Table Of ContentAstronomy&Astrophysicsmanuscriptno.LeBouquin (cid:13)c ESO2008
February2,2008
First result with AMBER+FINITO on the VLTI:
⋆
The high-precision angular diameter of V3879 Sgr
8
0
0 J.-B.LeBouquin1,B.Bauvir1,2,P.Haguenauer1,M.Scho¨ller1,F.Rantakyro¨1,andS.Menardi2
2
n 1 EuropeanSouthernObservatory,Casilla19001,Santiago19,Chile
a 2 EuropeanSouthernObservatory,Karl-Schwarzschild-Str.2,85748Garching,Germany
J
3
Received;Accepted
]
h ABSTRACT
p
- Aims.OurgoalistodemonstratethepotentialoftheinterferometricAMBERinstrumentlinkedwiththeVeryLargeTelescopeInterferometer
o
(VLTI)fringe-trackingfacilityFINITOtoderivehigh-precisionstellardiameters.
r
t Methods.WeusecommissioningdataobtainedonthebrightsinglestarV3879Sgr.LockingtheinterferometricfringeswithFINITOallows
s
a ustorecordverylowcontrastfringesontheAMBERcamera.Byfittingtheamplitudeofthesefringes,wemeasurethediameterofthetarget
[ inthreedirectionssimultaneouslywithanaccuracyof25micro-arcseconds.
Results.WeshowedthatV3879Sgrhasaroundphotospheredowntoasub-percentlevel.Wequicklyreachedthislevelofaccuracybecause
1
thetechnique used isindependent fromabsolute calibration(atleast for baselines that fullyspanthevisibilitynull). Webrieflydiscuss the
v
potentialbiasesfoundatthislevelofprecision.
6
Conclusions.TheproposedAMBER+FINITOinstrumentalsetupopensseveralperspectivesfortheVLTIinthefieldofstellarastrophysics,
0
5 likemeasuringwithhighaccuracytheoblatenessoffastrotatingstarsordetectingatmosphericstarspots.
0
. Keywords.Techniques:interferometric-Instrumentation:interferometers
1
0
8
0 1. Introduction observingasinglestarmodeledbyaUniformDiskofdiameter
: ∅,thefringevisibilityµdropsaccordingtothefollowinglaw:
v
In optical, long-baseline interferometry,the most popular ob-
i
X servable is the contrast (also called the visibility) of the in- µ2 =µ2(λ,t).A2(∅B ) (1)
0 λ
r terferometricfringesthatappearwhensuperposingthe beams
a where
comingfromseveraldistanttelescopes.Themajorlimitationis
therandomopticaldelayintroducedbytheatmosphericturbu-
B isthespatialfrequencyoftheobservation,givenbythera-
λ
lence, which make these fringes jitter around on the detector
tio of the distance between the telescopes B projected on
byaquantitylargerthanthefringespacing.Practically,fringe
thesky(calledthebaseline)andtheobservingwavelength
blurringisavoided,eitherbyreducingtheintegrationtimetoa
λ.
fewmilliseconds,whichpreventsobservationsoffainttargets;
A istheAiryfunction(theFouriertransformofadiskofuni-
orbyusingadedicatedfringe-trackingfacility,thepurposeof tary size). The function A2 actually goes to zero (fringes
which is to stabilize fringes by measuring and correcting the disappear)for a disk of diameter∅ ≈ 1.22/B . After this
λ
opticaldelayinreal-time.Fringe-trackingisgenerallyusedto
firstnullthefringesreappear,butatlowervisibility(second
observefainterobjectsortoincreasethespectralresolution,but
lobe).
this is not the only application.Anotherimportantgain is the µ2 is the interferometric response of the instrumental chain,
possibilityofrecordingverylow-contrastfringesthatthatrise 0
alsocalledthetransfer-function.Itchangeswiththeinstru-
abovethenoiselevelafterintegrationtimeslongerthanafew
mental setup and the atmospheric conditions. Therefore,
seconds.
it has to be frequentlycalibrated by observingunresolved
Such small fringes are produced by astronomical objects stars, or starswith knowndiameters.Statistical errorsand
spatially resolvedby the interferometer.More precisely when fluctuationsofthistransfer-functiongenerallydominatethe
errorbudgetwhentryingtoestimatethediameterwithhigh
Sendoffprintrequeststo:J.B.LeBouquin accuracy.
e-mail:[email protected]
⋆ Based on observations collected during technical time at the BecauseofthestructureofEq.1,collectingvisibilitypointsin
EuropeanSouthernObservatory,Paranal,Chile. thevicinityofthefirstnulloftheA2functionmakesthediam-
2 J.-B.LeBouquinetal.:FirstresultwithAMBER+FINITOontheVLTI
G2 K0L0M0 Table1.Targetparameters.
U1
H0
Target HD K Spectral Published∅inK
G0
E0 J1 Name Number (mag) Type (mas)
D0
B0C0 V3879Sgr 172816 -0.5 M4III 8.09±0.271
A0
I1 J2 νLib 133774 1.61 K5III 2.76±0.032
C1
B1
A1 B2C2 D1 SpectraltypesandK-bandmagnitudeshavebeenextractedfromthe
C3
B3 Simbaddatabase.Diametershavebeenextractedfrom:
B4 D2 G1 1:LunarOccultationmethod(Richichietal.1998)
B5
2:Indirectmethod,reportedinCHARM2(Richichietal.2005)
0.04 0.20
D0−H0 G1−D0 H0−G1
0.03
µ20.02 0.15 µ
2.2.Observations
0.01 0.10
0.00 0.00 We obtained data at the VLTI during the night of 2007 May
20 30 40 50 60 20 30 40 50 60 20 30 40 50 60
1, with the relocatable 1.8m AuxiliaryTelescopes AT2, AT3,
and AT4 placed respectively at stations G1, D0, and H0.
Fig.1. VLTI array configurationduringthe observation(top) Ground baseline length is 64m for baseline D0-H0, and 71m
and correspondingsimulated visibility-curves(solid line, bot- for baselines G1-D0 and G1-H0. AMBER was configured in
tom), assuming the uniform disk diameter of V3879 Sgr medium resolution mode (R∼1500) with a spectral window
(7.56 mas). FINITO tracks the fringes along D0-H0 and G1- 1.95−2.25µm.Duringthenight,werecorded22files(orex-
D0 inthe H-band(star symbols),whileAMBER recordsdata posures) on the brightsemi-regularpulsatingstar V3879Sgr.
ofthethreebaselinesacrosstheK-band(circlesymbols).The Houranglesofobservationsrangefrom−01:20to01:15.Each
horizontalaxesarethespatialfrequenciesB ,markedinmeter file is composedof 70framesof 1sintegrationtime each (in-
λ
permicron,theverticalaxesarethesquaredandlinearvisibil- stead of the 50ms integration time generally used when the
ities. fringes are not locked by FINITO). At the beginning of the
observation,wealsorecorded6fileswiththesameinstrumen-
talsetuponthecalibratorstarνLib.Thestellarparametersof
eterestimationmuchlesssensitivetothetransfer-functionun-
V3879SgrandνLibaresummarizedinTable1.
certainty. For instance, measuring the exact spatial frequency
Due to the combination of the V3879 Sgr angular size,
at which the fringes disappear gives an estimation of ∅, for-
the baseline lengths and the FINITO working wavelength,
mally independent from µ2, since one can use the relation:
0 we were able to lock the fringes near the second visibility-
∅≈1.22/B .
λ lobe maximum on baselines D0-H0 and G1-D0 (see Fig. 1).
In this paper, we demonstrate the feasibility of this tech-
Simultaneously, AMBER was recording data around the first
nique at the Very Large Telescope Interferometer (VLTI, see
visibilitynullwithbaselinesH0-G1andG1-D0,andatthevery
Scho¨lleretal.2006)byusinganadequatesetupofthefringe-
bottomofthefirstlobewithD0-H0(whichhadasmallerpro-
tracker FINITO (Gaietal. 2004) and of the scientific instru-
jected baseline because of the star position in the sky). For a
ment AMBER (Petrovetal. 2007). Section 2 describes the
givenbaseline,AMBERrecordsnotasinglepoint,butarange
instrumental setup, the observations, and the data reduction.
of B because it spectrally disperses the light across the K-
Section 3 details the results and discusses the obtained accu- λ
band.Asexpected,fringecontrastsestimatedfromtheFINITO
racy.Thepaperendswithbriefconclusionsandperspectives.
real-timedisplaywereintherange10−15%,dependingonthe
baselineandthehourangle.Duringtheobservations,FINITO
2. Observationsanddatareduction providedalockingratiosystematicallylargerthan80%(mean-
ing that in each AMBER file, we recorded about 55 of the
2.1.FringetrackingatVLTI
70 frames with loop closed). However, we noticed that the
FINITOperformancedegradeswhenthefringevisibilitygoes
AdescriptionoftheVLTIfringe-trackingfacilitycanbefound
below10%.Wewerenotabletoclosetheloopwithvisibilities
inGaietal.(2004).Werecallhereonlyitsprincipleandmain
smallerthan5%.
characteristics. The FINITOinstrumentrecordstwo baselines
ofatelescopetriangle.WideH-bandinterferometricfringesare
formedbytemporallymodulatingtheopticalpathsbeforethe
2.3.Datareduction
beam combination. Output signals are processed in real-time
withamodifiedABCDalgorithm.Themeasuredfringephases Step 1: We used the standard AMBER pipeline amdlib to
are used to reject fringe motion for frequencies below 20Hz. convert the raw-data frames into uncalibrated square visibili-
When the loop is closed, atmosphericperturbationsare atten- ties, following the reduction procedure described in detail by
uateddownto0.15µmRMS(performanceroutinelyachieved Tatullietal. (2007). We kept the 50% best frames sorted by
onthe1.8mAuxiliaryTelescopesbutnotyetonthelarger8.2m signal-to-noiseratioonthefringecontrast.Thisefficientlydis-
UnitTelescopes). cardedtheframesrecordedwhiletheFINITOloopwasopen.
J.-B.LeBouquinetal.:FirstresultwithAMBER+FINITOontheVLTI 3
D0−H0 G1−D0 H0−G1 D0−H0 G1−D0 H0−G1
1.2 1.1 0.010 0.15
1.0
µ2cal0.8 0.9 µcal µ2 0.005 0.10 µ
0.6
0.000
0.4 0.6 0.00
2.0 2.1 2.2 2.0 2.1 2.2 2.0 2.1 2.2 0.010 0.15
Fig.2. Transfer-function(observedvisibilitiescalibratedfrom µ2 0.005 µ
0.10
the stellar diameter of Table 1) measured by AMBER on the
0.000
referencestar ν Libin functionof thewavelengthinmicrons. 0.00
ThesolidlineisalinearfitofEq.2intherange2.0-2.26µm. 0.010 0.15
µ2 0.005 µ
Step2: Tocomputeanestimationofthetransfer-function,we 0.10
fitthedataobtainedonthecalibratorνLibbyafunctionofthe 0.000
0.00
form:
λ−λ 30 32 34 36 30 32 34 36 30 32 34 36
µ2 =α(1+β 0) (2)
cal ∆λ
whereλ and∆λarethecentralandthefullrangeofobserved Fig.3. Selectedsquaredvisibilitycurves.Thedataandthefit
0
wavelengths;and µ2 are the observedsquared visibilities on areshownforthethreebaselinesandforthreenon-consecutive
cal
ν Lib, calibrated from the stellar diameter of Table 1. Data acquisitions(UTtime07:20,09:45,and10:03,fromtoptobot-
and associated fit are displayed in Fig. 2. We decided to re- tom).ThehorizontalaxesarethespatialfrequenciesBλmarked
strict our analysis to the range 2.0-2.26µm in order to avoid inmeterpermicron,the verticalaxesarethesquaredandlin-
the feature around 1.97µm. Discussing this feature is clearly earvisibilities(leftandrightscalesrespectively).Thetracking
outthescopeofthispaper,andmoreimportantlythisdoesnot performancesonbaselineD0-H0degradedstronglyatthevery
affectourresults.Wethenremovedthechromaticslopeofthe endofthenight,explainingthevisibilitylossesseenonD0-H0
transfer-functionfromtheV3879Sgrvisibilities: andH0-G1onthebottomline.
λ−λ
µ2 =µ2raw /(1+β ∆λ0) (3) that 1) visibility errors are realistic and not cross-correlated,
and2)thereisnoothersourceofvisibilityerror.Thelatteras-
whereµ2 aretheobservedsquaredvisibilitiesonV3879Sgr.
raw sumptionisdiscussedinSec.3.1.Asampleofselectedfitsfor
Note that we do not correct from the absolute value of the differenthouranglesis displayedin Fig. 3, and thecomputed
transfer-function, but only from its slope versus the wave-
diametersaredisplayedinFig.4.
length.Therefore,ourcalibratedV3879Sgrvisibilitiesarenot
equal, but proportionalto the real visibilities, and this multi-
plicativefactorshouldbeindependentfromλ. 3. Resultsanddiscussion
Our results show that V3879 Sgr has a round photosphere to
Step 3: To extract uniform disk diameters, we fit indepen- sub-percentaccuracy. Its diameter is about 7.56±0.025mas,
dently each data set µ2(B ) by Eq. 1, considering both the andthisvalueisconsistentinallmeasureddirections.Because
λ
transfer-function µ2 and the diameter ∅ as free parameters. of its location in the sky, V3879 Sgr has been previously ob-
0
Because of the consecutive lobes of Eq. 1, the fit has several served several times with lunar occultation. We note that our
minima.To avoidbeingtrappedbyan obviouslywrongmini- valueis aboutten times moreprecise andwithin 2σfromthe
mum,weusedasstartingpointthealreadypublisheddiameter 8.09±0.27masreportedbyRichichietal.(1998).Inthiswork,
∅ = 8.09mas and an ideal transfer-function µ2 = 1. During V3879 Sgr is reported as a visual variable (∆ = 0.5m over a
0
the fit process, we assumed that these two parameters do not period of 50 days). Pulsations or a patchy atmosphere could
vary with λ (the star has a constant diameter and the slope explainthepotentialdiameterdiscrepancy.Yet,systematicer-
of the transfer-function versus the wavelength has been cor- rors not taken into account in our computation and/or in the
rected). Our fit also assumed the square visibility effectively publishedvaluesmightalsoexplainthediscrepancy.
to go down to zero between the first and the second lobe.
This could be wrong if the target shape departs from central-
3.1.Diameteraccuracy
symmetry.However,bylookingatthedatadisplayedinFig.3,
it is clear that the recorded minima on baselines H0-G1 and OnbaselineG1-D0thedispersionbetweentheconsecutiveex-
G1-D0arefullycompatiblewithzero(min(µ2)= 0±0.0002), posuresis±0.4%andisfullycompatiblewitherrorbarscom-
andthereforethisassumptionhasnoeffectontheresults. puted by the fit process. On baseline H0-G1 the dispersion is
Finally, statistical error-bars on the visibilities are propa- ±1%,butisalsofullycompatiblewiththefiterrorbars.Onthe
gatedthroughthefitproceduretoestimatetheresultinguncer- contrary,onbaselineD0-H0thedispersionisabout±1.5%,and
tainties on the fit parameters∅ and µ2. The formula assumed issignificantlylargerthanthefiterrorbars.SinceFINITOwas
0
4 J.-B.LeBouquinetal.:FirstresultwithAMBER+FINITOontheVLTI
G1−D0 D0−H0 H0−G1
7.8
G1−D0 H0−G1
5
>
−
mas) 7.6 mas) 0
D ( h (
U ort D0−H0
N
7.4
−5
−50 0 50 100 −5 0 5
Baseline Angle (deg) East (mas) −>
Fig.4. MeasuredUniformDiskdiameterforV3879Sgr.Errorbarsdonottakeintoaccountthepotentialsystematicerrors,but
onlythestatisticscomingfromthesquaredvisibilityerrors.Intherightpanel,theerrorbarsaretypicallysmallerthanthesymbol
size.Theshadedregionsshowthe±1%limitsaroundtheaveragedsize.
workingonbaselinesD0-H0andG1-D0,wecannotblamethe
0.98 1.06 1.13 1.20 1.27
fringe-tracking loop or a complicated FINITO artifact in the 0.10 1.32%
AMBERdata-reductionsoftware.
) β=0.08 1.06%
To test the influence of the calibration of the transfer- as
m
functionslopeontheresults(Step2ofSect.2.3),wesimulated ( 0.79%
r
observationswithanartificialvisibilityslopeβoverthespatial o 0.05
frequencyrange.Fakedataaregivenbytheformula: err β=0.04 0.53%
r
e
et 0.26%
m
B −B0 a
µ2 =A2(∅B ).(1+β λ λ) (4) Di 0.00 0.00%
simu λ ∆Bλ β=0
25 30 35
where B0 and ∆B are the central and the full range of spa-
λ λ
tial frequencies of the simulation. We used a different def- Fig.5. Simulatedbiasonthediameterinfunctionofthecen-
inition than in Sec. 2.3, step 2 in order to define Eq. 4 in tralspatialfrequency(markedinmeterspermicrons),andfor
a dimensionless manner. We chose the same target diameter, variousβparameters.Thegrayzoneareobservationsspanning
baselinelength,spectralresolutionandspectralwindowasfor the first visibility null (the visibility null is at 33.5µm/m and
the real observations. Practically, this dimensionless compu- thespatialfrequencyrangeis5µm/m).Additionalitalicscales
tation remains valid as long as the ratio B0λ/∆Bλ is constant aredimensionlessquantities:∅.Bλ forthehorizontalaxis,and
(B0λ/∆Bλ ≈ 8.2inourdataset).Wethenfitthesimulateddata ∆∅/∅inpercentfortheverticalaxis.
withthesameprocedureasusedinStep3ofSect.2.3.Theesti-
mateddiameterisdisplayedinFig.5,infunctionofthecentral
3.2.Potentialbiases
spatialfrequencyB0 andfordifferentvaluesofβ.
λ
Clearly, a remaining instrumental visibility slope has lit- Inourwork,weseetwospecificpotentialbiases,bothrelated
tle impact on the estimated diameter for observations span- to the calibration of the spatial frequencies B : the precision
λ
ning the visibility null. The latter acts as a strong “locking onthebaselinelengthitself,andtheprecisionontheAMBER
point”inthefitprocess.Ontheotherside,whenobservingat spectral calibration. Note that these issues are generally ig-
B ∼ 27µm/m, as with the D0-H0baseline, a changeof0.08 nored in optical interferometric data analysis since they are
λ
intheslopeofthetransfer-functionleadstoanerrorof0.1mas largelydominatedbythetransfer-functioninstabilities.
(i.e. 1.3%) on the diameter. Our favored explanation for the Concerning the baseline length, at VLTI, the three-
additionaldispersiononbaselineD0-H0isaslightfluctuation dimensionalvectorbetweenthetwoprimarymirrorsofatele-
ofthetransfer-functionslopebetweentheexposures(probably scopepairisknownwithanaccuracyofaboutonemillimeter
duetoatmosphericseeingandcoherencetime).Asamatterof (conservativeestimation).Thiscorrespondsto∼0.015%ofthe
fact,thisalsoprovestherobustnessofthepresentedmethodon smallestbaselineofourobservations(60m).Thisvalueissig-
thetwootherbaselines. nificantlysmaller thanourcomputedstatisticalerrorsandcan
J.-B.LeBouquinetal.:FirstresultwithAMBER+FINITOontheVLTI 5
be completelyignored.Anotherimportantissue relatedto the – Finally, by associating fringe-tracking in the second lobe
baselinelengthisthepupiltransferquality.Ifatelescopebeam withbaselinebootstrapping,onecanrecordvisibilitypoints
isvignettedononeside,thebaselineisslightlyshiftedonthe inthethirdvisibilitylobe.There,observablesbecomevery
otherside,sincetheeffectivelyusedsectionoftheprimarymir- sensitivetothelimb-darkeningstrengthanditsspectralde-
rorisnolongercenteredaroundthemirrorcenter(referencefor pendency,whichwillallowthoroughtestsofstellaratmo-
thebaselinemodel).InAMBER,thepupilisnormallynevervi- spheremodels.
gnettedmorethan20%,whichcorrespondstoashiftofafew
tenthsofthemirrorsize.Ifweassumeaprimary-mirrorsizeof Acknowledgements. The authors want to warmly thank the com-
plete VLTI team (Science Operations astronomers and engineers)
1.8m, anda shiftof 10%, the relativeerror onthe baseline is
for all the work accomplished on the FINITO and AMBER instru-
∼0.3%.Thisvalueisatthelevelofourprecision.
ments. Thiswork isbased on observations made withthe European
ConcerningtheAMBERspectralcalibrationaccuracy,the
Southern Observatory telescopes obtained from the ESO/ST-ECF
situationislessclear.Thisaccuracyisnotavailableatallinthe
Science Archive Facility. This research has made use of the
literature.Ina crudecomparisonofourAMBERspectrawith
Smithsonian/NASA Astrophysics Data System (ADS) and of the
atmospheric transmission curves in the K-band, we estimate Centre de Donnees astronomiques de Strasbourg (CDS). All calcu-
thepotentialspectralerrorto belessthan0.02µm.Thistrans- lationsandgraphicswereperformedwiththefreewareYorick1.
lates into a 1% error at 2µm (conservative estimation). This
issignificantlylargerthanourprecisiononthebestbaselines,
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bythisinstrumentalerrorsource. Gai,M.,Menardi,S.,Cesare,S.,etal.2004,inNewFrontiers
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a diameter of 7.56±0.025mas in three directions simultane-
ously.Wereachedsuchsub-percentaccuracywithoutspending
additional time on calibrators since the technique is indepen-
dentfromabsolutecalibration(atleastforbaselinesthatfully
spanthevisibilitynull).Weshowthat,atthislevelofprecision,
severalsystematicerrorsourceshavetobetakenintoaccount,
for example the spectral calibration of the instrumentand the
pupillateralposition.
From the scientific pointof view, this work opens several
perspectivesfortheVLTIinthefieldofstellarastrophysics:
– ByusingtheAMBER+FINITOsetuppresentedinthispa-
per, onecan measurea stellar diameterin threedirections
simultaneously with high accuracy. This can be used to
constrain quickly the oblate photosphere of fast-rotating
stars.
– By using the same setup, one can precisely measure the
value of the visibility minimum between the visibility
lobes. Any departure from zero, even small, proves the
presence of asymmetric features on (or above) the stellar
surface, such as convective or magnetic starspots (in our
V3879Sgrdataset,thisminimumiscompatiblewithzero,
seeFig.3). 1 http://yorick.sourceforge.net
