Evolution of Magnetic Field and Energy in A Major Eruptive Active Region Based on SDO/HMI Observation

1.2 MB·English

by  Xudong Sun

Accepted January16,2012
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
EVOLUTION OF MAGNETIC FIELD AND ENERGY IN A MAJOR ERUPTIVE ACTIVE REGION BASED ON
SDO/HMI OBSERVATION
Xudong Sun1,2, J. Todd Hoeksema1, Yang Liu1, Thomas Wiegelmann3, Keiji Hayashi1, Qingrong Chen2, Julia
Thalmann3
Accepted January 16, 2012
ABSTRACT
2 We report the evolution of magnetic field and its energy in NOAA active region 11158 over 5 days
1 based on a vector magnetogram series from the Helioseismic and Magnetic Imager (HMI) on board
0
the Solar Dynamic Observatory (SDO). Fast flux emergence and strong shearing motion led to a
2
quadrupolar sunspot complex that produced severalmajor eruptions, including the first X-class flare

n of Solar Cycle 24. Extrapolated non-linear force-free coronal fields show substantial electric current
a andfree energyincreaseduring earlyflux emergenceneara low-lyingsigmoidalfilamentwith sheared
J kilogauss field in the filament channel. The computed magnetic free energy reaches a maximum of

7 ∼2.6×1032 erg, about 50% of which is stored below 6 Mm. It decreases by ∼0.3×1032 erg within
1 1 hour of the X-class flare, which is likely an underestimation of the actual energy loss. During the
flare,the photosphericfieldchangedrapidly: horizontalfieldwasenhancedby28%inthe coreregion,

] becomingmoreinclinedandmoreparalleltothepolarityinversionline. Suchchangeisconsistentwith
R
the conjectured coronal field “implosion”, and is supported by the coronal loop retraction observed
S by the Atmospheric Imaging Assembly (AIA). The extrapolated field becomes more “compact” after
. the flare, with shorter loops in the core region, probably because of reconnection. The coronal field
h
becomes slightly more sheared in the lowest layer, relaxes faster with height, and is overall less
p
- energetic.
o
Subject headings: Sun: activity — Sun: photosphere — Sun: corona — Sun: surface magnetism
r
t
s
a 1. INTRODUCTION rectly monitors the AR’s evolution and provides infor-
[
Extreme solar activity is powered by magnetic energy mation on its non-potential nature (e.g. Schrijver et al.
1 2005). In addition, field extrapolation models based on
(e.g.Forbes 2000). Flux emergenceandshearingmotion
v the vector boundary may provide valuable diagnostics
introduce strong electric currents and inject energy to
4 of the changing coronal field (e.g. R´egnier & Canfield
the active region (AR) corona. Coronal fields are sub-
0 2006; Thalmann & Wiegelmann 2008; Jing et al. 2009).
sequently reconfigured, accumulating large amounts of
4 TherecentlylaunchedHeliosphericandMagneticImager
magnetic free energy. When the overly energetic field
3 (HMI; Schou et al. 2011) on board the Solar Dynamic
gets destabilized, part of its excess energy is released
1. rapidly,withpowerenoughtodriveexplosivephenomena Observatory (SDO) therefore presents a unique oppor-
0 such as flares and coronal mass ejections (CMEs). Dur- tunity to better understand the AR energetics with its
2 ing this process, fast, irreversible changes of the photo- full disk, high resolution and high cadence vector mag-
1 sphericfieldhavebeenobservedasthepossibleimprintof netograms.
: Here we reportthe evolutionof magnetic field and en-
v the coronal activity, including transverse field and mag-
ergy in NOAA AR 11158 using a series of HMI vector
i netic shear increase (e.g. Wang et al. 1994; Wang 2006)
X magnetogramsandanon-linearforcefreefield(NLFFF)
and longitudinal field decrease (Sudol & Harvey 2005).
extrapolation. This 5-day uninterrupted, 12-minute ca-
r Hudson(2000)suggestedthatthe energylossduringthe
a dencedatasetallowsustostudyindetailboththe long-
explosion causes “implosion” of the coronal field, which
term,gradual evolution,aswellastherapid changesdur-
is supported by recent observations (Ji & Wang 2007;
ing an X-class flare and CME eruption. We briefly de-
Liu & Wang 2010).
scribethe datasetandthe extrapolationmethodinSec-
This “storage-release”picture provides a scenario suc-
tion 2. The long-term evolution and the rapid changes
cessful in explaining many observed phenomena (e.g.
are discussed in Sections 3 and 4, respectively. In addi-
Schrijver 2009). However, detailed knowledge of the
tion to the HMI data, we employ coronal and chromo-
process is still lacking, especially in a quantitative spa-
sphere images, such as those taken by the Atmospheric
tially and temporally resolved manner (e.g. Hudson
ImagingAssembly(AIA; Lemen et al.2011)onSDO for
2011). In this sense, uninterrupted, frequent photo-
context and validation of the results.
spheric vector field observation may be crucial, as it di-
2. VECTOR MAGNETOGRAMS AND FIELD
[email protected]
1W. W. Hansen Experimental Physics Laboratory, Stanford EXTRAPOLATION
University,Stanford,CA94305,USA. The HMI instrument on SDO observes the full Sun at
2Department of Physics, Stanford University, Stanford, CA
6 different wavelengths and 6 polarization states in the
94305, USA.
3Max-Planck-Institut fu¨r Sonnensystemforschung, Max- FeI6173˚Aabsorptionline. Filtergramswith0.5′′ pixels
Planck-Str. 2,37191Katlenburg-Lindau,Germany. arecollectedandconvertedtoobservablequantitiesona
2 Sun et al.
a HMI Vector Field b Vertical Current Density
Flux
cancelation
25 Mm P0 25 Mm
N0 Pores
P1
1000 0.025
PIL

N1
−1000 −0.025
1500 [G] [A m −2]
Sunspot
2011.02.14_20:35:20 UT rotation 2011.02.14_20:35:20 UT
c d
AIA 171 Å NLFFF Field Line
25 Mm 25 Mm
Filament Filament
Overlying loops
Loops to N1
360 0 0.0 2

0 0
[D N] [A m −2]
2011.02.14_20:35:25 UT 2011.02.14_20:35:20 UT
Fig.1.—Observationsandmodelingresultsfor2011February1420:35UT,about5hoursbeforetheX-classflare. (a)RemappedHMI
vector magnetogram for the center region of AR 11158 as viewed from overhead. Vertical field (Bz) is plotted in the background; blue
(red) arrows indicate horizontal field (Bh) with positive (negative) vertical component. Contours are plotted at ±600 G. (b) Vertical
current density (Jz) derived from 5-pixel Gaussian-smoothed vector magnetogram. Contours are forBz and are identical to (a). Part of
thepolarityinversionline(PIL) isplotted asthick cyancurve. (c)Image fromAIA 171˚Aband showingthecoronamagnetic structures.
ThedottedboxinthecenterindicatestheFOVofFigure2a. (d)SelectedfieldlinesfromtheNLFFFextrapolationplottedoveracutout
fromthevertical fieldmap. Thelinesarecolor-codedbythe verticalcurrentdensityattheirfootpoints (seethecolorbar); redfieldlines
correspondtostrongcurrentdensity. ThewhitedottedboxindicatetheFOVof(a)and(b). TheFOVsof(c)and(d)areidentical,about
218×218Mm2,or302′′×302′′. Featuresofinterestaremarkedineachpanel;seetextfordetails. (Ananimationofthevector fielddata
setfortheentire5-dayperiodisavailableintheonlinejournal.)
rapidtimecadence. Forthevectormagneticdatastream, the most general case,
each set of filtergrams takes 135 seconds to complete.
Toobtainvectormagnetograms,Stokesparametersare ∇×B =αB, (1)
first derived from filtergrams observed over a 12-minute
interval and then inverted through a Milne-Eddington B·∇α=0, (2)
based algorithm, the Very Fast Inversion of the Stokes
Vector (VFISV; Borrero et al. 2011). The 180◦ az-
with the torsionparameter, α, varyingin space but con-
imuthal ambiguity in the transverse field is resolved by
stantalongeachfieldline. Weuseanoptimization-based
animprovedversionofthe“minimumenergy”algorithm
NLFFFalgorithm(Wiegelmann2004)toextrapolatethe
(Metcalf1994;Metcalf et al.2006;Leka et al.2009). Re-
coronal field from the magnetograms in a Cartesian do-
gions of interest (ROIs) with strong magnetic field are
main. A preprocessing procedure removes most of the
automatically identified near real time (Turmon et al.
net force and torque from the data so the boundary
2010). A detailed descriptiononthe productionand rel-
can be more consistent with the force-free assumption
evant characteristics,specifically for the data set for AR
(Wiegelmann et al. 2006). For reference, we also con-
11158, can be found in Hoeksema et al. (2012). Out-
struct a potential field (PF) from the same observation
standing questions regardingdata reduction are also de-
using the vertical component of the field and a Green
scribed there.
function algorithm (e.g. Sakurai 1989). The magnetic
The magnetic field above the lower chromosphere
free energy (E ) can be inferred by subtracting the PF
f
largely satisfies the force-free criteria (Metcalf et al.
energy (E ) from the NLFFF energy (E ), where the
P N
1995), where currents align with the magnetic field. For
energy is computed from the field strength within a cer-
Magnetic Evolution from SDO/HMI 3
tain volume V:
TABLE 1
B2 B2 Estimated fieldparametersin the filament
Ef = N dV − P dV. (3) channel.
8π 8π
ZV ZV
Here the subscripts N and P denote NLFFF and PF Parametera Unit Crosssectionb Nearaxisc
respectively. We note that the VFISV inversion scheme A Mm2 59.9 4.2
for HMI has the magnetic filling factor held at unity, so Φa 1020Mx 4.87 0.49
theobtained“magneticfield”isessentiallyaveragedflux hBi 103G 0.97±0.27 1.20±0.05
density. Inthecontextofthiswork,wedonotdistinguish h|γ|i degree 26±16 11±8
these two and use the unit Gauss (G) throughout. hJhi mAm−2 19±9 43±5
hαi Mm−1 0.27±0.15 0.46±0.05
We use 600 vector magnetograms of NOAA AR
hLi Mm 29±5 24±3
11158 with a cadence of 12 min, from 2011 Febru- hφi Turns 0.64±0.17 0.92±0.17
ary 12 to 16 (see online animation of Fig. 1 for the a All parameters are estimated fromuniformlysampled
data set). The images are de-rotated to the disk cen- pointsonaverticalcrosssectionthroughtheNLFFFex-
ter and remapped using Lambert equal area projection trapolationdomain,markedas“CS1”inFigure2. Angle
(Calabretta & Greisen2002;Thompson2006). The field brackets refers to the mean value. The notations are as
vectorsaretransformedtoHeliographiccoordinateswith follows: crosssectionareaA,axialfluxΦa,fieldstrength
B,inclinationangleγ,horizontalcurrentdensityJh,tor-
projection effect removed (Gary & Hagyard 1990). For sional parameter α, loop length L, twist angle φ. The
direct analysis of the photospheric field, we use full res- inclination angle is measured with regard to the photo-
olution data at about 360kmpix−1 (0.5′′). For extrapo- sphere,rangingfrom−90◦ to90◦ with0◦ forhorizontal
lation, we bin the data to 720 kmpix−1 (about 1′′) and fimealdtedanudsisniggneqcuoantsiiosnteBnt1.wφitihsdpiovliadreitdyboyf2Bπzt.oαshioswesthtie-
adopt a computation domain of 216×216×184 Mm3 estimatednumberofturns.
(300×300×256). b Values are calculated within the Jh > 10 mAm−2
contour in Figure 2e and reported as mean ± standard
Because the preprocessed bottom boundary emulates deviationwhenapplicable.
the magnetic field in the chromosphere,we assigna uni- cValuesarecalculatedwithintheJh>36mAm−2con-
form altitude of 720 km (1 pixel) to this layer where tour;thecentroidisnear3Mminheight.
the field has become largely force-free (Metcalf et al.
1995) and use it through out the study. In general, we called “magnetic tongue” (e.g. Luoni et al. 2011). Fast
limit the field-of-view (FOV) for analysis to the center sunspotrotationandflux cancellationare alsoobserved.
184×144×115 Mm3, covering most of the strong field AIA 171 ˚A observation of the extreme-ultraviolet
region. Uncertainties are reported as mean ± standard (EUV) light emitting plasma roughly outlines the coro-
deviation unless specified otherwise. nal magnetic field (Fig. 1c). As a validation of our field
The extrapolation is performed at 1-h cadence. For extrapolation,we plot selected field lines for comparison
the 9 h around the X-class flare the full 12-min cadence andcolor-codethemaccordingto|J |attheirfootpoints
z
isutilized. Forconvenience,wechooseFebruary1500:00 (Fig. 1d). Brighter color, such as red, corresponds to
UT as time 0 (T = 0 h) and use this convention when stronger |J |. The modeled field lines with strong cur-
z
needed. TheARpassedcentralMeridianonearlyFebru- rents indicate non-potential structures, and are qualita-
ary 14 (−22.2 h). The X2.2 flare (W21S21) started at tivelyingoodagreementwithobservation. Inparticular,
1.7h(February1501:44UT)andpeakedat1.9h(01:56 fieldlinesrootedinthecoreregion(regionsnearthema-
UT)intheGOESsoftX-ray(SXR)fluxandwasaccom- jorPIL)morphologicallyresembletheobservedEUVfil-
panied by a front-side halo CME (Schrijver et al. 2011). ament. Incontrast,potential-likeloops(withweakercur-
rent)furtherawayfromthecenterarenotwellrecovered,
3. LONG-TERM EVOLUTION especially on the north side. A more detailed discussion
3.1. An Illustrative Snapshot on the extrapolation can be found in Appendix A.
A closer look at the core region, summarized in Fig-
We use a snapshot taken at 20:35 UT on Febru-
ure 2, reveals a close match between the shape of the
ary 14, about 5 h before the X-class flare, to illus-
filament and the photospheric PIL. There seem to be a
trate the magnetic field structures in AR 11158 when
few faint strands in the dark filament: NLFFF extrapo-
it is well developed. It mainly consists of two bipoles
lation suggests that an ensemble of highly sheared loops
(P0/N0 and P1/N1 in Fig. 1a, P denoting positive and
thread the plasma. These loops are rooted in P1/N0 in-
N negative) that form a complex quadrupolar structure
sideanarrowstripofstrong-current,high-αdistribution
(Schrijver et al.2011). Thetotalunsignedmagneticflux
along the PIL. These loops are typically low-lying, with
(|Φ|) is about 2.7×1022 Mx and the flux is balanced to apexes well below 10 Mm. We note the broad distri-
within1%. Verticalfield(Bz)inthecenterofumbracan bution of photospheric α, mainly from 0 to 0.5 Mm−1
be as strong as 2600 G. Strong shearing motion exists (Fig. 2d), necessitating the non-linear treatment of any
between P1/N0as wellas amongsta few newly emerged realistic modeling attempts.
pores. The horizontal field (Bh) in the AR center is Figure 2e shows in the backgroundthe computed hor-
largelyparalleltothemajorpolarityinversionline(PIL; izontal current density (J ) in a vertical plane perpen-
h
Fig.1a),nearwhichstrongverticalelectriccurrents(Jz) dicular to the PIL (near “A” in panel c). The projected
are present (Fig. 1b). On the south side of the PIL, an magneticfieldvectorsonthiscrosssectionrotatearound
elongated strip of positive flux following P1 forms a so- an axis at about 3 Mm altitude; J peaks at the same
h
height. Signatures of twisted flux ropes, such as an X-
4 http://sun.stanford.edu/~xudong/Article/field.mp4 point or a hollow core J distribution around its axis
h
4 Sun et al.
a d5
AIA 171 Å Unsharp Masked 2011.02.14_20:35:25 UT HMI α
20 Strand
Filament 4 Near PIL
CS1 %)
m) CS2 Overlying loops e ( 3
c
M n
Y ( 10 ure 2
c
c
0 O
0 1
Loops to N1
0 0
0 10 20 30 40 −0.2 0.0 0.2 0.4 0.6 0.8
X (Mm) α (Mm−1)
b e
HMI α; NLFFF Field Line 2011.02.14_20:35:25 UT NLFFF B; J Cross Sect. 1
h
20
CS1
m) 10
Mm) CS2 N0 P1 e (M
Y ( 10 0.5 ud
Altit 5 A
0
0
−0.5
[Mm− 1]
0
c f
HMI Preprocessed B 2011.02.14_20:35:20 UT Cross Sect. 2
20
CS1
m) 10
Mm) CS2 N0 P1 e (M To N0 10[0G0]
Y ( 10 C B A 1000 Altitud 5 C 50
0
0
−1000 0
1000 [G ] To N1 [×10−3 A m − 2]
0
0 10 20 30 40 0 5 1 0
X (Mm) Distance (Mm)
Fig.2.— Close-up view of the AR core field structure for the 2011 February 14 20:35:20 UT frame. (a) Unsharp masked AIA 171 ˚A
image. TheFOVisdenoted bythedotted boxinFigure1c. Twostraightlinesshow thebaselinesofthe verticalcrosssections (CS1and
CS2)throughthecomputationdomainplottedinpanels(e)and(f). YellowdottedlinesaremanuallydrawntooutlinethedarkS-shaped
filament plasma. One of the faintstrands appearing inthe filament as well as afew bright overlyingloops aremarked onthe image. (b)
Selected NLFFF field lines. The torsional parameter, α, derived from preprocessed magnetogram is shown as background. Contours are
forBz =±600G;thecyanlineisforthePIL.(c)Preprocessed,remappedHMIvectormagnetogramshowingtheemulatedchromospheric
field. The yellow contours indicate the 90% level of the magnetic connectivity gradient metric, N˜ (equation B2 in Appendix B). The
contourisanindicatoroftheintersectionofquasi-separatrixlayer(QSL)withthelowerboundary. A,B,andCmarkfeaturesofinterest.
(d)Histogramofαdistributioninthe FOVofpanel (b). Thepeaknear 0.46Mm−1 comes fromtheregionalongthePIL.(e) Horizontal
currentdensity(Jh)distributiononaverticalcrosssection(CS1)withprojectedNLFFFfieldvectors. Onlythecomponentperpendicular
tothecrosssectionisshownforJh. Thewhiteandblackcontours arefor10and36mAm−2 Jh,respectively. (f)Similarto(e), showing
inverse-polarityconfiguration (CS2),wherefieldvectors turnupwardfromrighttoleft.
(e.g. Bobra et al. 2008; Su et al. 2011) are not obvious. gauss field is strong compared with previously mod-
Using AIA 304 ˚A images (Fig. 3) where the filament eled plage filaments (e.g. Aulanier & D´emoulin 2003;
plasma is best defined, we estimate the width of the Guo et al.2008;Jing et al.2010) andrecentobservation
EUV filament to be about 6 Mm, slightly wider than (e.g. Kuckein et al. 2009). We estimate the field twist
it appears in the 171 ˚A band. The apparent length is angle as φ = αL/2 (Longcope et al. 1998) with L being
at least 90 Mm. We choose the 10 mAm−2 J con- the loop length and find an average of 0.6 turn, with
h
tour (Fig. 2e) as a proxy for the filament cross section about 0.9 turn near the Jh maximum.
as it encloses a region comparable to the observed fil- Thefieldline mappingappearsto“bifurcate”nearthe
ament width. A summary of the estimated field pa- PIL on the east side (“B” in Fig. 2c). Some EUV loops
rameters in this region (filament channel) are listed in originate from the P1 magnetic tongue connect back to
Table 1. In particular, the field strength (B) near N0;othersdeviatefromthePILandconnecttoN1more
the J maximum is about 1200 G. This inferred kilo- than 50Mm away (Fig. 1c and 2a). The photospheric α
h
Magnetic Evolution from SDO/HMI 5
changes sign here as well. We exploit the extrapolation A pair of newly emerged pores (P2/N2 in Fig. 3c)
and calculate the magnetic connectivity gradient metric with a few 1020 Mx flux undergo fast shearing on
N˜ (equation B2 in Appendix B) on the lower bound- the northeasternsideandsubstantiallyreconfigure
ary (D´emoulin et al. 1996). High-N˜ contours show the the coronal field. Smaller recurrent eruptions take
photospheric intersection of the quasi-separatrix layers place above these pores throughout the next two
(QSLs). They divide the magnetic tongue into two dis- days. At the same time, the filament appears to
tinctive regions (Fig. 2c), where the computed field con- bestretched. Itincreasesinlength,becomessome-
nectivities diverge. whatwarped(perhapselevated)onthewesternend
In addition, an interesting “inverse-polarity” configu- and extends further west to P0 (Fig. 3c). Simul-
ration (e.g. Mackay et al. 2010, and references therein) taneous flux cancellation is observed between P1
exists nearby too, where horizontal field on the photo- andN3,whichmayactfavorablytothesubsequent
sphere points from negative vertical polarity side to the eruptions.
positive (near “C” in Fig. 2c). On the verticalcross sec-
− Toward the end of the 5-day period (bottom two
tion shown in Figure 2f, projected field vectors form a
rows of Fig. 3), flux emergence becomes episodic,
“concave-up” configuration. Loops turn upward here or
sometimesovertakenbyfluxcancellation(Fig.4a).
become nearly parallel to the photosphere.
Nevertheless,theshearingbetweenN0andP1con-
tinues. The integrated |J| in the AR core region
3.2. Evolution of Magnetic Field
shows little sign of decreasing, and is fluctuating
We show five representative snapshots of the evolv- within 10% of the pre-flare value. A similar trend
ing AR in Figure 3 (see online animation for the en- is present in |I| as well (Fig. 4b). Over time, the
tire 5-day evolution with full cadence). The left and converging motion between sunspots of the same
middle columns show B and negative AIA 304 ˚A im- polaritystartstosimplifytheregiontowardamore
z
ages, respectively. The right column shows the verti- bipolar structure. The filament seems to survive
cal integration of absolute current density (J) over the multiple eruptions and is still visible at the end of
lowest 10 Mm as derived from the NLFFF extrapola- the 5 days.
tion. Patternsofstrongcurrentconcentrationmayserve
as a proxy for the non-potential coronal structures (e.g.
Schrijver et al. 2008). 3.3. Evolution of Magnetic Energy
Here we highlight a few key features of the magnetic We now consider the distribution of the magnetic free
field evolution. For reference,the total unsignedflux |Φ| energy based on the NLFFF extrapolation. Spatially,
and its change rate (d|Φ|/dt) are plotted in Figure 4a; the low-lying, current-carrying core field demonstrates
the photosphericunsignedcurrent(|I|)inFigure4b; the strongconcentrationof free energy in the AR core,from
GOES SXR flux in Figure 4g. the chromosphere to the lower corona. The free energy
density (ǫ ) appears largely co-spatial with the current
f
− The early stage of the AR development (top two distribution (Fig. 3 right column). At T = 0 h, the
rows of Fig. 3) features fast flux emergence that 20% level contour of the peak ǫ (vertically integrated)
f
coincides with the appearance of a pronounced fil- accountsforonly9%oftheARarea(Fig.3c),but77%of
ament. Such fast emergence continues for about 1 theoverallfreeenergy. Theheightprofileofǫ plottedin
f
day (Fig. 4a) with a rate of several 1020 Mxh−1, Figure4fshowsthatabout50%ofallfreeenergyisstored
mainly in the aforementioned two bipoles P0/N0 below 6 Mm, and 75% below 11 Mm. We note that the
and P1/N1 (Schrijver et al. 2011). Note that N0 maximum free energy density occurss at about 3 Mm
consists of two sunspots, the western one emerges altitude, corresponding to the height of the peak in J
h
much later. AIA images show frequent brighten- (Fig. 2e). These distribution patterns remain relatively
ing as P1 and N0 converge and collide; new mag- stable after the filament becomes well defined in AIA
netic connectivities are being established rapidly images around -36 h.
in the corona. A filament becomes visible along ThetemporalprofilesofthetotalNLFFFandPFmag-
the PILwithinafewhours. AlongthePIL,signifi- neticenergy(E andE )inFigure4croughlyscalewith
N P
cantelectriccurrentinjectionappearstotakeplace the unsigned flux. On the other hand, the estimated
(Figs.3band4b). Duringthisinterval,thenet(un- magnetic free energy E in Figure 4d shows interesting
f
balanced)currentineachmagneticpolarityalsoin- variations in time and appears sensitive to AR activity,
creasesdrastically,hinting thatthe newly emerged as one would expect. We plot the ratio E /E in Fig-
N P
flux is highly non-potential (Schrijver 2009). ure 4e as an additional measurement of the AR’s non-
potentiality. Uncertainties reported in this section only
− After the initial fast flux emergence (third row of represent the effect of spectropolarimetric noise and are
Fig. 3), the sunspot complex developsfurther with obtained from a pseudo Monte-Carlo method (see Sec-
slower flux emergence but lasting strong shearing tion 5.1). Systematic uncertainties from the extrapola-
motion between P1 and N0. The injection of cur- tion algorithm may be greater. Again, several key fea-
rent through the photosphere clearly slows down tures are highlighted below.
(Fig. 4b). However, the vertically integrated |J|
still increases by about 25% over a period of 40 − Rapid free-energy injection during flux emergence.
h, suggesting a net build-up process in the corona. E increases drastically following the flux emer-
f
gence(Fig.4aandb). Freeenergyconcentrationis
5 http://sun.stanford.edu/~xudong/Article/evo.mp4 seeninthevicinityofthefilament(Fig.3b),andǫ
f
6 Sun et al.
120
a 02.12_19:59:19 UT 02.12_19:59:22 UT 02.12_19:59:19 UT
c) 80 N0 P0
arcse P0 100 0 400 0 2. 6
Y ( 40 N1 P1 −1000 0 0.1
HMI [G] [D N] Integrated [×105 A m − 1]
Vertical Field T = −52 h AIA 304 Å T = −52 h Current Density T = −52 h
0
120
b 0 2.13_07 :59:20 UT 0 2.13_07 :59:22 UT 0 2.13_07 :59:20 UT
c) 80 N0 P0 Filament Filament
e
s
c
ar
Y ( 40 N1 P1
T = −40 h T = −40 h T = −40 h
0
120
c 0 2.14_23 :59:20 UT 0 2.14_23 :59:22 UT 0 2.14_23 :59:20 UT
P2
c) 80 N2 N3 P0
se N0 P1
c
ar
Y ( 40 N1
T = 0 h T = 0 h T = 0 h
0
120
d 0 2.15_11 :59:20 UT 0 2.15_11 :59:22 UT 0 2.15_11 :59:20 UT
c) 80
e
s
c
ar
Y ( 40
T = 12 h T = 12 h T = 12 h
0
120
e 0 2.16_11 :59:20 UT 0 2.16_11 :59:22 UT 0 2.16_11 :59:20 UT
c) 80
e
s
c
ar
Y ( 40
T = 36 h T = 36 h T = 36 h
0
0 40 80 120 160 0 40 80 120 160 0 40 80 120 160
X (arcsec) X (arcsec) X (arcsec)
Fig.3.—FivesnapshotsoftheevolvingAR11158. TheyaretakenataboutT =−52h,−40h,0h,12h,and36h,withFebruary1500:00
UTastime0. Leftcolumn: HMIBz asinnativecoordinate(asrecordedbycamera). Middlecolumn: negativeAIA304˚Aimageshowing
chromosphere and transition region structures in which the AR filament is best discernible. Right column: vertically integrated current
densityfromNLFFFextrapolationoverthelowest10Mm. Thethicksolid,thinsolid,anddottedcontoursareforsimilarlyintegratedfree
energydensityat80%, 50%,and20% ofthepeakvalueforframeT =0h. Images areremappedback tothenative coordinatefordirect
comparisonof HMIand AIA observations. Thebox in(b) indicates the field-of-viewof Figure 10for aflux-emerging region. Features of
interestaremarkedinsomepanels;seetextfordetails. (Ananimationoftheentire5-dayperiodisavailableintheonlinejournal.)
at all altitudes increases significantly (Fig. 4f). In Careful inspections of the vector magnetogram re-
particular,E showsatwelve-foldincreasefrom-55 veals signatures of emerging flux tubes, which we
f
h to -45h, reaching1.07×1032 erg andamounting discuss in Section 5.1.
to 43% of the final maximum E two days later.
f
The ratio of E /E peaks at about 1.57 at -45 − Gradual energy build-up and decay. After the ini-
N P
h. Significantchangesinthecoronalstructuresen- tial fast increase, E accumulates at a slower rate
f
sue,asconveyedbytheAIAimages(animationfor (Fig. 4d). The AR has attained a well-developed
Fig. 3). Flux change rate and E then plateau for quadrupolar topology. The growth rate of E and
f f
afewhours,andE /E dropsbacktoabout1.30. the ratio E /E are both nearly constant. Simi-
N P N P
lar trends can be found for the post X-flare stage,
Magnetic Evolution from SDO/HMI 7
-72h -48h -24h 0h 24h 48h
Unsigned flux×22 (10 Mx) 0123 a F luxU nchsiagnngeed rfalutex 02468 Flux change rate×20-1(10 Mx h)
nt b
e 6 Unsigned current
urr A)
signed c×13 (10 24
n
U
c
12
g) NLFFF
ergy 32 er 8
n 0 PF
E×1 4
(
0
d
gy g) 2
er er
e en32 10 1 2.6 Fre e energy
e×
Fr (
0 1.9
1.6 e E / E
F 1.28 NLFFF PF
P
E
/ F 1.4 1.24
FF 0h 2h 4h 6h 8h
NL 1.2
E

y
m) 20 f T = 0h 1ensit -3m)
M d c
Altitude ( 10 755%0% ac accucmu.m. 0ee energy ×4(10 erg
-2W m) 10-4 g X2.2 X Fr
x ( 10-5 M
u
S fl 10-6 C
E
O 10-7 B
G
02/12 02/13 02/14 02/15 02/16 02/17
Date
Fig.4.—Evolutionof magneticenergy andrelatedquantities ofAR 11158over 5days. (a)Total unsigned magnetic flux(|Φ|)and6-h
smoothedfluxchangerate(d|Φ|/dt). (b)Totalunsignedcurrent(|I|). (c)MagneticenergyderivedfromtheNLFFFandPFextrapolation
(EN and EP). (d) Estimated magnetic free energy (Ef). (e) Ratio between the NLFFF and PF energy (EN/EP). (f) Time-altitude
diagram of average magnetic free energy density in the AR center (FOV of Fig. 5(f)). Dotted lines indicate the height below which the
accumulatedvaluesreach50%and75%ofthetotal. CurveontheleftshowstheheightprofileforT =0h. (g)GOES5msoft-Xrayflux
(1–8 ˚A channel). The 5 frames in Figure 3 are marked as circles. Flux and current are derived using only pixels with |Bz| greater than
100G. Errorbarsin(c)-(e)showtheestimatedeffectofnoiseandareplottedevery6h,butareusuallytoosmalltobeseen. Insetsof(d)
and(e)show resultswitha12minutecadence from-1hto8h(shaded greyband). Errorbarsrightbeforeandafter theX-classflarein
theseinsetsaremorevisible. TheverticaldottedlinesindicatethepeaktimeoftheX-classflareat1.9h.
8 Sun et al.
except now E starts to decrease and the region
f
relaxes to a more potential state (Fig. 4d and e). TABLE 2
Flare-relatedchangein magneticenergyandphotospheric
The energydissipationrateinthe coronaprobably
field.
hasexceededthegrowthratefromthephotosphere
as the flux emergence slows down (Fig. 4a). Parametera Unit Pre-flareb Post-flareb Differencec
− Step-wise energy loss during the X-class flare. Ef Ef 1032erg 2.47±0.03 2.13±0.03 −0.34±0.04
reaches(2.47±0.03)×1032ergpriorto theX-class EN/EP - 1.29±0.00 1.25±0.00 −0.04±0.01
flare,accountingforabout23%ofthetotalenergy. hh|BBhz|ii 110033GG 01..9260±±00..0032 01..9513±±00..0031 +-258%%
During the flare, Ef displays a step-wise sudden hBi 103G 1.66±0.01 1.87±0.01 +13%
decrease(Fig.4dandinset). The1haverageofEf h|γ|i degree 36±1 29±1 −19%
before and after the flare differ by about (0.34± h|Jz|i mAm−2 36±2 27±1 −25%
0.04) × 1032 erg, 14% of the pre-flare E . This hαi Mm−1 0.48±0.03 0.30±0.02 −37%
f
value situates atthe lowerend ofwhat is adequate a Ef and the ratio EN/EP are computed using the center region
to power a typical X-class flare (e.g. Hudson 2011, (184×144×115Mm3) ofthe extrapolation domain. Other param-
andreferencestherein)andmaybe intrinsicallyan etersarefortheARcorephotospheric fieldwithintheboxedregion
inFigure5c. Notations aresameasTable1.
uclnedaerrdeisstcimonattiniouni,tyaaslsdoisacpupseseadrsiinntSheectEion/E5.1.anAd b For Ef and EN/EP, pre-flare values are calculated from the av-
N P erage of 5 frames between 00:47 to 01:35; post-flare between 02:11
ǫf height profile. Sudden energy decrease is also and02:59. Uncertaintiesareestimatedeffectfromnoise. Foralloth-
found during the earlier M-6.6 flare (-30.4 h) with ers,pre-flarevaluesarecalculated forthe01:35frame;post-flarefor
02:11. Valuesarereportedasmean±standarderrorforcomparison.
a smaller magnitude. c DifferenceforEf orEN/EP isthe absolutevalue, others areper-
centagedifferences.
Thecontinuousmonitoringofthe ARfreeenergywith
relatively high temporal/spatial resolution is made pos-
sible, for the first time, by the HMI vector field obser- addition,theazimuthofBhappeartochangeinafashion
vations. This is especially useful for the study of ma- such that they become better aligned and more parallel
jor eruptive events. Due to the nature of the extrap- tothe PILinits vicinity(Fig.7aandb), consistentwith
olation method, changes in E here are determined by previous reports (e.g. Wang et al. 1994). After the flare,
f
the boundary conditions. Therefore, the step-wise en- α appears to be smaller, suggesting the field is perhaps
ergy loss found during the X-class flare must be related less twisted. A summary of the pre- and post-flare field
torapidandsignificantfieldchangesonthephotosphere. parameters is provided in Table 2.
We consider this change in detail in Section 4. These fast changes suggest a scenario in which the
change of coronal connectivity, probably induced by re-
4. FLARE-RELATED RAPID CHANGE connection,feedsbacktothephotosphere. Inparticular,
Figure 5 illustrates the rapid magnetic field changes newly reconnected loops with footpoints located in the
duringtheX-classflare. Strongandpermanentenhance- flareribbons, both shorterandmore parallelto the PIL,
ment of B in the AR core was reported by Wang et al. area priori consistentwiththeobservations. Wediscuss
h
(2011) based on HMI linear polarization signal, and is the topic further in Section 5.2. Morphologically, the
confirmed here by full Stokes inversion. From 01:35 UT changes are in line with the conjectured magnetic “im-
to 02:11 UT, the mean B along PIL (Fig. 5c and d) plosion” (Hudson 2000): a decrease in coronal magnetic
h
increasesfromabout1200Gtoover1500G,28%within energy during explosive events should lead the coronal
0.6h. ChangesinB appearlesssignificant(Fig.5eand field to contract, resulting in a “more horizontal” pho-
z
f): mean |B | decreases by about 5%. We skip the two tospheric field (Hudson et al. 2008). Here we analyze a
z
framesinbetween(01:47and01:59UT)toavoidpossible series of NLFFF snapshots and monitor the Jh distribu-
artifacts from flare emission (see Section 5.2). tion on a vertical cross section throughthe computation
Shown in Figure 6, the difference image of pre- domain(Fig. 5a and b). The patterns show an apparent
and post-flare B bears a striking resemblance to the contracting motion at flaring time owing to the altered
h
Hα flare ribbons observed by the Solar Optical Tele- boundary condition (see online animation). The apex
scope (SOT; Tsuneta et al. 2008) on the Hinode satel- of the outermost Jh contour lowers by about 3 Mm in
lite (Kosugi et al. 2007). The elongated regions that are Figure 5b.
swept by the evolving ribbons or lying in between show MotionsofcoronalloopsfartherawayfromtheARcore
significant B enhancement, whereas patches with de- provide evidence for the conjecture. During flares and
h
cayed B appear on both the north and south sides. In CMEs, a depletion of magnetic energy leads to smaller
h
thenarrowregionalongthePIL,distributionofB shifts magnetic pressure gradient, and loops must contract to
h
by about 300G in the histogram (Fig. 7c), displaying a reach a new balance (e.g. Liu & Wang 2010). We show
strong boost in the kilogauss range. On the other hand, AIA 171 ˚A observation for this event in Figure 8. Ex-
|B | often decreases where B increases, but the signals pansionofthecoronalstructureandfaintcircularpropa-
z h
are weaker and appear to be mixed with the opposite. gatingfrontsarevisible startingaround01:48UT,prob-
The distribution of |B | gently decays in the strongest ably linkedto CME initiation(Schrijver et al. 2011). At
z
part, but otherwise remains similar (Fig. 7d). about 01:50 UT, the southern potential-like loops sud-
The combined effect is that the field becomes overall denly move inward; the northern loops follow immedi-
stronger and more inclined in the AR core (Fig. 7e). In ately(see onlineanimationfor Figure8). The retraction
6 http://sun.stanford.edu/~xudong/Article/flare.mp4 7 http://sun.stanford.edu/~xudong/Article/contract.mp4
Magnetic Evolution from SDO/HMI 9
20 a 01:35:20 UT b 02:11:20 UT sity 50
n
e
Mm) nt d−2m)
Altitude ( 10 ntal curre×−3(10 A 25
o
z
ori
H 0
0 1 0 2 0 3 0 0 1 0 2 0 3 0
Distance (Mm) Distance along cut (Mm)
1500
c 01:35:20 UT d 02:11:20 UT
30 G)
d (
Mm) 20 al fiel 1000
Y ( Penumbra Penumbra ont
10 Penumbra Penumbra oriz
H
0 PIL 0 PIL 0 500
0 1 0 2 0 3 0 4 0 5 0 0 1 0 2 0 3 0 4 0 5 0
2400
e 01:35:20 UT f 02:11:20 UT
30
G)
m) 20 eld (
Y (M cal fi 0
10 erti
V
0 0 0 −2400
0 1 0 2 0 3 0 4 0 5 0 0 1 0 2 0 3 0 4 0 5 0
X (Mm) X (Mm)
Fig.5.— Rapid field changes at the photosphere and in the corona during the 2011 February 15 X-class flare. (a) Jh distribution on
a vertical cross section as derived from NLFFF extrapolation, before the flareat 01:35:20 UT. Only the component perpendicular to the
crosssectionisincluded. Thelocationofthecrosssectionisindicatedinpanels(c)-(f)asalongstraightline. Thedotted,dashedandsolid
contoursindicatevaluesof2,10,and36mAm−2respectively. (b)Sameas(a),for02:11:20UTaftertheflare. (c)RemappedBhobserved
byHMIfor01:35:20UTasviewedfromoverhead. Thedotted(solid)linesshowcontourfor1600G(1200G). Placeswithsignificantfield
changearemarkedbyarrowsandboxes. (d)Sameas(c),for02:11:20UT.(e)RemappedBz at01:35:20UT.Thedotted(solid)contours
are for ±2000 G (±1000 G). (f) Same as (e), for 02:11:20 UT. The large yellow box indicates the region evaluated in Figure 9(d). (An
animationofthisfigureisavailableintheonlinejournal.)
a ∆B b ∆|B | c SOT Hα
h z
20
m)
M
Y (
10 400 400

−400 −400
0 [G ] [G ] 01:53:14 UT
0 10 20 30 0 10 20 30 0 10 20 30
X (Mm) X (Mm) X (Mm)
Fig.6.— Difference images of pre- and post-flare magnetic field. (a) Difference of Bh between 02:11:20 UT and 01:35:20 UT. The two
frames are kept in the native coordinates without remapping, but are co-aligned with Carrington rotation rate to the nearest full pixel.
ContoursareforthemeanBz ofthetwoframes,at±600G. (b)Differenceimageof|Bz|. (c)HαflareribbonsobservedbyHinode/SOT
at01:53:14UT,nearflarepeakandroughlymidwaybetweenthetwoHMIframes.
10 Sun et al.
a b
10 10
m)
M
5 5
Y (
01:35:20 UT 02:11:20 UT
0 0
0 5 10 15 0 5 10 15
X (Mm) X (Mm)
8 c 4 d e
01:35:20 UT
6
%) 6 3 02:11:20 UT
e (
c 4
n 4 2
e
urr
cc 2 1 2
O
0 0 0
500 1000 1500 2000 500 1000 1500 2000 0 20 40 60 80
B (Mx cm−2) |B| (Mx cm−2) γ (degree)
h z
Fig.7.— Close-up view of the pre- and post-flare vector field in the AR core region. (a) Remapped vector magnetogram for 01:35:20
UT.TheyellowcontouristhePIL;theboxedregionisidenticaltoFig.5c. (b)Sameas(a),for02:11:20UT.(c)HistogramsofBh attwo
differenttimes,intheboxedregioninpanel(a). (d)Histogramsfor|Bz|. (e)Histogramsforinclinationangle|γ|.
350 a 40 b
300 30
0 43 km s−1
Slit 1 20
250 m)
M
sec) 200 g slit ( 100 Slit 1
c n
Y (ar 150 n alo 40 c
o
Slit 2 4000 siti 30
100 0 Po 18 km s−1
20
100
50
[D N] 10
01:48:01 UT AIA 171 Å Slit 2
0 0
0 5 0 10 0 15 0 20 0 25 0 30 0 35 0 01 :40 01 :50 02 :00 02 :10 02 :20
X (arcsec) Time (UT)
Fig.8.—ObservedEUVcoronalloopretractions. (a)AIA171˚Aimageat01:48:01UTonFebruary15,aftertheonsetofflare. Twoslits
that are largely perpendicular to the loops are used to obtain the time-position diagrams in the following panels. Arrows along the slits
indicatetheapproximatedirectionofthetransversemotion. (b)Time-positiondiagramforslit1constructedbystackingatimesequence
ofcoaligned imageslicesfromlefttoright. Onlytheimages withthenormalexposure timeareused, resultingina24s cadence. Images
arecoalignedtosub-pixelaccuracy. Thedotted lineshowsaninwardloopcontraction patternwithatransversespeedof43kms−1. The
horizontal patterns in the upper half are from the features in the background. Loop oscillations are visible. (c) Same as (b), for slit 2.
Dotted line shows a transverse speed of 18kms−1. Patterns of expanding loops also appear around 01:50 UT, moving from position 20
Mmtoward0. (Ananimationofthisfigureisavailableintheonlinejournal.)