On the Recovery of the Star Formation History of the LMC from the VISTA Survey of the Magellanic System

1.6 MB·English

by  L. Kerber

Astronomy&Astrophysicsmanuscriptno.vmcpaper (cid:13)c ESO2009
January26,2009
On the Recovery of the Star Formation History of the LMC from
9
0 the VISTA Survey of the Magellanic System
0
2
LeandroKerber1,2,Le´oGirardi1,StefanoRubele1,3,andMaria-RosaCioni4
n
(fortheVMCTeam)
a
J

6 1 OsservatorioAstronomicodiPadova–INAF,Vicolodell’Osservatorio5,I-35122Padova,Italy
2 2 UniversidadedeSa˜oPaulo,IAG,RuadoMata˜o1226,CidadeUniversita´ria,Sa˜oPaulo05508-900,Brazil

3 DipartimentodiAstronomia,Universita`diPadova,Vicolodell’Osservatorio2,I-35122Padova,Italy
]
O 4 CenterforAstrophysicsResearch,UniversityofHertfordshire,HatfieldAL109AB,UK
C
Received9October2008/Accepted
.
h
p ABSTRACT
-
o
TheVISTAnear infraredsurvey oftheMagellanic System(VMC) willprovide deep YJK photometry reaching starsintheoldest turn-off
r s
t pointallover theMagellanicClouds(MCs).Aspartofthepreparationforthesurvey, weaimtoaccesstheaccuracyintheStarFormation
s
a History (SFH) that can be expected from VMC data, in particular for the Large Magellanic Cloud (LMC). To this aim, we first simulate
[ VMCimagescontainingnotonlytheLMCstellarpopulationsbutalsotheforegroundMilkyWay(MW)starsandbackgroundgalaxies.The

simulationscoverthewholerangeofdensityofLMCfieldstars.Wethenperformaperturephotometryoverthesesimulatedimages,accessthe
1
expectedlevelsofphotometricerrorsandincompleteness,andapplytheclassicaltechniqueofSFH-recoverybasedonthereconstructionof
v
colour-magnitudediagrams(CMD)viatheminimizationofachi-squared-likestatistics.WeverifythattheforegroundMWstarsareaccurately
1
recovered by the minimizationalgorithms, whereas thebackground galaxiescan be largelyeliminated fromthe CMD analysis due totheir
3
1 particular colours and morphologies. We then evaluate the expected errors in the recovered star formation rate as a function of stellar age,
4 SFR(t),startingfrommodelswithaknownAge–MetallicityRelation(AMR).Itturnsoutthat,foragivenskyarea,therandomerrorsforages
. older than∼ 0.4Gyr seemtobeindependent of thecrowding; thiscanbeexplained by acounterbalancing effect between thelossof stars
1
duetoadecreaseinthecompleteness,andthegainofstarsduetoanincreaseinthestellardensity.Foraspatialresolutionof∼0.1deg2,the
0
randomerrorsinSFR(t)willbebelow20%forthiswiderangeofages.Ontheotherhand,duetothesmallerstellarstatisticsforstarsyounger
9
0 than∼0.4Gyr,theouterLMCregionswillrequirelargerareastoachievethesamelevelofaccuracyintheSFR(t).IfweconsidertheAMRas
: unknown,theSFH-recoveryalgorithmisabletoaccuratelyrecovertheinputAMR,atthepriceofanincreaseofrandomerrorsintheSFR(t)
v
byafactorofabout2.5.ExperimentsofSFH-recoveryperformedforvaryingdistancemodulusandreddeningindicatethattheseparameters
i
X canbedeterminedwith(relative)accuraciesof∆(m−M)0 ∼ 0.02magand∆EB−V ∼ 0.01mag,foreachindividualfieldovertheLMC.The
propagationoftheselattererrorsintheSFR(t)impliessystematicerrorsbelow30%.ThislevelofaccuracyintheSFR(t)canrevealimportant
r
a imprintsinthedynamicalevolutionofthisuniqueandnearbystellarsystem,aswellaspossiblesignaturesofthepastinteractionbetweenthe
MCsandtheMW.
Keywords.MagellanicClouds–Galaxies:evolution–Surveys–Infrared:stars-Hertzsprung-Russel(HR)andC-Mdiagrams–Methods:
numerical
1. Introduction geredand proceedsin time, fromthe smallest to galactic-size
scales, and how these processes depend on dynamical effects
Determining the star formation histories (SFH) of the
(e.g.Harris&Zaritsky2007;Harris2007a).
MagellanicClouds(MC)isoneofthemostobviousgoalsinthe
TheMagellanicCloudsarealsoarichlaboratoryforstud-
studyofnearbygalaxies,foraseriesofreasons.First,thisSFH
ies ofstar formationand evolution,andthe calibrationof pri-
does likely keep record of the past interactions between both
mary standard candles, thanks to the simultaneous presence
CloudsandtheMilkyWay(Olsen1999;Holtzmanetal.1999;
of a wide variety of interesting objects such as red clump gi-
Smecker-Haneetal. 2002; Harris&Zaritsky 2004), which
ants,Cepheids,RRLyrae,longperiodvariables,carbonstars,
are still to be properly unveiled (Kallivayaliletal. 2006b,a;
planetarynebulae,thetipoftheredgiantbranch(RGB),dust-
Beslaetal.2007;Piateketal.2008).DetailedSFHstudiesmay
enshroudedgiants,pre-mainsequencestars,etc.Althoughthe
also provide unvaluable hints on how star formation is trig-
systemcontainsseveralhundredsofstarclustersforwhichage
Sendoffprintrequeststo:L.Kerber andmetallicitycanbemeasured,thebulkoftheinterestingstel-
e-mail:[email protected] larobjectsareactuallyinthefieldandirremediablymixedby
2 Kerberetal.:SFHRecoveryoftheLMCfromVMCSurvey
the complex SFH, and also partially hidden by the presence Another particularity of the VMC survey is that, once
of variable and patchy extinction across the MCs. Unveiling started, its data flow will be so huge that algorithms of anal-
this complexSFH may help in calibrating stellar properties– ysishavebettertobepreparedinadvance,intheformofsemi-
likeluminosities,lifetimes,periods,chemicaltypes,etc.–asa automated pipelines. Similar approaches have been/are being
functionofageandmetallicity. followed by some ambitious nearly-all-sky (SDSS, 2MASS),
In the last two decades, many authors demonstrated micro-lensing (MACHO, OGLE, EROS), and space astrome-
that recovering the SFH of the MC from optical photom- try(e.g.Hipparcos,GAIA)surveys.
etry is indeed feasible and well worth of the effort. Such Inthispaper,wedescribepartofthepreparatoryworkfor
works are, usually, based either on deep Hubble Space thederivationoftheSFHfromVMCdata,whichcanbesum-
Telescope (HST) photometry reaching the oldest main se- marisedinthefollowingway:FirstwesimulatetheVMCim-
quence turn-off for small MC areas (e.g. Gallagheretal. ages for the LMC (Sect. 2), where we later perform the pho-
1996; Holtzmanetal. 1999; Olsen 1999; Elsonetal. 1997; tometry and artificial stars tests (Sect. 3) that allow us to ac-
Smecker-Haneetal.2002;Ardebergetal.1997;Dolphinetal. cess the expected levels of photometric errors, completeness,
2001;Javieletal.2005),oronrelativelyshallowground-based and crowding,and the contaminationby foregroundstars and
photometrycoveringlargerareasovertheMCs(Stappersetal. backgroundgalaxies.Wethenproceedwithmanyexperiments
1997; Gardiner&Hatzidimitriou 1992; Harris&Zaritsky of SFH-recovery (Sect. 4), evaluating the uncertainties in the
2001, 2004). Only in very few cases (e.g. Gallartetal. 2004; derivationoftheSFHasafunctionofbasicquantitiessuchas
Noe¨letal. 2007) have the ground-based optical photometry thestellardensityovertheLMC,theareaincludedintheanal-
beendeepenoughtoreachtheoldestmainsequenceturn-offs. ysis, and the adopted values for the distance and reddening.
TheVISTASurveyoftheMagellanicSystem1 (VMC,see Doing this, we are able to present the expected random and
Cionietal. 2007, Cioni et al., in preparation)is an ESO pub- systematicerrorsinthespace-resolvedSFH.Suchinformation
licsurveyprojectwhichwillprovide,inthenext5years,crit- maybeusefultoplancomplementaryobservationsandsurveys
ical near-infrared data aimed – among other goals – to im- oftheLMCinthenextfewyears.Furtherpaperswillpresent
prove upon present-day SFH determinations. This will hope- the perspectives for the Small Magellanic Cloud (SMC), as
fully open the way to a more complete understandingof how well as better explore the effect in the recovered SFH due to
starformationrelatestothedynamicalprocessesunderwayin theuncertaintiesassociatedwiththeMCgeometry,differential
the system, andto a moreaccuratecalibrationof stellar mod- reddening,initialmassfunction,fractionofbinaries,etc.
elsandprimarystandardcandles.RegardingtheSFH,thekey
contributions of the VMC survey will be: (1) It will provide 2. SimulatingVMCdata
photometryreachingasdeepastheoldestmainsequenceturn-
offoverthebulkoftheMCsystem,asopposedtothetinyre- Our initial goal is to obtain realistic simulationsof VMC im-
ages,containingalloftheobjectsthatareknowntobepresent
gionssampledbyHST,andthelimitedareacoveredbymostof
towardstheMCsandlikelytobedetectablewithinthesurvey
thededicatedground-basedobservations.(2)VMCwillusethe
depth limits. These objects are essentially stars belonging to
near-infraredYJK passbands,hopefullyreducingtheerrorsin
s
theMWandtheMCs,andbackgroundgalaxies.Moreover,an
theSFH-recoveryduetovariableextinctionacrosstheMCs.
essentialcomponentofthe imagesis thehighsignalfromthe
On the other hand, the use of near-infraredinstead of op-
infraredsky.Eachoneofthesecomponentswillbedetailedbe-
ticalfilterswillbringalongsomecomplicatingfactors,likean
low.Diffuseobjectssuchasemissionnebulaeandstarclusters
higherdegreeofcontaminationoftheMCphotometrybyfore-
will,forthemoment,beignored.
groundstarsandbackgroundgalaxies,andtheextremelyhigh
noisecontributedbythesky,especiallyintheK band.
s
Indeed,VMCwillbethefirstnear-infraredwide-areasur- 2.1.VISTAandVMCspecifications
veytoprovidedatasuitablefortheclassicalmethodsofSFH-
VMC will be performed with the VIRCAM camera mounted
recovery2. With the new space-based near-infrared cameras
at the 4m VISTA telescope at ESO’s Paranal Observatory in
(the HST/WFC3 IR channel, and JWST) and ground-based
Chile.VIRCAM has162048×2048detectorswhich,withthe
adaptive optics facilities, observations similar to VMC ones
image scale of 0.339′′ per pixelon average,covera sky area
will likely be available for many nearby galaxies. VMC may
of0.037deg2each.Thebasicmodeoftheobservationswillbe
becometheprecursorofdetailedSFH-recoveryintheopening
to perform6 exposures(paw-prints)with thesubsequentcon-
windowof near-infraredwavelengths. Demonstratingthe fea-
structionof1.0×1.5deg2tiles.Inthefollowing,wewilladopt
sibilityofVMCgoals,therefore,isofmoregeneralinterest.
the area of each detector (i.e. 0.037deg2) as the basic unit of
oursimulations.
1 Seehttp://www.vista.ac.ukand
The specifications of the VMC survey will be detailed in
http://www.star.herts.ac.uk/∼mcioni/vmc/
anotherpaper(Cionietal., inpreparation).Forouraims, suf-
forfurtherinformation.
ficeittomentionthefollowing:Despiteforthecrowdedfields,
2 The previous attempts of Cionietal. (2006a,b) based on
itisexpectedthattheobservationswillbesky-noisedominated.
IJK data, were based on the shallow observations from DENIS
s
and 2MASS, which are limited to the upper RGB and above. ThemeanskybrightnessatCerroParanalisof17.2,16.0,13.0
Consequently, they could access the general trends in the mean age mag arcsec−2 in YJKs, respectively.The requiredseeing is of
andmetallicityacrosstheMCs,butnotthedetailedage-resolvedSFH. 1.0′′ (FWHM)intheY band,beingthemostcrowdedregions
Kerberetal.:SFHRecoveryoftheLMCfromVMCSurvey 3
Fig.1. TheareaVMCwilllikelycoverintheLMC(solidline) Fig.2. A series of Marigoetal. (2008) isochrones in the
andSMC(dashedline)asa functionofthesurfacedensityof UKIDSS photometric system. The figure shows the absolute
RGBstars,N .ThefractionofthecoveredareaineachMC, (M ,Y−K)CMDaswellastheapparent(K,Y−K)onefora
RGB K
forfourrangesofdensity,isalsoshowninthetopofthefigure. typicaldistancetotheLMC.Stellarmassesandisochroneages
andmetallicitiesarealsoindicatedinthefigure.
observed in nights with seeing better than 0.8 ′′. The target- Given the present situation, we have so far used the
tedsignal-to-noiseratio(SNR)isequalto10atmagnitudesof UKIDSSsystemasasurrogateofthefutureVISTAone.Tests
21.9,21.4,20.3magrespectively.Thephotometriczero-points using the preliminary VISTA filter curves (Jim Emerson, pri-
inoursimulationswerefixedviatheVISTAexposuretimecal- vatecommunication)indicateverysmalldifferencesinthesyn-
culator, so as to be consistent with these values. Considering thetic photometry, typically smaller than 0.02 mag, between
these survey limits, in our simulations we include all objects VISTAandUKIDSS.3
brighterthanKs =22.5,whichattheLMCdistancecorrespond Stellar isochrones in the UKIDSS system have been re-
toastellarmassof∼0.8M⊙ inthemainsequenceturn-off. cently provided by Marigoetal. (2008)4. The conversion to
VMCtileswillcovermostoftheMagellanicSystem,sum- the UKIDSS system takes into account not only the photo-
mingto a totalareaof 184deg2 (see Cionietal. 2007, Cioni sphericemission fromstars, butalso the reprocessingof their
et al., in preparation, for details). Fig. 1 shows a histogram radiation by dusty shells in mass-losing stars, as described in
of the total area to be observed as a function of the den- Marigoetal. (2008). The filter transmission curves and zero-
sity of upper RGB stars, N , which is defined as the num- point definitions come from Hewettetal. (2006). The stellar
RGB
ber of 2MASS stars inside a box in the K vs. J − K CMD models in use are composed of Girardietal. (2000) tracks
s s
(0.60 ≤ J −K ≤ 1.20and12.00 ≤ K ≤ 14.00fortheLMC for low- and intermediate-mass stars, replacing the thermally
s s
and 12.30 ≤ K ≤ 14.30 for the SMC), for each unit area of pulsing asymptotic giant branch (AGB) evolution with the
s
0.05deg2.Noticethehighermeanandmaximumstellardensi- Marigo&Girardi(2007)ones.Inthispaper,thesemodelsare
tiesoftheLMC,ascomparedtotheSMC.Thestellardensities further complemented with white and brown dwarfs as de-
varyoveranintervalofabout2.5dex. scribed in Girardietal. (2005, also Zabot et al., in prepara-
tion),andwiththeBertellietal.(1994)isochronesformasses
higher than 7 M . Fig. 2 presents some of the Marigoetal.
⊙
2.2.StarsintheUKIDSSphotometricsystem (2008) isochrones in the M vs. Y−K diagram, for a wide
K
range in age and metallicity. As can be readily noticed, the
Since VISTA is still being commissioned at the time of this
writing, the throughputs of VISTA filters, camera, and tele-
3 Throughoutthispaper,wewillnamethe2.2µmfilterasK when
scopearestillnotavailable.ItishoweverclearthattheVISTA s
referring to VISTA, 2MASS and DENIS, and as K when referring
photometric system will be very similar to the UKIDSS one,
tooursimulationsandtoUKIDSSdata.Noticehoweverthat,forall
withthedifferencesbeingmainlyinthehigherperformanceof practicalpurposes,theactualdifferencebetweenthesefiltersisnota
VISTA,andinthefactthatVISTAwilluseaK-shortfilter(Ks) matterofconcern.
similartothe2MASSone. 4 http://stev.oapd.inaf.it/dustyAGB07
4 Kerberetal.:SFHRecoveryoftheLMCfromVMCSurvey
isochronescontain the vastmajority of the single objectsthat Grocholskietal. 2006; Kerberetal. 2007) and field stars
canbeprominentinthenear-infraredobservationsoftheLMC, (Coleetal. 2005; Carreraetal. 2008), together with a con-
going from the lower Main-Sequence (MS) stars, up to the stant SFR(t). Since the SFR(t) in the LMC is clearly spatial
brightest AGB stars and red supergiants. The stellar masses dependent (Holtzmanetal. 1999; Smecker-Haneetal. 2002;
intheMSandtheapparentmagnitudefora typicalLMCdis- Javieletal. 2005), the assumption of a constant SFR(t) shall
tance, (m−M) = 18.50 (Clementinietal. 2003; Alves 2004; be consideredas just a way to ensurea uniformtreatmentfor
0
Schaefer2008)arealsoindicatedinthisfigure.We recallthat allstellarpopulationsovertheLMC.
ourmodelscontain,inaddition,thevery-lowmassstars,brown In terms of distance we are initially using the canonical
dwarfs and white dwarfs, which are importantin the descrip- valueof(m−M) =18.50(Clementinietal.2003;Alves2004;
0
tionoftheforegroundMWpopulation(Marigoetal.2003). Schaefer2008) also adoptedby the HST Key Projectto mea-
Theinterstellarextinctioncoefficientsadoptedinthiswork sure the Hubble constant (Freedmanetal. 2001), whereas for
doalsofollowfromMarigoetal.(2008):AY =0.385AV,AJ = the reddening we are assuming a value of EB−V = 0.07, typi-
0.283AV,andAK = 0.114AV,whichimplyEY−J = 0.351EB−V calfortheextinctionmapsfromSchlegeletal.(1998).Forreal
andEY−K =0.931EB−V.Theyhavebeenderivedfromsynthetic VMCimages,thesetwoparametersareexpectedtobefreepa-
photometryappliedtoaG2VstarextinctedwithCardellietal. rameters, since the LMC presentsdisk-like geometrieswith a
(1989)extinctioncurve.Althoughtheapproachisnotthemost significant inclination (∼ 30–40 deg) (vanderMarel&Cioni
accurate one (see Girardietal. 2008), it is appropriate to the 2001;vanderMareletal.2002;Nikolaevetal.2004)andnon-
conditionsofmoderatereddening(EB−V <∼ 0.2mag)typicalof uniform extinction (Zaritskyetal. 2004; Subramaniam 2005;
theMagellanicClouds. Imara&Blitz2007).
Thesimulationoftheinputphotometriccataloguesandthe
Finally the assumed values for the remaining inputs are:
generation of artificial images are described in the next sub- the Chabrier (2001) lognormalIMF 6 , and f = 30% with
bin
sections.Inbrief,theinputcataloguesfortheLMC(Sect.2.3) a constant mass ratio distribution for m /m > 0.7 7. There
2 1
and the foregroundMW stars (Sect. 2.4) come from the pre-
arenostrongreasonstoexpectsignificantdeviationsforthese
dictionsmadewiththeTRILEGALcode(Girardietal.2005),
choices,especiallyfortheIMFsincewearedealingwithstars
that simulates the photometry of resolved stellar populations
withmassesapproximatelybetween0.8and12.0M wherethe
⊙
following a given distribution of initial masses, ages, metal-
IMFslopeseemstobeuniversalandsimilartotheSalpeterone
licities, reddenings and distances. The catalogues of back-
(Kroupa2001,2002).Concerningthefractionofbinaries,our
groundgalaxies(Sect.2.5)arerandomlydrawnfromUKIDSS
choice is consistentwith the valuesfoundforthe stellar clus-
(Lawrenceetal.2007).Thesimulationofimagesisperformed
tersintheLMC(Elsonetal.1998;Huetal.2008).Forthemo-
with the DAOPHOT and ARTDATA packages in IRAF5
ment, these will be consideredas fixed inputs. Furtherpapers
(Sect. 2.6), always respecting the photometriccalibration and
will use simulationsin orderto quantifythe systematic errors
expectedimagequalityrequiredbytheVMCsurvey.
intherecoveredSFHintroducedbytheuncertaintiesrelatedto
thesechoices.
2.3.TheLMCstars
ThestellarpopulationsfortheLMCaresimulatedasan“addi- 2.4.TheMilkyWayforeground
tionalobject”insidetheTRILEGALcode(Girardietal.2005),
TheMWforegroundstarsaresimulatedusingtheTRILEGAL
wheretheinputparametersforafieldare:
code as described in Girardietal. (2005). Towards the MCs,
– thestarformationrateasafunctionofstellarage,SFR(t);
thesimulatedstarsarelocatedbothinadiskwhichscale-height
– thestellarAMR,Z(t)or[M/H](t);
increasingwithage,andinaoblatehalocomponent.Diffusein-
– thetotalstellarmass,M ;
tot,LMC terstellarreddeningwithin100pcoftheGalacticPlaneisalso
– thedistancemodulus,(m−M) ;
0 considered,althoughitaffectslittlethenear-infraredphotome-
– thereddening,E =3.1A ;
B−V V try.
– theInitialMassFunction(IMF),ψ(M);
i In Girardietal. (2005), it has been shown that for off-
– thefractionofdetachedunresolvedbinaries, f .
bin plane line-of-sights,TRILEGALpredictsstar countsaccurate
As commentedbefore, for conveniencewe are simulating to within about 15% over a wide range of magnitudes and
an area of0.037deg2, equivalentto a 2048×2048VIRCAM down to J ≃ 20.5 and K ≃ 18.5. This accuracy is confirmed
detector. The value of Mtot,LMC is suitably chosen such as to by the K <∼ 20.5 observationsof Gullieusziketal. (2008) for
generatethe total numberof RGB stars observedby 2MASS, a field next to the Leo II dwarf spheroidal galaxy. Moreover,
NRGB,insidethissamearea. Marigoetal. (2003) shows that TRILEGAL describes very
In the LMC simulations presented in this paper, we well the position of the three “vertical fingers” observed in
adopt an input AMR consistent with the one given by stel- 2MASSK vs. J−K diagrams.Similarly-comfortingcompar-
s
lar clusters (Olszewskietal. 1991; Mackey&Gilmore 2003;
5 IRAF is distributed by the National Optical Astronomy 6 Withaslopeα ∼ −2.3for0.8 < m/M < 5.0andα ∼ −3.0for
⊙
Observatory,whichisoperatedbytheAssociationofUniversitiesfor m>5.0M ,wheretheSalpeterslopeisα=−2.35.
⊙
Research in Astronomy (AURA) under cooperative agreement with 7 Thisisthemassratiointervalinwhichthesecondarysignificantly
theNationalScienceFoundation. affectsthephotometryofthesystem.
Kerberetal.:SFHRecoveryoftheLMCfromVMCSurvey 5
isonswithUKIDSSdata(includingtheY band)arepresented
inSect.3.2below.
Althoughpredictingstarcountswithanaccuracyofabout
15%maybegoodenoughforourinitialpurposes,wearework-
ingtofurtherimprovethisaccuracy:Inshort,weareapplying
the minimisation algorithm described in Vanhollebekeetal.
(2008) – which was successfully applied to the derivation of
BulgeparametersusingdataforinnerMWregions–torecal-
ibrate the TRILEGAL disk and halo models. It is likely that
before VMC starts, foreground star counts will be predicted
withaccuraciesoftheorderof5%.
2.5.Thebackgroundgalaxies
In orderto simulate the populationof galaxiesbackgroundto
the MCs, we make use of the large catalogues of real galax-
iesobtainedbytheUKIDSSUltra-Deep(UDS;Foucaudetal.
2007)andLargeAreaSurveys(LAS;Warrenetal.2007),from
theirDataRelease3(December2007).TheLASincludesdata
for an area of 4000 deg2 down to K = 18.4, for YJK filters,
whereastheUDSincludesanareaof0.77deg2observeddown
toK ∼23,butonlyforJHKpassbands.
Inourinputcatalogueforeachsimulation,weincludethe
numberof UKIDSS galaxies expectedfor our total simulated
area.Moreprecisely,werandomlypickupfromtheUDScat-
alogue, a fraction of galaxies given by the ratio between the
areascoveredbyUDSandbyourimagesimulation.Fromthe
catalogue,we extracttheir J and K magnitudes,and morpho-
logicalparameters(positionangle,size,andaxialratio).Inthis
way, our simulations respect the observed K-band luminosity
functionofgalaxies,andtheirJ−Kcolourdistribution,downto
faintmagnitudes.The Y-band magnitudes,instead, have been
assignedinthefollowingway:wetaketheJ−Kcolourofeach Fig.3. An image simulation for the area next to the star
galaxyintheUDS,andthenrandomlyselectagalaxyfromthe cluster NGC1805 (α = 5.03 h, δ = −66.07◦), for a sin-
LASwhich hasthe mostsimilar J −K (within0.2 mag),and gle 2048×2048 array detector of VIRCAM. This is a false-
takeitsY−J.ThismeansthattheY−Jvs.J−Krelationfrom color image where blue-green-red colours were associated to
LASisbeingextrapolateddowntodeepermagnitudes8. the YJK filters, respectively. The location corresponds to a
logN ∼ 2.00 in Fig. 1. The detector area corresponds to
RGB
0.0372 deg2 (11.6× 11.6 arcmin) in the sky, which is about
2.6.Simulatingimages
1/40 of a single VIRCAM tile, and 1/5000 of the total VMC
Once defined the input catalogues for stars and galaxies we surveyarea.Thetwosmallpanelsatthebottompresentdetails
simulated the images inside IRAF, in accordance with the ofthesimulatedstars,stellarclustersandgalaxiesfor2.9×2.9
VISTA and VMC specifications (see Sect.2.1). The basic se- arcmin and 0.7× 0.7 arcmin areas. At the LMC distance the
quenceofsteps(andtheIRAFtask)performedforagivenfilter toppanelcorrespondsapproximatelytoaboxof175×175pc,
isthefollowing: whereasthebottompanelscorrespondto44×44pcand11×11
pc,respectively(1′′ ∼0.25pc).
1. Definition of the image size (rtextimage) and introduction
oftheskybrightnessandnoise(mknoise);
larprofilewithrandompoissonianerrorsinthenumberof
2. simulation of a Gaussian stellar profile (gauss) respecting
electrons;
the expected seeing for an image of a photometric cali-
4. addition of galaxies (mkobject) in the previous image
brated (using the VISTA ETC v1.3) delta function with a
respecting all information concerning the morphological
knownnumberofelectrons;
type,positionangle,sizeandaxialratio.
3. addition of the LMC and MW stars in the sky images
(addstars)followingthepreviouscalibratedGaussianstel-
Toassureauniformdistributionoftheobjectsintheimage,
8 Thisisofcourseacrudeapproximationsincedeepersurveyssam- starsandgalaxiesarealwaysaddedatrandompositions.Fig.3
plelargergalaxyredshifts.However,itisjustifiedbythelackofdeep- showsanexampleofimagesimulationforatypicalfieldinthe
enoughYdata,andbythelittleimpactthatsuchfaintgalaxieshavein LMCdisk.Thefalse-colourplotevidencesthecolourandmor-
ourstellarphotometry(seeSect.3.2). phologicdifferencesbetweenstarsandbackgroundgalaxies–
6 Kerberetal.:SFHRecoveryoftheLMCfromVMCSurvey
withthelatterbeingsignificantlyredderthantheformer.Inthe
sameimage,wehaveinsertedtwopopulousstellarclusterstyp-
icalfortheLMCwithdifferentages,massesandconcentration
ofstars(followingaKing’sprofile),justtoillustrateourcapac-
itytosimulatealsothiskindofstellarobject.
3. Performingphotometryonsimulateddata
3.1.ApertureandPSFphotometry
TheIRAFDAOPHOTpackagewasusedtodetectandtoper-
formaperturephotometryinoursimulatedimages.Candidate
starsweredetectedusingdaofind,withapeakintensitythresh-
old for detection set to 4σ , where σ corresponds to the
sky sky
rmsfluctuationintheskycounts.Theaperturephotometrywas
carriedoutrunningthetaskphotforanapertureradiusof3pix
(∼1.0′′).
Thephotometricerrorsandcompletenesscurvesthatcome
from this aperture photometry in our simulated LMC images
can be seen in Fig. 4. The photometricerrors in this case are
estimated using the differences between the input and output
magnitudes;morespecifically,foreachsmallmagnitudebinwe
Fig.5. Example of (K, Y−K) CMD from aperture photome-
compute the half-width of the error distribution, with respect
try in a simulated image for the VMC survey. The choices
tothemedian,thatcomprises70%oftherecoveredstars.The
in the parameters represent a field of ∼ 0.1 deg2 with ∼ 105
completeness instead is simply defined as the ratio between
stars (log(N ) = 2.00) following a constant SFR(t) and a
total number of input stars, and those recovered by the pho- RGB
AMRtypicalfortheLMCclusters(seedetailsinthetext).The
tometry package.Fig. 4 presents the results for differentsim-
colours represent the density of points in a logarithmic scale.
ulations covering a wide range of density of field stars in the
The information aboutapproximatedstellar masses, ages and
LMC, fromthe outer disk regionsto the centre regionsin the
metallicitiescanbeobtainedfromFig.2.
bar(seeFig.1).Noticethatinthesesimulationswearefollow-
ingtherequirementthatthemostcentralandcrowdedregions
(logN ≥2.50)willbeobservedunderexcellentseeingcon-
RGB
ditionsonly.
dentaretheAGB,redsupergiants,RGB,redclump(RC),Sub-
It can be noticed that the VMC expected magnitudes at
Giant Branch (SGB) as well as the MS, from the brightest
SNR=10 for isolated stars (Y = 21.9, J = 21.4, K = 20.3)
and youngeststars down to the oldest turn-off point. In com-
is well recoveredin the simulationsfor the lowestdensity re-
parison,the present-daynear-infraredsurveysof the MCs are
gions,attestingthecorrectphotometriccalibrationofoursim-
completeonlyforthemostevolvedstars –excludingthosein
ulatedimages.Fortheseregionsthe50%completenesslevelis
the most crowded regions, and those highly extincted by cir-
reachedatY ∼22.5,J ∼22.2andK ∼21.8.
cumstellar dust. DENIS and 2MASS, for instance, are lim-
Crowdingsignificantlyaffectsinthequalityoftheaperture
photometry,makingthestarsmeasuredincentralLMCregions ited to Ks <∼ 14, revealing the red supergiants, AGB and
upper RGB, and including just a tiny fraction of the up-
toappearsignificantlybrighter,andwithlargerphotometricer-
per MS(Nikolaev&Weinberg2000; Cionietal. 2007). IRSF
rors,thanin the outermostLMCregions.As shownin Fig.4,
crowding clearly starts to dominate the noise for fields with (Katoetal.2007)extendsthisrangedowntoKs <∼16.6,which
isdeepenoughtosamplethe RCandRGB bump,butnotthe
logNRGB >∼ 2.00 that correspond to about 20% (7%) of the SGBandthelow-massMS.
totalareacoveredin the LMC(SMC) (see Fig.1). Therefore,
PSFphotometryisexpectedtobeperformedwhenevercrowd-
ingwillpreventagoodaperturephotometryoverVMCimages. 3.2.ComparisonwithUKIDSSdata
ThesignificantimprovementsthatcanbereachbyaPSFpho-
tometry are also illustrated by the thick black lines in Fig. 4. Since the present work depends on simulations, it is impor-
These results correspond to a PSF photometry applied to the tanttocheckiftheyreproducethebasiccharacteristicsofreal
LMCcentre(logN = 2.90),wherethePSF fittingandthe data already obtained under similar conditions. UKIDSS rep-
RGB
photometryweredoneusingtheIRAFtaskspsfandallstar. resents the most similar data to VMC to be available for the
Figure 5 shows an example of CMD obtained from the moment.Therefore,inthefollowingwewillcompareasimu-
aperture photometry in a simulated field with an intermedi- latedUKIDSSfieldwiththerealone.
ate level of density in the LMC. This figure reveals the ex- For this exercise, we take the 0.21 deg2 field towards
pected CMD features – and the wealth of information – that Galactic coordinates ℓ = −220◦,b = 40◦, which due to its
will become available thanks to the VMC survey: well evi- similar distance from the Galactic Plane as the MCs, offers a
Kerberetal.:SFHRecoveryoftheLMCfromVMCSurvey 7
Fig.4. Photometric errors (left panels) and completeness curves (right panels) in the artificial YJK images for the LMC for
differentlevelsofcrowding.Thethincurvespresenttheresultsfortheaperturephotometrycoveringtheentireexpectedrange
of density of field stars (logN = 1.50, 1.75, 2.00, 2.25, 2.50, 2.75, 2.90, see also Fig. 1). The three highest density levels
RGB
were simulated with the smallest values for seeing required for the LMC centre. The thick black line illustrates the results of
performingPSFphotometryforthehighestdensitylevel(logN = 2.90).TheexpectederrorinmagnitudeforaSNR=10is
RGB
shownbythedashedline.
goodopportunitytotesttheexpectedlevelsofMilkyWayfore- Themostimportantpointofthemodel–datacomparisonof
ground,andthegalaxybackground. Fig. 6, however, is that the simulations reasonably reproduce
We have taken the original image from the UKIDSS the numbers (with errors limited to ∼ 20%), magnitudes and
archive, and performed aperture photometry with both coloursof the observedobjects.This givesus confidencethat
DAOPHOT (Stetson 1987) ad SExtractor (Bertin&Arnouts ourMCsimulationscontainthecorrectcontributionfromfore-
1996). A image for the same area has been simulated using groundMilkyWaystarsandbackgroundgalaxies.
UKIDSSspecifications(pixelscale, SNR, etc.)andsubmitted
to the same kindof catalogueextraction.Fig. 6 showsthe re-
sults,comparingtheK vs.Y−KdiagramsfortheUKIDSSob- 4. RecoveringtheSFH
served (left panel)and simulated (rightpanel) fields, for both
4.1.Basics
stars(bluepoints)andgalaxies(redpoints).Starsandgalaxies
wereseparatedusingtheSExtractorStellarityparameterst.We The basic assumption behind any method to recoverthe SFH
adoptedst>0.85forstars,andst≤0.85forgalaxies. from a composite stellar population (CSP) is that it can be
Both DAOPHOT ad SExtractor aperture photometries considered as a simply sum of its constituent parts, which
turnedouttoberemarkablyconsistentwiththeonesprovided are ultimately simple stellar populations (SSPs) or combina-
bytheCambridgeAstronomicalSurveyUnit(CASU)datare- tions of them. Therefore determining the SFH of any CSP –
ductionpipeline.ThisisverycomfortingsincetheCASUwill like the field stars in a galaxy – means to recover the rela-
adopt the same data reduction pipeline to the future VISTA tiveweightofeachSSP.Themodernstellarpopulationanaly-
data. The histograms at the right and top of the CMD pan- sisinthelate80’s(Tosietal.1989;Ferraroetal.1989)andin
els show the object number count distribution in both colour the early 90’s (Tosietal. 1991; Bertellietal. 1992) – marked
and magnitude. As can be appreciated, our simulated objects by the advent of the first CCD detectors – was done assum-
distribute very similarly in colour and magnitude as the ob- ingparameterizedSFH,whichrevealedthemaintrendsinthe
servedones.Thediscrepanciesarelimitedtoafewaspectsof SFH butwasstilllimitedbya smallnumberofpossiblesolu-
thesimulations,forinstancethepeakinthecolourdistribution tions.ThetechniquestorecovertheSFHfromaresolvedstel-
at Y−K ∼ 1.3 is clearly narrower in the models than in the lar population started to become more sophisticated with the
simulations.Thispeakiscausedbythindiskdwarfslessmas- works of Gallartetal. (1996b,a), but they were significantly
sivethan0.4M (Marigoetal.2003),anditsnarrownessinthe improved by Aparicioetal. (1997) and Dolphin (1997), who
⊙
modelscouldbeindicatingthatTRILEGALunderestimatesthe developedforthefirsttimestatisticalmethodstorecovernon-
colourspreadofthesevery-lowmassstars. parameterizedSFHfromtheCMDofaCSP.Inpracticethese
8 Kerberetal.:SFHRecoveryoftheLMCfromVMCSurvey
Fig.6.AcomparisonbetweentheaperturephotometryfromUKIDSSimagedata(left)andthecorrespondingsimulation(right),
fora 0.21deg2 area towardsℓ = −220◦,b = 40◦. The photometrywas performedusing bothDAOPHOT and SExtractor.The
main panels show the CMD obtained combining DAOPHOT photometry with SExtractor star/galaxy classification (blue/red
dots,respectively).Thehistogramsshowthe totalcolourandmagnitudedistributionsofstarsandgalaxies(blueandredlines,
respectively).
two works were the first to deal with a finite number of free The classical approach to determine the set of rs is
j
independentcomponents,obtainedbyaddingthepropertiesof to compute the differences in the number of stars in
SSPs inside small, but finite, age and metallicity bins. These each CMD box between data and model, searching for
“partialmodels”(Aparicioetal.1997)aresocomputedforage a minimisation of a chi-squared-like statistics. This kind
andmetallicitybinsthatshouldbesmallenoughsothattheSSP of approach was applied for the first time to recover the
properties change just little inside them, and large enough so SFH of a real galaxy by Aparicioetal. (1997), and has
thatthelimitednumberofbinsensuresreasonableCPUtimes been successfully used in the analysis of the field stars
for the SFH-recovery. Furthermore, being the partial models in the dwarf galaxies in the Local Group (Gallartetal.
computed for the same and constant star formation rate in- 1999; Dolphin 2002; Dolphinetal. 2003; Skillmanetal.
side each age bin, implied that they needed to be generated 2003; Coleetal. 2007; Yuk&Lee 2007), including the MCs
only once, saving a large amount of computational resources (Olsen 1999; Holtzmanetal. 1999; Harris&Zaritsky 2001;
(Dolphin2002). Smecker-Haneetal.2002;Harris&Zaritsky2004;Javieletal.
Considering that a CMD is a distribution of points in a 2005; Chiosi&Vallenari 2007; Noe¨letal. 2007). Although
plane divided into N boxes, these ideas can be expressed theseworkshaveincommonthesamebasicideaofhowtore-
box
(Dolphin2002)by covertheSFH,thereareclearvariationsintermsoftheadopted
statisticsandstrategytodividetheCMDinboxes(Gallartetal.
mi =Xrjci,j (1) 2005).
j An interesting alternative to recover the SFH from the
wherem isthenumberofstarsinthefullmodelCMDforan analysis of CMDs is offered by the maximum likelihood
i
CSPintheith box,r istheSFRforthe jth partialmodel,and technique using a Bayesian approach (Tolstoy&Saha 1996;
j
c isthenumberofstarsintheCMDforthe jth partialmodel Hernandezetal. 1999, 2000; Vergelyetal. 2002). In this ap-
i,j
intheith CMDbox. proach the basic idea is to establish for each observed star
Noticethattheaboveequationisinfactwrittenintermsof a probability to belong to a SSP (based on the expected
Hess diagrams since we are dealing with the number of stars number of stars from this SSP in the position of the ob-
inCMDs.Soitmeansthatthe“observed”Hessdiagramfora served star in the CMD). Doing it for all observed stars,
CSPcanbedescribedasasumofindependentsyntheticHess one can recover the SFRs that maximises the likelihood be-
diagramsofpartialmodels,beingthecoefficientsr theSFRsto tween data and model. It is interesting to note that in the re-
j
bedetermined.Fig.7,tobecommentedlater,illustratethegen- cent years there is an increasing number of papers applying
erationofsuchsyntheticHessdiagramsforthepartialmodels this kind of technique for a wide range of problems, which
oftheLMC. include the determination of physical parameters of stellar
Kerberetal.:SFHRecoveryoftheLMCfromVMCSurvey 9
Fig.7.Simulated(K,Y−K)CMDillustratingthebuildingofpartialmodelsfortheanalysisofLMCstellarpopulationsandits
foregroundMWstars.Panel(a)showsthetheoreticalstarsgeneratedfromTRILEGAL,correspondstothefollowingrangesin
log(t/yr):8.00–8.40(red),8.40–8.80(green),8.80–9.20(blue),9.20–9.60(cyan),9.60–10.00(magenta),10.00–10.15(yellow),
plustheforegroundMW(black).Panel(b)showsthesameafterconsideringtheeffectsofphotometricerrorsandcompleteness.
Panel(c)istheHessdiagramforthesumofallpartialmodels.Panels(d)and(e)showtheinputSFR(t)andAMR,respectively,
thelatterincomparisonwithLMCclusters(squares–datafromMackey&Gilmore2003;Kerberetal.2007;Grocholskietal.
2006,2007).Toavoidanextremelylargesizeforthisfigureonly5%ofallstarstypicallyused(∼107)tobuildthepartialmodels
areshowninthetoppanels.
clusters(Jørgensen&Lindegren2005;Naylor&Jeffries2006; fortheVMCdata,usingtheframeworkofthe StarFISHcode
Hernandez&Valls-Gabaud2008)aswellasofindividualstars (Harris&Zaritsky 2001, 2004), the χ2-like statistics defined
(Nordstro¨metal.2004;daSilvaetal.2006). byDolphin(2002)assumingthatstarsintoCMDboxesfollow
a Poisson-distributeddata, and a uniformgrid of boxesin the
It is beyond the scope of the present work to discuss in
CMD.
depth the particularity of each aforementioned approach, but
there are no strong reasons to believe that one can intrinsi-
callyrecoveramorereliableSFHthantheother(Dolphin2002; 4.2.StarFISHandTRILEGALworkingtogether
Gallartetal.2005).Soforaquestionofsimplicityandcoher-
TheStarFISHcode9 hasbeendevelopedbyHarris&Zaritsky
ence with the majority of the works devoted to the MCs, we
(2001) and successfully applied by Harris&Zaritsky (2004)
adoptedtheclassicalminimisationofachi-squared-likestatis-
tics technique to determine the expected errors in the SFH 9 Availableathttp://www.noao.edu/staff/jharris/SFH/
10 Kerberetal.:SFHRecoveryoftheLMCfromVMCSurvey
and Harris (2007b) to recover SFHs for the MCs inside
the context of the Magellanic Clouds Photometric Survey
(Zaritskyetal.1997,MCPS)10.Thiscode,originallydesigned
to analyse CMDs built with UBVI data from the MCPS, and
usingPadovaisochrones(Girardietal.2000,2002),offersthe
possibilityofdifferentchoicesforgeneratingsyntheticHessdi-
agrams(setofpartialmodels,CMDbinningandmasks,com-
binationofmorethanoneCMD,etc.)andχ2-likestatistics,be-
ingalsosufficientlygenerictobeimplementedfornewstellar
evolutionarymodels,photometricsystems,etc.
AsillustratedinFig.7,theTRILEGALcodecanalsosim-
ulate the synthetic Hess diagram for a set of partial models,
with the advantage of easily generating them in the UKIDSS
photometricsystem,allowingalsoagreatercontrolofallinput
parametersinvolved(seeSect.2.3).Thereforewedecidetodi-
rectly providethese Hess diagrams to StarFISH, using it as a
platform to determine the SFRs for our VMC simulated data
by means of a χ2-like statistics minimisation. The search of
thebestsolutionisdoneinternallyinStarFISHbytheamoeba
algorithm that uses a downhill strategy to find the minimum
χ2-likestatisticsvalue.
Fig.9. Errors in the recovered SFR(t) in terms of the mean
AnextrapossibilityofferedbyTRILEGAListheconstruc-
SFR(t) (top panel) and input SFR(t) (bottom panel). The in-
tion of an additionalpartial modelfor the MW foreground11.
put simulations correspond to a typical LMC disk region
Indeed,thisisdonebysimulatingtheMWpopulationtowards
(logN = 2.00) inside a single VIRCAM detector (∼
the galactic coordinates under examination, for the same to- RGB
0.037 deg2). The centralsolid line correspondsto the median
tal observed area but averaging over many simulations so as
solution found over 100 realizations of the same simulation,
to reducethe Poisson noise. Thispartialmodelis providedto
whereastheerrorbarscorrespondtoaconfidencelevelof70%.
StarFISH and used in the χ2-like statistics minimization to-
getherwiththoseusedtodescribetheMCpopulation.Withthis
procedure,thepresenceoftheMWforegroundistakenintoac-
4.3.Results:Inputvs.outputSFR(t)
countintheSFHdetermination,withoutappealingtothe(often
risky) proceduresof statistical decontaminationbased on the AnexampleofSFH-recoveryispresentedintheHessdiagrams
observationofexternalcontrolfields. To ourknowledgement, ofFig.8.Theinputsimulation(leftpanel)wasgeneratedfora
this is the first time that such a procedureis adoptedin SFH- constantSFR(t),foranareaequivalentto1VIRCAMdetector
recovery work. Notice that, once the MW foreground model (0.037 deg2) inside a region with a stellar density typical for
is well calibrated, its correspondingrj could be set to a fixed theLMCdisk(logNRGB = 2.00,thatproducesatotalnumber
value,insteadofbeingincludedintotheχ2-likestatisticsmin- ofstarsof N ∼ 5×104).Forthissimulation,StarFISHfits
stars
imization. thesolutionrepresentedinthemiddlepanel.Notsurprisingly,
thedata–modelχ2-likestatisticsresiduals(rightpanel)arere-
Figure7illustratesthegenerationofacompletesetofpar-
markablyevenlydistributedacrosstheHessdiagram.
tial models, covering ages from log(t/yr) = 8.00 to 10.15 (t
Figure 9 presentsthe median of recoveredSFR(t), and its
from0.10to14.13Gyr)dividedinto11elementswithawidth
of∆logt = 0.20each,andfollowinganAMRconsistentwith error, obtained after performing 100 realizations of the same
simulation.Asexpected,themedianSFR(t)overthis100real-
theLMCclusters(seethepaneld,andSect.2.3).Inthisfigure
izationsreproducesremarkablywelltheinputone,withnoin-
we havegroupedthepartialmodelsin just6 age ranges(plus
dicationofsystematicerrorsintheprocessofSFH-recovery12
theMWforegroundone)justforaquestionofclarity.Whatis
. The error bars correspond to a confidence level of 70%,
remarkableinthefigureisthehighdegreeofsuperpositionof
the differentpartialmodelsoverthe RGB regionofthe CMD which means that 70% of all individual realizations are con-
fined within these errorbars. Errorbarsare almost symmetri-
– except of course for the partial model correspondingto the
calwithrespecttotheexpectedSFR(t).Furthermore,errorsare
MWforeground.TheMSregionoftheCMD,instead,allowsa
goodvisualseparationofthedifferentpopulationsovertheen- typicallybelow0.4inunitsofmeanSFR(t)(toppanel),which
tireagerange,evenafterconsideringtheeffectsofphotometric means uncertainties below 40% (bottom panel) for almost all
ages.Theonlyexceptionistheyoungestagebinwhichpresents
errorsandincompleteness.
errorsintheSFRthatareabouttwotimeslargerthanthosefor
theintermediate-agestellarpopulations.
10 http://ngala.as.arizona.edu/dennis/mcsurvey.html 12 Asaconsequence,thetotalintegraloftheSFRisalsowellrecov-
11 Seehttp://stev.oapd.inaf.it/trilegal ered.