Table Of ContentAstronomy&Astrophysicsmanuscriptno.alphaCen2015 (cid:13)cESO2016
January8,2016
α ⋆
Parallax and masses of Centauri revisited
DimitriPourbaix1,⋆⋆ andHenriM.J.Boffin2
1 Institutd’Astronomieetd’Astrophysique,UniversitéLibredeBruxelles(ULB),Belgium
e-mail:[email protected]
2 ESO,AlonsodeCórdova3107Vitacura,Casilla19001Santiago,Chile
Received30/11/2015;accepted04/01/2016
6 ABSTRACT
1
0 Context.DespitethethoroughworkofvanLeeuwen(2007),theparallaxofαCentauriisstillfarfrombeingcarvedinstone.Any
2 derivationoftheindividualmassesisthereforeuncertain,ifnotquestionable.Andyet,thatdoesnotpreventthissystemfrombeing
usedforcalibrationpurposeinseveralstudies.
n
Aims.Obtainingmoreaccuratemodel-freeparallaxandindividualmassesofthissystem.
a
Methods.WithHARPS,theradialvelocitiesarenotonlyprecisebutalsoaccurate.TenyearsofHARPSdataareenoughtoderive
J
thecomplementofthevisualorbitforafull3DorbitofαCen.
7 Results.WelocateαCen(743mas)rightwhereHipparcos(ESA1997)hadputit,i.e.slightlyfurtherawaythanderivedbySöder-
hjelm(1999). Thecomponents arethusabitmoremassive thanpreviously thought (1.13and 0.97M for Aand Brespectively).
⊙
] Thesevaluesarenowinexcellentagreementwiththelatestasteroseismologicresults.
R
S Keywords. astrometry–(stars)binaries:spectroscopic–techniques:spectroscopy
.
h
p
1. Introduction componentsofαCen,yieldinganupwardrevisionofthemasses.
-
o Owingtothespecialinterestoftheasteroseismologycommunity
The Sun is a single star and as such is among the minority
r for this system, an international team was gathered later on to
tof solar-like stars which are mostly within binaries or multi-
s obtainsomeaccurateradialvelocitiesofbothcomponents.The
aplesystems(Duquennoy&Mayor1991;Halbwachsetal.2003;
outcomewas a set precise radialvelocitieswhich were used to
[Raghavanetal. 2010; Whitworth&Lomax 2015). Our closest
quantify the relative convective blue shift of both components,
neighbour– the system comprisingα Centauri A, B and Prox-
1 assuming the individual masses and the parallax of the system
ima Centauri – is therefore more representative. α Centauri A
v (Pourbaixetal.2002).
and B (HIP 71683/1), with spectral types G2V and K1V, are
6 Even if it turned out to be a false detection (Hatzes 2013;
3in a binary system with an orbital period close to 79.91 years
Rajpauletal. 2015), the announcementof a planetarycompan-
6(Heintz1982;Pourbaixetal.1999;Torresetal.2010)andadis-
ion around α Cen B (Dumusqueetal. 2012) suddenly resur-
1tance of 1.35 pc. The A and B pair offers a unique possibil-
rected the interest of the planet hunters for that stellar system
0ity to study stellar physics in stars that are only slightly dif-
(Kaltenegger&Haghighipour 2013). We therefore decided to
.ferent from our own Sun. Their masses – 1.1 and 0.9 Msun
1 determine for the first time, in a self-consistent manner, the
0– nicely bracket that of our neighbour star, and they are only individual masses, the parallax, and the net shift caused by
6slightlyolderthantheSun.Thus,αCenisanideallaboratoryfor
gravitation and convection, using an extensive set of homoge-
1stellar evolution (e.g.Kervellaetal. 2003; PortodeMelloetal.
neousandaccurateradialvelocitiesofbothcomponentsfromthe
:2008; Brunttetal. 2010; Bazotetal. 2012), asteroseismology
v ESOHARPSsciencearchive.Theobservationsaredescribedin
(Kjeldsenetal. 2008;deMeulenaeretal. 2010) andextra-solar
i Sect.2whiletheadoptedmodelusedtofitthemisdescribedin
Xplanet searches (Dumusqueetal. 2012; Rajpauletal. 2015;
Sect.3.ResultsarelistedinSect.4anddiscussedinthecontext
rBergmannetal.2015;Endletal.2015).Assuchitiscrucialto
ofasteroseismologyinSect.5.
adetermine with the highest accuracy the properties of the two
starsinαCen,whichcanbedoneasdouble-linedspectroscopic
visualbinaries,thusofferingahypothesis-freedeterminationof
2. Observationaldata
the distance and individual masses (Pourbaix 1998). One also
needs to have the most precise orbital elements to disentan- α Cen has been the target of many radial velocities (RV) mea-
gle any other effects, such as oscillations or the presence of a surements,especially, with HARPS, the High AccuracyRadial
planetary-masscompanion. velocity Planet Searcher at the ESO La Silla 3.6m telescope.
Pourbaixetal. (1999) presented the first simultaneous ad- ThevacuumandthermallyisolatedHARPSinstrumenthasbeen
justment of the relative positions and radial velocities of both especiallydesignedforhigh-precisionradialvelocitiesobserva-
tions(Mayoretal. 2003), reachingfor examplea dispersionof
⋆ Based on data obtained from the ESO Science Archive Faci-
0.64ms−1over500days(Lovisetal.2006).
lityunderrequestnumbersHBOFFIN/190700,Pourbaix/192287,Pour-
baix/192364, Pourbaix/192404, Pourbaix/192552, Pourbaix/192630, The velocitiesof bothcomponentsof α Cen were retrieved
andPourbaix/199124. fromtheHARPSarchivemaintainedbyESO:2015velocitiesfor
⋆⋆ SeniorResearchAssociate,F.R.S.-FNRS,Belgium Aand4303forB.Despitethepossibilityofselectingthetarget
AA/2015/27859,page1of4
A&Aproofs:manuscriptno.alphaCen2015
ontheESOarchiveinterface,avisualinspectionwasnecessary 3. Model
toassignthevelocitiestotherightcomponent.Furtherimposing
The model used by Pourbaixetal. (1999) assumes that the
that the seeing does not exceed 1 arcsec so as to avoid α Cen
measured radial velocities represent the radial velocities of the
A contaminating α Cen B and vice versa (as suggested by the
barycentreofeachcomponent:
referee, Xavier Dumusque), limited these observations to 710
and1951forAandBrespectively.Theimportanceofthisdata V =V −K (ecosω +cos(ω +v)),
A 0 A B B (1)
set lies in the simultaneousor quasi simultaneousobservations V =V +K (ecosω +cos(ω +v)),
B 0 B B B
ofbothcomponentswithaninstrumentthatprovidesRVsonan
whereV denotesthesystemicvelocity,ω theargumentofthe
almostabsolutescale. 0 B
periastronofcomponentB,etheeccentricity,vthetrueanomaly,
WeusedtheradialvelocitiesprovidedbytheHARPSpipe-
andK arethesemi-amplitudesoftheradialvelocitiesofboth
line. For α Cen A, the RV is obtained by cross-correlating the A,B
components.
spectrawithaG2VfluxtemplatewhichistheFouriertransform
Whereas thatassumption was realistic in the past when the
spectrometer (FTS) spectrum of the Sun (Kuruczetal. 1984),
radialvelocities were precise to a few hundredmeters per sec-
andcalibratedsoastohaveanoffsetinthezero-pointof102.5
m s−1 (Molaroetal. 2013). For α Cen B, the cross-correlation ond,some effects popup as soon as the precisionimproves.In
order to recover the accuracy of the barycentre velocity, these
wasdonewithaK5template.Themedianofthevelocitypreci-
sionforAandBarerespectively0.16and0.12ms−1(Fig.1). effects have to be corrected for, either individually or globally.
Withrelativeradialvelocitiesofbothcomponents,theseeffects
wouldhavetobemodelled.WithHARPSmeasuringbothcom-
ponentsinthesamereferenceframe,itispossibletomeasurethe
correctiontobeappliedglobally.
Assumingthegravitationalredshiftandconvectiveblueshift
ofagivencomponentdonotchangeoverthespectroscopicob-
servationbaseline,theneteffectofthetwoshiftsisjustavertical
translation of the radial velocity curve (the dates of the mini-
mumsandmaximumsofthecurveremainunchanged).Nomor-
phologicalchangeofthecurveitselfisanticipated.Theneteffect
ofthefourshiftsis thereforea verticaltranslationof onecurve
withrespecttotheother.
Suchaverticaltranslationcaneasilybemodelledwithanad-
ditionaltermin,say,theradialvelocityofcomponentB(Eq.1):
V =V +K (ecosω +cos(ω +v))+∆V . (2)
B 0 B B B B
Itisworthpointingthat,whereasPourbaix(1998)advocatedfor
asimultaneousadjustmentofthevisualandspectroscopicdata,
this∆V termhastobeintroducedbecausethesolutionsforV
B A
and V are obtained simultaneously! Indeed, if the two curves
B
weremodelledindependently,twodistinctV wouldbeobtained
0
but K and K wouldrepresentthe semi-amplitudesofthe two
A B
curves. Without ∆V , the simultaneousfit introducesa bias on
B
V ,K ,andK .
0 A B
Theorbitofthestellarsystembeingouronlygoal,noshort
timescalevariation(Dumusqueetal.2011,2015)ismodelledin
Fig. 1. Distribution of the estimated radial velocity uncertainties re- thepresentinvestigation.
portedbytheHARPSpipelineforcomponentA(left)andB(right).
4. Results
The HARPS data cover 11 years only (13% of the orbital
period),but at the crucialtime when the radial velocitiescross Despite the absence of visual departure between the fit of the
(seeFig.2).TheHARPSdatawerecompletedwithsomeolder presentdataset with and without ∆ V , the parallaxes differ by
B
ESO data (Endletal. 2001), obtained with the Coudé Echelle 2%(smallerwithoutshift),directlyimpactingthetotalmassby
Spectrograph(CES)atthe1.4-mCoudéAuxiliaryTelescopeand thesame amountasthe fractionalmassremainsessentially un-
later,atthe3.6-mtelescope,bothinLaSilla,toextendthebase- changed.Thereducedχ2increasesfrom1.01to1.21withoutthe
line and to help improvingthe precision of the fractionalmass shift.Therevisionofthemodelisthusjustified.Theorbitalele-
(κ= M /(M +M )).Thesevelocitiesbeingrelative,thedatasets mentsaregiveninTab.1togetherwiththe2002resultsandthe
B A B
ofAandBwereshiftedtosharetheHARPSzeropoint. orbitisplottedinFig.2.
These very accurate radial velocities were complemented Therevisedorbitalparallax(743±1.3mas)issmallerthan
with the same visual observations (both micrometric and pho- thevaluederivedbySöderhjelm(1999)fromtheHipparcosob-
tographic)asusedinourpreviousinvestigation(Pourbaixetal. servationsandadoptedbyPourbaixetal.(2002).Itissomewhat
1999).Accordingtoitswebportal,theWashingtondoublestar closer to the original Hipparcos value, 742 ± 1.42 mas (ESA
catalogue (Hartkopfetal. 2001) holds 37 additional visual ob- 1997), and rules out the result obtained in the revision of the
servations(upto2014.241)withrespecttoouroriginalinvesti- Hipparcoscatalogue(vanLeeuwen2007)wherethe parallaxis
gation.ThesedatawerekindlyprovidedbytheWDSteamand 754.81±4.11mas.Eventhoughtheparallaxisdifferent,theto-
addedtothe1999datasetforthesakeofcompleteness.Inprac- talmassofthesystemperfectlymatchesthe’photometric’esti-
tice,noparameterfromthevisualorbitwasaffected. mate from Malkovetal. (2012), thus indicating some possible
AA/2015/27859,page2of4
DimitriPourbaixandHenriM.J.Boffin:ParallaxandmassesofαCentaurirevisited
flaw in their mass-luminosity relation. Our value of the mass
of component B seems to favour the asteroseismology-based
0.97± 0.04 M by Lundkvistetal. (2014) over the 0.921 M
⊙ ⊙
basedonisochroneinterpolation(Boyajianetal.2013).
Table 1. Orbital solutions from Pourbaixetal. (2002), this work us-
ingHARPSandsomeolderESOCoudéEchellevelocities(Endletal.
2001).
HARPS+ESO
Element Original CoudéEchelle
a(′′) 17.57±0.022 17.66±0.026
i(◦) 79.20±0.041 79.32±0.044
ω(◦) 231.65±0.076 232.3±0.11
Ω(◦) 204.85±0.084 204.75±0.087
e 0.5179±0.00076 0.524±0.0011
P(yr) 79.91±0.011 79.91±0.013
T (Julianyear) 1875.66±0.012 1955.66±0.014
V (kms) −22.445±0.0021 −22.390±0.0042
0
̟(mas) 747.1±1.2(adopted) 743±1.3
κ 0.4581±0.00098 0.4617±0.00044
∆V (m/s) 0.0(adopted) 329±9.0
B
M (M ) 1.105±0.0070 1.133±0.0050
A ⊙
M (M ) 0.934±0.0061 0.972±0.0045
B ⊙
Fig.3. Radialvelocityresidualsof bothcomponents (top: A;bottom:
Intheparticularcaseofthissystem,∆V canbeinterpreted B)resultingfromtheorbitalfit.TheHARPSdataarealllocatedafter
B 2000.TheolderdataarefromESOCoudéEchelle(Endletal.2001).
astheneteffect,forcomponentBonly,ofthedifferentialgrav-
itationalredshift,differentialconvectiveblueshiftandtemplate
mismatch. Indeed, the template used for componentA is a G2
Thevelocityresidualsagainsttheorbithaveastandarddevi-
maskcalibratedagainstasteroids.TheradialvelocitiesofAare ationof 4.56and 3.26m s−1 for A andB respectively(Fig. 3).
thereforeasclosetoabsoluteaspossible.ComponentBwasre-
Forthe HARPS dataonly,the standarddeviationsare 3.44and
ducedusinga K5 mask insteadof K1 (thecommonlyaccepted 2.74ms−1 withthelatterlikelyoverestimatedduetosomeout-
spectraltype).
liers in 2009 not filtered out by the constraint on the seeing.
Those values, especially for B, are consistent with the residu-
alsobtainedbyDumusqueetal.(2012)beforetheycorrectedfor
-20.0 othereffects(e.g.rotationalactivity,...).
5. Discussion
-21.0
Théveninetal. (2002) could not find any asteroseismologic
)
m/s model consistent with the masses obtained by Pourbaixetal.
(k -22.0 (2002)and,instead,proposed1.100±0.006M⊙and0.907±0.006
y M⊙forαCenAandBrespectively.Theseresultsweresomehow
cit confirmedbyKervellaetal.(2003)throughthemeasurementof
o
el theangulardiameterofbothcomponentsandadoptingthe par-
v
al -23.0 allax by Söderhjelm (1999). Combining their own results with
di thoseofThéveninetal.(2002),theyalsoderivedalikelyparal-
Ra laxof745.3±2.5mas.
Using asteroseismology only, Lundkvistetal. (2014) ob-
-24.0
tained1.10±0.03M and0.97±0.04M ,veryconsistentwith
⊙ ⊙
ourvalues.Theyalsoderived1.22±0.01R and0.88±0.01R
⊙ ⊙
fortheradiusofcomponentAandBrespectively,matchingthe
-25.0 valuesobtainedbyKervellaetal. (2003).Adoptingthe angular
diametersfromthelatter(8.511±0.020masand6.001±0.034
1993.18 Time 2013.40 masforAandB)andourrevisedparallaxyield1.231±0.0036
R and0.868±0.0052R fortheradiiofAandB,alsoingood
⊙ ⊙
agreementwithLundkvistetal.(2014).
Fig.2.RadialvelocitiesofalphaCen(filledforcomponentAandopen
forB).DiabolosdenotetheHARPSarchiveddataandsquarestheolder
ESOdata(Endletal.2001)alreadyusedbyPourbaixetal.(2002).On
6. Conclusions
this portion of the orbit, fitting ∆ V or setting it to 0 is not visually
B
distinguishable.
As stressed by several authors (Torresetal. 2010;
Halbwachsetal. 2016), obtaining stellar masses at the 1%
AA/2015/27859,page3of4
A&Aproofs:manuscriptno.alphaCen2015
level is crucial for astrophysics. Accounting for ∆V made
B
it possible to reach that level of precision (and hopefully of
accuracyaswell)forαCenwithoutanyad-hocassumptionover
asoshorttimescale.Thereviseddistanceandmassesmatchthe
valuesindependentlyderivedbyastroseismology.
Acknowledgements. Wethankthereferee,XavierDumusque,forhissuggestion
about filtering the HARPS dataset according to the seeing. This research has
madeuseoftheWashingtonDoubleStarCatalogmaintainedattheU.S.Naval
ObservatoryandtheSimbaddatabase,operatingatCDS,Strasbourg,France.
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