex structures lying above PILs in the solar atmosphere where a set of magnetic field lines wraparound along its central axis more than once (Gibson & Fan 2006). The results of the NLFFF extrapolation suggeststhe presence of two MFRs in the AR NOAA 12673 at the site of the M-class flares on 2017 September 7 (Figure11). Interestingly, the MFRs in the AR seem to wrap around each other forming a “double-decker flux rope” system.Double-decker flux rope system was first identified by Liu et al. (2012). While studying an eruptive M1.0 class flare,they observed two vertically well separated filaments lying above a single PIL that remained stable for a few daysbefore the upper branch erupted in association with an M-class flare. Based on their multipoint and multiwavelengthanalysis, they concluded that both filament branches emerged from beneath the photosphere with a vertical separationof ≈
13 Mm between the two branches. Few hours before the eruptive flare, filament threads within the lower branchlifted up and merged with the upper branch, triggering its eruption. Cheng et al. (2014) reported another case ofdouble-decker flux ropes associated with an X-class eruptive flare from the sigmoidal AR 11520. They found theprimary MFR to be formed ≈
40 hours before the flare via tether-cutting reconnection between two J-shaped arcades.The second flux rope became evident in the hot coronal channels just ≈ ≈ ≈
40 hours.Both the M-class flares initiated with very localized brightenings at the sigmoid, immediately followed by a colli-mated plasma ejection (Figures 3 and 5). During the evolution of the flares, we identified the appearance of a smallfilament while the localized brightening persisted beneath the filament (Figure 4). The photospheric magnetogram andextrapolated coronal magnetic field configuration clearly revealed the source region of the eruption to be bipolar withhigh shearing (Figure 11). Further, both the positive and the absolute negative flux decayed prior to the flares from theflaring region (Figure 9(b)). We interpret this evolution as observational signatures of photospheric flux cancellationat PIL which is recognized for its association with small-scale magnetic reconnections (van Ballegooijen & Martens1989) leading to the formation of MFRs which was well elaborated in subsequent studies (see e.g., Amari et al. 2010;Xue et al. 2017; Panesar et al. 2018; Mitra et al. 2020). For both flares, localized (E)UV brightenings, underneath theapparent location of the filament body, were observed during their onset. We interpret these findings as evidences forthe tether-cutting model of solar eruptions (Moore & Roumeliotis 1992; Moore et al. 2001). Among the observablesignatures of tether-cutting reconnection, compact EUV and HXR brightenings beneath an erupting MFR (or middleof the sigmoid) and collimated plasma outflows may be highlighted (Raftery et al. 2010; Liu et al. 2013; Chen et al.2014, 2016, 2018). While investigating the onset processes of a solar eruption, Chen et al. (2018) observed clear signa- mpulsive-eruptive homologous flares from mini-sigmoid Figure 11.
Panel (a): HMI LOS magnetogram showing the photospheric configuration of the active region NOAA 12673 priorto the flaring activity. Panel (b): NLFFF extrapolation results at 2017 September 07 09:45 UT showing coronal connectivitiesbetween different parts of the complex AR. Multiple flux ropes were identified in the extrapolation volume which are shown byblue and green lines. NLFFF extrapolated field lines are drawn over the photospheric region shown inside the blue box in panel(a). In panel (c) we only show the two flux ropes situated in the flaring region within the AR, constituting a double-deckerflux rope system. The FOV of panel (c) is approximately indicated in panel (a) by the green box. Panel (d): distribution ofmagnetic decay index (n) above the PIL indicated by the red curves in panels (a) and (c). The yellow dashed-dotted line inpanel (d) approximately indicate the height of the double-decker flux rope system. The blue dashed and red solid curves inpanel (d) refer to contours of n=1.0 and 1.5, respectively. The white arrow in panel (d) indicate a region within the heightof flux ropes, characterized by decay index n ≈ tures of flux cancellation from the flaring region, bidirectional jets, and change in the topology of the hot loops duringthe precursor phase. They argued that bidirectional jet-like flows occurred as a result of interaction of two coronalloop structures. This led them to conclude that the onset process of the eruption was tether-cutting reconnection.The events reported in this article evolved with unidirectional jets which differs from the bidirectional jets reported by2 Mitra et al.
Chen et al. (2018). However, EUV images of the flaring region confirm that the location of the occurrences of the jetswere closely associated with the initial brightenings beneath the filaments (Figures 3(e), (m) and 6(d)) which furthersupports the tether-cutting reconnection between the two MFRs in the double-decker flux rope system.It is noteworthy that, both the M-class flares initiated with highly collimated, unidirectional plasma outflow (Figures3, 5, 6) for a relatively short duration ( ∼ ∼ h crit ) of torus instability for 60 two-ribbon flares. Their study revealed that on averagethe critical height where the decay index reached a value of n=1.5 was h crit = 36 . ± . n crit = 1 . − . h crit ≈ h crit = 36 . ± . h crit = 21 ±
10 Mm).We further explored the application of kink instability toward the triggering of the flux ropes by computing thetwist numbers. Our analysis reveals the average twist associated with the flux ropes to be | T w | ≈ | T w | ≈
2. In view ofthis result, we could not establish any conclusive evidence of kink instability as a possible triggering mechanism in ourevent. mpulsive-eruptive homologous flares from mini-sigmoid
SDO and
RHESSI teams for their open data policy.
SDO is NASA’s mission under the Living Witha Star (LWS) program.
RHESSI was NASA’s mission under the SMall EXplorer (SMEX) program. We also thankJulia K. Thalmann for help in the NLFFF extrapolation. This work is supported by the Indo-Austrian joint researchproject No. INT/AUSTRIA/BMWF/ P-05/2017 and OeAD project No. IN 03/2017. A.M.V and K.D also thank theAustrian Science Fund (FWF): P27292-N20. We also thank the anonymous referee for his/her constructive commentsthat helped us improve the overall quality of this article.REFERENCES
Allen Gary, G., & Hagyard, M. J. 1990, Solar Physics, 126,21Amari, T., Aly, J.-J., Mikic, Z., & Linker, J. 2010, ApJL,717, L26Antiochos, S. K., DeVore, C. R., & Klimchuk, J. A. 1999,ApJ, 510, 485Archontis, V., & Hood, A. W. 2013, ApJL, 769, L21Asai, A., Shibata, K., Hara, H., & Nitta, N. V. 2008, ApJ,673, 1188Aulanier, G. 2014, in IAU Symposium, Vol. 300, Nature ofProminences and their Role in Space Weather, ed.B. Schmieder, J.-M. Malherbe, & S. T. Wu, 184–196Aulanier, G., D´emoulin, P., Schrijver, C. J., et al. 2013,A&A, 549, A66Aulanier, G., Janvier, M., & Schmieder, B. 2012, A&A,543, A110Aulanier, G., T¨or¨ok, T., D´emoulin, P., & DeLuca, E. E.2010, ApJ, 708, 314Bateman, G. 1978, MHD instabilitiesBaumgartner, C., Thalmann, J. K., & Veronig, A. M. 2018,ApJ, 853, 105Benz, A. O. 2017, Living Reviews in Solar Physics, 14, 2 Berger, M. A., & Prior, C. 2006, Journal of Physics AMathematical General, 39, 8321Bhatnagar, A. 1996, Ap&SS, 243, 105Bilenko, I. A. 2017, Geomagnetism and Aeronomy, 57, 952Brueckner, G. E., & Bartoe, J. D. F. 1983, ApJ, 272, 329Brueckner, G. E., Howard, R. A., Koomen, M. J., et al.1995, Solar Physics, 162, 357Carmichael, H. 1964, NASA Special Publication, 50, 451Chandra, R., Filippov, B., Joshi, R., & Schmieder, B. 2017,SoPh, 292, 81Chen, B., Yu, S., Reeves, K. K., & Gary, D. E. 2020, ApJL,895, L50Chen, H., Duan, Y., Yang, J., Yang, B., & Dai, J. 2018,ApJ, 869, 78Chen, H., Zhang, J., Cheng, X., et al. 2014, ApJL, 797, L15Chen, H., Zhang, J., Li, L., & Ma, S. 2016, ApJL, 818, L27Cheng, X., Ding, M. D., Zhang, J., et al. 2014, ApJ, 789, 93Clyne, J., Mininni, P., Norton, A., & Rast, M. 2007, NewJournal of Physics, 9, 301Cranmer, S. R. 2009, Living Reviews in Solar Physics, 6, 3Dalmasse, K., Chandra, R., Schmieder, B., & Aulanier, G.2015, A&A, 574, A37D´emoulin, P., & Aulanier, G. 2010, ApJ, 718, 1388 Mitra et al.
DeRosa, M. L., Wheatland, M. S., Leka, K. D., et al. 2015,ApJ, 811, 107Ding, M. D., Qiu, J., & Wang, H. 2002, ApJ, 576, L83Domingo, V., Fleck, B., & Poland, A. I. 1995, SoPh, 162, 1Duan, A., Jiang, C., He, W., et al. 2019, ApJ, 884, 73Fletcher, L., Dennis, B. R., Hudson, H. S., et al. 2011,SSRv, 159, 19Gary, D. E., Chen, B., Dennis, B. R., et al. 2018, ApJ, 863,83Gibson, S. E., & Fan, Y. 2006, Journal of GeophysicalResearch (Space Physics), 111, A12103Gibson, S. E., Fletcher, L., Del Zanna, G., et al. 2002, ApJ,574, 1021Gopalswamy, N., M¨akel¨a, P., Xie, H., Akiyama, S., &Yashiro, S. 2009, Journal of Geophysical Research (SpacePhysics), 114, A00A22Gou, T., Veronig, A. M., Dickson, E. C., Hernand ez-Perez,A., & Liu, R. 2017, ApJL, 845, L1Green, L. M., T¨or¨ok, T., Vrˇsnak, B., Manchester, W., &Veronig, A. 2018, SSRv, 214, 46Guo, J., Dumbovi´c, M., Wimmer-Schweingruber, R. F.,et al. 2018, Space Weather, 16, 1156Heinemann, S. G., Temmer, M., Farrugia, C. J., et al. 2019,SoPh, 294, 121Hirayama, T. 1974, Solar Physics, 34, 323Hou, Y. J., Zhang, J., Li, T., Yang, S. H., & Li, X. H. 2018,A&A, 619, A100Hurford, G. J., Schmahl, E. J., Schwartz, R. A., et al. 2002,SoPh, 210, 61Janvier, M., Aulanier, G., Bommier, V., et al. 2014, ApJ,788, 60Janvier, M., Aulanier, G., Pariat, E., & D´emoulin, P. 2013,A&A, 555, A77Jiang, Y. C., Chen, H. D., Li, K. J., Shen, Y. D., & Yang,L. H. 2007, A&A, 469, 331Joshi, B., Kushwaha, U., Cho, K.-S., & Veronig, A. M.2013, ApJ, 771, 1Joshi, B., Kushwaha, U., Veronig, A. M., & Cho, K.-S.2016, ApJ, 832, 130Joshi, B., Kushwaha, U., Veronig, A. M., et al. 2017a, ApJ,834, 42Joshi, B., Thalmann, J. K., Mitra, P. K., Chandra, R., &Veronig, A. M. 2017b, ApJ, 851, 29Joshi, B., Veronig, A., Manoharan, P. K., & Somov, B. V.2012, in Multi-scale Dynamical Processes in Space andAstrophysical Plasmas, ed. M. P. Leubner & Z. V¨or¨os(Berlin, Heidelberg: Springer Berlin Heidelberg), 29–41Joshi, B., Veronig, A., Cho, K. S., et al. 2009, ApJ, 706,1438 Kahler, S. W., Akiyama, S., & Gopalswamy, N. 2012, ApJ,754, 100Karpen, J. T., Antiochos, S. K., & DeVore, C. R. 2012,ApJ, 760, 81Kliem, B., & T¨or¨ok, T. 2006, Physical Review Letters, 96,255002Kopp, R. A., & Pneuman, G. W. 1976, SoPh, 50, 85K¨unzel, H. 1960, Astronomische Nachrichten, 285, 271Kushwaha, U., Joshi, B., Cho, K.-S., et al. 2014, ApJ, 791,23Lemen, J. R., Title, A. M., Akin, D. J., et al. 2012, SoPh,275, 17Lin, R. P., Dennis, B. R., Hurford, G. J., et al. 2002, SoPh,210, 3Liu, C., Deng, N., Lee, J., et al. 2013, ApJL, 778, L36Liu, C., Deng, N., Liu, R., et al. 2015, ApJL, 812, L19Liu, L., Cheng, X., Wang, Y., & Zhou, Z. 2019, ApJ, 884,45Liu, L., Cheng, X., Wang, Y., et al. 2018a, ApJ, 867, L5Liu, L., Wang, Y., Zhou, Z., et al. 2018b, ApJ, 858, 121Liu, R., Kliem, B., Trk, T., et al. 2012, The AstrophysicalJournal, 756, 59Liu, W., Jin, M., Downs, C., et al. 2018c, ApJ, 864, L24Liu, W., Petrosian, V., Dennis, B. R., & Jiang, Y. W. 2008,ApJ, 676, 704Liu, Y. 2008, ApJL, 679, L151Manoharan, P. K., van Driel-Gesztelyi, L., Pick, M., &Demoulin, P. 1996, ApJL, 468, L73Maurya, R. A., & Ambastha, A. 2009, SoPh, 258, 31Maurya, R. A., Vemareddy, P., & Ambastha, A. 2012, ApJ,747, 134Mitra, P. K., & Joshi, B. 2019, ApJ, 884, 46Mitra, P. K., Joshi, B., & Prasad, A. 2020, SoPh, 295, 29Mitra, P. K., Joshi, B., Prasad, A., Veronig, A. M., &Bhattacharyya, R. 2018, ApJ, 869, 69Mohamed, A. A., Gopalswamy, N., Yashiro, S., et al. 2012,Journal of Geophysical Research (Space Physics), 117,A01103Moore, R. L., Cirtain, J. W., Sterling, A. C., & Falconer,D. A. 2010, ApJ, 720, 757Moore, R. L., & Roumeliotis, G. 1992, in Lecture Notes inPhysics, Berlin Springer Verlag, Vol. 399, IAU Colloq.133: Eruptive Solar Flares, ed. Z. Svestka, B. V. Jackson,& M. E. Machado, 69Moore, R. L., Sterling, A. C., Hudson, H. S., & Lemen,J. R. 2001, ApJ, 552, 833Moore, R. L., Tang, F., Bohlin, J. D., & Golub, L. 1977,ApJ, 218, 286Moraitis, K., Sun, X., Pariat, ´E., & Linan, L. 2019, A&A,628, A50 mpulsive-eruptive homologous flares from mini-sigmoid25