Detection of ultra-weak magnetic fields in Am stars: beta UMa and theta Leo

0.32 MB·

by  A. Blazère

Astronomy&Astrophysicsmanuscriptno.article_Am_v10 (cid:13)cESO2016
January11,2016
Detection of ultra-weak magnetic fields in Am stars:
β UMa and θ Leo
A.Blazère1,2,3,P.Petit2,3,F.Lignières2,3,M.Aurière2,3,J.Ballot2,3,T.Böhm2,3,C.P.Folsom2,3,4,M.Gaurat2,3,
L.Jouve2,3,A.LopezAriste2,3,C.Neiner1,andG.A.Wade5
1 LESIA,ObservatoiredeParis,PSLResearchUniversity,CNRS,SorbonneUniversités,UPMCUniv.Paris06,Univ.ParisDiderot,
SorbonneParisCité,5placeJulesJanssen,92195Meudon,France
e-mail:[email protected]
2 UniversitédeToulouse,UPS-OMP,InstitutdeRechercheenAstrophysiqueetPlanétologie,Toulouse,France
3 CNRS,InstitutdeRechercheenAstrophysiqueetPlanétologie,14AvenueEdouardBelin,F-31400Toulouse,France
4 IPAG,UJF-Grenoble1/CNRS-INSU,UMR5274,38041Grenoble,France
6
5 DepartmentofPhysics,RoyalMilitaryCollegeofCanada,POBox17000StationForces,Kingston,ONK7K0C6,Canada
1
0
January11,2016
2

n
ABSTRACT
a
J
Context.AnextremelyweakcircularlypolarizedsignaturewasrecentlydiscoveredinspectrallinesofthechemicallypeculiarAm
8 starSiriusA.Aweaksurfacemagneticfieldwasproposedtoaccountfortheobservedpolarizedsignal,buttheshapeofthephase-
averagedsignature,dominatedbyaprominentpositivelobe,isnotexpectedinthestandardtheoryoftheZeemaneffect.
] Aims.WeaimatverifyingthepresenceofweakcircularlypolarizedsignaturesintwootherbrightAmstars,βUMaandθLeo,and
R
investigatingthephysicaloriginofSirius-likepolarizedsignalsfurther.
S Methods.WepresenthereasetofdeepspectropolarimetricobservationsofβUMaandθLeo,observedwiththeNARVALspectropo-
. larimeter.WeanalyzedallspectrawiththeLeastSquaresDeconvolutionmultilineprocedure.Toimprovethesignal-to-noiseratio
h
anddetectextremelyweaksignaturesinStokesVprofiles,weco-addedallavailablespectraofeachstar(around150observations
p
eachtime).Finally,weranseveralteststoevaluatewhetherthedetectedsignaturesareconsistentwiththebehaviorexpectedfromthe
-
o Zeemaneffect.
r Results.Thelineprofilesofthetwostarsdisplaycircularlypolarizedsignaturessimilarinshapeandamplitudetotheobservations
t previouslygatheredforSiriusA.Ourseriesoftestsbringsfurtherevidenceofamagneticoriginoftherecordedsignal.
s
a Conclusions.Thesenewdetectionssuggestthatveryweakmagneticfieldsmaywellbepresentinthephotospheresofasignificant
[ fractionofintermediate-massstars.ThestronglyasymmetricZeemansignaturesmeasuredsofarinAmstars(featuringadominant
single-sign lobe) are not expected in the standard theory of the Zeeman effect and may be linked to sharp vertical gradients in
1
photosphericvelocitiesandmagneticfieldstrengths.
v
9 Keywords. Stars:magneticfield–Stars:chemicallypeculiar-Stars:individual:βUMaandθLeo
2
8
1
1. Introduction However,itisstronglysupportedbymanyoftheirobservational
0
properties(e.g.,Braithwaite&Spruit2015).
.
1About 5% to 10% of hot stars (stars with O, B, and A spec-
0tral types) are found to be strongly magnetic with a longitudi- Recently, a longitudinal magnetic field much weaker than
6nalmagneticfieldstrengthinexcessof100G(e.g.,Wadeetal. any previous detection in intermediate-mass stars has been dis-
12013; Aurière et al. 2007), which is generally associated with covered in the early A star Vega (Lignières et al. 2009). The
:a simple and stable field geometry (e.g., Lüftinger et al. 2010; spectropolarimetric time series was interpreted in terms of a
v
iSilvester et al. 2014). However, the physical origin and even surface magnetic field distribution using the Zeeman-Doppler
X
some basic properties of these magnetic fields are still poorly Imagingtechnique(ZDI,Petitetal.2010),unveilingapeaklocal
runderstood. The current paradigm, the fossil field hypothesis, fieldstrengthofabout7G(Petitetal.2014a).Theresultsofthat
a
describesthismagnetismastheremnantofmagneticfieldaccu- study support the view that Vega is a rapidly rotating star seen
mulatedorproducedduringanearlyphaseofstellarlife.Inthis nearlypole-on,andthereconstructionofthemagnetictopology
conceptual framework, magnetic fields observed in these stars at two epochs revealed a magnetic region of radial field orien-
today are proposed to result from a seed field in the molecular tation,closelyconcentratedaroundtherotationpole.Vegamay
cloud from which the star was formed, rather than being cur- wellbethefirstconfirmedmemberofamuchlarger,asyetunex-
rentlyproducedbyanactivedynamoasintheSun.Thisinitial plored,classofweaklymagnetichotstars.Weakmagneticfields
field may also have been amplified during the early phases of ofthesamekindwerealsosearchedforintwonormalBstars,γ
the evolution of the star, when it was temporarily surrounded Peg(Neineretal.2014a)andιHer(Wadeetal.2014),although
by an extended convective envelope hosting a global dynamo. no magnetic fields were detected in both stars with a precision
In practice, the fossil field theory leaves many basic questions of0.3-0.4G.However,Wadeetal.(2014)demonstratethat,ifa
unanswered, such as the precise origin of this magnetism and large-scale magnetic field identical to the ZDI magnetic geom-
its low incidence among intermediate-mass and massive stars. etry of Vega existed in γ Peg and ι Her, no detection would be
Articlenumber,page1of11
A&Aproofs:manuscriptno.article_Am_v10
expectedatthislevelofaccuracygiventhespectrallineproper- Table1.FundamentalparametersofβUMaandθLeo
tiesofbothB-typetargets.
βUMa θLeo
The only other example of a weak Stokes V detection in
spectrallinesofanintermediate-massstarhasbeenreportedfor Spectraltype A1V A2V
the bright Am star Sirius A (Petit et al. 2011). For this object, Teff 9480K±10Ka 9280±10Ka
however, the polarized signature observed in circular polariza- logg 3.82b 3.65c
tion is not a null integral over the width of the line profile, as Mass 2.64±0.01Ma 2.94±0.2Ma
(cid:12) (cid:12)
expectedintheusualdescriptionsoftheZeemaneffect.Instead, Radius 3.021±0.038Rd 4.03±0.10Re
(cid:12) (cid:12)
theStokesVlineprofileexhibitsapositivelobedominatingthe vsini 46±3km/sf 23±3km/sf
negative one (in amplitude and integrated flux). The interpreta- L 72±11a 127±13a
(cid:12)
tionofaZeemanoriginwasfavoredbyPetitetal.,inparticular Frac.age 0.778a 0.943a
afterexcludingthepossibilityofaninstrumentalcrosstalkfrom Metallicity -0.03g -0.13g
linear to circular polarization. However, the abnormal shape of aZorec&Royer(2012) bAllendePrietoetal.(1999)
thepolarizedprofileremainedapuzzleandrequiredfurtherin- cAdelmanetal.(2015) d Boyajianetal.(2012)
vestigation. eMaestroetal.(2013) f Royeretal.(2002)
The motivation to progress on this topic is strong because gAnderson&Francis(2012)
the discovery of a new, potentially widespread class of weakly
magneticAstarsoffersimportantnewinformationaboutthedi-
chotomybetweenstrongandweakmagneticfieldsintepidstars. Thefundamentalparametersofbothtargetsarepresentedin
Inanattempttointerpretthisdivision,Aurièreetal.(2007)pro- Table2.ThetwoobjectsareearlyA-typetargets.Bothofthem
posedascenariobasedonthestabilityofalargescalemagnetic benefit from an interferometric estimate of their radius, which
configurationinadifferentiallyrotatingstar,leadingtoestimat- is distinctly larger than the radius of main sequence stars of
ingacriticalfieldstrengthabovewhichmagneticfieldscanre- similar spectral types. Accordingly, their surface gravities are
mainstableonlongtimescales,whilemagneticfieldsbelowthis foundtobebelowmainsequencevalues.Highluminosityvalues
limit would likely be destroyed by the internal shear. More de- complete this picture, confirming that both targets are already
tailedmodelsincluding2Dand3Dnumericalsimulations(Jouve ontheirwayoffthemainsequence.Usingevolutionarymodels
etal.2015;Gauratetal.2015)tendtoconfirmtheexistenceofa matchingthepositionofbothstarsintheH-Rdiagram,Zorec&
criticalfieldinsuchconfigurations,wherethepre-mainsequence Royer (2012) find that the fractional age on the main sequence
contractionisapossiblewaytoforcedifferentialrotation.Onthe ofβUMaandθLeoareequalto0.778and0.943,respectively,
other hand, the magnetic dichotomy might simply be the result givingfurthersupporttotheideathatbothstarshavecompleted
oftwodifferentmagneticfieldgenerationprocesses.Braithwaite most of their path on the main sequence. That β UMa is re-
&Cantiello(2013)proposethatVega-likemagneticstarsarethe ported to belong to the Ursa Majoris association gives another
result of the slow evolution of magnetic configurations charac- constraintontheage,whichisestimatedtobearound500Myr
terizedbyweakinitialmagnetichelicityandarguethatitshould for this group of stars (Monier 2005). Based on Spitzer mea-
bewidespreadamongmostintermediate-massandmassivestars. surementsofIRexcess,Balleringetal.(2013)attributeagesof
Meanwhile,Ferrarioetal.(2009)proposethatthesmallfraction 310Myrand500MyrtoβUMaandθLeo,respectively,which
ofstrongmagneticfieldscouldbeproducedinearlystellarmerg- is too young to be reconciled with other stellar parameters, but
ingevents. mayprovideanadditionalhintthatθ Leoismoreevolvedthan
In the rest of this paper, we first present the two bright Am βUMa.
stars selected for this study. We then present the observations The projected rotational velocities estimated for both stars
andtheanalysismethodsused.Aseriesoftestswasperformed are fairly typical of values reported for Am stars (Abt 2009).
toconstrainthephysicaloriginoftherecordedpolarimetricsig- In the absence of any direct estimate of the rotation period of
naturesfurther,andfinallywediscussourresultsinthebroader our targets, it cannot be determined whether the higher vsini
contextofweaklymagneticstarofintermediatemass. valuereportedforβUMaislinkedtoafasterrotationorhigher
inclinationangle.
2. Selectedtargets
3. Dataanalysis
Here, we present the results of deep spectropolarimetric cam-
paigns carried out for two bright Am stars in which magnetic DataweretakenwiththeNARVALspectropolarimeter(Aurière
fieldswerepreviouslyundetected(Aurièreetal.2010).Amstars 2003,Silvesteretal.2012)inoperationatthetwo-meterBernard
arechemicallypeculiarstarsexhibitingoverabundancesofiron- LyotTelescope(TBL)atthesummitofPicduMidiObservatory
group elements such as zinc, strontium, zirconium, and barium intheFrenchPyrénées.Thishighresolutionspectropolarimeter
and deficiencies of a few elements, particularly calcium and is specially designed and optimized to detect stellar magnetic
scandium. Most Am stars also feature low projected rotational fields through the polarization they generate in photospheric
velocities,ascomparedtonormalAstars(Abt2009).Thetargets spectrallines.ThepolarimetricunitismountedattheCassegrain
ofthisstudyareβUrsaMajoris(HD95418)andθLeonis(HD focusofthetelescopeandallowstwoorthogonalstatesofagiven
97633).AbundancesmeasuredforβUMaplacethisstaramong polarization (circular or linear) to be recorded throughout the
targetsfeaturingweakAmcharactericticswithnoticeableover- entire optical domain, thanks to the high achromaticity of its
abundanceinVii,Mnii,Nii,Niii,Zni,Srii,Yii,Zrii,andBaiiand polarimetric optics. The upper part of the polarimeter contains
underabundances in Hei, Ci, Cii, and Scii (for more details see the guiding camera, an atmospheric dispersion corrector, and a
Adelmanetal.2011).ThesourceθLeoisalsoontheweakside calibration wheel. Following that, the main polarimetric device
of Am abnormality, with large reported overabundance in Sii, constitutesthreeFresnelrhombretarders(twohalf-waverhombs
Vii,Crii,Srii,Yii,andZriiandBaiiandunderabundanceinAii, thatcanrotateabouttheopticalaxisandonefixedquarter-wave
Caii,Scii,Mnii,andNii,(Adelmanetal.2015). rhomb),whichareusedtoperformthepolarimetricanalysis.The
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A.Blazèreetal.:Detectionofultra-weakmagneticfieldsinAmstars:βUMaandθLeo
light emerging from the retarders is sent to a Wollaston prism, procedure (Donati et al. 1997, Kochukhov et al. 2010) to each
consisting of two orthogonal calcite prisms that are cemented spectrumofbothstars.Thismethodisacross-correlationtech-
together,actingasapolarizingbeamsplitter. nique for computing average pseudo-line profiles from a list of
The two beams of light emerging from the beamsplitter are spectrallinesinordertogetamultiplexincreaseintheS/N.This
transmittedbysome30mofopticalfibertothebench-mounted powerful technique, based upon several rough approximations
spectrograph,whereanimageslicerconvertsthecircularimage (additivelineprofiles,wavelength-independentlimb-darkening,
of the fiber head into a pseudo-slit shape.. The spectrograph self-similar local profile shape, weak magnetic fields), makes
provides complete coverage of the optical spectrum from 3700 use of the possibility of describing stellar spectra as a line pat-
to 10500 Å on 40 echelle orders with a spectral resolution tern convolved with an average pseudo-line profile. Here, we
of about 65000 in polarimetric mode. The spectrograph unit choosetocomputetheLSDStokesIandVpseudo-profilesfor
containsadoublesetofhigh-reflectancecollimatorscutfroma all available photospheric lines. Our line lists are taken from
single680mmparabolicmirrorwithafocallengthof1500mm. the VALD atomic data base (Piskunov et al. 1995; Kupka &
The grating is a 79 gr/mm monolithic grating with dimensions Ryabchikova 1999) using the respective effective temperature
of 200 by 400 mm, and the cross-dispersion is achieved by a andloggofbothstars(Table2).Ourlinelistsareextractedusing
high dispersion prism. The camera lens is a fully dioptric f/2 Teff = 9,500K and log g=4.0 for β UMa and Teff = 9,250K
388 mm focal length lens with a 210 mm free diameter. The andlogg=3.5forθLeo.Werejectthelineswhosedepthisless
spectrographthermalstabilityiskepttowithin0.1K,thanksto than 1% of the continuum. By doing so we obtain a mask of
theuseofadouble-layerthermalenclosure. 1,173 lines and 1,133 lines for β UMa and θ Leo, respectively.
Then,weadjustthedepthofthelinesinthemasktofittheob-
Alldatausedinthepresentpaperarecollectedinthepolari- served line depths. To reduce the noise per spectral bin further
metricmodemeasuringStokesV(circularpolarization).Tomin- andthenreducethespectralresolutionofLSDlineprofiles.In-
imize systematic errors, one complete Stokes V sequence con- stead of the default spectral bin spanning 1.8 kms−1 at a spec-
sists of four successive subexposures taken with the half-wave tral resolution of 65,000, we used 9 kms−1 for β UMa and 5.4
rhombsorientedatdifferentazimuths.Thisfollowsthemethod kms−1 for θ Leo, which leaves us with about ten velocity bins
ofSemeletal.(1993)toreducetheamplitudeofpossiblespuri- inthepseudolineprofile.Withthismodificationofthespectral
oussignaturesofinstrumentalorigin.Thisstrategyalsoprovides resolution, the additional gain in the S/N is a factor of 2.1 for
a strong test to discard the possibility of a spurious signal by βUMaand1.7forθ Leo.ThenightlyaveragedS/Nsofthere-
computinga“null”spectrum.Thisiscalculatedfromadifferent sulting Stokes V LSD profiles (i.e., the average of the S/Ns of
combinationofthefoursubexposuresconstitutingthepolarimet- individual profiles) are between 45,000 and 77,000 for β UMa
ricsequence(Donatietal.1997),anditshouldnotdisplayany andbetween25,000and48,000forθLeo(TableA).Thedisper-
signal. This “null” check parameter is automatically produced sionoftheS/NbetweenindividualStokesVsequenceofagiven
for each Stokes V sequence.The data are reduced by Libre- nightisoftenthelowestduringnightsfeaturingthehighestaver-
Esprit, a dedicated and fully automated software (Donati et al. ageS/N,becauseoftheexcellent(andstable)skytransparency.
1997)specificallydevelopedforreducingechellespectropolari- Polarized signals remain undetected in individual LSD
metric data and optimized for NARVAL. Libre-Esprit proceeds StokesVpseudo-profilesofourtwotargets.However,theirtyp-
inthreesteps:thefirststageconsistsofperformingageometri- ical S/N remains far too low to detect polarized signatures as
calanalysisfromasequenceofcalibrationexposures;theposi- weak as the one previously reported for Sirius A (Petit et al.
tionandshapeofordersisderivedfromameanflatfieldimage, 2011).TofurtherimprovetheS/N,wecoaddallavailableLSD
while the details of the wavelength to pixel relation along and profiles for each star, resulting in one “grand average” pseudo-
across each spectral order is obtained from comparison frames line profile. This method was successfully used for Vega (Lig-
obtainedfromaThArlampandaFabry-Perotsetup.Thesecond nièresetal.2009,Petitetal.2010)andSirius(Petitetal.2011)
stepperformsspectrumoptimalextraction(Horne1986;Marsh todetectsignatureswithamplitudesaslowasabout10−5 ofthe
1989),usingthegeometricalinformationderivedinstep1.Alast continuumlevel.TocoaddtheLSDprofiles,weweighteachin-
stepconsistsofrefiningthewavelengthcalibrationusingtelluric dividualLSDprofileproportionallytoitssquaredS/N:
linesrecordedinthereducedspectrum,thereforereachingara-
dial velocity accuracy close to 30 m.s−1 (Moutou et al. 2007). (cid:88)n
Spectra processed with Libre-Esprit include the flux and polar- w =S/R2/ S/R2
i i i
ization information, as well as the “null” spectrum computed i=0
from two different combinations (dubbed “Null1” and “Null2”
inourplots)anderrorbarsateachwavelengthpointinthespec- wherew andS/R aretheweightandS/Noftheith pseudopro-
i i
trum. file.
The source β UMa was observed in March/April 2010 and We choose here to keep all profiles in this process, even
March/April 2011 for a total of 149 spectra. For its part, θ Leo those with the lowest S/N (LSD profiles with S/N lower than
was observed in January/March/April 2012, March/April 2013, 10,000 represent 16 observations for β UMa and 2 for θ Leo),
andMay/June2014foratotalof171spectra(seeTableAforthe because this systematic rejection was found to provide us with
detailed distribution of observations among individual nights). nothingmorethanamarginalmodificationoftheresult(andno
For each star, the exposure time was adjusted to reach a peak noticeable improvement). The grand average LSD profiles are
S/NthroughouttheStokesVspectrumbetween1,000and2,000 presented in Fig. 1. With the large number of spectra collected
per1.8km.s−1 bin,dependingonweatherconditions.Theserel- here,thecoadditionofallprofilesincreasestheS/Nbyafactor
atively high values are safely away from the saturation level of ≈ 10, compared to individual profiles. The resulting S/N of the
theEEVdetectorusedinfastreadoutmode. grandaverageVprofilesis653,640forβUMaand512,370for
In the absence of any detectable polarized signatures in in- θLeo(usingthenormalizationparameterslistedinTableB.1).
dividualspectrallinesofβUMaandθ Leo,weapplythewell- One limitation of this rough co-addition method is that
knownandcommonlyusedLeastSquaresDeconvolution(LSD) we average together observations taken at different rotational
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A&Aproofs:manuscriptno.article_Am_v10
phases. In the absence of any known rotation period, we as- 4.2. PossibleinstrumentalartifactsathighS/N
sume our data are distributed over all rotation phases with the
The very high S/N achieved to detect weak polarimetric sig-
same probability. We therefore lose any phase-resolved infor-
natures in intermediate-mass stars raises the question of possi-
mation,andtheaxisymmetricsurfacestructures(i.e.,structures
ble instrumental effects that could contribute to generate spu-
symmetricaboutthespinaxis)arethemostlikelytosurvivethe
rious signatures in NARVAL Stokes V sequences. All spectra
coadditionprocessandactuallycontributetothegrandaverage.
obtainedforourstudydisplayapeakS/Nbelow2,000,andthe
Thisstrategyis,however,successfulatreducingthenoiselevel
majorityofthemarekeptbelow1,500.AtsuchS/Nvalues,we
enoughtopermitthedetectionofcircularlypolarizedsignatures
safelystayawayfromthesaturationregimeofthedetector(S/N
in both stars, while the null profiles remain free of any feature
above2,000forstandardearly-typestars).Wenotethatsubsets
abovenoiselevel.
extracted from our complete time-series display consistent sig-
ReducedspectraareprovidedbyLibre-Espritwithanormal-
natures, regardless of the S/N of the subset, as highlighted by,
ized continuum, although the actual resulting continuum typi-
e.g., Fig. 5. In any case, most spurious signatures generated by
callydeviatesbyupto15%fromunity,especiallyinthebluest
nonlinearbehaviorofthedetectorareexpectedtoshowupinthe
orders of the spectra. To test the impact of this imperfect auto-
Null1andNull2checkprofiles(especiallyiftheS/Nisfluctuat-
matedprocessingontheresultofourLSDanalysis,wenormal-
ingfromonesubexposuretothenext),whichisnotseenhere.
izedeachofthe40echelleordersforeachspectrum(seeNeiner
et al. 2014b) with the continuum task of IRAF1. The new nor- Fromanempiricalpointofview,westressthatthesignatures
malization improves the S/N of the individual LSD profiles by recordedsofarforSiriusA(Petitetal.2011;Kochukhov2014)
about 5%. We notice that the upgraded normalization changes displayasimilarshapeusingthreedifferentinstrumentalsetups
theresultingLSDprofilesslightly,howevertheimprovementis (ESPaDOnS,NARVAL,HARPSpol)andthreedifferentmodels
verymarginal,evenattheextremelyhighS/Nofourgrandav- of CCD detector and two different reduction pipelines, giving
erageprofiles.Inspiteofthelimitedqualityofthedefaultcon- strong confidence in a stellar origin of the polarized signature.
tinuum normalization, the robustness of LSD is mainly due to Wefinallyemphasizethatanumberofstarsbelongingtoseveral
thelargenumberoflinestakenintoaccountintheLSDprocess, classes were previously observed at a comparable S/N, which
compared to hotter stars for which the improved normalization resulted in no Stokes V detection in two normal B stars (Wade
is more useful. As a consequence, we simply consider here the etal.2014;Neineretal.2014b),inadefiniteStokesVdetection
spectra normalized with Libre-Esprit for consistency with the (with a standard Zeeman shape) for the λ Boo star Vega (Lig-
previousstudiesonVega(Lignièresetal.2009,Petitetal.2010) nières et al. 2009), and in a definite Zeeman detection (again
andSirius(Petitetal.2011)inwhichthedefaultrenormalization with a standard shape) for the cool giant Pollux (Aurière et al.
wasused. 2009).
Anotherpotentialsourceofinstrumentalartifacts,especially
forveryweakStokesVsignatures,ispossiblecrosstalkfromlin-
4. Results eartocircularpolarization.ThiseffectisdocumentedforNAR-
VALandESPaDOnS(e.g.,Silvesteretal.2012).StokesQand
4.1. LSDprofileswithcompletelinemask
UspectrawereobtainedforSiriusAbyPetitetal.(2011),fea-
turing no polarimetric signal at a level that could significantly
The Stokes I, V, Null1 and Null2 co-added LSD profiles of β
contribute to the Stokes V signal. The same profile shape ob-
UMaandθLeoareshowninFig.1.TheydisplayclearStokesV
tainedforSiriusAusingthreeinstrumentsaffectedbydifferent
signaturesattheradialvelocityoftheStokesIlineprofiles.The
crosstalklevelsis,initself,anindependentevidencethatlinear
circularly polarized signal observed for both stars covers most
polarizationdidnotcontaminatetheStokesVsignature.
of the width of the line and is mostly symmetric about the line
centroid.Inbothcases,apositivelobedominatesthesignal.No Consideringthiscontextasawhole,weconcludethatacon-
detectablesignalisseenintheNull1andNull2controlprofiles. vincingbodyofevidencenowexiststosafelyconcludethatthe
We computed the detection probability of the Stokes V signal StokesVsignalobservedforβUMaandθLeomostlikelyhasa
by using the χ2 test proposed by Donati et al. (1992), getting a stellarorigin.
detectionprobabilityof∼100%forbothstarswithafalsealarm
probabilitybelow10−11 forβUMaandequalto6.5×10−6 forθ
4.3. EstablishingtheZeemanoriginofStokesVsignatures
Leo. Outside of the stellar lines, we obtained a marginal signal
detectionforβUMa,duetothenegativebumpintheStokesV 4.3.1. Methodoutline
continuumshowingupataradialvelocityofaround-200kms−1.
This continuum feature, not observed for θ Leo, may be due to The shapes of the signatures in the Stokes V profiles (mainly
residualsoflineblends(Kochukhovetal.2010). constituted of a positive lobe) are not expected in the standard
WenotethattheStokesVsignaturesdetectedintheco-added theory of the Zeeman effect, which predicts that lobes of posi-
LSD profiles probably stem from a significant fraction of the tive and negative signs should be observed, resulting in a zero-
individual LSD profiles, as various subsets from our complete integral Stokes V profile. This surprising observation, and the
data set (e.g., observations taken during a given year, see Fig. extremelylowamplitudeoftherecordedsignatures,raisenatu-
5) display the same signal when co-added separately, although ral concerns about possible artifacts that may contribute to the
withahighernoiselevel.Thesingle-epochsubsetsareobtained observedpolarizedsignal.Consideredalltogether,thestandard
over a timespan that is much longer than the longest possible series of tests detailed in Sect. 4.1 provides us with strong ev-
rotationperiodofthetwotargets,sothattheco-additionprocess idence that the recorded signatures are stellar in origin. Other
of many individual rotational phases should result, in all cases, convincingevidenceincludesthepossibilitythatcrosstalkfrom
in a filtering of any signatures resulting from nonaxisymmetric linear to circular polarization is not involved (Petit et al. 2011)
magneticstructures. andthatnosimilarsignatureswereobservedinotherhotortepid
starsstudiedatasimilarlevelofaccuracy(Lignièresetal.2009;
1 ImageReductionandAnalysisFacility,http://iraf.noao.edu/ Wade et al. 2014; Neiner et al. 2014b), in spite of a strictly
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A.Blazèreetal.:Detectionofultra-weakmagneticfieldsinAmstars:βUMaandθLeo
identical instrumental setup. HARPSpol observations reported profilesarecorrectedfora∼10%differenceinequivalentwidth
by Kochukhov (2014) also confirm that the peculiar signature observedintheirassociatedStokesIprofile.Becauseofahigher
reported for Sirius A is still obtained when using a completely noiselevelthanobtainedwiththecompletelinemask,thehigh-g
differentinstrumentanddifferentreductionsoftware. andlow-gprofilesofβUMaandθLeodonotdisplayanystatis-
Evenifinstrumentaleffectscanbesafelyexcluded,thephys- tically conclusive differences. The overplotted running average
ical origin of the signal still requires further investigation. We helps to improve the situation, showing that the high-g signals
propose here a series of tests to ascertain the Zeeman origin of possesshigheramplitudesthantheirlow-gcounterparts.Wenote
therecordedsignal.ThebasicideaisthattheamplitudeofZee- that their amplitude ratio is roughly consistent with the g ratio,
mansignaturesisexpectedtodependonvariouslineparameters although this point is difficult to establish with high accuracy
(Landé factor, wavelength, line depth), so that a careful selec- (evenwiththerunningaverage)becauseofthelevelofnoise.
tion of spectral lines for the LSD procedure should confirm or As second test, two sublists were defined from our original
refute this dependence in our data. We therefore run again the list by containing lines with a wavelength lower (resp. greater)
LSD process using a number of new line lists, extracted from thanthemeanwavelengthoftheoriginallist(TableB.1).Fora
ouroriginallistbutfeaturingaselectionoflineswhereoneline givenstar,theStokesVprofileswerecorrectedforthe∼30%dif-
parameterhasbeenrestrictedtoagivenrange.Intheweakfield ferenceinequivalentwidthobservedintheirassociatedStokesI
approximation, Stokes V signals are related to line parameters profiles. The outcome of this test is illustrated in Fig. 3, which
accordingtothefollowingequation: illustrates a marginally larger amplitude of the Stokes V signal
whenthewavelengthincreases.Asfortheprevioustest,wecom-
putedamovingaverageofthesignaltoconfirmthetrendthatis
V ∝g.λ2.B .∂I/∂λ (1)
0 (cid:107) otherwise completely hidden in the noise and to check that the
trendobservedinbothAmstarsisconsistentwiththeoutcome
where λ represents the wavelength of the line profile, B the
0 (cid:107) obtainedforα2CVn.
line-of-sight projection of the magnetic field vector, and g the
effective Landé factor. At a given value of B , the amplitude of Asalasttest,wedefinetwosublistsusingspectrallineswith
(cid:107)
an average depth lower (resp. greater) than the mean depth of
StokesVisthereforeexpectedtofollowsimplevariationswith
theoriginallist(TableB.1).TheStokesVLSDprofilesobtained
λ ,g,andwiththelinedepth.
0
As a reference, we use here the standard Ap star α2 CVn fromthesublistsaredisplayedinFig.4and,forourtwoAmstars
andourreferencestar,clearlyshowaloweramplitudewhenever
and a NARVAL observation downloaded from PolarBase (Petit
theaveragelinedepthissmaller.Thisoutcomeisexpectedinthe
etal.2014b)andalreadyusedbySilvesteretal.(2014).Thestar
α2 CVnisbrightandvariableA0pwithvsini=18±0.5kms−1, caseofasignatureofmagneticorigin,butalsoformostinstru-
an effective temperature of 11600 ± 500 K, and a logarithmic mentalartifacts.
surfacegravityequalto3.9±0.1(Silvesteretal.2014).Itsspec- Fromtheseriesoftestspresentedhere,onlytheonewithlow
tral properties are therefore reasonably similar to β UMa and θ versus high Landé factors was performed by Petit et al. (2011)
Leo,exceptitsslightlyhighersurfacetemperature.Theinterest- for Sirius A. For consistency, we used their observing material
ingcharacteristicofα2 CVnisitsstrongandorganizedsurface toreproducewithSiriusAthethreetestsappliedtoβUMaand
magnetic field (locally up to 2 kG), resulting in very large cir- θ Leo. The result, not shown here, is fully consistent with the
cularly polarized signatures. We applied our series of tests to conclusions reached in the present study. Considered together,
thisreferencestartobetterhighlighttheexpectedresultsinthe thisseriesoftestsstronglysuggeststhatthecircularlypolarized
presenceofastrongmagneticfield,withnegligiblenoiseinthe signaturesobtainedforthethreebrightAmstarsobservedsofar
polarizedprofile. haveaZeemanorigin.
The average line parameters for all submasks used to com- Basedonthisconclusion,itistemptingtoestimatethesur-
pute the new LSD profiles are listed in Table B.1. They vary facefieldstrengthfromoursetofmeasurements,usingtheclas-
slightlyfromonestartothenextmostlybecauseofthedifferent sicalcenterofgravity(orfirstmoment)method(Rees&Semel
VALDmodelsemployed.Thelargeststar-to-stardifferencesare 1979).Wemuststress,however,thatthiswidelyusedtechnique
observedwhenwedefinethelinesublistsaccordingtoawave- isbasedonthestandardassumptionthattheStokesVsignature
length threshold. We also list in Table B.1 the normalization is antisymmetric about the line center, which is very far from
parameters used for the LSD procedure, forcing a normalized the actual shape of our Stokes V signatures. A purely symmet-
wavelengthof500nmeverywhere,exceptwhenwesetawave- ric signature (closer to what is obtained for β UMa and θ Leo)
length threshold, in which case we force a normalized Landé will be interpreted as a zero longitudinal field strength, regard-
factorequalto1.2.Finally,wecorrectforanydifferenceinthe lessoftheamplitudeoftheStokesVsignal,similarlytodipolar
depthofStokesIprofiles,exceptwhenthesubmasksaredefined fieldsobservedattherotationalphaseofacrossoverconfigura-
withalinedepththreshold. tion (e.g., Aurière et al. 2007). The situation here is obviously
different, because the large time span of data collection is very
unlikelytoberestrictedtoacrossoverphase.Nevertheless,such
4.3.2. OutcomeforβUMaandθLeo
ameasurement(andinparticularitserrorbar)providesuswitha
As a first test, we ran LSD for two submasks containing lines qualitymeasureofthesensitivityofthemagneticdiagnosisthat
with an average Landé factor g lower (resp. greater) than the canbecomparedtosimilarstudies.Thefirstmomentestimateof
meanLandéfactoroftheoriginallinelist(seeTableB.1).Here- themagneticfieldprovidesuswithafieldstrengthof−1±0.8G
after,weconsiderthenormalizingLandéfactorsusedaspartof forβUMaand−0.4±0.3GforθLeothatisunsurprisinglycon-
the LSD procedure, since it is the relevant quantity for direct sistent with zero (as previously reported with Sirius A). As an
comparison of different LSD profiles. (The normalizing g val- attempt to propose a more relevant proxy of the field strength,
ues follow the same trend as the average Landé factors of the we calculate the equivalent width (EW) of the Stokes V signa-
submasks.) The resulting Stokes V profiles are plotted in Fig. tureandnormalizethisEWbytheoneoftheStokesIprofile.By
2 for the two Am stars and the control Ap star. The Stokes V doing so, we obtain a normalized EW equal to 1.96×10−4 for
Articlenumber,page5of11
A&Aproofs:manuscriptno.article_Am_v10
βUMa,and5.44×10−5 forθLeo.ForSiriusA,thenormalized flows and magnetic fields invoked to justify their shape. Rel-
EWisequalto6.68×10−5. atively strong magnetic fields are also involved in asymmetric
solar Stokes V profiles, although the very weak disk-integrated
signatures reported here do not tell much about local magnetic
5. Discussion strengths,whichcouldpotentiallyberatherlargeinthecaseofa
verytangledfieldgeometry.
5.1. PeculiarStokesVsignaturesinAmstars
TheabsenceofanysimilarphenomenoninApstars(inspite
The observations presented here provide new clues to the of masses roughly identical to those of Am stars) may simply
weak polarized signatures produced in the photospheres of be related to the lack of any significant surface turbulence due
intermediate-massstars.WereportthedetectionofweakStokes tothestrongmagneticfieldspermeatingtheirphotosphere(Fol-
V signatures in two of the brightest Am stars, which comple- som et al. 2013) and, in the case of Bp stars, to a photospheric
ments the previous detection of a similar polarized signal for temperature too high to allow for a thin convective shell, even
Sirius A (Petit et al. 2011)2. Considered together, the three po- in the absence of their magnetic field. The situation is different
larimetricdetectionsconstitutea100percentdetectionratesofar for Am stars, for which high-resolution spectra have revealed
inoursampleofbrightAmstars,suggestingwidespreadsimilar stronger microturbulence than for normal A stars (Landstreet
signaturesinthisstellarclass. etal.2009),aslongastheireffectivetemperatureremainsbelow
about 10,000 K, a condition fulfilled by our two targets and by
Allsignalsobservedtonowpossessroughlythesameshape,
SiriusA.Theveryshallowconvectiveshellproducingthisturbu-
with one positive lobe roughly symmetric about the line cen-
lentvelocityfieldmayhostsupersonicconvectionflows(Kupka
ter and occupying most of the width of the line profile. Neg-
etal.2009).Thiscouldprovidethesourceofsharpvelocityand
ative lobes surrounding the positive one, if they exist, do not
magneticgradientsneededtoproducestronglyasymmetricpro-
exceed the noise level in the data sets available to us. These
files.Shockstravelinginthissuperficialturbulentzonemayalso
profileshapesdisplayingnetcircularpolarizationareatypicalof
contributetoamplifyanyexistingmagneticfield,aspreviously
Zeeman signatures observed in other classes of magnetic stars,
proposed in the context of the Mira star χ Cygni (Lèbre et al.
where the integral of the Stokes V profile is generally close to
2014).
null. This peculiar shape naturally prompts questions about the
In any case, a physical model able to produce a convincing
origin of these polarized spectral features. The tests conducted
reproduction of the peculiar polarized signatures reported for
in our study show that these unexpected signatures depend on
Am stars still needs to be developed. Preliminary simulations
spectral line parameters (wavelength, Landé factor, line depth),
ofStokesVprofileswithvelocityandfieldgradientsshowthat
asexpectedfromaZeemansignal.
signatures such as those observed in beta UMa, theta Leo, and
Stokes V profiles that are nearly symmetric about the line
Sirius A can be reproduced (C. Folsom, priv. comm.). Without
center are common. These patterns are temporarily observed
suchatoolatourdisposal,anyquantitativedescriptionoftheas-
when two magnetic poles of an inclined dipole are seen on the
sociatedsurfacemagneticfieldsisoutofreach,sincetechniques
visible hemisphere of a star, close to the limb, and therefore
with different radial velocities (at the so-called crossover rota- commonlyusedtoestimatestellarmagneticfieldstrengths(like
the center-of-gravity method) are not suited to model Stokes V
tional phases). This simple interpretation is, however, very un-
profilesfollowingsuchunexpectedshape.Inpractice,magnetic
likely here since our co-added LSD profiles mix data collected
strengths derived for β UMa and θ Leo by applying the usual
overtimespansmuchlongerthanthetypicalrotationperiodsof
methods canonly provide uswith alower limit ofa few tenths
Amstars,mergingalargenumberofrandomrotationphases.A
ofagaussonthesurfaceaxisymmetricfieldcomponent,which
dominanttoroidalmagneticfieldcomponentisalsoabletogen-
isconsistentwiththeestimateavailableforonSiriusA.
eratesymmetricStokesVprofiles(Donatietal.2005),although
thisspecifictypeofmagneticgeometryshouldnotproduceany
netcircularpolarization,asobservedhere.Inanycase,apurely 5.2. OriginofthemagnetismofAmstars
geometric explanation is not able to account for the absence of
negativelobesintheStokesVprofiles. With only small number of objects observed so far and polari-
Anumberofcoolactivestarswerereportedtodisplayweak metric signatures close to the detection limit, our observations
net circular polarization after integration over LSD line pro- onlyofferafewhintstothephysicalingredientsinvolvedinthe
files (Petit et al. 2005; Aurière et al. 2008; Morgenthaler et al. generationoftheweaksurfacemagneticfieldsobservedinAm
2012; Aurière et al. 2011; Tsvetkova et al. 2013; Lèbre et al. stars.
2014). However, no similar findings have been reported so far An important clue to distinguishing between a dynamo-
in strongly magnetic massive stars or intermediate-mass stars, generatedfieldandmostotherscenariosisthelong-termevolu-
andtheverysubtleeffectreportedforcoolstarsisnowherenear tionoftheobservedmagneticfield,becauseadynamo-generated
theextremestituationreportedhere.Forcoolstars,theproposed fieldislikelytoexperiencesometemporalvariabilityonasec-
interpretation was adapted from solar physics, where abnormal ular timescale. By splitting our data sets into subsets limited to
Stokes V are routinely described (e.g., Solanki 1993) and at- agivenyearofobservation,weareabletogetafirstglimpseat
tributedtosimultaneousverticalgradientsinvelocitiesandmag- thestabilityofthepolarimetricsignal(Fig.5).Wefindthatsig-
neticfieldstrengths(LópezAriste2002andreferencestherein). naturesrecoveredoneyearapartareconsistentwitheachother,
Single-lobedsignaturesresemblingthoserecordedforAmstars showing that any variability over this timespan remains below
canbelocallyobservedinsolarmagneticelements(Viticchié& thenoiselevel.Thisoutcomeisconsistentwithsimilarattempts
Sánchez Almeida 2011; Sainz Dalda et al. 2012), but they are forSiriusAandVega.
more difficult to justify in the case of disk-integrated measure- Surface brightness inhomogeneities are usually associated
ments(asobtainedforunresolvedstars)becauseoftheorganized withthestructuredmagneticfieldproducedbyaglobaldynamo.
Thelackofanyrotationperiodestimateavailableintheliterature
2 an observation confirmed by independent HARPSpol observations forβUMaandθ Leosuggeststhatanysuchbrightnesspatches
carriedoutbyKochukhov(2014). must take place on relatively small spatial scales or be limited
Articlenumber,page6of11
A.Blazèreetal.:Detectionofultra-weakmagneticfieldsinAmstars:βUMaandθLeo
to a very low contrast. We note that the recent discovery of ro- Aurière,M.,Wade,G.A.,Silvester,J.,etal.2007,A&A,475,1053
tational modulation in Am stars of the Kepler field by Balona Ballering,N.P.,Rieke,G.H.,Su,K.Y.L.,&Montiel,E.2013,ApJ,775,55
et al. (2015) was limited to targets that are significantly cooler Balona,L.A.2013,MNRAS,431,2240
Balona,L.A.,Catanzaro,G.,Abedigamba,O.P.,Ripepi,V.,&Smalley,B.2015,
than the objects of our study. A possibility is that the deeper
MNRAS,448,1378
convectiveenvelopeofstarsintheKeplersamplemaybemore Böhm,T.,Holschneider,M.,Lignières,F.,etal.2015,A&A,577,A64
favorabletotheonsetofalarge-scaledynamo.Averysensitive Boyajian,T.S.,McAlister,H.A.,vanBelle,G.,etal.2012,ApJ,746,101
method,suchastheoneemployedbyBöhmetal.(2015)tode- Braithwaite,J.&Cantiello,M.2013,MNRAS,428,2789
Braithwaite,J.&Spruit,H.C.2015,ArXive-prints
tect very faint starspots on Vega, may be the key to unveiling
Donati,J.-F.,Paletou,F.,Bouvier,J.,&Ferreira,J.2005,Nature,438,466
surface features on weakly magnetic Am stars like those stud-
Donati,J.-F.,Semel,M.,Carter,B.D.,Rees,D.E.,&CollierCameron,A.1997,
iedhere.Wealsonotethelackofdocumentedflaringeventsfor MNRAS,291,658
these bright and well-studied stars, again in contrast to claims Donati,J.-F.,Semel,M.,&Rees,D.E.1992,A&A,265,669
forcoolerintermediate-massstarsobservedwithKepler(Balona Ferrario,L.,Pringle,J.E.,Tout,C.A.,&Wickramasinghe,D.T.2009,MNRAS,
400,L71
2013;Balonaetal.2015).
Folsom,C.P.,Likuski,K.,Wade,G.A.,etal.2013,MNRAS,431,1513
Gaurat,M.,Jouve,L.,Lignières,F.,&Gastine,T.2015,A&A,580,A103
Horne,K.1986,PASP,98,609
5.3. Towardasystematicexplorationofweakmagneticfields
Jouve,L.,Gastine,T.,&Lignières,F.2015,A&A,575,A106
inAmstars Kochukhov,O.2014,inPuttingAStarsintoContext:Evolution,Environment,
andRelatedStars,ed.G.Mathys,E.R.Griffin,O.Kochukhov,R.Monier,&
Theultra-deeppolarimetriccampaigncarriedoutforthreebright G.M.Wahlgren,389–397
Am stars is far from exhausting the exploration of this stellar Kochukhov,O.,Makaganiuk,V.,&Piskunov,N.2010,A&A,524,A5
class.Themostnoticeabledifferencebetweenthesestarsisthat Kupka,F.,Ballot,J.,&Muthsam,H.J.2009,CommunicationsinAsteroseis-
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β UMa and θ Leo seem to be located near the end of the main
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sequence,whileSiriusAisamorestandardmainsequenceob-
tronomiquedeBeograd,65,223
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turesinanyobviousway. Lignières,F.,Petit,P.,Böhm,T.,&Aurière,M.2009,A&A,500,L41
LópezAriste,A.2002,ApJ,564,379
While Sirius A and θ Leo share a low projected rotational
Lüftinger,T.,Fröhlich,H.-E.,Weiss,W.W.,etal.2010,A&A,509,A43
velocity,βUMadisplaysahighervsinivalue,althoughitisnot Maestro,V.,Che,X.,Huber,D.,etal.2013,MNRAS,434,1321
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inclinationeffectsinthisparameter.ThelargernormalizedEW Monier,R.2005,A&A,442,563
Morgenthaler,A.,Petit,P.,Saar,S.,etal.2012,A&A,540,A138
ofthepolarimetricsignalreportedforβUMamaybeafirsthint
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ofarotationaldependenceoftheweakmagnetismofAmstars,
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Acknowledgements. WeacknowledgesupportfromtheANR(AgenceNationale Silvester,J.,Kochukhov,O.,&Wade,G.A.2014,MNRAS,444,1442
delaRecherche)projectImagine.ThisresearchhasmadeuseoftheSIMBAD Silvester,J.,Wade,G.A.,Kochukhov,O.,etal.2012,MNRAS,426,1003
databaseoperatedattheCDS,Strasbourg(France)andofNASA’sAstrophysics Solanki,S.K.1993,SpaceSci.Rev.,63,1
DataSystem(ADS).CPFissupportedbytheANRgrant"Toupies:Towardsun- Tsvetkova,S.,Petit,P.,Aurière,M.,etal.2013,A&A,556,A43
derstandingthespinevolutionofstars".GAWacknowledgesDiscoveryGrant Viticchié,B.&SánchezAlmeida,J.2011,A&A,530,A14
supportfromtheNaturalScienceandEngineeringResearchCouncil(NSERC) Wade,G.A.,Folsom,C.P.,Petit,P.,etal.2014,MNRAS,444,1993
ofCanada.Wearegratefultothereferee,IosifRomanyuk,forconstructivecom- Wade,G.A.,Grunhut,J.,Alecian,E.,etal.2013,IAUS302,ArXive-prints
ments. 1310.3965
Zorec,J.&Royer,F.2012,A&A,537,A120
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Articlenumber,page7of11
A&Aproofs:manuscriptno.article_Am_v10
βUMa
1.5e-05
2e-05 low g
1e-05
high g
V/Ic 5e-006
-5e-06
1e-05
1.5e-05
1e-05
N/Ic 5e-006 V
0
-5e-06
1
I/Ic -1e-05
βUMa
0.95
-200 -100 0 100 200 -200 -100 0 100 200
velocity (km/s)
θLeo
1e-05 1.5e-05
low g
high g
V/Ic 0 1e-05
-1e-05 5e-06
4e-06
2e-06
N/Ic 0 V 0
-2e-06
-4e-06
-6e-06 -5e-06
1
I/Ic0.95 -1e-05
θLeo
-1.5e-05
-200 -100 0 100 200 -200 -100 0 100 200
velocity (km/s) v (km/s)
Fig. 1. Coadded LSD profiles in Stokes I (bottom) and V (top). The
twoavailable“null”controlparametersNull1andNull2areshownin
themiddlepanel.Top:βUMaobservations.Bottom:Samefigureforθ 0.008
Leo.Allprofilesarenormalizedtothecontinuumlevel.
high g
0.006 low g
0.004
0.002
V/Ic 0
-0.002
-0.004
-0.006 α2 CVn
-200 -100 0 100 200
velocity (km/s)
Fig.2.Top:ComparisonoftheStokesVprofilesobtainedbyselecting
photosphericlinesoflow(redthinline)andhigh(greenthinline)mag-
neticsensitivityforβUMa.Thethickredandgreenlinesrepresenta
movingaverageoverthreespectralbinsofthethinlines.Center:same
figureforθLeo.Bottom:sameforα2CVn.Allprofilesarenormalized
tothecontinuumlevel.
Articlenumber,page8of11
A.Blazèreetal.:Detectionofultra-weakmagneticfieldsinAmstars:βUMaandθLeo
βUMa
3e-05
low depth
red wavelength high depth
blue wavelenght
2e-05
1e-05
1e-05
V/Ic 0 V
0
-1e-05
-1e-05
βUMa
-2e-05
-200 -100 0 100 200 -200 -100 0 100 200
velocity (km/s) v (km/s)
θLeo
low depth
high depth
red wavelegnth 2e-05
1e-05 blue wavelength
1e-05
0
V/Ic 0 V
-1e-05
-2e-05
-1e-05
-3e-05
θLeo
-200 -100 0 100 200 -200 -100 0 100 200
velocity (km/s) v (km/s)
α2 CVn
red wavelength 0.01 low eeq
blue wavelength high eeq
0.005
0.005
V/Ic 0 V 0
-0.005
-0.005
-200 -100 0 100 200 -300 -200 -100 0 100 200 300
velocity (km/s) v (km/s)
Fig.3.SameasFig.2forphotosphericlinesoflow(thinredline)and Fig.4.SameasFig.2forphotosphericlinesoflow(thinredline)and
high(thingreenline)wavelength. high(thingreenline)centraldepth.
Articlenumber,page9of11
A&Aproofs:manuscriptno.article_Am_v10
1.5e-05
2010
2011
1e-05
5e-06
V/Ic
0
-5e-06
βUMa
-200 -100 0 100 200
velocity (km/s)
1e-05 2012
2013
2014
V/Ic 0
-1e-05 θLeo
-200 -100 0 100 200
velocity (km/s)
à
Fig.5.Top:MeanStokesVprofilesforthedifferentyearsofobserva-
tionofβUMa.Bottom:samefigureforθLeo.
Articlenumber,page10of11