The Quasi-Biennial Periodicity (QBP) in velocity and intensity helioseismic observations

0.36 MB·English

by  R. Simoniello

Astronomy&Astrophysicsmanuscriptno.rsimoniello˙man˙v3 (cid:13)c ESO2012
January16,2012
The Quasi-Biennial Periodicity (QBP) in velocity and intensity
helioseismic observations
The seismic QBP over solar cycle 23
R.Simoniello1,W.Finsterle1,D.Salabert2,R.A.Garc´ıa3,S.Turck-Chie`ze3,A.Jime´nez4,andM.Roth5
1 PMOD/WRCPhysikalisch-MeteorologischesObservatoriumDavos-WorldRadiationCenter,7260DavosDorf,Switzerlande-mail:
[email protected],[email protected]
2 2 Universite´ deNiceSophia-Antipolis,CNRSUMR6202,ObservatoiredelaCoted’Azur,BP4229,06304NiceCedex4,France
1 e-mail:[email protected]
0 3 LaboratoireAIM,CEA/DSM-CNRS-Universite´ParisDiderot;CEA,IRFU,SAp,centredeSaclay,F-91191,Gif-sur-Yvette,France
2 e-mail:[email protected],[email protected]
4 IAC,InstitutodeAstrofis´ıcadeCanarias,38205,LaLaguna,Tenerife,Spaine-mail:[email protected]
n 5 KiepenheuerInstituteforSolarPhysics,Freiburge-mail:[email protected]
a
J Received9September2011/Accepted12January2012

3
1 ABSTRACT

] Aims.WelookedforsignaturesofQuasi-BiennialPeriodicity(QBP)overdifferentphasesofsolarcyclebymeansofacousticmodes
R
ofoscillation.Low-degree p-modefrequenciesareshowntobesensitivetochangesinmagneticactivityduetotheglobaldynamo.
S Recentlyhavebeenreportedevidencesinfavoroftwo-yearvariationsinp-modefrequencies.
. Methods.Long high-quality helioseismic data are provided by BiSON(Birmingham Solar Oscillation Network), GONG (Global
h
OscillationNetworkGroup),GOLF(GlobalOscillationatLowFrequency)andVIRGO(VariabilityofSolarIRradianceandGravity
p
Oscillation) instruments. We determined the solar cycle changes in p-mode frequencies for spherical degree ℓ=0, 1, 2 with their
-
azimuthalcomponentsinthefrequencyrange2.5mHz≤ ν ≤3.5mHz.
o
r Results.WefoundsignaturesofQBPatalllevelsofsolaractivityinthemodesmoresensitivetohigherlatitudes.Thesignalstrength
t increaseswithlatitudeandtheequatorialcomponentseemsalsotobemodulatedbythe11-yearenvelope.
s
a Conclusions.ThepersistentnatureoftheseismicQBPisnotobservedinthesurfaceactivityindices,wheremid-termvariationsare
[ foundonlytimetotimeandmainlyoverperiodsofhighactivity.Thisfeaturetogetherwiththelatitudinaldependenceprovidesmore
evidences infavorof amechanism almost independent anddifferent fromtheonethat bringsup tothesurface theactiveregions.

1 Therefore,thesefindingscanbeusedtoprovidemoreconstraintsondynamomodelsthatconsiderafurthercycliccomponentontop
v ofthe11-yearcycle.
3
7 Keywords.Methods:dataanalysis-Sun:helioseismology-Sun:activity
7
2
1. 1. Introduction in the polar region and weaker around the equator and more
0 overtheperiodicityfromnorthernandequatorialregions(≈2.8
2 Evidencesin favor of shorter periodicitiesthan the 11-yearpe- years)isdifferentfromtheoneinsouthernregions(≈1.5years).
1 riod, ranging from days to years in solar activity proxies, are More recently the same authors, investigating a longer dataset
: verywellknowninliterature.Forshort-terms,theSunoftenex- recorded from 1939 to 2005, concluded that the non-constant
v
i hibits 27-day and 13.5-day periodicities, while the regime be- period lengths is the manifestation of a unique quasi-biennial
X tween days and 11 years are referred as mid-term periodicities activitycycle(Vecchioetal.,2009).
r (Bai, 2003). Among these, particularly prominent are the ones Sincethediscoveryofthecorrelationbetweentheobserved
a
between1.5-4years(Vecchioetal.,2009).Wewillrefertothem global acoustic mode (p-mode) parameters and the solar mag-
as Quasi-Biennial Periodicity (QBP). This phenomenon has netic activity cycle (e.g. Woodard&Noyes, 1985; Palle´etal.,
been observed in radio flux on 10.7cm (Belmontetal., 1996), 1989;Elsworthetal.,1993),itbecameevidentthattheacoustic
total solar irradiance (Penzaetal., 2006), flares and sunspots modescanalsobeusedasadiagnostictoolofthesolarcycle.In
(Akioka,1987;Mursulaetal., 2003;Valde´s-Galicia&Velasco, particular with high-quality and continuous helioseismic data,
2008) and green coronal emission line (Vecchio&Carbone, deeper analysis revealed that mode amplitudes are suppressed
2008; Vecchioetal., 2009). It also seems to appear only time with increasing magnetic activity, while mode frequencies are
to time tending to be more important over periods coinciding shifted towards higher values as the solar cycle approaches its
with solar maxima and are not recognized as typical feature maximum at low and high-angular degree (Howeetal., 1999;
of every cycle (Krivova&Solanki, 2002; Knaacketal., 2004; Kommetal., 2000; Jime´nez-Reyesetal., 2001; Chaplinetal.,
Cadavidetal.,2005;Lietal.,2006).ThissuggeststhattheQBP 2001; Salabertetal., 2004; Salabert&Jime´nez-Reyes, 2006;
might be closely linked to the strength of the global dynamo. Simonielloetal.,2010).Whileforthemodeamplitudesapossi-
Coronal data have shown a latitudinal dependence of the sig- bleexplanationintermsofmodeconversionhasbeenprovided
nalstrength(Vecchio&Carbone,2008).Itisparticularlystrong (Simonielloetal., 2010), we still lack the basic understanding
1
R.Simonielloetal.:QBPfromhelioseismicobservations
of the mode frequency shift. F-modes can help to understand mic QBP occurs only time to time and during periods of high
this variability and the confrontation of observations to pre- activity. Furthermore we carried out this analysis for each of
dictions seem to show some structural effects (Lefebvreetal., the sectoral(m=ℓ) and zonal (m=0)componentsof low-degree
2009).Unfortunately,aproperintroductionofsub-surfacemag- modes(withoutaveragingoverthe azimuthalcomponents)and
netic field is still lacking. So this does not allow to properly thisisthenoveltyoftheworkwithinthistopic.Wealsoinvesti-
estimate the structural consequences of this important factor. gatedifandtowhichextentthemid-termperiodicityislinkedto
The form and the degree dependence of the shifts, anyway fa- the appearanceof active regionsinduced by the main dynamo.
vor near-subsurface phenomenon, but however they cannot be To this aim we carried out a correlation analysis between each
purely explained by structural changes, the magnetic field is azimuthal(m)-componentsoflow-degreemodefrequenciesand
somehow involved in the mechanism (Goode&Dziembowski, activityindiceslinkedtostrongand/orweakmagneticfieldsover
2002; Dziembowski&Goode, 2004). Recently the argument differentphases of solar cycle 23. It is importantto investigate
that the solar cycle variation in the global mode frequency are the phasewise variation in correlation between low-ℓ frequen-
due to the global averaging of active regions (Hindmanetal., ciesandactivityindicesaswell,becauseearlierstudyofthem-
2001) has been only partially supported by the observations components were confined to intermediate degree modes only
(Tripathyetal., 2010). It has been argued that the weak com- (Jainetal., 2009). Furthermore, acoustic waves, depending on
ponentofthemagneticfield(turbulentorhorizontalfield)must theirsphericaldegreeandazimuthalcomponent,aremoresensi-
betakenintoaccountinordertofullyexplaintheobservedmode tivetolow-midlatitudesorhigherlatitudes.Thereforetheanal-
frequencyshift. ysisoftheazimuthalcomponentsallowedusalsotohavesome
Recentobservationsin p-modefrequencieshavealsoshown hints on the role playedby strongand/orweak fields with lati-
the presenceof a 2-yearmodulationmostprominentoverperi- tudesassourcesoftheQBP.
ods coinciding with solar maxima. The properties of the seis- Theseismicinvestigationofthemid-termperiodicitymight
mic QBP have been interpreted as the visible manifestation of help us to gain a deeper insight on the globalpropertiesof the
aseconddynamomechanism(Benevolenskaja,1995,1998a,b), Sunasforexampleonthesolardynamotheoryaswellasonstel-
induced by the strong latitudinal shear located below the sur- larcycles:mid-termperiodicitieshavealreadybeenobservedin
faceat≈0.95solarradius(Schouetal.,1998).Theseconddy- fast rotator stars and therefore the better understanding of this
namoitselfcannotexplaintheobservedmodulationinthesignal shortperiodicbehaviorintheSunmighthelpilluminatethein-
strength and therefore it has been supposed that when the 11- terpretationofthissignalofsolar-likestars.
yearcycleisinitsstrongphase,buoyantmagneticfluxaresent
upward by the main dynamointo shallower layers, thus allow-
2. Helioseismicdataanalysis
ingtheseismicQBPtobemainlydetectedoverperiodsofsolar
maxima(Fletcheretal.,2010).Howeveritisstillamatterofde- 2.1.Modevisibility
bateifthisseconddynamomechanismisindeedbehindtheQBP
Low-degreemodesaredetectedeitherinSun-as-a-starobserva-
observedinactivityproxiesandinsolarseismicdata.Infact,re-
tionsorthroughhighlyspatiallyresolvedimages.Inthefirstsce-
centobservationsofrapidlyrotatorstarshaveshownsignatures
nariothemodesareobservedinaveragesmadeoverthevisible
ofQBP, whosestrengthincreaseswith increasingmagneticac-
diskofDopplervelocityorintensityvariations.Inthiscaseonly
tivityanditgetsstrongeratpolarregions.Ithasbeensupposed
the modes that satisfy the condition ℓ +m = even are visible,
thattheunstablemagneticRossbywavesinthetachoclinemight
becauseofthenear-perpendicularinclinationoftheSunwithre-
bebehindit(Zaqarashvilietal.,2010,2011).Ifthisisalsotrue
spect to the Earth.In observationswith high spatial resolution,
forsolartypestarisstillanundergoinginvestigation.
thevisiblediskissampledinmanypixelsandthecollectedim-
Thep-modespatialconfigurationcanbedescribedbyspher-
agesaredecomposedintotheirconstituentsphericalharmonics,
icalharmonicswitheachmodebeingcharacterizedbyitsspher-
givingaccesstoall2ℓ+1componentforeachdegree.
icalharmonicdegreeℓandazimuthalorderm.Modeswithℓ≤3
arenamedlow-degreemodesandconverselytosurfaceactivity
indices,theyalso soundtheinterioroftheSunbeingshapedin 2.2.Sun-as-a-starobservationsfromgroundbasednetwork
deeperlayers.Thereforetheymightfeelmagneticchangesthat
have yet to manifest at the surface or it might also be possible Birmingham Solar Oscillation Network (BiSON) has been op-
thatthedisturbanceswillneverreachtheSun’ssurface.Byav- erating since 1976 and makes unresolved solar disc observa-
eragingtheindividual p-modefrequencyshiftsoveralllow(ℓ)- tions.Itconsistsof6resonantscatteringspectrometers,thatper-
values, observational findings pointed to seismic signatures of form Doppler velocity measurementsin integratedsun light of
QBPoverthelongextendedminimumcharacterizingtheendof theKFraunhoferlineat7699Å(Chaplinetal.,1995).Thedata
solarcycle23andbeginningofsolarcycle24(Broomhalletal., are dominated by the Doppler variations from the low-degree,
2009a; Fletcheretal., 2010). Further evidencesin favor of this ℓ, modes. The nominal height is at ≈260 km above the photo-
feature have been reported in low-degree modes by investigat- sphere (e.g. Jime´nez-Reyesetal., 2007). We analyzed the data
ing the spherical degree dependence (Broomhalletal., 2011), providedbyBiSONinstrumentsfrom11thApril1996to4thof
but some authors have cast doubts, because they didn’t spot April2009.Thislongdatasetwassplitintocontiguous365-day
any significant trend during periods of low activity (Jainetal., serieswithfouroverlapsof91.25days.Estimatesofthe p-mode
2011).Wedecided,therefore,toinvestigatethepropertiesofthe frequenciesforℓ=0,1,2wereextractedfromeachsubsetbyfit-
seismicQBPbyusingseveralhelioseismicinstrumentsinveloc- ting a modified Lorentzian model to the data using a standard
ity and intensity data coveringa period that goes from the end likelihoodmaximizationmethod(Fletcheretal.,2009).
of solar cycle 22 up to the beginning of solar cycle 24. Each
observational program can provide more stable and/or accu-
2.3.Sun-as-a-starobservationsfromspace
rate data depending on instrumental features (Broomhalletal.,
2009b; Salabertetal., 2011). Thereforeby comparingdifferent The GlobalOscillationat Low Frequency(GOLF)instrument,
observationswehavebeenabletocheckwhetherornottheseis- onboardtheSOlarandHeliosphericObservatory(SOHO)satel-
2
R.Simonielloetal.:QBPfromhelioseismicobservations
lite, is devoted to the search of low-degree modes (Gabriel et
al. 1995). It works by measuring the Doppler shifts of the Na
lineat5889Å(D1)and5896Å(D2).Duetothemalfunctioning
of the polarization system, GOLF is working in a single-wing
configurationandithasbeenprovedthatitisalmostapureve-
locitysignal(Palle´etal.,1999).Theone-wingconfigurationhas
beenchangingduringthe14yearsofobservationsasfollows:1)
1996-1998inthe blue-wingconfiguration;2) 1998-2002in the
red-wingconfiguration;3)uptodayintheblue-wingconfigura-
tion(Ulrichetal.,2000;Garc´ıaetal.,2005).
Due to the formation heights of the spectral lines, in the
blue-wingconfiguration,GOLFobservesat ≈330km, while in
the red-wing configuration at ≈480 km (Jime´nez-Reyesetal.,
2007). Although the changing observational height affects the
p-modeamplitudedetermination(Simoniello&Salabert,2009;
Simonielloetal.,2010),itdoesn’taffectthe p-modefrequency.
Fig.1.Solarcyclechangesinp-modefrequencyshifts(µHz)for
WeanalyzedthedataprovidedbyGOLFinstrumentsfrom11th ℓ=0, 1, 2 from VIRGO (green), BiSON (black), GONG (pur-
April 1996 to 4th of April 2009 and the estimates of p-mode
ple)andGOLF(blueandredtoidentifythecorrespondingwing
frequency shifts have been extracted by applying the same fit-
configuration)observationsoversolarcycle23andbeginningof
ting method as in BiSON. This differs from the one applied to
solarcycle24.
VIRGOandGONGℓ=0integrated.We, therefore,verifiedthat
bothfittingsmethodsreturnedconsistentresults.
The Solar PhotoMeters (SPM) of the Variability of so-
GONG webpage between the 29th of June 1995 and the 24th
lar IRradiance and Gravity Oscillations (VIRGO) package
of December 2009. Very few outliers were removed from the
(Fro¨hlichetal.,1995,1997)aboardSOHOsatellite,consistsof
followinganalysisusingthequalityflagsprovidedbytheGONG
three independent photometers, centered around 402, 500 and
team.
862 nm (the blue, green, and red channel respectively). They
measure the spatially integrated solar intensity over a 5 nm
bandpass at a one minute cadence. The data obtained by the 2.5.Frequencyshiftdetermination
VIRGO/SPM instrument over the mission have been of uni-
formlyhigh quality, whetherbefore or after the loss of contact Thetemporalvariationsofthe p-modefrequenciesweredefined
withthespacecraftforseveralmonthsin1998.Eachoneofthe as the difference between the frequenciesof the corresponding
three differentsignalsobservesthe Sun-as-a-staroscillationsat modesobservedatdifferentdatesandreferencevaluestakenas
differentheightsinthesolaratmosphere(Jime´nezetal.,2005). theaverageovertheyears1996-1997.Theweightedaveragesof
these frequency shifts were then calculated between 2500 and
The data provided by VIRGO instruments cover almost
3500µHz.Furthermoreforeachsphericaldegreetheshiftsfrom
14 years of data, starting on the 11th April 1996 up to 8th
the VIRGO green, blue and red channels have been averaged.
April 2010. This dataset was split into contiguous 365-day
Theshiftsforeachsphericaldegreewiththesame|m|obtained
with four overlapsof 91.25days. The power spectrum of each
bytheazimuthalanalysisofGONGhigh-resolveddatahavealso
subseries was fitted to estimate the mode p-mode parameters
beenaveraged.
for ℓ=0,1,2 using a standard likelihood maximization function
(Salabertetal., 2007). Each mode componentis parameterized
usingaasymmetricLorentzianprofile. 3. QBPsignaturesin p-modefrequenciesoversolar
cycle23
2.4.High-resolvedobservationsfromgroundbasednetwork
3.1.SphericaldegreedependenceoftheQBPoverthe
11-yearcycle
The Global Oscillation Network Group (GONG) consist of
six instruments deployed worldwide to provide nearly contin- We looked for the existence of QBP signatures in p-mode fre-
uous and stable velocity images of the Sun. GONG instru- quencyshiftsoverthe11-yearcycle.Fig.1showsthespherical
ment is based on a Michelson interferometer called a Fourier degree dependence of the shift as seen from VIRGO, BiSON,
Tachometer (Beckers&Brown, 1978). It works by using the GONG and GOLF datasets. We introduced an artificial offset
Ni line at 676.8nm and the observational height is approx- between the curves to better compare the seismic features. We
imately at 213 km. The network started to be fully operat- can spot several seismic signatures that might be linked to the
ing since May 1995. Time series of 36 days (the so-called QBPsignal:
GONG month) are produced and the individual frequencies - for ℓ=0 modes over the minimum of solar cycle 22 and
of the azimuthal components are determined up to ℓ = 150 beginning of solar cycle 23 (1995-1997), GONG observations
over subseries of 108 days by concatenating three GONG show a seismic signature of a QBP. Following the ascending
months. These frequenciesare afterwardsmade publicly avail- phase of solar cycle 23 in BiSON and GONG, between 1997-
able(http://gong2.nso.edu/archive/). 1999,wefindafurthermodulationofabout2years.Thissigna-
Theℓ=0GONGtimeseriesbetweenMay7th1995andMay turedoesn’tappearinGOLFandVIRGOdata,probablydueto
3rd2008wasanalyzedinasimilarmannerasforVIRGOdata, the loss of SOHO in June 1998.During the maximumof solar
returningestimatesofthemodefrequenciesofℓ=0,1,2.Inorder activity the modes show up with a clear double peak structure
toanalyzetheazimuthalcomponentsindividually,wemadeuse in all datasets. Over the descending phase BiSON, GOLF and
of the frequencytables of the ℓ= 1,2 modesavailable from the VIRGOagreequitewell,showingthesamedownwardtrendnot
3
R.Simonielloetal.:QBPfromhelioseismicobservations
characterized by any modulation. GONG data, instead, shows
anoscillatorysignalaroundDecember2003.Towardstheendof
solarcycle23andbeginningofsolarcycle24(2006-2009),we
observeaQBPinalldatasetalthoughinGOLFandVIRGOdata
areparticularlyprominent;
-inℓ=1modestherearenotracesofQBPovertheascending
phaseinBiSON,GOLFandVIRGOdata.InsteadGONGshows
a modulation around July 1998. Over the maximum phase we
foundacleardoublepeakstructureinalldataset,butinGONG
is more pronounced. In GONG, BiSON and GOLF, over the
descending phase, we might spot two further modulations be-
fore December 2003 and before September 2006. that are in-
steadabsentinVIRGOdata.Overthelongextendedminimum
ofsolarcycle23onlyVIRGOshowsa furtherperiodicityafter
September2006;
-inℓ=2modeswefoundovertheminimumofsolarcycle22
andbeginningofsolarcycle23(1995-1997)aseismicsignature
of a QBP from GONG observations. We found the same sig-
nature in GONG data in ℓ=0 mode. Over the ascending phase,
a strong peak of almost 2-year length around 1998 in VIRGO
Fig.2.Solarcyclechangesinp-modefrequencyshifts(µHz)for
andGOLFdataispresent.Thissignalmightbeanartefactdue them-componentsofℓ=1,2modesasseenfromGONGobser-
to the loss of the satellite between June and September 1998.
vations.
Over the maximum phase we founda doublepeak structure in
BiSON,GONGandGOLFobservations.Thedescendingphase
ischaracterizedbyaverywellmodulatedsignalofabout2years,
although in BiSON, GOLF and VIRGO is more pronounced. FurthermorethepresenceoftheQBPsignaloverperiodsoflow
During the minimumof solar cycle 23, we spotin BiSON and activity is not peculiar of solar cycle 23, as guessed by some
GOLF data a clear signature of a furtherperiodicitystarting in authors(Fletcheretal.,2010).
September2006andendingbeforeJune2009.
In summary we foundsignatures of biennial modulationin
3.2.AzimuthaldependenceoftheQBPoverthe11-year
allobservationalprogramme,buttherearedifferencesinthedata
cycle
sets.Thesignalstrengthofmid-termvariationsisweakercom-
paredtothe11-yearsignal.Inarecentpaperthemodevisibility We used GONG data to look for QBP signal in the azimuthal
inGOLFdataappearsdifferentinthetwowing-configurations, components of the dipole (ℓ=1) and quadrupole (ℓ=2) mode.
being slightly better during red-wing period (Salabertetal., Fig.2showsthesolarcyclechangesinp-modefrequencyshifts.
2011). This might explain why the faint signal of the QBP is The sectoral components exhibit a stronger 11-year envelope
lessprominentinGOLFdata.Forintensityobservationsfurther compared to the zonal ones. This finding clearly confirms the
aspects need to be taken into account, like the selection of the differentsensitivityofthemodestomagneticchangeswithlati-
spectralregionintheobservationsthataffectthemodevisibility tude.Theℓ=1,m=0seemstoshowamid-termperiodicityover
ofthemodesinphotometricmeasurements(Nuttoetal.,2008). theendofsolarcycle23withanupwardtrendstartingsoonafter
Furthermore the continuum intensity data samples a different September2006.Ifwelook,instead,atℓ=1m=1component,we
(i.e.deeper)regionwherethetemperaturevariationsinducedby spotthedoublepeakstructureoverthemaximumofsolaractiv-
theacousticoscillationsmaybequitesmall. ityasalsoobservedinintegratedsunlightobservations.Afurther
By analyzing the spherical degree dependence of p-mode mid-termperiodicityseemstooccuracrossSeptember2006,and
frequencyshift,wedetectedlikelysignaturesofthe2-yearperi- the same structure appears in GONG (integrated) and BiSON
odicityatall levelsof solaractivity,instead surfaceactivityin- data. Looking at both m-components of the quadrupole mode,
dicesmainlyshowitoverperiodscoincidingwithsolarmaxima. thesolarmaximaisalsocharacterizedbythetypicaldoublepeak
We also noticed that away from the solar maximum, the QBP structure.Thenoverthedescendingphase,them=2component
showsupineachlowdegreemodeoverdifferentperiodsofso- shows one smoother signature of QBP across September 2006
laractivityphase.Thisresultsfromthedifferentspatialconfig- as in ℓ=1, m=1. The zonal component,instead, seems to show
urationofthemodesoverthesolardisk.Forexample,wefound a further periodicity starting soon after September 2006 as we
seismicsignaturesoverthelowactivityphaseinthemodesℓ=0, already found in the mode ℓ=1, m=0. Therefore the azimuthal
2butnotinthedipolemodeℓ=1.Inintegratedsunlightobserva- analysis bringsmore evidencesthat overthe minimumactivity
tionsduetothemodevisibility,theobservedℓ=1frequencyisa phase of solar cycle 23 the QBP might have occurred at high
weightedmeasurementofthevisiblecomponents(ℓ=1,|m|=1), latitudes.
while in the case of the ℓ=2 mode, the fitted frequency corre-
sponds to the weighted measurement of the zonal (ℓ=2, m=0)
4. LatitudinaldependenceoftheQBPsignal
and sectoral ( ℓ=2, |m|=2) components (Jime´nez-Reyesetal.,
2004). The spatial structure of the oscillation means that the strength
sectoral|m|=ℓaremoreconcentratedaroundequatoriallatitudes
4.1.ModulationintheQBPsignalstrength
than the zonalcomponents(m=0),and is particularlytrue with
increasing ℓ (Christensen-Dalsgaard, 2002). As consequence To better reveal the seismic signatures of the QBP signal, we
the contribution to the QBP signal over the minimum activity took out the 11-year dependence by using a boxcar of 2.5
might have its origin at higher latitudes (Salabertetal., 2009). years,asalreadydonein(Fletcheretal.,2010).Fig.3showsthe
4
R.Simonielloetal.:QBPfromhelioseismicobservations
Fig.4. The QBP signalin the zonaland sectoralcomponentof
thedipoleandquadrupolemodefrequencyshiftsafterthedom-
Fig.3. The QBP signal in each low-degree p-mode frequency inant11-yrsignalhasbeenremovedfromGONGhigh-resolved
shifts after the dominant 11-yr signal has been removed. The observations.
colorlegendisthesameasFig.1.
4.2.QBPsignalstrengthoverhighandlowactivityphase
The zonal and sectoral components of the quadrupole mode
changes in p-mode frequencyshifts due to the presence of the show clear signatures of the QBP signal over periods coincid-
QBP signal for ℓ=0, 1, 2 over solar cycle 23. GONG, BiSON, ingwithsolarmaxima.Bycomparingthepeak-amplitudeofthe
VIRGO and GOLF observations point to a modulation of the m-components over this activity phase, the signal seems to be
signalstrength in phase with the solar cycle in agreementwith of comparable strength at different latitudes. But as the strong
previousfindings(Fletcheretal.,2010;Broomhalletal.,2011). magnetic fields are confinedat low-mid latitudes, the compari-
Italsoseemsthatthemodulationaffectsmoretheℓ=1,2modes sonshouldbecarriedoutoverperiodsoflowactivity,whenthe
compared to ℓ=0. This is a further evidence of the higher sen- magnetism of the Sun at low as well as high latitudes is dom-
sitivity to low-mid latitudes of the sectoral modes. Therefore inated by weak fields. To this aim we might attempt to com-
we might also argue that the observed QBP signal in the sec- parethestrengthofthepossiblesignaturesoftheQBPsignalwe
toralmodesmightcomemainlyfromlow-midlatitudes.If itis found over the years 2006-2009.For the quadrupolemode the
indeed the case, the signal at equatorial regions is of compa- strengthislargerforthem=0comparedtom=2componentand
rable strength (or even larger) to the QBP signal produced at thesamefeatureoccursinthedipolemode.Asconsequencethis
high latitudes. This conclusion won’t be correct at this stage. might be a further hint that the QBP signal at high latitudes is
The magnetic field, depending on its strength and inclination largerthantheoneatlow-midlatitudes.
(Schunker&Cally,2006),affectsthesizeoftheacousticcavity,
wherethemodepropagates.Butastheacousticcavitydecreases
4.3.InvestigatingthesignificanceoftheQBPsignaturesover
when the spherical degree increases, therefore, to get informa-
solarcycle
tion on the strength of the signal coming at different latitudes,
we have to compare sectoral and azimuthal componentsof the Evidences in favor of QBP have been found in all the
same spherical degree. Fig. 4 shows the QBP signal over so- modes. In order to investigate their significance, we ap-
larcycle23forthem-componentsofthedipoleandquadrupole plied the wavelet analysis developed by Torrence and Compo
modes.Theresidualsforℓ=1,m=0mightindicatethepresence (Torrence&Compo,1998)tothesphericalandazimuthalcom-
ofaQBPacrossJuly1998andsoonafterSeptember2006.Ifwe ponentsofthemodes.WeshowtheresultsonlyforGONGob-
look,instead,atℓ=1m=1component,wespotanice-increasing servations,asthefindingsforthesphericaldegreeanalysisfrom
trend in the signal strengthof the QBP overthe ascendingand the different datasets are in good agreement. Fig. 5 shows the
maximumphaseofsolarcycle23.Afurtherperiodicityseemsto wavelet analysis carried out for each spherical degree. Within
occuracrossSeptember2006,andthesamestructureappearsin the cone of influence the local wavelet power spectrum identi-
GONG(integrated)andBiSONdata.Lookingatthezonalcom- fies theQBP signaloverthe years1998-2004of solarcycle23
ponentof ℓ=2, we find over the solar maxima the typical dou- in all low-degree modes. The significant periodicity at 90% of
blepeakstructureandafurthermid-termperiodicitysoonafter confidence level occurs at T=1.7 for ℓ=0,2, while for ℓ=1 we
September2006as in ℓ=1, m=0. The residuals for the sectoral have two peaks above the 90% confidence levelcorresponding
componentshowsa nice-increasingtrendinthe signalstrength to T=1.7 and T=2.1. Fig. 6 - 7 shows the wavelet analysis for
oftheQBPovertheascendingphaseofsolarcycle23.Afurther theazimuthalcomponentsofthemodes.Inthiscasewedropped
2-yearmodulationmighthavebeenoccurredacrossSeptember down the significantlevel at 80% to show that there are signa-
2006 as found also in ℓ=1, m=1. The azimuthal analysis con- turesofQBPsignalovertheminimumactivityphaseinthezonal
firmsthe modulationin the signalstrengthmainlyoccurringin componentsofthemodes.Thesignificantperiodicityat80%of
thesectoralcomponentsofthemodesandalsothatoverthelong confidenceleveloccursatT=1.7forℓ=1,m=0,T=2.1forℓ=1,2
extendedminimumofsolarcycle23thesourcesofthemid-term andm=1,2andT=1.6forℓ=2,m=0.Itisinterestingtonotethat
periodicitymightbelocatedathighlatitudes. the zonal modes show a slightly different periodicity from the
5
R.Simonielloetal.:QBPfromhelioseismicobservations
Fig.5.(a)Thelocalwaveletpowerspectrumforℓ=0,1,2.Whiterepresentareasoflittlepower,redthosewiththelargestpower.
Solidringsidentifyareasatpowerof0.001,0.002,0.005overtimeandonlythosethatachieved90%confidencelevelarelabelled.
(b)Globalwaveletpowerspectrum.Thedottedlinearethe90%ofconfidencelevel.
Fig.6.ThesameasinFig.5fortheℓ=1m=0,1.Solidringsidentifyareasatpowerof0.0050,0.0075,0.01overtimeandonlythose
thatachieved80%confidencelevelarelabelled.
Fig.7.ThesameasinFig.6forℓ=2m=0,2.
onedetectedinthesectoralcomponents.Thismightbetheresult 5. p-modefrequencyshiftcorrelationcoefficient
ofthegreatersensitivitytohigherlatitudesofthezonalmodes. withactivityproxiesoverthe11-yearcycle
To further investigate this point, it will be important to study
the properties of the QBP signal in the azimuthal components 5.1.Sphericaldegreedependenceofthecorrelation
ofintermediate-highdegreemodes.Thereareevidences,infact, coefficient
showingthattheperiodicityfromnorthern(500 ≤ θ ≤ 900)and
equatorial(−450 ≤ θ ≤ 450)regionsdiffersfromtheoneinthe The correlation analysis between p-mode frequency shift and
southernregions(−500 ≤θ≤−900)(Vecchio&Carbone,2008). surface activity measures might improve our understandingon
the role played by strong and weak fields in the QBP signal.
We,therefore,decidedtoinvestigatethedegreeofcorrelationbe-
Insummarythewaveletanalysisconfirmsthatafurtherpe- tween p-modefrequencyshiftandtwo activity proxies:MWSI
riodicityof≈ 2-yearsisindeedpresentinthedataatconfidence (MountWilsonSunspotIndex)andF10.7index.TheMWSIval-
level of 90%. Furthermore the findings seem also to point to a ues are determined as a summation over pixels where the ab-
likely persistent nature of the QBP signal, since we foundevi- solute value of the magnetic field strength is greater than 100
dencesthatthismid-termperiodicityisalsopresentoverperiods gauss.WehavechosenMWSIbecauseitislinkedtothestrong
oflowactivityphase. componentofthetoroidalfieldsgeneratedbytheglobaldynamo.
6
R.Simonielloetal.:QBPfromhelioseismicobservations
Fig.9. The degree of correlation between p-mode frequency
shiftsoftheazimuthalcomponentsofthemodesandMWSIand
Fig.8. The degree of correlation between p-mode frequency
RF.ThecolorsbaridentifyMWSI(pink)andRF(purple).
shifts of low degree modes (ℓ=0,1,2 from left to right) and
MWSI(toppanel)andRF(bottompanel)overdifferentphases
of solar activity. The colors bar identify the observationalpro-
gramme,whoselegendisthesameasFig.1.
5.2.Azimuthaldependenceofthecorrelationcoefficient
It is possible to investigate the latitudinal dependence of the
correlationcoefficientbyusingthesinglem-componentsofthe
Thesefieldsaremainlylocatedatlow-midlatitudes.F10.7(RF) modesprovidedbyGONGdata.
represents,instead, anintegratedactivityproxyandtells usthe Fig.9comparesthedegreeofcorrelationbetweenthezonal
irradianceat2.8GHzatchromosphericheightscomingmainly and sectoralcomponentsof dipole and quadrupolemodeswith
from the Quiet Sun background emission and also Sunspots, MWSIandRF.Thesectoralcomponentsseemstocorrelatebet-
Plages.Thisproxythereforeisagoodmeasureoftheweak(lo- ter with both activity proxies over different phases of the so-
cated at high latitudes) and strong magnetic fields (mainly at lar cycle compared to the zonal modes. Previous works have
low-midlatitudes). shown that the central frequency of each multiplet is best cor-
related with the global activity measure, while the individual
We investigated the degree of correlation of p-mode fre-
m-component frequencies are more sensitive to the latitudinal
quency shift with MWSI and RF by splitting the whole cycle
indifferentphasesasfollows: distribution of activity (Howeetal., 1999; Antiaetal., 2001;
Howeetal.,2002).Thereforethecorrelationanalysismightsug-
- AP=Ascending Phase from 22 September 1996 until 26
gestthatthezonalmodesarebettercorrelatedwithresolvedac-
June1999
tivityindexthattakesintoaccountthelatitudinaldependenceof
-MP=MaximumPhase1999June27to2003January12
solarmagneticactivity.Tocheckuponthispoint,itwillbeim-
-DP=DescendingPhaseJanuary13200326untilJuly2007 portanttofurtherextendthecorrelationanalysistotheazimuthal
-mP=minimumPhaseupto2009. components of intermediate - high degree modes investigating
We used the Spearman’s rank correlation in preference to thedegreeofcorrelationwithresolvedactivityindex.
thePearson’scorrelationbecausethePearson’srankcorrelation
assesses the linear correlation between two sets of data. The
5.3.Conclusions
Spearman’srankcorrelationisless specific.While some ofthe
data sets we compare may be linearly related this is not defi- Evidences of QBP have been found in the individual low -ℓ
nitelytrueineverycase.Fig.8showsthecorrelationcoefficient degree modes as well as in their corresponding azimuthal m-
for ℓ=0, 1, 2 mode frequency shifts with MWSI (upper panel) components at all levels of solar activity. The strength of the
and RF (bottom panel) over different phases of solar cycle for QBPsignalseemstobemodulatedbythe11-yearenvelope,but
BiSON, GONG, GOLF and VIRGO. We find that the degree the effect is more significant at low-mid latitudes compared to
ofcorrelationof p-modefrequencyshiftwithMWSIdecreases higher ones. This modulation might explain the coupling be-
overthemaximumphaseindependentlyfromℓvalue.Ifwelook tween the strength of the main global dynamo and the appear-
atRFwefindhighercorrelationcomparedtoMWSIalloverdif- anceoftheQBPmainlyoverperiodscoincidingwithsolarmax-
ferentphasesofthesolarcycle.Thesefindingsareinagreement ima.Whenthesolarcycleisextremelyweak,themagneticflux
with previous results (Jainetal., 2009) and they confirm that processedbythemaindynamoisnotstrongenoughtobringup
behind the mode frequency shift the active regions are not the themid-termperiodicitysignalinthosesurfaceactivityindices
onlyplayers.The other importantfeatureis the anticorrelation relatedtothetoroidalcomponentofthemaindynamo.
overtheminimumof solarcycle23forℓ=0,2.Inthese modes ThesignaturesofQBPhavealsobeendetectedoverthemin-
therearetracesoftheQBPsignal.Thismightbetheresultofthe imumphaseofsolarcycle23with80%ofconfidencelevel.The
differentbehaviorofthe surfaceactivitymeasureoverthe long likely persistent nature of the 2-year periodicity in the seismic
extendedminimum.WhileMWSIwentdowntounprecedented analysismust be investigated,butprobablyshowsa permanent
leveluntil 2009,Radio Flux shows alreadyan upward trend in and periodic phenomenonthat stands in the sub-surface layers
February2008.Thismightexplainthehigherdegreeofanticor- in addition to a pure presence of a magnetic field. The occur-
relationwithRFcomparedtoMWSI. renceoftheQBPsignaloverperiodsofsolarmaximaaswellas
7
R.Simonielloetal.:QBPfromhelioseismicobservations
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Funding 200020-120114. This work utilizes data obtained by the Global Salabert, D., Fossat, E., Gelly, B., Kholikov, S., Grec, G., Lazrek, M., &
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agreement with the National Science Foundation. The data were acquired 1S
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R.Simonielloetal.:QBPfromhelioseismicobservations
ActivityIndex Modeofoscillation DataSource AP MP DP mP
MWSI ℓ=0 BiSON 0.88 3−5 0.50 0.06 0.98 1−12 -0.52 0.18
GONG 0.80 2−3 0.43 0.09 0.87 1−5 0 0.1
VIRGO 0.94 4−7 0.36 0.2 0.95 4−10 0.42 0.3
GOLF -0.98 4−10 0.27 0.3 0.97 1−11 0.36 0.4
ℓ=1 BiSON 0.91 4−6 0.52 0.04 0.94 2−9 0.26 0.5
GONG 0.97 1−7 0.63 8−3 0.82 1−5 -0.20 0.8
VIRGO 0.92 3−6 0.40 0.13 0.94 3−9 0.67 0.08
GOLF 0.92 4−6 0.2 0.5 0.96 2−11 0.52 0.18
ℓ=2 BiSON 0.92 4−6 0.52 0.05 0.94 2−9 0.26 0.5
GONG 0.87 2−4 0.60 0.01 0.95 2−10 -0.2 0.8
VIRGO 0.77 1−3 0.46 0.08 0.92 3−8 0.19 0.65
GOLF 0.90 1−5 0.48 0.07 0.90 1−7 0.36 0.38
RF ℓ=0 BiSON 0.87 5−5 0.71 3−3 0.99 2−16 -0.52 0.2
GONG 0.80 2−3 0.55 0.02 0.83 1−5 0.40 0.6
VIRGO 0.96 2−8 0.94 1−7 0.97 7−13 -0.24 0.57
GOLF 0.99 6−12 0.72 2−3 0.98 1−14 0.023 0.9
ℓ=1 BiSON 0.97 4−9 0.68 5−3 0.95 2−10 0.88 4−3
GONG 0.97 1−7 0.74 9−4 0.80 5−5 0.93 4−11
VIRGO 0.95 2−6 0.58 0.02 0.93 4−11 -0.14 0.7
GOLF 0.96 9−8 0.67 6−4 0.98 1−13 -0.05 0.9
ℓ=2 BiSON 0.97 4−9 0.89 7−6 0.91 7−8 -0.86 6−3
GONG 0.87 2−4 0.49 0.06 0.94 1−9 -0.40 0.6
VIRGO 0.77 1−3 0.83 1−4 0.93 8−9 -0.43 0.3
GOLF 0.91 5−6 0.89 7−6 0.93 1−8 -0.78 0.02
Table1.TheSpearmanncorrelationcoefficientandsignificancebetweenActivityIndecesandlowdegree p-modefrequencyshift
overdifferentphasesofsolaractivity.
ActivityIndex Modeofoscillation AP MP DP mP
MWSI ℓ=1,m=0 0.48 0.1 -0.05 0.8 0.55 0.03 -0.14 0.7
ℓ=1,m=1 0.79 1−3 0.68 0.01 0.80 1−4 0.33 0.34
ℓ=2,m=0 0.41 0.16 0.65 0.01 0.39 0.13 0.30 0.13
ℓ=2,m=2 0.69 9−3 0.88 7−5 0.95 1−8 0.39 0.3
RF ℓ=1,m=0 0.52 0.06 0.16 0.6 0.54 0.03 -0.36 0.3
ℓ=1,m=1 0.78 1−3 0.65 0.01 0.81 1−4 0.50 0.2
ℓ=2,m=0 0.44 0.13 0.69 0.02 0.38 0.15 -0.57 0.89
ℓ=2,m=2 0.64 0.02 0.87 1−4 0.94 4−8 0.95 0.3
Table2.ThesameasTable1butfortheazimuthalcomponentoflowdegreemodes.
9