Quasi-Periodic Particle Acceleration in a Solar Flare
Brendan P. Clarke, Laura A. Hayes, Peter T. Gallagher, Shane A. Maloney, Eoin P. Carley
DDraft version February 9, 2021
Typeset using L A TEX twocolumn style in AASTeX63
Quasi-Periodic Particle Acceleration in a Solar Flare
Brendan P. Clarke ,
1, 2
Laura A. Hayes , Peter T. Gallagher , Shane A. Maloney ,
1, 2 andEoin P. Carley
1, 2 School of Cosmic Physics, Dublin Institute for Advanced Studies, Dublin, D02 XF85, Ireland School of Physics, Trinity College Dublin, Dublin 2, Ireland Solar Physics Laboratory, Heliophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA (Received 17 November, 2020; Revised 27 January, 2021; Accepted 7 February, 2021)
Submitted to ApJABSTRACTA common feature of electromagnetic emission from solar flares is the presence of intensity pulsationsthat vary as a function of time. Known as quasi-periodic pulsations (QPPs), these variations in fluxappear to include periodic components and characteristic time-scales. Here, we analyse a GOES M3.7class flare exhibiting pronounced QPPs across a broad band of wavelengths using imaging and time-series analysis. We identify QPPs in the timeseries of X-ray, low frequency radio and EUV wavelengthsusing wavelet analysis, and localise the region of the flare site from which the QPPs originate via X-ray and EUV imaging. It was found that the pulsations within the 171 ˚A, 1600 ˚A, soft X-ray (SXR),and hard X-ray (HXR) light curves yielded similar periods of 122 +26 − s, 131 +36 − s, 123 +11 − s, and137 +49 − s, respectively, indicating a common progenitor. The low frequency radio emission at 2.5 MHzcontained a longer period of ∼
231 s. Imaging analysis indicates that the location of the X-ray and EUVpulsations originates from a HXR footpoint linked to a system of nearby open magnetic field lines. Ourresults suggest that intermittent particle acceleration, likely due to ‘bursty’ magnetic reconnection, isresponsible for the QPPs. The precipitating electrons accelerated towards the chromosphere producethe X-ray and EUV pulsations, while the escaping electrons result in low frequency radio pulses in theform of type III radio bursts. The modulation of the reconnection process, resulting in episodic particleacceleration, explains the presence of these QPPs across the entire spatial range of flaring emission.
Keywords:
Sun: flares – Sun: oscillations – Sun: EUV radiation Sun: X-rays Sun: radio INTRODUCTIONQuasi-periodic pulsations (QPPs) are an importantfeature observed in solar and stellar flare emission(Nakariakov & Melnikov 2009; Van Doorsselaere et al.2016; Kupriyanova et al. 2020). This puzzling phe-nomenon lacks a concrete definition, however, they aretypically described by variations in the flux from a flareas a function of time that appear to include periodiccomponents and time-scales that typically range from 1s up to 1 min, and in extreme cases from ≤ Corresponding author: Brendan P. [email protected] observed during the impulsive phase of solar flares, how-ever, in recent years it has become clear that they canpersist through to the decay phase, after the impulsiveenergy release (Hayes et al. 2016; Dennis et al. 2017;Hayes et al. 2019).QPPs have been reported in a broad range of wave-lengths from decametric radio (Li et al. 2015; Carleyet al. 2019), through to extreme ultra-violet (EUV) andX-rays, (Dominique et al. 2018; Dolla et al. 2012), andeven γ rays (Nakariakov et al. 2009; Li et al. 2020). Sta-tistical studies suggest that QPPs are a common fea-ture, especially in larger flaring events (Sim˜oes et al.2015; Inglis et al. 2016; Hayes et al. 2020). Within thedecimetric waveband, QPPs can manifest as a sequenceof type III radio bursts emanating from the corona as aconsequence of accelerated beams of electrons escaping a r X i v : . [ a s t r o - ph . S R ] F e b Clarke et al. a.a.b.
Figure 1. (a): SDO/AIA 171 ˚A passband image of the sunon 2015 Nov 4. The active region associated with the eventis visible in the dashed box at the disk center. (b): TheGOES SXR light curves showing the occurrence of the M3.7class flare. The dashed grey line shows the time at which theimage in panel a was taken. along open magnetic field lines away from the flare site(Aschwanden et al. 1994; Ning et al. 2005; Kupriyanovaet al. 2016). In contrast, QPPs in the EUV are typi-cally observed to originate from the hot plasma in thecoronal loops of a flaring region (Van Doorsselaere et al.2016). In addition to studies of QPPs analysed withinspecific spectral domains, some research has been donefocusing on events containing QPPs across a wide bandof wavelengths. For example, Aschwanden et al. (1993)investigated the timing of HXR pulsations with respectto pulsations seen in radio wavelengths (100-300 MHz)and found evidence for a strong causal connection. Ad-ditionally, Tajima et al. (1987) found that current loopcoalescence can lead to quasi-periodic amplitude oscil-lations in the microwave, X-ray, and γ -ray wavebands.More recently, Kumar et al. (2016) presented a multi-wavelength analysis of QPPs found to be occurring in HXR, radio (25–180, 245, 610 MHz), and EUV wave-lengths.Several models have been proposed as explanationsfor the presence of QPPs in solar and stellar flares(McLaughlin et al. 2018) which are typically categorisedas oscillatory or self-oscillatory processes. In the regimeof oscillatory processes, QPPs are interpreted as a sig-nature of magnetohydrodynamic (MHD) oscillations in-ducing periodic motions about an equilibrium in theflaring region. This explanation has been promising forsome events, as some observed periodicities of QPPs arein good agreement with that of the timescales of MHDwaves in the corona (Nakariakov & Melnikov 2009).There is widespread observational evidence for MHDwaves existing in the corona and it is possible that kink,toroidal, longitudinal, or sausage modes could causesome of the thermal and non-thermal intensity varia-tions that we observe.For example, kink mode oscillations have been re-ported that have an overlapping timescale ( ∼ ulti-wavelength pulsations via time-dependent particle acceleration ∼ ∼ R (cid:12) ) Pre-flare phase Impulsive phase Decay phase a.b.
Figure 2. (a): The normalised SXR light curve from GOES(1-8 ˚A) at the time of the flare. (b): The time deriva-tive of the SXR emission and the HXR light curve fromFERMI GBM (25-50 keV). The QPPs present are labelledone through seven. Here, we see a clear illustration of the Ne-upert effect and indicate the seven primary QPPs analysedin this work.
The flare presented in this paper is a GeostationaryOperational Environmental Satellite (GOES) M3.7 classflare that occurred on 04-Nov-2015. An overview of theactive region located at the center of the solar disk asobserved in 171 ˚A is shown in Figure 1a and the lightcurves of the flare from the GOES X-Ray Sensor (XRS)in two channels (1-8 ˚A in red and 0.5 - 4 ˚A in blue)is shown in Figure 1b. In Section 2, the instrumentsused for this study: The Atmospheric Imaging Assem-bly (AIA) on board the Solar Dynamics Observatory(SDO) (Lemen et al. 2012a), the Reuven Ramaty HighEnergy Solar Spectroscopic Imager (Lin et al. 2002),the WAVES instrument on board the WIND satellite(Bougeret et al. 2008), The Gamma-ray Space Telescope(GBM) onboard Fermi (Meegan et al. 2009), and theGOES XRS are briefly introduced. Details of the anal-ysed event and data analysis techniques are also includedin this section. In Section 3, we present our observa-tions alongside our analysis of the QPPs. In Section 4,we present a discussion and interpretation of the workbefore concluding our findings in Section 5.
Clarke et al. INSTRUMENTATION, OBSERVATIONS, ANDDATA ANALYSIS2.1.
Instrumentation and observations
The GOES XRS measures the solar SXR fluxes inte-grated over the entire solar disk. It has a cadence of 2s with two channels of 0.5-4 ˚A and 1-8 ˚A. In this work,we primarily focus on the 1-8 ˚A channel as it exhib-ited the most pronounced QPPs. Figure 2a shows thislight curve. The pre-flare, impulsive, and decay phasesare also indicated. The event began at 13.31 UT andpeaked at 13.52 UT. Figure 2b shows the time derivativeof this light curve with the HXR light curve observed byFERMI GBM (25-50 keV) overplotted. The Neuperteffect, which refers to the observed phenomenon thatnon-thermal HXR emission coincides temporally withthe rate of rise of the thermal SXR emission (i.e. thederivative), is observed here as it is clear that the pulsa-tions in the SXR derivative are coincidental with thoseobserved in the HXR emission (Neupert 1968). Thisrelates the HXR flux from the flare ‘footpoints’ to thethermal SXRs observed from the heated plasma. Weidentify seven distinct pulsations throughout the eventas shown in Figure 2b. One can see that these pulsationsall occur during the impulsive phase of the flare. This in-dicates that the mechanism producing these QPPs mustbe able to modulate the acceleration of electrons. How-ever, it is clear that some pulsations do persist into thedecay phase within the SXR emission.The most pronounced pulsations we observed withAIA were from the 171 ˚A and 1600 ˚A passbands. Imagesfrom these passbands were used to analyse the period-icity and spatial distribution of the QPPs in EUV. Thecadences of these images were 12 s and 24 s, respec-tively. The 171 ˚A passband is dominated by the Fe XIline and most represents emission from the corona andupper transition region while the 1600 ˚A passband isdominated by C IV and images primarily the upper pho-tosphere/transition region (Lemen et al. 2012b). Theseimages enable us to estimate the layer of the atmospherefrom which the QPPs we observe originate and how theyrelate to one another.RHESSI observed the event up until 13:43 UT be-fore entering spacecraft night. This allowed us to im-age the location of the HXRs produced during the flarefor our analysis. Although RHESSI was unable to ob-serve all the HXR emission throughout the flare, FermiGBM captured this information which we incorporateinto our analysis. The WIND/WAVES RAD2 instru-ment was used to gather radio data. Dynamic spectrafrom 0.02-13.85 MHz (cadence: 16.188 s) were analysedto investigate the low-frequency aspect of the QPPs in the event. The emission at these wavelengths manifestsin the form of type III radio bursts which are a resultof plasma emission (Reid & Ratcliffe 2014). Within thismechanism, the frequency, f p , of the radiation is propor-tional to the local electron density n e via f p ∼ √ n e . a. WAVES RAD 2
171 ÅAIA1600 ÅAIA1-8 ÅGOES25-50 keVFERMI a.b. ~ 16.23 R ⊙ Time lag for beam speed: 0.3 ± 0.2 c
Figure 3. (a): Dynamic spectrum from WIND/WAVESRAD2 showing a series of pulsed type III radio bursts. (b):Multi-wavelength light curves observed from a number ofinstruments. From top to bottom the lightcurves go fromlonger to shorter wavelenghts. This is a proxy for altitudeof the flaring emission source with the radio data represent-ing emission originating from high in the corona down to theHXR emission originating from the footpoints. The black,orange, red, and blue light curves have QPPs well correlatedin time. The green light curve shows the radio emission at 2.5MHz. This frequency was chosen as it captured each pulsemost effectively. The radio QPPs have a longer periodicitywhich we elaborate on in the discussion section. Lines drawnfrom pulses 1 and 7 show the time lag needed for the sourceelectron beams of typical speeds to reach 16 R (cid:12) (approxi-mate height of the radio source) from the flare site. ulti-wavelength pulsations via time-dependent particle acceleration ∼ R (cid:12) .Together, we can use these data to determine infor-mation about the periodicity and location of the QPPsobserved from the HXR footpoints through to the uppertransition region and corona. The altitude at which eachdifferent waveband emits differs significantly. For exam-ple, the HXRs are produced through bremsstrahlung bynon-thermal electrons colliding with the chromospherewhile the type III radio bursts are produced via plasmaemission. Figure 3 is summary of the QPPs analysedin this work. Figure 3a shows the dynamic spectrum ofthe radio emission containing a sequence of type III ra-dio bursts and Figure 3b shows the EUV, SXR and HXRlight curves in which we identify 7 distinct QPPs. TheEUV light curves were extracted from the QPP sourceregion we identified which is explained in Section 3.2.2.2. Data analysis and imaging
Wavelet analysis using a Morlet wavelet was per-formed on the multiwavelength light curves to determinetheir periodicities using the software developed by Tor-rence & Compo (1998). This technique is a powerful toolfor searching within time-series for periodic signaturesas, unlike Fourier analysis, it provides a 2D spectrumof both frequency and time allowing one to assess if aquasi-periodic signature varies in time (De Moortel et al.2002).In order to more accurately determine the period ofthe QPPs via the wavelet analysis, the slowly varyingbackground trend of the flare emission was removed fromeach time-series. This process is shown in Figure 4 forthe case of the SXR emission from GOES. To do this, aspline fit was constructed using a 3rd order polynomialwith 28 samples between nodes. The fit was then sub-tracted from the original data resulting in a time-seriescontaining only the modulation of the emission result-ing from the QPPs. This process was repeated for eachtime-series we analysed. No subtraction was requiredfor the radio light-curve at 2.5 MHz as there was littlebackground in this data. Care was taken to ensure eachfit accurately represented the slowly varying background http://atoc.colorado.edu/research/wavelets/ a.b. Figure 4.
Example of the background subtraction techniqueused to isolate the QPPs. (a): The time derivative of theSXR emission is shown in red with a spline fit to the overalllarge-scale slowly varying emission overplotted in black . Thefit excludes the shorter time-scale variation of the QPPs. (b):The subtraction of the fit from the SXR emission resulting ina time-series containing the QPPs without the slowly varyingbackground emission. emission in order to avoid introducing any artefacts dur-ing the subtractions.In addition to carrying out the wavelet analysis onthe multi-wavelength detrended time-series, we also per-formed the same analysis on the relevant data withoutdetrending in order to cross-check our results. This anal-ysis is provided in the appendix of this paper. We alsomanually determined the period of the QPPs. This wasachieved by visually identifying the time of each pulseand plotting these times against pulse number (1-7).The period can then be simply estimated by fitting astraight line to this data and finding the slope.The PIXON algorithm was used to image the RHESSIHXR sources. It seeks a superposition of circularsources of different sizes and parabolic profiles that mostreplicate the modulations measured by the detectors,while maintaining the fewest degrees of freedom possi-ble. PIXON is thought to provide accurate image pho-tometry in comparison to the other faster algorithmssuch as CLEAN (Hurford et al. 2002). Images taken
Clarke et al. by SDO/AIA were used to analyse the most prominentpulsations in the EUV regime which were found in the171 ˚A and 1600 ˚A passbands. Time-series were con-structed from these images by integrating the emissionover various regions of the flare in order to localise thearea producing the pulsations. This is discussed fur-ther in Section 3.2. Additional data analysis was car-ried out to estimate the height of the source producingthe radio emission via the Newkirk Jr. (1967) electrondensity model. This height was determined to be ∼ R (cid:12) . Figure 3b shows the time lag required to reachthis height from the flaring region with beam speeds of0.1-0.5 c. Type III radio bursts typically have sourceelectron beam velocities of ∼ RESULTSAcross the electromagnetic spectrum, the impulsivenature of the event begins at ∼ ∼ ∼ R (cid:12) . Lines drawn from the peaks of pulses 1 and 7from the 171 ˚A curve are shown that indicate the timedelay required for electron beams of velocities between0.1 and 0.5 c to reach this height. For both pulse 1and 7, there appears to be radio pulsations that occurat the expected times. This analysis suggests that the electron beam speeds are close to the typical value of0.3 c for type III radio bursts. It is clear that the ra-dio QPPs at 2.5 MHz are less correlated with the higherfrequency radiation. There are a number of reasons forwhich one would not expect a one-to-one relation be-tween radio pulsations produced via plasma emission ininterplanetary space and the higher frequency emissionproduced via bremsstrahlung/heating close to the flaresite despite originating from the same populations ofaccelerated electrons. These differences are elaboratedupon in the discussion section.3.1. Periodicities
For each lightcurve, wavelet analysis was conductedover the same time period: 13:34-13:54 UT. The errorfor each result was taken as the range over which theglobal power spectrum was above the 95% significancecurve. The analysis was carried out on the detrendedlight curves. However, the appendix includes the sameanalysis for the data without detrending. The resultsagreed in both cases.Figure 5a shows the wavelet analysis that was carriedout on the GBM 25-50 keV lightcurve. In this plot,the HXR time-series, the wavelet power spectrum, illus-trating power at particular periodicities as a function oftime, and the global power spectrum are shown. A pe-riod of 137 +49 − s was found in this channel. Figures 5b,6, and 7 show this same analysis for the SXR, EUV, andradio wavelengths, respectively. The SXR emission con-tained a period of 123 +11 − s, while the pulsations withinthe 171 ˚A and 1600 ˚A light curves yielded periodicitiesof 122 +26 − s and 131 +36 − s, respectively. The 2.5 MHzlight curve was found to have significant period at atime-scale of ∼
231 s. The time-scales of the QPPs in inthe 171 ˚A, 1600 ˚A, SXR (1-8 ˚A), and HXR (25-50 keV)are therefore all in good agreement within error. Theseresults are summarised in Table 1.In addition to calculating the periods of the lightcurves via wavelet analysis, we also estimated themmanually by visually identifying peaks. Figure 8 showsthe time of the HXR, EUV, and SXR pulsations versuspulse number (see pulses 1-7 in Figure 3). The slopeof this line provides an estimate of the period. Theresult was found to be ∼
109 s. This agrees with the
Table 1.
Comparison of the periods found in the lightcurvesfor each analysed wavelength via wavelet analysis. The ca-dence of the data in each case, ∆ t , is also shown. λ ∼
231 s 122 +26 − s 131 +36 − s 123 +11 − s 137 +49 − ∆ t ulti-wavelength pulsations via time-dependent particle acceleration ~123 s~137 s a.b. FERMI GBM (25-50 KeV)GOES Derivative (1-8 Å)
Figure 5.
Wavelet analysis of the detrended (a): HXR and (b): SXR derivative emission from the flare. The periods werefound to be 137 +49 − s and 123 +11 − s, respectively. The error is taken as the range over which each global power spectrum is above95% significance. results of the wavelet analysis within error. For theradio emission at 2.5 MHz, this analysis was done forthe four main peaks in the time-series, shown in greenin Figure 7 as well as seven peaks which include loweramplitude pulsations, shown in blue in Figure 7. Thisresulted in periods of ∼
230 s and ∼
157 s, respectively. Therefore, this result matches well with the waveletanalysis when only the four main peaks are accountedfor. When the less significant peaks are included, wesee that the period draws closer to that of the higherfrequency radiation. The matching time-scales of the171 ˚A, 1600 ˚A, SXR, and HXR light curves indicate that
Clarke et al. ~131 s~122 s a.b.
Figure 6. (a): Wavelet analysis of the detrended emission at 171 ˚A. (b): Wavelet analysis of the emission at 1600 ˚A. Theperiods were found to be 122 +26 − s and 131 +36 − s respectively. the mechanism producing the QPPs in these wavebandsmust have the same progenitor, that is also likely relatedto the radio emission observed. Our interpretation ofthese results and the relationship between the emissionin each waveband is detailed in Section 4. ulti-wavelength pulsations via time-dependent particle acceleration § ~231 s Figure 7.
Wavelet analysis of the radio emission at 2.5 MHz. The period was found to be ∼
231 s.
230 s 157 s 109 s
Figure 8.
Pulse number versus time of each pulse. The 7HXR/SXR/EUV pulses shown in Figure 3 are plotted usingthe circle symbols. The slope of the straight line fitted tothe data provides an estimate of the period: ∼
109 s. Forthe radio emission at 2.5 MHz, this analysis was done for thefour main peaks in the time-series, as well as for seven peaksin the case where lower amplitude peaks are included. Thisresulted in periods of ∼
230 s and ∼
157 s, respectively.
Spatial analysis
To investigate spatially the regions of the flare fromwhich the QPPs originate, we conducted imaging anal-ysis using RHESSI and SDO/AIA. No radio imaging in-strument was available during the observation. Firstly, we used the PIXON algorithm to determine where thenon-thermal HXRs originated from. The imaging wascarried out over an energy band of 35-70 keV duringthe available time period when RHESSI was observingthe event before entering spacecraft night: ∼ ∼
50 Mm and a loop height of ∼
25 Mm. Thiswas estimated by measuring the separation of the HXRfootpoints and assuming a semi-circular geometry of theloops.These HXRs are produced through non-thermalbremsstrahlung through interaction of the flare acceler-ated electrons with the dense chromosphere which acts a‘thick-target’ (Brown 1971). The mechanism modulat-ing the HXRs that produces the observed QPPs mustbe causing a sequence of episodic or ‘bursty’ energy re-leases that intermittently accelerates electrons result-ing in a modulation of the non-thermal bremsstrahlung0
Clarke et al. a. b. c. d.f. g. h.e.
K1 K2 K3K1 K2 K3
Figure 9.
Spatial analysis of QPPs. (a): Image of the flaring region in 1600 ˚A taken at the time of the first QPP. The RHESSIimage of the three HXR footpoints is overlaid which are labelled within three kernels as K1, K2, and K3. K1 and K2 lie alongone flare ribbon while K3 is located on the other. This image was constructed using the PIXON algorithm over the availabletime period during which RHESSI captured the emission. This time period is shown in magenta with the time-series data in (b).(b-d): Light curves of the HXRs observed by GBM and RHESSI (25-50 keV) and the light curves extracted from the 1600 ˚Aimages taken by AIA at each HXR source location. The light curves were constructed by integrating over the pixels containedin the boxes surrounding the HXR sources in (a). The same analysis is done for the 171 ˚A images as shown in (e-h). It wasfound that the emission in EUV from within K1 produced light curves containing QPPs most correlated with those seen in theHXR emission (b+f). This localises the source of the QPPs to this region of the flare site which is close to a nearby system ofopen and closed magnetic field lines. The animation related to this Figure, provided in the online version of this article, showsthe evolution of the flare at each time step from 13:34 - 13:53 UT. emission. We discuss this further and its relevance tothe QPPs in the other wavebands in Section 4.To determine the location within the flaring regionproducing the QPPs in the 171 ˚A and 1600 ˚A emis-sion, we created time-series from the images taken fromSDO/AIA. To localise the QPP source, we integratedthe emission from each image over each region of theentire active region using various kernel sizes, generatedtime-series for each of these kernels for the duration ofthe flare, and compared the profiles of the time-seriesto that of the HXR emission. This allowed us to obtainthe flux from within each test kernel at each time-stepto compare to the HXR emission. It was found thatthe kernel that produced the most prominent QPPs, aswell as having the same characteristic periodicity as theHXR QPPS, spatially coincided with the location andsize of the HXR source at K1. Figure 9b and 9f illus-trate this in that there is a strong correlation betweenthe QPPs in the EUV emission extracted from K1 andthe HXR emission. The EUV emission from K2 and K3is significantly less correlated to the HXR emission asshown in Figures 9c, 9d, 9g, and 9f. The animation associated with Figure 9, available inthe online version of this article, shows the evolutionof the flare at each time step. It is clear that there isan asymmetry between the light curves obtained for theEUV emission at each HXR source location with K1 be-ing the most correlated to the HXR QPPs. This analysissuggests that K1 is the region of the flare site in whichthe QPPs originate. Figure 10 shows an additional com-parison of the EUV emission from K1 (QPP source) andthe emission obtained from two test regions not associ-ated with the HXR sources. Here, we can see againthat integrating each time step over K1 produces QPPshighly correlated with the HXR emission while doing sofor each test kernel does not. This trend continues nomatter which region of the flare is used to construct theEUV time-series.K1 is associated with open magnetic field lines, iden-tified in the potential field source surface extrapolation(PFSS) shown in Figure 11. PFSS models provide anapproximation of the coronal magnetic field up to 2.5 R (cid:12) based on the observed photospheric field (Schrijver& De Rosa 2003). Here the PFSS is calculated using ulti-wavelength pulsations via time-dependent particle acceleration Test kernel A Test kernel BK1 (QPP source) a. Test kernel ATest kernel BK1 (QPP source)
FERMI 25-50 keV b. K2 K3
Figure 10. (a): SDO/AIA 171 ˚A passband image of theflare site on 2015 Nov 4. Shown are the QPP source (withinK1), the additional two HXR sources (within K1 and K2),and two test kernels representing the arbitrary regions of themap. (b): The time-series obtained from K1 (QPP source)compared against those obtained from the test kernels. It isclear that the time-series constructed using the test kernelsare uncorrelated to the HXR QPPs while the light curveobtained from K1 matches the HXR profile. pfsspy (Stansby et al. 2020). This magnetic field ge-ometry allows for a mechanism for the escape of theelectrons responsible for producing the radio emission.In the following section, we discuss the interpretation ofthese data and what proposed models of QPP genera-tion allow for these observations. DISCUSSION AND CONCLUSIONSOur results indicate that the EUV (171 ˚A and 1600 ˚A),SXR, and HXR QPPs contain approximately the sameperiodicity. We also observe QPPs in the low frequency radio domain in the form of a sequence of type III ra-dio bursts that occur during the time of the flare thathave a longer periodicity. Our spatial analysis suggeststhat the EUV and HXR QPPs originate from the sameregion of the flare - the HXR footpoint at K1. Thispoints towards a scenario in which intermittent particleacceleration is occurring due to a process inducing time-dependent magnetic reconnection. This particle accel-eration occurs in a quasi-periodic fashion and results inbursty non-thermal bremsstrahlung that modulates theHXR emission occurring at the footpoints. The EUVemission would then be a consequence of this process asthe ambient plasma is heated as the precipitating accel-erated particles lose their energy.The asymmetry of the EUV pulsations present at eachHXR source, as shown in Figure 9, suggests that theelectrons from the reconnection site must be preferen-tially accelerated between the closed loops and open fieldlines close to K1. Figure 11 shows these systems of openand closed field lines obtained via a PFSS extrapolation.It is likely that the radio emission observed is a con-sequence of the same intermittent particle accelerationthat resulted in the EUV and HXR pulsations. How-ever, the electrons accelerated along the open magneticfield lines from flare region result in the radio emissionwhile it is the precipitating electrons accelerated towardsthe chromosphere which result in the HXR/SXR/EUVemission. Unfortunately no imaging observations atthese radio frequencies are available during this event,and so we could not image the radio source to localiseits origin. However, there are no nearby active regionsat the time of the flare that could have coincidentallyproduced this radio emission.To explain our observations we interpret the QPPsidentified in this flare in terms of pulsed electron accel-eration caused by time-dependent intermittent recon-nection. In Figure 12 we show a cartoon scenario of theflare site to illustrate how the QPP sources are related tothe magnetic field configuration. Following each burst ofelectron acceleration, those that escape upwards alongthe open magnetic field lines result in the type III QPPs,and those that travel along closed lines precipitate inthe chromosphere to cause the QPPs we observe in hardX-ray and EUV. But what causes the reconnection andparticle acceleration itself to be quasi-periodic? As men-tioned in the introduction, this could be due to eitherthe process itself being time-dependent (self-oscillatory)or indeed due quasi-periodic triggering of magnetic re-connection due to external MHD waves. We can ruleout the latter, as it is unlikely as there are no activeregions nearby.2
Clarke et al.
Figure 11.
Potential Field Source Surface (PFSS) extrapolation showing the geometry of the magnetic field lines of the flaringregion overlaid on the AIA 171 ˚A image. The open field lines are plotted in red and the closed lines in white. It is clear that theK1 has an open field line source and we propose that the interaction between the closed and open field lines at this footpointresult in ‘bursty’ magnetic reconnection giving rise to the QPPs we observe. The open field lines allow the flare-acceleratedelectrons to escape that produce the Type III radio emission.
Plasmoid magnetic island reconnection or oscillatoryreconnection are both good candidates. Given that theperiod of the QPPs analysed in this work match wellwith the simulations in McLaughlin et al. (2012) (105-121.5 s), this mechanism may be responsible. McLaugh-lin et al. (2012) outline how the interaction of magneticflux emerging from the tachocline with an existing mag-netic topology such as a flaring system can result in os-cillatory reconnection and pulsed particle acceleration.It is possible that this flux emergence is localised to theregion of the flare site we identified as the QPP source.This could then give rise to the QPPs we observe acrossthe electromagnetic spectrum. However we are unableto rule out the possibility of plasmoid magnetic islandreconnection or other self-oscillatory processes. Thereare a number of arguments that point towards a rela-tion between the HXR/SXR/EUV QPPs and the radioQPPs we observe despite them having different periodsaccording to our wavelet analysis. We outline belowour argument that they are indeed a consequence of thesame progenitor.1. The emission mechanism involved that pro-duces the radio (plasma emission) versus the mecha-nism producing the EUV, SXR, and HXR (non-thermalbremsstrahlung/heating) are very different in nature -i.e incoherent free-free emission versus coherent collec-tive emission. In the plasma emission mechanism, ac-celerated electron beams travel to large heights (for thefrequencies we observe) along open magnetic field lines,induce the growth of Langmuir waves, and then these Langmuir waves must interact to finally produce radioemission (Melrose 2017). Many factors, such as theelectron energy (which can vary from pulse to pulse),velocity dispersion, Coulomb collisions, Langmuir wavegrowth and interaction, to name a few, play a role ingenerating the emission. It is a multi-stage process,and variability in any of these stages can change thecharacteristics of the radio pulses. In contrast, the elec-trons producing the higher energy radiation, via non-thermal bremsstrahlung and subsequent heating of thesurrounding plasma, must only travel from the accel-eration site within the flaring region to the chromo-sphere. Bremsstrahlung then occurs quickly followedby instantaneous heating resulting in co-temporal pul-sations in the EUV, SXR, and HXR wavebands (Whiteet al. 2011). Due to these factors, it is expected thatnot every HXR/SXR/EUV pulsation would have a cor-responding radio burst, as we observe, despite being aconsequence of the same intermittent particle accelera-tion.2. The region of the flare site we have identified asthe QPP source is in close proximity to open and closedmagnetic field lines. This magnetic field geometry al-lows for reconnection to occur between the open andclosed field lines, providing a natural route for the es-caping electrons to produce the radio emission and theprecipitating electrons to produce the X-rays/EUV asshown in Figure 11.3. The time delay between the HXR emission and theonset of the prominent type III radio bursts is consis- ulti-wavelength pulsations via time-dependent particle acceleration -B +B -B QPP Source Closed field lines (Flare Arcade)RibbonRibbon
K1 K2 K3+B+B -B -B-B
Figure 12.
Cartoon of the flaring region illustrating thelikely mechanism through which we observe the episodic par-ticle acceleration resulting in QPPs in EUV, radio, SXR, andHXR. The QPP source footpoint is related to the open andclosed field lines allowing for the escape of the electrons re-sulting in the radio emission and the precipitation of theelectrons giving rise to the higher frequency emission. tent with the estimated distance over which the radioelectron beam sources must travel before they emit at2.5 MHz, as shown in Figure 3. This source height of ∼ R (cid:12) was obtained by the Newkirk Jr. (1967) electrondensity model.4. The wavelet analysis of the 2.5 MHz light curve onlypicks up the four main peaks in the time series. Smalleramplitude peaks fail to contribute significantly to theresult. In Figure 8 we manually find the period by iden-tifying the four most prominent peaks, which matchesthe result of the wavelet analysis. However when thesmaller amplitude peaks are accounted for, amountingto a total of 7 pulses, the period of the radio emissioncomes within error of the period of the HXR/SXR/EUV.An additional difficulty in accurately calculating the pe-riod of the radio emission is that certain bursts are moreintense at different frequencies as is clear in the dynamicspectra. However, from inspecting Figure 13 where theHXR emission is overplotted on the dynamic spectrum,there is quite a clear relation between the radio burstsand the HXR peaks when the entire frequency band istaken into account.Cairns et al. (2020) point out that a type II radioburst occurs at the time of this flare and suggest that theassociated shock may be responsible for accelerating the electrons that result in the low frequency radio emission.However, considering the arguments above (points 1-4),we conclude that it is more likely that the type III radiobursts are due to pulses of electron beams acceleratingalong the open magnetic lines close to the QPP sourceregion. Additionally, the dynamic spectra of the radioemission from kHz to GHz shows traces of type III burststhat extend to high frequencies, above the frequency ofthe type II burst (see Cairns et al. (2020) Figure 15).This suggests that they originate from a region closer tothe flare site.In summary, A multi-wavelength analysis of QPPsin an M-class flare has been conducted. Several in-struments were used to allow for the analysis of theHXR, SXR, EUV, and radio emission detected duringthe event. The 171 ˚A, 1600 ˚A, SXR, and HXR lightcurves yielded similar periods of 122 +26 − s, 131 +36 − s,123 +11 − s, and 137 +49 − s, respectively, indicating a com-mon underlying mechanism, while the radio emissionat 2.5 MHz contained a longer period of ∼
231 s. X-ray and EUV imaging enabled us to localise the QPPsource to a region of the flare site associated with openmagnetic field lines. We found that the time delay be-tween the X-ray/EUV emission and the radio emissionis consistent with the estimated distance over which theelectron beam sources must travel. We discuss the dif-ferences between the emission mechanisms responsiblefor the HXR/SXR/EUV emission versus the radio emis-sion and determine that the QPPs in each waveband arelinked to the same populations of accelerated electrons.We conclude that the QPPs in this event are due tosome time-dependent self-oscillatory reconnection mech-anism. Magnetic reconnection occurring in this burstyfashion injects populations of non-thermal electrons intothe flare site giving rise to the sequence of pulses we ob-
Figure 13.
The HXR emission from FERMI GBM (25-50 KeV) overplotted against the dynamic spectrum fromWIND/WAVES showing the low frequency radio emissionin the form of a sequence of type III radio bursts. Clarke et al. serve in the SXR, HXR, and EUV as electrons collidewith the chromosphere while the electrons acceleratingaway from the flare site along open magnetic field linesproduce the type III radio bursts. This work providesnew evidence that oscillatory reconnection can naturallygenerate quasi-periodic periodic pulsations providing anexplanation for their presence across the entire spatialrange of flaring emission. This work also shines lightonto the nature of energy release in flares and providesnew insight into how QPPs may be localised to specificregions within flare sites. Future work that investigatesthe details and conditions required for the triggering ofmagnetic reconnection in this bursty fashion is needed.ACKNOWLEDGMENTSThis work has been supported by the European SpaceAgency PRODEX Programme (BPC) and the Govern-ment of Ireland Studentship from the Irish ResearchCouncil. L.A.H. is supported by an appointment to theNASA Postdoctoral Program at Goddard Space FlightCenter, administered by USRA through a contract withNASA. We also thank the anonymous referee whosecomments helped to improve this paper.
Facilities:
SDO (AIA), RHESSI, WIND (WAVES),FERMI (GBM),GOES/XRS
Software: sunpy (The SunPy Community et al. 2020;Mumford et al. 2020) pfsspy (Stansby et al. 2020) mat-plotlib (Hunter 2007) ulti-wavelength pulsations via time-dependent particle acceleration A. WAVELET ANALYSIS WITHOUT DETRENDING TECHNIQUE ~137 s~123 s a. b.
FERMI GBM (25-50 KeV)GOES Derivative (1-8 Å)
Figure 14.
Wavelet analysis of the (a): HXR and (b): SXR derivative emission from the flare without detrending. The periodswere found to be 137 +64 − s and 123 +6 − s, respectively. The error is taken as the range over which each global power spectrum isabove 95% significance. Clarke et al. ~122 s~131 s a.b.
Figure 15. (a): Wavelet analysis without detrending of the emission at 171 ˚A. (b): Wavelet analysis without detrending of theemission at 1600 ˚A. The periods were found to be 122 +17 − s and ∼
131 s respectively.
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