Can rotation explain the multiple main sequence turn-offs of Magellanic Cloud star clusters?

0.59 MB·English

by  Leo Girardi

Mon.Not.R.Astron.Soc.000,1–6(2011) Printed11January2011 (MNLATEXstylefilev2.2)
Can rotation explain the multiple main sequence turn-offs of
Magellanic Cloud star clusters?
1 1 2 3
Le´o Girardi , Patrick Eggenberger , Andrea Miglio
1
0 1OsservatorioAstronomicodiPadova–INAF,Vicolodell’Osservatorio5,I-35122Padova,Italy
2 2ObservatoiredeGene`ve,Universite´deGene`ve,51chemindesMaillettes,1290Sauverny,Switzerland
3Institutd’AstrophysiqueetdeGe´ophysiquedel’Universite´deLie`ge,Alle´edu6Aouˆt,17B-4000Lie´ge,Belgium
n
a
J
ToappearinMNRASLetters
0
1

ABSTRACT
]
R ManyintermediateagestarclustersintheMagellanicCloudspresentmultiplemainsequence
S turn-offs (MMSTO), which challenge the classical idea that star formation in such objects
. tookplaceovershorttimescales. Ithasbeenrecentlysuggestedthatthepresenceoffastro-
h
tators among main sequence stars could be the cause of such features (Bastian&deMink
p
2009),hencerelaxingtheneedforextendedperiodsofstarformation.Inthisletter,wecom-
-
o pute evolutionary tracks and isochrones of models with and without rotation. We find that,
r for the same age and input physics, both kinds of models present turn-offs with an almost
t
s identical position in the colour-magnitudediagrams. As a consequence, a dispersion of ro-
a tationalvelocitiesin coevalensemblesofstarscouldnotexplainthepresenceofMMSTOs.
[
Weconstructseveralsyntheticcolour-magnitudediagramsforthedifferentkindsoftracksand

1 combinationsofthem.ThemodelsthatbestreproducethemorphologyofobservedMMSTOs
v areclearlythoseassuminga significantspreadin thestellar ages–aslongas∼ 400Myr–
0 addedtoamoderateamountofconvectivecoreovershooting.Onlythesemodelsproducethe
8 detailed“golfclub”shapeofobservedMMSTOs.Aspreadinrotationalvelocitiesalonecan-
8 notdoanythingsimilar.Wealsodiscussmodelsinvolvingamixtureofstarswithandwithout
1
overshooting,asanadditionalscenariotoproducingMMSTOswithcoevalpopulations.We
.
1 findthattheyproduceturn-offswithavaryingextensionintheCMDdirectionperpendicular
0 tothelowermainsequence,whichareclearlynotpresentinobservedMMSTOs.
1
1 Keywords: Stars:evolution–Hertzsprung-Russell(HR)andC-Mdiagrams
:
v
i
X
r 1 INTRODUCTION pretationadoptedbytheabove-mentionedworks.Insupportofthis
a
interpretation,thereisthefactthatasubsampleoftheintermediate-
There is now conclusive evidence that many star clusters in the ageclusterscontainadualclumpofredgiants(Girardietal.2009),
MagellanicCloudspresentdoubleormultiplemainsequenceturn- indicativeofboththeonsetofelectrondegeneracyinstellarcores,
offs (MMSTO). The first hints of this phenomenon have been andofa∼ 0.15M⊙ spreadinturn-offmasseswhichiscompati-
advanced by Bertellietal. (2003) and Baumeetal. (2007), and blewiththeoneindicatedbythecolorspreadintheturn-offregion
werebasedonground-baseddatafortheLMCclustersNGC2173 (Rubeleetal.2010,andworkinpreparation).
and NGC 2154. Much more impressive and conclusive, how- This interpretation however is not an easy one, when one
ever, were the evidences brought by Mackey&BrobyNielsen considers the challenges it poses to the theory of star and clus-
(2007),Mackeyetal.(2008),Goudfrooijetal.(2009)fortheclus- ter formation (see e.g. Goudfrooijetal. 2009; Conroy&Spergel
ters NGC 1846, NGC 1806, and NGC 1783 in the LMC, and 2010). Note also that the prolonged star formation probably oc-
Glattetal.(2008)forNGC419intheSMC,basedonmuchdeeper curred in situ, within the relatively shallow potential well of .
photometryobtainedwiththeAdvancedCameraforSurveys(ACS) 105 M⊙clusters,andarenotduetothemergingofdifferentclus-
onboardtheHubbleSpaceTelescope(HST).Inallthesecases,the ters(Goudfrooijetal.2009).
presenceofabroadorMMSTOclearlystandsoutevenfromavi-
Thereis,however,anamazingcoincidenceregardingtheage
sualinspectionoftheCMDs.Miloneetal.(2009)revisedtheavail-
scalesinallthesecases.ForallLMCclusterswiththeclearpres-
ableACSphotometryfor16intermediate-ageLMCclusters,find-
enceofMMSTOsintheabove-mentionedpapers,theageinterval
ingevidenceforbroadturn-offsinabout70%ofthem.
betweentheyoungestandoldestturn-offrangesfromabout150to
The easiest interpretation of MMSTOs is that these clusters ∼300Myr,whereastheclustersthemselveshaveallagesbetween
containtwoormoregenerationsofstarsformedoneaftertheother, 1and2Gyr(seeMiloneetal.2009).NGC419intheSMCindi-
overatimespanofafewhundredsofMyr.Thisisindeedtheinter- catesamaximumagespreadof700Myr,butagainforameanage
2 Girardiet al.
Figure 1. The evolutionary tracks computed for this work (dark solid lines), together with isochrones derived from them (narrow lines, in color in the
electronicversion),forthenon-rotating,rotating,andovershootingcases(fromlefttoright,respectively).Theisochronesagesgo,fromtoptobottom,from
log(t/yr)=8.5to9.3atstepsof0.1dex.Asareferencetotheeye,theisochroneswithagesof0.5,1and2Gyraremarkedwithadifferentcolour.
of1.5Gyr(Rubeleetal.2010).IntermsofCMDfeatures,theMM- evalmodelswithadispersionofrotation,withthatofnonrotating
STOsalwayscoveramagnituderangeofabout∼0.5maginpass- modelswithadispersionofages,inproducingtheMMSTOfeature
bandslikeV orI,and∼0.15magincolourslikeV−I.TheMM- observedintheLMCclusterNGC1846.Thebasicconclusionsare
STOphenomenumisobservedinstarclusterslocatedoverallover discussedinSect.4.
theLMCdiskandalsointheSMC,althoughitseemstobepref-
erentiallyobservedinthemostmassiveobjects(Conroy&Spergel
2010). The homogeneity in the mean ages of clusters with MM-
STOs could be indicating dramatic large-scale events in the past 2 MODELSOFROTATINGSTARSANDISOCHRONES
historyoftheMagellanicClouds,thatcouldhaveaffectedthefor-
We start computing a series of evolutionary tracks with initial
mationofmanyofitsmoremassiveclustersinasimilarway.Or,
massesintheintervalrelevantforMMSTOs.Aninitialheavyele-
perhaps,thiscoincidenceissimplysuggestingustolookforacom-
mentsmassfractionofZ = 0.008,suitableforLMCpopulations
pletelydifferentinterpretationtotheMMSTOphenomenum.
ofyoung-to-intermediateages,isadopted.
Bastian&deMink (2009) have so far advanced theonly al-
Themain-sequenceevolutionofmodelswithandwithoutro-
ternativeexplanationforsuchCMDfeatures,namelythattheMM-
tation is computed by using the Geneva stellar evolution code
STOsappearinaggregatesofcoevalstars,duetothecolordisper-
(Eggenbergeretal. 2008). The standard mixing-length formalism
sion caused by the presence of fast rotators among the main se-
forconvection(Bo¨hm-Vitense1958)isusedwithasolarcalibrated
quence stars. Their suggestion is based on simple considerations
valueofthemixing-lengthparameter.Overshootingfromthecon-
abouttheshapeofstellarevolutionarytrackswithandwithoutro-
vective core into the surrounding radiatively stable layers is not
tation,onsomeobservationalfacts,andonsomelesswell-justified
included.Rotatingmodelsarecomputedwithaninitialvelocityon
assumptions,namelythat:
theZAMSof150kms−1,whichcorrespondstoatypicalvaluefor
• asignificantfractionofmainsequencestarsrotatewithveloc- rotatingstarsinthemassinterval between1.5and3M⊙ studied
itiesofabout∼ 0.4timesthecriticalbreakupvelocity,Ωcrit (see here (e.g. Royeretal. 2007). 1 Note that the ratio ω = Ω/Ωcrit
Royeretal.2007); ofthesemodelsremainsalwaysinferiorto0.7,sothattheeffects
• rotationcausesstarstoshift,ingeneral,toreddercoloursand relatedtothevariationwithcolatitudeoftheeffectivetemperature
slightlybrighterluminositiesinCMDs; arenegligible(Ekstro¨metal.2008).Thesemodelsincludeacom-
• for themost massive stars, close totheMSTO,the effect of prehensivetreatmentofshellularrotation(Zahn1992)andmerid-
ional circulation is treated as a truly advective process (for more
rotation is quite similar throughout the main-sequence evolution,
details, see e.g. Eggenbergeretal. 2010). The rotating and non-
sothattheeffectsareconsideredasdisplayedwhenstarsreachthe
rotating models share the same initial parameters except for the
endofthemainsequence;
• theeffectofrotationgetslessimportantatsmallermasses,and inclusionofshellularrotation.
disappearsformassessmallerthan∼1.2M⊙. Thesetwosetsarecomplementedbyonewithoutrotationbut
with overshooting from the convective core, computed with the
Notethatthecombinationofallthesedifferenteffectsisrequiredto samecode.Theovershootingparameterissettoαov =0.25pres-
explaintheshapeoftheobservedMMSTOs.Inaddition,strongly surescaleheights(seeMaeder&Meynet1989fordetails).
bi-modaldistributionsofrotationalvelocitiesareneededtoexplain ThetracksarepresentedinFig.1.Theycoverallevolutionary
thefewcasesinwhichtheturn-offappearasadoublefeature.
Inthispaper,weinvestigatewhetherrotationdoesreallybe-
haveinthewaysuggestedbyBastian&deMink(2009).Ouranal- 1 NotehoweverthatforthelowermetallicitiesoftheLMCandSMC,the
ysisisbasedonisochronescomputedwithdetailedmodelsofro- medianrotationvelocitymightbesomewhathigherthanintheSolarNeigh-
tating stars (Sect. 2), and do not suffer from the approximations bourhoodsamplefromRoyeretal.(2007).Thisdifferencehoweverisun-
adopted by them. In Sect. 3 we compare the performance of co- likelytoaffectthemainargumentsdiscussedinthefollowing.
RotationandMMSTOs 3
Figure2.Leftpanel:HRdiagramofthedifferentisochronesobtainedinFig.1,forthesameageof1.58Gyr.Right:asyntheticHRdiagramwherethesame
isochronesarepopulatedby104M⊙followingaChabrier(2001)log-normalIMF.Toavoidtheexcessivesuperpositionofpointsinthediagram,theywere
displacedbyrandomGaussianerrorsof0.01dexinlogLand0.0025dexinlogTeff.
stagesfromthezero-agemainsequence(ZAMS)uptoeitherHe- ferent,itisthecombinedeffectofchangesinthemorphologyofthe
ignition,ortheRGB-bumpoflessmassivestars. evolutionarytracks,andofthechangesintheirlifetimes.
The same figure presents a set of isochrones derived from The increase in the main sequence lifetimes caused by ro-
them. Despite the relatively large mass interval between succes- tation, in particular, isquite remarkable (see Palaciosetal. 2003;
sivetracks,theinterpolationalgorithm(thesameasinGirardietal. Eggenbergeretal.2010)andconstitutesoneofthemainfactorsin
2000) works very well and produces isochrones with all the fine playhere.AsdiscussedinEggenbergeretal.(2010),classicalmod-
detailsoftheoriginaltracks,especiallyalongtheMSTOregion.In elswithavrot =150km/shaveasimilarincreaseintheirmainse-
ordertoincludethelowermainsequenceintheisochrones,thenew quencelifetimesasmodelswithamoderateamountofovershoot-
gridsoftrackshavebeencomplementedwithGirardietal.(2000) ing,thatisαov =0.1.Suchanincreaseinthelifetimesofrotating
non-rotatingtracksofM 6 1.0M⊙,which,fortheagesconsid- starshasbeen ignored inBastian&deMink (2009), and thishas
eredinthiswork,arealwaysveryclosetotheZAMS. beendeterminantinleadingtotheirdifferentconclusions.
The two sets of tracks without overshooting make the basic IntherightpanelofFig.2,wepresentsyntheticHRdiagrams
setwithwhichwewilldiscusstheeffectofrotationontheCMDs. corresponding to 1.58-Gyr old clusters with and without rotation
We recall that these tracks do follow, qualitatively, the changes – in this latter case assuming that all stars rotate with the same
in the stellar Teff and L due to rotation that are at the base of initialvelocity–andwithovershooting,foratotalmassof104M⊙
Bastian&deMink(2009)work. followingtheChabrier(2001)log-normalIMF.Thispanelclearly
evinceswhataretheregionsofthediagrameffectivelypopulated
bystars.Inparticular,onemaynoticethatthedifferencesbetween
non-rotatingandrotatingmodelsisnotdramatic,ifoneconsiders
3 SYNTHETICCMDSANDCOMPARISONWITHDATA onlytheregionwheretheMSTOisdrawn.
Then, using the TRILEGAL code (Girardietal. 2005), we
LetusnowconsidertheeffectthatrotationhasintheCMDsofstar
simulatepopulations intheCMD inwhichMMSTOsareusually
clusters.Letusassumeforthemomentthatallthestarsinclusters observed,namelytheF555Wvs.F555W−F814W(approximately
withmultipleturn-offshaveexactlythesameageandinitialchem- V vs.V−I)diagramforthefiltersinthetheACS/WFCcameraon-
icalcomposition.Thetheoreticalentitiessuitabletodescribesuch
boardHST.SuchsimulationsareshowninFig.3.Thebolometric
asituationarethestellarisochrones.Inthefollowing,wewillcen-
correctiontablesinusearedescribedinGirardietal.(2008).The
terourdiscussiononisochronescomputedforanageof1.58Gyr,
simulatedphotometryisdisplacedbytheabsolutedistancemodu-
however we advance that very similar conclusions would be ob-
lusof18.5magandaV-bandforegroundextinction0.2mag,which
tainedforanyagebetween1and2Gyr.
arevaluestypicalofLMCstarclusters.Then,photometricerrorsof
In the left panel of Fig. 2, we superpose isochrones of the σ = 0.01magareappliedtothephotometry, soastohelpinthe
same age computed for the 3 cases mentioned in Sect. 2, in the
visualisation of the densest parts of the CMDs without however
HRdiagram.Theresultissomewhatsurprising:contrarilytowhat
modifying their morphology in any appreciable way. All simula-
sustained in Bastian&deMink (2009), models with rotation do tionsinclude afractionof 20%ofbinarieswithmassratiosuni-
not present a cooler and fainter turn-off2 with respect to their
formlydistributedbetween0.4and1.Thetotalmassisassumedto
non-rotatingcounterparts.Instead,theyhaveaslightlyhotterand beof2.4×104M⊙,followingaChabrier(2001)log-normalIMF.
brighterturn-off.Thisresultcannotbeeasilyinferredwhilelook-
The models in the top row of Fig. 3, from (a) to (c), are
ing only at the evolutionary tracks in Fig. 1, which at first sight
for a single age of 1.58 Gyr, and using each one of the 3 sets
seemtosuggestthatrotatingmodelshaveabroadermainsequence,
of tracks presented in this work. These top panels illustrate the
hencebeingabletoextendtocoolertemperatures,assustainedin
modest effect thatbinarieshaveintheseCMDs,inaway similar
Bastian&deMink(2009).Thisistrueonlyforpairsofevolution-
to the synthetic CMDs already presented by many authours (e.g.
arytracksofthesamemass.Whatweseeintheisochronesisdif-
Bertellietal.2003;Kerberetal.2007;Mackeyetal.2008).
PanelsinthesecondrowofFig.3representattemptstopro-
duceMMSTOsbyaddingstellarmodelswithdifferentproperties
2 Throughoutthispaper,turn-offisintendedasthetipofthelocuscontin- butagainforthesamesingleage.Panel(d)showsthecaseofmod-
uouslypopulatedbystarsalongthemainsequence. elswithandwithoutrotationandotherwiseidenticalphysics.This
4 Girardiet al.
Figure3.Panels(a)–(i)presentsyntheticCMDsillustratingtheeffectofdifferentprescriptionsregardingthedistributionsofinitialrotationalvelocitiesvrot,
overshootingefficiencyαov,andagestamongtheclustersstars.Allthesemodelsassumeamodestfractionofbinariesandsmallphotometricerrors.For
comparison,panel(j)showstheACS/WFCdataforthecentralregionoftheLMCstarclusterNGC1846(fromGoudfrooijetal.2009),withitswelldefined
MMSTO.Foreachpanel,weprovidethenumberofobjectsintheturn-offregiondefinedby19<F814W<21.5and0.2<F555−F814W<0.8.The
toprowshowsmodelsforasingleageandfor(a)norotationwithoutovershooting,(b)rotationwithoutovershooting,and(c)norotationwithoutovershooting.
Thesecondrowshowmixedmodels,againforasingleage:amixtureof(d)rotatingandnonrotatingstars,withoutovershooting,(e)starswithandwithout
overshooting,withoutrotation,and(f)non-rotatingstarswithovershooting,togetherwithrotatingstarswithoutovershooting.Itisevidentthatnoneofthese
casesproducesthepeculiar“golfclub”shapeoftheobservedMMSTO.Inthethirdrow,from(g)to(i),wehavethesamemodelsasunthetoprow,butnow
withthestarformationspanningandintervalof400Myr.ThesimilaritywiththeobservedMMSTOisevident,especiallyinthepanel(i),correspondingto
modelswithamoderateefficiencyofconvectiveovershootingbutnorotation.
RotationandMMSTOs 5
correspondstothesituationfavouredbyBastian&deMink(2009) betteralternative, forthemoment, thanaccepting that prolonged
asbeingattheoriginofMMSTOs.Ascanbenoticed,ourresults star formation has probably occurred in these clusters, although
produceadramaticallynarrowMSTO,clearlyverydifferentfrom we are aware of the great challenges it represents for dynamical
both theobserved one and thoseillustratedinBastian&deMink modelsofstellarandclusterformation.
(2009). We are also aware that stellar rotation – and fast rotators –
Panel (e) instead explores the case in which there is a mix- occurs anyway among the cluster stars. What is evinced by our
ture of stars with different efficiencies of core overshooting, but modelsissimplythattheeffectoffastrotationonCMDsismod-
observed at the same age. In this case the MSTO opens into a estandmorelikelysimilartothecolourandmagnitudedispersion
compositefeature,withtwodistinctMSTOs.However,thebrighter causedbybinaries,ratherthanthedramaticdrawingofMMSTOs
MSTO(correspondingtotheovershootingmodels)isclearlymuch advocatedbyBastian&deMink(2009).Followingourreasoning,
moreextended tolarger radii(towards thetop-right corner of the thedetectionoffastrotatorsattheMMSTOsisjustexpected,and
figure)thanthefainterMSTO.Thisagaincontrastswithobserva- wouldnotsupportBastian&deMink2009’hypothesisunlessthe
tions,inwhichtheMMSTOsareseentohaveaboutthesameex- fastrotatorsareallobserved atthereddest MSTO.Thisisanas-
tensioninthedirectionperpendiculartothelowermainsequence. pecttobetackledbyfutureobservationsofrotationinclusterstars,
Finally,thepanel (f)shows thecombination of non-rotating stars as those recently announced by Plataisetal. (2010) for the open
withovershooting,togetherwithrotatingstarswithoutovershoot- clusterTr20.
ing, so as to simulate an hypothetical reduction of the extent of Inconclusion,theexplanationbasedonprolongedperiodsof
theovershootingregiondrivenbyrotation.Thiscombinationpro- SFH seems to be the only surviving one, in this moment, to ex-
duces CMDs slightly more similar to the observed one, but does plain the origin of MMSTOs in Magellanic Cloud clusters. De-
notreproduceitsdetailedshape;inparticular,itcanbenoticedthat spite the perplexities and difficulties it may cause to star for-
thefainterturn-off,correspondingtorotatingmodelswithoutover- mation theories, the presence of dual red clumps in some clus-
shooting, is again less extended in the direction perpendicular to ters (Girardietal. 2009) and the high quality of the results ob-
themainsequencethanthebrighterone.Thisdiscrepancycannot tained from the modelling of their CMDs (Rubeleetal. 2010;
be remediated imposing that the fast rotators have some residual Rubeleetal.2011)stronglyfavourthisinterpretation.Detectionof
amount of overshooting, since this would increase their lifetimes chemical self-enrichment in clusterswithMMSTOswould likely
andmovethefainterturn-off towardsthebrighter one,creatinga bethedecisivedatatoconfirmordisprovethisexplanation.
situationsimilartotheoneinpanel(d).Theadoptionoffasterrota-
tionalvelocitiesinmodelswithoutovershootingwouldalsomove
thefaintestturn-offupwardsinasimilarway.
ACKNOWLEDGMENTS
The thirdrow of Fig. 3, from (g) to(i), presents the models
derived from each set of homogeneous tracks, but now assuming WethankP.Goudfrooij forproviding theNGC1846dataplotted
thatstarformationproceededataconstantrateintheageinterval in Fig. 3. The same data can be obtained from the Multimission
from1.3to1.7Myr.ThesimilaritywiththeobservedMMSTOis ArchiveattheSpaceTelescopeScienceInstitute(MAST).STScI
now evident, especially in the panel (i),corresponding to models isoperatedbytheAssociationofUniversitiesforResearchinAs-
withasingleefficiencyofovershootingbutnorotation. tronomy,Inc.,underNASAcontractNAS5-26555.WethankS.de
Mink, N. Bastianand theanonymous referee for theconstructive
comments,andA.Bressanforthehelpinbuildingtheisochrones.
L.G.acknowledgessupportfromcontractASI-INAFI/009/10/0.
4 FINALCONSIDERATIONS
Thepresentworkdemonstratesthatstellarrotation,aspredictedby
detailed evolutionary models, produces features in CMDs which
REFERENCES
are quite different from those illustrated in Bastian&deMink
(2009). We find that, despite the changes that rotation causes in BastianN.,deMinkS.E.,2009,MNRAS,398,L11
theHRdiagramofevolutionarytracks,theirlongerlifetimesmake BaumeG.,CarraroG.,CostaE.,Me´ndezR.A.,GirardiL.,2007,
the isochrones derived from these tracks to have a MSTO posi- MNRAS,375,1077
tionalmostindistinguishablefromthosederivedfromnon-rotating BertelliG.,etal.,2003,AJ,125,770
models.Itfollowsthatcoevalisochronesderivedfromrotatingplus Bo¨hm-VitenseE.,1958,ZeitschriftfurAstrophysik,46,108
non-rotatingtracks–withotherwiseidenticalphysics–arenotable ChabrierG.,2001,ApJ,554,1274
todescribethedetailedshapeoftheobservedMMSTOsinMagel- ConroyC.,SpergelD.N.,2010,arXiv:1005.4934
lanicCloudclusters. EggenbergerP.,etal.,2008,Ap&SS,316,43
Ontheotherhand,Fig.3andthecarefulCMD-reconstruction EggenbergerP.,etal.,2010,A&A,509,A72
workbyRubeleetal.(2010)andRubeleetal.(2011)demonstrate Ekstro¨mS.,MeynetG.,MaederA.,BarblanF.,2008,A&A,478,
that the other possible explanation for the origin of MMSTOs – 467
namely prolonged histories of star formation taking place in the GirardiL.,BressanA.,BertelliG.,ChiosiC.,2000,A&AS,141,
clusters–doesprovideexcellentqualitativeandquantitativefitsof 371
the CMD in the clusters NGC 419 and NGC 1751. This despite GirardiL.,etal.,2008,PASP,120,583
these latter clusters present dual red clumps in addition to MM- GirardiL.,GroenewegenM.A.T.,HatziminaoglouE.,daCosta
STOs,whichrepresentsabigadditionalchallengetoCMD-fitting L.,2005,A&A,436,895
algorithms.Itishardlyconceivable,aftertheresultsfromthiswork, GirardiL.,RubeleS.,KerberL.,2009,MNRAS,394,L74
thatacoevalpopulationofstarswithadispersionintheirrotational GlattK.,etal.,2008,AJ,136,1703
velocities, couldproduce aCMD-fittingthat evenapproaches the Goudfrooij P., Puzia T. H., Kozhurina-Platais V., Chandar R.,
quality reached in those CMD-fitting works. We are left with no 2009,AJ,137,4988
6 Girardiet al.
KerberL.O.,SantiagoB.X.,BrocatoE.,2007,A&A,462,139
MackeyA.D.,BrobyNielsenP.,2007,MNRAS,379,151
MackeyA.D.,BrobyNielsenP.,FergusonA.M.N.,Richardson
J.C.,2008,ApJ,681,L17
MaederA.,MeynetG.,1989,A&A,210,155
Milone A. P.,Bedin L. R., Piotto G., Anderson J., 2009, A&A,
497,755
PalaciosA.,TalonS.,Charbonnel C.,ForestiniM.,2003, A&A,
399,603
PlataisI.,etal.,2010,inBulletinoftheAmericanAstronomical
SocietyVol.41,.p.475
RoyerF.,ZorecJ.,Go´mezA.E.,2007,A&A,463,671
RubeleS.,etal..,2011,MNRAS,submitted
RubeleS.,KerberL.,GirardiL.,2010,MNRAS,403,1156
ZahnJ.-P.,1992,A&A,265,115