Searching for links between magnetic fields and stellar evolution. I. A survey of magnetic fields in open cluster A- and B-type stars with FORS1

0.54 MB·English

by  S. Bagnulo

Astronomy&Astrophysicsmanuscriptno.4223 c ESO2008
(cid:13)
February4,2008
Searching for links between magnetic fields and stellar evolution
⋆
I. A survey of magnetic fields in open cluster A- and B-type stars with FORS1
S.Bagnulo1,J.D.Landstreet2,E.Mason1,V.Andretta3,J.Silaj2,andG.A.Wade4
6 1 EuropeanSouthernObservatory,Casilla19001,Santiago19,Chile.e-mail:[email protected], [email protected]
0 2 Physics&AstronomyDepartment,TheUniversityofWesternOntario,London,Ontario,CanadaN6A3K7.
0 e-mail:[email protected], [email protected]
2
3 INAF-OsservatorioAstronomicodiCapodimonte,salitaMoiariello16,80131Napoli,Italy.e-mail:[email protected]

n 4 DepartmentofPhysics,RoyalMilitaryCollegeofCanada,P.O.Box17000,Station‘Forces’Kingston,Ontario,CanadaK7K7B4.
a e-mail:[email protected]
J

3 Received:19September2005/Accepted:12January2006
2

ABSTRACT
1
v
Context. About5%ofuppermainsequencestarsarepermeatedbyastrongmagneticfield,theoriginofwhichisstillmatterofdebate.
6
1 Aims. Withthisworkweprovideobservationalmaterialtostudyhowmagneticfieldschangewiththeevolutionofstarsonthemainsequence,
5 andtoconstraintheoryexplainingthepresenceofmagneticfieldsinAandB-typestars.
1 Methods. Using FORS1in spectropolarimetric mode at theESO VLT, we havecarried out a survey of magnetic fieldsin early-type stars
0 belongingtoopenclustersandassociationsofvariousages.
6 Results. Wehavemeasuredthemagneticfieldof235early-typestarswithatypicaluncertaintyof 100G.Inoursample,97starsareApor
0 Bpstars.Forthesetargets,themedianerrorbarofourfieldmeasurementswas 80G.Afieldhasb∼eendetectedinabout41ofthesestars,37
/ ∼
h ofwhichwerenotpreviouslyknownasmagneticstars.Forthe138normalAandB-typestars,themedianerrorbarwas136G,andnofield
p wasdetectedinanyofthem.
-
o
r
t Keywords.Stars:magneticfields–Stars:chemicallypeculiar–Stars:evolution–Polarization–Techniques:polarimetric
s
a
:
v
1. Introduction portantproblemsremain unsolved.Amongthese are two ma-
i
X jorquestions.First,althoughthereisstrongevidence(e.g.,the
The presence of strong ( 1kG) magnetic fields in some of
r ∼ stability of the observedfields, the lack of symptomsof Sun-
a the A- and B-type stars of the upper main sequence has been
like activity, and the lack of any important correlation of ob-
knownformorethan50years(Babcock1947).Thesefieldsare
served field strength with rotationalangular velocity)that the
almostinvariablyassociatedwithasuiteofotherunusualchar-
observed fields are fossil fields, it is not yet clear how these
acteristics,whichinclude(a)specificangularmomentumofthe
fields evolve during the main sequence phase. Secondly, al-
orderof10% orless of the typicalvaluefor normalmain se-
thoughitisbelievedthatthebasicmechanismleadingtoboth
quencestarsofsimilarmass;(b)quiteanomalousatmospheric
chemicalanomaliesandtoatmosphericinhomogeneitiesisthe
chemicalcomposition,whichistofirst approximationafunc-
competitionbetweengravitationalsettling,radiativelevitation,
tion of effective temperature(and thus is apparentlyan atmo-
and various hydrodynamic processes, the interplay of these
spheric rather than a global feature); and (c) variation of the
processesisstillverypoorlyunderstood.
spectrum,lightandmagneticfieldwiththestar’srotationalpe-
Inthissituation,itishelpfultolooktoobservationstoguide
riod,thatclearlyindicatethepresenceofquitesignificantabun-
physical theory. One kind of information about the magnetic
danceinhomogeneitiesandofa magneticfield notsymmetric
Ap and Bp stars (hereafter referred to as magnetic Ap stars)
abouttherotationaxis.
that has been almost entirely lacking is the age of observed
Although considerable progress has been made in under-
stars.Goodageinformationwouldbeveryusefulfordiscern-
standingthephysicalprocessesatworkinthesestars,manyim-
ingsystematicevolutionarychangesinfieldstrength,chemical
⋆ BasedonobservationsmadewithESOTelescopesattheParanal composition,rotationrates,etc.Thegenerallackofusefulage
Observatory under programme ID 068.D-0403, 070.D-0352, 272.D- informationaboutmagneticApstarsoccursbecausealmostall
5026,073.D-0498,and074.D-0488 of the bright magnetic Ap stars are field stars. Even with the
2 S.Bagnulo,J.D.Landstreet,E.Mason,etal.:AsurveyofmagneticfieldsinopenclusterA-andB-typestarswithFORS1
accurateparallaxesnowavailablefromtheHipparcosmission, ofthepresentsurveyofmagneticclusterstarswefirstconsider
theuncertaintiesinluminosityandeffectivetemperatureofAp the extent to which ages and masses may be derived for the
starsarelargeenoughthatplacingthemintheHRdiagramonly starsinthefield.
sufficestodetermineveryroughlytheirstageofevolution(see
Temperaturesformanyoffieldstarsmaybeestimatedus-
Sec2.1below).
ingavailableUBV,uvby,orGenevaphotometry,togetherwith
TheobviouswaytoobtainimprovedagesformagneticAp calibrationsprovidedbySte¸pien´ &Dominiczak(1989),Hauck
stars is to observe such stars in open clusters. Until recently & North (1993), and Napiwotzki, Scho¨nberner, & Wenske
suchastudyhasnotbeenpossiblebecauseclusterApstarsare (1993).Luminositiesrequiredistancesandbolometriccorrec-
mostly fainter than V 6 or 7, beyond the limit of accurate tions. Distances to many nearby Ap stars have recently been
≈
magneticfield measurementswith availableinstruments.This accuratelydeterminedbytheHipparcosproject(seeGomezet
situation has changed due to the development of a new gen- al.1998);fortheApstarsnearerthanabout100pc,therelative
eration of highly efficient spectropolarimeters and observing distance errors are less than about 10%. The bolometric cor-
strategies,andtheiravailabilityonlargetelescopes.Inparticu- rections required have been discussed by Lanz (1984). Thus,
lar,theFORS1spectropolarimeterononeoftheESO8mVLT it is now possible to place a large number of Ap stars on the
telescopeshasbeenshowntobeapowerfultoolformeasuring HR diagram, and, using the evolution tracks for stars of vari-
fieldsinveryfaintApstars.Ithasrecentlybeenusedtodetect ousmasses,toestimateboththemassandtheageofindividual
afieldinastarofV =12.88,thefaintestmagneticApinwhich stars.ThisexercisehasbeencarriedoutbyGomezetal.(1998),
afieldhaseverbeendetected(Bagnuloetal.2004). by Po¨hnlet al. (2005), and by Kochukhov& Bagnulo (2006)
Anotherveryimportantdevelopmenthasbeenthesubstan- for a very large sample of nearby Ap stars, and by Hubrig,
tialincreaseinthenumberofprobablemagneticApsidentified North, & Mathys (2000) for a special sample of particularly
in clusters, particularly by the systematic surveys of Maitzen slowlyrotatingmagneticApstars.Infact,asdiscussedbelow,
andhiscollaborators.Furthermore,theavailabilityofveryac- thismethodislimitedbylargeuncertainties.
curate proper motions for a very large number of stars from
EffectivetemperaturesofmagneticApstarsarestillsome-
the Hipparcos mission and the Tycho-2 catalogue has greatly
what uncertain, more so than for normal main sequence stars
facilitatedthecorrectseparationofclustermembersfromfore-
because of the peculiar energy distributions of Ap stars (see
groundandbackgroundstars.
Ste¸pien´andDominiczak1989).ArecenttabulationbySokolov
ThetimeisnowclearlyripeforstudyingmagneticApstars
(1998) of effective temperatures for nearly 70 Ap stars, with
inclusterstoobtainforthefirsttimeareasonablylargesample
comparisonstoearlierdeterminations,suggeststhattheuncer-
ofmagneticApstarsofknownabsoluteandevolutionaryages.
taintyinT typicallyabout5%,or 0.02dex.
eff
We have started to carry out such a survey, using the FORS1 ±
For Hipparcos parallaxes, the distance uncertainty at 100
spectropolarimeter.Thefirststageofthissurveyisreportedin
pc is about 8% (or about 0.035dex), and increases with the
this paper. Section 2 discusses the rationale and scope of this
distance itself. There is also an uncertainty in the appropri-
survey,inparticularwhattheadvantagesareofstudyingopen
ate bolometric correction (BC) to apply. First of all, there is
cluster stars compared to studying field stars, why FORS1 at
an uncertainty of 0.1mag in the estimate of the BC of a
the VLT is an ideal instrument for this survey, and how indi-
∼
normal A-type star (due in part to the uncertainty in T ).
vidualtargetshavebeenselected.Sections3–6describehow eff
Then, for Ap stars, one has to apply a correction to the nor-
themagneticfieldcanbedeterminedfromobservationsofpo-
malBC.AccordingtoLanz(1984)thiscorrectionisuncertain
larized spectra in terms of basic physics, observing strategy,
by 0.2mag. Finally, there is the uncertainty as to whether
datareduction,and B determination.Thesesectionscontain,
z ∼
h i oneshouldapplytheLutz-Kelkercorrection,about0.1magat
forotherFORS1 users,adetaileddiscussionofthe optimized
100pc.Takingtheseeffectstogether,fornearbyfieldstars,the
techniqueswehavedevelopedforfieldmeasurement,andmay
uncertaintyin M is 0.3mag,i.e., 0.1dexin log(L/L ).
be skipped by readers interested mainly in the observational bol
∼ ∼ ⊙
Theseuncertainties,onceconvertedinthe(logt,M/M )plane,
results. In Sect. 7 and 8 we present and discuss the observa-
⊙
correspondtoageuncertaintiesthatmaybeaslargeashalfthe
tionsobtainedduringthissurvey.Conclusionsarepresentedin
mainsequencelife.
Sect.9.
Fourexamplesofthiskindofinferenceareshownintheup-
perpanelofFig.1,forstarsofabout2.5M and4.0M ,each
2. Thescopeofthissurvey ⊙ ⊙
consideredforanagenearthebeginningofitsmainsequence
lifetimeandneartheend.Comparisonismadewiththetracks
2.1.Whyopenclusterstars?
ofSchalleretal.(1992)forZ = 0.02.Thestarpositionsinthe
The final goal of this series of papers will be to obtain ages, HRdiagram,withtheiruncertainties(shadedboxes),areshown
masses, and magneticfield strengthsfor a substantialnumber intheupperleftpanel.Thededucedpositionsintheage-mass
ofApstars,andstudywhetherthereareevolutionarychanges diagramareshownintheupperrightpanel.Itisclearthatthe
in the magnetic field strength. The magnetic (and sometimes errorboxesforobservationalcharacteristicsofApstarstrans-
theabundance)propertiesofalargesampleofApstarsinthe late intoageswhich are sufficientlyuncertainthatone cannot
field around the Sun are already known (e.g., Mathys 2004, resolveatleastthefirsthalfofthemainsequencelifetime.The
Cowley & Bord 2004). In principle, our evolutionary study situationissomewhatbetterneartheendofthemainsequence
couldbebasedonthesedataoffieldstars.Tojustifytheneed life,wheretheisochronesarefartherapart,buttypicallyanage
S.Bagnulo,J.D.Landstreet,E.Mason,etal.:AsurveyofmagneticfieldsinopenclusterA-andB-typestarswithFORS1 3
Z = 0.020
Z
AM10255075 100 10 25 5075100
S%%%% % % % %%%
5.0
3.0
4.5
M=5
2.5 4.0
M=4
n
L/LSu 2.0 3.5MSun
g M=3 3.0M/
o
l
1.5 M=2.5 2.5
M=2 2.0
1.0
M=1.7 1.5
4.30 4.20 4.10 4.00 3.90 3.80 7.0 7.5 8.0 8.5 9.0
log T [K] log t [yrs]
eff
Z = 0.008
Z
AM10255075 100 10 25 5075100
S%%%% % % % %%%
5.0
3.0
4.5
M=5
2.5 4.0 Fig.1. Top panels: the position of a
M=4 star in the HR diagram, and the star’s
n positiontransformedintoadiagramof
g L/LSu 2.0 M=3 33..05M/MSun asugmeiansgathfautnwcetioknnoowf estffeellcatrivmetaesms,paesr--
o
l 1.5 M=2.5 aTthueretr±an5s%foramnadtiolunmuisneossisttyan±d0a.r1d edveox-.
2.5
lution tracks for Z = 0.02 (Schaller et
M=2 al.(1992);severalfractionalages(frac-
2.0
1.40.30 4.20 4.10 4.0M=01.7 M=31.5.90 3.80 7 .0 7.5 8.0 8.5 9.01.5 tatirroaennslaofobfremmlleaaditni.oBnseoaqtsutoienmncthepealnitfoeeplscp:oatmhneepllsse,atbemdue)t
log T [K] log t [yrs] using tracks of metallicity Z = 0.008
eff
(Schaereretal.1993)
uncertainty of the order of 25% of the total main sequence A change in [Fe/H] of 0.4dex correspondsto a changein
±
lifetimeistobeexpected. metal abundanceof abouta factor of 2.5. This is just the dif-
ference in abundancebetween the evolutioncalculationswith
A further uncertainty in the transformation from the
Z = 0.008 and Z = 0.02 provided by the Geneva group
(logT ,log(L/L ))tothe(logt,M/M )planecomesfromthe
eff
⊙ ⊙ (Schalleretal.1992;Schaereretal.1993).Repeatingthetrans-
factthatwedonotknowaccuratelythebulkchemicalcomposi-
formation from the (logT , log(L/L )) to the (logt, M/M )
tionofanyfieldApstar,andthuswedonotknowwhatchem- eff
plane for Z = 0.008, we find the res⊙ults shown in the low⊙er
ical composition should be assumed in the theoretical tracks
panels of Fig. 1. (We have used the same values of T and
used for the comparison. To estimate the size of this effect, eff
log(L/L )asintheupperpanels.)Theeffectoftheuncertainty
weconsidertherangeofabundances([Fe/H])presentinopen
inbulkc⊙hemicalcompositionistoaddroughlyanother 0.25
clusters young enough to still have Ap stars (say logt < 9). ±
uncertainty to the deduced fraction of the main sequence life
Searching the WEBDA database (e.g. Mermilliod & Paunzen
completedbyaparticularstar.Overall,weseethatknowledge
2003),wefoundthatthisrangeisoftheorderof0.4dex.This
ofT andlog(L/L )providesuswithmassestimatesaccurate
result is confirmed by examination of the younger clusters in eff
⊙
to about 10%, but provides only poor age resolution, espe-
the catalogue of Chen, Hou, & Wang (2003). This range of ±
ciallyinthefirsthalfofthemainsequencelife(seealsoFig.4
abundancesmay represent a reasonable estimate of the range
ofKochukhov&Bagnulo2006).
ofvaluesof[Fe/H]presentinnearbyfieldstars.
4 S.Bagnulo,J.D.Landstreet,E.Mason,etal.:AsurveyofmagneticfieldsinopenclusterA-andB-typestarswithFORS1
Thesituationissubstantiallyimprovedifthestarisamem- 2.2.WhyFORS1attheVLT
ber of a cluster or association. The absolute age of the star is
Todecideonasuitableobservingstrategy,wemustdetermine
then known with essentially the precision of the cluster age.
what field strength we wish to detect. Among Ap stars in the
The uncertainty of this number varies from cluster to cluster,
local field, it appears that the median root-mean-square ob-
mainly because of the difficulty of deciding exactly where to
servedline-of-sightfieldstrength B isoftheorderof300G
placetheclusterturnoff.Typicallytheuncertaintyinlogtisof h zi
(Bohlender&Landstreet1990).Weassumethatthiswillalso
theorderof 0.2dex,about 50%oftheabsoluteage(seefor
± ± be typical of cluster Ap stars. In order to detect such a small
example Castellani et al. 1992), although more accurate ages
value, it is important for the survey to achieve measurement
are sometimes reported (e.g. Carrier et al. 1999). This repre-
uncertainties of the order of 100G or less, as far as possible
sents a very considerableimprovementin absolute age, espe-
independentofthestar’seffectivetemperatureandv sini.
ciallyforastarintheearlypartofitsmainsequencelife.Ifwe e
Inprinciple,wemaycarryoutasurveybysearchingeither
knowonlypositionintheHRdiagram,astarwithanactualage
of107yrandamainsequencelifetimeof109yrwouldhavean forvisibleZeemansplittingofspectrallinesinasimpleinten-
ageuncertaintyoftheorderof3108yr,whilethesamestarina sityspectrum,orbysearchingforthecircularpolarizationsig-
clusterwouldhaveanageuncertaintyofroughly3106yr.Only nature of a global field of simple structure. Although Mathys
and collaborators (e.g., Mathys et al. 1997) have shown that
forastarinaboutthelastthirdofitsmainsequencelifeisthe
Zeeman splitting may be detected in some tens of field stars,
age uncertaintynotsubstantially improvedby knowingthat it
thisrequiresquitespecialcircumstances(i.e.,v siniatmosta
is in a cluster. Another advantage of studying cluster stars is e
few kms 1, and field strength at least 2 kG) that are not met
thatonemaydeterminetheappropriateclusterbulkmetallicity −
inmostoftheknownmagneticApstars.Polarizationmeasure-
(andhencedecidewhatevolutiontrackstouseforcomparison)
ment is generally a far more sensitive and broadly-applicable
bystudyingthelowermainsequencestars.
methodoffielddetectionthanobservationofZeemansplitting.
The masses of cluster stars can be determined with simi-
Two main methods of measurement are currently in use
larmethodsandsimilar(orbetter)accuracythanforlocalfield
fordetectingthe circularpolarizationproducedby a non-zero
stars. The values of T are known with about the same ac-
eff value of B . One method exploits the Zeeman polarization
curacy as for local field stars, and there are the same uncer- h zi
in metal lines (e.g., Babcock 1958; Preston & Ste¸pien´ 1968;
taintiesforthebolometriccorrection.Hipparcosparallaxesare
Mathys&Hubrig1997;Wadeetal.2000;Elkin,Kudryavtsev,
normallynotavailable,butthevalueofluminosityisobtained
&Romanyuk2003).Fieldmeasurementbythismethodusually
fromtheobservedV magnitudetogetherwiththecluster’sap-
relies on circular spectropolarimetry with a resolving power
parent distance modulus (V M ). Recent determinations of
distance modulus by main se−queVnce fitting appear to achieve tRha≥n,3s1a0y4,.1I5ftohre2s0takrmissqu1itaenbdriaghritc,hwsitpheactvreumsin,fiiveladlueerrsomrsalσler
an accuracy of about 0.2mag (e.g., Robichon et al. 1999). − B
± assmall asa few G canbe achieved(Shorlinetal. 2002).On
This accuracy is generally obtained out to distances well be-
theotherhand,themeasurementuncertaintydependsstrongly
yondthosefewclustersforwhichaccurate( 25%)parallaxes
± onspectraltype(whichdeterminesthenumberofusablelines
are available.Furthermore,if we knowthe clustermetallicity,
and their intrinsic depths) and on v sini. In observationscol-
wecandecidewhichevolutiontrackstouse.Theprecisionof e
lectingsimilartotalnumbersofphotons,thestandarderrorof
the mass determination of cluster stars is about 10% if the
± fieldmeasurementcanvarybyafactoroforder102.
bulkcompositionisnotknown,andsomewhatbetterifitis.
A secondmethodemploysthe Zeemanpolarizationinthe
Our conclusion is that an age derived using only the po- wings of the Balmer lines. These lines may be observedwith
sition in the HR diagram of an individualAp star in the field quitelowresolvingpower(R 103),usingeitherinterference
is at present sufficiently uncertain to be of little value except filters(e.g.,Borra&Landstree∼t1980)oralow-dispersionspec-
for stars near the end of their main sequence lives (although trograph(Bagnuloetal. 2002). Since theBalmer linesare in-
importantconclusionscan still be drawn from statistical con- trinsicallybroad,thepolarizationsignalmaybeafactorof10
siderations:seePo¨hnletal.(2005)andKochukhov&Bagnulo smallerthaninthemetallines,andthebestachievablestandard
2006).Incontrast,ifthestarisamemberofaclusterofknown errorsareoforder30–50G(Landstreet1982).However,since
age, it is possible to determine accurately both the mass and theBalmerlinesarealwaysquitedeep,anddonotvarymuch
age(orfractionofmainsequencelifeelapsed).Therefore,the instrengthamongAandBstars,andsincetheoverallprofileat
study of Ap stars that are cluster members is of great value R 103ishardlyaffectedbyrotation,thismethodcanprovide
in understandingthe temporalevolutionof rotation,magnetic sta≈ndard errors that are fairly uniform simply by surveying a
fields,andatmosphericchemistryinallmagneticApstars. sampleofstarstoaspecifiedsignal-to-noiseratio.
AtpresentonlyafewclusterApstarcandidatesareknown The(spectro-)polarimetersnowinusemakebothkindsof
to be magnetic. The total number of clusters for which mag- fieldmeasurement.However,limitationsimposedbylowover-
netic observationshad beenpublishedis eight,with a total of allefficiencyand(usually)modesttelescopeaperturehavelim-
13starssurveyed.Inaddition,extensivesurveyshadbeencar- ited most of the B field measurements to stars not much
z
h i
riedinfortheOriOB1(Borra1981)andScoOB2associations fainter than V = 6. This magnitude limit has effectively pre-
(Thompsonetal.1987).Accordingly,wehavedecidedtocarry ventedanyserioussurveyofmagneticfieldsinclusterApstars,
outa surveyof magneticstars in openclustersto provideage asonlyahandfulofclustersandassociationshaveasignificant
informationforasubstantialsampleofApstars. numberofApstarsbrighterthanV = 6.Withalimitingmag-
S.Bagnulo,J.D.Landstreet,E.Mason,etal.:AsurveyofmagneticfieldsinopenclusterA-andB-typestarswithFORS1 5
neticaroundV =6,oneisrestrictedtoclustersandassociations tiveto abroaddepressionnear5200Åin theenergydistribu-
notmuchmorethan100pcaway,sincetheabsolutemagnitude tionofmostApstars(e.g.,Kupka,Paunzen,&Maitzen2003).
ofanApstaristypicallyintherangeof M 1to+1.Only In particular, Maitzen and collaborators (e.g., Maitzen 1993)
V
∼ −
halfadozenclustersarethisnear. have developeda narrow band photometricindex (∆a) which
ThedevelopmentoftheFORS1spectropolarimeterforthe isreasonablysensitivetothe spectralpeculiaritiesofAp stars
ESO Very Large Telescope (VLT) has changed the situation with effective temperatures in the range 8000 14000K.
∼ −
dramatically. FORS1 incorporates a multi-object low disper- Maitzen’sgrouphassystematicallyobtained∆aphotometryof
sionspectrographwithpolarizingoptics.Inpolarimetricmode, manyclusterstoidentifyApstars.The∆asystemhasalsobeen
spectra with R 103 may be obtained for up to nine objects used by Joncas & Borra (1981) to search for Ap stars in the
simultaneously∼inafield7 square.Bagnuloetal.(2002)have OrionOB1association.
′
shown that FORS1 can be used very effectively as a Balmer- ItisalsoknownthattheZindex,whichcanbecomputedfor
linepolarimeterforfieldmeasurement.Sincethisinstrumentis the many cluster stars for which Geneva photometry is avail-
mountedonan8mtelescope,andhasaveryhighthroughput, able, is a powerfuldiscriminant of Ap stars in approximately
thelimitingmagnitudeismuchfainterthanwithearlierinstru- the same temperature range as the ∆a index (e. g. Kramer &
ments.Bagnuloetal.(2004)haveusedFORS1todetectafield Maeder1980;Hauck&North1982).
in a star of V 13 in 2.8 hours of observation, and showed We have made extensive use of the WEBDA cluster
≈
thatitispossibletoreachaprecisionofσB 102 Ginabout database(e.g.Mermilliod&Paunzen2003),Simbad,andacat-
∼
1hourofintegrationatV = 10.Withalimitingmagnitudeof alogueofcandidateclusterApstarsbyRenson(1992).
10orevenfainter,wecansurveyclustersandassociationsout
Most of the surveysdiscussed abovehave made a serious
to several hundredpc, and the numberof clusters that can be
effort to determine cluster memberships, mainly on the basis
studiedrisestoroughly100.InadditionBagnuloetal.(2002)
of spatial location and apparent magnitude. However, recent
have shown that the low resolution does not prevent the use
work based on and stimulated by the Hipparcos astrometric
of metallinesto measurethe magneticfield in starswith rich
spacemissionhasledtoamajorexpansionintheavailabledata
metallicspectra.Thisfactmaybeusedtoincreasethesensitiv-
on parallaxes and proper motions. Hipparcos parallaxes (e.g.
ity of field measurementsin some stars. A third advantage of
Gomez et al. 1998) provide a valuable membership discrimi-
FORS1isthatinclusters,itisoftenpossibletoobserveseveral
nantouttoabout300pcformanyclusterstars.Evenmoreim-
stars simultaneously. We have used this capability to observe
portantly,theTycho(Høgetal.1998)andTycho-2(Høgetal.
multipleApcandidatestars,butalsonon-Apclustermembers
2000)propermotioncataloguesnowprovidepowerfultestsof
inthehopesofmakingserendipitousfielddetections.
membershipouttonearlyonekpc,foramuchlargernumberof
This survey is biased toward stars with longitudinal field stars, asdemonstratedforexamplebyRobichonetal. (1999),
ofabsolutevaluelargerthanabout200–300G,butisnotbi- deZeeuwetal.(1999),andDias,Le´pine,&Alessi(2001).
ased with respect to vsini. Any bias with respect to spectral
Using the resources discussed above, a database contain-
type is primarily a feature of the previous classification pro-
ing a variety of information on more than 200 suspected Ap
grammes that have identified candidate magnetic Ap stars in
clustermembersinmorethan70clustersandassociationswas
clusters,ratherthanafeatureimposedbyaninstrumentalfield
constructed and used for the selection of the targets. In gen-
detection sensitivity that depends on the star’s spectroscopic
eral,wehavegivenhighestprioritytostarswhichappeartobe
features.
probableApstars,andprobableclustermembers,butwehave
alsoobservedanumberofstarsforwhichatleastoneofthese
criteria was uncertain. Up to the present time, we have been
2.3.Thetargetlist
abletoobserve(oroccasionallyfindintheliterature)magnetic
Twoproblemsariseintheselectionofalistofsuitabletargets observationsofabout1/3ofthestarsinourdatabase.
forasurveyofmagneticfieldsinclusterstars:(a)identification Clustermembershipwillbediscussedinthesecondpaper
ofcandidateApstarsinthefieldofindividualclusters(mostof inthisseries(Landstreetetal.,inpreparation,hereafterreferred
the known Ap stars are field stars) and (b) determination of to as Paper II), where we will analyze the astrophysical and
clustermembership. evolutionaryresults of our surveyin more detail. The present
Numerous studies have identified probable Ap members paperfocusesonthemagneticobservationsthemselves.
of clusters and associations. Surveysfor Ap/Bp cluster mem-
bers based on low-dispersion spectroscopy were reported by
Hartoog (1976, 1977), and by Abt (1979). Probable Ap stars
3. Thebasicformulae
have also been reported from a number of studies of indi-
vidual clusters (e.g. Dachs & Kabus 1989). Furthermore, the Thediagnostictoolforstellarmagneticfieldsusedinthiswork
Michigan Spectral Survey (e. g. Houk & Smith-Moore 1988) has been proposed by Bagnulo et al. (2002). Here we review
hasprovideduniformMKclassificationsforalargenumberof andelaboratethismethod.
HDstarsinthefieldsofclusterssouthofδ=+5◦.Thisallowed Themeanlongitudinalmagneticfield Bz ,i.e.,thecompo-
ustoselectsomeApstarsthatarepossibleclustermembers. nentofthemagneticfieldalongthelineohfsigihtaveragedover
Another important source of identifications of cluster Ap the visible stellar disk, can be measured through the analysis
stars has been the use of photometric indices that are sensi- of the circular polarizationof spectral lines. In the weak field
6 S.Bagnulo,J.D.Landstreet,E.Mason,etal.:AsurveyofmagneticfieldsinopenclusterA-andB-typestarswithFORS1
regime (i.e., when the Zeeman splitting is small compared to 4.1.Instrumentmode
thelineintrinsicbroadening)wehave(e.g.Landstreet1982)
SpectropolarimetrywithFORS1canbeperformedintwodif-
V 1 dI ferentobservingmodes:fastmodeandfimsmode.Fastmodeis
= g C λ2 B , (1)
I − eff z I dλ h zi usedforobservationsofindividualobjectsthatcanbeacquired
‘fast’ with a simple centering on the slit. Fims mode permits
whereg is the effectiveLande´ factor(1 forH Balmer lines,
eff one to place slitlets on up to nine targets within a 6.8 6.8
′ ′
see Casini& LandiDegl’Innocenti1994),V istheStokespa- ×
fieldofview(multi-objectspectropolarimetry).Wheneverour
rameter which measures the circular polarization, I is the to-
maintargetswereinafieldincludingotherstarsofsimilarmag-
tal(unpolarized)intensity,λisthewavelengthexpressedinÅ,
nitude, we observed in fims mode. In this way, in addition to
B isthelongitudinalfieldexpressedinGauss,and
h zi polarizedspectraofApstars,weobtainedpolarizedspectraof
e numerousnormalAandB-typeclusterstars.
C = ( 4.67 10 13Å 1G 1) (2)
z 4πm c2 ≃ × − − −
e
4.2.Grismchoice
whereeistheelectroncharge,m theelectronmass,andcthe
e
speedoflight.ForatypicalA-staratmosphere,theweak-field
We have used the grisms 600B and 600R, which cover the
approximationholdsforfield strength< 1kG formetallines,
spectral ranges 3450–5900Å, and 5250–7450Å, respectively.
∼
andupto 10kGforHlines.
∼ Grism 600B covers all H Balmer lines from Hβ down to the
A least-squarestechniquecan beused to derivethelongi-
Balmer jump; grism 600R covers Hα. Both grisms have 600
tudinalfieldviaEq.(1).Weminimisetheexpression groovesmm 1,andyielddispersionsof1.20Å,and1.08Åper
−
pixel, respectively. With a 1 slit width they provide spectral
(y B x b)2 ′′
χ2 = i−h zi i− (3) resolvingpowersof780and1160,respectively.
σ2
Xi i For this study, grism 600B seems a better choice than
600R.AlthoughHαismoresensitivetothemagneticfieldthan
where, for each spectral point i, y = (V/I), x =
i i i
individualHBalmerlinesatshorterwavelengths(theZeeman
g C λ2(1/I dI/dλ),andbisaconstant.Foreachspectral
− eff z i × i effect depends quadratically upon wavelength), the combined
pointi,thederivativeofStokesI withrespecttowavelengthis
analysisofseveralBalmer linesfromHβdownto theBalmer
evaluatedas
jumpleadstoasmallererrorbarthantheanalysisofHαonly.
dI Furthermore, the flux of an A-type stars is larger in the blue
= Ni+1−Ni−1 (4)
dλ!λ=λi λi+1−λi−1 tahsahnoirntetrhientreegdr,attihoenretfiomreeuthseinsgagmreismSN6R00cBanrabteherreathchanedgwrisitmh
where i is thephotoncountat wavelengthλi. The estimates 600R. On the other hand, it should be noted that the useful
N
for the errors on the parameters Bz and b are given by the field of view in fims mode dependson the spectral range that
h i
diagonal elements of the inverse of the χ2 matrix (see, e.g., onewishestocover:thelargerthespectralrangethatoneneeds
Bevington1969). to observe,thesmaller thespatialregionwhereonecanplace
Theapplicationofaleast-squarestechniqueisjustifiedif slitlets.Hence,infimsmode,grism600Roffersmoreflexibil-
itythangrism600B,asitsusefulwavelengthcoveragecorre-
B σ σ (5)
h zi xi ≪ yi spondsto Hα only, which doesnot puta strong constrainton
thefieldofview.In(ESOperiod)P68weusedgrism600R(in
(see,e.g.,Bevington1969),where
combinationwith the order separation filter GG435). In P70,
2 1 2 dI 2 1 2 P72,P73,andP74,weusedgrism600B(withnoordersepa-
σ2 = g C λ2 σ2+ σ2 (6) rationfilter).
xi − eff z i  −I2! dλ ! I I! dI/dλ
(cid:16) (cid:17)  i  0.5Foorr0m.8os.toftheobservations,wehaveusedaslitwidthof
and ′′ ′′
σ2 =σ2[(V/I)]
yi i 4.3.CCDreadout
Forthe stars studiedin thiswork,we haveverifiedthat,at all
In polarimetric mode, overheads represent a significant frac-
observedwavelengths,Eq.(5)isverified.
tion of the total telescope time. Ultra-high SNR observations
(needed to reach the wanted uncertainty of 100G) require
∼
multiple exposures, hence, multiple CCD readouts. We mini-
4. Instrumentandinstrumentsetup
mizedtheCCDreadouttimeasfollows.Incaseofobservations
The Focal Reducer/Low Dispersion Spectrograph FORS1 of of individual stars (fast mode) we used a windowed read-out
theESOVLTisamulti-modeinstrumentequippedwithpolari- mode of 2048 400 pixels. In case of multi-object observa-
×
metricoptics.Theinstrumentcharacteristicsandperformances tions(fimsmode)wherethefullsize oftheCCD wasneeded,
are outlinedby Seifertetal. (2000) andin the FORS1/2 User we used a 4-port readout. The lowest available gain was se-
Manual(VLT-MAN-ESO-13100-1543).InthissurveyFORS1 lected, asto maximisethe actualelectroncapacity,hence,the
hasbeenusedasalowresolutionspectropolarimeter. SNRthatcanbereachedwitheachsingleexposure.
S.Bagnulo,J.D.Landstreet,E.Mason,etal.:AsurveyofmagneticfieldsinopenclusterA-andB-typestarswithFORS1 7
5. Datareduction plateangles.Wefoundthatthislattermethodoccasionallyin-
troducesspuriouspolarizationsignals.
5.1.Framepre-processing,spectrumextractionand
Wavelength calibration typically led to RMS scatter of
wavelengthcalibration 0.1pixelsandmaximumerrorof 20kms 1.Thefinetun-
−
∼ ≤
ing of wavelength calibration based on night sky lines could
Thedatahavebeenreducedandoptimallyextractedusingstan-
not be performed. Therefore the accuracy of the wavelength
dard IRAF routines. All the science frames have been bias
calibration is restricted by instrument flexures, which are ex-
subtracted with the corresponding master bias obtained from
pectedtobelessthan1pixeluptoazenithdistanceof60 (see
◦
a series of five frames taken the morning after the obser-
FORS1/2 User Manual). Numerical tests show that this is of
vations. No flat fielding procedure has been applied to our
negligibleimpactonthe determinationofthemeanlongitudi-
data. By performing reduction experiments with and without
nalmagneticfield, usingthe methoddescribedby Bagnuloet
flat-fielding, we have verified that flat fielding does not in-
al.(2002)andelaboratedbelow.
fluence significantly the final computation of the Stokes pro-
files. In fact, flat fields obtained with the grism 600B are
severelyaffectedbyinternalreflectionsfromtheLongitudinal 5.2.ObtainingStokesV
Atmospheric Dispersion Corrector (LADC). Frames obtained
Circularpolarizationmeasurementsareperformedbyinserting
in fims mode were read out in four ports. The CCD is thus
the quarter-wave plate and the Wollaston prism into the opti-
divided in four quadrants, each of them characterized by its
calpath.A combinationofexposurestakenatdifferentwave-
ownbiaslevelandgain.Inordertocompensateforthediffer-
plate orientationsallows one to minimise the contributionsof
entgains,wemultipliedeachscienceframesbytheratioofan
spurious (instrumental) polarization. The FORS user manual
imagingscreenflatreadoutinoneportandanimagingscreen
explains that instrumentalpolarization cancels out to the first
flatreadoutoutinfourports.
orderifStokesV isobtainedfrom
Whenextractingthespectrawefoundthattheuseofstan-
dardextractionapertures( 10 pixelswidth) introducedarte- V 1 fo fe fo fe
∼ = − − , (7)
factsintotheStokesV spectrum.Thisproblemwassolvedus- I 2 fo+ fe! − fo+ fe! 
ing aperturesas large as 4 5 times the spatial FWHM of  α=−45◦ α=+45◦
thespectrum,i.e.,typicall∼y50−pixelswidth.Aperturesthatare where fo and fe aretheordinaryandextraordinarybeams,re-
not symmetric about the flux peak have been used for stars spectively,andαisthepositionangleoftheretarderwaveplate
close to the edge of the slit. This occurred occasionally for (infact,notethattheFORS1/2manualgivestheformulawith
targets observed in fims mode. We used a high-order ( 15) the opposite sign). Another possibility is to obtain Stokes V
Legendrefitting functionto trace the spectrum1. Lower∼order from
functionswereusedonlyinthecaseoflowSNRsecondarytar- V r 1
= − (8)
gets (typically in framesobtained in fims mode) and/orin the I r+1
caseofspectrathelengthofwhichoccupiedjustafractionof
where
theCCD(againinfimsframes,dependingonthepositioningof
theslitlets). r2 = (fo/fe)α=−45◦
Sky subtraction was performeddifferently for spectra ob- (fo/fe)α=+45◦
tained in fast and fims mode.In the first case the sky subtrac-
(e.g.,Donatietal.1997).WehaveverifiedthatEqs.(7)and(8)
tionwasperformedselectingsymmetricregionsontheleftand
giveconsistentresultsbothforStokesV and B .
z
rightsideofeachspectrum(typicallybetweenpixel40and50 h i
TheerrorbarassociatedwiththeStokesV/I,computedvia
fromthecentralpeak),andfittingthosewithaChebyshevpoly-
Eq.(7)is
nomial.Inthecaseofdataobtainedinfimsmode,wheneverthe
starwasnotpositionedatthecenteroftheslitlet, theskywas σ2[(V/I)] = fe 2σ2 + fo 2σ2 +
ewsetimfoautneddothnajtussktyo-nseubretrgaicotnioantoisnneostidceriotifctahleinsptehcetrsuemns.eInthfaatcitt, (cid:18)(cid:16)(fo+fefe)2(cid:17)2σ2fo +(cid:16)(fo+fofe)2(cid:17)2σ2fe(cid:19)α=−45◦ (9)
(fo+fe)2 fo (fo+fe)2 fe
doesnotsignificantlyaffectthefinalresults.Insomecases,we (cid:18)(cid:16) (cid:17) (cid:16) (cid:17) (cid:19)α=+45◦
preferrednotto performsky-subtractionatall, because ofthe Equation(9)canbesimplifiedasfollows.Letusassume
presenceofLADCreflectionsclosetothespectrum.
σ2 = σ2 = fo = fe =
The FORS1 calibration plan includes wavelength calibra- (cid:16) fo(cid:17)α=±45◦ (cid:16) fe(cid:17)α=±45◦ (cid:0) (cid:1)α=±45◦ (cid:0) (cid:1)α=±45◦ N
tions frames obtained at all retarder waveplate positions used where is an estimate of the photoncount in a given wave-
N
for the science. However, we found that the best and safest lengthrange.Formpairsofobservations(i.e.,oneexposureat
strategyistouse,foracompletesetofsciencedata,justasin- α = 45 , and one exposure at α = 45 , repeated m times),
◦ ◦
−
gle wavelength calibration frame, and not match science and Eq.(9)becomes
wavelengthcalibrationframesaccordingtotheirretarderwave-
1
σ2[(V/I)]= (10)
4m
1 ThehighorderofthefittingfunctionisjustifiedbythehighSNR N
thatmakesitpossibletotraceveryaccuratelythespectrumacrossthe Equation(10)simplystatesthattheerrorbaronV/I decreases
CCD. as1/√ .Thepolarizationinagivenwavelengthrangecanbe
N
8 S.Bagnulo,J.D.Landstreet,E.Mason,etal.:AsurveyofmagneticfieldsinopenclusterA-andB-typestarswithFORS1
measuredwithan0.1%uncertaintyifatleast2.5 105photons totaltimeforasinglepointing.Usinggrism600Bwitha0.5
′′
×
are accumulatedbothin the ordinaryandin the extraordinary slit width, we can obtain a peak ADU count of 30000 in
∼
beam,andineachofthetwoexposuresofapair. about 10 minutes shutter time for a V = 11 12 A-type star
Inordertodetectweakmagneticfields(< 300G)withthe (dependingontheweatherconditions),andin−just1minutefor
techniqueusedinthiswork,onehastoobta∼inultrahighSNR V =8.5 9.5.
(>1500Å 1)observations.Evenwitha8mtelescope,thiscan −
−
b∼eachievedonlyonrelativelybrightstars(V < 13,ifwelimit
the shutter time to < 2h). Due to the limite∼d CCD well ca- 5.3.Theuseofaσ-clippingalgorithm
pacity, multiple exp∼osures have to be taken. From a practical ThesimplestmethodtoobtainV/I istoaddupallspectraob-
pointofview,onehasto setthe exposuretime toa valuethat tainedinthesamebeamandwithsameretarderwaveplatepo-
maximises the photon count without risk of CCD saturation sition, and then use Eq. (7). However,reductionproductscan
(e.g., by adjusting the exposure time to get a peak count of be improved by using a σ-clipping algorithm as follows. For
30000 ADU per pixel), and then take several pairs of expo- eachwavelengthsteponecalculates
sures with the retarder waveplate at the +45 and 45 po-
◦ ◦
−
psAiitDxioeUlnsai.nndEtqhgueaasftoitolhlneow(n1ui0nm)gbcwearnayob.feLeleeextcputrlsiocnditselfiypneerexApMrDesUass,etdshoeinthAtaeDtramUcstpuoeafrl (cid:16)VI(cid:17)ij = 12(cid:18)ffiioo−+ffiiee(cid:19)α=−45◦ −(cid:18)ffjjoo+−ffjjee(cid:19)α=+45◦ (12)
photoncount is given by gM. Letus also define as the i, j=1,2,...,m 
s
N A
ratiobetweentheADUintegratedinapixelcolumnalongthe where m is the total number of pairs of observations. Then,
direction perpendicular to the dispersion, and the peak ADU onecalculatesthemedian(V/I)fromthem2(V/I) values,and
ij
in the central pixel. The error bar on the circular polarization the median absolute deviation (MAD), i.e., the median of the
measuredin the wavelengthinterval∆λ coveredby 1 pixelis distribution d
givenby
(V/I) (V/I) .
1 | ij− |
σ2[(V/I)](∆λ)= (cid:16) (cid:17)
4mg sMmax Settingσ=d1.48MAD(e.g.,Huber1981,pp.107–108),those
A
whereMmaxisthepeakADU. (V/I)ijvaluesforwhich
RecallingthepropertiesofaGaussian,wecanwrite =
s
A (V/I) (V/I) > σ
1.065FWHM. With a plate scale of 0.2 per pixel, as in the ij
′′ | − | K
caseofFORS1,andwith0.8 seeing, 4.Assumingg =
′′ As ≃ arerejectedd(wetypicallyadopted =3).Theprocedureisit-
2.9(atypicalvaluefortheFORS1“lowgain”readoutmode), K
erateduntilnopointsarerejected,butfromtheseconditeration
andsettingasapeakvalueM =30000ADU,weget
max on,themedian(V/I)isreplacedbytheweightedaverage
1
σ[(V/I)](∆λ)≃8×10−4 √m . (11) (V/I)= (V/I)dij σ−2[(V/I)ij]/ σ−2[(V/I)ij], (13)
Xij Xij
Equation (11) allows one to calculate the number of pairs of
exposuresthatareneededtomeasureV/Iwithagivenerrorbar. wherethesumisobviouslyextendedovertheK (V/I) values
ij
Forinstance,withapairofexposuresathalftheCCDfullwell, that have notbeen rejected by the σ-clippingalgorithm(K
≤
onegetsanerrorbarcloseto0.1%.Togobelowthethreshold m2),andσ2 (V/I) isgivenbyEq.(9).
ij
ofan0.01%errorbar(ifpossibleatall)oneshouldobtain64 Ifnovalhueinthiem2 setof(V/I) pairshasbeenrejected,
ij
pairsofexposures.
and if we assume thatthe errorsgivenby Eq. (9) are approx-
We found that measuring V/I with an accuracy of a few
imately equalfor all spectra, we can estimate the error bar of
units in 10 4 per Å in the continuum near to Hβ allowed
− (V/I)as:
us to measure magnetic fields with an error bar between 50
and 100G. Therefore,we decided that our observingstrategy 1
σ2 (V/I) ′ σ2[(V/I)] . (14)
wouldbebasedonaseriesoffourpairsofexposures(following ≃ m
n h io
thesequenceα = +45 , 45 , 45 ,+45 ,etc.).However,we
◦ − ◦ − ◦ ◦ An alternative estimate of the same error bar can be ob-
couldlimitthenumberofpairsofexposuretofouronlywhen
tainedasfollows:
weobtainedtelescopetimeinvisitormode,whichallowedus
tooptimizetheexposuretimebasedontheweatherconditions. 1
σ2 (V/I) ′′ [(V/I) (V/I)]2 . (15)
DuringP72 and P73 we were allocated telescope time in ser- ≃ m2(m 1) ij−
n h io − Xij
vicemode,andwereforcedtosettheexposuretimetoconser-
vativelylowvaluestobesuretoavoidCCDsaturation.Inthese In practice, at each wavelength step, we adopt the error
casesthenumberofpairsofexposureswasincreasedfromfour bar given by the maximum among the values obtained from
tosixoreighttoguaranteeasufficientSNR. Eq. (14) and Eq. (15). The abovetwo expressionswill be de-
Thought must be given to the ratio between shutter time rivedin detailinAppendixA,togetherwith moregeneralex-
andoverheadtime,asthelatter( 20minutesforaseriesof4 pressionsvalidforthecaseofoneormoreexposuresrejected
∼
pairsofexposures)mayrepresenta substantialfractionofthe bytheσ-clippingalgorithm.
S.Bagnulo,J.D.Landstreet,E.Mason,etal.:AsurveyofmagneticfieldsinopenclusterA-andB-typestarswithFORS1 9
5.4.Measuring B
z
h i
The mean longitudinal field B is obtained as explained in
z
h i
Sect. 3, using V/I obtained via Eq. (13). Following common
statistics guidelines, one should consider a detection as ‘defi-
nite’whenevertherelation
B /σ B 3 (16)
z z
|h i| h i ≥
(cid:2) (cid:3)
issatisfied.
Weencounteredanumberofcasesforwhichthefieldwas
detected at about 3-σ level, and where minor changes in the
data reductionwould transforma marginaldetection in a null
orinadefinitedetection.Althoughthesecasesshouldcertainly
beinvestigatedviaadditionalobservations,wetriedtoextract
further informationfrom the available spectra, to formulate a
morerobustandreliablecriterionforfielddetection.
First, we decided to explore an alternative method for the
determinationofthemeanlongitudinalfield.Fromtheindivid-
ualpairsofV /I andI givenbyEqs.(12),wecalculatedm2
ij ij ij
B values,andtheweightedmeanlongitudinalfield
z ij
h i
B = B σ 2 B / σ 2 B . (17)
z ′ z ij − z ij − z ij
h i h i h i h i
Xij h i Xij h i
Thecorrespondingerrorbarσ B wascalculatedas
z ′
h i
m ( B B (cid:2))2 (cid:3)
σ2 B = ij=1 h ziij−h zi′
h zi′ P m2(m 1)
(cid:2) (cid:3) −
For each star, we systematically checked the consistency be-
tween the B value determined through the average V/I ob-
z
tWaieneadlsovicahhEecqk.ie(d13w)haenthdetrhtehehBrezila′tvioanlue obtained via Eq. (17). BFiaglm.2e.rlihnBezsi.EmaecahspuarenmelernetfserosftoHaDdiff9e4r6e6n0tofbrsoemrviinngddivaitdeuaasl
specifiedinthefigure.The B valuesmeasuredfromHβand
z
B /σ B 3 (18) h i
z ′ z ′ bluewardBalmerlinesareplottedwithfilledcirclesatthecor-
|h i | h i ≥
(cid:2) (cid:3) responding wavelength. The B determination from Hα ob-
wassatisfied. z
h i
tainedon2002-02-04isarbitrarilyplottedwithanemptycircle
Second,weperformedasystematicanalysisofmetallines.
atλ = 4600Å.Thesolidlinescorrespondto B obtainedus-
Aspointedoutearlier,Eq.(1)isformallyvalidonlyunderthe z
h i
ingallBalmerlinesfromHβdowntotheBalmerjump,andthe
weak-field approximation. Therefore, in principle, B mea-
z
h i dotted lines indicate B obtained from the metal lines with
surements by our method should be performed only on H z
h i
grism 600B. The dashed line in the second panel shows the
Balmer lines. Furthermore, H Balmer lines are well sampled
B value obtainedfrom the metallines observedwith grism
evenat the low resolutionof our observations,whereasmetal z
h i
600R.
linesare unresolved.Nevertheless,we foundthatthe B de-
z
h i
termined via metal line analysis is consistent with that mea-
suredfromHBalmerlines,providedthat B is< 800G(see
Sect. 6.2). Therefore we decided to analyhzezithe∼metal lines, (Borra& Landstreet1975), the HβBalmer line(Bohlenderet
al. 1993),andmetallic lines(Mathys1994;Mathys& Hubrig
i.e.,toapplytheleast-squarestechniquetospectralregionsfree
1997).Moreover,HD94660isthestarobservedbyBagnuloet
fromHBalmerlines.Inaddition,wedetermined B usingthe
h zi al.(2002)todevelopthetechniqueusedinthiswork.
whole spectrum, i.e., including both Balmer and metal lines.
Thelogofourobservationsand B measurementsisgiven
TheoutcomeofthisanalysiswillbediscussedinSect.6. h zi
in Table 1. Note thaton2002-02-04we obtainedtwo consec-
utive B measurements: the first one with grism 600B, the
z
6. MagneticfielddeterminationsfromBalmerlines secondh oniewithgrism600R.
vs.fielddeterminationsfrommetallines Figure2showsthe B measurementsobtainedfromboth
z
h i
theBalmerandthemetallines.The B valuesobtainedfrom
6.1.Themagnetic“standard”starHD94660 h zi
the Balmer lines blueward of Hβ are consistent among them-
Inordertocompareourresultswiththoseobtainedthroughdif- selves,andmarginallyconsistentwiththe B valueobtained
z
h i
ferenttechniques,werepeatedlyobservedawellknownmag- from Hα. With the exception of the measurement taken on
netic Apstar: HD 94660(= KQ Vel).Previous B measure- 2001-03-22,the B valuesobtainedfromthe metallines are
z z
h i h i
ments of HD 94660 were obtained using the Hα Balmer line not consistent with those obtained from Balmer lines. This is
10 S.Bagnulo,J.D.Landstreet,E.Mason,etal.:AsurveyofmagneticfieldsinopenclusterA-andB-typestarswithFORS1
Table1. B measurementsoftheV =6.1ApstarHD94660=KQVel.Date,UT,andsignaltonoiseratio(SNR)arecalculated
z
h i
asexplainedinthecaptionofTableA.3.ObservationsobtainedinP66hadbeenalreadypublishedbyBagnuloetal.(2002).
B (G) B (G) B (G)
h zi h zi h zi
Period DATE UT Balmerlines metallines fullspectrum SNR Grism
P66 2001-03-22 23:54:00 2085 85 2100 100 2260 65 1550 600B
− ± − ± − ±
P68 2002-02-04 08:43:13 2335 57 2141 52 2226 37 2100 600B
− ± − ± − ±
P68 2002-02-04 08:56:09 2083 75 2516 34 2439 31 2150 600R
− ± − ± − ±
P70 2003-02-08 09:41:49 2574 57 2051 48 2260 38 2150 600B
− ± − ± − ±
P74 2005-01-30 09:33:45 2432 50 2002 43 2190 32 2300 600B
− ± − ± − ±
differences (even though each may be internally consistent).
Systematicinconsistenciesbetween B determinationsinAp
z
h i
starsobtainedwithdifferentchemicalelementsorwithdiffer-
enttechniqueshavebeenalreadyfoundinpreviousworks(see,
for instance, Ryabchikova et al. 2005, who analysed several
observationsofHD24712).
6.2.WeakfieldApstars
Using all our data collected for Ap stars, we show here that
the metal line analysis and the Balmer line analysis produce
consistentresultswhentheweakfieldhypothesisissatisfied.
Figure 4 shows the B values obtained from metal lines
z
h i
versus those obtained from Balmer lines for the observedAp
stars.Itappearsthatthetwomethodsgiveconsistent B val-
z
ues for B < 800G. Above the 1kG level, differehnceis be-
z
tweenB|ahlmie|r∼lineandmetallinetechniquebecomenoticeable
or even striking. E.g., for HD 310187 we obtained from the
Balmerlines B = 6519 55G,andfromthemetallineswe
z
h i ±
obtained B =3784 59G.Ingeneral,abovethe1kGlevel,
z
h i ±
the modulus of B determined from Balmer lines is larger
z
h i
than that from the metal lines, as we would expect from the
Fig.3. Longitudinal field determinations of HD 94660. The earlierbreakdownoftheweakfieldexpressionformetallines.
solid line is a fit to the Bz determinationsfrom metal lines. Summarizing,itappearsthatifthefieldisweak,bothmeth-
h i
We have used a first-orderFourier expansion.At phase 0.075 odsareconsistent,andeachgivesanindicationwhetherthestar
wehaveconsideredthe Bz determinationobtainedwithgrism ismagneticornotindependentoftheother.
h i
600Bandnottheoneobtainedwithgrism600R.Forthestar’s Figure 5 compares the distributions of the error bars for
rotationperiodwe adopt2800d (Landstreet& Mathys2000), B obtained via Balmer and metal line analysis for the ob-
z
andthezerophasepointisatJD=2446500.0. shervied Ap stars. We see that the distribution of the error bars
calculatedviametallineanalysisisbroaderthanthatobtained
fromBalmerlines.ThisisdueprimarilytothefactthatBalmer
probably due to the fact that Eq. (1) is valid only under the lines have similar strength in all A and B-type stars, whereas
weak field approximation (which in this case is correct for metal lines may change greatly from star to star. For a given
Balmerlinesbutnotformetallines).Notealsothatthe B val- SNR,theerrorbarsobtainedviametallineanalysisaresmaller
z
h i
uesmeasuredviametallineanalysisarenotconsistentamong inspectrathatarericherinmetallinesthaninspectrathatare
themselvesifwecomparedataobtainedwithgrism600Band poorer in metal lines. As expected, for a set of observations
grism 600R. The comparison between B values obtained ofsimilarSNR,theBalmerlineanalysisleadstoresultschar-
z
h i
fromHBalmerlinesandmetallineswillbefurtherdiscussed acterisedbymorehomogeneouserrorbarsthanthemetalline
inSect.6.2. analysis.
Wealsocomparedour B determinationsofTable1with
z
h i
those previously obtained in the literature, adopting for the
7. Observations
star’srotationperiod2800d(Landstreet&Mathys2000).The
resultsareshowninFig.3.Ingeneral,itappearsthat B val- Inthissurveywehaveobserved97Apstars,138normalAand
z
h i
uesobtainedfromBalmerlinesarenotconsistentwiththe B B-type stars, and 22 non early-type stars. All these stars are
z
h i
determinations obtained using metallic lines. It seems likely candidate members of the open clusters (or the associations)
that different methods used to evaluate B bear systematic listed in Table 2. Figure 6 gives an overview of the range in
z
h i