NASA Technical Reports Server (NTRS) 20140006640: Coronal Magnetic Field Measurement from EUV Images Made by the Solar Dynamics Observatory

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TheAstrophysicalJournal,744:72(7pp),2012January1 doi:10.1088/0004-637X/744/1/72
(cid:2)C2012.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedintheU.S.A.
CORONALMAGNETICFIELDMEASUREMENTFROMEUVIMAGESMADEBY
THESOLARDYNAMICSOBSERVATORY
NatGopalswamy1,NariakiNitta2,SachikoAkiyama1,3,PerttiMa¨kela¨1,3,andSeijiYashiro1,3
1NASAGoddardSpaceFlightCenter,Greenbelt,MD20771-0001USA
2Lockheed-MartinSolarandAstrophysicsLaboratory,PaloAlto,CA94304,USA
3TheCatholicUniversityofAmerica,Washington,DC20064,USA
Received2011May29;accepted2011September13;published2011December14
ABSTRACT
By measuring the geometrical properties of the coronal mass ejection (CME) flux rope and the leading shock
observedon2010June13bytheSolarDynamicsObservatory(SDO)mission’sAtmosphericImagingAssembly
we determine the Alfve´n speed and the magnetic field strength in the inner corona at a heliocentric distance of
∼1.4 Rs. The basic measurements are the shock standoff distance (ΔR) ahead of the CME flux rope, the radius
ofcurvatureofthefluxrope(R ),andtheshockspeed.WefirstderivetheAlfve´nicMachnumber(M)usingthe
c
relationship, ΔR/R =0.81[(γ−1) M2 + 2]/[(γ +1)(M2 −1)],whereγ isthe only parameter thatneeded tobe
c
assumed.Forγ =4/3,theMachnumberdeclinedfrom3.7to1.5indicatingshockweakeningwithinthefieldof
viewoftheimager.TheshockformationcoincidedwiththeappearanceofatypeIIradioburstatafrequencyof
∼300MHz(harmoniccomponent),providinganindependentconfirmationoftheshock.Theshockcompression
ratio derived from the radio dynamic spectrum was found to be consistent with that derived from the theory of
fast-modeMHDshocks.FromthemeasuredshockspeedandthederivedMachnumber,wefoundtheAlfve´nspeed
toincreasefrom∼140kms−1to460kms−1overthedistancerange1.2–1.5Rs.Byderivingtheupstreamplasma
densityfromtheemissionfrequencyoftheassociatedtypeIIradioburst,wedeterminedthecoronalmagneticfield
to be in the range 1.3–1.5 G. The derived magnetic field values are consistent with other estimates in a similar
distance range. This work demonstrates that the EUV imagers, in the presence of radio dynamic spectra, can be
usedascoronalmagnetometers.
Keywords: magneticfields–shockwaves–Sun:corona–Sun:coronalmassejections(CMEs)–Sun:radio
radiation
Online-onlymaterial:animation,colorfigures
2.OBSERVATIONSANDANALYSIS
1.INTRODUCTION
The 2010 June 13 CME was observed in several EUV
wavelengthsbySDO/AIA.Here,weusetheAIA193Åimages.
The idea of a shock standing ahead of a magnetic structure
The CME was described as a bubble by Patsourakos et al.
ejected from the Sun was proposed by Gold (1955, 1962),
(2010), who treated the CME as a sphere and reported on the
whichwassoonconfirmedbyspaceobservations(Sonettetal.
early kinematics of the CME. Here we focus on the overlying
1964).Extensivetheoryoftheshockstandoffdistancehasbeen
shock structure that surrounds the flux rope and its standoff
developedforEarth’sbowshock(see,e.g.,Bennettetal.1997
distance. Physical properties of the shock structure have also
andreferencestherein).Russell&Mulligan(2002)appliedthe
been reported by Ma et al. (2011). Kozarev et al. (2011) also
standoff distance derived by Farris & Russell (1994) to the
identifiedtheshockwaveandreportedontheimplicationsfora
caseofashockdrivenbyaninterplanetaryfluxrope(magnetic
possiblesolarenergeticparticleevent.Unliketheseauthors,we
cloud)toexplainthecurvatureofthefluxropederivedfromin
focusonthestandoffdistanceoftheshockasafunctionofthe
situobservations.Gopalswamy&Yashiro(2011)demonstrated
heliocentricdistancetoderivetheupstreammagneticfield.
that the method can be applied to shocks driven by flux
rope coronal mass ejections (CMEs) observed in the Solar
2.1.EUVObservations
andHeliosphericObservatory/LargeAngleandSpectrometric
Coronagraph Experiment (SOHO/LASCO) images at several Since 2010 February, the AIA has been taking full-disk
solar radii from the Sun. White-light shock structures are coronalimagesoftheSuninsevenEUVchannelsrepresenting
observed for relatively fast CMEs (Gopalswamy et al. 2009; a wide range of temperatures. The pixel resolution is 0(cid:4).(cid:4)6 and
Ontiveros & Vourlidas 2009). In this paper, we apply the thebasiccadenceis12s(seeLemenetal.2011formoredetails
standoffdistancetechniquetoaCME-drivenshockobservedon oftheinstrument).Herewesampletheimagesin193Åevery
2010June13intheEUVimagesobtainedbytheAtmospheric minutestartingfromthetimethefirstsignaturesoftheeruption
ImagingAssembly(AIA;Lemenetal.2011)onboardtheSolar wereobserved.TheeruptionoccurredfromactiveregionNOAA
DynamicsObservatory(SDO;Schweretal.2002).Gopalswamy 1079fromthesouthwestlimb(S25W84)inassociationwithan
& Yashiro (2011) had computed the ambient density in the M1.0flare.Figure1showsrunningdifferenceimages,inwhich
coronausingthepolarizedbrightnessimageofthecorona,but weseetheevolutionoftheCMEasaseriesofsnapshotsfrom
herewederivedthedensityfromtheaccompanyingtypeIIradio the very early stage at 05:34:54 UT–05:41:54 UT. The shock
burstobservedbytheHiraisoRadioSpectrograph(HiRAS)in structurebecomesclearinthe05:37:54UTimageandisvisible
Japan(Kondoetal.1997). throughouttheobservation.
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TheAstrophysicalJournal,744:72(7pp),2012January1 Gopalswamyetal.

0.1Rs

05:34:54 05:35:54 05:36:54 05:37:54

05:38:54 05:39:54 05:40:54 05:41:54

Figure1.SnapshotsoftheCMEfromSDO/AIA193Ådifferenceimages.Asmallsectionoftheimagesfromthesouthwestcornerisshown.Thearrowpointsto
theearlystageoftheCME.Thescaleoftheimagesisalsoindicatedonthefirstframeintermsofasolarradius(Rs).Theopticallimbisalsodrawn.Afullcadence
(12s)movieoftheeventisincludedasanelectronicsupplementintheonlinejournal.
(Ananimationandacolorversionofthisfigureareavailableintheonlinejournal.)
TheshockstructureconnectstotheEUVwavefeaturemov-
ingawayfromtheeruptionsite,moreclearlyseenatlatertimes. Flux
This is consistent with the interpretation that the EUV wave Rope
isafast-modeshocksurroundingtheCMEfluxrope(see,e.g.,
Veronigetal.2010).Weidentifytheinnercircularfeatureasthe
fluxropethatdrivestheshock.Thereisasuddenchangeinthe
shapeofthefluxropeindicatingrapidexpansioninthelateral
directionbetween05:36:54and05:37:54UT.Interestinglythis
is the time the shock became distinctly visible. Full-cadence
datashowthatadiffusestructureformedaheadofthefluxrope
at 05:36:54 UT. This coincided with the onset of the metric
type II radio burst (see below). The overall position angle
extent (including the shock) was ∼37◦ by the time the CME
lefttheSDO/AIAfieldofview(FOV).Thefluxropeitselfsub- Shock
tended an angle of only ∼17◦. The CME first appeared in the
LASCO/C2 FOV at06:06 UT,when theleading edge was al-
ready at 2.57 Rs. The speed within the LASCO FOV is only
320kms−1 andtheCMEhasapositionangleextentof∼33◦. 2010/06/13 05:39:54 UT
Clearly, the flux rope seems to have decelerated significantly
R = 0.13Rs; R = 1.26Rs; R = 1.35Rs
bythetimeitreachedtheoutercorona.Thepositionangleex- c fl sh
tentsuggeststhattheLASCOCMEmustbetheexpandedflux Figure2.SDO/AIAdifferenceimageat193Åshowingthefluxropeandthe
rope.TheCMEdoesnotshowthediffuseshockstructureinthe shock structure surroundingit. The heliocentric distances of the shock (Rsh,
LASCOFOV,suggestingthattheshockmighthaveweakened markedbythe“+”symbol)andthefluxrope(Rfl)areshown.Theredcrosses
anddissipatedbythetimeitreachedtheLASCOFOV.There- arethepointsonthefluxropeusedforfittingthecircle.Thebluecrossmarks
thecenterofthefittedcircle.Theradiusofthecirclefittedtothefluxropeis
fore,thespeedmusthavepeakedsomewherebetween1.5and
2.57Rs.WithouttheSDOobservations,theconnectionbetween theradiusofcurvature(Rc)ofthefluxrope.
(Acolorversionofthisfigureisavailableintheonlinejournal.)
thetypeIIburst,theshock,andthefluxropewouldnothavebeen
revealed.
The shock structure is better described in Figure 2 with the Thus,thethicknessofthesheathbecomesthestandoffdistance
projection of the flux rope on the sky plane fitted to a circle. oftheshockaheadofthefluxrope.
We identify the radius of this circle as the minor radius of the The heliocentric distance of the shock (R ) was measured
sh
flux rope and also the radius of curvature of the shock driver. at six instances from 05:36:54 UT to 05:42:54 UT, traveling
The shock itself is not resolved, but the broad diffuse feature from ∼1.19 Rs to 1.46 Rs. The flux rope leading edge (R )
fl
aheadofthefluxropeistheshocksheath.Theleadingedgeof was observed from ∼1.13 Rs to 1.38 Rs before its leading
the shock sheath is expected to be the shock. We identify the edge left the SDO/AIA FOV after 05:43:54 UT. The standoff
positionoftheleadingedgeofthesheathastheshocklocation. distance(thedifferencebetweenR andR )steadilyincreased
sh fl
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TheAstrophysicalJournal,744:72(7pp),2012January1 Gopalswamyetal.
1.8
0.25
Shock Rsh=3.7E−7t2+5.6E−4t+0.9 Rc=−6.7E−10t3+9.7E−7t2−0.2E−4t+0.06
Flux Rope R=6.2E−7t2−1.1E−4t+1.1
fl
] 0.20
s
R 1.6 ]
[ s
e R
nc s [
a u 0.15
st di
Di 1.4 Ra
c e
ri p
nt o 0.10
e R
c x
o u
eli 1.2 Fl
H 0.05
Type II Onset & Type II Onset &
Shock Onset (a) Shock Onset (b)
1.0 0.00
05:32 05:36 05:40 05:44 05:32 05:36 05:40 05:44
UT (Start Time 2010/06/13 05:30:54) UT (Start Time 2010/06/13 05:30:54)
Figure3.(a)Height–timeplotoftheshockandfluxropewiththequadraticfittothemeasurements.AllheightsrefertotheSuncenter.One-minutedifferenceimages
wereused.Theshockfirstappearedonlyat05:36:54UT,whichcoincidedwiththeonsetofthemetrictypeIIburst.Theerrorbarsontheheightsgivestandard
deviationsoffourindependentmeasurements.TheequationsofthefittedcurvesareRsh(t)=3.7×10−7t2 + 5.6×10−4t + 0.9andRfl(t)=6.2×10−7t2−1.1×
10−4t + 1.1,wheretisthetimeinsecondsfrom05:30:54UT.(b)Timeevolutionofthefluxroperadius(alsoknownasminorradius)obtainedbyfittingacircleto
thefluxropecrosssection.Theerrorbarsrepresenttheerrorsinfittingthecircle(themaximumerroris±0.01Rswithmostpointshavingamuchlowererror).The
solidcurveisthethird-orderpolynomialfittothedatapoints,whoseequationisRc(t)=−6.7×10−10t3 + 9.7×10−7t2−0.2×10−4t + 0.06withtinseconds
from05:30:54UT.
from ∼0.02 Rs to 0.13 Rs when both the flux rope and the inthevicinityoftheshock,soa150MHzfrequencyimpliesa
shock were observed. The flux rope radius is the same as localplasmadensityof2.8×108cm−3,whichisconsistentwith
theradiusofcurvature(R ),whichdoubledduringthefluxrope the shock formation close to the solar surface (0.19 Rs above
c
transitthroughtheSDO/AIAFOV.Thisisalimbevent,sowe the surface). The radio dynamic spectrum from the Hiraiso
are looking at the cross section of the flux rope, with its axis RadioObservatoryinFigure4showsthatthefundamentaland
roughlyperpendiculartotheskyplane.Notethattheradiusof harmonic components are visible, so there is no ambiguity in
curvatureofthefluxropeisinitiallysimilartohalfoftheflux relating the emission frequency to the plasma frequency. The
ropeheightabovethelimb,butrapidlyincreasesatthetimeof harmonic component is visible better than the fundamental
shock formation. The eruption is from W84, so the projection component. The average drift rate of the type II burst is
effectsareexpectedtobeminimal:thetrueheightsandspeeds ∼0.28 MHz s−1, which is typical of metric type II bursts (see
areexpectedtobelargeronlyby<0.6%,whichisnegligible. Gopalswamyetal.2009).Theharmoniccomponentalsoshows
Figure 3 shows the height–time plots of the shock, the flux band splitting, which indicates that the emission comes from
rope,andtheradiusofthefluxrope.Theaveragespeedsofthe behindandaheadoftheshock(Smerdetal.1974;Vrsnaketal.
fluxropeandshockare330kms−1and644kms−1,respectively. 2004; Cho et al. 2007). At the five times marked in Figure 4,
Theaverageexpansionspeedofthefluxropeis∼160kms−1. theupper(f )andlower(f )bandsareatfrequencies(186,156),
2 1
The diameter of the flux rope increases with the same speed (162, 128), (146, 118), (128, 104), (115, 90) MHz, indicating
as the radial speed of the flux rope. In Figure 3(a), the anaverageseparationof∼28MHz.Thefrequencyratiof /f is
2 1
height–time measurements are fitted with second-order poly- directlyrelatedtothedensityjumpacrosstheshockbecausef
1
nomials. Both the flux rope and the shock show increase in andf correspondtoemissionaheadandbehindtheshock.The
2
speed through the SDO FOV. The sudden increase in the flux average value of f /f = 1.24, which corresponds to a density
2 1
rope radius between 05:36:54 UT and 05:37:54 UT is associ- compressionof1.54acrosstheshock.
ated with the rapid expansion of the flux rope and coincides ToderivethemagneticfieldfromtheAlfve´nspeed,oneneeds
with the shock formation. A third-order polynomial fit to the the ambient plasma density at the shock nose. For the 2010
flux rope radius shows a complex evolution compared to the June13event,wecanusethetypeIIradioburstobservationsto
leadingedgeofthefluxropeandtheshock.Fromthefirstthree gettheplasmadensitybecause theemissiontakesplaceatthe
points,weestimateanaverageexpansionspeedof∼42kms−1, localplasmafrequency(f )anditssecondharmonic(2f ).Since
p p
whichjumpsto136kms−1by05:37:54UTaroundthetimeof f = 9 × 10−3n1/2 MHz with the electron density n in cm−3,
p
shockformation.TheradialspeedoftheCMEfluxropeisonly onecanobtainnfromthedynamicspectrumbyidentifyingf .
p
∼245kms−1atthetimeofshockformation. Theemissionaheadoftheshockisfromtheunshockedcorona,
so the emission occurs at a lower frequency (f ) compared to
1
2.2.RadioObservations thecompresseddownstream(f2>f1).Weneedtousethelower
frequency (f ) to get the upstream plasma frequency (f ) and
1 p1
TheshockformationobservedinEUVremarkablycoincided density (n ): f = f /2. Figure 4 shows that the band split-
2 p1 1
with the onset of a metric type II burst at 05:37:00 UT at the ting is clear between 05:39:30 and 05:43:30 UT. Three of the
frequencyof300MHz(harmonic)and150MHz(fundamental). SDO/AIA frames overlap with this interval: at 05:39:54,
Type II radio bursts are emitted at the local plasma frequency 05:40:54, and 05:41:54 UT, so we get f = 128, 118, and
1
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TheAstrophysicalJournal,744:72(7pp),2012January1 Gopalswamyetal.
Figure4.RadiodynamicspectrumfromtheHiraisoRadioSpectrograph(HiRAS)showingthetypeIIburststartingfrom∼05:37UTuntilabout05:47UTbeyond
whichitismaskedbytheinterferenceinthe50–60MHzfrequencyrange.Thebandsplittingisclearbetween05:39:30and05:43:30UT.
(Acolorversionofthisfigureisavailableintheonlinejournal.)
104 MHz giving the upstream densities (n ) as 5.1, 4.3, and corresponds with n = 5.1 × 107cm−3. At 05:39:54 UT, we
2 1
3.3inunitsof107cm−3 atthesetimes. measureΔR=9.1×10−2 RsandR =0.134Rs,soδ =0.68,
c
whichwhensubstitutedinEquation(2)withγ =4/3givesM=
2.3.CoronalMagneticField 1.56.WeuseR measuredat05:38:54UTand05:40:54UT,to
sh
getthelocalshockspeedat05:39:54UTasV ∼721kms−1,
Thestandoffdistancemethodtoderivethecoronalmagnetic sh
which in turn gives V = V /M = 462 km s−1. Putting n =
field involves measuring the leading edges of the CME flux A sh
5.1×107 cm−3 andV =462kms−1 inEquation(3),weget
rope(R )andtheleadingshock(R )atthenoseandmeasuring A
fl sh B=1.51Gcorrespondingtoaheliocentricdistanceof1.35Rs.
the radius of curvature (R ) of the flux rope fitted to a circle
c
(seeGopalswamy&Yashiro2011).ThestandoffdistanceΔR= Dulk&McLean(1978)derivedtheradialdependence
Rsh − Rfl is related to the shock Mach number (M) and the B(r)=0.5(r −1)−1.5, (4)
adiabaticexponent(γ;Russell&Mulligan2002):
whereristheheliocentricdistance.Atr=1.35Rs,thisformula
ΔR/R =0.81[(γ −1)M2+2]/[(γ +1)(M2−1)]. (1) givesB=2.4G,whichis∼60%higherthanourvalue.
c
Table1showsthederivedmagneticfieldvaluesforthetimes
HerewetaketheMachnumbertobetheAlfve´nMachnumber. duringwhichtheshockandradiomeasurementsareavailable.
Intermsoftherelativestandoffdistanceδ =ΔR/Rc,theMach ThemagneticfieldalsodeclinessteadilywithintheSDO/AIA
numbercanbewrittenas FOV. Note that the flux rope was observed before the shock
M2 =1+[1.24δ−(γ −1)/(γ +1)]−1. (2) formation and the shock left the SDO/AIA FOV before the
flux rope did. The Mach number was determined assuming
Measuring δ and assuming γ, one can get the Alfve´n Mach γ = 4/3. The numbers in parentheses correspond to γ =
5/3. The Mach number steadily declines from 3.72 in the
number. Note that the second term on the right-hand side of
beginningto1.49justbeforetheshocklefttheSDOFOV.The
Equation(2)needstobepositiveforashock,whichimposesa
minimum value of δ = 0.115 for γ = 4/3 and 0.202 for γ = ambientAlfve´nspeedsteadilyincreases,reachingamaximum
5/3.Inordertogetthemagneticfieldstrength(B),weneedthe of 462 km s−1 and then declines by a few percent in the next
two measurements. The Alfve´n speed decline directly reflects
upstreamAlfve´nspeed(V )andtheplasmadensity(n).Since
A
V = V /M, where the shock speed V is obtained from the the decrease in the local shock speed obtained from three
A sh sh
consecutiveheight–timemeasurementsoftheshock(exceptfor
timeseriesofR measuredintheEUVimages.Inthecoronal
sh
the first and last measurements). It is possible that the shock
region we are interested in, the solar wind speed is negligible
indeed begins to weaken around thistime,but we do not have
comparedtotheshockspeed.Themagneticfieldstrengthinthe
sufficientinformationbecauseofthelimitedSDOFOV.
upstreammediumisgivenby
ThenumbersinTable1areshowngraphicallyinFigure5.The
B =4.59×10−7V n1/2 G. (3) Alfve´nspeedofthecoronainFigure5(a)isobtainedusingthe
A
“local shock speed” method described above. In Figure 5(b),
All we need is the upstream density, which can be derived the shock speeds used are from the quadratic fit shown in
directly from the emission frequency of the type II burst as Figure 3(a). The slight decline in Alfve´n speed is likely to be
explained in Section 2.2. For example, at 05:40 UT, the upper alocalfluctuation,whichissmoothedoutbythequadraticfit.
and lower bands of the harmonic component have frequencies TheMachnumberdeclinesthroughtheSDO/AIAFOVinboth
f =162andf =128MHz,respectively.Thelocalplasmafre- casesbecauseitsderivationdoesnotdependontheshockspeed.
2 1
quenciesarethereforef =81andf =64MHz,respectively, Thelowerγ valueresultsinahigherAlfve´nMachnumber.The
p2 p1
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TheAstrophysicalJournal,744:72(7pp),2012January1 Gopalswamyetal.
5 600 5 600
Mach Number γ =4/3 Mach Number γ =4/3
Alfven Speed (Local) γ =5/3 Alfven Speed (Fit) γ =5/3
500 500
4 4
er s] er s]
mb m/ mb m/
Nu 400d [k Nu 400d [k
h e h e
c 3 e c 3 e
a p a p
M S M S
n 300n n 300n
e e e e
v v v v
Alf 2 Alf Alf 2 Alf
200 200
(a) (b)
1 100 1 100
11..00 11..22 11..44 11..66 11..00 11..22 11..44 11..66
Heliocentric Distance of the Shock [Rs] Heliocentric Distance of the Shock [Rs]
Figure5.(a)DerivedMachnumberandAlfve´nspeedforγ =4/3and5/3.TheAlfve´nspeedwasderivedusinglocalshockspeedobtainedfromthreeconsecutive
height–timemeasurements.(b)Sameasinpanel(a)exceptthattheAlfve´nspeedisobtainedusingashockspeedderivedfromasecond-orderfittotheheight–time
plot(seeFigure3(a)).
(Acolorversionofthisfigureisavailableintheonlinejournal.)
Table1.
ShockandFluxRopeMeasurementsandtheDerivedPropertiesoftheCoronaforγ =4/3(5/3)
Time Rsh Rfl ΔR Rc δ Vsh fp1 n1 M VA B
UT (Rs) (Rs) (Rs) (Rs) (kms−1) (MHz) (×107)cm−3 (kms−1) (G)
05:34:54 ... 1.15 ... ... ... ... ... ... ... ... ...
05:35:54 ... 1.16 ... ... ... ... ... ... ... ...... ...
05:36:54 1.19 1.17 0.014 0.080 0.18 531 ... ... 3.72(...) 143(...) ...
05:37:54 1.23 1.20 0.037 0.115 0.32 568 ... ... 2.21(2.76) 257(206) ...
05:38:54 1.29 1.23 0.060 0.126 0.47 682 78 7.5 1.80(1.99) 378(342) 1.50(1.36)
05:39:54 1.35 1.26 0.092 0.136 0.68 721 64 5.1 1.56(1.64) 462(439) 1.51(1.43)
05:40:54 1.41 1.30 0.108 0149 0.73 663 59 4.3 1.52(1.59) 435(416) 1.31(1.25)
05:41:54 1.47 1.34 0.126 0.162 0.77 644 52 3.3 1.49(1.55) 432(415) 1.15(1.10)
05:42:54 ...... 1.38 ... ... ... ... 45 2.5 ... ... ...
Alfve´nspeedontheotherhandislowerforthehighervalueofγ The active region was very small and had an area of only
becauseforagivenshockspeed,theAlfve´nspeedisinversely 10 msh (http://kukui.ifa.hawaii.edu/ARMaps/Archive/2010/
proportional to the Mach number. Weakening of the shock is 20100613.1632_armap.png).Therefore,itislikelythatthequiet
evident even when the shock speed is increasing because of coronabecamedominantatloweraltitudesthanexpected.Mag-
therapidincreaseintheambientAlfve´nspeed.Itappearsthat neticfieldvaluesfromothertechniquesareshownforcompari-
thepresentobservationscorrespondtotheincreasinglegofthe son:Fineschietal.(1999),Mancusoetal.(2003),andChoetal.
Alfve´nspeedclosetothecoronalbase(Mannetal.1999,2003; (2007).Thesevaluesareingeneralagreementwithours,except
Gopalswamyetal.2001).Gopalswamyetal.(2001)foundthat fortheFineschietal.(1999)datapointat1.4Rs.
theAlfve´nspeedstartsincreasingaroundaheliocentricdistance
of1.4Rs.Inthepresentcase,theincreaseseemstohavestarted 2.4.ShockCompressionRatio
abitclosertotheSun.Asnotedbefore,theshockseemstohave
Finally, we check the consistency of our analysis from the
dissipatedbythetimetheCMEreachedtheLASCO/C2FOV.
compressionratio(downstreamdensityn toupstreamdensity
Figure 6 shows the derived magnetic fields from the shock 2
n )obtainedfrombandsplittingtothetheoreticalvalue.From
measurements for γ = 4/3 and 5/3 at four instances when 1
thedynamicspectrum,n /n issimply(f /f )2=(f /f )2.For
the upstream plasma density is available from the radio ob- 2 1 p2 p1 2 1
the four instances in Figure 4 we get the compression ratio as
servations. Our magnetic field value at the lowest height
1.42,1.60,1.53,and1.51.Thefirstofthesevaluesisnotvery
is not reliable because the band splitting is not clear (see
accurate because the split bands are not very well defined at
Figure4).AlsoshownaretheDulk&McLean(1978)empiri-
this time. Assuming that the shock is quasi-perpendicular at
cal relations for the magnetic field in the active region corona
theselowheights,wecanusethesimplifiedformula(Draine&
and a quiet-Sun magnetic field model B(r) = a/r2 with two
McKee1993),
values of the constant a: 2.2 and 2.6. Our values are clos-
est to the quiet-Sun curve with a = 2.6. The model curves n /n =2(γ +1)/{D+[D2+4(γ +1)(2−γ)M−2]1/2}, (5)
showthattheactiveregionblendswiththequietcoronaaround 2 1
1.4Rs(seealsoGopalswamyetal.2001);inthepresentcase, where D = (γ−1) + (2/M 2 + γ/M2) and M = V /C is
s s sh s
it seems to have happened at a lower heliocentric distance.
the sonic Mach number. For a 2 MK corona, the sound speed
5
TheAstrophysicalJournal,744:72(7pp),2012January1 Gopalswamyetal.
Table2.
ShockPropertiesfromTheoryandMeasurementsforγ =4/3(5/3)andSoundSpeed=128kms−1
Time Rsh Vsh M Ms n2/n1 n2/n1 β
(UT) (Rs) (kms−1) (Radio) (Theory)
05:38:54 1.29 682 1.80(1.99) 5.33 1.42 1.93(2.01) 0.11(0.14)
05:39:54 1.35 721 1.56(1.64) 5.63 1.60 1.67(1.71) 0.08(0.09)
05:40:54 1.41 663 1.52(1.59) 5.18 1.53 1.61(1.65) 0.09(0.09)
05:41:54 1.47 644 1.49(1.55) 5.03 1.51 1.57(1.61) 0.09(0.10)
10 it with the Alfve´n speed to get the coronal magnetic field
γ =4/3 Fineschi et al. (1999) strength.Themagneticfieldstrengthobtainedisconsistentwith
γ =5/3 Mancuso et al. (2003) other estimates from different techniques. Given the paucity
B=0.5(r−1)−1.5 Cho et al. (2007) of coronal magnetic field measurements, this technique will
prove to be very useful in obtaining the field strengths in the
coronal region where energetic events originate. Acceleration
G] a=2.6 ofenergeticparticlesbyCME-drivenshocksoccursaroundor
[ abovetheheliocentricdistancesconsideredhere,andhenceour
B
nal a=2.2 rinevsuolltvsepdroivnidsehoucsekfualcccoenlesrtaratiionntstohneothrieems.aTgnheetimcfiagelndetsitcrenfigetlhd
oro 1 B=a r−2 measurement is also important in providing ground truth to
C theextrapolationtechniquescommonlyemployedinobtaining
coronalmagneticfieldsfromthephotosphericorchromospheric
magnetograms. CME measurements have become routine and
the shock structure is readily discerned from white light and
EUV observations, so this technique can be used whenever a
CME drives a shock. Normally CME observations are used in
derivingthepropertiesoferuptiveevents,butherewehaveused
1.0 1.2 1.4 1.6 1.8 2.0 them to derive the properties of the ambient medium through
Heliocentric Distance of the Shock [Rs] whichtheCME-drivenshockpropagates.
Figure6.Derivedcoronalmagneticfieldvaluesforγ =4/3and5/3usingthe Intheanalysiswehavetacitlyassumedthattheradioemission
plasmadensitiesinferredfromthelowersidebandofthetypeIIradioburst.The comes from near the nose of the shock. We have no imaging
Dulk&McLean(1978)empiricalrelationforthemagneticfieldaboveactive observation at radio wavelengths, so we cannot justify this
region[B(r)=0.5(r−1)−1.5]coronaandaquiet-Sunmagneticfieldmodel
assumption. However, at such low heights in the corona, we
B(r)=a/r2witha=2.2and2.6arealsoshown.Magneticfieldvaluesfrom
doexpecttheshocktobequasiperpendicularatmostlocations,
othertechniquesareshownforcomparison.
so the nose region certainly is favored because of the highest
(Acolorversionofthisfigureisavailableintheonlinejournal.)
shockstrength.Iftheradioemissionoriginatesfromtheflanks
oftheshock,thentheestimatedmagneticfieldcorrespondstoa
C ∼128 km s−1, so M ∼5 for the measured shock speeds.
s s slightlylowerheight.Notethattheoverallpositionangleextent
Maetal.(2011)estimatedanupstreamtemperatureof1.8MK, isonly∼33◦,sowhenthenoseisat1.4Rs,theflank15◦ away
similar to the value assumed here. Substituting for M and M
s fromthenoseisataheightofonly1.35Rs.Byassumingthat
and taking γ = 4/3 in Equation (5), we get n /n consistent
2 1 theradiosourceislocatedatthenose,wearemakinganerrorof
with the values derived from the radio dynamic spectrum (see ∼4%intheheightatwhichthefieldestimateismade.Itisalso
Table 2). The first value of n /n shows the largest deviation,
2 1 possiblethattheradioemissioncomesfromanextendedregion
buttheradiomeasurementsarenotveryaccurateforthistime.
aroundthenosewheretheMachnumberissignificantlygreater
Thecompressionratioandmagneticfieldstrengthobtainedby
than1,sotheheightoftheshocknoseisarepresentativeheight.
Maetal.(2011)atoneinstance(05:40UT)areconsistentwith
Itmustbepointedoutthattheupstreamdensitycanbeobtained
ourvalues.NotethatMaetal.(2011)didnotusethestandoff
byothermeanssuchasspectroscopicobservationsandcoronal
distancetechniquetogetthemagneticfield.Table2alsoshows
brightness measurements (see, e.g., Bemporad & Mancuso
theplasmabeta(β =C 2/V 2)usingC =128kms−1 andV
s A s A 2010). In this respect, our method of obtaining the Alfve´n
fromTable1.Thevaluesareconsistentwithalowbetacorona
speed is robust and can utilize density measurements from
asexpected. many different instruments/techniques to obtain the magnetic
field.
3.DISCUSSION ThederivedAlfve´nspeedinthelowcoronaisconsistentwith
previous estimates based on models of density and magnetic
Theprimaryfindingofthispaperisthattheshockstructure
fieldinthecorona(Mannetal.1999,2003;Gopalswamyetal.
surrounding the CME flux rope near the Sun can be used to
2001;Warmuth&Mann2005).Inparticular,Gopalswamyetal.
infer the coronal magnetic field strength. The shock standoff
(2001) estimated that the minimum in the fast-mode speed
distanceandtheradiusofcurvatureofthefluxropearedirectly
occurs around 1.4 Rs and could be as low as 230 km s−1 and
related to the Alfve´nic Mach number of the shock and the
thespeedincreasesatlargerheights.TheAlfve´nspeedshown
adiabatic index. From the measured shock speed, we obtained
inFigure5isconsistentwiththisestimate.Themagneticscale
the Alfve´n speed assuming the adiabatic exponent. From the
heightismuchlargerthantheheliocentricdistancerangeover
emission frequency of the type II radio burst produced by
whichwemadethemagneticfieldmeasurements.Forexample,
the shock, we get the upstream plasma density and combine
6
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