Table Of ContentDoubts about the crucial role of the rising-tube mechanism in
the formation of sunspot groups
A.V.Getlinga,∗,R.Ishikawab,A.A.Buchnevc
aSkobeltsynInstituteofNuclearPhysics,LomonosovMoscowStateUniversity,Moscow,119991Russia
4 bHinodeScienceCenter,NationalAstronomicalObservatoryofJapan,2-21-1Osawa,Mitaka,Tokyo,181-8588Japan
1 cInstituteofComputationalMathematicsandMathematicalGeophysics,Novosibirsk,630090Russia
0
2
y
a
M Abstract
SomepreliminaryprocessingresultsarepresentedforadatasetobtainedwiththeSolarOptical
2
1 Telescope on the Hinode satellite. The idea of the project is to record, nearly simultaneously,
the full velocity and magnetic-field vectors in growing active regions and sunspot groups at a
] photosphericlevel.Ourultimateaimistoelaborateobservationalcriteriatodistinguishbetween
R
themanifestationsoftwomechanismsofsunspot-groupformation—therisingofanΩ-shaped
S
fluxtubeofastrongmagneticfieldandtheinsituamplificationandstructuringofmagneticfield
.
h byconvection(theconvectivemechanismisbrieflydescribed).
p Observations of a young bipolar subregion developing within AR 11313 were carried out
-
o on9–10October2011.Duringeach2-hobservationalsession,5576-ÅfiltergramsandDoppler-
r gramswereobtainedatatimecadenceof2min,andoneortwo32-min-longspectropolarimetric
t
s fast-modescansweredone.Basedontheseriesoffiltergrams,thetrajectoriesofcorksarecom-
a
puted,usingatechniquesimilartobutmorereliablethanlocalcorrelationtracking(LCT),and
[
comparedwiththemagneticmaps. Atthisstageoftheinvestigation,onlytheverticalmagnetic
2 fieldandthehorizontalflowsareusedforaqualitativeanalysis.
v
Accordingtoourpreliminaryfindings,thevelocitypatterninthegrowingactiveregionhas
7
nothing to do with a spreading flow on the scale of the entire bipolar region, which could be
7
0 expected if a tube of strong magnetic field emerged. No violent spreading flows on the scale
8 of theentiregrowingmagneticregioncanbeidentified. Instead, normalmesogranularandsu-
1. pergranularflows are preserved. Signs of small-scale structuring of the magnetic field can be
0 detectedintheareawherenewspotsdevelop,andsignsofthepresenceofseparatricesbetween
4 the magnetic polarities can be found, such that the surface flows converge to but not diverge
1
fromtheseseparatrixcurves. TheobservedscenarioofevolutionseemstoagreewithBumba’s
:
v inference that the developmentof an active region does not entail the destruction of the exist-
i ing convective-velocityfield. The convectivemechanismappearsto be better compatible with
X
observationsthantherising-tubemechanism.
r
a In the umbras of the well-developed sunspots, flows converging to the umbra centres are
revealed.Spreadingstreamsarepresentaroundthesespots.
Keywords:
solarphotospere;solarconvection;magneticfields;sunspotformation;Hinodeobservations
PreprintsubmittedtoAdvancesinSpaceResearch May13,2014
Figure 1: A magnetogram ofthe “trilobite” series demonstrating the emergence ofsunspot 10926. This series was
obtainedwiththeSolarOpticalTelescopeontheHinodesatelliteinDecember2006.Blackrepresentsnegativepolarity,
andwhiterepresentspositive.AdaptedfromthemovieavailableviaalinkinNASA(2007).
1. Introduction
The idea that the magnetic field of a bipolar sunspot group originates from the emergence
ofanΩ-shapedflux-tubeloopwasconsideredtobevirtuallyindisputableforalongtime. This
rising-tubemodelassumesthatthefluxtube,formedinthegeneralsolartoroidalmagneticfield
deepintheconvectionzone,carriesupwardthefieldthatisassumedtobeoriginallystrong.This
mechanismreceivedmuchattentionafterthewell-knownstudybyParker(1955),whoinvoked
magneticbuoyancytoaccountfortheriseofflux-tubeloops,andhasbeenrevisitedbyanumber
ofinvestigatorsoverseveraldecades.Interestinganalysesofthismodelweremade,inparticular,
byCaligarietal.(1995,1998);numericalsimulationsofthismechanismbasedonfullsystemsof
MHDequationshavealsobeencarriedout(see,e.g.,Fanetal.,2013;Rempel&Cheung,2014,
andreferencestherein).
Inrecentyears, however,therising-tubemodelhasmoreandmorebeenobjectedbasedon
bothrecent,verydetailedobservationaldataandcurrentviewsoftheprocessesinthedeeplay-
ers. Firstofall,ifitisadopted,onehastoaccountfortheoriginofthecoherenttubeofstrong
magneticfield;tothisend,someadditional,fairlyartificialassumptionsneedtobeintroduced.
Second, a very important point is that the pattern inferred from this model for photospheric
flows and magnetic fields on the scale of the growing magnetic region disagrees with the pat-
tern actually observed on the Sun (see, e.g., Kosovichev, 2009, and the brief description of a
remarkablemagnetogramgivenbelow in thisIntroduction);we shallsee thatthe resultsof the
presentstudyalsoscarcelyconformtothescenariothatshouldbeexpectedinthecaseofemer-
genceofalargetubeofstrongfield. Itwasalsonotedthatthebehaviourofthetiltangleofthe
bipolar magnetic regionsis not consistent with the predictionsbased on the rising-tube model
(Kosovichev&Stenflo,2008;Kosovichev,2009).
∗Correspondingauthor
Emailaddresses:[email protected](A.V.Getling),[email protected](R.Ishikawa),
[email protected](A.A.Buchnev)
2
Wepostponesummarisingtheweakpointsoftherising-tubemodeltotheconclusivesection
ofourpaperandgivenowonlyanimpressiveexampleoftheobservedfeaturesthatdonotsup-
portthismodel. Thisexamplecanbefoundinthemovieshowingtheso-calledsolar-“trilobite”
magnetogramseries, which was obtainedon the Hinode satellite using the Solar Optical Tele-
scope (SOT) in nearly the same way as the magnetogramsconsidered here (see Kosugietal.,
2007;Tsunetaetal., 2008, andSection3), inDecember2006(NASA,2007). Asnotedinthe
discussionata“LivingwithaStar”workshop(September2007;seethecitedwebpageofNASA
news), these Hinode observations of emergent sunspot 10926 “challenge traditional views of
sunspot formation.” Specifically, the trilobite data show a sunspot-formationprocess differing
from whatoccursif “a ‘rope’of strong magneticfield beachesthe visible surface of the Sun.”
AccordingtoMarcDeRosa(LockheedMartinSolarandAstrophysicsLaboratoryinPaloAlto,
Calif.),whocoinedthenametrilobiteforthefeatureinquestion,“Theemergenceofthesunspot
magnetismprogressedinaverycomplexmanner,withsmallpiecesappearingtoself-assemble
intolarger,morecoherentstructures.”
Indeed,ourinspectionofthe“trilobite”movieshowsthat,althoughspreadingflowsrelatedto
theemergingmagneticfieldcanbenotedinthismovie,theyarefinelystructuredandformcells
resemblingconvectioncellsratherthanauniqueflowsystemonthescaleoftheentiremagnetic
region(seetheupperleftquadrantofFig.1).Furthermore,spreadingflowsareassociatedlocally
with each developingmagneticisland ratherthan “globally”with the entirecomplexmagnetic
configuration (which could be expected if a tube emerged). In its appearance, such spreading
issimilarto theflowaroundaneffervescenttabletonthewatersurface. Anexampleofsucha
“tablet”isthemagneticfeatureintheright-handsideofthemagnetogram,whichresemblesthe
trilobitefossilanimal.1
Thus, the rising-tubemechanismnolongerappearsto determinea paradigmin the investi-
gationofthedevelopmentoflocalmagneticfields. Onthe otherhand,alternativemechanisms
havebeensuggestedintheliterature.
Before mentioning some of them, let us introduce necessary terminological conventions.
While the rising-tube mechanism assumes the original presence of an intense flux tube of the
globaltoroidalmagneticfieldindeeplayers,otherknownmechanismsdonotrequireanystrong
initialfieldensuringsomeinsitu magnetic-fieldamplificationandstructuring. We restrictour-
selvesonlytoprocessesonscalesnolargerthanthesizeofanactiveregion;theywillbereferred
tohereaslocalmechanisms. Ontheotherhand,localprocessesonscalessmallcomparedwith
the granular size, which do not play any decisive role in the formation of active regions, will
alsofallbeyondourscopeofattention. LocalMHDmechanismswithinductiveself-excitation
ofmagneticfieldsstronglycoupledwithfluidmotionsareofparticularinterest,sincethereisa
variety of possibilities for their manifestation undersolar conditions. They are usually termed
local dynamo mechanisms. If the local dynamo action is due to thermal convection, we shall
assignsuchadynamotolocalconvectivedynamos;theywillbediscussedinthenextsection.
TheideaoflocalMHDdynamotracesbacktoGurevich&Lebedinsky(1946),whorelated
theamplificationprocesstotheeffectsofplasmamotions;however,theydidnotattributedthese
motionstoconvectionandevendidnotspecifyanyparticulartypeofmotion.
Kitchatinov&Mazur(2000)investigateda hydromagneticinstabilitythatcanactonscales
large compared to the granular size, producing a magnetic-flux concentration similar to those
observedinsunspots. Theprocesscruciallydependsonthepresenceoffluidmotionandonthe
1Strictlyspeaking,thefeatureresemblingatrilobiteemergedsomewhatlaterthanthemagnetogramshowninFig.1
wastaken.Weusetheword“trilobite”simplyasanidentifierofthewholeseriesofimagesunderdiscussion.
3
Figure2:Tverskoi’storoidaleddywindingamagneticfieldline. Onetoroidalsurfaceofthefamilyformingthevortex
isshownwithamagneticfieldlinethathasaccomplishedfourrevolutionswithfluidparticlesmovingoverthissurface.
Twoantiparallelheavyverticalarrowsmarkthefluxconcentrationsofoppositepolarities(slightlyabove).
quenching of eddy diffusivity by the enhanced magnetic field with the plasma cooling down.
Thisisalocalmechanism,which,however,isnotadynamointhestrictmeaningofthisterm.
Another local mechanism, which also does not qualify as a dynamo, is related to the so-
callednegative-effective-magnetic-pressureinstability(NEMPI),seeWarneckeetal.(2013)and
references therein. It results from the suppression of the total turbulent pressure (the sum of
hydrodynamicandmagneticcomponents)bythemagneticfield.
2. Convectivemechanism: basicideaanditsimplications
Toourknowledge,nolocalMHDdynamomechanismswereconsideredfor20yearssince
the study by Gurevich&Lebedinsky(1946). Tverskoi(1966) was likely the first to suggest a
convective mechanism of local dynamo. He considered a simple kinematic model describing
theformationofamagneticbipolebyanaxisymmetrictoroidaleddyin aperfectlyconducting
fluid, whichheconsidereda schematicrepresentationofaconvectioncell(morespecifically,a
supergranularcellwasmeant). TheactionofTverskoi’smechanismisillustratedinFig.2. The
fluidparticlesmoveincirculartrajectories,concentricinanymeridionalsection.Suchavelocity
field isspecifiedin an orthogonalcoordinatesystemr, ϕ, χ, whereϕ isazimuthalangleandr
andχarepolarcoordinatesinthemeridionalplaneϕ=const. Thefluidvelocityis
V =V =0, V =V (r)[1+(r/a)cosχ]−1,
r ϕ χ 0
where a is the radius of the circle r = 0 and V is an appropriatelychosen function such that
0
V (r) = 0 at any r exceeding a certain value r < a. Obviously, the circles of a given radius
0 0
r =constformatoroidalsurface. OnesuchsurfaceisshowninFig.2. Themagneticfieldlines,
which are initially straight and horizontal, are wound by the fluid motion aroundthe tori; one
magnetic field line is shown in the figure. The solution of the induction equation obtained by
Tverskoicontainsacomponentthatgrowsmonotonicallywithtime. Ifa−r ≪a,themagnetic
0
fieldlinesformtwofluxconcentrations,withoppositelydirectedmagneticfields,inthecentral
partof theeddy. Theyaremarkedin thefigurewith two heavyantiparallelverticalarrowsbe-
low them. The azimuthal arrangementof these concentrationscorrespondsto the direction of
the initialfield. Tverskoi’spredictionwas laterqualitativelyconfirmedbynonlinearnumerical
simulationsof magnetoconvectionin the formof a patternofhexagonal,Be´nard-typecells. In
4
these simulations, the flow was strongly stabilised by the conditions of periodicity in the hor-
izontal directions(Getling, 2001; Dobler&Getling, 2004). The calculated magnetic field was
stronglyamplifiedandformedabipolarstructuresimilartothatfoundbyTverskoidevelopsin
eachconvectioncell. Inaddition,theverticalcomponentofthemagneticfieldwasenhancedin
thecontactzonesbetweenthehexagonalcells,i.e.,intheintercellularlanes.
In essence, Tverskoi has demonstrated that the topology of the flow is very important in
terms of the MHD effects of convection. He conjectured that supergranular convection cells,
interactingwiththeazimuthalcomponentoftheglobalmagneticfield2 innearlythesameway
as such eddies interact with the horizontal initial field, could produce the magnetic fields of
bipolar sunspot groups. In this case, as can be seen from Fig. 2, the east–west orientation of
thebipolarmagneticstructureswouldresultfromtheeast–westdirectionoftheglobalazimuthal
field, with the same arrangementof polarities as in the case of the rise of a tube. The action
ofthismechanismwouldbecontrolledbytheglobalazimuthalmagneticfield, whichprovides
initialconditionsforeachindividualfield-amplificationevent. Thus,Tverskoi’smodelappears
tobeassuccessfulastherising-tubemodelintermsofagreementwiththeglobalpropertiesof
solaractivitysuchastheHalepolaritylaw.
Other local dynamos, which are based on granular and supergranularmotions in the quiet
photosphere, can accountfor fairly disordered magnetic fields on very small scales (Cattaneo,
1999; Vo¨gler&Schu¨ssler, 2007). In essence, only Stein&Nordlund(2012) suggested a con-
vectivemechanismthatcanbeconsideredanalternativetotherising-tubemodel. Theynumeri-
callysimulatedtheformationofanactiveregionviathefluxriseduetoconvectivemotions.The
computedscenarioisnotrelatedtothepre-existenceofacoherentfluxtube.Initially,auniform,
untwisted,horizontalmagneticfieldispresent,whichsubsequentlyformsmagneticloopswitha
widerangeofscales. However,theinitialfieldisrequiredtobefairlystrong,andonlyamoder-
atemagnetic-fieldamplification,byafactorofaboutthree,canbeachieved. Furtherstudiesof
MHDconvectioninthecontextoflocaldynamoweredone,e.g.,byKitiashvilietal.(2013).
Itisnowclear,however,thatTverskoi’sconvectivemechanisminitsoriginalformcanhardly
describetheactualprocesses. Withoutgoingintodetails,we onlynotethefollowing: first, the
stabilityoftheconvectioncellwindingthemagneticfieldlinesiscompletelybeyondthescope
of the model, although stability is of crucial importance for the efficiency of the mechanism;
second,well-developedsunspotgroupsaretypicallylargerthansupergranules.
Nevertheless, Tverskoi’s model, if it is modified in some way, appears to be able to catch
someimportantaspectsoftheprocessesforminglocalmagneticfields. Itcaneasilybeimagined
that especially large and energeticcells sometimesoriginatein the convectionzone and, inter-
actingwiththeglobalazimuthalfield,occasionallygiverisetostrongbipolarmagneticfields. It
isinthisrespectthattheycontrastwiththeubiquitous“normal”supergranules,whichcouldbe
expectedtoproducesmaller-scalefields. Ontheotherhand,theconvectivemechanismcanalso
act on smaller spatial scales, being responsible for the developmentof various local magnetic
features. Itcanalsoactinparallelwiththeprocessofmagnetic-field-linesweeping.
SomestepsweremadetomodifyTverskoi’smechanismsoastoextenditsareaofapplica-
bility. Specifically, simulations of magnetoconvectiondevelopingfrom random initial thermal
perturbationswerecarriedoutforadomainfarexceedingtheexpectedcharacteristicconvection
wavelengthinthehorizontaldirections(Getling,Kolmychkov&Mazhorova,2013,seeFig.3).
Theinitialmagneticfieldwasassumedtobeuniformandhorizontal. Attheinitialevolutionary
2Inthissection,sincewediscussthepropertiesoftoroidaleddies,wedonotusethecommonlyacceptedtermtoroidal
magneticfieldtoavoidterminologicalconfusionsandprefertospeakabouttheglobalazimuthalfield.
5
Figure3: Gray-scalemapoftheverticalmagnetic-fieldcomponent, Bz,inahorizontal planelocatedneartheno-slip
upperboundaryofthecomputationdomaininasimulationrunforaRayleighnumberofRa ≈ 50Rac (whereRac is
thecriticalRayleighnumber),aPrandtlnumberofPr=30,amagneticPrandtlnumberofPrm =300andaHartmann
numberofHa=0.01(Getling,Kolmychkov&Mazhorova,2013).Thedomainmeasures8×8×1.Themagneticfieldis
shownforatimeof10tν(tνbeingthetimeofviscoustransferacrossthelayer);themagnetic-fieldstrengthsrangefrom
−28.5to17.2(intheunitsoftheinitialfieldstrength);atthesametime,thefieldstrengthatthemid-heightofthelayer
rangesfrom−116.7to162.1.
stage, a system of cells develops in the form of irregular polygons. It was shown that cellu-
lar magnetoconvectioncan producebipolar (and also diverse more complex)configurationsof
asubstantiallyamplifiedmagneticfield. Thisoccursbothintheinnerpartsofconvectioncells,
wheremagneticfieldlinesare“wound”bycirculatoryfluidmotion,andinthenetworkformed
by their peripheralregionsdue to the “sweeping” of magneticfield lines. The topologyof the
flowplaysafundamentalroleintheoperationofthismechanism,anditcanbeexpectedthatthe
basicregularitiesoftheprocessshouldmanifestthemselvesinnearlythesamewayondifferent
spatialscales.
Obviously, the manifestations of the rising-tube and convective mechanisms should sub-
stantially differ. The point is to find observational criteria to distinguish between the action
of either of them. With this aim in view, we developed an observational program to study
the evolution of both the velocity and magnetic fields in growing active regions. This pro-
gram (operation plan) is intended for implementation with the SOT on the Hinode spacecraft
(Tsunetaetal., 2008; Suematsuetal., 2008; Shimizuetal., 2008) and has been designated as
HOP181(http://www.isas.jaxa.jp/home/solar/hinode op/hop.php?hop=0181).Itcon-
sists in simultaneous recording and analysing the dynamics of the velocity and magnetic full-
vector fields on the photospheric level. We present here some preliminary, purely qualitative
resultsofprocessingthedataobtainedataninitialimplementationstageoftheprogram.
3. Observationsanddataprocessing
TheobjectofobservationswasthebipolarmagneticstructurethatemergedwithinAR11313
duringtheearlyevolutionofthisstructure,on9–10October2011;theregionwasthennearthe
centreofthesolardisc. Five2-h-longobservationalsessionswerecarriedoutwithintervalsthat
variedfrom3h40minto6h30min.
6
Duringeachsession,a150′′×163′′fieldofviewwasobservedusingtheNarrowbandFilter
Imager (NFI) of the SOT at two wavelength positions of FeI λ5776 Å with a time cadence of
2minandapixelsizeof0.16′′. Thisyieldedaseriesofphotosphericimages,whichcanbeused
to calculate horizontal velocities,3 and a series of Dopplergramsrepresenting the line-of-sight
velocities. Simultaneously, the same FOV was scanned with the Spectro-Polarimeter(SP; see
Ichimotoetal.,2008;Litesetal.,2013)oneortwotimesasession. TheSPscanwasdoneinthe
so-calledfast modewith a pixelsize of0.32′′, taking32minto obtainoneSPmap. To derive
full-vector magnetic fields from these SP observations, we used the MERLIN inversion code
(Litesetal.,2007),whichassumedaMilne–Eddingtonatmosphere. Atthisinvestigationstage,
however,wedidnotusedatafortheline-of-sightvelocityandtangentialmagneticfield.
Theprocessingofthedataincluded:
(1) subsonicfilteringbasedonFastFourierTransform;
(2) constructingDopplergrams;
(3) an intensity-scaling procedureenhancing the image contrast by means of cutting off the
tailsofapixel-intensityhistogramandsubsequentlinearmappingoftheremainingportion
ofthehistogramtothewholeadmissibleintensityrange;
(4) alignment of the images and Dopplergramsof each series with one another and, after a
properspatialscaling,withthemagnetogram;
(5) determinationofthehorizontal-velocityfieldusingatechniquebasedonthesameprinciple
asthestandardlocal-correlation-tracking(LCT)methodbutmorereliable(seeGetling&Buchnev,
2010, for a description) and construction of cork-motion maps. This technique differs
fromthestandardLCTprocedureinaspecialchoiceoftrialareas(“targets”),whosedis-
placementsaredeterminedbymaximizingthecorrelationbetweentheoriginalandvarious
shiftedpositionsofthetarget.Specifically,anareaischosenasatargetinacertainneigh-
borhoodofeachnodeofapredefinedgridifeitherthecontrastortheentropyofthebright-
nessdistributionreachesitsmaximuminthisarea. Thehorizontalvelocitiesobtainedare
then interpolatedto the positionsof imaginary“corks” using the Delaunay triangulation
and affine transformations specified by the deformation of the obtained triangles at the
timestepconsidered.
The maps obtained at step (5) represent the trajectories of imaginary “corks” that follow
thevelocityfieldinferredfromaseriesofimagesandattributed,tosomeapproximation,tothe
materialflow. We comparedthe trajectorymapswith the mapsof the magneticfield fortimes
closetothemid-timesofthecorrespondingseries.
Samples of the maps, which were qualitatively compared, are shown in Fig. 4. For each
session, acontrast-enhancedFeIλ5576Åimage,acork-trajectorymapandamapoftheline-
of-sightmagneticfieldarepresented. Thetrajectoryofeachcorkinavelocitymapstartswitha
blackdotandterminatesatabrightwhitedot.Inmostcases,the2-hlengthofthesessionissuf-
ficientforthecorkstoreachstagnationsegmentsoftheirtrajectories,wherethecorksnolonger
move over the photosphericsurface. The stagnation segments should obviouslycorrespondto
downflowareasinthevelocityfield.
3Sincetheareaofinterestwaslocatednearthesolar-disccentreand,moreover,correctionsforprojectioneffectsare
notimportantfromthestandpointofourgoal,wedonotmakedifferenceherebetweenthetransversal(tangential)and
horizontalvectorcomponentsandalsobetweentheline-of-sightandtheverticalcomponent.
7
(a) (b)
Figure4:Comparisonofintensitymaps(top),horizontal-velocityfields(middle)andline-of-sightmagnetograms(bot-
tom)obtainedduringthefirst(a)andthird(b)observationalsessions(at18–20hof9Octoberand06–08hof10October
2011,respectively;theintensitymapsandmagnetogramsweretakenatthemid-timesoftheseintervals).Thetrajectory
8
ofeachcorkinthevelocitymapstartswithablackdotandterminatesatabrightwhitedot. Lightanddarkareasinthe
magnetogramscorrespondtotwosignsofthemagneticfield.
4. Results
Ascan beseen froma comparisonbetweenthetoppanelsofFigs4a and4b, a fairlylarge
bipolarsunspotgrouphasalreadyformedintheareaunderstudybythetimeofthefirstobserva-
tionalsession.Atnearlythesametime,anewgroupstartsdevelopingbetweenthemainspots,in
thelefthalfofthefieldofview.Thisprocessbecomesmainlyaccomplishedbythethirdsession
(Fig.4b).
ThemiddlepanelsofFigs4aand4brepresentthevelocityfieldbymapsofcorktrajectories.
To make some features of the flow better distinguishable, the velocity map of Fig. 4a is addi-
tionallypresentedhereinanenlargedforminthetoppanelofFig.5togetherwithaschematic
outline of the most pronounced features in the bottom panel, both being plotted on the same
scale. In the velocity maps, severalareas of local divergentflows apparentlycorrespondingto
supergranulescan be identified; fourof them are markedwith closed short-dashedcontoursin
thebottompanelofFig.5. Thesesupergranule-sizedflowsareverysimilarintheirappearance
to “normal”supergranularflowsin thequietphotosphereasdetectedusingthesame technique
(Getling&Buchnev,2010,Fig.2)
A carefulconsiderationofthe two velocitymapsrevealsneitheranyspreadingflow on the
scaleofthedevelopinggroupnoranyflowsmoreintensethannormalsupergranularconvection.
Thisisespeciallyevidentfromthecork-trajectorymapofthefirstsession(middlepanelofFig.4a
andupperpanelofFig.5),whichcorrespondstoanearlydevelopmentstageofthenewsunspot
group. Atthisstage, a large-scalespreadingflow wouldbewellpronouncedin the case ofthe
emergenceofastrongfluxtube.However,nolarge-scaleoutflowfromthelocationofdeveloping
group can be foundin the map; in contrast, local spreadingflows on meso- and supergranular
scalesunaffectedbyanylarge-scaledisturbancesareobserved.
As concerns the maps for the third session (Fig. 4b), a stream seemingly related to the
newly formed magnetic feature can be seen in the central part of the middle panel. It issues
from the vicinity of the point with coordinates of (50 Mm, 60 Mm) in the middle panel of
Fig.4b,ismainlydirectedrightwardanddoesnotresembleaspreadingflow.Themagnetogram
inthebottompanelofthesamefigureexhibitsfaintsignsofsmall-scalecellularstructuringof
the magnetic field on the left of the field-of-viewcentre, within the area where the new active
processes occur. Such structuring is hardly compatible with the idea of flux-tube emergence.
Thisisadditionalevidenceagainstthepresenceofaspreadingflowthatcouldbeassociatedwith
the emergenceof an Ω-shapedloop of intense magnetic-fluxtube, all the moreso because the
emergenceprocesswouldmainlyhaveterminatedbythattime.
Inthevelocitymaps,brightcurvesstretchingoverlongdistancescanbedistinguished,which
appear as condensationsof the end segmentsof the cork trajectories approachingthese curves
from two sides, i.e., as separatrices between oppositely directed flows. Two such curves are
shown as solid curves in the scheme of Fig. 5, bottom. Quite likely, they are merely due to
aggregatevisualeffectsofcentrifugalflowsindifferentsupergranules;however,eveninthiscase,
thispatterndisagreeswiththevelocityfieldthatcouldbeexpectedinthecaseofemergenceof
anintensefluxtube.
Apart from our discussion of the formation mechanisms for strong local magnetic fields,
it is interesting that our trajectory maps reveal some details of flow structure related to well-
developedsunspots. Althoughthebrightnessinhomogeneitiesin the umbrasofthe main spots
are not distinguishable by eye, they are nevertheless sufficient to visualise the structure of the
velocityfield. AsFig.4indicates,thereareflowsconvergingtotheumbracentres. Atthesame
time,divergingflowscanbeseenaroundthesespots.
9
10
Figure5:Top:enlargedmapofthehorizontal-velocityfieldshowninthemiddlepanelofFig.4a;bottom:schematicout-
lineofsomefeaturespresentinthismap,viz.,linesofconvergence(solidcurves),contoursofareasoccupiedbysunspot-
relateddivergentflows(long-dashedcurves)andcontoursofmostpronouncedsupergranules(short-dashedcurves).
