Discovery of correlated evolution in solar noise storm source parameters: Insights on magnetic field dynamics during a microflare
DDraft version February 25, 2021
Typeset using L A TEX twocolumn style in AASTeX63
Discovery of correlated evolution in solar noise storm source parameters:Insights on magnetic field dynamics during a microflare.
Atul Mohan
1, 2 Rosseland Centre for Solar Physics, University of Oslo, Postboks 1029 Blindern, N-0315 Oslo, Norway Institute of Theoretical Astrophysics, University of Oslo, Postboks 1029 Blindern, N-0315 Oslo, Norway (Received 16-Dec-2020; Accepted 17-Feb-2021)
Submitted to ApJLABSTRACTA solar type-I noise storm is produced by accelerated particle beams generated at active regionsundergoing magnetic field restructuring. Their intensity varies by orders of magnitude within sub-second and sub-MHz scales. But, the morphological evolution of these sources are not studied at thesescales, due to the lack of required imaging cadence and fidelity in metrewave bands. Using data fromthe Murchison Widefield Array (MWA), this work explores the coevolution of size, sky-orientation andintensity of a noise storm source associated with a weak microflare. The work presents the discoveryof two correlated modes of evolution in the source parameters: a sausage like ‘S’ mode where thesource intensity and size shows an anti-correlated evolution; and a torsional like ‘T’ mode where thesource size and sky-orientation shows a correlated evolution. A flare mediated mode conversion isobserved from ‘T’ to ‘S’ for the first time in these sources. These results support the idea of buildup of magnetic stress energy in braided active region loops, which later go unstable causing flares andparticle acceleration until they relax to a minimally braided state. The discovered mode conversioncan be a future diagnostic to such active region phenomena.
Keywords:
Sun: flares — Sun: solar radio flares — Sun: Energetic solar particles — Sun: Solar activeregion magnetic fields INTRODUCTIONSolar type-I noise storms are usually associated withactive regions and sunspots, during times of flaring orlarge scale magnetic field restructuring (Elgaroy 1977;Kathiravan et al. 2007; Iwai et al. 2011). The brightradio emission is a result of coherent plasma emis-sion mechanisms triggered by flare-accelerated electronbeams trapped in active region magnetic field structures(Ginzburg & Zhelezniakov 1958; Melrose & Sy 1972).However, there has been observations of noise storms, es-pecially weak ones with flux enhancements typically lessthan 100 SFU (1 SFU = 10 W m − Hz − ), which couldnot be associated with any particular flares (Smith &McIntosh 1962; Le Squeren 1964). The deciding criteriafor a noise storm to occur, and for a flare or active region Corresponding author: Atul [email protected] to be linked to a noise storm are not well understood.Relatively recent works using multi-waveband data andsensitive modern radio arrays demonstrated that type-I sources can also be related to small scale magneticenhancements and weak EUV brightening with no nec-essary flaring or major magnetic field restructuring (e.g.Iwai et al. 2012; Li et al. 2017; Suresh et al. 2017; Mo-han et al. 2019a). Since the accelerated electrons beamsdriving the noise storm emission are produced at recon-nection sites in these time varying magnetic field struc-tures, their energy and spatial distribution functions areexpected to evolve at similar scales (e.g. Gordovskyy &Browning 2012; James & Subramanian 2018; Fyfe et al.2020). These could leave observable signatures in thenoise storm source morphology. However, to study thesource dynamics in tandem with its sub-second and sub-MHz scale flux variability (e.g. Wild 1957; Elgaroy &Ugland 1970; Guedel & Benz 1990; Sundaram & Subra-manian 2005), high fidelity snapshot spectroscopic imag- a r X i v : . [ a s t r o - ph . S R ] F e b Atul Mohan ing at similar scales is essential. This remained a chal-lenge until the advent of modern interferometric arrayslike Murchison Widefield Array (MWA; Tingay et al.2013), LOw Frequency ARray (LOFAR; van Haarlemet al. 2013) and the Long Wavelength Array (LWA;Ellingson et al. 2013). A similar study was done ontype-III bursts by Mohan et al. (2019b). They reportedthe discovery of fast second-scale anti-correlated QuasiPeriodic Pulsations (QPPs) in the sizes and flux densityof type-III sources produced by a weak active regionjet. The authors linked it to sausage modes in the ac-tive region supported by magnetic field modelling andExtreme Ultra Violiet (EUV) images of the jet. Theyalso discovered pulsations in the source sky-orientation.This work will present the first study of simultaneoussub-second evolution of noise storm source parametersnamely size, sky-orientation and integrated flux den-sity. The event presented in Mohan et al. (2019a) (here-after M19) is chosen for this study since it is associatedwith a weak active region transient brightening (ARTB;Shimizu et al. 1992) with no major magnetic field re-structuring. Being weak, it can be assumed that severalphysical parameters remain practically unchanged dueto the event, increasing the odds for discovering localMHD or plasma perturbative modes. Section 2 describesthe observations and image analysis. Section 3 discussesthe emergent physical picture from the observed sourceevolution, followed by conclusions in Section 4. OBSERVATIONS AND ANALYSISThis study is based on archival data, recorded by theMurchison Widefield Array (MWA) Phase I on Novem-ber 3, 2014 from 06:08:02 to 06:20:02 UT. The observa-tion datasets had a bandwidth of 15.36 MHz, spectralresolution of 40 kHz and time resolution of 0.5s. Eachobserving session was 4 minutes long and centred at 199MHz from 06:08:02 – 06:12:02, 229 MHz from 06:12:02– 06:16:02 and again at 199 MHz 06:16:02 – 06:20:02.The shift in the observation band was not intended forthis study. An ARTB event occurred around the middleof the observation period, accompanied by a weak flaredetected by RHESSI in 3–12 keV band. GOES satellitesreported a simultaneous B6 class flare. The radio datahence covered the microflare from pre-flare to post-flarephase. Imaging was done using the Automated ImagingRoutine for Compact Arrays for the Radio Sun (Mondalet al. 2019) at 0.5 s cadence and 160 kHz frequency res-olution, using default parameters. The snapshot spec-troscopic brightness temperature maps were made usingthese images following the prescription in Oberoi et al.(2017) and Mohan & Oberoi (2017). The noise stormsource was resolved in all the images with a size greater the synthesised beam (beam) by ≈
20% on average andhad a 2D Gaussian morphology. The left panel of Fig.1shows noise storm source contours overlaid on an AIA94 ˚A image, during the flare. This source has an FWHMof 4 . (cid:48) × . (cid:48) along its principal axes, when the FWHMof the beam is 3 . (cid:48) × . (cid:48) . The beam-deconvolved source(“true source” hereafter) has ≈
37% of the beam size.Using the imfit task of Common Astronomy SoftwareApplications (CASA; McMullin et al. 2007), a 2D Gaus-sian function plus a constant background was fit to theburst source region in the images across time and fre-quency. The fitted constant accounted for the quiet Sunbackground. The beam was deconvolved from the best-fit Gaussian function to derive the true source dimen-sions: the major and minor axis widths ( σ major/minor );the position angle and the integrated flux density whichis the total flux within the FWHM sized ellipse. Areaof the true sources were estimated as πσ major σ minor .The errors on the best-fit parameters were appropriatelypropagated to calculate the errors in area. SPatially RE-solved Dynamic Spectra (SPREDS) for the true sourcewas made using the derived integrated flux density. Thisis shown in the bottom panels of Fig.1. The intermit-tent white patches show regions where either the datawere bad or the estimates were less than thrice their un-certainties. The top right panel of the figure shows aband averaged light curve for the source obtained fromSPREDS in red. The black curve is obtained by ap-plying a 20 s wide running mean window. 30 s QPPscan be seen riding over a nonthermal flux floor, whichrises during the flare. The GOES X-ray light curve inthe 1–8 ˚A band is shown in blue. The data is dividedinto three phases based on the flare evolution: Pre-flare,flare and post-flare. Subsequent sections will focus onthe spectro-temporal coevolution of the morphologicalparameters of the noise storm source (area and positionangle) in tandem with its integrated flux density dur-ing these phases. Earlier studies usually approached thenoise storm emission as a bright continuum, superposedwith spiky burst features (type-I bursts) (e.g. Mercier &Trottet 1997; Iwai et al. 2014; Suresh et al. 2017). Thiswork will analyse the emission as a whole, from an ac-tive source varying its flux and morphology in tandemwith the associated ARTB (microflare).2.1. Coevolution of source parameters
Figure 2 presents the temporal evolution of integratedflux density and median-subtracted position angle (here-after, position angle) of the source with its area dur-ing various phases. The data presented for the pre-flarephase is from a period devoid of strong bursts; the flarephase sample data is from a period of intense bursts; orrelated modes in noise storm source evolution Figure 1.
Top row: (Left) AIA 94 ˚A image of the Sun zoomed to the bright ARTB site. Overlaid are MWA 229 MHz contoursat 60, 70, 75, 80 ,85, 90, 95 & 99 % of the peak noise storm flux. Synthesized beam size: 3 . (cid:48) × . (cid:48) . (Right) Red curve shows thespatially resolved band averaged light curve for the noise storm source. Black curve is a 20 s running mean filtered light curverevealing the 30 s QPPs. Overlaid in blue is the GOES 1 – 8 ˚A light curve. The three event phases are demarcated. Bottomrow:
SPatially REsolved Dynamic Spectrum of the source during the three phases. A r e a ( a r c m i n ) I n t e g . f l u x d e n s . ( S F U ) P o s . a n g l e ( d e g ) Pre-flare (+06:09:05 UT)0.81.21.62.0 A r e a ( a r c m i n ) I n t e g . f l u x d e n s . ( S F U ) P o s . a n g l e ( d e g ) Flare (+06:13:30 UT)0 5 10 15 20 25 30Time (s)2345 A r e a ( a r c m i n ) I n t e g . f l u x d e n s . ( S F U ) P o s . a n g l e ( d e g ) Post-flare (+06:18:32 UT)
Figure 2.
Coevolution of integrated flux density, area andposition angle during different phases, within a 30 s window.The plotted data come from the mid frequency of the respec-tive bands. Start time of each data is given in the title. and the post-flare phase data is from a period well af-ter the radio flux dropped. The integrated flux density,area and position angle of the noise storm source showrapid variability with occasional strong pulses. These parameters also show periods of correlated evolution inall phases. For example, in the pre-flare phase, area andintegrated flux density show an anti-correlation in thefirst ≈ s . Later, they evolve correlated with a commonpeak around 18 s . Beyond 25 s the floor of the integratedflux density rises steadily, but the area varies around afixed floor. Their coevolutionary trend seems erratic inthis phase. Similar erratic nature is seen in position an-gle and area coevolution in the post-flare phase. Whenthe first ≈ s give an impression that the two param-eters are correlated, their trends dissociate around 15 s and become anti-correlated beyond 20 s . However, inthe flare and post-flare phases the anti-correlated evolu-tion of area and integrated flux density is evident. Simi-larly area and position angle show a correlated evolutionin the pre-flare and flare phases. To get a clear pic-ture of coevolution of these parameters in each phase, anormalised cross-correlation (NCC) analysis was carriedout. Source area was chosen as the base parameter withwhich the others where correlated. NCC functions wereevaluated for each pair of parameters, at every obser-vation frequency, by correlating their full time profilesat 0.5 s cadence in each phase. Fig.3 shows the NCCmatrices truncated at ± (cid:104) N CC (cid:105) ) was computed. Assum-
Atul Mohan F r e q u e n c y ( M H z ) Integ. flux density
100 50 0 50 100
Time lag (s) N CC Position angle
100 50 0 50 100
Time lag (s) . . . . . . N o r m . C r o ss C o rr e l a t i o n s Pre-flare phase F r e q u e n c y ( M H z ) Integ. flux density
100 50 0 50 100
Time lag (s) N CC Position angle
100 50 0 50 100
Time lag (s) . . . . . . N o r m . C r o ss C o rr e l a t i o n s Flare phase F r e q u e n c y ( M H z ) Integ. flux density
100 50 0 50 100
Time lag (s) N CC Position angle
100 50 0 50 100
Time lag (s) . . . . . . N o r m . C r o ss C o rr e l a t i o n s Post-flare phase
Figure 3.
Matrix plots present the NCC functions for in-tegrated flux density (left) and position angle (right) of thesource with respect to its area, for every observation fre-quency during different phases. The masked bands had manydata gaps. The line plot below each matrix plot is the bandaveraged NCC ( (cid:104)
NCC (cid:105) ). ing the coronal density model by Zucca et al. (2014),15 MHz (30 MHz) band corresponds to a region lessthan 10% (14%) of the pressure scale height of the localcorona. So, the mean physical and dynamical proper-ties are expected to be similar across this band, as seenin the NCC functions. Extending the same argument,since the central frequencies of the observation bandsdiffer only by 30 MHz, (cid:104) N CC (cid:105) for all phases belong tothe same coronal region. This work presents the discov-ery of correlated evolution in the three “independent”parameters that define a noise storm source. DISCUSSIONAnalysis of the effects of radiowave scattering andimaging artefacts in the observed trends, confirm theirnoise storm source origin. It also revealed that, despite (c)(a) (b) (d)
Figure 4. (a-c): Band averaged light curves of area, net fluxdensity and position angle of the true source after applying a30 s running mean filter. Vertical lines are marked every 30 s.(d): “T” mode schematic showing the correlated evolutionof area and position angle ( θ ) as a braid wind/unwind. Thesubscript min/max indicates the relative parameter values. the coevolution, the values of the parameters show nodefinitive trends amongst each other (See Appendix A).M19 showed that the noise storm source is part of alarge loop structure and is dynamically linked to a smallactive-region loop via a common magnetic footpoint(M19 Fig.11). The small loop underwent an ARTB dur-ing the flare phase, simultaneously enhancing the noisestorm activity. The EUV analysis of the ARTB regionrevealed a braided structure at ≈
12 Mm scale during theflare. The magnetic stresses continuously built up acrossthe braid could have been released via enhanced particleacceleration events, causing the rise in radio flux. Theradio light curve showed 30 s QPPs, which became moreregular during the ARTB (Fig.1). The Alfv´en speed es-timate (0.4 Mm s − ) from the magnetic field modellingand the QPP period provide a length scale of 12 Mmin the radio source region. This matches the braidingscale at the ARTB site. So, M19 suggested that theradio source and the ARTB region are probably drivenby their common footpoint, leading to the braiding oflocal loop structures at similar scales. The bright type-Ibursts seen in SPREDS are clumped within 30 s peri-ods which made the authors propose a periodic excita-tion of particle acceleration episodes like an avalanchewithin the local Alf´en timescale as the braided loops re-laxed their excess internal energy continuously pumpedin from below. The absence of trends between any twosource parameter values, support the picture of ran-dom particle acceleration episodes with differing scalesas part of an avalanche. Figure 4 shows the evolutionof area, integrated flux density and position angle of thetrue source, averaged across the band during differentphases. The data were smoothed by a 30 s running meanfilter. Vertical lines are marked every 30 s. I report the orrelated modes in noise storm source evolution Nature of correlated evolution & its implications
From Fig.3, it is inferred that there are two domi-nant modes of correlated evolution in source parameters:an area-position angle correlated mode (‘T’ mode here-after) and an area-integrated flux density anti-correlatedmode (‘S’ mode hereafter). The source area is a proxy tothe size of the region of instability driven by acceleratedelectron beams produced at particle acceleration sites,that are magnetically linked to the noise storm sourceregion. The source position angle is a proxy to the direc-tion or tilt of the propagating beams and the integratedflux density relates to the beam energy flux density. So,‘S’ mode can be envisaged as a sausage like mode wherethe area of the instability region and the energy fluxdensity of the beam electrons are anti-correlated. Sim-ilarly, ‘T’ mode is akin to a winding-unwinding modelike the illustration in Fig.4(d) where, size and orien-tation of the electron beam varies in a correlated man-ner as the braid switches from a tight to loose windingconfiguration. Figure 4(a-c) shows 30 s running meanfiltered trends for each parameter. Simultaneous 30 sQPPs are found in all parameters in every phase. TheseQPPs show a correlated evolution consistent with thedominant mode in that phase. Interestingly, the type-Ibursts which are seen clumped within the 30 s periodsalso show the same coevolutionary behaviour (Fig.2 &Fig.4). This could be because the accelerated beamscausing the bursts are jointly releasing the excess en-ergy accumulated in some mode (‘T’ and/or ‘S’) duringthe Alfv´en (QPP) timescale, across the local dominantbraid. The noise storm continuum could be comprisedof numerous unresolved low energy bursts. ‘T’ modedominates in the pre-flare phase. The flare phase marksthe rise of ‘S’ mode alongside ‘T’, which gives way for‘S’ in the post-flare phase. This hints at a conversion inthe dominant mode via the flare. The possible physicalimplications will now be discussed.3.1.1.
Pre-flare phase
The physical picture put forth by M19, suggest thatthe fast twisting motion in the magnetic strands drivenby the footpoint motions causes the energy build-up pri-marily in the ‘T’ mode. Sausage like ‘S’ mode is absentin this phase. The dominant braided structure goes un-stable at Alfv´en timescale of 30 s and release the excess energy via an avalanche of reconnection events produc-ing accelerated electron beams. They cause the observedbursts with the ‘T’ mode imprinted.3.1.2.
Flare and post-flare phase
The ‘T’ mode enhanced in the flare phase, possiblydue to the twisting of already critically braided fieldstructures. Simulations show that, this can cause kinkinstabilities in the loop and the excess energy gets re-leased as accelerated particle beams and local heating,followed by gradual internal restructuring (e.g. Gor-dovskyy & Browning 2012; Threlfall et al. 2018). ARTBand the X-ray flare are signs of heating. The radioflux hike could be due to increased particle accelerationevents. The rise of ‘S’ mode during flare phase is note-worthy. All these hint at a redistribution of the excess‘T’ mode energy to other degrees of freedom. In post-flare phase the ‘T’ mode gives way to ‘S’. This modeconversion is possibly a sign of a restructuring loop.Earlier studies on internally twisted loops targetedflares with strong hard X-ray and microwave emission,for measurements with good signal to noise ratio (e.g.Gordovskyy et al. 2012; Sharykin et al. 2018; Gor-dovskyy et al. 2020). Here, a new way is presented tostudy such loops by tracking the dominant modes of evo-lution in the associated bright noise storm sources, andthere by help bypass the constraint on flare energy. CONCLUSIONSThe coevolution of source area, sky-orientation andintegrated flux density of a noise storm, associated withan ARTB (microflare) is presented. This work presentsthe discovery of simultaneous and often correlated vari-ations in these parameters. Correlated quasi periodicpulsations (QPPs) in area, position angle and flux den-sity of the noise storm source are also discovered. Nor-malised cross correlation (NCC) analysis between theparameters during the pre-flare, flare and post-flarephases revealed two dominant modes of correlated evolu-tion: area-integrated flux density anti-correlated mode,named ‘S’ mode, like a sausage mode; area-position an-gle correlated mode, named ‘T’ mode, like a winding-unwinding mode. A conversion in the dominant modefrom ‘T’ to ‘S’ is discovered, mediated by the flare. Thiscan be a signature of the release of excess magneticstress energy built up in ‘T’ mode in the local coronalloops, during the flare. Eventually, the ‘T’ mode energydensity is redistributed to ‘S’ mode and particle energy.Such mode evolution patterns in associated noise stormsources can be used as diagnostics to study the evolu-tion of flaring loops, regardless of flare energy.
Acknowledgements:
This scientific work makes useof the Murchison Radio-astronomy Observatory (MRO),
Atul Mohan operated by the Commonwealth Scientific and Indus-trial Research Organisation (CSIRO). We acknowledgethe Wajarri Yamatji people as the traditional ownersof the Observatory site. Support for the operation ofthe MWA is provided by the Australian Government’sNational Collaborative Research Infrastructure Strat-egy (NCRIS), under a contract to Curtin Universityadministered by Astronomy Australia Limited. We ac-knowledge the Pawsey Supercomputing Centre, whichis supported by the Western Australian and AustralianGovernments. This work is supported by the ResearchCouncil of Norway through its Centres of Excellencescheme, project number 262622 (“Rosseland Centre for Solar Physics”). AM acknowledges support from theEMISSA project funded by the Research Council of Nor-way (project number 286853). AM acknowledges OlgaMohan for the graphical support. AM acknowledgesProf. Divya Oberoi, Surajit Mondal and the anonymousreferee for useful discussions. This research made use ofNASA’s Astrophysics Data System (ADS).
Facilities:
MWA, SDO(AIA), RHESSI and GOES
Software:
Numpy (Harris et al. 2020), Astropy (As-tropy Collaboration et al. 2013), Matplotlib (Hunter2007), CASA (McMullin et al. 2007), Sunpy (Commu-nity et al. 2015)APPENDIX A. ANALYSIS OF THE EFFECTS OF SCATTERING & IMAGING ARTEFACTSThe effect of radiowave scattering and the possible imaging artefacts in the observed parameter evolution will bediscussed here. Scattering changes the absolute source size, as a convolution by a Gaussian scatter function, the widthof which depends on the mean statistical properties of the ambient plasma (Arzner & Magun 1999; Kontar et al. 2017;Mohan et al. 2019b). The noise storm source region is located at around 1.14 R (cid:12) when the ARTB source was at ≈ R (cid:12) (See Fig 11. in M19). Though magnetically connected, the regions are spatially so far apart for the ARTBto have varied the ambient density fluctuation index ( δN/N ) at the noise storm region, sufficient enough to cause theobserved large fractional changes in its area by about a few to ≈ ≈
20 s leading todifferent antenna flagging schemes, which affected the beam structure. The solution from each calibration run wasapplied to make images in the intermediate time steps. In the flare phase, since source is very bright, high dynamicrange images could be obtained with just a few rounds of self calibration after applying calibration solutions frominitial time slice. Figure 5(d) shows the NCC between beam area and true source position angle which shows no sign orrelated modes in noise storm source evolution log(Integ. flux density (SFU)) A r e a ( a r c m i n ) Source properties Pre-flareFlarePost-flare R e l . p o s i t i o n a n g l e ( d e g )
200 100 0 100 200
Time lag (s) N o r m . c o rr FWHM sourcemajor / minor FWHM beammajor / minor Pre-flare Flare Post-flare200 100 0 100 200
Time lag (s) N o r m . c o rr Beam Area - Beam Position angle
Pre-flareFlarePost-flare 200 100 0 100 200
Time lag (s) N o r m . c o rr Beam Area - Source pos. angle
Pre-flareFlarePost-flare(a) Minor axisMajor axis(b)(c) (d)
Figure 5. (a): Area versus integrated flux density of the true source. The position angle of the true source relative to thebeam is color coded. (b):NCC function for the true source and the beam minor axes widths (Above) and major axes widths(Below). NCC values for minor axes are shifted by 0.5 for visual clarity. (c-d): NCC functions for the area and position angleof the beam (c), and for the beam area and the true source position angle (d). of correlated evolution in any phase, unlike the NCC of the true source data. These results increase the confidence inthe observed true source area - position angle trends and assures that they are not beam-driven.REFERENCES
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