A Helioseismic Survey of Near-surface Flows Around Active Regions and their Association with Flares

0.66 MB·

by  D. C. Braun

accepted Astrophys.J.Jan28,2016
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
A HELIOSEISMIC SURVEY OF NEAR-SURFACE FLOWS AROUND ACTIVE REGIONS AND THEIR
ASSOCIATION WITH FLARES
D. C. Braun
NorthWestResearchAssociates,3380MitchellLane, Boulder,CO80301, USA
accepted Astrophys.J. Jan 28, 2016
ABSTRACT
6
We use helioseismic holographyto study the associationof shallow flows with solar flare activity in
1
about 250 large sunspot groups observedbetween 2010and 2014 with the Helioseismic and Magnetic
0
Imager on the Solar Dynamics Observatory. Four basic flow parameters: horizontalspeed, horizontal
2
component of divergence, vertical component of vorticity, and a vertical kinetic helicity proxy, are

n mapped for each active region during its passage across the solar disk. Flow indices are derived
a representingthemeanandstandarddeviationoftheseparametersovermagneticmasksandcompared
J with contemporary measures of flare X-ray flux. A correlation exists for several of the flow indices,

9 especiallythose basedonthe speedandthe standarddeviationofallflowparameters. However,their
2 correlationwith X-ray flux is similar to that observed with the mean unsigned magnetic flux density
overthe same masks. The temporal variationof the flow indices are studied, anda superposedepoch

] analysis with respect to the occurrence to 70 M and X-class flares is made. While flows evolve with
R
the passage of the active regions across the disk, no discernible precursors or other temporal changes
S specifically associated with flares are detected.
.
h Subject headings: Sun: activity, Sun: flares, Sun: helioseismology, Sun: magnetic fields, sunspots
p
-
o 1. INTRODUCTION sisperformedbyHaber et al.(2004)indicatedthesecon-
r vergingflowsaresituatedabovedeeper outflows. A con-
t A fundamental question in solar physics is how mag-
s sensusappears to be thatthese flowshavespeeds on the
netic fields emerge from the solar convection zone into
a order of 50 m s−1 which may extend out to as much as
[ the solar atmosphere and then develop solar eruptions ◦
suchasflaresandCMEs(Fan2009;Schrijver2009). Itis 30 fromtheARcenters. However,Braun & Wan(2011)

1 widelyheldthathighlytwistedmagneticfields,emerging found that most outflows around ARs are compact and
v perhapsintoapre-existingfield,arerequiredforthe for- have flow speeds typical of the surrounding supergranu-
8 lation.
mation of active regions producing M- or X-class flares
3 Komm et al.(2004)firstbegantosystematicallychar-
(Schrijver 2009). Observations of the linkage between
0 acterizeARflows,deducedfromlow-resolutionRDanal-
subsurface flows and the twist, electric current content,
0 ysis,intermsoftheirhorizontaldivergenceandtheirver-
andotherpropertiesofactiveregions(hereafterARs)are
0 tical components of vorticity and kinetic helicity. That
important to understand, and perhaps even predict, the
. workwas the first to detect a hemispheric preference for
2 flarephenomenon. Considerableefforthas been spent in
0 studying the time evolution of magnetograms or contin- theverticalvorticityoftheflows,whichwascyclonicover
◦
6 uum imagesofactive regionsinorderto quantify photo- the 15 spatially-averaged flows both with and without
1 sphericmotionswhichmayleadtopredictiveindices(e.g. the removalof a large-scaledifferential rotation pattern.
v: Leka & Barnes2007;Schrijver2007;Welsch et al.2009). Using ring-diagramprocedures with considerably higher
resolution, Hindman et al. (2009) examined the diver-
i Helioseismicmeasurementsofsubsurfacemotionsextend
X the spatial volume over which AR properties, and their gence and vortical components of motions within about
200 magnetic regions. They confirmed cyclonic motions
r role in transporting magnetic helicity and current into
a the corona, can be explored. In addition, the direct in- near active regionboundaries, but also demonstratedan
anticyclonic trend associated with the cores of the ARs
ferenceofmassflowscomplementsmeasurementsofpho-
which are presumably dominated by the sunspot moats.
tospheric motions of (magnetic or continuum) features
More recently, Komm & Gosain (2015) have compared
(Wang et al. 2011; Beauregardet al. 2012; Wang et al.
the hemispheric preference, for long-lived activity com-
2014).
plexes,ofboththesubsurfacekinetichelicity,determined
Any detection and interpretation of photospheric or
from ground-based observations from the Global Oscil-
subsurface flow precursorsto flares requires understand-
lationNetworkGroup(GONG), andthe currenthelicity
ing the pre-existing flow fields, and their generalcharac-
as determined from synoptic vector magnetograms.
teristics, associated with active regions. Photospheric
Specifically to examine the relation between subsur-
outflows (called “moats”) extending past the penum-
face flows, deduced from from (low-resolution)RD anal-
brae of most sunspots have been studied for decades
ysis, and solar flares, Mason et al. (2006) surveyed the
(Brickhouse & LaBonte 1988). Larger converging flows
subsurfacevorticityofARs over43 Carringtonrotations
around active regions were first detected using local he-
using GONG and over 20 rotations observed using data
lioseismology (Gizon et al. 2001; Haber et al. 2001). In-
from the Michelson Doppler Imager (MDI) instrument
versemodelingusingring-diagram(hereafterRD)analy-
on the SOHO spacecraft. Both data exhibited a trend
[email protected] between the unsigned vorticity and the product of the
2 Braun
logarithmofflareintensityandmaximumunsignedmag- convenience we used the sunspot database maintained
netic flux, for ARs above a given flux threshold. An at NASA Marshall Space Flight Center2 which provides
expanded version of the GONG RD-based survey was daily averagesof the sunspot group properties including
used by Komm & Hill (2009) to demonstrate a correla- size and Carrington coordinates.
tion between X-ray flux and vorticity, with both quan- We identified 252 regions which met these criteria,
tities averaged over the disk passage of the ARs. The which represent approximately the largest 20% of all
flow measurements from this survey subsequently pro- NOAAnumberedsunspotgroups. Oursurveyincludesa
vided the basis for the development of an empirically- single region (AR 12017) which had a maximum area of
based parameter, based on the subsurface kinetic helic- only 160 µH but was responsible for 23 flares including
ity density, which showedspecific temporal variations 2- anX-classflare. OurfinalsampleincludesARsresponsi-
3 days before flares (including C, M, and X-class events; ble for all (43) X-class flares,86% (≈460) of the M-class
Reinard et al. 2010). Applying discriminant analysis to flares, and 72% (≈3600) C-class flares occurring during
a variety of both magnetic and subsurface-flow param- this time period.
eters, Komm et al. (2011a) suggest that the subsurface In spite of the size criteria for selection, the sample
flow parameters improve the ability to distinguish be- includes cases of relatively quiescent ARs which provide
tween flaring and non-flaring ARs. a basis for comparison with the more flare productive
Usingamuchsmallersampleof5flaringARs,butem- ones. For example, 137 ARs in the sample (i.e. slightly
ploying time-distance helioseismic methods with consid- more than half) produced neither M nor X-class flares
erably higher spatial resolution, Gao et al. (2014) found and17ofthoseproducednoC-classflareseither. Unfor-
sporadic and short-duration changes (called “bumps”) tunately for the statistician, the Sun does not appear to
in the kinetic helicity which, slightly more than half the emergelargenumbersofflare-freemagneticregionswith
time, occurred within about 8 hours (before or after) an a distribution of properties (e.g. size, sunspot number,
X-class flare. magneticflux)whichotherwisematchtheflaringregions.
The primarygoalin this study is to examine the asso- There are likely diminishing (and even detrimental) re-
ciationwithsolarflaresofnear-surfaceflowswithinsolar turnsinincludingsmallerflare-freeregionsinoursurvey.
magnetic regions. This association may include: (1) the That being said, we need to be mindful of selection bias
predilectionofflarestooccurinregionswithspecificflow when (1) assigning meaning (e.g. cause-and-effect) to
properties,and(2)anyprecursorof,or responseto,spe- associations of flows and flares, and (2) generalizing ob-
cific solar flares visible in the temporal evolution of the servations or inferences about the flow properties of our
flowpatterns. Todothiswemakeuseofnearlyfiveyears sample to other types of active regions.
of nearly continuous and high resolution SDO/HMI ob- For each AR, a 9.1 day long datacube is constructed
servations of approximately 250 of the largest sunspot from a Postel’s projection of the full-disk HMI Doppler-
groupscatalogedbyNOAA.Ourmotivationisnottore- grams and centered on the Carrington coordinates av-
produce or confirm any prior study, but to exploit the eraged over its disk passage. The remapped datacube
◦ ◦ ◦
high-resolutioncapabilitiesofhelioseismicholographyto spans 30 by 30 with a pixel spacing of 0.0573 . and
performan independent examination of the flows within is divided into 16 non-overlapping intervals of 13.6 hr
the largest active regions. It is necessary to place any duration for helioseismic analysis. For context, a set of
observedassociation(or lack thereof) between flows and remapped,cospatialandtime-averagedline-of-sightHMI
flares in the proper context. Consequently, a sub-goal is magnetogramsforeachintervalisconstructed,usingfull-
toprovideasurveyofthegeneralnear-surfaceflowprop- disk magnetogramssampled every 68 minutes. Time in-
erties oflargeNOAAsunspotgroups. For this study, we tervalsforwhichthemeanARlocationwasgreaterthan
◦
focusourattentiononspecificflowparameterswhichcan 60 from disk center, or for which gaps in the HMI data
be derived from inferences of the two-dimensional near- exceeded 30% of the 13.6 hr period are excluded from
surfacevectorflowfield,includingthehorizontalcompo- the survey. We are left with 3908 sets of helioseismic
nentofthe divergenceandthe verticalcomponentofthe measurements,defining a set to be a single AR observed
vorticity. We also examine the product of these, which over a unique 13.6 hr interval.
providesaproxyfortheverticalcomponentofkinetiche-
licity (Ru¨diger et al. 1999; Komm et al. 2007). A fourth 3. HELIOSEISMIC HOLOGRAPHY
parameter is the speed of the horizontal flow. Averages Helioseismic holography (hereafter HH) is a method
and standard-deviations of these basic parameters, as- which computationally extrapolates the surface acoustic
sessed over spatial masks constructed using HMI mag- fieldfromaselectedareaor“pupil”intothesolarinterior
netograms, provide a set of indices with with we search, (Lindsey & Braun 1997) in order to estimate the ampli-
using scatter plots and superposed epoch analysis, for tudes of the waves propagating into or out of a focus
correlations with solar flare activity. point at a chosen depth and position in the solar inte-
rior. These amplitudes are called the acoustic ingression
2. ACTIVEREGIONSELECTION
and egression respectively. To study travel-time anoma-
Thesampleofactiveregionsweconsiderconsistsofall lies sensitive to the flows one constructs cross covari-
sunspot groups assigned a number by NOAA between ances between the ingression and egression amplitudes
the start of HMI observations (2010 May) and 2014 De- using pupils which take the form of an annulus divided
cember, and which reached a size of at least 200 micro- into quadrants. This type of pupil configuration is the
hemispheres (hereafter µH). Although complete records basis for “lateral vantage” HH (Lindsey & Braun 2004),
of the the sunspot group properties are available1, for to which deep-focus methods in time-distance helioseis-
1http:ngdc.noaa.gov/stp/space-weather/solar-data/solar-features2/shutntspp:osto-larresgciioennsc/eu.smasff_cm.wnlasa.gov/greenwch.shtml
Near-surface Flows Around Active Regions and Flares 3
mology and common-depth-point reflection seismology (2007), which shows the sensitivity function computed
methods are analogous. For the results presented here, undertheBornapproximation,forlateral-vantageHHat
we choose a focus depth 3 Mm below the surface. a3Mmfocus-depth. Thefunctionhasabroadcontribu-
Travel-timemeasurementssensitivetohorizontalflows tionwhichispeakedaround3Mmdepth. Approximately
are extracted from cross-covariances between the egres- 60%ofthesensitivityoccursbetweendepthsof2–5Mm,
sionsandingressionscomputedinpupilsspanningoppo- witha30%(10%)sensitivityforshallower(deeper)flows.
site quadrantswhich extendin the east,west, northand
4. FLOWPARAMETERS
south directions from the focus. The methodologyis de-
scribed in detail in prior publications (e.g. Braun et al. Motivated by the the results of prior helioseismic sur-
2007; Braun & Birch 2008; Braun 2014). The steps in- veys or analyses of specific active-region flows, we con-
clude: (1) compute the 3D Fourier transform of the sider several flow parameters for study. These include
Postel-projected data in both spatial dimensions and in the vertical component of the vorticity
time,(2)extractthedatawithinthefrequencybandpass
∂u ∂u
2.5–5.5mHz,(3)applyaphase-speedfilter,(4)compute VOR= y − x,
∂x ∂y
egressionandingressionamplitudeswiththeappropriate
Green’s functions, (4) compute egression–ingressioncor- and the horizontal divergence
relations, and (5) measure travel-time differences. The
∂u ∂u
filteremployedinstep(3)helpstoreducenoisewithhigh y x
DIV= + .
spatial-frequency. It consists of a Gaussian function of ∂x ∂y
phase speed with a full width at half maximum of 9.2
km s−1 and is centered at 18.8 km s−1 which is tuned We also include a proxy for the vertical contribution
to the kinetic helicity (Ru¨diger et al. 1999; Komm et al.
to waves propagating horizontally at a depth of 3 Mm.
2007)
The designandutility offilters for lateralvantageHH is
HEL=VOR·DIV,
discussedfurtherbyBraun(2014). Step(4)iscomputed
by convolutions of the data cube with Green’s functions and the horizontal speed
computed with the eikonal approximation and using a
plane-parallelapproximation,whichiswellsuitedforthe |V|= u 2+u 2.
q x y
shallowfocus depthof3 Mm. Braun(2014)exploresthe
validity ofthis approximationin detail. The products of The proxy HEL is related to the vertical component of
these analyses are maps of travel-time shifts δτ , and the true kinetic helicity by a substitution of the hori-
ns
δτ , which represent standard north-south and west- zontaldivergencefor the verticalcomponent of the flow,
we
east travel-time differences. withtheratioofthetwogivenbythedensityscaleheight
in the anelastic approximation (Ru¨diger et al. 1999).
3.1. Flow calibration
If x and y denote westward and northward directions
Rather than carry out inverse modeling of the travel- respectively, than the sign of VOR as defined above is
timeshiftstoinferthethree-dimensionalvariationofthe positive (negative) for counterclockwise (clockwise) vor-
flows, we employ a simple calibration procedure. This ticalmotionasviewedfromabovethesolarphotosphere.
minimizes complications and uncertainties, due to the Prioranalyseshaveshownthattheverticalvorticityand
presenceofstrongphotosphericmagneticfields,inthein- kinetic helicity, with this sign convention,have antisym-
version methods (e.g. DeGrave et al. 2014). Travel-time metric properties, at least statistically, with respect to
shifts are related to the actual flows through a convo- the equator. This is true for convective motions in both
lution of the true flow components and the appropriate the quiet-Sun (supergranulation) field (Duvall & Gizon
sensitivityfunctions. Forourmeasurementswithafocus 2000)andformotionswithinactiveregions(Komm et al.
depth of 3 Mm, the sensitivity functions are sufficiently 2007). To facilitate the combination of flow quantities
compactin volumeso asto renderthe travel-timediffer- measured in ARs from both hemispheres, we switch the
encesreasonableproxiesforthehorizontalcomponentsof sign of VOR in the southern hemisphere, so that over
the near-surface flows themselves. HH analyses of near- the entire Sun a positive (negative) value of VOR is in-
surfaceflowsusingtravel-timeshiftsasflowproxieshave dicative of cyclonic (anticyclonic) motions. A positive
been carried out in prior studies (e.g. Braun et al. 2004; VOR, for example, implies counterclockwise rotation in
Braun & Wan 2011; Birch et al. 2013). Here, the travel- the northern hemisphere and clockwise rotation in the
time differences τ and τ are calibrated into west- southern hemisphere.
we ns
ward and northward vector components of a horizontal
4.1. Example: AR 11263
depth-independent flow (u , u ) by applying two differ-
x y
ent tracking rates to the same region of the Sun. These Figure1showsmapsofthefourbasicflowparameters,
ratesconsistof (1) the nominalCarringtonrotationrate compared to time-averaged line-of-sight magnetograms,
and (2) the nominalCarringtonrate plus a constantoff- for three consecutive time intervals and centered on AR
set. The tracking offset divided by the shift in τ be- 11263. The derivatives for evaluating VOR and DIV are
we
tweenthesetsofmeasurementsyieldsacalibrationfactor computedintheFourier(horizontalwavevector)domain.
of-7.5relatingthespeed(inunitsofms−1)tothetravel- To minimize high-frequency noise all of the maps are
time difference (in s). The minus sign reflects the fact smearedwithatwo-dimensionalGaussianwithaFWHM
◦
thatapositiveflowdirectedtothenorth(west)produces of 0.48 (5.8Mm). This region reached a maximum size
areductioninthecorrespondingnorth-south(west-east) of 720 µH (larger than 90% of the sample) and was re-
time difference. The range over the depth to which our sponsibleforoneX-classflareand3M-classflares. Qual-
calibrated flow is sensitive is discussed in Braun et al. itatively the features visible in the flow-parameter maps
4 Braun
ofAR11263arefairlytypicalforoursample. Thelargest with the flaring process. Consequently, the purpose of
speeds,reachingnearly1 kms−1, arefound surrounding the mask is to isolate the flows in magnetically relevant
sunspots and are associated with the moat flows. These pixels for further analysis. Recognizing that what de-
moats also produce the largest diverging signals in the fines“relevant”isunknown,weselectdifferentthresholds
DIVmaps. SurroundingtheseoutflowsintheDIV maps of photospheric magnetic field to construct these masks.
are regions of converging flows which extend, at most, Specifically,twosetsofmaskswithminimumflux-density
a few degrees beyond the moats. The vorticity and he- thresholdssetat50and200Gareused. Themaskspro-
licity maps exhibit complex patterns composed of com- vide alternatelyafairlygenerousorrestrictivedefinition
pact features with both signs and sizes as small as the of a magnetic region, with the goal to establish whether
◦
resolution imposed by our 0.48 smearing. There is a andhowtheresultsweobtaindependonthischoice. We
clear enhancement of the vorticity (and helicity) signals note that the stronger threshold primarily isolates the
within the strongest magnetic regions. Although some sunspotsandtheirimmediatevicinitieswhile theweaker
fraction of these signals may be attributed to the effects value includes considerable surrounding field. Figure 2
ofrealizationnoise,acarefulexaminationofthemapsre- shows pixel histograms for our flow-parameter maps for
vealsfeatureswhichpersistfromone14hrintervaltothe one interval centered on AR 11263 using the different
next. Successive vorticity maps, masked to isolate only masks.
regionswithflux densities greaterthan500G,arecorre- A strict use of the (unsigned) line-of-sight magne-
lated with values of Pearson’s coefficient equal to about togramscanproducehighlydiscontinuousmasksdue to,
0.4. Successive divergence maps have typical Pearson’s for example, false neutral lines in sunspot penumbrae
coefficients of about 0.6. which appear when the spots are near the limb. Conse-
Supergranulation in the magnetic-free regions have quently, we use thresholds basedonmaps ofa potential-
peak speeds on the order of ≈ 300 m s−1 which appear fieldextrapolationofthetotalfield,B ,fromtheline-of-
p
as ring-like features (weaker than the sunspot moats) in sight magnetograms. All of the masks are limited in the
◦
the maps of |V| and diverging centers surrounding by spatialdomainbya“boundingbox”spanning20 inlon-
◦
converging lanes in the DIV maps. gitude and 10 in latitude and centered on each NOAA
AR coordinate (e.g. the area shown in Figure 1). This
box was adequate for most of the active regions in our
10 10 10 1000 sample, however five regions (ARs 11339, 11520, 11944,
8 8 8
Mag 6 6 6 0 11967,and 12192) extend well beyond this area. Conse-
24 24 24 -1000 quently a larger (20◦×20◦) bounding box was used for
00 5 10 15 20 00 5 10 15 20 00 5 10 15 20 these five regions. For the purpose of comparison, we
10 10 10 700
8 8 8 alsoconstructa“quietmask”whichconsistsofallpixels
|V| 6 6 6
4 4 4 within the bounding box with |Bp|<50G.Distributions
2 2 2 0
00 5 10 15 20 00 5 10 15 20 00 5 10 15 20 for the flow parameters using these masks are indicated
10 10 10 100 by different colored histograms in Figure 2. Hereafter,
8 8 8
DIV 6 6 6 0 werefertothethreemasksasthe“200+Gmask,”“50+
4 4 4
2 2 2 -100 G mask,” and “quiet mask” respectively.
00 5 10 15 20 00 5 10 15 20 00 5 10 15 20
10 10 10 50
8 8 8
VOR 6 6 6 0
4 4 4
2 2 2 -50 10000 10000
00 5 10 15 20 00 5 10 15 20 00 5 10 15 20
810 810 810 2000 1000 1000
HEL 6 6 6 0
4 4 4
2 2 2 -2000 100 100
00 5 10 15 20 00 5 10 15 20 00 5 10 15 20
degrees 10 10
Figure 1. MagnetogramsandflowparametermapsforAR11263 1 1
for three successive time intervals. From the top row down are -100 -50 0 50 100 -100 -50 0 50 100
DIV (10-6 s-1) VOR (10-6 s-1)
maps of the: line-of-sight HMI magnetograms, near-surface hori- 10000
zontal speed |V|, divergence (DIV) proxy, vorticity (VOR) proxy 10000
and kinetic helicity (HEL) proxy (as defined in the text). The 1000
threecolumnsindicatesuccessive13.6hrnon-overlappingintervals 1000
overwhichthequantitiesshownareobtained. Themiddlecolumn 100
represents observations centered at 2011 Sept 4 00:58 UT. The 100
contoursintheright-mostcolumndefinemagnetic-fieldfluxdensi- 10 10
tiesof50(white)and200G(black)derivedusingapotential-field
extrapolation and smoothed for the purpose of this figure. The 1 1
grayscalescover therangeofvaluesindicated,withscalesinunits 0 200 400 600 800 1000 -2000 -1000 0 1000 2000
ofGforthemagnetograms,ms−1 forthespeed|V|,10−6 s−1 for |V| (m s-1) HEL (10-12 s-2)
DIVandVOR,and10−12 s−2 forthehelicityproxyHEL.
Figure 2. Distributionsofthefourflowparameters,DIV,VOR,
|V|, and HEL for one interval centered on AR 11263. The colors
Our aim is to quantitatively condense the spatially indicate histograms of each flow parameter over different masks
complexmaps,shownforexampleinFigure1,intoman- defined by the (potential-field) magnetic flux-density Bp: |Bp| >
ageable “flow indices,” which represent the the first and 200G(red),|Bp|>50G(blue)and|Bp|<50G(black). Themean
values of each distribution are indicated by the vertical markers,
second moments of their distribution over regions iso-
withappropriatecolor,descendingfromthetopofeachpanel. Note
lated by masks. It is the magnetic field which must, thatinthewingsofthedistributions,theredandbluecurvesare
by most conceivable means, link any near-surface flow nearlythesame.
Near-surface Flows Around Active Regions and Flares 5
The distributions in Figure 2 are substantially wider plitudes in magnetic areas. The result is that the signed
for magnetic pixels than for the quiet mask, confirming indices show spurious temporal variations as the AR ro-
the impression obtained by a visual examination of the tatesacrossthe disk, withhigher(lower)values nearthe
maps (e.g. Figure 1). It is also evident that the largest limbs (disk center). To remove this variation from each
values of all the flow parameters are confined within the ofthesignedflowindices,acorrectionfactorf(µ)/f(1)is
200+ G mask, which causes the wings of the histograms dividedoutofthe uncorrectedmeasurements,wheref is
for the 200+ and 50+ G cases to coincide nearly identi- aquadraticfittothedata(e.g. Figure3). Nocorrections
cally. WhileVORandHELdistributionsarenearlysym- are applied to the signed indices for which trends with
metricaboutzero,thedistributionsofthedivergencepa- distance from the central meridian (from east limb to
rameterDIV areskewedforallmasks,evenforthe quiet west limb), or with heliocentric angle, appear to be neg-
pixels. Prior studies of supergranular flows have also ligible(i.e.producetrend-relateddeviationsontheorder
demonstratedasymmetricdistributionsofthe horizontal ofa few percent or less of their standarddeviation). Ar-
divergence(e.g. Duvall & Gizon2000). It is alsoevident tifacts, which appear as pseudo flows pointing towards
that,fortheexampleintervalshowninFigure2,theDIV or away from disk center, are well known in other he-
parameter has a mean value which is positive (diverg- lioseismic measurements (e.g. Duvall & Hanasoge 2009;
ing flows) for the 200+ G mask, and negative (converg- Zhao et al. 2012; Baldner & Schou 2012). We note that
ing flows) for the mask constructed with the lower 50 G these large-scale low-amplitude (≤ 10 m s−1) artifacts
threshold. The former value is consistent with Figure 1 are very small compared to the flows observed within
whereitcanbeseenthatthe200+Gmaskfullycontains our spatially compact (AR-sized) masks.
the diverging sunspot moat. The 50+ G mask includes
both the sunspot moats and apparently a sufficient area
ocofnctornibvuertgioinnginflotwhesusprraotuianldavthereamgeo.ats to outweigh their −1m s) 560000
eaIsn,ssutuchdiaessowfitflhowloswa-vreersaogluetdioonveRrDsubmsettahnotidasl,lylalragreg-esrcaarle- 〉V| (200+ 340000
mfroomtiotnhsesduacthaiansodridffeerretnotiisaollartoetawteioankearrAeRo-ftreenlatreedmfloovweds 〈orr | 200
c 100
n
(e.g. Komm et al. 2004, 2007). This is neither necessary u
0
nordesiredwiththestrongcompactflowsignalsrevealed 0.5 0.6 0.7 0.8 0.9 1.0
with high-resolution HH. For reference, at a typical AR µ
◦
latitude of 15 , the differential rotation contributes a 600
background vorticity of about 0.3 ×10−6 s−1. This is −1s) 500
ts2we,roavneoddrdwaetirtsahnionyftrmhaetaegAnvRiatruimdeseaslbiktestlloaewsascthrhooewssnlathringeeFsdtiimgsuiergnenssaiol1snasonbod-f 〉V| (m 200+ 340000
the magnetic masks. 〈orr | 120000
c
4.2. Sample Distributions 0
0.5 0.6 0.7 0.8 0.9 1.0
We consider for further analysis the set of 16 flow in-
µ
dices which consistof the mean and standarddeviations
of the four basic flow parameters within either of the Figure 3. Top panel: uncorrected values of the speed |V|, av-
two flux-density masks. We use a notation such that, eraged over magnetic pixels with |Bp| > 200G, as a function of
µ, the cosine of the heliocentric angle. The solid line indicates a
e.g. fortheDIVparameter,thequantitieshDIVi50+ and quadratic polynomial fit f to the data. Bottom panel: corrected
std(DIV) representthe mean and standarddeviation valuesof|V|afterdividingoutthenormalizedfunctionf(µ)/f(1).
50+
ofDIVoverthepixelsinthe50+Gmask,andhDIVi
200+
and std(DIV) represent the analogous indices over Figure 4 presents histograms of eight of the flow in-
200+
the 200+ G mask. This is also applied for the other 12 dices for the entire sample of measurements. We also
indicescomputedfromthethreeparametersVOR,HEL, includeforcomparisonthedistributionsofthesamefour
and|V|andthetwomasks. Anadditional8indices,rep- parametersdeterminedusing the quiet-pixelmasks. Not
resenting the mean and standard deviations of the four shown (for brevity) are the distributions of the indices
flow basic parameters, over the quiet pixels within the based on the standard deviations of the four basic pa-
bounding box, are also computed for purposes of com- rameters. Qualitatively, they resemble the distributions
parison. These indices are denoted with a subscript q: oftheunsignedindices basedonaveragesofh|V|i,which
for example, hDIVi and std(DIV) . areshowninthelower-leftpanelofFigure4. InFigure4,
q q
The indices hDIVi, hVORi, and hHELi are signed about 280 (or 7% of the total) sets of measurements
quantities, while h|V|i, std(DIV), std(VOR), std(HEL), are excluded from the histograms for which the num-
and std(|V|) are not. We find a systematic variation in ber of pixels in the 50+ G mask fell below 104, which is
the unsigned quantities with distance of the AR from aboutone-thirdofthemedianareaoverthesample. This
the center of the disk. For example, Figure 3 illustrates cut-off effectively removes measurements centered on an
this systematic variation for the index h|V|i . Errors active region during time intervals prior to its eventual
200+
due to foreshortening may introduce noise for the helio- emergence in the photosphere.
seismic measurements performed away from the center There are a number of items worth noting in this fig-
of the disk. This noise appears be enhanced in ARs ure. The broadest distributions are observed for indices
and is possibly related to the suppression of wave am- derivedwiththe200+Gmask. Thus,thestrongestvari-
6 Braun
ation in the flow indices, among different ARs and time plots of each of our flow indices against the this flare
intervals,occursinthestrongestmagneticregions. Inad- productivity. For brevity, Figures 5 and 6 condenses the
dition,thespatiallyaveragedDIVindiceshaveclearsign correlations indicated by these scatter plots into binned
preferences,depending onthe magneticmask. Averaged averages of the 24 indices (i.e. the 16 AR indices and
over the 50+ G mask, the divergence is overwhelmingly 8 quiet indices) as functions of the X-ray flux. In gen-
negative,whiletheoppositeistrueforthe200+Gmask. eral, the signed indices for the 50+ and 200+ G masks
The nearby quiet regions have a distribution in hDIVi andtheirquiet-maskcounterpartsexhibitlittlevariation
which is largely positive. It is plausible that this arises with flare productivity. However, the the mean diver-
in largemeasurefromthe presence offlows directedinto gence assessed over the 200+ mask shows an apparent
the ARs which originate in the nearby quiet pixels and decrease with increasing X-ray flux. Further examina-
cross over the boundary defined by the 50 G threshold. tion reveals a similar (decreasing towards zero) trend of
The averaged vorticity index for the 50+ G mask also the mean divergence with other indicators of the size of
shows a clear (cyclonic) sign preference, but the quiet the active region, such as the integrated magnetic flux,
pixels and those abovethe 200G thresholdshow a more or simply the number of pixels, in the 200+ G mask.
symmetric distribution about zero. Nevertheless, there The exact reason for this is unknown, but seems to in-
isaclearpreferencefornegativehelicityasaveragedover dicate an increasing contribution of converging flows to
all (even quiet) masks. This arises if the spatially aver- the 200+ G mask as the size of active regions increases,
aged values of DIV and VOR are anti-correlated,as one even while the mean divergence over the larger 50+ G
mightexpectfromthe actionofthe Coriolisforcedue to mask stays nearly constant.
solar rotation.
50 50
101010000000 110100000000 -6-1DIV indices (10 s) 123400000 -6-1VOR indices (10 s) 123400000
10 10 -10 -10
0.00010.00100.01000.10001.0000 0.00010.00100.01000.10001.0000
X-ray flux (J m-2) X-ray flux (J m-2)
1 1
-20 -10 0 10 20 30 -6 -4 -2 0 2 4 6 400 2500
101010000000 〈DIV〉 (10-6 s-1) 110100000000 〈VOR〉 (10-6 s-1) -1|V| indices (m s) 123000000 -12-2HEL indices (10 s) 1125050000000000
0 -500
10 10 0.00010.00100.01000.10001.0000 0.00010.00100.01000.10001.0000
X-ray flux (J m-2) X-ray flux (J m-2)
1 1 Figure 5. Flow indices as functions of the flare productivity,
0 100 200 300 400 500 -400 -200 0 200 400 definedastheintegrated X-rayfluxsummedoverallflares within
〈|V|〉 (m s-1) 〈HEL〉 (10-12 s-2)
each AR and 13.6 hr time interval included in our survey. The
dotted (solid) lines connect flux-binned averages of indices rep-
Figure 4. Thedistributionsoverthesampleofmeasurementsof resenting the mean (standard deviation) of the flow parameters
indicatedontheverticalaxes. Thecolorsindicatethemaskused,
several of the spatially-averaged flow parameters. The red, blue,
where red, blue and black curves indicate the 200+ G, 50+ G,
andblack histograms represent spatial averages over the 200+ G,
and quiet masks. The vertical bars indicate the range defined by
50+G,andquietmasksrespectively(seetext). Themeanofeach
theaverage± onestandarddeviationforallpointswithinbinsof
distributionisshownbytheverticalmarker,withtheappropriate
the(logarithmofthe)X-rayflux. Forclarity,thescatteredpoints
color,descendingfromthetopofeachpanel.
show onlythe individualmeasurements whichwent intothe aver-
ages indicatedbythe top-mostcurveineach panel. Thevorticity
and helicity indices based on the mask averages (dotted curves)
aredifficulttodiscerninthetworightpanelsandarereplottedin
4.3. Flare Productivity
Figure6withanexpandedverticalscale.
Beforeexploringthe time variationofthe flowindices,
we examine the overall correlation between the indices The unsigned indices h|V|i, std(DIV), std(VOR),
with flare productivity over all ARs and time intervals. std(HEL), and std(|V|) over both magnetic masks show
WeuseNOAAeventreports3whichrecordtheintegrated increases for the most flare-active intervals (i.e. when
X-ray flux (in J m−2), times of the peak X-ray flux, and theX-rayfluxexceedsabout0.1Jm−2). Theamountof
associated active region number, for solar flares as ob- this increase is modest when compared to the spread of
servedwiththeGOESspacecraft. ForeachARandeach the measurements. Moreover, the correlation is similar
13.6 hr time interval, we integrate the X-ray flux of any to that observed with other magnetic properties. Fig-
observed flares in that AR and time to produce a mea- ure 7 shows that the averaged unsigned magnetic flux
sure of the flare productivity. We first examine scatter density, over either the 50+ or 200+ G masks, has a
similardependencewithX-rayflux. Thesimilarityofthe
3http:ngdc.noaa.gov/stp/space-weather/solar-data/solar-featurceosr/rseollaatrio-fnlsarbeest/wxe-ernayFs/iggouerse/s 5 and 7 raises the question
Near-surface Flows Around Active Regions and Flares 7
corresponding time-average of the standard-deviation
2 300
200 based index, e.g.
〈〉-6-1VOR (10 s) -101 〈〉-12-2HEL (10 s) --2110000000 and likew∆ihsVeOfoRrit5h0e+o≡thehrVsOigRsntied5d0(+VinO−dRihcV)e5sO0.+RFio5r0+A,R 11283,
-300
-2 -400 vertical lines denote the times of the X-class and M-
0.00010.00100.01000.10001.0000 0.00010.00100.01000.10001.0000 class flares. It is inevitable that flows, and thus the
X-ray flux (J m-2) X-ray flux (J m-2)
flow indices, will change as an AR evolves. The two
Figure 6. Theindicesbasedonthespatialaveragesofthevortic- regions shown in Figures 8 and 9 highlight the dilemma
ity(leftpanel)andhelicity(rightpanel)asfunctionsoftheX-ray in identifying flare-related flow changes. AR 11363 has
flux. These are the same quantities as shown in the right pan-
no large flares, but both regions undergo evolution of at
els of Figure 5 but with expanded vertical scales. The red, blue,
andblackcurvesindicatetheresultsforthe200+Gmask,50+G least some of the flow indices, e.g. ∆std(HEL)50+ or
mask,andthequietpixels,respectively. Theverticalbarsindicate ∆std(|V|) . In light of this, it is not clear how to in-
50+
the rangedefined bythe average ± onestandard deviation forall
terpret the variation of, say, ∆std(|V|) immediately
pointswithinbinsofthe(logarithmofthe)X-rayflux. 50+
prior to the onset of the X-class flare in AR 11283 on
of whether there exists a physical link between the ob- 2011 Sept 6.
served flow parameters and the onset of flares, or rather
simply that larger ARs provide a preferred environment AR11283
for both increased flows and (as is already known) flare e 0.4
occurrence. ng 0.2
a
ch 0.0
〉B| -0.2
〈| -0.4
400 2 4 6 8 10
k)
as
m
G
300 + 1
0
0
2
G) nge ( 0
〉B| ( 200 x cha -1
〈| nde
i 2 4 6 8 10
k)
100 s
a
m
G
+ 1
0
0 e (5 0
0.0001 0.0010 0.0100 0.1000 1.0000 ng
a
X-ray flux (J m-2) ch -1
x
e
d
Figure 7. Scatter plots, with binned averages, of the unsigned n
i
magnetic flux density averaged over the 200+ G (red) and 50+G 2 4 6 8 10
(blue)masksrespectively,asfunctionsoftheintegratedflareX-ray
2011 Sept
flux.
Figure 8. Thevariationintimeofthemeanunsignedmagnetic
fluxdensity(top panel) andflow indices determinedforthe 200+
5. TIMEVARIATIONOFFLOWPARAMETERS G mask (middle panel) and 50+ mask (bottom panel) G for AR
11283. All quantities are expressed in terms of their fractional
Figures 8 and 9 show examples of the temporal vari-
change from the time-averaged quantity (see text for details). In
ations of the flow indices for two ARs. One of these
thetoppanel,thered(blue)circlesconnectedbylinesofthesame
regions, AR 11283 was the site of one X-class flare and color, indicate the fractional change of the unsigned flux density
3 M-class flares, while the other, AR 11363 was a large, averaged over the 200+ G (50+ G) masks. In the middle and
bottompanels,thequantitiesshownare(fromtoptobottom)the
but relatively flare-free region (producing only 8 C-class
fractionalchangesof: hVORi(greencircles),hDIVi(purplecircles),
flares during its passage). The indices are plotted in hHELi(orange circles),h|V|i(black circles),std(VOR)(green tri-
termsoftheirfractionaldeviationfromatemporalmean. angles), std(DIV) (purpletriangles), std(HEL)(orange triangles),
For the unsigned indices, e.g. std(VOR) , this takes a and std(|V|) (black triangles). For clarity, each plot in the lower
50+ twopanelsisverticallydisplacedfromtheoriginbymultiplesof0.5
form
anddenoted bythe horizontal blacklines. Solid(dashed) vertical
lines denote the times of X-class (M-class) flares associated with
std(VOR) −std(VOR)
∆std(VOR) ≡ 50+ 50+, thisregion.
50+
std(VOR)
50+ Superposed Epoch (SPE) analysis (e.g.
where the horizontal bar denotes the average over time. Mason & Hoeksema 2010; Reinard et al. 2010) of
For the signed quantities, the change is relative to the the flow indices provides one method to reduce the
8 Braun
AR11363 tions with time relative to the flares. It is most likely
e 0.4 that this results from foreshortening and projection ef-
ng 0.2 fects related to the tendency of the AR to be positioned
a
ch 0.0 closertotheeast(west)limbatearly(later)timesinthe
〉B| -0.2 SPE averages than near the times of the flares. Indeed,
〈| -0.4 without the center-to-limb detrending performed on the
k) 2 4 6 8 10 unsigned flow variables (e.g. Figure 3) one sees similar
as temporal variations of those quantities as well.
m
G It is apparent (particularly by noting the units of the
+ 1 verticalscales), that the variationsover time of the SPE
0
20 averaged indices are considerably smaller than observed
e ( 0 within individual ARs. For example, fractional varia-
g
n
x cha -1 tpiroenssenotf iunpFtiogu4r0e%s 8inasntdd(9H.ELT)5h0e+soarmsetdq(u|Van|)t5it0i+esairne
nde the SPE-based averages show variations less than 10%.
i 2 4 6 8 10 Moreover,althoughthelattervariationsarestillnotable,
sk) they are not substantially largerthan expected from the
a
m standarderrorofthemeanasindicatedbytheerrorbars.
G
+ 1 MostSPE-averagedflowindices,includingthesignedin-
50 dices, exhibit time variations on the order of only a few
e ( 0 percent over the entire 6.8 days. On the other hand,
g
n
a somevariationsdoappearsignificantwhen,forexample,
h
x c -1 compared to their standard errors. This includes varia-
nde tionsinhDIVi50+,whichshow≈3%temporalvariations
i whichareontheorderofthreetimesthestandarderrors.
2 4 6 8 10
2011 Dec
Fdeingsuitryefl9o.w iTnhdeicevsarfioartioAnRin11t3im63e,osfhotwhenuinnsitghneedsammaegfnoertmicatfluaxs nge 0.1
Fthiigsurreeg8io.nTdhuerrinegatrheendoatXe-scloabssserovredM.-class flares associated with 〉B| cha 0.0
〈| -0.1
influence of quiescent (non-flare related) evolution while -3 -2 -1 0 1 2 3
k)
revealing possibly subtle flare-related changes. To as
m
achieve this, we identify flare times from the NOAA G
GOESrecordsofallXandM-classflaresassociatedwith + 0.1
0
the ARs in our survey. Each set of flow measurements 20
are assigned to a 13.7 hr-long time bin, based on the e ( 0
g
midpoint in time of the HMI Dopplergrams used in the an
analysis relative to the time of the peak X-ray flux of ch -0.1
x
the flare. The indices within each bin are averaged, nde
using 6 bins before and 6 bins after the onset of flares. i -3 -2 -1 0days relative to flare 1 2 3
Thus,theanalysiscoversabout169hr(6.8days)oftime sk)
a
around the occurrence of the flares. A data-coverage m
requirementwasstrictlyenforcedthat,foranycandidate + G 0.1
flare,the relevantflowmeasurementsareincludedinthe 0
5
SPE averages if, and only if, there are no gaps in those e ( 0
g
measurements over the entire 6.8 days. As discussed an
h
earlier, this may arise because of either unfavorable AR c -0.1
position (greater than 60◦ from disk center) or gaps dex
in the HMI data. This requirement ensures an equal in
-3 -2 -1 0 1 2 3
weighting, over the entire 6.8 days considered, of the
days relative to flare
contribution of each set of measurements. In spite of
this restriction, we are left with 70 flares (associated
Figure 10. ThevariationintimeoftheSPEaveragedflowindices
with 34 distinct ARs) in our binned averages. We note
over 70 X-class and M-class flares. The formatis the same as for
that all X and M flares within each AR are included Figure9exceptthattheabscissashowsthetimeoffsetindaysfrom
in the SPE analysis as the HH measurements allow, themidpointofthebinintervalstotheflareoccurrence. Notethat
theverticalscaleinallpanelsissubstantiallymagnifiedcompared
withoutrejectiondue to their proximityin time to other
to Figures 8 and 9 and that, in the lower two panels, offsets by
flares in the same region. multiples of 0.05 are applied to vertically separate each plot for
Figure 10 shows the results for the 70-flare average. clarity. Error bars represent the standard error of the mean. To
Along with the flow indices, the figure also shows the avoidclutter,onlyrepresentativeerrorbarsareshown.
SPE averagesof the magnetic flux densities, determined
over both the 50+ G and 200+ G masks. The averaged To assess whether the observedvariations in the SPE-
flux density show significant 5-10% quadratic-like varia- averaged indices are associated with the specific occur-
Near-surface Flows Around Active Regions and Flares 9
renceofflares,weperformaseparateSPEaveragingpro- results are qualitatively the same as illustrated with the
cedure substituting the GOES flare list with an equiva- examples shown in Figures 10. We have also specifically
lent list with randomized times. In this control list each examinedthepossibilityofchangesintheflowproperties
trueflare-timeisoffsetbyeitherδ or(δ−13)days,where attime-scalesshorterthan13.6hr. Fora subsetof ARs,
δisarandomtimebetween0and13days,andthechoice specifically those responsible for X-class flares, the HH
islimitedtotheoffsetwhichkeepstheARvisibletoHMI. analysis described in § 3 is repeated using datacubes 4.5
Pre-emergence intervals are excluded from the SPE by hr in length (one third the length of the original analy-
requiring a minimum pixel count of 104 over the 50+ G sis). For this subsample of ARs, we find no compelling
mask during the interval of the (pseudo) flare. evidence for significant changes in the flow parameters
Fromthiscontrollist,weobtainedtheresultsshownin on these shorter timescales.
Figure 11, based on averages with respect to 71 pseudo
flares. Compared with Figure 10, the similarity is quite 6. DISCUSSION
striking. Just as in the SPE analysis with respect to We have carried out helioseismic survey of the near-
actual X and M-class flare times, there are small, but surface flow parameters of 252 of the largest NOAA-
significant temporal variations in several flow parame- numbered sunspot regions, spanning a 4.5 year interval
ters. This is also apparently true for the magnetic flux between 2010 June and 2014 December. Although other
density as well. Indeed, the similarity in the time varia- comprehensive helioseismic surveys have been made, for
tionofh|B|i forthe twocasesreinforcesthe likelihoodof example,withdatafromGONG,oursurveyincludesflow
center-to-limbsystematics,ontheorderof5-10%,associ- measurementsmadewithgreaterspatialresolution. The
atedwiththedeterminationoftheline-of-sightmagnetic general properties of the horizontal flow divergence and
field. Many of the the flow indices, such as hDIVi and vertical vorticity are similar to, and confirm, prior re-
std(HEL),showsignificantvariationswithrespecttothe sults made at lower resolutions (e.g. Komm et al. 2004;
randomtimes,foroneorbothmagneticmasks,whichare Hindman et al. 2009). Specifically, we see that the typ-
similar in magnitude to those observed with respect to ical active region is characterized by strong outflows by
the true flare times. sunspotsintheARcenters,andsurroundedbysomewhat
weakerconvergingcountercells. Thevorticitysignalsare
considerably weaker than those associated with the hor-
izontal divergence, and likely include a larger fraction
ge 0.1 of realization noise. Nevertheless, active regions show
n
cha 0.0 small-scalevorticitysignalssignificantlyhigherthansur-
〉B| rounding quiet regions. The spatially-averaged kinetic
〈| -0.1 helicityproxyfordifferentmagneticmasksindicatesmall
-3 -2 -1 0 1 2 3 rotational motion consistent with Coriolis forces acting
k)
as on the converging or diverging flows components.
m
G There is a modest correlation with integrated flare X-
+ 0.1 rayfluxofseveraloftheflowindicesweexamined,includ-
0
0 ing the average speed, and the standard deviations over
2
e ( 0 the magnetic masks of all four basic parameters (speed,
g
an divergence,vorticityandkinetichelicity). Howeverthese
ch -0.1 correlations strongly resemble those obtained with basic
x
e magneticproperties,suchasthemeanunsignedfluxden-
nd
i -3 -2 -1 0days relative to flare 1 2 3 sity. The similarity of the results between the choice of
k) theflux-densitythresholdinthespatialmasksshowsthat
s
a
m thesecorrelationsprimarilyariseforflowswithinornear
+ G 0.1 the strongest flux and are little changed when weaker
0 fluxregionsareincluded. Overall,thetrendsresembleat
5
e ( 0 least qualitatively the findings of Komm & Hill (2009),
g
n albeit with substantially different flow parameters. We
a
h
c -0.1 cannot at this stage rule out the possibility that infor-
x
e mation characterizing the near-surface flows may, along
d
in with magnetic indicators, help distinguish between flar-
-3 -2 -1 0 1 2 3 ing and non-flaring AR or even predict flares such as
days relative to flare
suggested by Komm et al. (2011a).
Some differences between our flow indices and those
Figure 11. The variation in time of the SPE averages of flow
employed previously are worth noting. The “vortic-
indiceswithrespecttoasetof71randommomentsintime,selected
byapplyingrandomoffsetsfromthetimesofactualMandX-class ity”indicatorsdefinedbyKomm & Hill(2009)werecon-
flares. structed from relatively large spatial variations of the
horizontal components of vorticity, unlike the vertical
We have performed SPE analysis over different flare componentexaminedinthe presentstudy. Furthermore,
classes(e.g. X-classflaresalone,orflaresdefinedbytheir it is difficult to directly compare our near-surface in-
integrated, rather than peak, X-ray flux). Decreasing diceswiththeparameterdefinedbyReinard et al.(2010)
the lengthof the time intervalabout flareoccurrencein- whichisproportionalto,amongotherfactors,thespread
creasesthenumberofavailablemeasurementsandthere- in depth of kinetic helicity. On the other hand, in light
fore the statistics. However, in all cases examined, the of these results, it is reasonable to question why higher
10 Braun
resolution observations of converging flows (e.g. such as ful suggestions made by the referee. This work is sup-
characterized by the divergence-based indices examined ported by the Solar Terrestrial program of the National
here) do not show stronger association with flaring re- ScienceFoundationthroughgrantAGS-1127327awarded
gionsthanotherindicators. Thismightbeexpectedsince toNWRA. Additionalsupportis providedby the NASA
converging flows presumably comprise the near-surface Heliophysics program through contracts NNH12CF23C
components of the “vortex rings” (Komm et al. 2011b) and NNH12CF68C. SDO data is provided courtesy of
inferred from the ring-diagramresults to be strongly as- NASA/SDOandtheAIA,EVE,andHMIscienceteams.
sociated with flaring regions.
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the manuscript. We are also appreciative of the help- 705,821