Solar supergranulation revealed by granule tracking

0.58 MB·English

by  Michel Rieutord

Astronomy&Astrophysicsmanuscriptno.9077paper (cid:13)c ESO2008
February2,2008
Solar supergranulation revealed by granule tracking
MichelRieutord, Nade`geMeunier⋆,ThierryRoudier,SylvainRondi,FrancisBeigbederandLaurentPare`s
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0
0 Laboratoire d’Astrophysique de Toulouse et Tarbes, UMR 5572, CNRSet Universite´ Paul Sabatier Toulouse 3, 14 avenue E.Belin, 31400
2 Toulouse,France
n e-mail:[rieutord,roudier,francis.beigbeder,pares]@ast.obs-mip.fr, [email protected], [email protected]
a
J February2,2008

9
ABSTRACT
]
h
Context.SupergranulationisapatternofthevelocityfieldatthesurfaceoftheSun,whichhasbeenknownaboutformorethanfiftyyears,
p
- however,nosatisfactoryexplanationofitsoriginhasbeenproposed.
o Aims.Newobservationalconstraintsarethereforeneededtoguidetheoreticalapproacheswhichhesitatebetweenscenariosthateitherinvoke
r alarge-scaleinstabilityofthesurfaceturbulentconvectionoradirectforcingbybuoyancy.
t
s Methods.Usingthe14-MpixelCALAScameraatthePic-du-Midiobservatory,weobtaineda7.5h-longsequenceofhighresolutionimages
a
withunprecedented fieldsize. Tracking granules, we have determined thevelocity field at the Sun’s surface in great detail from a scale of
[
2.5Mmupto250Mm.

1 Results.Thekineticenergydensityspectrumshowsthatsupergranulationpeaksat36Mmandspansonscalesrangingbetween20Mmand
v 75Mm.Thedecreaseofsupergranularflowsinthesmallscalesisclosetoak−2-powerlaw,steeperthantheequipartitionKolmogorovone.The
9 probabilitydistributionfunctionofthedivergencefieldshowsthesignatureofintermittencyofthesupergranulationandthusitsturbulentnature.
6
3
1
Keywords.Convection–Turbulence–Sun:photosphere
.
1
0
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1. Introduction tletemperaturefluctuations(seeMeunieretal.2007a).Besides
0
: these scenarios, recent observations of Gizonetal. (2003)
v SupergranulationwasdiscoveredbyHart(1954)usingDoppler
addedsomewavelikepropertiestosupergranulation.
i images of the Sun. It appeared as an essentially horizontal
X Obviously, the supergranulation theory needs guidance
flowfield atatypicalscale of30Mm.Theoriginofthisflow
r from every available observational constraint. This letter
a field was first thought to be related to the second ionization
presentstheresultsoftheobservationsissuedfromtheCALAS
of helium, which providessome latentheat at a deptharound
project (a CAmera for the LArge scales of the Sun; see
10 Mm, compatible with their typical size (Simon&Weiss
Meunieretal. 2005), collecting a sequence of high resolution
1968). This scenario has been much debated because of the
widefieldimages,whichhaveallowedustocapturetheevolu-
weakness of the effect and the apparent vigour of the super-
tionofahundredsupergranulesatthedisccentreduring7.5h.
granular flow. Other ways of generating this velocity scale
Wecanthusgivenewconstraintsonthedynamicsofthesolar
rely on large-scale instabilities of the surface turbulent flow
surfaceinthesupergranulationrange.Afterabriefdescription
(Rieutordetal.2000),triggeredbythestrongdensitystratifica-
ofthedataset(Sect.2),weshowthespectralsideofthesuper-
tion.Inthisscenario,kineticenergyofgranules,thesmall-scale
granular flow (Sect. 3) as well as the probability distribution
convectivecells, isthoughttobepipedtoa largerscale byan
functionsofthedivergences(Sect.4);firstconclusionsfollow.
AKA-like effect (Gamaetal. 1994). However, other kinds of
large-scale instabilities are still possible, like a convectivein-
stability triggered by fixed-flux boundary conditionsimposed 2. Observationaltechniquesanddatareduction
by the small-scale granular convection (Rincon&Rieutord
2003). In thisapproach,thecoolingresultingfromthe granu- 2.1.Dataset
lationdoesnotsuppresstheconvectiveinstabilityofthelarger
On13March2007,weobservedtheSunatdisccentreduring
scales; because all the heat flux is carried by the small scale,
7.5 h using the Lunette Jean Ro¨sch at Pic du Midi, a 50 cm-
none is carried by the largescale instability, which shows lit-
refractor.Imagesweretakenatλ=575±5nm,witha14Mpixel
Sendoffprintrequeststo:M.Rieutord CMOS-camera (4560×3048 pixels), with 0.115 arcsec/pixel,
⋆ Present address: Laboratoire d’Astrophysique, Observatoire de thus coveringof 524×350arcsec2 (see Fig. 1). 10811 images
Grenoble,BP53,38041Grenoblecedex9 wereobtainedwitharegularcadenceofoneevery2.5s.Twoin-
2 Rieutordetal.:Solarsupergranulation
350"
524"
Fig.1.Bottomright:theCALASfieldofviewontheSun;thelargerectangleindicatesthesizeoftheimages,thesmallerone
showsthefieldwherethevelocitiescouldbecomputed,whilethesmallsquareshowsthefieldofviewoftheSOTinstrumenton
theHinodesatellitewhentrackinggranules.Top:thesupergranulationvelocityfieldwiththedivergencecontourssuperimposed
(scales shorter than 8 Mm have been filtered out). A time-window of 150 min was used. Bottom left: a zoom on granulation
showingtherelativesizesofgranulesandsupergranules.
dependentseriesof∼ 1400imageswerethenextracted.They Because of trackingdifficulties, the commonfield of each
samplethesamesolarsignalwithaperiodof20sbutarenoised serieswas reducedto ∼400×300arcsec2, thuscoveringa sur-
differently by the Earth atmospheric perturbations. The com- faceof290×216Mm2ontheSun(Fig.1).
parisonbetweentheoutputsofbothseriesallowsustoevaluate
theinfluenceoftheseeingandtesttherobustnessoftheresults
withrespecttothisnoise.
After recentering, subimages were k − ω filtered (with a
threshold of 7 km/s), so as to remove, as much as possible,
Earthatmosphericdistortion,whichisthemainsourceofnoise
forvelocitymeasurements(Tkaczuketal.2007).
Rieutordetal.:Solarsupergranulation 3
Fig.2. Kinetic energy spectra obtained for various time win- Fig.3. Same as in Fig. 2 but for the horizontaldivergence of
dows.Theverticaldottedlineindicatesthepositionofthepeak theflow,∂ v +∂ v (solidline),andfortheverticalvorticity,
x x y y
at 36.4 Mm. The vertical dashed line emphasizes the 10 Mm ∂ v −∂ v (dashedline);thesupergranulationpeakisclearly
x y y x
scale, usually taken as the upper limit of mesogranular scale. visibleatλ= 36Mminthedivergencespectrumbutabsentin
Twopowerlawsareshownoneachsideofthepeak,aswellas thevorticityone.Ak2-powerlawisgivenforcomparison.
theoneofsmall-scalenoise.
computed the spectral density of kinetic energy E(k) associ-
2.2.Velocityfields ated with the horizontalflowsthat we can measure.Itis such
that
Horizontal velocity fields have been obtained using the CST
granuletrackingalgorithm(Roudieretal.1999;Rieutordetal. 1 ∞
<v2 >= E(k)dk.
2007). As shown in Rieutordetal. (2001), granules’ motions 2 Z
0
trace large-scale velocity fields when the scale is larger than
E(k),whichiscomputedinthesamewayasinRieutordetal.
2.5Mm.Hence,wesampledthevelocityfieldwithabinof12
pixels(∼1Mm). (2000),isdisplayedinFig.2fortheflowsdeterminedwithvar-
ioustime-windows.Theshorttime-windowsof45mingiveus
Thevelocitiesareobtainedbytrackingthegranulesduring
10independentspectra,whichareaveragedtogether,whilethe
a giventime window.Thus, we have accessto averageveloc-
itycomponents,namelyv (i, j)andv (i, j),wheretheoverline wholeseries450mintime-windowgivesusonlyonespectrum.
x y
Note thatno spatial filteringwas appliedto the velocityfield.
referstothetimeaveragingimposedbythetimewindow.This
We see that E(k) ∝ k atsmallscale, whichis thesignatureof
averagingimprovesthesignal-to-noiseratio,butnaturallyde-
decorrelatedrandomnoise.
creasesthetimeresolution.Typically,theshortesttimewindow
These spectra clearly show the emergence of the spec-
thatcanbeusedis30min.
Althoughthefieldislarge,projectioneffectsofthespheri- tral range of the supergranulation as the length of the time-
windowincreases.Letuspointouttheremarkablestabilityof
calSunarestillofweakinfluence.Atmost,inthefieldcorners,
thewavenumberofthespectralpeakwhenthetimeaveragingis
thecorrectiononthevelocitywouldbelessthan4%,whichis
changed.Thisdemonstratesthatsupergranulationisagenuine
muchlessthanthenoise.
velocity field at the Sun’s surface. It is not the consequence
WeshowinFig.1anexampleofthesevelocityfields.The
oftime-averagingthesmall,fastturning-oversmallscales.Of
small-scalecomponentsoftheflow(withscalesbelow8Mm)
course,if theaveragingintervalislongenough(i.e.oftheor-
werefilteredoutusingDaubechieswavelets(seeRieutordetal.
deroftheturn-overtimescaleofsupergranulation),thespectral
2007). Figure 1 shows that robust steady supergranules live
peakwill moveto everlargerscales beforedisappearing.The
amonga wide varietyofflow structuresillustratingtheturbu-
maximumofthespectraldensityisatawavelengthof36Mm.
lentnatureofthesescalesandtheirwidespectralrange.
The FWHM of the peakindicatesthatsupergranulationoccu-
3. Thekineticenergyspectrum
piestherangeofscalesof[20,75]Mm.
A convenient way to view the dynamics of a flow is to ex- Thepresentmeanvalueofthediameterofsupergranulesis
amine the spectral content of the velocity field. We therefore slightlyhigherthanthepreviousdeterminations.Forinstance,
4 Rieutordetal.:Solarsupergranulation
Meunieretal.(2007b)findameandiameterof31.4Mmwitha
techniquebasedonthesegmentationofthedivergencefieldde-
rivedfromvelocitiesissuedfromalocalcorrelationtechnique
applied to SOHO/MDI white light images. DelMoroetal.
(2004) also use a divergence field but derived from time-
distancehelioseismology;theyfindameansizeof27Mm,sig-
nificantlysmallerthanours.
Bothoftheseresultsarebasedonthedivergencefieldand
itssegmentation.Thehistogramofsizesisthenusedtodeter-
mine the mean diameter of a supergranule. Such a technique
necessarily underestimates the actual scale of supergranular
flowsasonlypartofit (thepositivedivergences)is used.Our
spectra,whichdirectlyresultfromthemeasuredhorizontalve-
locities, incorporate all the components of the flow at super-
granulation scale, and thus better reflect the dynamical state.
NotethatablinduseofthedivergencespectruminFig.3would
pointtoascaleof∼23Mm.
In Fig. 2 we also indicate the best-fit power laws, which
mimic the sides of the supergranulation peak. We find that
E(k) ∼ k3 on the large-scale side and E(k) ∼ k−2 on the
small-scaleone.Thislatterpowerlawissteeperthanthe−5/3
Kolmogorovoneandmaybeaneffectofdensitystratification.
Fig.4. Histograms of the divergences; solid and dashed lines
To complete the spectral picture, we also show, in Fig. 3,
havethesamesolarsignalbutadifferentnoisefromtheEarth
thespectraofthehorizontaldivergenceofthevelocityfieldand
atmosphere. Scales below 8 Mm have been filtered out. A
theverticalvorticity.Beyondthek2-dependenceofthespectral
Gaussiandistributionwiththesamestandarddeviationisover-
densities, which is a consequence of the derivative of uncor-
plottedforcomparison.
relatednoise,we cansee thatthedivergencespectrumclearly
shows the supergranulation peak, while the vertical vorticity
shows no signal in this range. The vorticity does show some
compassesallthescalesrangingfrom20to75Mm,asshown
weaksignalhowever,butinthemesogranulationrange,below
bytheFWHMofthepeak.Exceptforitsamplitude,thispeakis
10Mm.
notsensitivetothetimewindowusedtomeasurethegranules’
4. Probabilitydensityfunctions
motions.Thesignalalsoclearlyappearsinthedivergencespec-
traldensity,butnotinthevorticity;itislikelythatvorticityat
Another way to look at the velocity fields is to consider the
supergranulationscale nearthe Sun’sequatoris muchweaker
probability density functions. Such distributions have been
anddoesnotemergefromthenoise.
computedforthevelocityfield,itsdivergenceanditscurl.We
show in Fig. 4 the distribution of the divergence field when Finally,ourdataconfirmthefactthatsupergranulationhas
scalesshorterthan8Mmhavebeenfilteredoutofthevelocity a noticeable degree of intermittency, clearly appearing in the
field.Thisdistributionclearlyshowsapositivewinglargerthan distributionofpositivedivergencevalues.
theGaussianone,associatedwithaskewnessof0.38.Wealso As far as the origin of supergranulationis concerned, the
notethatthenoiseoftheEarthatmosphereisweakenough,and scenarios mentioned in the introduction can be tested with
doesnotperturbtheresult.Thistrendtoanexponentialdistri- thesedata,eitherintherealspacewithvelocityfieldslikethe
bution is a signature of intermittency(e.g. Frisch 1995). This oneshowninFig.1orinthespectralspacewiththegivenspec-
result, with the same asymmetry between positive and nega- tra.
tive values, was also observedby Meunieretal. (2007b) with Further work on the observational side will focus on the
a completely different set of data and method. Thus, the in- determinationofthethirdcomponentofthevelocityfield,the
termittencyofsupergranulationseemstobearobustproperty. increaseofthefieldsizeandthereductionofthenoise,soasto
Exponentialwingsareusuallylessvisibleonthevelocity(e.g. further constrain the dynamicsof scales from the granulation
Vincent&Meneguzzi1991),and,indeed,arebarelynoticeable onetothe100Mmone.
inourdata.Asfarasvorticityisconcerned,thenoiseisunfor-
Acknowledgements. The CALAS project has been financially sup-
tunatelytoohightogiveconvincingmeasurements.
portedbytheFrenchministeryofeducation(ACI),bytheProgramme
5. Conclusions NationalSoleil-TerreofCNRSandtheObservatoireMidi-Pyre´ne´es.
Wearealsoverygratefultothe“Grouped’IntrumentationdesGrands
For the first time, it has been possible to follow the motion
Te´lescopes(GIGT)”ofthelaboratory,fortheirtechnicalhelpatvari-
of well-resolved granules in a large field of view. The spec-
ousphaseoftheproject,especiallytoSe´bastienBaratchartandElodie
tral peak of supergranulation has thus been determined in a Bourrec.WealsowishtothankRene´ Dorignacforhisefficientsup-
very direct manner. According to our data, supergranulation portinmechanicalrealizationsandPhilippeSabyforhishelpinsort-
has the most energetic motions at a scale of 36 Mm and en- ingouttherightcomputinghardware.SRwishestothanktheCNRS
Rieutordetal.:Solarsupergranulation 5
for itssupport during hisPhD thesiswhichmuch contributed tothe
project.
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