Properties of a Small-scale Short-duration Solar Eruption with a Driven Shock
Beili Ying, Li Feng, Lei Lu, Jie Zhang, Jasmina Magdalenic, Yingna Su, Yang Su, Weiqun Gan
DDraft version March 2, 2018
Preprint typeset using L A TEX style AASTeX6 v. 1.0
PROPERTIES OF A SMALL-SCALE SHORT-DURATION SOLAR ERUPTION WITH A DRIVEN SHOCK
Beili Ying , Li Feng , Lei Lu , Jie Zhang , Jasmina Magdalenic , Yingna Su , Yang Su , Weiqun Gan Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences,210008 Nanjing, China School of Astronomy and Space Science, University of Science and Technology of China, Hefei, Anhui 230026, China Max-Planck-Institut f¨ur Sonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077, G¨ottingen, Germany State Key Laboratory of Space Weather, National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China Department of Physics and Astronomy, George Mason University, Fairfax, VA 22030, USA Royal Observatory of Belgium, Belgium
ABSTRACTLarge-scale solar eruptions have been extensively explored over many years. However, the propertiesof small-scale events with associated shocks have been rarely investigated. We present the analysesof a small-scale short-duration event originating from a small region. The impulsive phase of theM1.9-class flare lasted only for four minutes. The kinematic evolution of the CME hot channel revealssome exceptional characteristics including a very short duration of the main acceleration phase ( < ∼
50 km s − ) and peak velocity ( ∼ − ).The fast and impulsive kinematics subsequently results in a piston-driven shock related to a metrictype II radio burst with a high starting frequency of ∼
320 MHz of the fundamental band. The typeII source is formed at a low height of below 1 . (cid:12) less than ∼ (cid:12) . We find that the CME ( ∼ × erg) and flare ( ∼ . × erg)consume similar amount of magnetic energy. The same conclusion for large-scale eruptions implies thatsmall- and large-scale events possibly share the similar relationship between CMEs and flares. Thekinematic particularities of this event are possibly related to the small footpoint-separation distanceof the associated magnetic flux rope, as predicted by the Erupting Flux Rope model. Keywords:
Sun: corona − Sun: coronal mass ejections (CMEs) − Sun: flare − Sun: flux rope − Sun:shock wave INTRODUCTIONCoronal mass ejections (CMEs) and flares are two mostimportant eruptive phenomena in the atmosphere of theSun, and are now regarded as the primary solar driversof geomagnetic storms and ionospheric disturbances onthe Earth. Theoretically and observationally, many re-searches found that a CME may originate as a magneticflux rope (MFR) which contains a coherent magneticstructure with magnetic field winding around its centralaxis (e.g., Chen 1989; Zhang et al. 2012; Wang et al.2015). In the Atmospheric Imaging Assembly (AIA;Lemen et al. 2012) field of view (FOV), MFRs can oftenbe observed in 131 ˚A and/or 94 ˚A passbands (e.g., Chenget al. 2013, 2014). Using AIA multi-wavelength observa-tions of a flaring active region, Reeves & Golub (2011)has constrained the temperature of MFRs to be between5 MK and 20 MK, which suggests that the MFRs could [email protected] reach flare-like temperatures. When MFRs are observededge-on above the limb, they show up as dark cavitiescharacterized by low densities and high temperatures(Gibson & Fan 2006; Gibson et al. 2010; Kucera et al.2012), exhibiting signatures of spiral motion of plasma(see details in Schmit et al. 2009). Due to the propertyof its high temperature, the MFR observed in the AIAimages is also termed as a “hot channel (HC)” (Zhanget al. 2012). When the HC transits into the FOV ofthe Large Angle Spectroscopic Coronagraph (LASCO;Brueckner et al. 1995), it often appears as a three-partCME structure (Illing & Hundhausen 1983).An MFR can form either before or during an eruption.Many researches have found indirect evidences of the ex-istence of MFR before the eruption, e.g., forward or re-verse S-shaped sigmoids (Rust & Kumar 1996; Canfieldet al. 1999; Tripathi et al. 2009), dark cavities (Low &Hundhausen 1995; Gibson et al. 2004; Dove et al. 2011),as well as filaments (Mackay et al. 2010; Guo et al. 2010; a r X i v : . [ a s t r o - ph . S R ] M a r Su et al. 2011). Patsourakos et al. (2013) presented thefirst direct evidence of a fast CME driven by the destabi-lization of a preformed coronal MFR. Song et al. (2014)witnessed the formation of an MFR during the eruption.Theoretically, CMEs have been presumed as the erup-tion of MFRs: some began with initial coronal FRs inequilibrium (Chen 1989; Vrˇsnak 1990; Chen & Garren1993; Gibson & Low 1998; Roussev et al. 2003), whileothers started with the emergence of FRs from belowthe photosphere (Wu et al. 1997; Fan & Gibson 2003;Manchester et al. 2004). Among the existing CME mod-els, the semi-analytic erupting flux-rope (EFR) model ofCMEs (Chen 1989; Chen & Kunkel 2010) has been testedwidely. The basic physical principle of the EFR modelis that the major radial Lorentz self-force (the Lorentz“hoop force”) accelerates coronal FRs. The EFR modelintroduced the distance S f between the two footpointsof the MFR at the base of the corona. It is suggestedthat S f is a key parameter to determine the dynamics ofMFRs.When the speed of a CME is higher than the localfast magnetosonic speed, a shock wave may be driven.If the CME as a driver pushes the plasma and its bodyexpands in all directions; meanwhile, the offset distancebetween shock front and CME ejecta always increasesin time, this type of shock can be regarded as a three-dimensional piston-driven shock (Vrˇsnak & Cliver 2008).Shock waves are accompanied by a type II radio burstobserved in the radio dynamic spectra as emission lanesslowly drifting to lower frequencies with time. The typeII bursts classically consist of two bands separated byapproximately a factor of 2 in frequency. The lower fre-quency (fundamental) band is approximately at the localplasma frequency f p , while the upper (second harmonic)band is roughly at 2 f p . The starting frequency of themetric type II emission associated with the coronal shockis usually less than 300 MHz with an average of about100 MHz (Gopalswamy et al. 2005). High starting fre-quency implies that the shock is propagating through ahigh density region and hence a low formation height.Some of the coronal shock waves propagate in the in-terplanetary space and become the source of type II ra-dio radiation in the decametric to kilometric wave range(Gopalswamy et al. 2005; Lu et al. 2017; Prakash et al.2017). In some of the type II burst events, fundamentaland/or harmonic bands are split into two morphologi-cally similar lanes (Nelson & Melrose 1985). A numberof explanations were suggested accounting for the mag-netic, Doppler, and geometrical effects (Kr¨uger 1979).Smerd et al. (1974) attributed the band split to the emis-sion from the upstream and downstream shock regions,demonstrating a potentially vital method that could offeran estimation of the corona Alfv´en velocity and magneticfield strength. Mini-filaments are small-scale features in the solar at-mosphere, which frequently occur across the entire disk.They have a spatial scale of a few tens of arcsecs andare the small-scale analog to large-scale filaments (Wanget al. 2000). Mini-filaments located at the edge of ac-tive regions often act as triggers of coronal jets (Honget al. 2016; Wyper et al. 2017). It is rare that thesemini-filaments are observed to be associated with CMEHCs. In this paper we present the analyses of such aCME event and its driven shock. Recently, Kumari et al.(2017) analyzed the same CME-driven shock, and usedthe shock to represent the near-Sun kinematics of theCME. In our study, we have not only investigated theshock properties much more extensively, but also givethe interpretations on what causes the particularities ofthis eruption event. We have quantified the character-istics of various eruption features: CME HC, its drivenbright front as the likely location of the shock, and theassociated flare. As the distance of footpoint separationof an MFR is suggested to be a key parameter to deter-mine its dynamics, we will investigate how the analyzederuption originating from a small source region differsfrom large-scale eruptions. Previous studies have foundequal partition of free magnetic energies between flaresand CMEs in large-scale eruption events (Emslie et al.2012; Feng et al. 2013). Similar energy estimate will alsobe carried out to check whether our small-scale eruptionfollows the same rule.The organization of the paper is as follows. In Sec-tion 2, we describe the observations of our small-scaleeruptive events taken by different instruments. In Sec-tion 3, the properties of the HC and associated brightfront/shock front, the impulsive compact flare, the CMEtravelling into LASCO FOV are analyzed. The deducedcoronal magnetic field is included as well. The last sec-tion summarizes the results and discusses the differencesand similarities between small-scale and large-scale erup-tions. INSTRUMENTS AND OBSERVATIONS2.1.
Instruments
The Atmospheric Imaging Assembly (AIA) launchedas a part of NASA’s
Solar Dynamics Observatory (SDO) mission provides high temporal (12 seconds) and spa-tial resolution (0.6” per pixel) full-disk images of thecorona at multiple wavelengths covering the tempera-ture from ∼ ∼
20 MK. The vector magne-togram data from the Helioseismic and Magnetic Imager(HMI) (Scherrer et al. 2012) aboard the SDO revealsthe magnetic field context of the source region of theeruption event. To examine the Soft X-ray (SXR) emis-sion of the associated flare, we study the data from
Geo-stationary Operational Environmental Satellite (GOES) , roperties of a Small-scale Short-duration Solar eruption With a Driven Shock Flare light curve03:20 03:25 03:30 03:35 03:40Start Time (04−Nov−15 03:15:02)0.11.010.0100.01000.010000.0 C oun t R a t e ( s − de t e c t o r s eg m en t − ) Det 1f,3f,4f,5f,8f,9f3 − 6 keV6 − 12 keV12 − 25 keV25 − 50 keV50 − 100 keV100 − 300 keV300 − 800 keV −9 −8 −7 −6 −5 −4 GO ES F L U X ( W m − ) ABCM
GOES 1−8 Å Figure 1 : The light curves of GOES 1-8 ˚A and RHESSI in multiple energy bands up to 800 keV.and discuss the Hard X-ray (HXR) emission through the
Reuven Ramaty High-Energy Solar Spectroscopic Imager(RHESSI) mission (Lin et al. 2002). For the associatedCME, we use the data from the Large Angle Spectro-scopic Coronagraph (LASCO) C2 aboard the
Solar andHeliospheric Observatory(SOHO) with the field of view(FOV) 1.5-6 R (cid:12) . In order to investigate the type II ra-dio burst associated with the CME-driven shock, we uti-lize the radio dynamic spectra from Learmonth Obser-vatory in Australia, with the frequency range of 25-180MHz, and the temporal resolution of 3 seconds, and fromCulgoora observatory whose frequency range of 18-1800MHz. 2.2. Event Overview
On November 4, 2015, an eruption occurred from asmall region at the edge of NOAA active region 12445(W70 o , N15 o ) located close to the west solar limb. TheGOES 1-8 ˚A SXR flux indicated by the black line in Fig-ure 1 shows that the M1.9-class flare in this event has ashort duration of about 18 minutes, and its flux startsto rise at 03:21 UT and peaks at 03:26 UT. RHESSIphoton light curves in different energy bands within 3-800 keV are also presented in Figure 1. The enhance-ment of the photon count rates in the high energy bandof 300-800 keV implies that the electrons were probablyaccelerated to high energies.Figure 2 is an overview of the AIA observations of theevent including the evolution of the mini-filaments (a-c), CME HC (d-i), and a bright front preceding the HC (f-i). Panels (a-c) present the evolution of mini-filamentsin AIA 211 ˚A ( ∼ ∼ ∼ ∼ ∼ ∼ Figure 2 : (a)-(c) Evolution of the mini-filaments as observed in AIA 211 ˚A ( ∼ ∼ ∼ roperties of a Small-scale Short-duration Solar eruption With a Driven Shock Figure 3 : SDO/AIA 94 ˚A ( ∼ ×
50 arcsec with mixedmagnetic polarities. Blue arrows in Figure 2 (d), (e) and(i) have the same coordinates. The upper arrow indicatesthe fixed footpoint of a coronal loop. As time elapses, thefootpoint becomes brighter and brighter. We infer thatthe accelerated electrons were released from the flaringregion, transported along the magnetic field lines indi-cated by the coronal loop structure, and deposited en-ergy at the other footpoint. The lower arrow is to markthe near top of the loop, and the change of the stand-offdistance between the loop top and the arrow shows theheight evolution of the loop top. Yellow arrows in Fig-ure 2 (d) and (e) indicate the position of the HC front.Figure 2 (f-i) are synthetic images with AIA 94 ˚A base-difference images in green channel and AIA 211 ˚A base-difference images in red channel observed from 03:24 UTto 03:26 UT. Figure 2 (i) displays the synthesized imageat the GOES peak time. Both a bubble-like HC boundedby a green curve and a bright front preceding the HCbounded by a white curve can be clearly seen. Followingthe evolution from Figure 2 (f) to (i), we can observe the northward deflection of HC which is further validated bythe LASCO image in Section 3.4. ANALYSIS AND RESULTS3.1.
Propagation and Expansion of the Hot Channel
In order to display the rising motion of the HC noseand flank as well as the lateral expansion of the HC flank,we select two slices (1 and 2) along its propagation di-rection as shown in Figure 3 (a), and three slices 4 to 6along the expansion direction of the HC flank which isperpendicular to the main propagation direction (slice 1)as shown in Figure 3 (b). Slice 3 is selected to track theHC deflection. In the minutes after ∼ ∼ ∼ (a) (b)(c) Figure 4 : (a) Base difference distance-time plots of the 94 ˚A passband along the slices 1, 2 and 3 as shown in Figure 3(a). The track marked by the white arrow denotes the distance evolution of the coronal loop. (b) Velocity evolution ofthe HC along slices 1, 2, and 3. The black-solid profile denotes the GOSE 1-8 ˚A SXR flux of the associated flare, andthe yellow (green) curve is the photon count rates in the high energy band of 100-300 (50-100) keV. (c) The evolutionof acceleration along slice 1. The vertical dotted lines indicate the transit time at ∼ ± σ = 6 Mm (12 Mm alongslice 3) are used at each distance-time data point. Thenthe velocity and acceleration are derived 100 times us-ing these randomly distributed distance values with thesame procedure described above. The derived error barsare indicated in Figure 4 (b) and (c). Figure 4 reveals that the kinematics of the HC alongits main propagation direction (slice 1) can be clearlydivided into three phases: a slow rise phase before03:22:50 UT with small velocity and acceleration, a fol-lowing fast rise phase from 03:22:50 UT to 03:24:10 UTwith a peak velocity of about 1800 km s − and a peakacceleration of about 50 km s − . The second phaseis the main acceleration phase. The third phase after03:24:10 UT is the residual acceleration phase and ischaracterized by a peak deceleration of about 30 km s − (more details can see Table 1 ).Figure 4 (b) demonstrates that the HC main acceler-ation phase coincides very well with the flare impulsivephase as indicated by the RHESSI light curves. It im-plies that the impulsive acceleration phase of the HCis closely related to the magnetic reconnection process.This scenario is in general consistent with the CME-flaretemporal relationship described in Zhang et al. (2001)and Zhang & Dere (2006). However, there are a fewparticularities we need to point out for this event. roperties of a Small-scale Short-duration Solar eruption With a Driven Shock (a) (b)(c) Figure 5 : (a) Base difference distance-time plots of the 94 ˚A passband along slices 4-6 as shown in Figure 3 (b). (b)The evolution of the HC width along slices 4-6 with different colors obtained from the data in panel (a). (c) Theevolution of the HC expansion velocity derived from the data in panel (b). The error bars in panel (c) are propagatedfrom the uncertainty of ± Table 1 : Different phases of the HC & the bright front (BF) along slice1
Time HC phase a BF phase b c Fast rise (main acceleration) Fast rise03:24:10 d Peak speed Peak speed03:24:10-03:33:30 Residual acceleration Deceleration phase03:25:00-03:39:00 — Type II burst lifetimeNotes: a The results of the HC are derived from AIA 94 ˚A images. b The results of the BF are derived from AIA multi-band images. c The spatial separation time between the HC and the BF along slice 2 is at 03:23:10 UT. d The separation time in space between the HC and the BF along slice 1. - The maximal acceleration rate of about 50 km s − during the main acceleration phase is two orders ofmagnitude larger than the average rate of 331 ms − given in Zhang & Dere (2006) and one order ofmagnitude larger than their maximal value of 4464m s − .- The duration of the main acceleration phase is nomore than two minutes, which is smaller than theminimal value of 6 minutes in Zhang & Dere (2006). - The acceleration magnitude (A) and the dura-tion (T) is in general following the rule pro-posed by Zhang & Dere (2006) that the shorterthe duration, the larger the acceleration. How-ever, the magnitude A of 50 km s − is higherthan the value derived from the scaling lawA(m s − ) = 10 , − (minute) derived in Zhang& Dere (2006).- The deceleration of the HC in the residual accel- eration phase with maximal value of about 30 kms − is much larger than the reported value of 131m s − in Zhang & Dere (2006).Figure 5 presents the lateral expansion properties ofthe HC flank. Figure 5 (a) includes three stack plotsof the AIA 94 ˚A base-difference intensity along slices 4-6. The derived HC widths along these three slices aredemonstrated in Figure 5 (b) in different colors. Thecorresponding expansion velocities and their associatederror bars are calculated with the same method as usedfor the propagation. Figure 5 (c) reveals that the ex-pansion velocity has a peak value of about 1350 km s − along slice 6 at 03:25:00 UT, and slows down to about1000 km s − .In this event, the duration of the M-class flare impul-sive phase is only about four minutes. The extreme fastspeed and acceleration could be a combination effect ofthe radial motion of HC geometric center and the expan-sion of the HC front in all directions. The expansion ofthe HC front could be caused by the magnetic reconnec-tion that adds new flux surrounding the existing compo-nent of the FR. In addition, the release of a good amountof energy in a very short time might also be the reason ofthe rather high value of deceleration. The decelerationis caused by the constraint of the magnetic field linesoverlying the HC as will be see in Section 3.4. We findthat the HC reached a distance of about 1.1 R (cid:12) when itattained the peak velocity at 03:24:10 UT in AIA FOV.In Zhang & Dere (2006), the analyses were based on theobservations with LASCO C1, C2, and C3 whose FOV isfrom 1.1 R (cid:12) . Therefore, our event can be regarded as acomplementary case for the statistics of the CME kine-matics. However, when comparing our event with someother events with the peak velocity also occurred below1.1 R (cid:12) (e.g. Cheng et al. 2014), the characteristics ofits high peak velocity, acceleration and deceleration, andshort energy release is still very prominent. Moreover,due to its very high velocity, although the deceleration isalso very high, the HC was able to reach the LASCO C2FOV and did not evolve to a failed-eruption event as inCheng et al. (2014) and Song et al. (2014).3.2. Piston-driven Shock Wave
Radio Type II Burst
Type II solar radio bursts are slowly drifting struc-tures identified in dynamic spectra. They are generallyconsidered to be radio signatures of shock waves. Elec-trons accelerated at the shock front generate Langmuirwaves which are converted to electromagnetic waves nearthe electron plasma frequency f p and 2 f p . Type II emis-sion bands are sometimes showing split to two lanes ofsimilar intensity and morphology, so called band split.This characteristic is frequently consider to be due to emission from the upstream and downstream shock re-gion (Smerd et al. 1974, 1975). In our event, the metrictype II burst, observed by the Learmonth and Culgooraradio spectrographs, exhibits a well defined fundamentaland a second-harmonic emission band (hereinafter F- andH-band, respectively), both being split in two parallellanes. To obtain complete F- and H-bands, we combinethe dynamic spectrum observed by the Learmonth ra-dio spectrograph in the frequency range of 25-180 MHz,and the dynamic spectrum observed by the Culgoora ra-dio spectrograph in the frequency range of 18-25 and180-1000 MHz. To further make the F- and H-bandsprominent, we reduce the noise level. The data points inthe radio-quiet time are selected as the background levelof radio emission in time intervals 03:12-03:20 UT and03:42-03:48 UT. For each frequency, we obtain a meanvalue of the background from the data in the chosen timeranges. Then, the intensity in each frequency is dividedby the obtained mean value correspondingly. The finalspectrum is presented in the upper panel of Figure 6.The type II burst signals commence at about 03:25:00UT with an unusual higher starting frequency of about320 MHz in the F-band, which is higher than 215 MHzderived in Kumari et al. (2017) for the same event. Theband-split structures are also visible which were not an-alyzed in Kumari et al. (2017). The distinguished F-andH-band emissions are marked by red pluses and black as-terisks, respectively. The segments with clear band-splitsignals are indicated by vertical dashed lines. We findthat the lower (higher) H-band frequency f HL ( f HU ) isproportional to the lower (higher) F-band frequency f F L ( f F U ) with f HL (cid:39) . f F L ( f HU (cid:39) . f F U ).On account of the longer lifetime of the lower branchof the H-band, we utilize f HL to derive the upstreamplasma frequency with f p (cid:39) f HL / .
93, and further ob-tain the electron density n in units of cm − with f p =9 × − n MHz. To convert the derived electron densityto a radial distance, a density model n ( r ) has to be in-voked. In our case, the hybrid model proposed by Vrˇsnaket al. (2004) is used, and it has a smooth transition fromthe active region corona to the interplanetary range: n [10 cm − ] = 15 . R + 3 . R + 1 R + 0 . R . (1)The inverted radial distances are illustrated by the redsquares in Figure 7. We can see that the Type II sourceformed at a low height below 1.1 R (cid:12) . The red solid lineis the corresponding cubic spline fitting. we have derivedthe velocity-time plot which is shown by blue squares inFigure 7. The associated error bars are propagated fromthe uncertainty in frequency of 5%. The motion of thetype II source slows down from 1750 km s − at 03:25 UTto 500 km s − at 03:38 UT.Band split in radio dynamic spectra is useful to infer roperties of a Small-scale Short-duration Solar eruption With a Driven Shock -Learmonth--Culgoora- Start Time ( 04-Nov-2015 03:11:59)1001000 F r equen cy ( M H z ) F r equen cy ( M H z ) Figure 6 : Radio dynamic spectrum from the Learmonth and Culgoora radio spectragraph. The spectrum in thefrequency range from 25 to 180 MHz is observed by Learmonth spectrograph, while the spectrum in the range of 18-25MHz and 180-1000 MHz is by Culgoora spectrograph. The bottom panel is the same as the top panel except for themarking symbols. In the bottom panel, the data points with visible band split signals are marked by the dashed lines.Red plus and black asterisk signs delineate the F- and H-band, respectively.0
Figure 7 : Properties of the type II bursts. The red squares represent the inverted radial distances of the type II burstusing the density model of Vrˇsnak et al. (2004). The blue square signs denote the shock radial speed derived from thetype II radio burst.shock wave properties (Vrˇsnak et al. 2001, 2002, 2004;Gopalswamy et al. 2012; Su et al. 2016). The instanta-neous split ∆ f ( t ) at the moment t is usually defined asthe difference ∆ f ( t ) = f U ( t ) − f L ( t ), where f U ( f L ) isthe frequency along the upper (lower) frequency branch.Then the relative instantaneous split is the ratio of∆ f ( t ) /f L ( t ) which spans in a range from 0.14 to 0.48.The derived relative split in our event is within the rangeof 0.05-0.6 obtained by Vrˇsnak et al. (2001). The com-pression ratio X is defined as the shock down-stream toup-stream density ratio n /n , and is a quantity whichcharacterizes the shock strength. In Figure 8 (a), thecompression ratio, deduced with n /n = ( f F U /f F L ) and n /n = ( f HU /f HL ) showing red and black signsrepresent X derived from the band split of F- and H-band, respectively. We find that the shock strengthdecreases from 2.2 to 1.3 within 14 minutes. To com-pute the Alfv´enic mach number M , we assume a quasi-perpendicular shock and adopt the formula introducedin Draine & McKee (1993), n n = 2( γ + 1) { D + [ D + 4( γ + 1)(2 − γ ) M − ] / } , (2)where D = ( γ −
1) + (2 /M s + γ/M ), γ is the adiabaticindex and set as 4 / /
3, and M s = V sh /C s is thesonic Mach number in which V sh is the radial speed ofthe shock presented in Figure 7, C s is the sound speed.For T=1.5 MK and m = 1 . × . × − g theaverage particle mass in the corona (Aschwanden 2005), and according to the formula C s = (cid:114) γpρ = (cid:114) γRTM = (cid:114) γkTm , (3)the sound speed is C s = 114 (127) km s − for γ = 4 / / M which can be de-rived from Equation (2) is shown in Figure 8 (b). The pri-mary uncertainty in M is propagated from the compres-sion ratio X . The calculated M values are indicated bydiamonds (triangles) with γ = 4 / / V A = V sh /M yields the Alfv´en speed decreasing with theheliocentric distance. Once we get V A , the magnetic fieldstrength in the upstream medium can be calculated: B = 5 . × − V A f p . (4)The upstream frequency f p has been obtained thereinbe-fore, and shown in Figure 8 (d). Dulk & McLean (1978)derived an analytical equation for B ( r ): B = 0 . r − − . , (5)where r is the heliocentric distance in units of solar radii.For r ( R (cid:12) ) = 1 . − .
1, our measurements are somewhathigher, but comparable with the value given by this for-mula. 3.2.2.
Imaging Observations
As indicated in Figure 2, a bright front appeared pre-ceding the HC. Figure 9 shows the evolution of the EUVbright front in AIA multiple wavelengths. The top im-ages of Figure 9 is observed at ∼ roperties of a Small-scale Short-duration Solar eruption With a Driven Shock (a)(c) (b)(d) Figure 8 : (a) Shock compression ratio X calculated from the band split along the F-band (red plus signs) and theH-band (black asterisks). The color code in panels (b)-(d) follow the same denotation. (b) Alfv´enic Mach number M derived with the method of Draine & McKee (1993) for γ = 4 / / V A derived from the ratio of the shock radial speed V sh to the Alfv´enic Mach number M . (d) Coronal magnetic-fieldstrength B obtained from V A and f p . The solid line is the profile derived from the empirical formula in Dulk & McLean(1978). The error bars in all panels are derived and propagated under the assumption of 5% uncertainty in frequency.bright front is clearly seen in AIA 193 ˚A and 211 ˚A im-ages, and only part of it can be distinguished in AIA 304˚A image at ∼ − at 03:24:10 UT and then deceler-ates. The vertical dashed line indicates the time whenthe bright front separates from the HC flank, while thedotted line denotes the separation between the HC noseand the bright front in space. At 03:25 UT, although thespeed of the bright front decreases to around 1200 kms − , it still reaches over the local Alfv´en speed shown in Figure 8 (c). In Kumari et al. (2017) the Gauribida-nur RAdioheliograPH (GRAPH) observations revealedthat the type II source at 03:31 UT was located immedi-ately above the EUV bright front observed at 03:26 UT.Therefore, in combination of the GRAPH source loca-tion, analyses of the type II burst in radio dynamic spec-tra, and EUV bright front evolution, we tend to believethat these bright fronts have close relationship with theshock fronts both in time and in space. At least after03:25 UT we can say that the bright fronts have gonethrough the nonlinear evolution and transformed into ashock wave. Before 03:25 UT the bright fronts may sim-ply be an EUV wave front.In Figure 11 (a), the inverted radial distances from thetype II radio burst are illustrated by the green squares,together with the bright front distance marked by theblue asterisks, which are traced in the AIA compositeimage along the direction of the nose. The blue andgreen solid lines are the corresponding cubic spline fit-tings. In Figure 11 (b), the distinction between the veloc-2 Figure 9 : SDO/AIA base difference images in 193 ˚A (left column), 211 ˚A (middle column) and 304 ˚A (right column)passbands. The time difference between the images in the first and second row is about 1.5 minutes (the time of eachframe is indicated in the inset labels at the top of each panel). The slices in panel (a) numbered as 1 (in blue), 2 (inyellow), and 7 (in red) delineate the regions along which the shock kinematics is characterized (see Figure 10, panel a).In panel (b) the slices 1 and 6 mark the same region pointed by the homologous slices in Figure 3 but with extendedlengths. The width of the slices is 2 arcseconds.ity derived from type II frequency drift and the velocitiesfrom AIA imaging observations can be seen. Figure 11(a) and (b) confirm non-radial propagation of the shockwave. Namely, the coronal electron density models de-scribe the change of density in radial direction, and theyare not very suitable for events with strongly non-radialpropagation. For the type II source, the radial distancesare calculated; while for the presumed shock in AIA im-ages, the distances are measured along a given non-radialdirection in the solar disk plane.We have also investigated the stand-off distances be-tween the HC and its driven shock along slices 1, 2 and 6.Figure 12 (a-c) are composite distance-time images along these three slices with red, green, and blue channels inAIA 211 ˚A, 94 ˚A, and 193 ˚A, respectively. The tracedshock and HC fronts are denoted by white and yellowplus signs. The measured widths of the HC and the shockalong slice 6 are indicated in. Figure 12 (d) with blacktriangles and asterisks, respectively. It can be found thatthe stand-off distance increases with time in this direc-tion. The expansion velocities of the HC are slightlylower than the velocities of the shock as demonstrated bythe orange triangles and asterisks.Figure 12 (e) includesthe distance-time and velocity-time plots of the HC andthe shock along the nose direction (slice 1) marked byblue and red symbols, respectively. The propagation ve- roperties of a Small-scale Short-duration Solar eruption With a Driven Shock (a)(b) Figure 10 : Top panel (a): Red-Green-Blue (RGB) representation of the synthesized base difference distance-time plotsalong the slices numbered as 1, 2, 7 in Figure 9 (a). The emission at 193 ˚A, 211 ˚A, and 304 ˚A are represented in thegreen, red, and blue channels, respectively. In the top panel, the composite distance-time plot only includes AIA 193˚A and 211 ˚A images, as there is almost no signal along slice 1 in 304 ˚A images. The plus signs in white color markthe tracked positions of the bright front. Bottom panel (b): Speed of the bright front along the slices 1, 2 and 7 (samecolor coding as in panel a of Figure 9; as derived from the tracks delineated by the white plus signs in the AIA tricolorframes shown in panel a). The vertical dashed and dotted line indicates the separation time between the HC and theEUV bright front along the flank and nose direction respectively shown in Figure 12. The error bars are propagatedfrom the uncertainty of ± ∼ (a) (b) Figure 11 : (a) Blue asterisks represent the bright front distance traced in the AIA tri-wavelength stack plot along slice1. Green squares represent the inverted radial distances from type II burst using the density model of Vrˇsnak et al.(2004). (b) Velocity evolution of the inferred shock. Green square signs denote the shock radial speed derived fromthe type II burst and plus signs represent the projected speeds of the shock in the AIA tri-wavelength image alongslices 2 and 7. The vertical dotted (dashed) lines have the same meaning as shown in Figure 10. The error bars of theshock radial speed (green) are derived and propagated under the assumption of 5% uncertainty in frequency.time fit to the piston-driven shock scenario (Warmuth2015). A piston-driven shock is generated by the fastand/or impulsive expansion of a driver in all directions,like in an explosion. In our case, the fast and impul-sive expansion of the HC drives the shock. During thisdriving phase, the shock wave propagation is controlledby the motion of the piston, and the stand-off distancebetween shock and piston increases. Once the piston de-celerates, the shock detaches and can continue its prop-agation, although now without additional energy supplyby the piston. The piston can be slower than the shock,and has to accelerate rapidly. ˇZic et al. (2008) found thatthe shock-formation time and shock-formation distanceare approximately proportional to the acceleration phaseduration of the piston, shorter for a higher source speedand acceleration. Therefore, the HC kinematics demon-strated in Figure 4 and Figure 5 can be used to interpretthe short shock-formation time and low shock-formationheight in our event.3.3.
Thermal Properties of the Eruption
We analyze the thermal properties of the HC andits piston-driven shock through the differential emissionmeasure (DEM) method, which measures the contribu-tion of plasma emission in a given temperature range.To reconstruct the DEM, we run the routine “XRT deminterative2.pro” in the Solar Software (SSW) package foreach pixel in the region of interest. The code was orig-inally developed by Weber et al. (2004) and has beenmodified slightly to work with AIA data (Cheng et al.2012). Figure 13 (a) and (b) present the EM in two dif-ferent temperature ranges for the HC driven shock and the HC. One can see that the shock region is primarilydominated by the plasma with log T = 6 . − .
5, andthe HC is heated to a temperature of log T = 6 . − . T = 6 . T = 6 . CME in LASCO Field of View
Due to the high speed of the HC, it propagates to theLASCO/C2 FOV although suffering a significant decel-eration. Figure 14 (a) and (b) show two snapshots dur-ing its propagation. Red dashed lines mark the lead-ing edge of the CME. Its internal structure is quite dif-fuse and does not show the classical three components:core, cavity, and front. Probably the material in mini-filaments involved in the eruption fell back to the surfaceso that they could not form a core in the LASCO FOV.We also notice that the propagation direction changesfrom southwest in the AIA FOV to equatorward in theLASCO FOV. The weak track, appearing in the distance-time plot along slice 3 in Figure 4 (a), also can reveal thedeflection of the HC at the edge of the AIA FOV. It ispresumably influenced by the overlying loops above theHC whose footpoints as marked by the red star in Fig- roperties of a Small-scale Short-duration Solar eruption With a Driven Shock (a) (d)(b) (e)(c) (f) Figure 12 : Panel (a): RGB representation of the synthesized running difference distance-time plot along slice 6 withthe 211 ˚A image in the red channel, the 193 ˚A image in the blue channel and the 94 ˚A image in the green channel.Panels (b)-(c): RGB representation of the synthesized base difference distance-time plots along slices 1 and 2. Inpanels (a-c), the shock and HC fronts are denoted by white and yellow plus signs, respectively. Panel (d): Lateralexpansion width of the HC (black triangles) and of its associated shock (black asterisks) along slice 6 (scale on theleft axis), along with their corresponding lateral expansion velocity (in orange color, scale on the right axis) as derivedfrom the smoothing cubic-spline fittings to the width-time data points. Panel (e): Distance-time (in blue color, scaleon the left axis) and velocity-time (in red color, scale on the right axis) plots of the HC (diamonds) and the shock(asterisks) along slice 1. Panel (f): Evolution of the distance (scale on the left axis) and velocity (scale on the rightaxis) of both the HC and the shock along slice 2. The dotted (dashed) lines indicate the time when the shock and theHC along slice 1 (slice 2) start to separate in space.6 (a) (b) ⇒ ⇑
Figure 13 : (a) EM in temperature range from 6 . − . . − . − . To derive the CME mass, we as-sume that it propagates in the plane of the sky and calcu-late the electron column density and the resultant massin each pixel according to the Thomson scattering theory(Feng et al. 2015a,b). The total mass is then derived bysumming the mass in the area defined by the red dashedlines in Figure 14. We find that the CME mass increaseswith time and later reaches an almost constant value.It has a magnitude of 10 g, but is subject to a largeuncertainty in the background subtraction. Because ofthe existence of a preceding CME indicated by the whitearrow in Figure 14 (a), the mass calculated from base-difference images may be under-estimated. Therefore, wesubtract two different backgrounds before mass calcula- tion. One is a 12-hour minimum image calculated as theminimum values of images from 00:45 UT to 12:57 UT,the other is a pre-event image at 03:45:09 UT. In Fig-ure 15 (b), the corresponding mass is delineated by thedashed line in the former case, by the dash dotted linein the later case. Their average is indicated by the solidline. Based on the computed mass, height, and velocity,we estimate the potential and kinetic energy of the CME.The obtained results are illustrated in Figure 15 (c) and(d). The magnitude of the potential energy is on an or-der of 10 erg, which is about one order of magnitudelarger than the kinetic energy. DISCUSSIONS AND CONCLUSIONSWe have made comprehensive study on the small-scaleshort-duration eruption associated with mini-filamentsoccurred on November 4th, 2015. The source region ofthe eruption is a small-compact area with multiple mag-netic polarities located at the edge of NOAA AR 12445 roperties of a Small-scale Short-duration Solar eruption With a Driven Shock ⇓ (a) (b) (cid:63)(cid:63) (c) Figure 14 : (a)-(b) White-Light coronagraph observations of the CME at different times. The red dashed line definesthe leading front of the CME, and the white arrow points to a preceding CME event. The white circle and plus signdefines solar disk and solar center, respectively. (c) Coronal magnetic field lines extrapolated with the PFSS methodover-plotted in the AIA 131 ˚A image. The footpoints of the streamer arcades overlying the HC are marked by two redstars.close to the west solar limb. Kumari et al. (2017) ana-lyzed the same shock event. In our paper we focused notonly on the analysis of the type II burst and shock, butalso on the analysis of its driver, i.e., the CME. We didnot use the shock to represent the near-Sun kinematics ofthe CME as in Kumari et al. (2017). We present detailedanalyses of the CME hot channel itself and its temporaryand spatial relationship with the shock. Through thestudy of HC-shock relationship, we then can infer whythe shock has an unusual high starting frequency andlow formation height which was not included in Kumariet al. (2017). The unusual large acceleration and highspeed of the HC are the cause of high starting frequency.Concerning the type II dynamic spectra, we used higher-resolution data in which band split can be observed whichallows us to further infer important parameters relatedto the shock than Kumari et al. (2017). Therefore, themain conclusions are listed below:- Although the kinematics of the HC is in generalconsistent with the scenario of three-phase evolu-tion, it has a very short duration (less than 2 min-utes) in the main acceleration phase, and has anexceptional high maximal acceleration rate ( ∼ − ), peak velocity ( ∼ − ), and maxi-mal deceleration rate ( ∼
30 km s − ), comparing tothe kinematic statistics in Zhang & Dere (2006).We also detect a very fast expansion along the HCflank with a peak velocity of about ∼ − .- The fast motion of the HC along different direc-tions acts as a piston and drives a fast shock. Thekinematic measurements including velocity, accel-eration, stand-off distance, etc., of the HC and itsdriven shock fit the piston-driven shock scenario.The analyses of the associated type II burst to- gether with the AIA imaging data reveals verylow starting height of the type II burst, at about1 . (cid:12) . The type II band split is used to constrainthe decrease of the shock compression ratio (2.2to 1.3), Alfv´enic mach number (1.9 to 1.3), fromwhere the Alfv´en speed (1000 to 400 km s − ) andthe coronal magnetic field strength (13 to 0.5 G)are derived in the heliocentric distance from 1.1 to2.3 R (cid:12) .- The thermal properties of the HC and its drivenshock are consistent with those derived for large-scale events based on the DEM analyses.- The CME observed in the LASCO/C2 FOV hasa small leading-edge velocity (390 km s − ), smallmass ( ∼ g), potential ( ∼ erg) and kinetic( ∼ erg) energy.Concerning flare and CME energetics, Emslie et al.(2012) and Feng et al. (2013) have found the energyequal-partition between the flare and the CME for large-scale eruptions. For this small-scale event, the total radi-ated output classified as the ‘final’ energy (Emslie et al.2005) is used to estimate the flare energy, and the sum ofthe potential and kinetic energy is a measure of the CMEenergy. The GOES and RHESSI observations show im-pulsive and short duration M1.9 flare, shorter than thatof those large-scale eruptions which often last for tens ofminutes to several hours in previous studies (Chamberlinet al. 2012; Feng et al. 2013; Cheng et al. 2014, 2015).Chamberlin et al. (2012) found that the total radiatedoutput of flares depends more on the flare duration thanthe typical GOES X-ray peak magnitude classification.Here, we estimate the output irradiance by using the dataof the EUV Variability Experiment (EVE; Woods et al.8 (a)(b) (c)(d) Figure 15 : Panel (a): Height-time plot of the CME leading edge. Panels (b)-(d): Mass, potential energy, and kineticenergy profiles, respectively, of the CME feature. The dashed lines represent the upper limit, which was obtainedfrom subtracting a 12-hour minimum image; and the dotted lines depict the lower limit, which was obtained fromsubtracting a pre-event image as the background. The average values of the upper and lower limits are denoted bythe solid lines.
Figure 16 : The irradiance in the range of 0.1-7nm recorded by the SDO EVE/ESP. The solid linepresents the absolute irradiance. The background andbackground-subtracted irradiance are delineated by dot-ted line and dashed line, respectively.2012) onboard SDO. The light curves of the 0.1-7 nmwaveband derived from the Extreme Ultraviolet Spectro-Photometer (ESP) is shown in Figure 16, and then usedto quantify the radiative output of the EUV emission.The integration of the background-subtracted irradiance over the flare duration yields the radiated output in 0.1-7nm is about 1 . × erg. The total radiated output is afew times larger than this value (Emslie et al. 2012). Wecan find that the flare probably consumes similar amountof magnetic energy to the CME (4 × erg) in thisevent. Due to the short duration of the flare, comparedwith the large-scale eruptions (Emslie et al. 2012; Fenget al. 2013), the released magnetic energy of this flare isabout one order of magnitude lower. Aschwanden (2016)selected 399 M and X class flare events and obtained theparameters of the associated CMEs. We find that theCME mass and energy, in this event, lies in the lower endof their statistics. Although the absolute quantities of theflare and CME energy are smaller, the very similar par-tition of the flare and CME energy along with a similarmulti-phase kinematics may imply that small- and large-scale events share similar relationship between flares andCMEs. Although we have found some common charac-teristics between the small- and large-scale eruptions interms of the flare-and-CME temporal and energetic re-lationships, we also need to understand what makes thisevent kinematically special, e.g., a very short impulsiveacceleration phase, and a very high acceleration. We ex-plore the Erupting Flux Rope model proposed by Chen(1989), in which there exists a relationship between the roperties of a Small-scale Short-duration Solar eruption With a Driven Shock a of an MFR (or a HC, its manifestation inAIA) and its geometrical size: a = d Zdt ∝ [ R ln(8 R/a f )] − , (6) R = Z + S f / Z . (7)where Z is the height of the centroid at the FR apex; R is the major radius of the current channel assumed to beuniform along the MFR; a f is the minor radius at thefootpoint which is also assumed as an invariant; S f isthe distance of FR footpoint separation. Chen & Krall(2003) found a scaling law related to the accelerationof CMEs and S f : there are two critical heights scaledwith S f in condition that the studied structure is anMFR, and the scale is given by Z ∗ = S f / Z m (cid:119) . S f , such that the height Z max where the accelerationof the centroid of the MFR apex is maximal satisfies Z ∗ < Z max < Z m . We speculate that S f is very smalland eventually leads to a very low Z max . According toEquation (6) and (7), there is also a tendency that thesmaller the major radius R is, the larger the accelerationof the MFR will be. Therefore, the large accelerationtogether with the low height at which the MFR reachesits maximal acceleration jointly produce a short durationof the impulsive acceleration phase.We are very grateful to anonymous referee for veryconstructive comments and suggestions. We thankJames Chen for his suggestions on the EFR model.We are also thankful to the World Data Centre ofthe Australian Bureau of Meteorology, Space WeatherServices for the Culgoora and Learmonth radio spec-trograph data. SDO is a mission of NASA’s LivingWith a Star Program, SOHO is a mission of interna-tional cooperation between ESA and NASA. 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