Energy Partition in Four Confined Circular-Ribbon Flares
aa r X i v : . [ a s t r o - ph . S R ] F e b Solar PhysicsDOI: 10.1007/ ••••• - ••• - ••• - •••• - • Energy Partition in Four Confined Circular-RibbonFlares
Z.M. Cai · Q.M. Zhang · Z.J. Ning · Y.N. Su · H.S. Ji © Springer ••••
Abstract
In this study, we investigated the energy partition of four confinedcircular-ribbon flares (CRFs) near the solar disk center, which are observedsimultaneously by SDO, GOES, and RHESSI. We calculated different energycomponents, including the radiative outputs in 1 −
8, 1 −
70, and 70 −
370 ˚A, totalradiative loss, peak thermal energy derived from GOES and RHESSI, nonther-mal energy in flare-accelerated electrons, and magnetic free energy before flares.It is found that the energy components increase systematically with the flareclass, indicating that more energies are involved in larger flares. The magneticfree energies are larger than the nonthermal energies and radiative outputs offlares, which is consistent with the magnetic nature of flares. The ratio E nth E mag of the four flares, being 0.70 − Keywords:
Flares, Dynamics; Flares, Energetic Particles; Heating, in Flares;Magnetic fields, Corona B Q.M. Zhang [email protected] Key Laboratory of Dark Matter and Space Astronomy, Purple MountainObservatory, CAS, Nanjing 210023, China School of Astronomy and Space Science, University of Science and Technology ofChina, Hefei 230026, China CAS Key Laboratory of Solar Activity, National Astronomical Observatories, CAS,Beijing 100101, China
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1. Introduction
Solar flares and coronal mass ejections (CMEs) are the most energetic activitiesin the solar system, which are considered as the main source of space weather(Fletcher et al. , 2011; Webb and Howard, 2012; Gopalswamy, 2016; Patsourakos et al. , 2020). The accumulated magnetic free energy (10 − erg) in activeregions (ARs) is released within a short period of time via magnetic reconnec-tion (e.g., Antiochos, DeVore, and Klimchuk, 1999; Amari et al. , 2000; Chen &Shibata, 2000; Lin and Forbes, 2000; Moore et al. , 2001). The released energygoes into the thermal energy of localized hot plasmas, kinetic energy of recon-nection outflows, kinetic energy of CMEs, nonthermal energies of the acceleratedelectrons and/or ions, and radiations from radio to hard X-ray (HXR) and even γ -ray wavelengths (Forbes and Acton, 1996; Stoiser et al. , 2007; Kretzschmar etal. , 2010; Milligan et al. , 2012; Caspi, Krucker, and Lin, 2014; Inglis and Christe,2014; Warmuth and Mann, 2016a,b). According to their association with CMEs,flares are classified into confined and eruptive types (e.g., Moore et al. , 2001;Cheng et al. , 2011; Su et al. , 2011, 2015; Veronig and Polanec, 2015; Li et al. ,2020; Kliem et al. , 2021). A large number of confined flares result from failedfilament eruptions due to the strong confinement of the overlying field (Ji et al. ,2003; Liu et al. , 2014; Sun et al. , 2015; Zhang et al. , 2015; Yang and Zhang,2018; Yan et al. , 2020). Sometimes, confined flares are triggered by loop-loopinteraction (Su et al. , 2013; Kushwaha et al. , 2014; Ning et al. , 2018).Contrary to two-ribbon flares, circular-ribbon flares (CRFs) are a special typeof flares that consist of a short, compact inner ribbon and a bright, outer ribbonwith a circular or elliptical shape (Masson et al. , 2009; Joshi et al. , 2015; Liu et al. , 2015; Hernandez-Perez et al. , 2017; Devi et al. , 2020; Kashapova et al. ,2020; Prasad et al. , 2020; Joshi, Joshi, and Mitra, 2021). The three-dimensional(3D) magnetic configuration of CRFs is usually related to a fan-spine structureassociated with a magnetic null point (Wang and Liu, 2012; Zhang et al. , 2012;Sun et al. , 2013; Hou et al. , 2019; Lee et al. , 2020; Liu et al. , 2020; Yang et al. ,2020; Zhang et al. , 2021). CRFs are occasionally accompanied by coronal jetsor cool surges (Zhang et al. , 2016; Li et al. , 2017; Xu et al. , 2017; Dai et al. ,2020; Zhang et al. , 2020). The dynamic evolution of CRFs, including magneticreconnection near the null point, particle acceleration and precipitation, chromo-spheric evaporation and condensation, are found to resemble those of two-ribbonflares (Zhang, Li, and Ning, 2016; Zhang, Li, and Huang, 2019).Till now, comprehensive investigations on energetics of eruptive flares areabundant (Emslie et al. , 2004, 2005, 2012; Milligan et al. , 2014; Warmuth andMann, 2016a,b). The energy partitions in flares and CMEs are comparable,especially for X-class eruptive flares (Feng et al. , 2013). Using multiwavelengthobservations from the Atmospheric Imaging Assembly (AIA; Lemen et al. , 2012)on board the
Solar Dynamics Observatory (SDO), the energetics of nearly 400eruptive flares were studied in detail (Aschwanden, Xu and Jing, 2014; Aschwan-den et al. , 2015, 2016, 2017). However, the investigation on energy partitionin confined flares is rare. Thalmann et al. (2015) studied an X1.6 flare in AR12192 on 2014 October 22. The nonthermal energy ( ∼ × erg) in flare-accelerated electrons is found to account for ∼
10% of the free magnetic energy
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Table 1.
Information on the four flares in our study. Here, t sta , t peak , and t end represent the start, peak, and end times of the flares in GOES 1 − t denotes the rough lifetime.Flare Date t sta t peak t end ∆ t AR Location Class(UT) (UT) (UT) (min)CRF1 10 − May − − Nov − − Dec − − Mar − before flare. Kushwaha et al. (2015) studied an M6.2 flare in AR 10646 on 2004July 14. The time evolution of thermal energy is found to show a good correlationwith the variations in cumulative nonthermal energy, validating the well-knownNeupert effect in confined flares. Zhang et al. (2019) explored various energycomponents in two homologous confined CRFs of the same class (M1.1) in AR12434, including the peak thermal energy, nonthermal energy in electrons, totalradiative loss of hot plasma, and radiative output in 1 − −
70 ˚A. Thetwo flares have similar energy partition, and the nonthermal energy is sufficientto provide the heating requirement incorporating the peak thermal energy andradiative loss.In this study, we selected four confined CRFs near the solar disk centerobserved by SDO/AIA (Song and Tian, 2018). In Section 2, we briefly describethe data sets and calibration. We are not interested in the triggering mechanismof each flare, which has been extensively studied. We focus on the estimation ofvarious energy components of flares in Section 3. The results are compared withprevious findings in Section 4. Finally, a summary is given in Section 5.
2. Data Sets and Calibration
The date/time, location, and GOES class of the four flares (CRF1, CRF2, CRF3,and CRF4) are listed in Table 1. Among the four flares, two are M-class and theothers are C-class. The flares were observed by SDO/AIA in extreme-ultraviolet(EUV) wavelengths (131, 171, and 304 ˚A). The AIA level 1 data were calibratedusing the standard Solar Software (SSW) program aia prep.pro . In Figure 1,the 171 ˚A images illustrate the whole evolution of the flares (see also the onlinemovies). The four flares share a basic similarity in evolution. The inner ribbonsand part of the outer ribbons brightened first. Then, the rest of the outer ribbonsbrightened sequentially, which is consistent with previous findings (Li et al. , 2017;Xu et al. , 2017). Finally, the brightness of flare ribbons declined gradually withtime and died out. It is noted that CRF1 was associated with a blowout coronaljet propagating in the northwest direction, while the remaining three flares werenot associated with jets.The line-of-sight (LOS) and vector magnetograms of the photosphere wereobserved by the
Helioseismic and Magnetic Imager (HMI; Scherrer et al. , 2012)
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CRF1CRF2CRF3CRF4
Figure 1.
Snapshots of the four flares in AIA 171 ˚A. The top row is for CRF1 and the bottomrow is for CRF4. (Four animations of this figure are available online.) on board SDO with cadences of 45 s and 720 s, respectively. The HMI level 1 datawere calibrated using the SSW program hmi prep.pro . The pre-flare vector mag-netograms were used to extrapolate the coronal magnetic field. Figure 2 showsvector magetograms of the four ARs hosting the flares. We carried out potentialfield extrapolation based on the LOS magnetograms using the Green’s functionmethod (Chiu and Hilton, 1977; Seehafer, 1978). To carry out the nonlinearforce-free field (NLFFF) modeling, we use vector magnetograms and the “op-timization” method (Wiegelmann, Inhester and Sakurai, 2006; Wiegelmann etal. , 2008). Pre-processing of the photospheric magnetograms is conducted beforeNLFFF extrapolation. Figure 3 shows the nonpotential magnetic configurations(blue lines) of the four flares. The bottoms of the boxes are EUV 304 ˚A images ofthe corresponding flares. It is clear that the magnetic configurations of the fourflares are dome-like, implying the existence of well-known fan-spine topology(e.g., Sun et al. , 2013; Zhang et al. , 2021). For CRF1, the direction of possiblespine line is consistent with the axis of the blowout jet (panel (a)). Besides, thefootpoints of field lines match the ribbons of the flares well, thus validating thereliability of NLFFF extrapolation.
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AR 11890
X (Mm)X (Mm) X (Mm)X (Mm) X (Mm) Y ( M m ) Y ( M m ) Y ( M m ) Y ( M m ) AR 11476AR 11936 AR 11991
CRF (cid:11) CRF (cid:12)CRF (cid:13) CRF (cid:14)
HMI vecB (cid:12)(cid:21)(cid:11)(cid:12)-(cid:21)(cid:23)-(cid:11)(cid:21) (cid:12)(cid:21):(cid:11)(cid:12):(cid:21)(cid:21) UT HMI vecB (cid:12)(cid:21)(cid:11)(cid:13)-(cid:11)(cid:11)-(cid:21)(cid:27) (cid:21)(cid:13):(cid:12)(cid:14):(cid:21)(cid:21) UTHMI vecB (cid:12)(cid:21)(cid:11)(cid:13)-(cid:11)(cid:12)-(cid:12)(cid:28) (cid:11)(cid:14):(cid:13)(cid:29):(cid:21)(cid:21) UT HMI vecB (cid:12)(cid:21)(cid:11)(cid:14)-(cid:21)(cid:13)-(cid:21)(cid:23) (cid:21)(cid:21):(cid:21)(cid:21):(cid:21)(cid:21) UT
Figure 2.
HMI vector magetograms of the four ARs hosting the flares. NLFFF extrapolationswere performed using these magnetograms. The red boxes indicate regions for calculating themagnetic free energy, where flares took place. (cid:1)(cid:2)-May-(cid:7)(cid:2)(cid:1)(cid:7) (cid:7)(cid:2):(cid:10)(cid:11):(cid:1)(cid:2) AIA_(cid:10)(cid:2)(cid:15)(cid:7)(cid:16)-Dec-(cid:7)(cid:2)(cid:1)(cid:10) (cid:1)(cid:15):(cid:15)(cid:15):(cid:10)(cid:15) AIA_(cid:10)(cid:2)(cid:15) (cid:2)(cid:11)-Nov-(cid:7)(cid:2)(cid:1)(cid:10) (cid:2)(cid:10):(cid:10)(cid:23):(cid:24)(cid:23) AIA_(cid:10)(cid:2)(cid:15)(cid:2)(cid:24)-Mar-(cid:7)(cid:2)(cid:1)(cid:15) (cid:2)(cid:2):(cid:1)(cid:11):(cid:7)(cid:1) AIA_(cid:10)(cid:2)(cid:15)CRF (cid:1) CRF (cid:7)CRF (cid:10) CRF (cid:15)
Figure 3.
Nonpotential magnetic configuration of the four flares (blue lines). The bottoms ofthe boxes are AIA 304 ˚A images of the flares.
The solar irradiance from a broad band ranging from 1 −
70 ˚A was directlymeasured by the
EUV SpectroPhotometer (ESP) belonging to the
Extreme Ul-traviolet Variability Experiment (EVE; Woods et al. , 2012) on board SDO. The
Multiple EUV Grating Spectrographs (MEGS)-A on board EVE, covering the6 −
37 nm range, records a complete spectrum with a time cadence of 10 s and aspectra resolution of 1 ˚A. The standard SSW program eve integrate line.pro was employed to integrate irradiance over 70 −
370 ˚A using the EVS spectraldata from MEGS-A. The soft X-ray (SXR) fluxes of the flares in 1 − T e ) and emissionmeasure (EM) of the SXR-emitting plasma were derived from the ratio of GOESfluxes (White, Thomas, and Schwartz, 2005). The HXR fluxes at different energybands were obtained from the Ramaty Hight Energy Solar Spectroscopic Imager (RHESSI; Lin et al. , 2002). We made HXR images using the CLEAN method
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Table 2.
Description of the observational parame-ters.Instrument λ Cadence Pixel Size(˚A) (s) ( ′′ )SDO/AIA 131, 171, 304 12 0.6SDO/HMI 6173 45, 720 0.6SDO/EVE 1 −
70 0.25 ...SDO/EVE 70 −
370 10 ...GOES 1 − −
50 keV 4.0 4.0 (Hurford et al. , 2002) at energy bands of 3 − −
12 keV. The observationalproperties of the instruments are listed in Table 2.
3. Energy Partition
Using multiwavelength observations, we calculated different energy components,including: (i) radiative outputs in 1 − −
70 ˚A, and 70 −
370 ˚A; (ii) ra-diative loss from the SXR-emitting plasma; (iii) peak thermal energy of theSXR-emitting plasma; (iv) kinetic energy in flare-accelerated electrons; and (v)magnetic free energy.
As described in Feng et al. (2013), the radiative output of a certain waveband( λ ) is derived by integrating the background-subtracted light curve ( f λ ), U λ = 2 πd Z t t f λ ( t ) dt, (1)where d ≈ . × m (1 AU) signifies the distance between the Sun andEarth, t and t represent the lower and upper time limits (Zhang et al. , 2019).In Figure 4, the left panels show SXR light curves of the flares in 1 − U − is calculated by integrating the background-subtracted fluxes betweenthe two dashed lines. The values of U − , falling in the range of (0.13 − × erg, are listed in the second column of Table 3.Likewise, the left panels of Figures 5-6 show light curves of the four flaresin 1 −
70 ˚A and 70 −
370 ˚A. The right panels of Figures 5-6 show background-subtracted light curves of the flares. The radiative outputs U − and U − are calculated in the same way. The values of U − , falling in the range of(2.8 − × erg, are listed in the third column of Table 3. The values of U − , falling in the range of (1.8 − × erg, are listed in the fourth SOLA: czm.tex; 22 February 2021; 1:31; p. 6 nergy Partition in Four Confined Circular-Ribbon Flares
Figure 4.
Left panels: SXR light curves of the flares in 1 − − column of Table 3. It is seen that U − is 15 −
24 times larger than U − andis ≥
200 times larger than U − , which are consistent with previous results foreruptive (Feng et al. , 2013) and confined flares (Zhang et al. , 2019). The totalradiative output ( U − ) in 1 −
370 ˚A of the flares are estimated to be the sumof U − and U − , i.e., U − = U − + U − . The total radiative loss from hot plasma emitting SXR can be expressed as: T rad = Z t t EM( t ) × Λ( T e ( t )) dt, (2) SOLA: czm.tex; 22 February 2021; 1:31; p. 7 ai et al.
Figure 5.
Left panels: light curves of the flares in 1 −
70 ˚A observed by SDO/EVE. The dashedlines indicate the background fluxes during the flares. Right panels: background-subtractedlight curves of the flares in 1 −
70 ˚A. The vertical dashed lines represent the lower and uppertime limits of integrals.
Table 3.
Event List with Component Energies in unit of 10 erg.Flare 1 − −
70 70 − T rad E th,G E th,R E th,G E th,R E nth E mag E nth E mag CRF1 0.163 41.0 1.90 2.9 20.00 6.26 3.2 130 172.0 75.6%CRF2 0.085 17.0 0.73 2.8 24.60 4.43 5.6 69 97.6 70.7%CRF3 0.030 6.1 0.30 0.75 5.27 3.45 1.5 19 25.2 75.4%CRF4 0.013 2.8 0.18 0.86 5.34 2.88 1.9 13 17.6 73.9% where Λ( T e ) denotes the radiative loss rate (Cox and Tucker, 1969), EM( t ) and T e ( t ) represent the time evolution of EM and T e . Figure 7 shows the dependenceof Λ on T e in the range of 10 -10 K obtained from CHIANTI 9.0 database byadopting the coronal abundances (Dere et al. , 2019).Figure 8 shows EM( t ) and T e ( t ) of the four flares derived from GOES obser-vations. The vertical dashed lines indicate t and t for integral in Equation 2.The values of T rad , being (0.75 − × erg, are listed in the fifth column ofTable 3. It is seen that T rad is several tens of times higher than U − (Feng etal. , 2013; Zhang et al. , 2019). SOLA: czm.tex; 22 February 2021; 1:31; p. 8 nergy Partition in Four Confined Circular-Ribbon Flares
Figure 6.
Left panels: light curves of the flares in 70 −
370 ˚A observed by SDO/EVE. Thedashed lines indicate the background fluxes during the flares. Right panels: background-sub-tracted light curves of the flares in 70 −
370 ˚A. The vertical dashed lines represent the lowerand upper time limits of integrals.
Figure 7.
Radiative loss rate Λ( T e ) as a function of temperature ( T e ) calculated from Chianti9.0 database. SOLA: czm.tex; 22 February 2021; 1:31; p. 9 ai et al.
Figure 8.
Time evolutions of T e and EM of the four flares obtained from GOES observations. The thermal energy of the hot plasma of flares is expressed as: E th = 3 n e k B T e f V = 3 k B T e p EM × f V , (3)where n e is the electron number density, V is the total volume of hot plasma,and f ≈ et al. , 2012; Warmuth and Mann,2016b). In the following, we calculate the peak thermal energy derived fromGOES and RHESSI (Warmuth and Mann, 2016b).For CRFs, whose outer ribbons hardly expand with time, V ≈ A / is assumedto be constant, where A denotes the flare area encircled by the outer ribbons(Zhang et al. , 2019). Figure 9 shows 131 ˚A images of the four flares encircled bythe white boxes when their brightness is nearly maximal. AIA 131 ˚A channel isdominated by the emissions of Fe xxi line (log T ≈ .
05) during flares (Lemen et al. , 2012). In Figure 10, the 131 ˚A light curves of the flares (blue lines) arecompared with the SXR light curves (purple lines), showing that the light curveshave good correlations with correlation coefficients of 0.96, 0.80, 0.94, and 0.90,respectively. Therefore, the hot plasma observed in 131 ˚A serves as a proxy ofSXR-emitting plasma. The areas of flares are calculated by summing up thepixels whose intensities are above an ad hoc criterion, which is taken to be ∼
20 times higher than the average intensity of the nearby quiet region. Theprojection effect of A is corrected by multiplying a factor of (cos µ ) − , where µ signifies the longitude of flare core. The corresponding A and V in 131 ˚A arelisted in the second and fourth columns of Table 4. Combining the four flares inthis study with the two M1.1 flares in AR 12434, it is found that the thermalsource volumes are systematically larger in M-class flares than C-class flares(Warmuth and Mann, 2020).Equation 3 indicates that the peak thermal energy is reached when T e √ EMis maximal. Using observations from GOES (Figure 8), we calculated the peak
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Figure 9.
AIA 131 ˚A images of the four flares near their peak times. Intensity contours ofthe images are drawn with black solid lines. The white boxes indicate the areas for calculatingthe light curves in Figure 10.
Table 4.
Evaluation of the area ( × cm ), volume( × cm ), and peak thermal energy ( × erg) ofhot plasma.Flare A A HXR V V HXR E th,G E th,R CRF1 4.63 2.69 1.00 0.44 20.00 6.26CRF2 4.86 1.78 1.07 0.24 24.60 4.43CRF3 2.11 2.46 0.31 0.39 5.27 3.45CRF4 2.16 2.36 0.32 0.36 5.34 2.88 values E th,G of the flares, which are listed in Table 3 and Table 4. The peakvalues E th,G fall in the range of (5.3 − × erg. The total heating require-ments of the flares, including the peak thermal energy and radiative loss, areestimated to be (0.6 − × erg. Conductive energy loss is not consideredin this study since conduction may be severely suppressed or conduction lossis recycled through conduction-driven evaporation (Warmuth and Mann, 2020).Note that CRF1 was accompanied by a blowout jet. The total thermal energyof CRF1 and the jet is estimated to be (2.3 − × erg, considering that the SOLA: czm.tex; 22 February 2021; 1:31; p. 11 ai et al.
Figure 10.
AIA 131 ˚A light curves (blue lines) and SXR light curves (purple lines) of thefour flares. thermal energies of jets account for to of the footpoint flares (Shimojo andShibata, 2000).Figure 11 shows the HXR images of the four flares near the HXR peak times.The energy bands are 6 −
12 keV for the two M-class flares and 3 − A and V are listed in the third and fifth columns of Table 4.Figure 12 shows selected HXR spectra of the four flares obtained from RHESSIobservations. The spectra are fitted with a combination of a thermal componentand a thick-target nonthermal component. The fitting is performed using thestandard SSW program thick2.pro in the OSPEX package. The parameters ofthermal component, including T in unit of MK and EM in unit of 10 cm − ,are labeled. Using Equation 3, the peak thermal energies ( E th,R ) derived fromRHESSI are calculated and listed in Table 3 and Table 4. The ratio of E th,G E th,R isaccordingly obtained and listed in the eighth column of Table 3. It is revealedthat the ratio is greater than 1.0 for all events, which is consistent with previousresults (Warmuth and Mann, 2020). To estimate the nonthermal energy in flare-accelerated electrons, we integratedthe power of injected electrons over time (Ning and Cao, 2010): E nth = Z t t P nth ( t ) dt = Z t t dE nth dt dt, (4) SOLA: czm.tex; 22 February 2021; 1:31; p. 12 nergy Partition in Four Confined Circular-Ribbon Flares
Figure 11.
HXR images of the four flares near the HXR peak times. The energy bands are6 −
12 keV for the two M-class flares and 3 − where t and t represent the start and end times of flare at energy band of25 −
50 keV. Here, P nth ( t ) can be calculated by integrating the electron power-law spectrum above a low-energy cutoff ( E c ) and below a high-energy cutoff( E h ≈
30 MeV): P nth ( t ) = dE nth dt = Z E h E c A E − δ dE , (5)where A is the electron flux in unit of 10 electrons s − , and δ is the power-law index of nonthermal electrons (see Figure 12). The values of E c are 20,30, 23, and 28 keV, respectively. Using Equation 4 and the above parameters,we estimated the total nonthermal energy in flare-accelerated electrons. Thevalues of E nth , falling in the range of (1.3 − × erg, are listed in the ninthcolumn of Table 3. The ratio of E nth /E th,G is between ∼ ∼ E c (Warmuth and Mann, 2020). Besides, wedid not consider the nonthermal energy in flare-accelerated ions. SOLA: czm.tex; 22 February 2021; 1:31; p. 13 ai et al.
Figure 12.
Selected HXR spectra of the four flares obtained from RHESSI observations andthe corresponding normalized residuals of the spectral fitting. The observed data are repre-sented by the points with error bars. The fitted thermal and nonthermal power-law componentsare drawn with dot-dashed lines and dashed lines, respectively. The sum of both componentsare drawn with thick solid lines. The fitted parameters, including T in unit of MK, EM in unitof 10 cm − , and power-law index of electrons are labeled. As mentioned in Section 2, Figure 2 shows the vector magnetograms of thefour ARs where flares took place. Both potential field and nonpotential fieldextrapolations were performed. Figure 3 shows the nonpotential magnetic fieldlines (blue lines) of the flares. The magnetic free energy ( E mag ) is defined as theexcess magnetic energy of the NLFFF ( E np ) relative to the energy of potentialfield ( E p ): E mag = E np − E p = Z V B np − B p π dV. (6) SOLA: czm.tex; 22 February 2021; 1:31; p. 14 nergy Partition in Four Confined Circular-Ribbon Flares
We calculated E mag in the flare regions as enclosed by the red boxes in Figure 2.The estimated E mag , ranging from 1.8 × to 1.7 × erg, are listed in thetenth column of Table 3. It is obvious that the free magnetic energies are largerthan the nonthermal energies and radiative output in 1 −
370 ˚A, indicating thatthe accumulated free energy before flare is sufficient to provide the kinetic energyin flare-accelerated energies and radiation, thus validating the magnetic natureof confined flares (Priest and Forbes, 2002). The ratio of E nth /E mag for CRFsfalls in the range of 70% −
76% (see the last column of Table 3), which is muchhigher than that of X-class eruptive flares (Feng et al. , 2013; Thalmann et al. ,2015). In other words, more free energy is converted into the kinetic energy offlare-accelerated electrons in confined flares than in eruptive flares, because alarge fraction of free energy is converted into the kinetic, thermal, and potentialenergies of CMEs for eruptive flares (Reeves et al. , 2010; Emslie et al. , 2012;Feng et al. , 2013).
4. Discussion
As mentioned in Section 1, Zhang et al. (2019) explored the energy partition intwo M-class CRFs. The radiative outputs in 1 − −
70 ˚A are obtainedusing the observations of GOES and SDO/EVE. Total radiative loss and peakthermal plasma are calculated using the observations of GOES and SDO/AIA.Nonthermal energy of electrons are derived using the observation of RHESSI (seetheir Table 2). The radiation in 70 −
370 ˚A, total solar irradiance, nonthermalenergy of ions, and dissipated magnetic free energy are estimated according toprevious statistical works. In this study, we calculated the radiation in 70 − et al. (2015) investigated an M6.2confined flare on 2004 July 14. The peak thermal energy and nonthermal energyare calculated to be 3.89 × erg and 3.03 × erg, respectively. Hence, theratio of E nth /E th reaches ∼ SOLA: czm.tex; 22 February 2021; 1:31; p. 15 ai et al.
Figure 13.
Energy components of the four events in this study and the previous two events inZhang et al. (2019). The six events are arranged with increasing flare importance (see text fordetail). The radiative outputs in 1 − −
70 ˚A, 70 −
370 ˚A, total radiative loss, peak thermalenergy derived from GOES and RHESSI, nonthermal energy in electrons, and magnetic freeenergy are labeled with red squares, green rectangles, blue diamonds, cyan hexagons, magentatriangles, yellow triangles, orange triangles, and black circles, respectively.
The right panel of Figure 14 shows the scatter plot of the six events toillustrate the relationship between the maximal temperatures of GOES ( T G inMK) and RHESSI ( T R in MK). It is seen that T R is higher than T G in mostcases and a good linear correlation exists between the two parameters. A linearfit yields T R = 1 . T G − .
85, which lies between T R = 1 . T G − .
12 (Battaglia,Grigis, and Benz, 2005) and T R = 1 . T G − .
61 (Warmuth and Mann, 2016a). Itis noted that our study has limitations due to the small sample size. Additionalstatistical studies using more events and numerical simulations are worthwhileto draw a decisive conclusion.
5. Summary
In this paper, we investigated the energy partition of four confined circular-ribbon flares near the solar disk center. Using multiwavelength observations fromSDO, GOES, and RHESSI, we calculated different energy components, includingthe radiative outputs in 1 −
8, 1 −
70, and 70 −
370 ˚A, total radiative loss, peak
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Figure 14.
Left panel: scatter plot showing the relationship between nonthermal energyand thermal energy (cyan circles) and heating requirement (magenta circles). Right panel:scatter plot showing the relationship between the maximal temperatures of GOES ( T G ) andRHESSI ( T R ). The correlation coefficient ( ∼ y = x curves. thermal energy derived from GOES and RHESSI, nonthermal energy in flare-accelerated electrons, and magnetic free energy before flares. The main resultsare as follows:1. The energy components increase systematically with the flare importance orpeak GOES flux, indicating that more energies are involved in larger flares.The magnetic free energies are larger than the nonthermal energies and radia-tive outputs of flares, which is consistent with the magnetic nature of flares.The ratio E nth E mag of the four flares, being 0.70 − Acknowledgements
The authors are grateful to the referee for valuable sug-gestions. The authors thank Drs. Tie Liu, Yanjie, Liu, and Ya Wang for helpfuldiscussion. SDO is a mission of NASA’s Living With a Star Program. AIAand HMI data are courtesy of the NASA/SDO science teams. This work isfunded by NSFC grants (No. 11790302, 11773079, 41761134088, 11473071), theInternational Cooperation and Interchange Program (11961131002), the YouthInnovation Promotion Association CAS, CAS Key Laboratory of Solar Activity,National Astronomical Observatories (KLSA202006), and the Strategic PriorityResearch Program on Space Science, CAS (XDA15052200, XDA15320301).
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