Table Of ContentAstronomy&Astrophysicsmanuscriptno. de_Meulenaer2013_Arxiv (cid:13)cESO2013
January11,2013
Deriving physical parameters of unresolved star clusters.
I. Age, mass, and extinction degeneracies
P.deMeulenaer1,2,D.Narbutis1,T.Mineikis1,2,andV.Vansevicˇius1,2
1 VilniusUniversityObservatory,Cˇiurlionio29,VilniusLT-03100,Lithuania
e-mail:[email protected]
2 CenterforPhysicalSciencesandTechnology,Savanoriu¸231,VilniusLT-02300,Lithuania
SubmittedOctober31,2012;AcceptedNovember28,2012
3
1 ABSTRACT
0
Context. Stochasticity and physical parameter degeneracy problems complicate the derivation of the parameters (age, mass, and
2
extinction)ofunresolvedstarclusterswhenusingbroad-bandphotometry.
n Aims. Wedevelopamethodtosimulatestochasticityanddegeneracies,andtoinvestigatetheirinfluenceontheaccuracyofderived
a physicalparameters.ThenweapplyittostarclustersamplesofM31andM33galaxies.
J Methods.Age,massandextinctionofobservedstarclustersarederivedbycomparingtheirbroad-bandUBVRIintegratedmagnitudes
0 tothemagnitudesofalargegridofstarclustermodelswithfixedmetallicityZ = 0.008. Massesofstarsforaclustermodelare
1 randomlysampledfromtheinitialmassfunction. Modelsofstarclustersfromthemodelgrid,whichhavealloftheirmagnitudes
locatedwithin3observationalerrorsfromthemagnitudesoftheobservedcluster,areselectedforthecomputationofitsage,mass,
] andextinction.
A Results. InthecaseoftheM31galaxy,theextinctionrangeiswideandtheage-extinctiondegeneracyisstrongforafractionofits
G clusters. Becauseofanarrowerextinctionrange,theage-extinctiondegeneracyisweakerfortheM33clusters. Byusingartificial
clustersample,weshowthatage-extinctiondegeneracycanbereducedsignificantlyiftherangeofintrinsicextinctionwithinthehost
.
h galaxyisnarrow.
p
Keywords. galaxies:starclusters:general
-
o
r
t
s1. Introduction dayspreferredapproach(e.g.,Popescu&Hanson(2009,2010);
a
Fouesneau&Lançon(2010);Fouesneauetal.(2012);Asa’D&
[Starclustersareimportantobjectsforunderstandingtheforma-
Hanson(2012))istouseaMonte-CarlosamplingofstellarIMF
tion and evolution of their host galaxies. It is considered that
1 tomodelintegratedcolorsofclustersandbuildanextensivegrid
most of star formation is clustered (Lada & Lada 2003), there-
v ofmodels,tocoverallpossibleage,massandextinctionranges.
8fore knowledge of the physical parameters of a cluster popu- Physicalparametersofstarclustersarethenderivedbycompar-
0lation(e.g.,age,mass,chemicalcomposition,andextinction)is
ingobservationstothegridofmodels.
0essentialforconstrainingthestarformationhistoryofthegalaxy.
2 Thecommonlyusedmethodforderivingthephysicalparam- Recently Asa’D & Hanson (2012) have derived the age
.eters of unresolved star clusters is based on comparing of their and extinction of star clusters in the Large Magellanic Cloud
1
(LMC) using the method of Popescu & Hanson (2010) that
0integratedbroad-bandphotometrycolorstothecolorsofsimple
takes stochasticity into account, and compared results to previ-
3stellar population (SSP) models; see, e.g., Anders et al. (2004)
ous derivations based on an isochrone fit to the resolved color-
1andBridžiusetal.(2008). However,thismethodisstronglybi-
magnitude diagrams (CMDs). They managed to constrain the
:asedbythepresenceoftwomajorproblems:
v age of clusters similar to the values found by the isochrone fit
Xi – degeneracybetweenvariousphysicalparametersofstarclus- only when previously known extinctions of individual clusters
ters,see,e.g.,Worthey(1994),Bridžiusetal.(2008).Forex- wereused.
r
a ample, a young cluster possessing high extinction can have In this paper, a method of deriving physical parameters is
colorssimilartoanolderobjectwithoutextinction–anage-
developedandappliedtostarclustersamples(integratedmulti-
extinctiondegeneracy;
band photometry) in two Local Group galaxies: 1) M31, using
– stochasticity, which is due to the random presence of a few
a catalog by Vansevicˇius et al. (2009), who derived cluster pa-
bright stars, which dominate the integrated photometry of
rametersusingSSPmethod,and2)M33,usingobjectscommon
unresolved clusters; see, e.g., Santos & Frogel (1997), De-
to catalogs of Ma (2012) for photometry and San Roman et al.
veikis et al. (2008), Maíz Apellániz (2009). Young clusters
(2009), who observed in resolved conditions with the Hubble
canhavesupergiantstarsthatsignificantlyreddentheirinte-
SpaceTelescope(HST)andestimatedage,mass,andextinction
grated colors. By using the SSP method, a much older age
basedonanisochronefittoclusterCMDs.
wouldbedeterminedfortheseclusters.
Usingthisdataandartificialclustersimulations,wedemon-
Although Cerviño & Luridiana (2006) have attempted to stratethatwhentheintrinsicrangeofextinctionwithinthehost
describe the problem of stochasticity analytically, the nowa- galaxy is rather narrow, it is not necessary to know the exact
Articlenumber,page1of10
value of the extinction for individual clusters to derive their Space of parameters
physicalparametersreliably. physical photometric
Thepaperisorganizedintothefollowingsections. Section2 a) b) −4.6
introduces our method of deriving physical parameters of clus-
)
terswhenstochasticityistakenintoaccount,§3describesagrid
M −4.4
oarftisfiimciuallactleudstcelrusstaemrpmleosd,ealns,d§§45parpepselinetssttheestmsoetfhtohdetmoeththeoMdo3n1 /m MU
(
andM33starclusters. og −4.2
l
−4.0
log(t/yr) −4.6 −4.4 −4.2 −4.0
M
2. Methodofderivingage,mass,andextinctionof B
starcluster
d) c)
There are presently two main methods used to derive physical )
parameters of star clusters based on a 3D grid (age, mass and M
extinction) of models, which take stochasticity effects into ac- /m MU σB
count. Thefirstisafastχ2minimizationapproachusedby,e.g., g( σ
o U
Popescu & Hanson (2010) and Beerman et al. (2012), the sec- l
ond, a more accurate but much slower approach, which builds
probabilitymapsintheage-mass-extinctionspacebyexploring
log(t/yr) M
all the nodes of the grid and selects the most probable solution B
(seee.g., Fouesneau&Lançon2010).
0.2
The method presented here also explores parameter proba-
y0.12 e) y f)
bility maps; however, by restricting the analysis to the models sit sit
locatedinthevicinityoftheobservedabsolutemagnitudes(the en en
d0.08 d
distancetotheobjecthastobeknown),wesignificantlyreduce y y 0.1
thecomputationtime. Theschemeofthemethodissketchedin bilit bilit
a0.04 a
Fig.1. b b
o o
A 3D grid of cluster models is built for every value of Pr Pr
0 0
the three physical parameters t, m, E(B − V)1; for simplicity 7 8 9 10 2 4 6
Fig.1(a)showsonlyagridforageandmass.Forthedescription log(t/yr) log(m/M )
ofthegrid,see§3. Eachnodeofthegridcontains1000models
Fig. 1. Scheme of the method for deriving physical parameters of
of the same age, mass, and extinction. They populate the pho-
star cluster. Panel (a) shows the grid of models (only age and mass
tometricparameterspace(absoluteUBVRImagnitudes). Figure
are displayed; same for extinction). These models are represented in
1(b)shows M and M withonly100modelspernodewithout
U B thephotometricspace(onlyM andM areshown)displayedinpanel
extinction,andtheusedmodelgridismuchmorecontinuousin U B
(b;only100modelspernodewithoutextinctionareshown). Inpanel
photometricparameterspace. (c)allthemodelssituatedwithin3–σ(circle)fromtheobservedabso-
When the observations are considered in Fig.1(c), along lutemagnitudesareselected.Panel(d)showsthenodesassociatedwith
with their errorbars (σ; hereafterwe use σ = 0.05 mag forall thesemodels.The1Dageandmassdistributionsoftheselectedmodels
are displayed as normalized histograms in panels (e) and (f), used to
thepassbandsofartificialandrealclustersamplesstudiedinthis
paper),whichingeneralcanbedifferentforeverymagnitude,all determinemostprobablevalues,indicatedbysolidverticallines;confi-
denceintervalsareindicatedbydashedlines.
the models situated within 3–σ from the observed magnitudes
are selected. Fig.1(d) shows the nodes to which the selected
models are associated. Other nodes do not play any role in the
3. Theage-mass-extinctiongridofmodels
derivation of parameters, therefore the speed of the algorithm
is increased significantly. Finally, the distributions of age and To derive physical parameters of star clusters with the method
mass, displayed in Figs. 1(e, f), are derived from the selected described in §2, a large age-mass-extinction grid of models is
models,asfortheextinction,whichisnotshowninthefigure. computed,byapplyingthealgorithmdescribedbyDeveikisetal.
(2008). Thestellarmassesaregeneratedrandomlysamplingthe
For the selected models (Fig.1(c) circle) we apply weights
IMF(correctedforbinaries; Kroupa2001)andtheirluminosi-
asfollows:forthemodelslocatedwithin1–σfromtheobserved
ties are derived from stellar isochrone of the selected age and
magnitude a weight of 0.68 is assigned, for the ones between
metallicityoftheclustermodel. Theprocessiscontinueduntil
1–σ and 2–σ – 0.28, and for the ones between 2–σ and 3–σ
thetotalmassofgeneratedstarsreachesthemassofthecluster
– 0.04. The probability density distributions displayed in Figs.
model. Then,takingthedistancetotheclusterintoaccount,the
1(e, f) are derived by normalizing the total area of each his-
magnitudes are computed using the Johnson-Cousins UBVRI
togramto1. Thesolutionistakenasthemaximumofthese1D
photometricsystem(MaízApellániz2006).
distributions. We compute confidence intervals (error bars) by
excluding the first and the last 16% of the area in histograms, For stellar models, we took the PADOVA isochrones2 from
following the method of “central interval” presented in §2.5.1 Marigo et al. (2008), with corrections by Girardi et al. (2010)
ofAndrae(2010). fortheTP-AGBphases. Themodelgridforasinglemetallicity
Z = 0.008 contains the following nodes: ages from log(t/yr)
1 WerefertoextinctionasE(B−V)hereafter. 2 PADOVAisochronesfrom“CMD2.4”:http://stev.oapd.inaf.it/cmd
Articlenumber,page2of10
P.deMeulenaeretal.:Derivingphysicalparametersofunresolvedstarclusters.
= 6.6 to 10.1 in steps of 0.05, masses from log(m/M ) = 2 to
(cid:12) Number of models per bin 3 10 30 100
5 in steps of 0.05. This gives 71 values of age and 61 values
of mass, and the grid consists of 1000 models per node, i.e. ∼ 10 5
4 × 106 stochastic models. To limit the number of models to
store in computer’s memory, extinction is computed when the
9
observedclusteriscomparedwiththegridofmodels. Itranges
fromE(B−V)=0to1instepsof0.02,therefore51valuesfor 4
theextinction. 8 d
d e
To accelerate computation of integrated magnitudes of e v
stochastic star cluster models, we defined a threshold in the eriv 7 a) deri 3 b)
icsoomchpruotneed,buynidnetergwrahtiicohnothfethteotsatlellluamrliunmosiintoysiotfyffauinnctetironstaarlosnigs yr) d10 M) 5
the isochrone. Above the threshold, which is defined to select (/t /m
20%ofthemostmassivestars,thecontributionofthehigh-mass log 9 og(
starsismodeledbythealgorithmofDeveikisetal.(2008). The l 4
models built by this improved procedure share the same prop-
8
erties as models built by simulating all stars of the cluster, but
requiremuchlesscomputationwithaspeedgainofafactor∼10.
7 c) 3 d)
4. Testofthemethodonanartificialclustersample 7 8 9 10 3 4 5
log(t/yr) true log(m/M ) true
4.1. Degeneraciesinanartificialclustersample
Fig. 2. Derived parameters of 10000 artificial clusters without ex-
We simulated artificial star cluster samples with known age, tinction. Panels (a) and (b) show age and mass for a sample without
mass, and extinction and used them as input clusters to evalu- photometricerrors; (c)and(d)forasamplewithGaussianphotomet-
atetheabilityofourmethodtoderivephysicalparameters. The ric errors of 0.05 mag. Panel (b) also shows the means and standard
artificialclustersamplesconsistof10000clusterswitharandom deviations(circleswitherrorbars)ofthederivedmassdistributionsfor
clusterswithtruemasslog(m/M )=3.0,3.5and4.0.Thedensityscale
ageinthelog(t/yr)rangeof[6.6,10.1]. Tosimulatethemassof (cid:12)
islogarithmic.
input clusters, we used a power-law cluster mass function with
index −2 in the range of log(m/M ) = [2.7, 4.3], so as to have
(cid:12)
more low-mass clusters in the sample. We have two artificial
samples: onewithoutextinctionandtheotherwithE(B−V)in whichisasignoftheage-extinctiondegeneracy. Itcreatestwo
therangeof[0.0,1.0]usingtheMilkyWaystandardextinction streaksaboveandbelowtheone-to-onerelationintherangeof
lawfromCardellietal.(1989). 8 (cid:46) log(t/yr) (cid:46) 9.5 that were already perceptible in the case
Figure2displaystheresultsforartificialclustersamplebuilt without photometric errors in Fig.3(a). However, including of
withoutextinction.Panels(a)and(b)showresultsoftheageand photometricerrorsdoesnotsignificantlyaffectthederivationof
mass of the artificial cluster sample without introducing pho- mass (panels b and e). We note that a gap in derived ages at
tometric observation errors. Panels (c) and (d) show the case log(t/yr) = 9.15isafeatureofisochroneduetotheincreasein
with Gaussian photometric errors of 0.05 mag randomly added theproductionrateofAGBstars,whichwasdiscussedinGirardi
to each magnitude of the sample clusters. The introduction of &Bertelli(1998).
photometric errors results in broadening around the one-to-one
ThesedegeneracystreakshavefirstbeenreportedbyFoues-
line.
neau&Lançon(2010).Thedegeneracystreakabovetheone-to-
InFig.2(b),theasymmetryobservedinthemassderivation
one line seen in Fig.3(d) concerns clusters that are young and
slightly favors high masses. This is because that in the grid of
thatpossessintrinsicallyhighextinction, butarederivedbythe
starclustermodels,thenodesofmodelswithhighermasshave
method as older and having lower extinction. Conversely, the
magnitudes that are less dispersed than the nodes with lower
streakofclustersbelowtheone-to-onerelationinvolvesobjects
mass models, as a consequence of stochasticity (see e.g., De-
thatarederivedasolderandthathavelowerextinctionthanthey
veikisetal.2008). Thus,whenthemodelsoftwonodesofdif-
doinreality. Thesefeaturesareimportanttokeepinmindwhen
ferentmassesarelocatedintheUBVRI“sphere”aroundtheob-
derivingthephysicalparametersofunresolvedstarclusters.
servation shown in Fig.1(c), the more massive node, with less
dispersed models, will dominate. To balance out the effect, a The treatment of the metallicity effects on the derivation of
clustermassfunctioncouldbeusedtodecreasetheimportance age,mass,andextinctionofstarclustersisthesubjectofaforth-
of the nodes of massive cluster models. Although Fig.2(b) comingpaper. Toillustratetheeffect,wederivedtheparameters
shows asymmetry, the means and standard deviations given at ofaclustersampleofZ =0.008metallicity,successivelywitha
log(m/M )=3.0,3.5,and4.0indicatethatthisphenomenonis modelgridofmuchlowermetallicity,Z =0.00013,andanother
(cid:12)
slight. one with much higher metallicity, Z = 0.03. In the first case,
Figure 3gives theresults of artificialclusters inthe case of the ages are systematically overestimated by ∼0.5 dex, the up-
extinction. Panels (a), (b), and (c) show the age, mass and ex- perstreakismoredeveloped,andtheloweronedisappears. The
tinction derived when there is no photometric errors, and pan- massesarealsooverestimatedby∼0.5dex, andthereisapref-
els (d), (e), and (f) when there are Gaussian photometric errors erenceforoverestimatedextinction. Inthesecondcase,theages
of 0.05 mag included. In Fig.3(d), in the case of photomet- are only slightly (∼0.1 dex) underestimated. The upper streak
ric errors and extinction, we observe that a broadening around decreases without vanishing, and the lower one becomes more
the one-to-one relation increases, especially for log(t/yr) (cid:38) 8, populated. Themassesareunderestimatedof∼0.1dex,andthe
whichisassociatedwithbroadeningintheextinction(panel f), extinctionisalmostunaffected.
Articlenumber,page3of10
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10
100
0.8
9
30
4
10
8 0.4
d
d e d 3
e v e
eriv 7 a) deri 3 b) eriv c)
yr) d10 M) 5 ) dV 0
log(/t og(/m −(EB 0.8 per bin
9 l s
el
d
4 o
m
of
8 0.4 er
b
m
u
N
7 d) 3 e) f)
0
7 8 9 10 3 4 5 0 0.4 0.8
log(t/yr) true log(m/M ) true E(B−V) true
Fig.3. Derivedparametersof10000artificialclusterswithextinctionrandomlychosenintherangeofE(B−V)=[0,1]. Panels(a),(b)and
(c)showage,mass,andextinctionforasamplewithoutphotometricerrors;(d),(e),and(f)forasamplewithGaussianphotometricerrorsof0.05
mag.
4.2. Isitpossibletoreducetheage-extinctiondegeneracy? 0.5. Theupperstreakisnotmodified,becausethelowerlimitof
theallowedextinctionrangewasnotchanged.
The upper and lower streaks in Fig.3(d) suggest that if a wide
Toquantifythereductionofthelowerdegeneracystreakdue
extinctionrangeisallowedinasimulatedsample,thenthereare
toreductionoftheextinctionrange,allthemodelssituatedinthe
possibilities that a cluster mimics an older one with lower ex- squareshowninFigs.4(a)and(d)werecounted.Thereare∼480
tinction, or inversely a younger one with higher extinction. If
clustersinthatregionforthewideextinctionrange(panela)and
thetrueextinctionrangeoftheclusterpopulationisnarrow,then only∼110forthelowextinctionrange(paneld). Thereduction
we could restrict the search for the extinction within a narrow of the extinction range from E(B−V) = [0, 1] to [0, 0.5] thus
range in the model grid, resulting in decrease of age-extinction
decreases more than four times the strength of the degeneracy
degeneracy.
streak.
InFig.4weshowresultsofthetestsforasampleof10000 We conclude that to reduce the degeneracy streaks seen in
artificialclusterswithtrueextinctionfromarangeof E(B−V) Fig.3(d),weshouldmakeareasonableassumptionontheextent
= [0, 0.5] and with Gaussian photometric errors of 0.05 mag of the possible extinction range within the galaxy hosting the
randomlyaddedtoeachmagnitudeofthesampleclusters. This studiedclusterpopulation.
clustersamplewasstudiedtwice,withdifferentallowedextinc-
tionrangesinthemodelgrid.
Inthefirsttest,theextinctionofthemodelgridwasallowed 5. Applicationofthemethodtorealstarclusters
to vary in a wide range, E(B−V) = [0, 1], shown in Fig.4(a,
5.1. TheM31galaxystarclustersample
b,c). Ifaclusterhasatrueextinctionof0.5,thenthemaximum
underestimation of its extinction can be from 0 to 0.5. But if a A star cluster catalog of 285 objects located in the south west
clusterhastrueextinctionof0,themaximumoverestimationof fieldoftheM31galaxywascompiledbyNarbutisetal.(2008)
its extinction could range from 0 to 1. This explains why the usingthedeep BVRI and H photometryfromtheSubarutele-
α
lowerstreak(i.e. clusterswithoverestimatedextinction)ismore scope,aswellasmultibandmapsbasedonHST,Galex,Spitzer,
extendedthantheupperoneinpanel(a). and2MASSimaging. TheUBVRI photometrywasderivedus-
Inthesecondtest,theallowedextinctionrangeofthemodel ing the Local Group Galaxy Survey data from Massey et al.
grid was reduced to a range of [0, 0.5]; Fig.4(d, e, f). The (2006). The magnitude limit of the cluster sample was set to
constraint onthe extinctionrange resultedin areduction of the theV =20.5mag.
lowerdegeneracystreak, seen inFig.4(d), whichisless devel- Vansevicˇiusetal.(2009)selected238clustersfromthatsam-
oped than in Fig.4(a). From the comparison of Figs.4(b) and ple,excludingtheoneswithstrongH emission,andcompared
α
(e),weseethatthemassislessaffectedbythedegeneracy. We their multiband colors to PEGASE (Fioc & Rocca-Volmerange
notethatonlythelowerstreakismodified,sinceonlythehigher 1997)SSPmodelstoderivetheirage,mass,metallicity,andex-
limit of the allowed extinction range was changed from 1.0 to tinction. Spitzer data was used to constrain the maximum ex-
Articlenumber,page4of10
P.deMeulenaeretal.:Derivingphysicalparametersofunresolvedstarclusters.
5
10
a) b) c)
100
0.8
9
30
4
10
8 0.4
yr) derived170 M) derived 35 ) derivedV 0 3
og(/t d) g(/m e) −(EB 0.8 f) er bin
l o p
9 l s
el
d
4 o
m
of
8 0.4 er
b
m
u
N
7 3
0
7 8 9 10 3 4 5 0 0.2 0.4
log(t/yr) true log(m/M ) true E(B−V) true
Fig.4. Derivedparametersof10000artificialclusterswithtrueextinctionrandomlychosenintherangeofE(B−V)=[0,0.5]withGaussian
photometricerrorsof0.05mag. Panels(a),(b),and(c)showage,massandextinctionwhenasampleisstudiedusingagridofmodelswithan
allowedextinctionintherangeof[0,1];(d),(e),and(f)showresultsforthesameclustersamplestudiedwithanarrowerallowedextinctioninthe
rangeof[0,0.5]. Panels(c)and(f)aredenserthaninFig.3,becausethesamenumberofclustersarelocatedonasmallerrangeofextinction. A
squareindicatedinpanels(a)and(d)isusedtoquantifythedegeneracyeffect.
tinction for each cluster. They reported ∼30 classical globular In Fig.6(a), when clusters are studied in a narrow allowed
clusters with low metallicity older than 3 Gyr. The remaining extinctionrange, E(B−V)=[0.04,0.5],thederivedagesshow
∼210 younger clusters were classified as objects belonging to thesamefeaturesasthemodelsstudiedinFig.3(d),reproduced
thedisk,withaveragemetallicityZ =0.008. Figure5showsthe hereinthebackgroundofthepanel. Thedegeneracystreaksde-
U − B vs B−V and U −V vs R− I diagrams of the 238 star velopaboveandbelowtheone-to-oneline,perpendicularlytoit,
clustersfromVansevicˇiusetal.(2009),comparedtothegridof and are marked by ellipses numbered “1” and “2” in Fig.6(a).
starclustermodelsbuiltin§3. As for the models in the background, the upper degeneracy
Since our grid of models has single metallicity, Z = 0.008, streak concerns clusters with overestimated age and underesti-
we attempted to exclude more metal-rich clusters from Van- matedextinction,shownbyellipse“1”inFig.6(g). Incontrast,
sevicˇius et al. (2009) sample by only selecting objects with forthelowerdegeneracystreak(ellipse“2”),theageisunderes-
galactocentric distance over 7 kpc. This subsample consists of timatedand extinctionisoverestimated. Sincetheupper streak
216 clusters and is displayed in Fig.5. It is studied with our (ellipse“1”)ismoredevelopedthanthelowerone(“2”),wein-
method described in §2, using the Milky Way standard extinc- terpret that as a result of too narrow an extinction range in the
tion law (Cardelli et al. 1989) and distance modulus to M31 of modelgridallowedE(B−V)=[0.04,0.5].
(m−M) =24.47derivedbyMcConnachieetal.(2005).
0 InFig.6(b),whenclustersarestudiedinawidermodelex-
Figure6presentstheage(panelsa,b,c),mass(panelsd,e,f) tinctionrange,E(B−V)=[0.04,1],theupperdegeneracystreak
andextinction(g,h,i)of211clusters(fromthe216sample)de- islesspopulated,andtheloweroneextends,meaningthatsome
rivedbyusingourmethod;forfiveclusters,nomodelwasfound of the clusters have overestimated extinction (ellipse “3”), also
withinthe3–σaroundtheobservedmagnitudes. Clusterswere showninpanel(h).
studied twice, first with a narrow extinction range E(B−V) =
[0.04, 0.5] allowed in the model grid, and second with a wider If the intrinsic range of extinction for a cluster sample is
one, [0.04, 1.0]. The first column (panels a, d, g) compares wide, as in the galaxy M31, then a narrow extinction range of
theage, mass, andextinctionderivedwhenanarrowextinction models produces extended an upper streak (ellipse “1”) and a
range is allowed vs the Vansevicˇius et al. (2009) results. The smaller lower streak (ellipse “2”), shown in Fig.6(a). In panel
secondcolumn(panelsb,e,h)comparestheage,mass,andex- (b),whentheallowedextinctionrangeofmodelsiswide,theup-
tinctionderivedwhenawideextinctionrangeisallowedvsthe per streak retracts and the lower streak develops. We conclude
Vansevicˇius et al. (2009) results. The last column (panels c, f, thatinagalaxywithwideextinctionrange,itisnotpossibleto
i) compares the results obtained with a wide extinction range deriveparametersfortheclustersaffectedbyage-extinctionde-
allowedvstheonesobtainedwithanarrowextinctionrangeal- generacyandadditionalconstraintsfortheextinctionareneeded;
lowed. e.g., Vansevicˇius et al. (2009) used a Spitzer emission map, to
Articlenumber,page5of10
−1.0
−1
−0.5
0
B V
− 0 −
U U
1
0.5
2
1.0
a) b)
1.5 3
−0.5 0 0.5 1.0 1.5 −0.5 0 0.5 1.0 1.5 2.0
B−V R−I
Fig.5. M31galaxystarclustersampleof238objectsfromVansevicˇiusetal.(2009)(circlesandstars)andthestudiedsampleof216objects
(stars)havinggalactocentricdistanceover7kpc. Panelsshow: (a)U−BvsB−V and(b)U−V vsR−I diagrams. Themodelgrid(without
extinction)usedtoderivephysicalparametersofclustersisdisplayedinthebackgroundwithindicatedreddeningvectorsfollowingtheGalactic
extinctionlaw.ThecontinuouslinetracesPADOVASSPofZ=0.008.
tracethedustlanesofM31andreducetheage-extinctiondegen- SincethemetallicitycontentoftheM33galaxyissimilarto
eracy. the one of the LMC (Bresolin et al. 2010), we assume that the
interstellar extinction law derived by Gordon et al. (2003) for
Figs. 6(d, e) show that for high-mass clusters we obtain
the LMC can be applied to the M33 cluster sample. As in San
lower masses than given by Vansevicˇius et al. (2009). Inspect-
Roman et al. (2009), we adopted the M33 distance modulus of
ingthemetallicityvaluesprovidedbyVansevicˇiusetal.(2009),
(m−M) =24.54(McConnachieetal.2005).
wenotethathigh-massclustershavemetallicitieslowerthanthe 0
Z = 0.008 used in our model grid. This could be a sign of the For the M33, U et al. (2009) derived the extinction of 22
metallicity effect on the derivation of physical parameters, and supergiants, which resulted in an extinction distribution cen-
willbeinvestigatedintheforthcomingpaper. tered on E(B − V) = 0.1. U et al. (2009) also used the data
of Rosolowsky & Simon (2008) to derive E(B−V) values for
58 HII regions, and show in their Fig.9 that extinction can be
5.2. TheM33galaxystarclustersample expectedtobeE(B−V)(cid:46)0.3forthoseregions(exceptfor3ob-
jects),withanaverageE(B−V)∼0.11. AforegroundGalactic
San Roman et al. (2009) reports observing of 161 clusters us- line-of-sight extinction in the direction of M33 of E(B−V) =
ing the HST, allowing them to evaluate their ages and extinc- 0.04isestimatedfromSchlegeletal.(1998)extinctionmaps.
tionsbyPADOVAGirardietal.(2002)isochronefittotheirre- WestudiedtheM33clustersusingtwodifferentallowedex-
solvedCMDs. Recently,Ma(2012)hasused392clustersfrom
tinction ranges for the model grid. The first one is narrow, ex-
the compiled catalog of Sarajedini & Mancone (2007) and im-
tendingbetweentheforegroundGalacticline-of-sightextinction
ages from Massey et al. (2006) to provide UBVRI broad-band
in the direction of M33 up to the higher limit given by U et al.
integratedphotometrydata. (2009),i.e, E(B−V)=[0.04,0.30]. Thesecondoneisawider
Thereare40clusterscommontoboththeSanRomanetal. extinctionrange,E(B−V)=[0.04,1.0],suchastheoneusedfor
(2009) and the Ma (2012) catalogs, making them interesting theM31case.
to compare the parameters derived from the resolved method Figure 8 presents the age (panels a, b, c), mass (panels d,
(isochronefittoCMDsbySanRomanetal.(2009))andstochas- e, f), andextinction(g, h, i)ofthe40clustersderivedbyusing
ticmethod,whichwasappliedheretotheintegratedphotometry ourmethod. Theresultsobtainedinthenarrowextinctionrange
dataofMa(2012). (panelsa,d,g)andthewideextinctionrange(panelsb,e,h)are
Figure7(a)presentstheU−BvsB−V diagramofthe392 comparedtotheonesobtainedbySanRomanetal.(2009)using
clustersfromtheMa(2012)catalogcomparedtothegridofclus- isochrone fit to CMDs. Panels (c, f, i) compare the results we
ter models. The selected 40 star clusters are also indicated. To obtained with the wide extinction range allowed vs the narrow
accountforcalibrationoftheBband,asdiscussedbyMa(2012), extinctionrangeallowed.Itshowsthatthedifferenceisrelatively
where he compared his photometry to previous works by Sara- small between the two kinds of solution, showing that the age-
jedini & Mancone (2007), Park & Lee (2007), and San Roman degeneracyisplayingaminorroleinthisM33clustersample.
et al. (2009), we shifted the B band to brighter magnitudes by The derived mass does not differ significantly, as seen in
0.1 mag for all clusters. We note that the parameter derivation Fig.8(f). Panels(g,h,i)revealthatonlyonefourthoftheclus-
resultsdonotchangewhentheBbandisnottakenintoaccount. ters are affected by an increase in extinction when the allowed
Articlenumber,page6of10
P.deMeulenaeretal.:Derivingphysicalparametersofunresolvedstarclusters.
extinction range is widened. Only some of them have a much Fioc,M.&Rocca-Volmerange,B.1997,A&A,326,950
higher derived extinction when the wide allowed extinction Fouesneau,M.&Lançon,A.2010,A&A,521,A22+
rangeisused. Thesefewclustersaffectedbytheage-extinction Fouesneau,M.,Lançon,A.,Chandar,R.,&Whitmore,B.C.2012,ApJ,750,60
Girardi,L.,Bertelli,G.,Bressan,A.,etal.2002,A&A,391,195
degeneracycanbeseeninpanel(c),appearingyoungerwhena
Girardi,L.,&Bertelli,G.1998,MNRAS,300,533
wideextinctionrangeisallowedthanwhentherangeisnarrow, Girardi,L.,Williams,B.F.,Gilbert,K.M.,etal.2010,ApJ,724,1030
asalreadyseeninM31clustersampleinFig.6(c). Gordon,K.D.,Clayton,G.C.,Misselt,K.A.,Landolt,A.U.,&Wolff,M.J.
2003,ApJ,594,279
Kroupa,P.2001,MNRAS,322,231
6. Conclusions Lada,C.J.&Lada,E.A.2003,ARA&A,41,57
Ma,J.2012,AJ,144,41
Wepresentedamethodthataimstoderivetheage,mass,andex- MaízApellániz,J.2006,AJ,131,1184
MaízApellániz,J.2009,Ap&SS,324,95
tinctionofunresolvedstarclustersbyusingbroad-bandphotom-
Marigo,P.,Girardi,L.,Bressan,A.,etal.2008,A&A,482,883
etryandtakingthestochasticsamplingofstellarmassesinclus- Massey,P.,Olsen,K.A.,Hodge,P.W.,etal.2006,inBulletinoftheAmeri-
ters into account. We investigated the behavior of the method canAstronomicalSociety,Vol.38,AmericanAstronomicalSocietyMeeting
on a sample of artificial star clusters, in order to trace the dif- Abstracts,939
ferentdegeneraciesbetweenparameters,fordifferentchoicesof McConnachie,A.W.,Irwin,M.J.,Ferguson,A.M.N.,etal.2005,MNRAS,
356,979
photometricerrorsandextinction.
Narbutis,D.,Vansevicˇius,V.,Kodaira,K.,Bridžius,A.,&Stonkute˙,R.2008,
Thesetestsallowedustoquantifytheage-extinctiondegen- ApJS,177,174
eracy. Wedemonstratedthatfortheintrinsicallynarrowextinc- Park,W.&Lee,M.G.2007,AJ,134,2168
tionrangeofthestarclustersample,theage-extinctiondegener- Popescu,B.&Hanson,M.M.2009,AJ,138,1724
Popescu,B.&Hanson,M.M.2010,ApJ,724,296
acycanberesolvedevenincaseswhereindividualexactextinc-
Rosolowsky,E.&Simon,J.D.2008,ApJ,675,1213
tionvaluesarenotknownforeachcluster. SanRoman,I.,Sarajedini,A.,&Aparicio,A.2010,ApJ,720,1674
Theage-extinctiondegeneracyhasbeenobservedinthereal SanRoman,I.,Sarajedini,A.,Garnett,D.R.,&Holtzman,J.A.2009,ApJ,699,
star cluster sample of Vansevicˇius et al. (2009) for M31 and to 839
Santos,Jr.,J.F.C.&Frogel,J.A.1997,ApJ,479,764
a lesser extent in the one composed of clusters common to the
Sarajedini,A.&Mancone,C.L.2007,AJ,134,447
Ma(2012)andSanRomanetal.(2009)catalogsforM33. The
Schlegel,D.J.,Finkbeiner,D.P.,&Davis,M.1998,ApJ,500,525
physicalparametersderivedbyourmethodfordifferentextinc- U,V.,Urbaneja,M.A.,Kudritzki,R.-P.,etal.2009,ApJ,704,1120
tionrangesineachcase,havebeencomparedtothevaluespro- Vansevicˇius,V.,Kodaira,K.,Narbutis,D.,etal.2009,ApJ,703,1872
videdinthesestudies,showingtheimpactoftheage-extinction Worthey,G.1994,ApJS,95,107
degeneracy,especiallywhenthetrueextinctionrangeoftheclus-
terpopulationiswide.
TheM31starclustersamplefromVansevicˇiusetal.(2009)
showedthatatrueextinctionrangeinthisgalaxyiswideenough,
sothattheage-extinctiondegeneracyissignificantlydeveloped,
making the parameters difficult to derive, especially for older
ages. Insuchcases,itispreferabletouseexternalconstraintson
theextinctionofindividualclusters.
The M33 star cluster sample shows little sign of age-
extinctiondegeneracy,sincethereisonlyasmalldifferencebe-
tweensolutionsinnarrowandwideextinctionranges.Therange
ofallowedextinctionof E(B−V)=[0.04,0.30]givesparame-
tersconsistentwiththeresultsofisochronefittoCMDsbySan
Romanetal.(2009).
Thefollow-uppaperwillbededicatedtostudyofthemetal-
licity effects to derive physical parameters of star clusters and
togainacompleteunderstandingofdegeneraciesintroducedby
stochasticeffects.
Acknowledgements. Wearegratefultotheanonymousrefereeforfruitfulcom-
ments,whichhelpedtoimprovethepaper.Thisresearchwasfundedbyagrant
(No.MIP-102/2011)fromtheResearchCouncilofLithuania.
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Articlenumber,page7of10
E(B−V)=[0.04,0.5] E(B−V)=[0.04,1.0] E(B−V)=[0.04,1.0]
10
1
9
)
yr
/
(t
g
o
l 8
2
3
7 a) b) c)
7 8 9 10 7 8 9 10 7 8 9 10
log(t/yr) from V09 log(t/yr) from V09 log(t/yr),E(B−V)=[0.04,0.5]
5
)
M
/
m 4
(
g
o
l
3
d) e) f)
3 4 5 3 4 5 3 4 5
log(m/M ) from V09 log(m/M ) from V09 log(m/M ),E(B−V)=[0.04,0.5]
3
0.8
)
V
− 2 1
B
(
E
0.4
g) h) i)
0 0.4 0.8 0 0.4 0.8 0 0.4 0.8
E(B−V) from V09 E(B−V) from V09 E(B−V),E(B−V)=[0.04,0.5]
Fig.6. M31: age,mass,andextinctionof211starclustersfrom(Vansevicˇiusetal.2009,asV09). Panels(a,d,g)showresultswhenanarrow
extinctionrangeofE(B−V)=[0.04,0.5]isallowedinthemodelgrid,comparedtoV09values.Panels(b,e,h)showresultsforawiderallowed
extinctionrange[0.04,1.0],comparedtoV09values.Panels(c,f,i)compareresultsobtainedinawideextinctionrangevstheonesobtainedina
narrowextinctionrange.Inpanels(a,b,c),adensitymapofFig.3(d)isreproducedtoshowregionsofage-extinctiondegeneracy.Errorbarsare
computedasdescribedin§2. SixclustersfromV09,whichhaveE(B−V)>1,arenotshowninpanels(g)and(h). Dashedellipses,numbered
“1”,“2”,and“3”,describemajorityofassociatedclustersintheageandextinctionpanels.
Articlenumber,page8of10
P.deMeulenaeretal.:Derivingphysicalparametersofunresolvedstarclusters.
−1.5
–1
−1.0
−0.5
0
B V
− 0 −
U U
1
0.5
2
1.0
a) b)
1.5 3
−0.5 0 0.5 1.0 1.5 −0.5 0 0.5 1.0 1.5
B−V R−I
Fig.7. M33galaxystarclustersampleof161objectsfromcatalogofSanRomanetal.(2010)(circlesandstars)andthestudiedsampleof40
objects(stars)commontoMa(2012)andSanRomanetal.(2009).Panelsshow(a)U−BvsB−V,and(b)U−VvsR−Idiagrams.Themodel
grid(withoutextinction)usedtoderivephysicalparametersofclustersisdisplayedinthebackgroundwithindicatedreddeningvectorsfollowing
theLMCextinctionlaw.ThecontinuouslinetracesPADOVASSPofZ=0.008.TheBbandmagnitudesofclusterswereshiftedby0.1mag.
Articlenumber,page9of10
E(B−V)=[0.04,0.3] E(B−V)=[0.04,1.0] E(B−V)=[0.04,1.0]
a) b) c)
9
)
yr
/ 8
(t
g
o
l
7
7 8 9 7 8 9 7 8 9
log(t/yr) from S09 log(t/yr) from S09 log(t/yr),E(B−V)=[0.04,0.3]
d) e) f)
5
)
M
/
m 4
(
g
o
l
3
3 4 5 3 4 5 3 4 5
log(m/M ) from S09 log(m/M ) from S09 log(m/M ),E(B−V)=[0.04,0.3]
g) h) i)
0.8
)
V
−
B
(
E
0.4
0 0.1 0 0.1 0 0.2 0.4
E(B−V) from S09 E(B−V) from S09 E(B−V),E(B−V)=[0.04,0.3]
Fig.8. M33:age,massandextinctionof40starclusterscommontocatalogsofMa(2012)and(SanRomanetal.2009,asS09).Panels(a,d,g)
showresultswhenanarrowextinctionrangeofE(B−V)=[0.04,0.3]isallowedinthemodelgrid,comparedtoS09values.Panels(b,e,h)show
resultsforawiderallowedextinctionrangeofE(B−V)=[0.04,1.0],comparedtoS09values.Panels(c,f,i)compareresultsobtainedinawide
extinctionrangevstheonesobtainedinanarrowextinctionrange.Inpanels(a,b,c),adensitymapofFig.3(d)isreproducedtoshowregionsof
age-extinctiondegeneracy.Error-barsarecomputedasdescribedin§2.
Articlenumber,page10of10
