The Distances to Open Clusters from Main-Sequence Fitting. III. Improved Accuracy with Empirically Calibrated Isochrones

1.2 MB·English

by  Deokkeun An

ASTROPHYS.J.655(2007)233-260
PreprinttypesetusingLATEXstyleemulateapjv.04/21/05
THEDISTANCESTOOPENCLUSTERSFROMMAIN-SEQUENCEFITTING.III.
IMPROVEDACCURACYWITHEMPIRICALLYCALIBRATEDISOCHRONES
DEOKKEUNAN1,DONALDM.TERNDRUP1,MARCH.PINSONNEAULT1,DIANEB.PAULSON2,
ROBERTB.HANSON3,ANDJOHNR.STAUFFER4
Astrophys.J.655(2007)233-260
ABSTRACT
Wecontinueourseriesofpapersonopenclusterdistanceswithacriticalassessmentoftheaccuracyofmain-
sequencefittingusingisochronesthatemployempiricalcorrectionstothecolor-temperaturerelations. Weuse
fournearbyopenclusterswithmulticolorphotometryandaccuratemetallicitiesandpresentanewmetallicity
7
forPraesepe([Fe/H]=+0.11 0.03)fromhigh-resolutionspectra.Theinternalprecisionofdistanceestimates
0 ±
is abouta factor of 5 better than the case withoutthe color calibrations. After taking into accountall major
0
2 systematic errors, we obtain distances accurate to about 2% – 3% when there exists a good metallicity esti-
mate. Metallicitiesaccuratetobetterthan0.1dexmaybeobtainedfromBVICKs photometryalone. We also
n
deriveaheliumabundanceforthePleiadesofY =0.279 0.015,whichisequalwithintheerrorstotheSun’s
a initialheliumabundanceandthatoftheHyades. Ourbe±stestimatesofdistancesare(m- M) =6.33 0.04,
J 0 ±
8.03 0.04, and 9.61 0.03 to Praesepe, NGC 2516, and M67, respectively. Our Pleiades distance at the
3 spect±roscopicmetallici±ty,(m- M) =5.66 0.01(internal) 0.05(systematic),isinexcellentagreementwith
1 several geometric distance measu0rements±. We have made±calibrated isochrones for - 0.3 [Fe/H] +0.2
availableonline. ≤ ≤
2
Subject headings: Hertzsprung-Russell diagram — open clusters and associations: individual (M67,
v
9 NGC 2516, Pleiades, Praesepe) — stars: distances — stars: abundances— stars: evolu-
4 tion—stars: activity
5
7
0 1. INTRODUCTION a clusterfainter thanexpectedfromits metallicity, andsolu-
6 Thedeterminationofaccuratedistancesisthekeytounder- tionsofthistypehavebeendiscussedintheliteratureforthe
0 standinghowstarsandtheGalaxyhaveformedandevolved. Pleiades (Belikov et al. 1998). However, this is difficult to
/ understandsincetheredonotseemtobenearbyfieldstarsof
h From protostarsin star-formingregionsto ancienttracers of
similar characteristics in the Hipparcos catalog (Soderblom
p the halo, improved distances have refined stellar evolution-
et al. 1998), and the helium enhancement would have to be
- ary theory and Galactic structure models (e.g., Reid 1999).
o enormous(Y 0.34). Inaddition,ithasbeensuggestedthat
TheHipparcosmission(Perrymanetal.1997)wasespecially
≈
tr valuable, providing trigonometric parallaxes for 105 stars the metal abundance from spectroscopy may have been sig-
s to precision of 1–2 mas (Perryman et al. 1997).∼These par- nificantlyoverestimated(Percivalet al. 2003). An argument
a was also made that distance estimates from theoretical stel-
allaxes, however, are only useful for individual stars within
:
v 100pc. Mostopenclustersaremuchmoredistantthanthis larmodelshavebeenoverestimatedforyoungclustersdueto
Xi ∼“horizon,”butahalf-dozenofthenearestclustershave10–50 unknown,age-relatedphysics(vanLeeuwen1999).
However,themostlikelyexplanationisrelatedtotheHip-
or more Hipparcosstars, yielding cluster parallaxesostensi-
r parcos parallaxes themselves. Pinsonneault et al. (1998)
a blyaccurateto5%orbetter(Mermilliodetal.1997;Perryman
showedthatthe12brightstarsnearthecenterofthePleiades
etal.1998;Robichonetal.1999;vanLeeuwen1999).
allhadvirtuallythesameparallax, 9mas,morethan1mas
Main-sequence(MS) fitting, also known as the photomet-
∼
largerthanthemeanparallaxforotherclusterstars. Theyat-
ric parallax method (e.g., Johnson 1957;Siegel et al. 2002),
tributedthistoalocalzero-pointerroroftheindividualstellar
has long been used to estimate distances to individual stars
parallaxes that are correlated over the Hipparcos’ 0.◦9 field
andstar clustersbeyondthelimitsofparallaxstudies,andis
of view (vanLeeuwen & Evans1998). These quasi-random
considered to be a robust and well-understoodtechnique. It
errorswerecausedbytheHipparcosgreat-circledatareduc-
wasthereforeabigsurprisewhentheHipparcosdistancesto
tions, as Makarov (2002, 2003) proved by re-reducing the
the Pleiades and Coma Ber open clusters were in disagree-
PleiadesandComarBerclusterparallaxesinadifferentway
ment with distances from the MS-fitting at more than a 3 σ
thatcorrectlyobtainstheabsolutezeropointofparallax. Ad-
level (Pinsonneault et al. 1998). It is difficult to reconcile a
ditional effects may result from the way the Hipparcos data
shortPleiadesdistancewithstellarinteriorandspectroscopic
were obtainedandanalyzed, and a moreelaboratereduction
abundance studies. A high helium abundance would make
of the Hipparcos parallaxes promises to produce improved
1Department of Astronomy, Ohio State University, 140 West18th Av- distances and better understood errors (van Leeuwen 2005;
enue, Columbus, OH43210; deokkeun,terndrup,[email protected] vanLeeuwen&Fantino2005).
state.edu. The discrepant Hipparcos result for the Pleiades subse-
2PlanetarySystemsBranch,Code693,NASAGoddardSpaceFlightCen- quentlyledtomanyeffortstodeterminethecluster’sdistance
ter,Greenbelt,MD20771;[email protected].
from binaries and independent parallax measurements (e.g.,
3University of California Observatories/Lick Observatory, Santa Cruz,
CA95064;[email protected]. Munari et al. 2004; Pan et al. 2004; Johns-Krull & Ander-
4InfraredProcessingandAnalysisCenter,CaliforniaInstituteofTechnol- son 2005;Soderblometal. 2005). These results supportthe
ogy,Pasadena,CA91125;[email protected]. longerdistancescalefromMSfitting,verifyingthattheHip-
2 Anetal.
parcosresultwasinerror. Withaformalerrorof 1%from tion to the adoptedreddeninglaw in a discussion of the dis-
∼
thesemeasurements,thePleiadesrepresentsasecondsystem tancetoNGC2516. Herewe extendtheerroranalysismore
(besidestheHyades)withasufficientlyaccuratedistancefor quantitatively, emphasizing photometric calibration issues
aprecisiontestofstellarevolutionarymodels. and the bias in distance estimates induced by the presence
Even though the controversyover the Pleiades distance is ofunresolvedclusterbinariesorfieldforeground/background
nowsettled,acriticalassessmentoftheMSfittingtechnique stars.
isstillrequiredtoreliablyestimateadistance.Infact,MSfit- This paper also explores the effect of metallicity on the
tingusingtheoreticalisochronesisacomplexprocessthatin- luminosity of the MS. Metallicity changes isochrone lumi-
volvesbothphysicalandempiricalconsiderations(e.g.,Stauf- nositiesmorestronglythanmanyotherinputparameters,and
fer 2001). There are, however, many opportunitiesto check the degree of sensitivity depends on the color index used.
the construction of the isochrones. Stellar evolution models This permits a purely photometric derivation of the metal-
canbetestedagainsttheSunandotherstars,suchaseclipsing licity (e.g., Pinsonneault et al. 1998, 2000; Stello & Nissen
binaries, that have accurate masses and radii. Furthermore, 2001;Terndrupetal.2002),whichcanbecomparedtometal-
multicolor photometry in nearby clusters and field stars can licities derived from high-resolution spectra. An agreement
beusedtotestthebolometriccorrectionsandcolor-effective between the photometric and spectroscopic metallicities, as
temperature(T )relationstotransformtheoreticalquantities we find in this paper, provides supporting evidence that the
eff
(luminosityandT )tomagnitudesandcolors(e.g.,Vanden- effectsofmetallicityonthetheoreticalquantities(L,T )and
eff eff
Berg&Clem2003). onthecolor-T relationsarecorrectlycomputed.
eff
In our first two papers of this series (Pinsonneault et al. ThedistancesinthispaperaretiedtotheHyadesdistance
2003,2004,hereafterPaperIandPaperII,respectively),we at(m- M) =3.33 0.01(d=46.34 0.27pc),thecluster’s
0
± ±
began a long-term effort to assess the accuracy of distances center-of-mass inferred from the Hipparcos catalog (Perry-
from MS fitting and to reduce or eliminate systematic er- manetal.1998).UnlikethecontroversialHipparcosdistance
rorsin the process, particularlythose arising from the trans- to the Pleiades, the large angulardiameter of the Hyadeson
formation of theoretical to observational quantities. In Pa- theskymakestheclusterparallaxlessvulnerabletothespatial
perI,wedemonstratedthatstellarmodelsfromtheYaleRo- correlation of the Hipparcos parallax (Narayanan & Gould
tating Evolutionary Code (YREC; Sills et al. 2000) are in 1999a,b;deBruijneetal.2001).
good agreement with masses and luminosities for the well- In § 2 we compile cluster photometry, metallicities, red-
studiedHyadeseclipsingbinaryvB22(Torres&Ribas2002). dening estimates, and information on binarity and member-
These models also satisfy stringent tests from helioseismol- ship, and present a metallicity for Praesepe from new high-
ogy, and predict solar neutrino fluxes in line with observa- resolutionspectra. In§3webrieflydescribetheconstruction
tions (Basu et al. 2000; Bahcall et al. 2001; Bahcall & Pin- of the isochrones. In § 4 we compute the distances to the
sonneault2004). InPaperII,weshowedthatthemodelspro- sampleclusterswiththereddeningfixedatpreviouslyknown
vide a good match to the spectroscopically determined tem- valuesanddemonstratethattheempiricalcorrectionsimprove
peratures (Paulson et al. 2003) for individual Hyades mem- theinternalprecisionoftheisochrones. In§5wesimultane-
berswithgoodparallaxes(deBruijneetal.2001). However, ouslysolvefortheclustermetallicity,reddening,anddistance
wefoundthatanyofthewidely-usedcolor-T relations(e.g., from the χ2 minimization. In § 6 we evaluate the effects of
eff
Alonso et al. 1995, 1996; Lejeune et al. 1997, 1998) fail to severalsystematicerrorsources,includingthosefromcluster
reproducetheobservedshapesoftheMSintheHyades;dif- binariesandfieldstar contamination. In§ 7 we discusssev-
ferencesinbroadbandcolorswereaslargeas 0.1mag.The eralimplicationsofourresults. In theAppendixwe address
∼
existenceofthesesystematicerrorsinthecolorsinthepres- issuesonthephotometriczeropointsoftheempiricalHyades
enceofagreementbetweenthespectroscopicandtheoretical isochrone.
L- T scalesstronglyimpliesthatthereareproblemswiththe
eff 2. OPENCLUSTERDATA
adoptedcolor-T relationsinsteadoferrorsinthetheoretical
eff
T scale.Therefore,weproposedempiricalcorrectionstothe 2.1. SelectionofClusters
eff
color-TeffrelationsfromLejeuneetal.(1997,1998)thatwere WeconsiderfournearbyGalacticopenclusterswithexten-
adoptedintheisochronecomputations. sive multicolor photometry: Praesepe (= M44; NGC 2632),
In this study, we generate a set of isochronesover a wide the Pleiades (= M45), M67 (= NGC 2682), and NGC 2516.
range of age and metallicity, and test the validity of the Thechoiceoftheseclusterswasmotivatedbyseveralfactors.
Hyades-based color-T corrections using extensive multi- All have well-determined estimates of metal abundance and
eff
color photometry of four well-studied nearby open clusters. reddening against which we can compare photometrically-
We show that isochrones employing the Hyades empirical derivedvalues. Samplesin Praesepe, the Pleiades, and M67
correctionsprecisely match the observedMS shapes, except are dominatedby knowncluster members, so we can exam-
where anomalously blue colors in young open clusters have inewhethertheHyades-basedcolorcalibrationfromPaperII
beenpreviouslynoted(Staufferetal.2003).Furthermore,we generates isochrones that precisely match the shapes of the
demonstratethattheempiricalcorrectionsimprovetheinter- MSin these clusters. Praesepehasextensiveinformationon
nalprecisionoftheisochronesbyexaminingtheconsistency binarity, so systematic errors in distances arising from the
of distances derived from several color-magnitude diagrams presence of binaries can be explored. M67 and NGC 2516
(CMDs). eachhavemodernphotometryfromtwoindependentstudies,
We also assess varioussources of systematic errors in the fromwhichwegaugethesizesoferrorsthatarisefrompho-
MS-fitting technique. Previously, Pinsonneault et al. (1998) tometriccalibrationissues. Inaddition,NGC2516hasarel-
consideredthe effectsof age, metalabundance,helium, red- ativelyhighreddeningcomparedtotheotherclusters,which
dening,andsystematicerrorsinthephotometry,demonstrat- allowsustoevaluatetheconsequencesofadoptingparticular
ing that these could not explain the short distance to the reddeninglaws.
Pleiades from Hipparcos. Terndrupet al. (2002)paid atten- The Pleiades is a special case because its distance has re-
DistancesfromMainSequenceFitting. III 3
TABLE1
RECENTMEASUREMENTSOFTHEPLEIADESDISTANCE
Reference Method (m- M)0
Narayanan&Gould(1999b) Movingcluster 5.58±0.18
Gatewoodetal.(2000) Ground-parallax 5.58±0.12
Makarov(2002) Hipparcosreanalysis 5.55±0.06
Munarietal.(2004) Eclipsingbinary(HD23642) 5.60±0.03
Panetal.(2004) Astrometricbinary(Atlas) 5.65±0.03
Zwahlenetal.(2004) Astrometricbinary(Atlas) 5.60±0.07
Johns-Krull&Anderson(2005) HSTparallax 5.66±0.06
Soderblometal.(2005) HSTparallax 5.65±0.05
Southworthetal.(2005) Eclipsingbinary(HD23642) 5.72±0.05
Weightedmean ··· 5.63±0.02
centlybeenaccuratelymeasuredfromastrometricandeclips- In Praesepe, stars with V <12 have V - I photometry on
ing binary studies and from ground- and space-based paral- theJohnsonsystemfromMendoza(1967)andCastelazetal.
laxes, allowing a precise test of distances derived from MS (1991),whilefainterstarshavephotometryontheKronsys-
fitting. Individualmeasurementsofthesestudiesaresumma- temfromUpgrenetal.(1979),Weis(1981),Stauffer(1982b),
rizedinTable1,andtheweightedaveragedistancefromthese and Mermilliod et al. (1990). Intercomparisonsshowed that
measurements is (m- M) =5.632 0.017. The Hipparcos theMendoza(1967)andCastelazetal.(1991)colorswereon
0
±
distances to the Pleiades and other clusters are discussed in the same system. The same is true for the Kron data except
§7.2. thatthephotometryfromUpgrenetal.(1979)requiredared-
We use cluster ages from Meynet et al. (1993) for the wardshiftof+0.03inV- I tomatchtheotherphotometry.In
K
Pleiades(100Myr),M67(4Gyr),andNGC2516(140Myr). thePleiades,starswithV <10haveV- I photometryonthe
Praesepe is generally considered to be the same age as the JohnsonsystemfromJohnsonetal.(1966),Mendoza(1967),
Hyades(e.g.,Mermilliod1981b);inPaperII,weassumedan andIriarte(1969),whilefainterstarshavephotometryonthe
age of 550 Myr for the Hyades, as derived from isochrones Kronsystem fromStauffer(1982a),Stauffer(1982c),Stauf-
withoutovershooting(Perrymanetal.1998). Aswedemon- fer(1984),Stauffer&Hartmann(1987),Staufferetal.(1989),
strate,theclusterdistancesareinsensitivetothechoiceofage. Prosseretal.(1991),andStaufferetal. (1994). Directcom-
parisonbetweentheMendoza(1967)photometryandthatof
Iriarte (1969) showed that they agree well for V - I 0.5,
J
2.2. Photometry but the Mendoza (1967) data are systematically redd≤er by
2.2.1. PraesepeandthePleiades 0.02magfor stars withV- IJ 0.5. We optedto adjustthe
≥
redMendoza(1967)photometryto placethemontheIriarte
We compiled optical photometry for Praesepe and the
(1969)scale.
Pleiades mainly from WEBDA (Mermilliod & Paunzen
2003)5 and the Open Cluster Database.6 Data in V and
2.2.2. M67andNGC2516
B- V forPraesepecamefromJohnson(1952),Dickensetal.
For M67, we used BVI photometry from Montgomery
(1968),andCastelaz et al.(1991). Followingthe suggestion C
by Dickens et al. (1968), we added +0.002toV and +0.006 et al. (1993, hereafter MMJ93) and also from Sandquist
totheirB- V tomatchtheJohnson(1952)data. Weadopted (2004,hereafterS04);theseareanalyzedseparately.S04pro-
vided a comparison between the two, revealing statistically
thephotometryfromCastelazetal.(1991)withoutalteration;
the average difference in B- V is +0.002 0.012, Johnson significantdifferencesbetweenthetwostudies. InTable2we
± compilethemeandifferencesinthephotometryforM67and
(1952) being redder, among 39 stars in common (including
for other clusters as is discussed below. The first column of
nonmembers). WecomparedthenumeroussourcesofV and
B- V in the Pleiades, but did not find statistically signifi- thetablelists theclustername,andthesenseofthecompar-
cantdifferencesinanysample. AtB- V &0.8,thescatterin isonis shown in the secondcolumn. Thelast threecolumns
displaythemeandifferenceanditsstandarderrorinV,B- V,
measurementsfromseveralsourcesoftenexceededthestated
andV- I , respectively. In comparison to S04, the MMJ93
photometricerrors;thismayresultfrombrightnessandcolor C
data are fainter in V and are redder in V - I . As shown in
changesfromstellar spots on rapidlyrotatingstars in young C
Figure5ofS04,thedifferencesarelargestforthosestarswith
open clusters (Stauffer et al. 2003). For stars in this color
range, as everywhere else, we simply averaged the several V- IC.1.0.
ForNGC 2516, we have independentphotometryin BVI
availablecolorsandmagnitudes. C
ThesituationinV- I islessstraightforwardbecausedata from Jeffries et al. (2001, hereafter JTH01) and from Sung
C
etal.(2002,hereafterS02).Neitherstudycomparestheirpho-
forPraesepeandthePleiades,likethosefortheHyades,came
from either the Johnson (V - I ) or the Kron (V - I ) sys- tometrywiththeother. InFigure1weplotthedifferencesin
J K
thephotometryfromthe twostudiesagainstrightascension,
tems. The colors on the Johnson system were transformed
to the Cousins (V- I ) system using an updatedtransforma- whichrevealsaposition-dependentdifferenceinV (butnotin
C
the colors). The sense of the differenceis thatthe photome-
tionequationasdescribedintheAppendix. TheKroncolors
trytowardstheeastisfainterintheS02study. Accordingto
weretransformedtotheCousinssystemusingthecubicpoly-
S02,photometryinthisportionoftheskywasobtainedona
nomialderivedbyBessell&Weis(1987).
non-photometricnightwhichwasthenadjustedtomatchthe
5Seehttp://obswww.unige.ch/webda/webda.html. dataintherestoftheirsurveyusingstarsalsoobservedunder
6Seehttp://spider.ipac.caltech.edu/staff/stauffer/opencl/index.html. goodconditions. Astheirpaperlistsonlytheaveragevalues,
4 Anetal.
TABLE2
DIFFERENCESINTHEPHOTOMETRY
Cluster Comparison h∆Vi h∆(B- V)i h∆(V- I)Ci
M67 MMJ93–S04 +0.017±0.002 +0.009±0.002 +0.022±0.001
NGC2516 S02–JTH01 +0.016±0.001 - 0.003±0.001 +0.011±0.001
Hyades Ground–Tycho-1a +0.012±0.002 - 0.009±0.001 ···
Praesepe Ground–Tycho-1a +0.009±0.007 +0.004±0.003 ···
Pleiades Ground–Tycho-1a - 0.017±0.003 +0.000±0.002 ···
r.m.s. ··· 0.015 0.006 0.017
aComputedforstarswithVT ≤9.
FIG. 1.—Comparison ofNGC2516photometry as afunction ofright
ascension(indegrees).ThedifferencesareinthesenseoftheS02minusthe
JTH01photometry.
FIG.2.—ComparisonofNGC2516photometry,excludingstarsobserved
we chose to use the photometry only from regions obtained undernon-photometricconditionsbyS02.Thedifferencesareinthesenseof
entirely under photometric conditions. However, there still theS02minustheJTH01photometry.
remainsignificantdifferences,asshowninFigure2,between rmsinmagnitudeandcolorsfortherelativelyfewstarswith
theJTH01andtheS02photometryevenwhentheeasterndata multiplemeasurements. Weassignedthismedianvaluetoall
inthelatterstudyareremoved. ComparedtotheJTH01val- data points in each bin as random photometric errors. For
ues,theS02dataarebrighterinV andredderinV- IC atthe NGC 2516, we followed the same binning procedure, then
top of the MS, but are fainter inV and bluer in B- V at the removed a systematic trend in the differences between the
faintend.ThemeandifferencesaresummarizedinTable2. JTH01andS02studiesbysubtractingalinearfunctioninV.
WethencomputedthermsofthedifferencesinV,B- V,and
2.2.3. AssignmentofRandomErrors V- I in each bin, divided these by √2, and assigned these
C
Mostofthecollatedphotometrylackserrorsforindividual errorstobothdatasetsassumingthateachstudywouldhave
stars, andthose errorsreportedby MMJ93, JTH01, and S02 aboutthe same errors. For M67, we followedthe same pro-
aretypicallyfromasmallnumberofrepeatobservations.Our cedure,firstmatchingthestarsbytheircoordinates,andcom-
MS-fitting procedure (§ 4.1) first removes stars that are sta- putingthermsofthedifferencesafterremovingasystematic
tistically separated from the MS, and this in turn requires a trendinV. S04reportstheerrorforeachstarbasedonalarge
suitableerrorforeachstar. number of measurements. We used those errors directly in
InPraesepeandthePleiades,wedividedthedataintobins ouranalysisoftheS04data,andassumedthatthescatterbe-
in V, each 2 mag wide, and then computed the median of tweenthetwostudieswasdominatedbymeasurementerrors
DistancesfromMainSequenceFitting. III 5
TABLE3 TABLE4
DIFFERENCESINTHETYCHOPHOTOMETRY SPECTROSCOPYINPRAESEPE
Cluster Comparison h∆BTi h∆VTi Teff logg ξ
Hyades Tycho-2–Tycho-1 - 0.009±0.002 - 0.006±0.002 IDa (K) (cms- 2) (kms- 1) logǫ σlogǫ [Fe/H]
Praesepe Tycho-2–Tycho-1 - 0.018±0.004 - 0.025±0.004 KW23 5700 4.5 0.5 7.78 0.05 0.10
Pleiades Tycho-2–Tycho-1 - 0.014±0.003 - 0.016±0.003 KW58 5850 4.5 0.5 7.80 0.06 0.12
KW304 5625 4.4 0.4 7.80 0.06 0.12
NOTE.—ComputedforstarswithVT ≤9. KW336 5600 4.5 0.4 7.79 0.06 0.11
aKW=KleinWassink(1927).
inMMJ93. We setthe errorsfortheMMJ93studyfromthe
rmsofthedifferenceswithrespecttotheS04data. brighterinV andalsobluerinV- K sincetheV andK data
s s
wereobtainedindependently.Thiscorrectionwasnotapplied
2.2.4. 2MASSKs totheisochronesusedinthispaper. IntheAppendixwedis-
WecalculatedV- K colorsfromtheAllSkyDataRelease cussotherissuesinvolvedintheisochronecalibration.
s
of the Two Micron All Sky Survey (2MASS) Point Source
Catalog (PSC).7 Here K designates the “short”-K filter in 2.4. MembershipandBinarity
s
2MASS (Carpenter 2001). Based on PSC flag parameters, Wealsocollatedinformationonbinarityandmembershipin
weexcludedstarsthatweresaturatedorundetected. Wealso PraesepeandthePleiadesfromWEBDAandtheOpenClus-
ignoredblendedor contaminatedsources. TheV- Ks errors ter Database. Any star that was listed as a nonmember for
weretakenasthequadraturesumofV errorsandthecatalog’s any reason (e.g., from photometry or radial velocities) was
“total”photometricuncertaintiesinKs. rejected. In Praesepe, there are extensive data on binarity
(e.g.,Mermilliod&Mayor1999;Bouvieretal.2001). Stars
2.3. SystematicErrorsinthePhotometry that were designated as likely or probable binary stars were
OuranalysisofsystematicerrorsintheMS-fittingmethod flagged. InthePleiades,aconsiderablenumberofstarshave
(§ 6.1) shows that calibration errors in the photometry con- binarity and membership information (Jones 1981; Stauffer
tribute significantly to the overall error budget. In addi- et al. 1991; Mermilliod et al. 1992; Schilbach et al. 1995;
tion to the direct comparisons between the studies of M67 Bouvieretal.1997;Belikovetal.1998;Morauxetal.2001).
and NGC 2516, we can use the Tycho-1 photometry (van Werejectedanystarwithamembershipprobabilitylessthan
Leeuwen et al. 1997) to check whether photometry of the 50%butkeptanystar thatdidnothave a membershipprob-
Hyades,Praesepe,andthePleiadesisonaconsistentsystem ability. S04 provides a list of single cluster members based
(the other clusters are too distant to have many stars in the on proper motion surveys and known binary systems in the
Tycho catalog). Here we assume that the Tychophotometry literatureandfurthereliminationofunrecognizedbinariesin
is consistently on the same scale in all parts of the sky. In CMDsfromhishigh-precisionphotometry. We usedthisin-
Table2,wedisplaythemeandifferencesbetweentheground- formationforbothMMJ93andS04photometryinthispaper,
basedphotometryfortheseclustersandtheTychovalues.The unlessotherwisespecified.
latterweretransformedtotheJohnsonsystemusingtheequa-
tions in Oja & Evans (1998) for V and in Mamajek et al. 2.5. MetallicityandReddening
(2002)forB- V. Thevaluesin the tablewere computedfor 2.5.1. NewSpectroscopyinPraesepe
starswithV 9.
T ≤ Obtainingaccuratedistancesrelativetoourcalibratingclus-
The comparison between the Tycho-1 values and the
ter, the Hyades, requires accurate relative metallicities be-
ground-baseddata is shown in Figure 3. The scatter is usu-
causetheluminosityoftheMSissensitivetothemetalabun-
allydominatedbyerrorsintheground-basedphotometryfor
dance. Aspartofthisstudy,wedeterminedanewmetallicity
V 8 and by the Tycho photometry for fainter stars. The
≤ forPraesepeusingthe samemethodusedtofindtheHyades
solid line in each panel denotes equality, while the dashed
abundance (Paulson et al. 2003). The relative abundance of
lineshowsthemeandifferencefromTable2.
PraesepewithrespecttotheHyadesshouldthereforebeaccu-
InTable3welistthedifferencesbetweentheTycho-1and
ratesincesystematicerrorsarisingfromthesolarabundances,
Tycho-2data(Høgetal.2000)forbrightstarsintheHyades,
employed model atmospheres, oscillator strengths, or effec-
Praesepe, and the Pleiades. The differenceswere computed
tivetemperaturescaleswouldbeminimized.
directly with the Tycho values (again for V 9), without
T ≤ WeobtainedspectraoffourPraesepestarswiththeMagel-
transformations to the Johnson system. Taken together, the
lanInamoriKyoceraEchelle(MIKE)spectrograph(Bernstein
datainTables2and3showthatthevariousstudiesprobably
etal.2003)ontheMagellan6.5mClaytelescopeatLasCam-
couldhavecalibrationerrorsontheorderof0.01–0.02mag
panasObservatory. A0.35′′wideslitgavearesolvingpower
inV,butsmallerinB- V. ThesituationinV- I islesswell
C of 55,000perresolutionelement(4pixels)andwavelength
determined, mainly because we have fewer studies to com- ∼
coveragefrom4500to9200Å.Thespectraareofhighqual-
pare.
ity,withS/N>100.
In Paper II we also noted that the Tycho-1 values for V
werebrighterthantheground-baseddataby+0.012;weopted ThespectrawerereducedusingstandardIRAF8 packages.
Thestellarparameters–T ,surfacegravity(logg),microtur-
to add this constantto the Tychodata beforeaveragingwith eff
the ground-based photometry. Had we chosen to adopt the
8 IRAF is distributed by the National Optical Astronomy Observatory,
space-basedscaleinstead,ourcalibratedisochroneswouldbe
whichisoperatedbytheAssociationofUniversitiesforResearchinAstron-
omy,Inc.,undercooperative agreementwiththeNationalScienceFounda-
7Seehttp://www.ipac.caltech.edu/2mass/. tion.
6 Anetal.
FIG. 3.—Differences inV (top)andB- V (bottom)betweentheground-basedandtheTycho-1photometry,aftertransformingthelatterintotheJohnson
system(seetext). ThedifferencesareinthesenseofthegroundminustheTycho-1values. Thesolidlineindicatesequality,whilethedashedlineisplottedat
theweightedmeandifferenceforstarswithVT ≤9(Table2).ThescatterforV>8mainlyreflectserrorsintheTychophotometry.
bulence (ξ), and [Fe/H] – were derivedfollowingthe proce-
dure in Paulson et al. (2003), and are listed in Table 4. We TABLE5
employedthespectralsynthesiscodeMOOG(Sneden1973) CLUSTERMETALLICITYFROM
HIGH-RESOLUTIONSPECTROSCOPY
and used stellar model atmospheres based on the 1995 ver-
sionoftheATLAS9code(Castellietal.1997).WithinIRAF,
Reference [Fe/H] s.e.m.
we used Gaussian fits to 15 FeI lines and nine FeII lines, a
Praesepe
subsampleofthoselistedinTable1ofPaulsonetal.(2003).
Boesgaard&Friela +0.09 0.03
The Teff was derived by requiring that individual line abun- Thispaper(adoptedvalue) +0.11 0.03
dancesbeindependentofexcitationpotentialandthatmicro- Pleiades
turbulence (ξ) be independent of line strength. Insisting on Cayreletal.(1988) +0.13 0.07
ionizationequilibriumbetweenFeIandFeIIallowedforthe Boesgaard&Frielb +0.03 0.02
Kingetal.(2000) +0.06 0.05
simultaneousdeterminationofloggwithTeffandmicroturbu- Weightedmean +0.04 0.02
lence(ξ). Errorsin Teff are 50K. We analyzeda reflected ··· (0.03)c
∼
lightspectrumoftheasteroidIrisinordertoobtainaninstru- M67
mentalcorrectiontothesolarlogǫ(Fe).Usingthiscorrection, GarciaLopezetal.(1988) +0.04 0.04
weobtained[Fe/H]=0.11±0.03(s.e.m.9) forthePraesepe HFroieblb&s&BoTehsograbaurrdn((11999921)) -+00..0062 00..0132
cluster. Tautvaišiene˙etal.(2000) - 0.03 0.01
Yongetal.(2005) +0.02 0.02
2.5.2. MetallicityandReddeningEstimatesintheLiterature Randichetal.(2006) +0.03 0.01
Weightedmean +0.00 0.01
Forotherclustersinthisstudy,weadoptedorcalculatedav- ··· (0.03)c
eragemetallicitiesfromhigh-resolutionspectroscopyassum- NGC2516
marized in Table 5. For the studies by Boesgaard & Friel Terndrupetal.(2002) +0.01 0.07
in Praesepe and the Pleiades, we have recomputedthe clus- aFrom Boesgaard (1989) and Friel & Boes-
teraveragesfromindividual[Fe/H]estimatesafterexcluding gaard (1992) after excluding known nonmem-
cluster nonmembers. The only existing measurement of the bers.
abundanceofNGC 2516using high-resolutionspectroscopy bFrom Boesgaard (1989) and Boesgaard &
Friel (1990) after excluding known nonmem-
is from Terndrupet al. (2002)which was derivedfrom only
bers.
twostars. cStandarddeviationofthemeasurements.
Table6listsreddeningestimatesfromavarietyofsources.
For the Pleiades, we adopted a uniform reddening inferred
from individual E(B- V) corrections for 157 stars (Breger
fromthe HI hole measurementbyBreger(1986). Although
1986;Stauffer&Hartmann1987;Soderblometal.1993)with
smallpartsoftheclustershowhigherreddening(e.g.,Eggen
those from the uniform reddening, but the differences were
1950; Mitchell & Johnson 1957), the stars in these regions
negligibleinourMSfittingrange(§4.2).Thereddeningmea-
constitute only a small fraction of our Pleiades sample, and
surementsforthePleiadesfromotherstudiesinTable6likely
mostoftheseweretaggedasoutliersfromourfilteringalgo-
representaclusteraverageincludingtheCOcloudregion.
rithm (§ 4.1). We compared magnitudes and colors derived
9Standarderrorofthemean. 3. CALIBRATEDISOCHRONES
DistancesfromMainSequenceFitting. III 7
TABLE6
CLUSTERREDDENINGINTHELITERATURE
Reference Method E(B- V) s.e.m.
Praesepe
Mermilliod(1981a) UBV 0.00 0.01a
Nicolet(1981) Geneva 0.011 0.005
Nissen(1988) uvby–βb 0.007 0.002
Weightedmean ··· 0.007 0.002
··· ··· (0.003)c
Pleiades
Mermilliod(1981a) UBV 0.04 0.01a
Nicolet(1981) Geneva 0.062 0.005
Breger(1986)d Sp-type,uvby–βb 0.044 0.003
Nissen(1988) uvby–βb 0.039 0.005
Weightedmean ··· 0.046 0.005
··· ··· (0.009)c
Breger(1986)[adoptedvalue]e Sp-type,uvby–βb 0.032 0.003
M67
Taylor(1980) Multipleapproaches 0.046 0.006
Eggen(1981) uvby–βb 0.050 0.013
Janes&Smith(1984) DDO 0.056 0.006
Bursteinetal.(1986) BHmapf 0.035g 0.005
Nissenetal.(1987) uvby–βb 0.032 0.006
Hobbs&Thorburn(1991) Teff–(B- V)0 0.065 0.018
Montgomeryetal.(1993) UBV 0.05 0.01
Schlegeletal.(1998) Dustmap 0.032 0.005h
Weightedmean ··· 0.041 0.004
··· ··· (0.010)c
NGC2516
Eggen(1972) UBV 0.125 0.025
Feinsteinetal.(1973) Sp-type,UBV 0.116 0.004
Snowden(1975) uvby–βb 0.120 0.014
Mermilliod(1981a) UBV 0.11 0.01a
Nicolet(1981) Geneva 0.114 0.012
Eggen(1983) uvby–βb 0.118 0.004
Verschoor&vanGenderen(1983) VBLUW 0.127 0.005
Nissen(1988) uvby–βb 0.109 0.007
Dachs&Kabus(1989) Sp-type,UBV 0.12 0.004
Sungetal.(2002) UBV 0.112 0.006
Weightedmean ··· 0.117 0.002
··· ··· (0.005)c
aAssignedvalueinthispaper.
bE(B- V)=E(b- y)/0.74(Cousins&Caldwell1985).
cStandarddeviationofthemeasurements.
dAverageovertheclusterfield.
eAverageovertheHIhole(seetext).
fBurstein&Heiles(1982).
gCorrectedforthesystematicdifferencewithSchlegeletal.(1998)of0.02mag.
hQuotedprecision(16%).
WeusedtheYRECtoconstructstellarevolutionarytracks thatthecorrectiontableisvalidovertheentiremodelgridin
at- 0.3 [Fe/H] +0.2in0.1dexincrements.Ateachmetal [Fe/H]andage.
≤ ≤
abundance, we ran a grid of masses from 0.2 to 8 M in Theisochronesconstructedinthiswayareavailableonline.
⊙
0.05- 1M⊙ increments depending on the stellar mass. The 10
scaled solar abundancemix from Grevesse & Sauval (1998)
and the helium enrichment parameter ∆Y/∆Z = 1.2 from
non-diffusion models were used; see Sills et al. (2000) and 4. DISTANCESATFIXEDREDDENING
PaperIfordetailedinformation.Thetrackswereinterpolated We now proceed to derive the cluster distances, adopting
togeneratetheoreticalisochronesatstellaragesfrom20Myr the reddeningvaluesfromTable 6. We dothis in two ways,
to4Gyr. eitherholdingthemetallicityfixedatthespectroscopicvalues
Stellar luminosities and Teff were initially converted toV, (Table5)ordeterminingaphotometricmetallicitythatbrings
B- V,V- IC, andV- Ks fromthe relationsbyLejeuneetal. thedistancesfromdifferentCMDsintoagreement. Ineither
(1997,1998). Toobtainfinergridsoftheisochrones,we in- case, we showthatthecalibratedisochronesimprovethe in-
creased the MV spacing of the isochrone points using a cu- ternal precision of distance estimates from the three CMDs
bicsplinetomatchthe∆MV =0.05spacingofourtabulated withB- V,V- IC,andV- Ksascolorindices,andV asalumi-
color-TeffcorrectionsinPaperII.Wethenlinearlyinterpolated nosityindex;hereafter(B- V,V),(V- IC,V),and(V- Ks,V),
the isochronesin both [Fe/H] and age at a fixed MV. We fi- respectively.
nallyappliedtheempiricalcolorcorrections,asdefinedinPa-
perIIandupdatedintheAppendixofthispaper.Weassumed 10Seehttp://www.astronomy.ohio-state.edu/iso/.
8 Anetal.
4.1. PhotometricFiltering
Before fitting isochrones, we identified and removedstars
that are far from the MS in comparison to the sizes of
their photometric errors. Such stars could be either fore-
ground/backgroundobjects or cluster binaries that stand off
fromtheMS.
ThefilteringprocessiterativelyidentifiestheMSasthelo-
cus of points of maximum density on the CMDs, indepen-
dently of the isochrones. As an initial step, we identified
the MS by hand, and then removed stars more than 1 mag
away inV. This was necessaryin particularforthe analysis
in NGC 2516, which shows many faint background stars in
itsCMDs(seebelow)thatwouldcomplicatefindingtheden-
sity maxima. The generousrejectioncriterionof 1 mag was
chosenso thatallcluster binarieswouldbe preservedatthis
stage.
Ateachstepoftheiteration,datapointsoneachCMDwere
sorted by V magnitude into non-overlapping groups: each
group contained √N points, where N is the number of data
pointswithinacolorrangeusedinthefiltering. Themedian
colors in each group were computed, and then the resulting
runofpoints(V vs. color)wasmadeintoasmoothcurveby
averagingeachpointwiththelinearinterpolationofadjacent
points.
WiththeabovetrialMS,wecomputedχ2 fromeachCMD
as
N N (∆V)2
χ2= χ2= i , (1)
i σ2 +(γσ )2+σ2
i=1 i=1 V,i i c,i 0
X X
where∆V istheV differencebetweentheith datapointand
i
MSatthecolorofthestarandσV,i andσc,i arethephotomet- FIG. 4.—ResultofthefilteringprocessinPraesepe. Allknowncluster
ricerrorsinV andcolor,respectively. Theerrorinthecolor binarieswereincludedtotestthefilteringalgorithm. Theplussignsarere-
contributesto the error in ∆V by the slope of the curve, γ, jectedpointsfromthefiltering,andopencirclesarethoseremaining. Filled
i i circlesareknownbinariesthatremainedafterthefiltering.Starsbrighterthan
which was evaluated at the star’s color. Because the above V=7wereexcludedbeforethefilteringalgorithmwasapplied.
constructedcurvewouldnotpreciselytracetheobservedMS
in thepresenceof outliers, we addedσ inquadratureto the
0
propagated photometric errors in the denominator. We ad-
justed the value of σ so thatthe totalχ2 is equalto N. Ini- Figure 4 illustrates the result of the filtering algorithm in
0
tially,werejectedalldatapointsastheMSoutliersiftheχ2 Praesepe. Hereweincludeallknownclusterbinariesbutex-
i clude stars with a low membership probability (§ 2.4). We
(the individual contribution to χ2) is greater than 9 (corre-
used all three CMDs in the filtering, but only the (B- V,V)
spondingto a3 σ outlier). We repeatedadjustingσ andre-
0 diagram is shown. The plus signs are rejected points from
jectingoutlierswiththereducedsetofdatapointsuntilthere
the filtering, and open circles are those remaining. Some of
remained no point with χ2 greater than the above threshold
i thestars onthe MSwere rejectedbecausetheywere filtered
value. WecombinedtheresultsfromallthreeCMDsandre-
inotherCMDs. Althoughmanybinariesremainafterthefil-
jectedstarsiftheyweretaggedasanoutlierfromanyoneof
tering (filled circles), their proximity to the MS would have
theCMDs.
a minorimpacton the deriveddistance. The bias in the dis-
We imposed an additional condition for the conver-
tanceduetotheremainingbinariesisdiscussedin§6.2from
gence of the algorithm because cluster binaries and fore-
artificialclusterCMDtests.
ground/background stars are often substantial populations
near the MS. We compared the rms of ∆V with its median
i
ofallabsolutedeviations(MAD).TheMADofaquantityx 4.2. IsochroneFittingandthePhotometricMetallicity
i
isdefinedby Theclusterdistanceswerefoundbyfittingisochronesover
MAD=1.483median(x - median(x)), (2) a range of metallicity with the adopted age of each cluster
| i i | (§2.1). TheisochroneswerereddenedtotheE(B- V)values
where the correction factor 1.483 makes the estimator con- inTable6.Weadoptedareddeningprescriptionforthebroad-
sistent with the standard deviation for a normal distribution bandcolorsbyBesselletal.(1998),whohaveassumedtheex-
(Rousseeuw 1990). The MAD is a more robust estimator tinctionlawofMathis(1990).Theirreddeningformulaewere
of the dispersionthan the standarddeviationin the presence computed from ATLAS9 synthetic stellar photometry for a
of outliers. Therefore,we reducedthe size of the χ2 thresh- widerangeofT ,andincludecolor-dependentreddeningre-
i eff
oldvalueifthefractionaldifferencebetweenthermsandthe sultingfromshiftsintheeffectivewavelengthsofbroadband
MAD of ∆V is larger than 5%, assuming median(∆V)=0. filters. The Bessell et al. formulae give reddening and ex-
i i
We repeated the above filtering steps by constructing a new tinction values for E(B- V)=0.30, so we linearly rescaled
MScurvefromtheremainingdataset. themaccordingto theassumed clusterreddening. Thecolor
DistancesfromMainSequenceFitting. III 9
Terndrupetal.2002).Figure5showshowthisprocessworks
fortheHyades,ourcalibratingcluster. Theopencirclesdis-
play the derived distances as a function of isochrone metal-
licity in each of the three CMDs with E(B- V) = 0.000 at
an age of 550 Myr. The lines connecting these points are
least-squares fits, and the labels to the left of the lines indi-
catethecorrespondingcolorindex.Theslopeinthe(B- V,V)
is larger than in the other two CMDs, indicating a greater
sensitivity of the isochrone luminosity to the metal abun-
dance.Wedefine[M/H] astheweightedaverageofthetwo
E
metallicitiesatwhichthe(B- V,V)distanceagreeswiththat
from (V - I ,V) and from (V - K,V), respectively. For the
C s
HyadesinFigure5,wederivethephotometricmetallicityof
[M/H] =+0.13 0.02, which is naturally the same as the
E ±
originallyassumedvalueintheisochronecalibration.
With thisdefinitionof the photometricmetallicity, we can
derive two distances at the adopted reddening. The first of
FIG.5.—ExampleofdeterminingaphotometricmetallicityintheHyades. these, designated as (m- M)0,S, is the weighted average dis-
Opencircles arethedistances derived fromCMDswithB- V,V- IC,and tance modulus from the three CMDs at the spectroscopic
V- Ksasafunctionofisochronemetallicity.Thesolidlinesconnectingthese [Fe/H]. The second distance, (m- M) , is the value deter-
pointsareleast-squaresfits,andthelabelstotheleftofthelinesindicatethe 0,E
correspondingcolorindex. Anageof550MyrandE(B- V)=0.000were minedatthephotometricmetallicity,[M/H]E.
assumed.Thephotometricmetallicityisdefinedastheaverage[M/H]where
theB- VlinecrossestheV- ICandV- Kslines. 4.3. Results
transformation by Carpenter (2001)11 was used to compute Figures 6-9 display the CMDs for each cluster. For Prae-
the reddening in V - K . For zero-color stars, we found sepeandthePleiades,knownbinariesandnonmemberswere
s
R A /E(B- V)=3.26, R E(V- I )/E(B- V)=1.32, excluded before we applied the photometric filtering. Stars
V V VI C
and≡R E(V- K)/E(B- V)=≡2.91.Forstarsinthemiddle thatremainedafterthefilteringareshownasopenpoints,and
VK s
ofourM≡S-fittingrange, (B- V) =0.8, we foundR =3.44, the rejected stars are shown as plus signs. With the exten-
0 V
sivebinaryandmembershipinformation,theCMDsofPrae-
R =1.37,andR =3.04.
VI VK
sepe (Fig. 6) are dominated by single cluster members, and
Foragivenisochrone,wecomputedeachindividualstar’s
therearefewstarsrejectedbythephotometricfiltering. The
distancemodulus(µ), anddefinedtheclusterdistancemod-
i
CMDsofthePleiades(Fig.7)showthatthefilteringroutine
ulus in each CMD as the “unweighted” median of µ, i.e.,
i
(m- M) median(µ). We computedthefittingerrorinthe identifiedlikelyclusterbinarieseffectively.Thesinglecluster
0 i
≡ membersfromS04areshownintheCMDsofM67(Fig.8),
distancemodulusoneachCMDas
none of which were rejected by the filtering algorithm. The
σ(m- M)=max σphot,MAD(µi) , (3) CMDsofNGC2516(Fig.9)arefromJTH01andhavealarge
√N numberofforeground/backgroundstarsasexpectedinanarea
(cid:20) (cid:21)
survey(forclarity,thepointsizefortherejectedstarswasre-
whereNisthetotalnumberofdatapointsusedinthefit. Here
ducedontheCMDsascomparedtotheotherplots).
N Isochronesatthespectroscopicmetallicitiesareoverlaidas
1 1
= , (4) solidlinesineachfigure,andinmostcasestheyareinexcel-
σp2hot i=1 σV2,i+(γiσc,i)2 lentagreementwiththeobservedshapesoftheMS.Inpartic-
X ular,thematchtothePraesepeMS(Fig.6),whichhasanage
wherethesamenotationisusedasinequation(1)exceptthat
and metallicity nearly identical to the Hyades, is good over
γ is the isochrone slope at the color of the star. We further
i almost7maginV. Weinterpretthisagreementasindicating
computed a “weighted” mean and a “weighted” median of
that the Hyades-based corrections to the color-T relations
thedistancemodulus,anddiscussthedifferencebetweenthe eff
defined in Paper II apply to all clusters, or at least to those
threedistanceestimatesalongwithothersystematicerrorsin
withmetallicitiesnottoodifferentfromthatoftheHyades.
§6.1.
ThereareafewcasesinwhichthematchtotheMSshapeis
For a given set of [M/H], age, and E(B- V), we fit
notasgoodasitisinPraesepe. InthePleiades(Fig.7),stars
isochrones in (B- V,V), (V - IC,V), and (V - Ks,V) over withB- V &0.9areconsiderablybluerthantheisochronein
0.4≤(B- V)0 ≤1.3. This color range is where the Hyades (B- V,V),althoughnotintheothertwoCMDs. This“blueK
calibration is most reliable (Paper II). There were only a
dwarf”phenomenonwasdiscussedbyJones(1972),Landolt
few Hyades members blueward of the range, and the cool
(1979),andvanLeeuwenetal. (1987),andatgreaterlength
end was set by the magnitude limit of the Hipparcos mis-
by Stauffer et al. (2003), who attributed it to stellar temper-
sion. The range correspondsto 0.48 (V- I ) 1.48 and
C 0 ature inhomogeneities caused by cool spots and plage areas
0.98 (V- K) 3.16. For non-zer≤oreddening≤,the fitting
≤ s 0≤ inrapidlyrotatingyoungstars. FromtheJTH01photometry,
rangesweremadecorrespondinglyredder.
it would appear that NGC 2516, which is about 40% older
We define the photometric metallicity [M/H] as the one
E than the Pleiades, does not share this phenomenon with the
thatbringsdistancesfromthreeCMDs intostatistical agree-
Pleiades (see Fig. 9). However, we show in § 7.1 that the
ment (e.g., Pinsonneault et al. 1998; Stello & Nissen 2001;
usage of the S02 data comes to a different conclusion with
supporting evidence from stellar rotational velocities. The
11 Updated color transformations 2MASS All-Sky Data Release can be data in (V - I ,V) for all clusters are somewhat bluer than
foundat C
http://www.ipac.caltech.edu/2mass/releases/allsky/doc/sec6_4b.html. the isochrone redward ofV - IC 1.6; this indicates a pos-
≈
10 Anetal.
FIG. 6.—CMDsofPraesepe,afterexcludingknownbinariesandstarswithlowmembershipprobability. Plussignsarephotometricallyrejecteddatapoints
fromthefilteringalgorithm,andopencirclesarethoseremaining. Thesolidlinesareempiricallycalibratedisochroneswithspectroscopicmetallicity(Table5),
whichwereadjusted forthereddening withtheliterature value (Table6). Fitting ranges areshownas horizontal bars. Thearrow denotes thedirection of
reddeningvectors.
FIG.7.—SameasFig.6,butforthePleiades.AsdiscussedbyStaufferetal.(2003),thePleiadesKdwarfsarebluerthanthegivenisochronein(B- V,V),but
notintheothertwoCMDs(seetext).Thedistancemodulusin(B- V,V)wasderivedat0.4≤(B- V)0≤0.8asshownbytheshorterhorizontalbar.