Globular clusters with Gaia

2.1 MB·

by  E. Pancino

Mon.Not.R.Astron.Soc.000,1–16(2013) Printed12January2017 (MNLATEXstylefilev2.2)
Globular clusters with Gaia
E. Pancino1,2(cid:63), M. Bellazzini3, G. Giuffrida4,2, S. Marinoni4,2
1INAF-OsservatorioAstrofisicodiArcetri,LargoEnricoFermi5,50125,Firenze,Italy
2ASIScienceDataCenter,ViadelPolitecnicoSNC,I-00133Rome,Italy
3INAF-OsservatorioAstronomicodiBologna,ViaRanzani1,40127,Bologna,Italy
4INAF-OsservatorioAstronomicodiRoma,ViadiFrascati33,00044MonteporzioCatone,Italy
12January2017
7
1
0
ABSTRACT
2

n The treatment of crowded fields in Gaia data will only be a reality in a few years from
a now.Inparticular,forglobularclusters,onlytheend-of-missiondata(publicin2022–2023)
J willhavethenecessaryfullcrowdingtreatmentandwillreachsufficientqualityforthefaintest

1 stars. As a consequence, the work on the deblending and decontamination pipelines is still
1 ongoing. We describe the present status of the pipelines for different Gaia instruments, and

wemodeltheend-of-missioncrowdingerrorsonthebasisofavailableinformation.Wethen
]
A apply the nominal post-launch Gaia performances, appropriately worsened by the estimated
crowding errors, to a set of 18 simulated globular clusters with different concentration, dis-
G
tance,andfieldcontamination.Weconcludethattherewillbe103–104 starswithastrometric
h. performancesvirtuallyuntouchedbycrowding(contaminatedby<1mmag)inthemajoritiy
p of clusters. The most limiting factor will be field crowding, not cluster crowding: the most
- contaminatedclusterswillonlycontain10–100cleanstars.Wealsoconcludethat:(i)thesys-
o temicpropermotionsandparallaxeswillbedeterminedto1%orbetterupto(cid:39)15kpc,andthe
tr nearbyclusterswillhaveradialvelocitiestoafewkms−1 ;(ii)internalkinematicswillbeof
s unprecendentedquality,clustermasseswillbedeterminedto(cid:39)10%upto15kpcandbeyond,
a
[ anditwillbepossibletoidentifydifferencesofafewkms−1orlessinthekinematics(ifany)
ofclustersub-populationsupto10kpcandbeyond;(iii)thebrighteststars(V(cid:39)17mag)will

1 havespace-quality,wide-fieldphotometry(mmagerrors),andallGaiaphotometrywillhave
v
1–3%errorsontheabsolutephotometriccalibration.
3
0 Keywords: astrometry–parallaxes–globularclusters:general
0
3
0
.
1
1 INTRODUCTION forallsources.GaiawaslaunchedinDecember2013(deBruijne,
0
Rygl,&Antoja2014),andthefirstdatareleasewasinSeptember
7 TheESA1 (EuropeanSpaceAgency)spacemissionGaia2 (Perry-
1 2016 (Gaia Collaboration et al. 2016b), containing positions and
man et al. 2001; Mignard 2005; Gaia Collaboration 2016a; Gaia
: white-light magnitudes for the best behaved stars, and additional
v Collaboration et al. 2016b) is the successor of Hipparcos (Perry- informationlikeparallaxesandpropermotionsfor(cid:39)2millionstars
i manetal.1997),withthegoalofprovidingastrometryforbillions
X observedpreviouslywithTycho-2(Høgetal.2000;Michalik,Lin-
ofpoint-likesourcesacrossthewholesky,withanerrorof24µas-
degren,&Hobbs2015;Lindegrenetal.2016).
r levelforstarsofG(cid:39)15mag.Gaiawillalsoprovidebroadbandmag-
a Gaia will observe not only stars, but also tens of thousands
nitudes and colours for all sources, down to the Gaia white-light
magnitude of G=20.7 mag (V(cid:39)21 mag). Low-dispersion spectra ofquasars,unresolvedgalaxies,Solarsystemobjects,manytran-
sientandvariableobjectslikesupernovae,andfinallytheinterstel-
will also be obtained in two broad bands with the red and blue
lar medium (Altavilla et al. 2012; Ducourant et al. 2014; Eyer et
spectrophotometers(BPandRP).Finally,Gaiawillproducespec-
al.2014;deBruijneetal.2015;Proft&Wambsganss2015;Zwit-
tra in the calcium triplet region with the RVS (the Radial Veloc-
ityspectrometer)downtoG(cid:39)17mag,fromwhichradialvelocities ter&Kos2015;Bachchan,Hobbs,&Lindegren2016;Tangaetal.
2016).Gaiawillalsoposeachallengebecauseofitsdataamount
(RVs). Object classification and parametrization will be possible
andcomplexity,pushingtheastrophysicalcommunityfartherinto
thepathofbigdataanddatamining(GaiaCollaboration2016a).
(cid:63) email:[email protected] Gaiaislimitedindensestellarfields,owingtotheon-board
1 A list of the acronyms used in this paper (Table A1) can be found in and downstreamtelemetry bandwidth.For spectroscopy,an addi-
AppendixA. tionallimitationisprovidedbythelargephysicalsizeofthedis-
2 http://www.cosmos.esa.int/web/gaia persed images and spectra on the focal plane. This has particular
(cid:13)c 2013RAS
2 Pancinoetal.
Table1.AdoptedGaiarelevantquantities.WenotethattheAFwindow
sizesarerelevantfortheastrometry;theBP/RPsizesforthephotometry,
chromaticitycorrection,andobjectclassificationandparametrization;the
RVSwindowsizesarerelevantforradialvelocity,objectparametrization
andabundanceanalysis.
Size Size Description
(”) (pix)
0.176789 1(AC) Acrossscan(AC)pixelsize
0.058933 1(AL) Alongscan(AL)pixelsize
0.176789 3(AL) GaiaPSF
2.121468 12(AC) ACwindowsize(AF,BP,andRP)
0.070720 12(AL) ALwindowsize(AF)a
1.767890 10(AC) ACwindowsize(RVS)
Figure1.TheGaianominalpassbandsfortheastrometricfield(G-band), 3.535980 60(AL) ALwindowsize(BPandRP)
theblueandredspectrophotometers(BPandRP),andtheradialvelocity 74.785977 1269(AL) ALwindowsize(RVS)
spectrometer(RVS).FigurecourtesyofC.Jordi.
aInsomeCCDcolumnsinAF,aswellasintheSMCCDcolumns,the
windowsarelongertoallowforbackgroundmeasurementsaroundthe
relevanceforstudiesoftheGalacticplane,thebulge,andglobular sources.Thelongerwingsofthesewindowscaninprinciplebeusedalso
clusters (hereafter, GCs). In the first few Gaia data releases, dis- tocheckthesourceprofilebehaviourourtsidenormalwindowlimits.
turbed sources like binaries, multiple stars, and stars in crowded
fields will likely not be part of the released material (Gaia Col-
• theAF(AstrometricField),providesastrometryandphotom-
laboration et al. 2016b). In any case, the inclusion of a sufficient
etryofpoint-likesourcesintheG-band,awhite-lightpassbandde-
sampleofstarsatthemainsequenceturn-offpointorfainter–with
finedbythetelescopeandinstrumenttransmissionandbytheCCD
good quality measurements – is very important for GC research. quantumefficiency(Figure1);
Therefore, only the latest few Gaia releases (2020–2023) are ex- • theBPandRPprovidelowresolutionspectra(R=λ/δλ=20-
pected to provide a significant breakthrough in GC research. To
100)intherangesshowninFigure1,andtheintegratedG and
preparethework,weexploreinthispapertheexpectedbehaviour BP
G magnitudes;thespectraarenecessaryforthechromaticitydis-
of Gaia data in several simulated Galactic GCs, adopting the of- RP
placementcorrectioninastrometricmeasurements;
ficialpost-launchGaiascienceperformancesandsomesimplified
• theRVS,providesR(cid:39)11700spectrainthecalciumtripletre-
recipestodescribeadditionaldeblendingerrorcomponents,based
gion,forstarsdowntoG(cid:39)17mag,dependingontheobject.
on the Gaia deblending pipelines. A very preliminary – and now
outdated–versionofthisworkwaspresentedbyPancino,Bellazz- Tosavetelemetrybandwidth,giventheenormousamountof
ini,&Marinoni(2013). dataproduceddailybyGaia,observationsineachinstrumentsare
The paper is organized as follows: in Section 2 we describe onlytransmittedforpixelscontainedinrectangularwindows,that
thecurrentstatusofcrowdingtreatmentinGaia;inSection3we followthedetectedpoint-likeobjectsalongthefocalplane.Forthe
present our crowding errors modeling; in Section 4 we describe faintstars,dataintheallocatedwindowsarebinnedintheACdi-
oursimulatedclustersandthecomputationofGaiaobservedquan- rectionbytheon-boardprocessingsoftware.Theadoptedwindow
titiesandfinalerrors;inSection5weexplorethesimulationsand sizesandrelevantquantitiesforourtreatmentofcrowdingarelisted
show the potential of Gaia data for GC studies; in Section 6 we inTable1.MoreinformationcanbefoundintheGaiamissionpa-
summarizethemainresultsanddrawourconclusions. per(GaiaCollaboration2016a).
2.1 Gaiadeblendinganddecontaminationpipelines
2 CROWDINGINGAIADATA
Crowdingtreatmentideallyrequiresapreliminaryevaluationofthe
Asmentionedintheprevioussection,Gaiaisacomplexspacemis-
sion,withtwodifferenttelescopesprojectingtheirlightonalarge crowding conditions of each source and transit, based on knowl-
common focal plane, captured by 106 different CCDs (Charged- edgeofthescene,i.e.,thedistributionandcharacteristicsofallthe
CoupledDevices),andpassingthroughdifferentinstruments.Gaia neighbouringsources,ascollectedbeforethecurrentobservation.
Different pipelines are employed for different instruments and to
scansthewholeskybyprecessingitsspinaxis,anddescribinggreat
treatdifferentcases.Herebelowwedescribethecurrentstatusof
circlesontheskythatslowlydriftwithitsprecession.Eachregion
isscannedfromaminimumof(cid:39)40times,toamaximumof(cid:39)250 theonesthatarerelevantforthepresentstudy.
times,withanaveragenumberof(cid:39)70passagesfortheAF,BPand
RP, and (cid:39)40 passages for RVS. All the CCDs in the focal plane
2.1.1 AFdeblending
arereadinTDI(Time-DelayedIntegration)modetocloselyfollow
Gaia’smovementacrossthesky.Onthefocalplane,stars“move” StarscloserthantheGaiaPSFwidth(whichisassumedhere3tobe
alongthescanningdirection,encounteringdifferentinstruments: 0.177”,seealsoTable1)canberecognizedasblendsalreadyinthe
• thefirsttwocolumnsoftheCCDarrayarecalledSkyMappers
(SM), and they are used for the on-board detection of point-like 3 Thevalueweadoptedisaconservativeestimate.TheGaiaeffectivePSF
sources;eachoftheSMcolumnsseesonlylightfromoneofthe variesacrossthefieldofviewandhasamedianvalueof0.103”(Fabricius
twotelescopes; etal.2016).
(cid:13)c 2013RAS,MNRAS000,1–16
GlobularclusterswithGaia 3
1
2 3 4 a)#
6
5 7 b)#
10
8
9
11 c)#
1
Figure2.AnillustrationofthecrowdingeffectsonBPandRPdispersed Figure3.SimplifieddescriptionoftransitsinBP/RP.Incase(a),twostars
images,withtheirassignedwindows(blackrectangles).Differentcasesare arecloserthanhalftheACwindowsize,andnomattertheorientationof
represented,somegoingbeyondthescopeofthepresentpaper.Starsare thesatellite,theywillalwaysbeassignedthesamewindow(ortruncated
representedbytheirsurfacedensityprofiles(solidcontours),withtheout- windows).Incase(b),twostarshaveadistancethatisinbetweentheAC
mostcontoursatthebackgroundlevel.Thebrighteststar(G=15mag)is andALhalfwindowsizes,anddependingontheorientation,theyaresome-
inwindow(2),whilethefaintestone(G=20mag)isinwindow(1).Stars timesassignedthesamewindow(ortruncatedwindow),sometimesdiffer-
fainterthantheGaiamagnitudelimit(G=20.7mag)areassignednowin- entwindows.Dependingontheirbrightness,theycanstillcontaminateeach
dow,likeforstar(3).Thecolouredportionsofthewindowsaretheback- other’swindow.Incase(c),thestarsarefartherapartthantheALwindow
groundsamples,ingreenwhentheyarefreefromcontamination,andin size,andtheyarealwaysassignedtwodifferentwindowsbut,ifoneofthe
redwhentheyarecontaminatedandcannotbeused.Whenstarsaretoo twostarsisverybright,itcanstillcontaminatetheothersignificantly.
close,theycanbeassignedtothesamewidowortwo(ormore)truncated
windows,likeincases(9),(10),and(11).Therearealsoemptywindows s
(virtualobjects)likeincase(6).FigurecourtesyofA.Brown.
the window (contaminants, with D<3.54”). This is illustrated in
Figure2,wheredifferentcasesareshowntogetherwiththeback-
astrometricprocessingofAFdata.Theseblendscanbedetected, groundevaluationregions,andinFigure3,showinghowthediffer-
forexample,fromthehigherrorsinthecentroiddeterminationand ingorientationandALprojecteddistancebetweensourcesaffects
itswobblingfromonetransittoanother,orbyphotometricvariabil-
windowassignment.
ity,radialvelocityvariability,oringeneralbecausethefitsofthe Forblendedsources,therearedifferentpipelinesthatcanbe
PSForLSFtothedatashowlargeresidualsorrequiremorethan used in different phases of the mission. Blind pipelines (without
onecomponent.
knowledgeofthescene)canbeappliedintheinitialphases,when
Assessing whether a star is isolated or has detected or sus- thehistoryofeachsourceindifferentinstrumentshasnotbuiltupto
pected companions is a crucial task. Multiple or blended objects asufficientlevel.Thetwo(ormore)blendedsourcescanberoughly
areredirectedtotheNSS(Non-SingleStars)pipelinewhereanat- modeledwithoutaprioriknowledgeoftheirexactpositions,astro-
tempt to model them as binary systems is carried out (Gaia Col-
physical parameters, and fluxes, just by modeling them with two
laboration2016a;Pourbaix2011).Ifnoneoftheavailablebinary
overlappingspectralenergydistributions.Thisapproachwassuc-
models or configurations produces a good fit to the data, then a cessfullyappliedtoGaiacommissioningdata4 ofbrightstars,re-
stochasticmodelisemployedtoderivepreliminaryparametersof
coveringthevastmajorityoftheTicho-2binaryanddoublestars.
thesecondary(ortertiaryandsoon)source.Thereforewecanas-
Onceafewtransitsareaccumulated,theycanbebetterdisentan-
sumethat–consideringalsothesmallGaiaPSF–thevastmajority glediftheyaremodeledsimultaneously(persourceratherthanper
ofNSSwillbeknown. transit),evenifthereisstillnotenoughinformationonthescene,
StarsthatarefurtherapartthanthetinyGaiaPSFareeasily
improvingthequalityofthereconstruction.Finally,oncethescene
deblended by the PSF fitting algorithms, with results much more
is well characterized and the history of the source is well devel-
similartoHST(HubbleSpaceTelescope)thantotypicalground-
oped,otherparametersofthemodelinglikethespectraltype,the
based telescopes. This is the main reason why – as we will see
projecteddistanceofthesourcesalongscan,andtherelativefluxes,
in the following – astrometric measurement uncertainties (and G
canbeusedtofurtherimprovetheinvolvedsourcesreconstruction.
magnitudes)areingenerallessaffectedbycrowding,unlikeBP/RP
For contaminated sources, it is necessary to know well the
andRVSmeasurements.
flux of the contaminating sources around, thus knowledge of the
scene is necessary. Each known source is modeled to reconstruct
2.1.2 BPandRPdeblendinganddecontaminationpipelines the flux even at large distances from the window (especially for
brightstars).Theamountofreconstructedcontaminatingfluxfrom
BP and RP transits of sources that are not isolated will be called neighboringsourcesiscomputedineachpixelofthecontaminated
here either blended or contaminated. The idea is that when the sourcewindow,andsubtracted.Forallthesereasons,decontamina-
sources are so close that they occupy the same window or inter- tionwillhavetobeperformedcontextuallywiththescenerecon-
fering windows in the vast majority of the transits (blends, with structionandcrowdingevaluation.
D<2.12”),theywillrequireadifferenttreatmentthanobjectsthat
willoftenbeassignedwellseparatedwindows,ortransitsthatare
just altered by the flux of a bright source that is well outside of 4 http://www.cosmos.esa.int/web/gaia/iow20150226
(cid:13)c 2013RAS,MNRAS000,1–16
4 Pancinoetal.
pipeline, called Source Environment Analysis (SEA) pipeline, is
basedontheFastStackimagereconstruction(Harrison2011;Gaia
Collaboration 2016a). The initial tests are promising and the re-
constructedimagescouldbeuseful,amongotherthings,totestand
improvethedeblendinganddecontaminationpipelinesaswell.
Therefore, the simulations presented in this paper, being
basedonthecurrentstatusofthedeblendinganddecontamination
pipelines,havetobeseenasgenerallypessimistic.
2.2 AnoteaboutcompletenessinGaiadata
AparticularlimitationoftheGaiadesignisrelatedtothenumber
of simultaneous object and background (virtual object) windows
Figure4.Effectoftheon-boarddetectiononcompleteness.TheBP/RPim- thatcanbeallocatedbytheon-boarddetectionalgorithmineach
ageofaGCwassimulatedwithGIBIS(GaiaInstrumentandBasicImage CCDandinanygivenmoment.Thisnumbervariesfrom(cid:39)35000
Simulator, Babusiaux 2005). The green rectangles are the assigned win- to1050000objectspersquaredegree,dependingontheinstrument
dows.Thereisanapparentlossofstarsaboveandbelowtheclustercenter,
(seeGaiaCollaboration2016a,formoredetails).Areasofthesky
where the AC stellar density is lower and windows have a lower proba- that can suffer from this limitation are clearly the Galactic bulge
biliyofbeingassignedtoasource.Thepercentageofstarslostisroughly
constantwithstellardensityineachtransit,buteachtransithasadifferent andplane,andallotherfieldsofviewthathappentooverlapthem
on the Gaia focal plane7. More relevant to the present study, the
orientation.Asaresults,theend-of-missionincompletenesswilltendtobe
flatterwithdistancefromthecenterthaninusualGCphotometries. limitation applies to the central regions of GCs, where the local
stardensitycanbeveryhigh.
Atthesingletransitlevel,completenessisalsoinfluencedby
2.1.3 RVSdeblendinganddecontaminationpipelines theon-boarddetectionalgorithm.EverysourcethatenterstheSM
The deblending phylosophy adopted by RVS is slightly differ- isassignedawindow,prioritizingbrighterobjectsdowntothelim-
itingmagnitude.Thewindowsfollowthestarsalongthefocalplane
ent from the one adopted in AF, or BP and RP. The deblending
asGaiascansthesky,andwhenthestarsexitthefield,thewindow-
pipelinesarebeingadaptedandreweittentomitigatethestraylight
slotsare“freed”andcanbeassignedtonewsourcesagain.Forthis
issues found after launch5 (Mora et al. 2016) that impact mostly
reason, the central dense areas of the clusters will – statistically
onRVSspectra,withanexpectedlossof(cid:39)1.4maginsensitivity
speaking–containmore(bright)stars,andthusobtainmorewin-
(Seabroke et al. 2016). We therefore based our modeling of de-
dowswithrespecttotheperipheryofthecluster,intheACdirec-
blendingerrorsonapreviousalgorithmthatwasbasedongeneral
tion.Differentscans,orientedintheskywithdifferentangles,will
geometricalconsiderations(AllendePrieto2008).
loosedifferentstarsandthusattheend-of-mission,eachstarthat
The treatment of contamination is instead part of the back-
is not entirely lost will have lost part of its transits. This is illus-
groundtreatment,thatisavitalpartofRVSprocessing,becauseof
tratedinthesimulatedclusterinFigure4,andisalsovisibleinthe
thelengthofthespectra(seeTable1).Thebackgroundisdivided
indiffusedandpoint-like,andtreatedseparately.Inbothcases,a ωCentauriactualGaiadatashowninapressrelease8.
We do not attempt to simulate these completeness effects in
modelingtakesplacebasedonknowledgeofthesceneandallavail-
thepresentpaper,astheywouldrequireafullend-of-missionsim-
abledataonstraylightandnearbyobjects.Themodelproducesan
ulationofdifferentlinesofsightinthesky,includingthedetailed
estimateofthetotalbackgroundintheRVSwindowsthatissub-
behaviouroftheon-boarddetectionalgorithms.
tracted from the source signal. Clearly, the model becomes more
andmoreaccurateasGaiadataareprogressivelyaccumulatedand
therefore the best results will be obtained towards the end of the
mission(K.Janssen,H.E.Huckle,andG.Seabroke,2015,private 3 MODELINGOFCROWDINGERRORS
communication).
As mentioned above, our goal is to illustrate what Gaia can do
forGCstudies,ratherthanattemptingarigoroussimulationofde-
2.1.4 Imagereconstructionandfuturepossibilities blendingerrors.Therefore,wewillmodelavailablesimulationsof
crowdedGaiadata,toderivesimpleformulaeswithasfewfreepa-
To facilitate the study of crowded areas, two paths are being fol-
rametersaspossible.
lowed.Ontheonehand,somecrowdedregionslikethecenterof The crowding error models derivation for different Gaia in-
ω Centauri or NGC 1818 in the Magellanic Cloud were imaged strumentsanddifferenttypesofblendsaredescribedinthefollow-
andtransmittedtothegroundin2DmodeintheSM6,duringcom-
ing sections. The models describe the expected percentage errors
missioning, and further regions might be observed in 2D during
on flux caused by crowding as a function of relevant parameters
the mission lifetime. The goal of these 2D images is to fully re-
constructthescenearoundeachGaiasourcetohelpimprovingand
testingthedeblendingalgorithmsincrowdedareas. 7 Werecallthattoobtainabsoluteastrometricmeasurements,Gaiaprojects
On the other hand, pipelines for the 2D image reconstruc- twodifferentlinesofsightonacommonfocalplane.Todisentanglesources
tion from individual Gaia transits are being developed. One such comingfromthetwoprojectedlinesofsight,eachoftheSM(SkyMapper)
CCDcolumnsseesonlyoneofthelinesofsight.Therefore,therewillbe
somefieldsthat–evenwithlowstellarbackground–willhappentooverap
5 http://www.cosmos.esa.int/web/gaia/news20141217 crowdedareasinsomefractionoftheirtransits.
6 http://www.cosmos.esa.int/web/gaia/iow20140206 8 http://www.cosmos.esa.int/web/gaia/iow20141113
(cid:13)c 2013RAS,MNRAS000,1–16
GlobularclusterswithGaia 5
0.25 0.20
Warmer contaminant (by 2000 K) 50% contamination
relative error on recovered flux 0.050.100.150.20 CSoaomleer Tceofnf tcaomntinaamn26int0315 a(0070bn%%%%yt (2ccccb0ooooo0nnnnt0tthttaaaa Kmm4mm0)iiiinnnn0aaaa0nnnn Ktttt) relative error on recovered flux 0.050.100.15 200% contamination
0.00 0.00
0.0 0.5 1.0 1.5 2.0
0.0 0.5 1.0 1.5 2.0
distance('')
distance ('')
Figure6.Thesimulatedpre-launchRVSdeblendingerrors,fordifferent
Figure 5. The simulated BP deblending errors as a function of distance
contaminationlevels,andoursimplifiedexponentialfits.Theshadedarea
(circles),basedonaG=15magstarwithTeff=4000K,andourderivederror (D<0.17”)isnotyettreatedinthecurrentRVSdeblendingpipelines,and
models(curves).Thedottedverticallinesmarktheapplicabilityrange,from
our fits there are extremely uncertain, therefore we will not provide any
theGaiaPSFsize(0.177”)tohalfthelengthoftheBP/RPwindows(1.76”).
simulationforclassicblendsinRVS.
Blendswithdifferentcharacteristicsareshown:coolerby2000K(small
circlesandsolidcurves),withthesametemperature(mediumcirclesand
dashedcurves),andhotterby2000K(largecirclesanddottedcurves).The onthefollowinganalysis.Iftherelativelysmallnumberofclassic
coloursrefertotherelativecontaminatingflux:17%(blue),50%(green), blendscomesasasurprise,ithastobenotedthatGaiaobservations
200%(yellow),and630%(red). onlyreachV(cid:39)21maginGCs,andthustheactualcrowdinglevels
aremuchlowerthanthoseofthetypicallydeeperphotometryfrom
thegroundorwithHST.
likethecontaminatingflux,contaminatingcolour,anddistanceof
Wewillalsoassumethattheactualdeblendingerrorsfollow
thecontaminatingobject(s).
therelationadoptedfortheBPandRPblends(seebelow),extrap-
Later,inSection4wewilltransformourfluxerrorsintoer-
olating the present simulations towards smaller source distances.
rorsonotherparameterslikepositions,parallaxes,propermotions,
While highly uncertain, this is our only available estimate of the
and radial velocities. We will then use these errors to worsen the
Gaia deblending capabilities at the present stage. For RVS there
nominalGaiapost-launchscienceperformances,dependingonthe
crowdinglevelsufferedfromeachofoursimulatedGCstars. currentlyarenoplanstoattemptdeblendingofsourcescloserthan
0.17”, and therefore we will not attempt to simulate the effect of
crowdingintheseRVSsources.
3.1 ‘Classic’blends
Weterminthispaperclassicblendsthosestarsthatarecloserthan 3.2 ‘Gaia’blends
the AF Gaia PSF (0.177”, see Table 1), and that will remain so
As discussed in Section 2.1.2, Gaia blends are all those cases in
alongthefiveyearsofGaiaobservations.Starsthatwillmoveapart
whichtwostarsarecloserthanhalftheACwindowsizeoftherel-
thankstotheirparallaxorpropermotiondifferences,orthathave
evantinstrument(Table1,theseallfallintocase(a)ofFigure3).
radialvelocitydifferencesthatallowtodeblendthem,willnotbe
BecausetheAFimagedeblendingwillbesimpler(theALprofile
consideredasclassicblends,buttreatedasnormalGaiablends(see
issharper)thanthatofBP,RP,andRVSspectra,wewillconserva-
below).
tivelybaseourestimateofcrowdingerrorsfordeblendingonaset
The precession of Gaia has an important implication for
ofBPandRVSsimulations.
crowding treatment: each time Gaia scans a particular region of
FortheBPandRPblendingsimulations,weusedaper-transit,
the sky, it is oriented differently, and thus the projected distance
partially informed deblending pipeline10 on the GIBIS (Gaia In-
oftwostarsintheSMcolumns,onwhichtheon-boardobjectde-
strument and Basic Image Simulator, Babusiaux 2005) simulated
tuerceti3o)n. aTnhderwefionrdeo,wasadsseisgcnrmibeendtianreSebcatsioedn,2a.r1e.1d,iffeveerenntth(eseceloFsiegs-t BGP=1s5pemcatrga.Tohfeasttayrpwicaasl bGleCndreeddwgiitahnot,thwerithsimTielffa=r4st0a0r0s,hKavainndg
ctolassismicublaletendrseahlaisvteicaacllhyanthceeetorrboersdceabulesneddebdy,adltehboluengdhiintgiswdhiffiencuslot eitherTeff=4000or6000K,G=15.75or17.00mag,andatdifferent
distancesequalto0.25,0.5,and1.0(cid:48)(cid:48)(seeFigure5).
manyobservablesenteriterativelythedeblendingprocedurealong
We then modeled the deblending (relative) errors on the re-
thewholemission.
coveredfluxasanexponentialαeβD,whereDisthedistancebe-
Inthispaper,wewillassumethatallblendsofstarscloserthan tweenthetwoblendedstars.Thecoefficientsαandβvarywiththe
theGaiaPSFwillberecognizedassuch,thankstothemissionlong
lifetime,itstinyastrometricandphotometricerrors,andsophisti-
cateddataanalysismethods.Becauseofthelimitednumberofclas- 10 ForadetaileddescriptionofthevariousBP/RPdeblendingpipelines,
sicblends9,thisassumptionisnotgoingtohaveasignificantimpact seeSection2.1.2.Whatwemeanhereby‘partiallyinformed’isthatwe
usedinformationontheblendedstarspositionsinAF,butwedidnotuse
any other information, such as astrophysical parameters (Teff, logg, AV,
9 From5to8%ofthetotalnumberofstarsinoursimulations,including [Fe/H]) and therefore we assumed we did not know the spectral energy
fieldstars,areclassicblends,dependingontheparticularcluster.Theclas- distributionoftheinvolvedsources.Thisisstillapessimisticassumption,
sicblendsaremostlyintheinnerpartsofGCs,within1’approximately. becausetowardstheendofthemissionthiskindofinformationwillbecome
FormoredetailsseeSection4.4. availableanditerativelyimprovedwitheverydataprocessingcycle.
(cid:13)c 2013RAS,MNRAS000,1–16
6 Pancinoetal.
temperaturedifferenceandtherelativecontaminatingflux,respec-
tively,asillustratedinFigure5.ForRP,thedeblendingerrorswere
arbitrarilymultipliedby1.5,owingtothegenerallywiderALshape
ofthespectra,thatproducesworsedeblendingresultsthaninBP.
These simplified recipes are intentionally pessimistic, to accom-
modateforunexpectedsourcesoferror.Theapproximaterangeof
validityofthemodel(highlightedinFigure5)goesfromtheGaia
PSFsizetohalftheALsizeoftheBPandRPwindows.Asdis-
cussedintheprevioussection,weappliedanextrapolationofthis
relationtoD<0.17”toclassicblends,forlackofamoredetailed
studyatthisstage.
ForRVS,theonlyavailabledeblendingsimulationswerecom-
putedbeforelaunch(AllendePrieto2008,seealsoFigure6),when
the windowing scheme and backgound treatment were different
(see Section 2.1.3). Thus, the error modeling presented here will
bemuchmoreuncertainforRVSthanforBPandRP,orforAF.
Thetemperatureorcolourdifferencebetweentwosourceshaslit-
tleimpactonthedeblendingabilityoftheRVSpipelines,because
the spectral shape is approximately flat along the RVS windows.
Whatmostlycountsistherelativecontaminatingflux.Asaresult,
the best-fitting exponential laws had a constant β, and α varying
withtherelativecontaminatingflux.Asmentionedabove,wedid
notextendthemodelbelowthePSFsizeforRVS(shadedregionin
Figure7.Thelogarithmicdensityprofiles(leftpanels)andradialvelocity
Figure6).
dispersionprofiles(rightpanels)forthetwosyntheticclusterswithcon-
centration parameter c=1.0 (top panels) and c=2.5 (bottom panels). The
redlinesarethecorrespondingtheoreticaldensityprofiles(leftpanels)and
3.3 Contaminants ±3σcontoursaboutthesystemicvelocityforKing(1966)modelswiththe
sameparameters.
Forcontaminatedstars(cases(b)and(c)inFigure3),therecon-
struction of star fluxes at distances larger than the window size
is subject to a variety of uncertainty sources, and the relevant For RVS, the discrete background pipelines are being
pipelines will be effective only when a sufficient history is accu- presentlyintegratedandtested,sonosimulationsareavailableat
mulatedtobuildascene.Notonlythestarspositionsareneeded, the moment and we just extended our simplified treatment of the
but also their spectral energy distributions. Additionally, a com- RVS blends (previous section) to RVS contaminants, as done for
pletecharacterizationofthePSFprofilesACandAL,atdifferent BPandRP,usingtheappropriatewindowsizes.
wavelengths and positions on the focal plane will be fundamen-
tal.Thereforenodetailedsimulationsareavailableatthemoment
(Section2.1.2). 4 CLUSTERSIMULATIONS
However,wedoknowthatastep-likebehaviourisexpectedin
theerrorsat1.76(cid:48)(cid:48),wheretheprocessingswitchesfromdecontam- Wesimulated18differentglobularclusters,assummarizedinTa-
inationtodeblending,inthesensethatdecontaminationpipelines ble2,withdifferentconcentration,backgroundcontamination,and
performslightlyworsethanthedeblendingones.Therewillbe,on distance.Thefinalsimulatedclusters,aftertheGaiascienceperfor-
purpose,a‘greyarea’inprojecteddistancebetweensources,where mancesandthecrowdingerrorsimulationsareincluded,arepre-
bothpipelineswillbeapplied,forcross-validationpurposes.Some sentedinTable3.
testswereperformedtodevelopthecurrentdecontaminationalgo-
rithms(Piersimonietal.2011,,andDeLuise,privatecommunica-
4.1 3Dsimulatedclusters
tion).Accordingtothosetests,wedecidedtoroughlyapproximate
the decontamination errors with a factor of 2 worsening with re- The simulated clusters were computed with the McLuster code12
specttodeblendingerrors.Thisisapessimisticassumption. (Ku¨pperetal.2011),thatisdesignedtoproduceinitialconditions
Ourmodelingofdecontaminationresidualerrorsisappliedto for N-body simulations. We used the code version (mcluster sse)
contaminantstarswithdistancesrangingfromhalftheACwindow whichimplementsthestellarevolutionrecipesbyHurley,Pols,&
sizetothefullALwindowsizeortothecontaminatingstar’s‘size’, Tout(2000).
whichever is larger. We modeled the contaminating stars sizes as Weproducedtwoclusterscontaining800000stars,withpo-
a linear function of G magnitude (L. Pulone and P. M. Marrese, sitions and velocities drawn from equilibrium King (1966) mod-
2008,privatecommunication,seealsoFigure2).Starsfainterthan els.Thetwoclustersdifferedonlyintheirconcentrationparameter,
G(cid:39)15magaregenerallysmallerthantheBPandRPALwindow c=log(r/r ),onehavingc=1.0andtheotherc=2.5.Amongthekey
t c
size11. inputparametersforthesimulation,thehalf-massradiuswascho-
sentoproducea(projected)half-lightfinalradiussimilartowhat
typicallyobservedforGalacticglobularclusters:4pcforthec=1.0
11 Withourlinearrelation,aG=2magstarwouldbeabletosignificantly clusterand3pcforc=2.5one(seealsoHarris1996,andfollowing
contaminatestarsupto34.4(cid:48)(cid:48).Thesebrightstarsarerare:inoureighteen
simulatedGCsthereisonlyonefieldstarbrighterthanthat,appearingin
thesixdiskGCs. 12 http://www.astro.uni-bonn.de/∼akuepper/mcluster/mcluster.html
(cid:13)c 2013RAS,MNRAS000,1–16
GlobularclusterswithGaia 7
Table2.Simulatedclusterspropertiesandcrowdingevaluationresults.Foreeachofthe18simulatedGCswelist(seetextformoredetails):(1)theGC
IDnumber;(2)theGCconcentrationparameter,c=log(rt/rc);(3)theGCprojecteddistance;(4)thetypeofsimulatedbackground;(5)thetotalnumberof
simulatedstars(GCandbackground)aboveGaiadetectionlimit;(6)thenumberofGCmembers;(7)thenumberofclassicblends;(8)thenumberofGaia
blends;(9)thenumberofcontaminatedstars;(10)thenumberofcleanstars,i.e.,contaminatedbylessthan0.1%influx(roughly1mmag);(11)thequickGC
designationusedinthepaper;and(12)someexamplesofGCswithsimilardistance,concentration,andbackgroundfieldcontamination.
Cluster c distance background ntot nGC nclassic nblends ncontam nclean Designation Similarto
(dex) (kpc)
#1 1.0 5 halo 73385 72510 4621 45101 52142 16093 Easycase M13,M92
#2 1.0 10 halo 30200 29325 3521 21550 23754 4275 M92
#3 1.0 15 halo 14027 13152 2203 10312 11203 1495 NGC5053
#4 1.0 5 disk 54923 26816 1028 14115 17289 7379 M71
#5 1.0 10 disk 33435 5328 326 3302 3812 1164 Intermediatecase M56,NGC2298
#6 1.0 15 disk 29737 1630 123 1048 1208 311 M79
#7 1.0 5 bulge 1537592 71996 9833 69887 71600 218 M22,NGC6553
#8 1.0 10 bulge 1494601 29005 5620 28497 28919 36 M9,NGC6638
#9 1.0 15 bulge 1478538 12942 2998 12762 12911 15 Pal11
#10 2.5 5 halo 73385 72510 11902 47043 53029 15623 M5
#11 2.5 10 halo 30200 29325 6914 21977 23944 4117 M3
#12 2.5 15 halo 14027 13152 3663 10407 11176 1525 NGC5466
#13 2.5 5 disk 54923 26816 3236 15372 18085 6946 M92,Pal10
#14 2.5 10 disk 33435 5328 906 3491 3968 1055 M79,NGC1851
#15 2.5 15 disk 29737 1630 292 1097 1250 300 M15
#16 2.5 5 bulge 1537592 71996 16564 70125 71648 190 NGC6540,NGC6558
#17 2.5 10 bulge 1494601 29005 8726 28556 28924 40 NGC6325,NGC6342
#18 2.5 15 bulge 1478538 12942 4378 12770 12914 13 Difficultcase M54,NGC6517
updates). Among the key input stellar population parameters, we wellwiththepredictionsbyKing(1966),wherethetotalmassis
adoptedanageof12Gyr,ametallicityofZ=0.0003,correspond- obtainedbysummingthemassesofallindividualstars.
ingto[Fe/H]=–1.79dex,andaKroupa(2001)IMF(InitialMass
Function).Thesimulationswereperformedwithoutincludingbi-
naries, for simplicity, and the resulting clusters are spherical and 4.2 Simulatedfieldcontamination
non-rotating.
WesimulatedthefieldGalacticpopulationinthreedirectionsusing
Themainimplicationsofourchoicesofinputparametersare:
theBesanco¸nmodels14(Robinetal.2003,andreferencestherein),
(i)ablueHB(HorizontalBranch)morphology,whichmaybeuse-
includingkinematicsandwithoutobservationalerrors.Themodels
fultotesttheperformanceofGaiaonrelativelyhotstars,and(ii)
produced catalogues of magnitudes (in the Johnson-Cousins sys-
astellarM/L ratiolarger((cid:62)3insteadof(cid:54)2)thanwhattypically
V tem), 3D positions, and 3D motions. We adopted the “standard”
observed in Galactic globular clusters having a present day mass extinctionlawofferedbytheBesanco¸nsimulator,ameananddif-
function compatible with a low-exponent power law (Paust et al. fusedabsorptionof0.7mag/kpc,neglectingsmallscalevariations,
2010). The high M/L ratio is also due to a relatively large frac-
V anddecreasingawayfromtheGalacticplanewithasmoothEinasto
tionofdarkremnants:(cid:39)25%oftheclustermassiscontributedby
profile (for more details, see Robin et al. 2003). We selected all
objectswithM>M(cid:12)13.Independentlyoftherecipesgivingraiseto availablespectraltypesinamagnituderangeof0<V<25mag.The
suchalargefractionofdarkremnantsandtheiractualnature,this
simulationswerecomputedina0.7×0.7degsquarecentredoneach
isnotaconcernforourpurpose:theonlyeffectisthatthepotential
ofthefollowingthreedirections(seealsoTable2):
well may be slightly deeper than for most real clusters and, con-
sequently, the velocity dispersion is slightly larger, at fixed total • aratherempty“halo”fieldatl=150andb=80deg,containing
luminosityandscaleradius.Whatisrelevantforusisthatthecen- (cid:39)2300starsintotal;thisismeanttorepresentthebestcasesoflow
tralvelocitydispersionisstillintherightrangeandthatthemodel backgroundcontaminationinGaiaobservations;
isself-consistent. • anextremelydense“bulge”fieldatl=5andb=5deg,contain-
Theresultingsimulatedclustershaveabsoluteintegratedmag- ing almost 6 millions of stars, which should cover even the most
nitudesofMV=–7.6mag,i.e.,justabovethepeakoftheclusters crowdedGaiaobservations,whentworelativelycrowdedlinesof
luminosityfunction(MV=–7.4mag,accordingtoBrodie&Strader sightoverlaponthefocalplane(seealsoSection2);
2006).Theclustersprojectedsurfacedensitydistributionsarewell • a crowded “disk” field in the anticenter direction, at l=180
fittedbyaKing(1966)profile,whenobtainingrc(thecoreradius) and b=0, containing roughly 140000 stars, with a relatively high
fromthefit.Finally,thederivedcentralvelocitydispersionsagree extinction of up to (cid:39)2 mags in V band (even if these values are
only reached in (cid:39)25% of the known GCs in Harris 1996); while
not as extreme as the bulge line of sight, this direction provides
13 Darkremnantsarewhitedwarfstars,neutronstars,andblackholes.Re-
cently,comparablefractionsofdarkremnantswereobtainedwithstate-of-
the-artclustermodelingbySollimaetal.(2015)andSollimaetal.(2016). 14 http://model.obs-besancon.fr/js
(cid:13)c 2013RAS,MNRAS000,1–16
8 Pancinoetal.
Table3.Column-by-columndescriptionofthefinalsimulatedstars,that 0
1. D=5 kpc halo
willonlybeavailableintheelectroniceditionofthejournal,andatCDS.
8 D=10 kpc disk
s 0. D=15 kpc bulge
d
Content Column Units Description assicblenxvec$V2 0.40.6 cc==12..05
cl
f 2
0.
Cluster (1) Clusternumber
0
Star (2) StarID 0.
RA(cid:48) (3) (deg) PositionalongtheRAdirection 0
Dec(cid:48) (4) (deg) PositionalongtheDecdirection 1.
δcoord (5) (deg) ErroronRA(cid:48)andDec(cid:48) 0.8 xvec$V1
(cid:36)µµδµRDAec(cid:48)(cid:48) ((((9678)))) (((mmm(aaamsssayyysrrr)−−−111))) RDEParAerrcoa(cid:48)(cid:48)lrplpaorrxonopppeerrormpmeoorttimioonontion Gaiablendsxvec$V2 0.40.6
δ(cid:36) (10) (mas) Parallaxerror f 0.2
G (11) (mag) G-bandintegratedmagnitude
0
δG (12) (mag) Gmagnitudeerror 0.
GBP (13) (mag) GBPintegratedmagnitude 1.0
GδGRBPP ((1154)) ((mmaagg)) GGRBPPimntaeggnriattueddemerargonritude nts 0.8 xvec$V1
a
MδGeRmPbership ((1167)) (mag) TGrRuPemmaegmnbiteurdsehieprror ntaminc$V2 0.6
oe 4
Note:ThepseudocoordinatesRA(cid:48)andDec(cid:48)arejustdistancesfromthe Gaiacxv 20.
centerindeg,nottrueskycoordinates.Thetruemembership,inthecaseof f 0.
classicblends,relatestothebrighteststaroftheblend.Itis1forcluster 0
0.
membersand0forfieldstars.
0 100 200 300 400 500 600
Distancxev ferocm$V c1enter ('')
stillseverecrowdinglevels–ontheGalacticplane–coupledwith
significantreddening.
Figure8.ResultsofthecrowdingevaluationonsimulatedGCs.Eachpanel
displaystherelativefractionofclassicblends,Gaiablends,andcontam-
inants as a function of distance from the GC center. Only stars that are
blendedorcontaminatedbyatleast0.01magsintotal(i.e.,(cid:39)1%oftheir
4.3 SimulatedGaiameasurements flux)areshowninthefigure.Onlyclassicblendshaveasignificanteffect
ontheastrometricperformances,whileBP/RPandRVSaresignificantly
Each of the two clusters (see Section 4.1) was projected at three affectedalsobyGaiablendsandcontaminants.
different distances of 5, 10, and 15 kpc and combined with each
of the three backgrounds, to produce the 18 clusters in Table 2.
Atypicalsystemicradialvelocityof100kms−1 wasassignedto ontheconsideredinstrumentandonthetypesofblends(Section3).
eachcluster(broadlycompatiblewiththevalueslistedintheHarris Weadoptedanexhaustivealgorithmforneighborssearch15.
1996,catalogue,initsmostrecentversion),whileapropermotion The relative number of each type of neighbours (classic
of–5masyr−1inboththeRAandDecwasassignedtoallclusters blends, Gaia blends, contaminants) for the 18 simulated clusters
(broadlycompatiblewiththevaluesmeasuredby,e.g.,Dinescuet isshowninFigure8asafunctionofdistancefromtheGCcenter.
al.1999).Distanceswerealsoconvertedintoparallaxes. Ascanbeseen,theparameterthatdominatesthefractionofclassic
Integrated Gaia magnitudes G, G , and G (see also Sec- blendsistheGCconcentration:corecollapsedclustershavemore
BP RP
tion2andFigure1)wereobtainedforeachstarusingtheformu- thantwicethenumberofclassicallyblendedstarsintheircentral
laeprovidedbyJordietal.(2010,usingtheircoefficientsfromTa- partscomparedtonormalGCs.Thevastmajorityofclassicblends
ble3),startingfromtheB–Vcolour.Forextinction,weadoptedthe areintheGCcentralregions,andareblendsofGCmemberswith
pessimistichypothesisthattheclusterreddeningwasequaltothe otherGCmembers.Distanceandreddeninghaveacuriouseffect:
correspondingbackgroundfield’shighestvalue(i.e.,asiftheclus- becauseGCsbecomefainterwithincreasingdistanceandredden-
terwasentirelybehindthefieldpopulation).Whilethisassumption ing, their luminosity function crosses the detection limit of Gaia
is not completely realistic, it gave us the possibility of exploring where it is less populous. As a consequence, not only the num-
higherreddeningconditions,atleastforthediskprojections.This berofstarsdetectedbyGaiadecreases,butalsotheprobabilityof
yieldedanA of0.062magforthehaloprojections,0.080magfor
V
thebulgeprojections,andof2.149magforthediskprojections.
15 Inotherwords,weloopedoverthelistof(relevant)starsandcomputed
distanceswithallother(relevant)stars,oneobjectatatime.Thiswasneces-
sarybecausesmarterneighboursearchespre-computeadistancematrixto
4.4 Crowdingevaluation increasecomputationspeed,andthereforetendtosaturatecomputermem-
oryfordatasetscontainingmorethan105 objects(HendraGunadi2011).
ForeachsimulatedstarineachGC,wecountedallneighbors(with OurbulgesimulatedGCscontainafewmillionstars,andseveraltensof
fluxabove0.1%ofthestar)withinaspecifieddistance,depending millionsofrelevantpairs.
(cid:13)c 2013RAS,MNRAS000,1–16
GlobularclusterswithGaia 9
blending,andsotheblendsandcontaminantfractions.Ontheother shiftonthesingleGaiameasurementcouldamoutto500–800µas,
hand,theeffectoffieldcontaminantsistoincreasethefractionof depending on the spectral type and on the position along the fo-
Gaiablendsandcontaminantsatalldistancesfromthecenter.Ex- cal plane. By averaging out transits and by correcting the effect
tremecasesarethebulgebackgroundGCs,wherethevastmajority of spectral type with G -G , the residual end-of-mission errors
BP RP
ofstarsareblendedand/orcontaminatedtosomedegreeatallradii, would amount to 0.4–1.4 µas (Jordi et al. 2006)16 in most of the
mostlybyfieldstars. well-behaved stars. However, for objects with non-stellar or pe-
We listed in Table 2 some key quantities resulting from the culiar colours, such as a Quasar or a (multiple) stellar blend, the
crowdingevaluation.Ascanbeseen,thenumberofstarsthatare residualerrorcouldbestillberoughly30µas,ascomputedfrom
clean(i.e.,contaminatedbylessthan1mmag)canbesubstantial thetypicalresidualcentroidshiftdifferencebetweenaBandanM
when the background is not extreme. The vast majority of Gaia star,afterchromaticitycorrection(Jordietal.2006).Wethusap-
blendsandcontaminantswillbeknown,asalargefractionofthe proximated linearly17 the additional chromatic error as 0.002 µas
classicblends(seeSection2.1.1).Therefore,itwillalwaysbepos- for each K of temperature difference between each blended stars
sibletoselectareliablesampleofcleanstarsfromGaiadata. pair(bothclassicandGaiablends),multipliedbytherelativecon-
Additionally,wereportherethatalreadyinthefirstGaiare- taminatingflux.Thetypicalresidualsfromchromaticerrorscaused
lease,whichdoesnotcontainstarsintruncatedwindowsorstars bycrowdingareofafewµas,butcanbesubstantiallyhigherfor
withlow-qualitymeasurements(GaiaCollaborationetal.2016b), companionsthatareverybrightorhaveaverydifferentcolour(up
morethan200000starswereactuallydetectedintheωCenfield. to(cid:39)30–50µasinoursimulations).
Thiscompareswellwithour#1cluster,whichisreasonablecon- ForRVerrorcomputations,thefirstconsiderationisthatev-
sideringthehighermassofωCen,andgivessupporttothefigures erytime a star is contaminated by another star with a net RV dif-
discussedaboveandreportedinTable2. ference above (cid:39)30 km s−1 (roughly the Gaia resolution element
FWHM),thereisachanceofseparatingthetwoRVs,dependingon
therelativefluxcontamination.Thepercentageoffluxcontamina-
4.5 SimulatedGaiaerrors tion(obtainedasinSection3)wasusedtodegradethesignalofthe
contaminated(orblended)star.Wethusrecomputedthemagnitude
TocomputetheGaiaerrors,wecombinedthepost-launchGaiasci-
ofeachblendedorcontaminatedstar,takingintoaccounttheresid-
enceperformances(GaiaCollaboration2016a)withourcrowding
ual errors after deblending or decontamination. We similarly re-
error estimates. For the magnitudes we combined the two errors
computedthecolourstakingintoaccounttheresidualcolourerrors.
in quadrature, because they are fully independent. For the astro-
TherecomputedcoloursandmagnitudeswerefedintotheRVerror
metric and spectroscopic measurements, the crowding errors are
equation(GaiaCollaboration2016a),toderivetheerroronRVim-
notfullyindependentfromtheGaiascienceperformances,because
pliedbythemagnitudeandcolourdeblendingerrors.Thesecond
they both depend on the star magnitude. Therefore we conserva- considerationisthatanartificialRVshiftofroughly30kms−1can
tivelysummedtheerrorsinmodulus. alsobeobtainediftwoblendedstarsareoffset,intheALdirection,
byatleast4ALpixels(or0.235”),thereforewetreatedthesestars
asintheabovecase.WefinallydidnotattempttosimulateanyRV
4.5.1 Crowdingerrors
measurementforstarscloserthantheGaiaPSF(i.e.,oneACpixel
We used the modeling described in Section 3, which provided a or0.177”)asexplainedpreviously.Moreover,wedidnotcompute
relative error on the flux of each star, caused by the various type RVsorRVerrorsforstarsfainterthanG=16mag.
ofblendsandcontaminantsaffectingit.Thesemodelederrorsrep-
resent well the crowding errors for G, G , and G , i.e., on the
BP RP
photometry. 5 RESULTS
Toevaluatethecrowdingerrorsonastrometry,weconsidered
two components: the error on centroiding and a chromatic shift. Weillustrateinthefollowingsectionsthetypeofdataqualitywe
Forthecentroidingerrors,onlyclassicblendswereconsidered,be- expect from Gaia at the end of the mission, based on our simu-
causeonlystarscloserthanthePSFareexpectedtohaveasignifi- lations.Asmentionedalready,givenalltheconservativeassump-
cantimpactonthefinalcentroidmeasurementofastar.Weexpect tionsandtheuseofpreliminarydeblendingpipelines,thepresented
that the PSF of a star will be perturbed by the residual flux left results have to be considered pessimistic, in the sense that the
bytheclosecompanionsafterthedeblendingprocedure,andthese pipelineswillbemoresophisticatedinafewyearsfromnow.
residualswilldependonthecontaminatingfluxanddistanceofthe WewillshowinallfiguresthreesimulatedGCs:aneasycase
blending stars, as modeled in Section 3. We therefore computed withD=5kpc,c=1.0,andahalobackground(cluster#1,plottedin
thepercentualfluxintheresidualsasanaverageofthebendedstar greeninallfigures);anintermediatecasewith10kpc,c=1.0,anda
andtheblendingones,weightedondistanceandfluxoftheblend- diskbackground,witharelativelyhighreddeningforGCs(cluster
ing stars. We then assumed that the percentual centroiding error #5,plottedinyellow);andadifficultcasewithD=15kpc,c=2.5,
causedbyblendingwasequaltothisresidualcontaminatingflux,a and a bulge background, which is an extreme condition for Gaia
pessimisticassumption.Theresultingcentroidingerrorscausedby (cluster#18,plottedinred).
crowdingaretypicallyoftheorderof∼10µasyr−1(withmaximum
valuesof∼100),buttheyaffectarelativelylownumberofstarsin
16 TheseestimateswerecomputedusingtheGaiafiltersystem,nowabon-
eachGC(seeTable2).
doned,buttherearenootherestimatesavailableoftheGaiaresidualchro-
For the chromaticity correction, we know that chromatic ef-
maticdisplacementintheliteratureatthemoment.
fectsforGaiaarerelevant,becauseofitshighaccuracy,andthey 17 Theentityofthechromaticcorrectionerrorscausedbycrowdingissmall
arecorrectedusingtheBP/RPinformation.Ifanerrorismadeon forthesimulatedGCs(afewµasorµasyr−1)comparedtotheGaiascience
thatcolourdeterminationbecauseofblends,theerroristransported performances(seealsoFigure10),andthereforealinearapproximationwas
intotheastrometricmeasurementsaswell.Itwasestimatedthatthe consideredadequate.
(cid:13)c 2013RAS,MNRAS000,1–16
10 Pancinoetal.
6000 1:2
4000 1yr)¡01::80
mas0:6
(
2000 ¹0:4
±
0:2
0 0
¡2:0 ¡1:5 ¡1:0 ¡0:5¢¹(m0asyr¡1) 0:5 1:0 1:5 2:0 12 13 14 15 16G(mag1)7 18 19 20 21
400 1:2
300 1yr)¡01::80
200 mas0:6
(
100 ±¹0:4
0:2
0 ¡2:0 ¡1:5 ¡1:0 ¡0:5¢¹(m0asyr¡1) 0:5 1:0 1:5 2:0 0 12 13 14 15 16G(mag1)7 18 19 20 21
800
1:2
600 1yr)¡01::80
400 mas0:6
(
200 ¹0:4
±
0:2
0
2:0 1:5 1:0 0:5 0 0:5 1:0 1:5 2:0 0
¡ ¡ ¡ ¡ ¢¹(masyr¡1) 12 13 14 15 16G(mag1)7 18 19 20 21
Figure9.Histogramsofdifferencesbetweenthefinalanderror-freesim- Figure 10. Final simulated proper motion errors, including the effect of
ulatedpropermotionsoftheeasy(greenhistogram),intermediate(yellow
crowding)fortheeasy(greenpoints),intermediate(yellowpoints),anddif-
histogram),anddifficultcases(redhistogram).Onlyclustermembersare
ficultcases(redpoints),asafunctionoffinalsimulatedGmagnitude.Only
shown.Theresultingabsolutedisplacementsinthesystemicpropermotion
clustermembersareshown.
determinationisofabout1–10µasyr−1,correspondingtoerrorsof<0.1%.
Wenotethattheintrinsicdispersionisoftheorderof100µasyr−1,andthe
final,simulatedoneis300–600µasyr−1,whenincludingallstarsdownto
G(cid:39)20.7mag. clustersarealwayseasilyseparatedfromthefieldpopulation,ex-
cept in the case of the extreme bulge background. In the follow-
ingsections,wewillselecttheprobablememberswithaloosecri-
5.1 Propermotions terium,i.e.,starswithin1masyr−1fromthesystemicGCmotion,
andwithastrictcriterium,i.e.,within0.3masyr−1 fromthesys-
Because proper motions are determined with AF, the impact of
crowdingislessseverethanonBP/RPspectro-photometry,oron temicGCmotion.
RVSspectra.Figure9showsthehistogramofthedifferencesbe-
tweenthefinalpropermotion–includingallerrorsources–and
the initial error-free simulated one, for the known cluster mem-
5.1.1 Measurementofderivedquantities
bers. The median systemic proper motion can be recovered with
abiasof5–10µasyr−1,i.e.,withasystematicerrorofroughly0.1– ToassessthederivedquantitiesthatwillbemeasurablefromGaia
0.2%.TheintrinsicspreadofthesimulatedGCsisoftheorderof data,weperformedabasictestontheeasycaseGC.Weexcluded
100µasyr−1,dependingontheGC.Theobservedspreadisaround all stars that were clearly unrelated to the GC with a very loose
400–500µasyr−1,ifoneincludesallthesimulatedstarsdownto proper motion selection (±3 mas yr−1) and all the classic blends.
themagnitudelimit.Itisalmostentirelyexplainedwiththenomi- We then converted proper motions in the RA and Dec directions
nalpost-launchperformancesappliedontopoftheintrinsicspread, intovelocities,usingtheGCdistanceandpropagatingitserror(see
especiallywhenincludingfaintstars.Infact(seeSection4.5.1)the Section5.2).WethenestimatedtheRVspreadsσ andσ asa
RA Dec
crowdingerrorsontheaffectedstarsareintheworstcasesafew functionofdistancefromtheGCcenterwiththeirerrors.Weused
100µasyr−1 forthecentroidingdetermination,and(cid:39)30µasyr−1 themaximumlikelihoodestimationmethod(MLE)withthelike-
forchromaticityerrorscausedbyGBP/RPcrowdingerrors. lihood formulation described by Pryor & Meylan (1993), Walker
Concerningindividualstars,Figure10showsthebehaviourof etal.(2006)andMartinetal.(2007),whichtakesintoaccountthe
thefinalsimulatederrorsasafunctionofGmagnitude.Itcanbe errorsonmeasurementsaswell.TheactualerrorsontheRVdis-
usefultocomparethesesimulationswiththefirstresultsfromthe persionsineachradialbinareofabout0.4–1.4kms−1.Theresultis
HSTPROMOprojectforM15(HubbleSpaceTelescopePROper displayedinFigure12,showingthatGaiawillbeabletodetermine
MOtionproject,Bellinietal.2014).Theirtypicalerroraroundthe theradialprofileoftheRVdispersionofnearbyGCswitherrorsof
G=15magis5–10timeshigherthantheerrorexpectedfromGaia, about1kms−1inthenearestGCs.
about0.1masyr−1,butatG=21magtheyareabouthalftheGaia Moreingeneral,wecansaythat:
error, at 0.5 mas yr−1. Moreover, HST proper motions can reach
several magnitudes below the Gaia limit. On the other hand, the (i) PropermotionsobtainedbyGaiainGCswillallowthestudy
advantageofGaia’spropermotionsisthattheycoveralargerarea of dynamical relaxation in the 5–10 closest GCs (see also Sec-
aroundeachGC–actually,thewholesky–andthattheyareabso- tion5.3andFigure14).Thisisbecauseatleastafewmagnitudes
lutepropermotions. below the GC turn-off point are required to adequately sample a
WeshowinFigure11thetypicalvectordiagramsofallsimu- rangeofstellarmasses.Figure14clearlyshowsthatthisispossi-
latedstars,includingfaintstarsandbackgroundcontaminants.The bleonlyforclustersat(cid:39)5kpcorless,becauseoftheGaiadetection
(cid:13)c 2013RAS,MNRAS000,1–16