Table Of ContentSolarPhysics
DOI:10.1007/•••••-•••-•••-••••-•
Fast magnetoacoustic waves in a fan structure above
the coronal magnetic null point
H. M´esz´arosov´a1,2 · J. Dud´ık2,3 ·
M. Karlicky´2 · F. R. H. Madsen1 ·
H. S. Sawant1 ·
3
1 Received;accepted
0
(cid:13)c Springer••••
2
n
Abstract We analyze the 26 November 2005 solar radio event observed in-
a
J terferometrically at frequencies of 244 and 611MHz by the Giant Metrewave
1 Radio Telescope (GMRT) in Pune, India. These observations are used to make
1
interferometricmapsoftheeventatbothfrequencieswiththetimecadenceof1s
] from06:50to07:12UT.Thesemapsrevealseveralradiosources.Thelightcurves
R
of these sources show that only two sources at 244MHz and 611MHz are well
S
correlatedintime.TheEUVflareismorelocalizedwithflareloopslocatedrather
.
h away from the radio sources. Using the SoHO/MDI observations and potential
p
magnetic field extrapolation we demonstrate that both the correlated sources
-
o are located in the fan structure of magnetic field lines starting from a coronal
r
t magnetic null point. Wavelet analysis of the light curves of the radio sources
s
a detects tadpoles with periods in the range P = 10–83s. These wavelet tadpoles
[
indicate the presence of fast magnetoacoustic waves that propagate in the fan
1 structureofthecoronalmagneticnullpoint.Weestimatetheplasmaparameters
v
inthestudiedradiosourcesandfindthemconsistentwiththepresentedscenario
5
involving the coronal magnetic null point.
8
4
Keywords: Sun: corona – Sun: flares – Sun: radio radiation – Sun: oscillations
2
. – Methods: data analysis
1
0
3
1
: 1National SpaceResearchInstitute(INPE), Ave.dos
v
Astronautas 1758,1221-0000Sa˜oJos´edosCampos,SP,
i
X Brazil, (e-mail:[email protected],[email protected])
2AstronomicalInstitute oftheAcademyofSciences,
r
a CZ-25165Ondˇrejov,CzechRepublic,
(e-mail:[email protected],[email protected])
3Dept.ofAstronomy,PhysicsoftheEarthandMeteorology,
FacultyofMathematics,PhysicsandInformatics,Comenius
University,SK-84248Bratislava,SlovakRepublic,
(e-mail:[email protected])
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M´esz´arosova´etal.
1. Introduction
It is commonly believed that the primary energy release regions in solar flares
are located in the low corona (Aschwanden, 2005). Radio spectral and imaging
observations in the decimetric and metric wavelength ranges in combination
with magnetic field extrapolations are consideredto be very promising tools for
a study ofthese processes.Unfortunately, imagingobservationsofsolarflaresin
the decimetric range are very rare. In the metric range, such observations are
commonly done by the Nan¸cay radioheliograph(Kerdraon and Delouis, 1997).
To successfully combine radio observations and magnetic extrapolations, the
radio observations have to include sufficiently precise positional information.
Such a combination was done e.g. by Trottet et al. (2006), where a detailed
analysis of radio spectral and imaging observations in the 10–4500MHz range
was presented for the 5 November 1998 flare. Subramanian et al. (2007) have
studied a post-flare source imaged at 1060MHz to calculate the power budget
for the efficiency of the plasma emission mechanism in a post-flare decimet-
ric continuum source. Aurass, Rausche, and Mann (2007) have analyzed the
topologyofthepotentialcoronalmagneticfieldnearthesourcesiteofthemeter-
decimeterradiocontinuumtofindthatthisradiosourceoccursnearthe contact
of three separatrixes between magnetic flux cells. Aurass et al. (2011) have ex-
amined meter-decimeter dynamic radio spectra and imaging with longitudinal
magneticfieldmagnetogramstodescribemeter-wavesources.Chen et al.(2011)
have used an interferometricdm-radio observationand nonlinear force-free field
extrapolation to explore the zebra pattern source in relation to the magnetic
field configuration. Zuccarello et al. (2011) investigated the morphological and
magnetic evolution of an active region before and during an X3.8 long duration
event. They found that coronal magnetic null points played an important role
in this flare.
Acomprehensivereview ofmagnetic fields andmagnetic reconnectiontheory
aswellasobservationalfindingswasprovidedbyAschwanden(2005).Thetopo-
logical methods for the analysis of magnetic fields were reviewed in Longcope
(2005) and the 3D null point reconnection regimes in Priest and Pontin (2009).
McLaughlin, Hood, and De Moortel (2011) have presented a review of the the-
oretical studies of the MHD waves in the vicinity of the magnetic null points.
Furthermore, Afanasyev and Uralov (2012) have studied analytically the prop-
agation of a fast-mode magnetohydrodynamic wave near a 2D magnetic null
point.Usingthenonlineargeometricalacousticmethodtheyhavefoundcomplex
behaviorofthesewavesinthevicinityofthispoint.Inspiteofthewealthofthe-
oreticalworkpresentedin these papers,the authorsconcludedthatthere is still
noclearobservationalevidenceforthepresenceofMHDwavesnearnullpointsof
themagneticfield.WenotethatthisisalsoinspitethefactthatMHDwavesare
commonly observed in the solar corona (De Moortel, Ireland, and Walsh, 2000;
Kliem et al., 2002;Harrison, Hood, and Pike, 2002;Tomczyk et al., 2007;Ofman and Wang, 2008;
De Moortel, 2009;Marsh, Walsh, and Plunkett, 2009;Marsh, De Moortel, and Walsh, 2011).
Sinceboththestandingandpropagatingmagnetoacousticwavesmodulatethe
plasma density and the magnetic field in the radio source (Aschwanden, 2005),
some modulation of the radio emission by both these waves can be expected.
SOLA: gmrt.tex; 14 January 2013; 2:11; p. 2
Fastmagnetoacoustic wavesinafanstructure
Figure 1. Solar maps with mainsources associated with the 26 November 2005 radioevent
observedat7:01:30UTbytheGMRTinstrument.RegionsU1–U3andD1–D3wereidentified
as the main radio sources at 244 and 611MHz, respectively. The magenta circle in the left
panel has the diameter of 32arcmin and indicates an approximate position and size of the
visiblesolardisk.Diskcentersareshownbyacross.Thecrosshasdimensionsof400”inboth
directionstoindicatethe scaleinthemaps.Synthesized beam dimensionsgivingtheerrorin
GMRTpositionsarerepresentedbythesmallovalsshownonthebottom rightcorners.
Roberts, Edwin, and Benz (1983, 1984) studied impulsively generated fast
magnetoacousticwavestrappedinastructurewithenhanceddensity(e.g.loop).
They showed that these propagating waves exhibit both periodic and quasi-
periodic phases.Nakariakov et al. (2004)numericallymodelled impulsively gen-
erated fast magnetoacoustic wave trains and showed that the quasi-periodicity
is a consequence of the dispersion of the guided modes. Using wavelet analy-
sis, these authors found that typical wavelet spectrum of such fast magnetoa-
coustic wave trains is a tadpole consisting of a broadband head preceded by
a narrowbandtail.
Thetadpolesascharacteristicwaveletsignaturesoffastmagnetoacousticwave
trains wereobservedinsolareclipse data (Katsiyannis et al., 2003) as wellas in
radiospectraofdecimetricgyrosynchrotronemission(M´esza´rosov´aet al., 2009a),
and also in decimetric plasma emission (M´esza´rosov´aet al., 2009b). While the
tadpoles in the gyrosynchrotronemissionwas detected simultaneously at all ra-
diofrequencies,thetadpolesintheplasmaemissiondriftedtowardslowfrequen-
cies.Thistypeof“driftingtadpoles”wasstudiedindetailsinM´esza´rosov´a,Karlicky´,and Ryba´k
(2011) in the radio dynamical spectrum with fibers.
The observed parameters of fast magnetoacoustic waves reflect properties of
the plasma in the waveguides where these waves are propagating. Therefore,
one could use observed waves and their wavelet tadpoles as a potentially useful
diagnostic tool (Jel´ınek and Karlicky´, 2009; Jel´ınek and Karlicky´, 2010) for de-
terminingphysicalconditionsinthesewaveguides,(e.g. loopsorcurrentsheets).
Karlicky´, Jel´ınek, and M´esza´rosov´a(2011)comparedparametersofwavelettad-
poles detected in the radio dynamical spectra with narrowband spikes to those
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M´esz´arosova´etal.
Table 1. Time evolution of the individual GMRT
sources.
Source Starttime Timeofmax Endtime
[UT] [UT] [UT]
U1 6:58:04 7:01:30 7:04:03
U2 6:57:59 7:01:30
U3 6:58:20 7:06:45
D1 6:58:05 7:03:52 7:05:11
D2 6:58:54 6:59:33 7:04:00
D3 6:58:13 6:58:43 7:01:59
computedin the modelwith the Harriscurrentsheet.Basedonthis comparison
the authors proposed that the spikes are generated by driven coalescence and
fragmentationprocessesinturbulentreconnectionoutflows.Wenoteherethat,in
general, flare current sheets can be formed not only near magnetic null points,
but also e.g. between interacting magnetic loops. Jel´ınek and Karlicky´ (2012)
numericallystudiedimpulsivelygeneratedmagnetoacousticwavesfortheHarris
current sheet and a density slab. In both cases they find that wave trains were
generated and propagated in a similar way for similar geometrical and plasma
parameters.
Inthispaper,weanalyzeararedecimetricimagingobservationofthe26Novem-
ber 2005 solar flare made by the Giant Metrewave Radio Telescope (GMRT).
Combing the results of this analysis with the magnetic field extrapolation (Sec-
tion 3), we presenta scenarioofthis radioevent. For the first time, we detected
the magnetoacoustic waves in the radio sources (Section 4) located in the fan
of magnetic field lines connected with a coronal null point. The basic plasma
parameters in the radio sources are estimated and the results are discussed
(Section 5).
2. Observations and data analysis
The B8.9 solarflareoccurredon 26November2005inthe active regionsNOAA
AR 10824and 10825locatednear the disk center.The flarelastedfromapprox-
imately 06:31 to 07:49UT with the GOES maximum at 07:05UT.
The radio counterpart of this flare was a 22 minutes long radio event lasting
from the 06:50 to 07:12UT recorded by the Giant Metrewave Radio Telescope
(GMRT) in Pune, India. The Michelson Doppler Imager (MDI, Scherrer et al.
1995) onboard the SoHO spacecraft (Domingo, Fleck, and Poland, 1995) per-
formed routine full-disk observations with a 96 minute cadence. The magne-
togramnearestto the radio eventwasobservedat 06:24UT. The EUV counter-
parts of this flare were observed by the Extreme Ultraviolet Imaging Telescope
(Delaboudini`ere et al., 1995) onboard the SoHO spacecraft.
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Fastmagnetoacoustic wavesinafanstructure
Figure 2. Selected contour maps showing the time evolution of the emission sources at
244MHz(upperpanel)and611MHz(bottompanel).Thetimes(UT)areinblue.Synthesized
beam dimensions representing the error in GMRT positions are shown as small green circles
on the bottom leftcorners of maps at 6:57UT.Upper panel: Positions of the sources U1–U3
(inred)areindicatedonthemapat6:58:30UT.Bottompanel:PositionsofthesourcesD1–D3
(inred)areindicatedonthemapat6:59UT.
2.1. GMRT observations and data analysis
On26November2005,theGMRT observedtheSunattwofrequencies,244and
611MHz.TheGMRTinstrument(Swarup et al., 1991;Ananthakrishnan and Rao, 2002;
Mercier et al., 2006)isaradiointerferometerconsistingof30fullysteerableindi-
vidualradiotelescopes.Eachtelescope hasa parabolic antennawith a diameter
of 45m and 16 of these individual antennas are arranged in an Y shape array
with each arm having length of 14km from the array centre. The remaining 14
telescopes are located in the central area of 1km2. The interferometer operates
at wavelengthslonger than 21 cm, with six frequency bands centeredon the 38,
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M´esz´arosova´etal.
Figure3. Lightcurvesofthe26November2005radioeventobtainedfromtheGMRTmaps.
Upper panel: Radio fluxes at 244MHz corresponding to the sources U1 (blue), U2 (dashed
green) and U3 (dotted red). Bottom panel: Radio fluxes at 611MHz corresponding to the
sourcesD1(blue), D2(dashedgreen)andD3(dotted red).
153,233,327,610,and1420MHzfrequencies.Themaximumresolutiondepends
on the configuration, and varies between 2 and 60arcsecs.
The observed interferometric data at 244 and 611MHz were Fourier trans-
formed to generate a series of 1320 snapshot images of the Sun at 1 second
time-cadence, from 06:50 to 07:12UT. The images were cleaned using the algo-
rithm developed by Schwab (1984) and rotated to correct for the solar North.
The synthesized beam dimensions giving the GMRT positional error are are
77.7 × 50.8 and 17.7 × 13.4arcsec at 244 and 611MHz, respectively.
An example of the observations showing the main radio sources is shown in
Figure1.Onthisfigure,sixsourcescanbeidentified,threeforeachfrequency.At
the frequencyof244MHz,the sourcesareoutlinedinthe leftpanelanddenoted
asU1,U2,andU3.Themainsourcesatthefrequency611MHzareshowninthe
right panel of Figure 1 and labelled as D1, D2, and D3. The evolution of these
sources during the radio event is shown in Figure 2. Positions of the individual
radio sources U1–U3 and D1–D3 are shown in red. Notable is the merging of
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Fastmagnetoacoustic wavesinafanstructure
Figure 4. Superposition of the radio sources at 244MHz (orange contours) and 611MHz
(bluecontours)observedat06:59UTontopofthephotosphericmagneticmapobtainedwith
the SoHO/MDI at 6:24UT. Individual radio sources are labelled. The MDI magnetogram is
saturatedto±103G.Heliographiccoordinates areshownfororientation. SolarNorthisup.
the sources U1 and U2 at around 6:59UT. The source U3 remains far from the
others (U1 and U2).
Weconstructedlightcurvesoftheindividualradiosourcesbyenclosingthese
sources in rectangular regions on the GMRT maps. The light curves are shown
in Figure 3. The radio fluxes at 244MHz corresponding to the sources U1, U2,
and U3 are shown in the upper panel as the blue, dashed green and dotted red
lines, respectively. The radio fluxes at 611MHz frequency corresponding to the
sources D1 (blue), D2 (dashed green) and D3 (dotted red) are present in the
bottom panel. The calibration of the individual fluxes is relative only and is
expressed in arbitrary units (a.u.).
Analysis of these time series of radio fluxes shows different time evolution
profiles for the different radio sources. The sources U1, D1, and D3 show about
5 minutes durations with a well defined main peak. On the other hand, the
sources U2, U3, and D2 show profiles with a gradual rise and several peaks on
top of a roughly constantbackground.The temporal properties ofthese sources
arepresentedinTable1.Thestartandendtimesofeachsourceweredetermined
as the times when the fluxes were above or below half the average flux of the
whole burst profile of the source, respectively.
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Figure 5. Superpositionoftheradiosources(sameasinFigure4)ontopoftheSoHO/EIT
195˚A observations taken at 7:48UT. The EIT 195˚A observations are saturated to 2×103
DNs−1px−1 and shown in logarithmic intensity scale for better visibilityof fainter emitting
loopsystems.Theflarearcadefootpointsobservedusingthefilter304˚Aat07:19UTareshown
aswhitecontourscorrespondingto103 DNs−1px−1.
Thecross-correlationcoefficientsbetweenpairsofallGMRTUandDsources
show that there is only one pair with correlation higher than 75%. This pair is
the sourcesU1andD1 with the cross-correlationcoefficientof81%.This degree
of correlation indicates that these radio sources can have a common origin.
The maximum of the cross-correlationcoefficient is flat if the time lag of U1
with respect to D1 ranges 0–50s. It indicates that first parts of radio fluxes D1
and U1 are correlated by some fast moving agents (possibly beams) and the
second parts by slowly moving agents (possibly waves).
2.2. Photospheric magnetic field and the EUV flare
The GMRT interferometric observations offer the advantage of direct spatial
comparisonwiththephotosphericmagneticfieldandtheEUVflaremorphology,
as observed by the SoHO/MDI and SoHO/EIT instruments, respectively. The
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Fastmagnetoacoustic wavesinafanstructure
Table 2. BasicparametersderivedforradioburstsatGMRTfrequencies.
Frequency Source Fundamental Plasmadensity Firstharmonic
frequencyaltitude altitude
[MHz] [Mm] [cm−3] [Mm]
244 U1–U3 48 7.4x108 86
611 D1–D3 22 4.6x109 40
comparisonofthe radiosourcesloci with the MDI magnetogramis presentedin
Figure 4. The magnetogram was observed at 06:24UT and rotated to the time
06:59 corresponding to the radio observations using the SolarSoftware routine
drot map.pro. The time ofthe radioobservations,06:59UT,ischosenbecauseit
corresponds to the times of the first radio peaks in the sources U1 and D1.
Theradiosourcesarelocatedinaquadrupolarmagneticconfigurationconsist-
ingoftwoactiveregions,NOAA10824and10825(Figure4).Bothactiveregions
arebipolarwithaβ-configuration.TheAR10824islocatedapproximatelyatthe
heliographiclatitudeof≈−13◦ andcontainsawell-developed,leadingnegative-
polarity sunspot. Other polarities consist of plage regions or pores, which is the
case also for the AR 10825 located at latitudes of ≈ −7◦. A notable feature is
that the radio sources are not located on top of the main magnetic polarities,
but, in general, they overlie weak-field regions.
TheSoHO/EITinstrumentwasperformingfull-discobservationsinthe195˚Afil-
terwithacadenceofapproximately12minutes.Observationsinotherfilters,i.e.
171, 284 and 304˚A were performed at 07:00, 07:06 and 07:19UT, respectively.
Due to poor pointing information of the EIT instrument, the EIT 304˚A ob-
servations were coaligned manually with the MDI observations by matching
the EIT 304˚A brightenings with small magnetic polarities observed by MDI,
whichshowgoodspatialcorrelation(Ravindra and Venkatakrishnan, 2003).We
estimate the error of this manual coalignment to be ≈ 5arcsec.
In the EIT 304˚A observations, three flare arcade footpoints are discernible,
shown in Figure 5 as white contours corresponding to the observed intensity
3 −1 −1
of 10 DNs px . All three footpoints are located well within the AR 10824,
with one of them in the positive polarity and the other two in the negative
polarities North of the sunspot. EIT 195˚A observations show cooling system of
flare loops connecting these three footpoints. The flare loops are well-visible at
195˚Aat07:48UTandareshowninFigure5.Theglobalmagneticconfiguration
of AR 10824 is that of a sigmoid with large shear. The magnetic configuration
of the neighboring AR 10825 is near-potential.
Comparison of the loci of the radio sources with the EUV flare morphology
(Figure 5) shows that the radio sources have no direct spatial correspondence
with the EUV flare loops or their footpoints. The source D3 is an exception,
since it overliesa portionof the flare loops. The sourcesU1, U3, D1 and D2 are
located in the area of weak EUV emission.
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3. Magnetic structure of active regions NOAA 10824 and 10825
3.1. Magnetic field extrapolation and the altitude of the radio emission
To investigate the relationship between the radio sources and the structure of
the magnetic field of active regions NOAA 10824 and 10825, we performed an
extrapolationof the SoHO/MDI magnetogram(Figure 4) observedat 06:24UT
prior to the flare and associated radio events. The extrapolation was carried
out in linear force-free approximation, where the magnetic field B~ given by the
solution of the equation
∇~ ×B~ =αB~ , (1)
for α=const. The solutionis subjectto the boundarycondition B (x,y,z =0)
z
given by the observed magnetogram, where 0 < x < L and 0 < y < L . The
x y
constant α is subject to the condition α < αmax = 2π/max(Lx,Ly), otherwise
the magnetic field is non-physical. We utilized the Fourier transform method
developed by Alissandrakis (1981) and Gary (1989). This method allows for
extrapolationofthepartoftheobservedmagnetograminacarthesiangeometry.
The computational box is shown in Figures 6 and 7.
We calculated a range of linear force-free models with various values of α.
However, the flare loops are poorly approximated with α = const., even with
large values of α close to αmax. The reason for this probably is the presence
of differential shearwithin the active region(Schmieder et al., 1996). Moreover,
usinglargevaluesofαleadstopoorfittotheobservedshapeofthecoronalloops
intheAR10825,whichisclosetothepotentialstate(α=0).Therefore,wechose
to extrapolate in the potential approximation. We also note that the potential
approximationdoes usually a good job in capturing the topologicalstructure of
the active region(though notat sigmoidlocations, e.g. Schmieder and Aulanier
2003).
Tocomparethe3Dmagneticfieldgeometrywiththelocioftheradiosources,
observed in a 2D plane of the sky, the approximate altitude at which the radio
emissionoriginatesmustbe determined.Todothat,weconsiderthe parameters
of the radio bursts (at GMRT frequencies) and the solar atmosphere density
model (Aschwanden, 2002) for the radio plasma emission at fundamental fre-
quency and the first harmonic (see also Section 3.2). We use Aschwanden’s
density model because it was derived from radio observations. The basic pa-
rameters of the radio sources are derived and summarized in Table 2 where the
plasma density values belong to the fundamental frequency altitude.
3.2. Magnetic topology and its relation to radio sources
The extrapolated magnetic field contains a pair of coronalmagnetic null points
betweenthetwoactiveregions.Thenegativeandpositivecoronalnullpointsare
denotedbyred(SE)andblue(NW)arrowsinFigure6.Onthisfigure,thedark-
red and dark-blue contours correspond to positive and negative photospheric
polarities, respectively, with B =±50and500G. Since the magnetic field of
z
AR 10825is weaker,the null points are located closer to this active regionthan
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