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Mem.S.A.It.Vol.87,610 (cid:13)c SAIt 2008 Memoriedella HST proper motions in Galactic globular clusters L.L.Watkins1,4, R.P.vanderMarel1,A.Bellini1,A.T.Baldwin1,2,P.Bianchini3,andJ.Anderson1 7 1 1 SpaceTelescopeScienceInstitute,3700SanMartinDrive,BaltimoreMD21218,USA 0 2 Dept.ofPhysics&Astronomy,LouisianaStateUniv.,BatonRouge,LA70803,USA 2 3 MaxPlanckInstituteforAstronomy,Ko¨nigstuhl17,D-69117Heidelberg,Germany 4 e-mail:[email protected] n a J Abstract.Propermotions(PMs)arecrucialtofullyunderstandtheinternaldynamicsof 7 globular clusters (GCs). To that end, the Hubble Space Telescope (HST) Proper Motion 2 (HSTPROMO) collaboration has constructed large, high-quality PM catalogues for 22 GalacticGCs.Wehighlightsomeofourexcitingrecentresults:thefirstdirectly-measured ] A radial anisotropy profiles for a large sample of GCs; the first dynamical distance and mass-to-light(M/L)ratioestimatesforalargesampleofGCs;andthefirstdynamically- G determinedmassesforhundredsofblue-stragglerstars(BSSs)acrossalargeGCsample. . h Key words. globular clusters: general – proper motions – stars: blue stragglers – stars: p distances–stars:kinematicsanddynamics–stars:luminosityfunction,massfunction - o r t s 1. Introduction ityanisotropyprofiles;2)dynamicaldistances a andM/Ls;and3)massesoftheirBSSpopula- [ The HSTPROMO collaboration is using PMs tions.Herewebrieflyhighlighttheresultsfrom 1 to revolutionise our dynamical understanding eachstudy. v of many objects in the universe – includ- 6 ing stars in globular and young star clusters; 6 Local Group galaxies, including Andromeda, 2. Velocityanisotropy 1 theMagellanicCloudsandanumberofdwarf Dynamicalmassestimatesaredegeneratewith 8 0 spheroidals; and even AGN black hole jets – anisotropy,sounderstandingtheanisotropyin . thankstotheexquisiteastrometricprecisionof a stellar system is crucial to successful mass 1 HST (vanderMareletal.,2014).1 determination. 0 Aspartofthisongoingwork,Bellinietal. In Watkins et al. (2015a), we began by 7 (2014)recentlypresentedasetofinternalPM making a series of cuts to select high-quality 1 : catalogues for 22 Galactic GCs, measured us- samplesofbrightstars.Byrestrictingthemag- v ing archival data from HST. In Watkins et al. nituderangeofthesamplestoonlythosestars i X (2015a), Watkins et al. (2015b), and Baldwin brighter than 1 mag below the main-sequence etal.(2016),weusedthesecataloguestostudy turn off (MSTO), we limited the stellar-mass r a 3differentaspectsoftheGCsample:1)veloc- rangeineachsample,andsocouldneglectthe effect of stellar mass on the kinematics and 1 http://www.stsci.edu/∼marel/hstpromo.html consider only the spatial changes. The quality Watkins:HSTpropermotionsinGalacticGCs 611 fit 1/10Rhalf Rcore Rhalf 1.05 1.6 1.00 1.4 1.2 σr0.95 /σr1.0 σ/t σt 0.90 0.8 0.6 0.85 core 0.4 NGC2808 half-light 101 102 105 106 107 108 109 1010 R[arcsec] trelax[yr] Fig.1. Velocity anisotropy as a function of Fig.2. Velocity anisotropy as a function of relax- projected distance from the cluster centre for ationtimeforallGCsinoursample.Thered(blue) NGC2808. The black points show the binned ve- points show the values estimated at the core (half- locity anisotropy profile and the blue lines show a light)radius.TheGCsareisotropicinregionswith simple fit. The red (green, orange) line marks the relaxation times shorter than a characteristic time half-light(core,one-tenthofthehalf-light)radius. (dashedline)andthenbecomeincreasinglyradially anisotropicwithincreasingrelaxationtime. cutsweremadetoeliminatestarsforwhichthe 3. Dynamicaldistancesand PMs were poorly measured or for which the mass-to-lightratios uncertaintieshadbeenunderestimatedassuch starscanintroducebiasesintokinematicanal- GC distances are typically estimated using yses.Wethenconstructedbinnedvelocitydis- photometric methods that compare the appar- persionandanisotropyprofilesforeachGC. entandabsolutemagnitudesofstarsforwhich Figure1showsthebinnedanisotropypro- theabsolutemagnitudesareknownormaybe file for NGC2808 (black points). This GC is inferred, such as RR Lyrae stars. M/Ls are isotropicatitscentreandbecomesmildlyradi- typically inferred from via stellar population ally anisotropic with increasing distance from synthesis(SPS)modelling.However,bothdis- the centre. This trend is typical for all GCs tances and M/Ls can be estimated using dy- in our sample; to quantify this, we used the namicalmodellingwhenbothPMandline-of- fits (blue lines) to estimate the anisotropy at sight(LOS)velocitydataexist.Thephotomet- the core and half-light radii (green and red ric and dynamical methods use very different lines) and compared these values to estimates typesofdatatoconstrainthesamefundamen- of the relaxation times at these radii (Harris, talproperties,sotheircomparisoncanserveas 1996, 2010 edition). Figure 2 shows the re- acrucialtestofbothmethods. sultsofthiscomparison.NearlyallGCsappear InWatkinsetal.(2015b),weusedcleaned to be isotropic out to their core radii; there- samples of bright stars to construct PM ve- after, some remain isotropic out to their half- locity dispersion profiles and then compared lightradii,whileothersbecomemildlyradially these against LOS velocity dispersion profiles anisotropic, with the degree of anisotropy in- fromtheliterature.Thiswasonlypossiblefor creasing with relaxation time. The black lines 15 of the 22 GCs, the remaining GCs had showafittothedatawithabreakbetweenthe insufficient (or even no) LOS data available. isotropicandanisotropicregionsatthecharac- From this analysis, we estimated dynamical teristictimemarkedbythedashedline. distances and M/Ls for each GC, which we This analysis offers a way to estimate the compared against photometric distances from vital anisotropy of a GC using its relaxation Harris (1996, 2010 edition) and SPS M/Ls time,whennoPMdataisavailable. fromMcLaughlin&vanderMarel(2005). 612 Watkins:HSTpropermotionsinGalacticGCs 0.6 8.8 6.4% Strader+(2011) Laughlin 0.4 − ± 4 McLaugHhSliTnP+R(2O0M05O) Mc Υ)/ΥMcLaughlin−000...202 Υ[M/L]V(cid:12)(cid:12)23 − Υour−0.4 1 ( −0.6 0 0.15 0.10 0.05 0.00 0.05 0.10 0.15 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.5 − − − − − − − − − (Dour−DHarris)/DHarris [Fe/H][dex] Fig.3.Fractionaldifferencebetweenthedynamical Fig.4. M/L estimates as a function of metallicity. and photometric distances versus fractional differ- Blue points show our dynamical M/Ls and green ence between the dynamical and SPS M/Ls. Both pointsshowSPSM/Ls.TheSPSmodelspredictan the distances and the M/Ls show pleasing agree- upturninM/Lformetal-richGCs,whereasourdy- ment,highlightingtherobustnessofbothdynamical namicalM/Lspredictadownturn.Thisbehaviouris andphotometricmethods. consistentwithastudyof200M31GCsbyStrader etal.(2011)(blackpoints). Figure3showsthefractionaldifferencein the dynamical and photometric distances ver- ergy.Asaresult,highmassstarstendtomove sus the fractional difference in the dynamical more slowly than low mass stars; this is true andSPSM/Ls.Themeandifferenceinthedis- even if the GC is only in partial equipartition. tanceswasjust−1.7±1.9%,indicatingexcel- This effect can be expressed as σ ∝ M−η (1), lentagreementandhighlightingtherobustness where σ is the velocity dispersion of a stellar of both methods. The mean difference in the populationofmassM,and0≤η≤0.5quanti- M/Lswas−8.8±6.4%,showingslightlymore fiesthedegreeofequipartitionintheGC. scatterbutstillconsistentwithin1.3σ. BSSs are an apparent extension of the Figure 4 shows the M/Ls as a function of main-sequenceinaGC,bluerandbrighterthan GC metallicity Harris (1996, 2010 edition). theMSTO.MoststarsbrighterthantheMSTO Our dynamical M/Ls are shown in blue and inaGCareevolvedstars,withapproximately theSPSM/Lsareshowningreen.Weseethat equalmassesasthelatterstagesofstellarevo- the dynamical and SPS M/Ls are consistent lutionaresofast.However,BSSsarebelieved forthemetal-poorGCs([Fe/H]< −1dex),but tohaveformedviamass-transferorstellarcol- that they diverge for the metal-rich GCs: the lisions within a binary system, thus making SPSM/Lsincreasewithincreasingmetallicity, them a more massive population. So, as a re- whereasthedynamicalM/Lsdecrease.Thisis sult of equipartition in a GC, we expect them consistentwiththebehaviournotedinastudy tobemovingmoreslowly. of200M31GCsbyStraderetal.(2011)(black In Baldwin et al. (2016), we used a series points)andhasbeenattributedtotheeffectsof of colour and magnitude cuts to select sam- masssegregation(Shanahan&Gieles,2015). ples of BSSs in 19 of our 22 GCs, finding 598 BSSs in total. We then calculated binned velocity dispersion profiles for the BSS sub- 4. Blue-stragglerkinematicsand samples and for the evolved stars. Figure 5 dynamicalmassestimates shows the colour-magnitude diagram (CMD) Frequent two-body stellar interactions in GCs for NGC6341; the box shows the cuts used allowthestarstoexchangeenergy;overtime, toselecttheBSSs(bluediamonds).Theblack the stars move towards a state of energy points show the evolved stars and the red di- equipartition,wheretheyallhavethesameen- amond marks the MSTO. Figure 6 shows the Watkins:HSTpropermotionsinGalacticGCs 613 14 NGC 6341 BSS MCMC Chain All Bright Stars 0.25 Bright Star Best Fit Blue Stragglers 15 BSS Best Fit r) y 0.20 W 16 s/ F814 ma m 17 (σ 0.15 18 BSS 0.10 BSS Selection Cuts NGC 6341 19 MSTO 20 40 60 80 100 0.2 0.0 0.2 0.4 0.6 m m R (arcsec) F606W− F814W Fig.5. CMD for NGC6341. The BSSs are shown Fig.6. Binned PM dispersion profiles for asbluediamondsandtheboxshowsthecutsmade NGC6341. The orange points show the profile toselectthem.Theblackpointsshowtheevolved- for the evolved-stars and the orange line shows a starsample,andthereddiamondmarkstheMSTO. fit to the points. The black points show the profile fortheBSSs;theblacklineisabestfittotheBSS profilethatisassumedtobeascaledversionofthe orangeline,thebluelinesshowthescatterinthefit. dispersionprofilesfortheBSSs(black)andthe evolvedstars(orange)inNGC6341. Onaverage,wefoundthattheBSSdisper- Acknowledgements. Supportforthisworkwaspro- sionswerelowerthantheevolved-stardisper- vided by grants for HST programs AR-12845 (PI: sions,indicatingthattheBSSsareindeedmore Bellini) and AR-12648 (PI: van der Marel), pro- massive. Furthermore, by estimating the de- vided by the Space Telescope Science Institute, whichisoperatedbyAURA,Inc.,underNASAcon- greeofequipartitionineachGCfromtheseries tractNAS5-26555. of N-body simulations presented in Bianchini etal.(2016),wewereabletouseequation(1) toestimatetheaverageBSSmassMBSSineach References GC as a function of the MSTO mass M . MSTO Then by estimating the MSTO mass in each Baldwin,A.T.,Watkins,L.L.,vanderMarel, GC,wewerethusabletoestimatethemassof R.P.,etal.2016,ArXive-prints eachBSSpopulation.Wefoundanmassratio Bellini,A.,Anderson,J.,vanderMarel,R.P., of M /M = 1.50±0.14andanaverage etal.2014,ApJ,797,115 BSS MSTO mass M = 1.22±0.12 M , ingood agree- Bianchini, P., van de Ven, G., Norris, M. A., BSS (cid:12) mentwithpreviousBSSmassestimates. Schinnerer, E., & Varri, A. L. 2016, MNRAS,458,3644 Harris,W.E.1996,AJ,112,1487 5. Conclusions McLaughlin, D. E., & van der Marel, R. P. 2005,ApJS,161,304 PMs are crucial to fully understand the in- Shanahan,R.L.,&Gieles,M.2015,MNRAS, ternal dynamics of GCs. To that end, the 448,L94 HSTPROMO collaboration has constructed Strader, J., Caldwell, N., & Seth, A. C. 2011, large, high-quality PM catalogues for 22 AJ,142,8 GalacticGCs.Wehighlightedsomeofourex- vanderMarel,R.P.,Anderson,J.,Bellini,A., citingrecentresults:thefirstdirectly-measured et al. 2014, in Astronomical Society of the radialanisotropyprofilesforalargesampleof PacificConferenceSeries,Vol.480,,43 GCs;thefirstdynamicaldistanceandM/Les- Watkins, L. L., van der Marel, R. P., Bellini, timatesforalargesampleofGCs;andthefirst A.,&Anderson,J.2015a,ApJ,803,29 dynamically-determined masses for hundreds —.2015b,ApJ,812,149 ofBSSsacrossalargeGCsample.