Table Of ContentMem.S.A.It.Vol.1,1
(cid:13)c SAIt 2008 Memoriedella
HST Proper Motions of Stars within Globular
Clusters
A.Bellini1,R.P.vanderMarel1,andJ.Anderson1
3
1
0 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD, 21218, USA
2 e-mail:[email protected]
n
a
J Abstract. The stableenvironment of space makes HST anexcellent astrometrictool. Its
0 diffraction-limitedresolutionallowsittodistinguishandmeasurepositionsandfluxesfor
1 starsallthewaytothecenterofmostglobularclusters.Apartfromsmallchangesdueto
breathing, its PSFsand geometric distortion have been extremely stable over its 20-year
] lifetime.Therearenowover20globularclustersforwhichthereexisttwoormorewell-
R separatedepochsinthearchive,spanningupto10+years.Ourphotometricandastrometric
S techniques have allowed us to measure tens of thousands of stars per cluster within one
. arcminfromthecenter,withtypicalproper-motionerrorsof∼0.02mas/yr,whichtranslates
h to∼0.8km/sforatypicalcluster.Thesehigh-qualitymeasurementscanbeusedtodetect
p thepossiblepresenceofacentralintermediate-massblack hole,andputconstraintsonits
- mass. In addition, they will provide a direct measurement of the cluster anisotropy and
o
equipartition. We present preliminary results from this project, and discuss them in the
r
t contextofwhatisalreadyknownfromothertechniques.
s
a
[ Keywords.Astrometry:propermotions–Stars:PopulationII–Galaxy:globularclusters
1
v
1. Introduction Although the stable environmentof space
8
3 offersunsurpassedimagequalityandstability,
We measured high-precision proper motions
3 reaching high-precision astrometry (and pho-
(PMs) in the cores of 23 globular clusters
2 tometry)requiresacarefultreatmentofpossi-
(GCs) forwhich goodHST data exist. We fo-
. ble systematic effects: undersampling, space-
1 cusedourattentiononACS/WFC,ACS/HRC,
0 and WFC3/UVIS exposures, which provide and time-variable PSF models, geometric-
3 distortion corrections, charge-transfer ineffi-
smallerpixelsizes,higherstabilityofthegeo-
1 ciency, and transformations between dithered
metricdistortionsolution,andhigherdynamic
: images. All these issues have been properly
v range than other HST detectors. The biggest
addressed by our group, and we are working
i step forward provided by our velocity mea-
X in further improving our solutions (Anderson
surements will be the large number of PMs
r & King 2006a,2006b,Bellini & Bedin 2009;
a within the crowdedcore of each cluster, from Anderson&Bedin2010;Bellini,Anderson&
the tip of the red-giant branch down to faint
Bedin2011).
main-sequence stars. The time baseline for
Weconsidereachexposureasrepresenting
theseclustersgoesfrom2upto10years.
a stand-aloneepoch,and transformedstar po-
Sendoffprintrequeststo:A.Bellini sitions from each exposureonto the reference
2 Bellini:HST propermotionsofglobularclusters
Table1
AnalyzedClustersandPMcatalogssize
Cluster Nsources Cluster Nsources
NGC104 106000 NGC6388 37000
NGC288 15000 NGC6397 14000
NGC362 74000 NGC6441 57000
NGC1851 88000 NGC6535 4000
NGC2808 17000 NGC6624 2000
NGC5139 293000 NGC6656 54000
NGC5904 71000 NGC6681 28000
NGC5927 63000 NGC6715 74000
NGC6121 9000 NGC6752 47000
NGC6266 57000 NGC7078 76000
NGC6341 84000 NGC7099 2000
NGC6362 8700
Fig.1. Top panels: proper-motion diagrams in the
core of the GC NGC 6681. From left to right: all
measuredsources(redcrossesmarkthelocationof
frame (usually the GC treasury catalogs from
2 galaxies in the field); selected cluster members,
Sarajedinietal.2007).Then,foreachstarwe
selectedSgrdSphmembers,andfieldstars.Bottom
fit the two position components as a function panels:CMDsforallsources,GCmembers(black),
of the epoch, assuming linear motion. We it- SgrdSphmembers(azure),andfieldstars(yellow).
eratively rejected the most extreme point if it
isnotinagreementwiththetrendtowithinits
expectederror. – internal motions: to study kinematics and
Inthefollowing,wewillgiveanintroduc- dynamicsofGCs;
tory view of the project, anticipated scientific – multiple-populations individual kinemat-
results,andsomeexamples. ics/dynamics: to look for fossil signatures
ofadifferentformationprocess;
– Absolute motions: e.g., using background
2. Thecatalogs
galaxiesorfieldstarsasareference;
Table 1 lists analyzed clusters and the num- – geometricdistance:bycomparingtheline-
ber of objects for which we measured high- of-sightvelocitydispersionwiththatonthe
precision proper motions. The field-of-view planeofthesky;
variesfromclustertocluster,dependingonthe – GCsrotationontheplaneofthesky:from
detector used and the overlap among epochs. ameasureofthestellarvelocitiesasafunc-
The proper motion accuracy is of the order tion of position angle in different radial
of 0.8 km/s for well-exposed stars at a typi- bins;
calclusterdistance,assuminganaveragetime – Equipartition: from the analysis of stars’
baseline.ThesePMmeasurementsarestillpre- velocity dispersion as a function of the
liminary,andweareintheprocessoffinetun- theirmass;
ingourtechniquestofurtherimprovethemand – radialmassdistribution:bystudyingstars’
minimizepossiblesourceofsystematics. velocity dispersion as a function of their
distancefromtheclustercenter;
– (an)isotropy:by comparingtangentialand
2.1.Anticipatedscienceresults radialcomponentsofstars’motion;
– full3Ddynamics:incasealsoline-of-sight
High-precisionpropermotionsinGCsallowus
velocitiesareknown;
to undertake quite a large variety of scientific
– constraints on the presence of an
investigations.Tonameafew:
intermediate-mass black hole: looking
– cluster-fieldseparation:inordertostudya both for fast-moving individual stars
bona-fidesampleofclustermembers; and for an increase in central velocity-
Bellini:HST propermotionsofglobularclusters 3
Below, we will show a few examples of
what can be done with high-precision proper
motions.
2.2.Absolutepropermotions
Figure 1 shows proper-motion diagrams (on
top)andthecorrespondingCMDs(onbottom)
for NGC 6681. It is clear from the figure that
wecan:(i)clearlyseparateclustermembers(in
black) from field stars (in yellow); (ii) isolate
Sgr dSph stars (in azure) in the background;
and(iii)resolvetheinternalmotionoftheclus-
ter(becausethestellardispersionintheproper
motion diagrams is far largerthan that of Sgr
dSph stars, which in turn reflects our internal
proper motion errors). We quickly identified
by eye two galaxies with sharp nuclei in our
images, and marked theirposition on the top-
left panel, with red crosses. Their average lo-
cation on the proper-motion diagram can be
used to define the zero-point of the absolute
motion of cluster, field (and in turn, constrain
theGalaxypotential),andSgrdSphstarsinthe
Fig.2.Velocity-dispersionanalysisforNGC6752. background.
Top panels show the selection of main-sequence
starsinbinsofmagnitude(left)andradialdistance
fromtheclustercenter(right).Inthebottompanels, 2.3.Masssegregationandequipartition
foreachradialintervalweplottheaveragevelocity
dispersionasafunctionofthemagnitude. Thanks to the extended field-of-view (up to
∼100 arcsec or more) of most of the clus-
ters(typicallybeyondthehalf-lightradius),the
availability of high-precisionPMs evenin the
denseclusterscore,and,mostimportantly,the
factthatwe can now measurekinematicsasa
functionof the positionon the mainsequence
(stellar mass), for the first time we have the
possibilitytodirectlystudyindetailthedegree
of equipartitionof each cluster(bymeasuring
atthesametimestars’velocityandmass),us-
ingthousandsofstarsandtwocomponentsof
themotion.
Fig.3.hσ iasafunctionoftheradialdistancefor Figure2illustratesthecaseforNGC6752.
V
allNGC6752starsinthefield. The top panels show the main sequence of
thecluster(whichwedividedinto15equally-
populatedmagnitudebins,ontheleft),andthe
total field-of-view (divided into 8 radial in-
dispersion-profile (van der Marel & tervals, on the right). The eight panels below
Anderson2010); show, for each radialinterval, the average ve-
– etc... locity dispersion hσ i within each magnitude
V
4 Bellini:HST propermotionsofglobularclusters
bin.Wecaneasilysee,fromthefigure,thatin-
ner stars move, on average, faster than outer
ones.Moreover,moremassivestarsareslower
than less massive ones. In Figure 3 we ex-
tended our analysis to all stars, regardless of
theirevolutionarystage,andplottheirhσ ias
V
a function of the logarithmic radial distance
from the cluster center. The distribution ap-
pears, within the errors, to be flat inside ∼3
coreradii,thenitdropssteeply.
One way to infer whether a cluster has
reached equipartition is to measure the slope
of the average velocity dispersion vs. stellar
mass in the log-log plane: a value of −0.5
wouldmean thattheclusteris in fullequipar-
tition. On the other hand, a flat slope implies
no equipartition at all. In Figure 4 we show
Fig.4. Average velocity dispersion vs. Mass fora
thisslopeforasampleofeightGCs. Thepre-
sampleof8clusters,inthelog-logplane.Thescale
liminary slopeswe measuredrange fromzero
ratiooftheaxesisthesameinallpanels.Itisclear
to−0.5,andsuggestthattheparadigmthatall
thatthepower-lawrelationbetweenaverageveloc-
GCs have reachedequipartitionlongago may
itydispersionandstellarmassdoesnothaveauni-
notbevalid. versalslope.
3. Conclusions
Bellini, A., & Bedin, L. R. 2009, PASP, 121,
Our preliminary results clearly demonstrate 1419
the power of high-precision proper motions Bellini,A.,Anderson,J.,&Bedin,L.R.2011,
of globular clusters. Many scientific applica- PASP,123,622
tions will benefit from this project. Once our Sarajedini, A., Bedin, L. R., Chaboyer, B., et
analysis has been completed, we will make al.2007,AJ,133,1658
our proper-motion catalogs available to the vanderMarel,R.P.,&Anderson,J.2010,ApJ,
astronomical community, with photometry in 710,1063
the available filters. Moreover, we will pro-
ducestackedimagesofthefieldswithaccurate
WCS headers, so that users can easily cross-
identify stars in our catalogs with other sur-
veys.
Acknowledgements. A.B., R.P.vdM, and J.A. ac-
knowledge support from STScI grants GO-11988,
GO-12274,GO12656,andGO-12845.
References
Anderson, J., & King, I. R. 2006a, ACS/ISR
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Anderson, J., & King, I. R. 2006b, ACS/ISR
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Anderson,J.,&Bedin,L.R.2010,PASP.122.
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