1. Internal motions in star clusters Gordon Drukier Dept. of Astronomy, Yale University Yale Astrometry Workshop — 21 July 2005 Gordon Drukier Dept. of Astronomy, Yale University Yale Astrometry Workshop — 21 July 2005

2. Why? Kinematics: Velocity structure of the cluster Mass distribution Distance Dynamics Kinematics: Velocity structure of the cluster Mass distribution Distance Dynamics

3. Planning the observations e: proper motion error (km/s) a: centering accuracy (pixels) r: plate scale (mas/pixel) d: distance (kpc) t: time baseline (years) N: Number of frame pairs e: proper motion error (km/s) a: centering accuracy (pixels) r: plate scale (mas/pixel) d: distance (kpc) t: time baseline (years) N: Number of frame pairs e=4.74√2 ard/t√N Example: ACS/HRC a=0.03 r=27 mas/pixel, N=20 e= σ 0 /3 NGC 6752 d=4kpc, σ 0 =12 km/s t=1.2 years NGC 6388 d=10kpc, σ 0 =19 km/s t=2 years M71 d=4kpc, σ 0 =2 km/s t=7 years Example: ACS/HRC a=0.03 r=27 mas/pixel, N=20 e= σ 0 /3 NGC 6752 d=4kpc, σ 0 =12 km/s t=1.2 years NGC 6388 d=10kpc, σ 0 =19 km/s t=2 years M71 d=4kpc, σ 0 =2 km/s t=7 years Now, assuming you have some proper motions, what can you do with them?

4. [King et al. (1998)] NGC 6397: HST/WFPC2 32 mo. baseline

5. [King et al. (1998)] NGC 6397: HST/WFPC2 32 mo. baseline

6. Members Non-members [Richer et al. (2004)] M4: HST/WFPC2 6 year baseline M4: HST/WFPC2 6 year baseline White dwarf sequence! Bottom of the main sequence

7. M4: HST/WFPC2, 5 years [Bedin et al. (2003)] M4 Galactic bulge QSO

8. Absolute proper motion & Galactic rotation constant [Bedin et al. (2003)] A - B = V0/R0 = 27.6 ± 1.7 km s-1 kpc-1

9. [Anderson & King (2003)] 47 Tuc: HST/WFPC2 5 yr baseline SMC

10. [Anderson & King (2003)] SMC motion with respect to 47 Tuc

11. [Anderson & King (2003)] core radius SMC with respect to 47 Tuc Relative motion in RA, -4.716 ± 0.035 mas yr-1; Relative motion in declination, -1.357 ± 0.021 mas yr-1; Absolute motion in RA, 5.64 ± 0.20 mas yr-1; Absolute motion in declination, -2.05 ± 0.20 mas yr-1; Rotational proper motion, 0.233 ± 0.055 mas yr-1. SMC with respect to 47 Tuc Relative motion in RA, -4.716 ± 0.035 mas yr-1; Relative motion in declination, -1.357 ± 0.021 mas yr-1; Absolute motion in RA, 5.64 ± 0.20 mas yr-1; Absolute motion in declination, -2.05 ± 0.20 mas yr-1; Rotational proper motion, 0.233 ± 0.055 mas yr-1.

12. [van Leeuwen et al. (2000)] ω Cen: Yale-Columbia 26”, 239 year effective baseline

13. [van Leeuwen et al. (2000)] ω Cen: Yale-Columbia 26”, 239 year effective baseline

14. μrμr μrμr μtμt μtμt

15. Radial & Tangential proper motion profile

16. Velocity Dispersion Profile

18. Anisotropy?

19. [McNamara et al. (2003)] M15: HST/WFPC2 8 year baseline Lines are at ± 1mas/year

20. M15 [Gerrsen et al. (2003)] [McNamara et al. (2003)]

21. M15 [Gerrsen et al. (2003)] [McNamara et al. (2003)]

22. [Drukier et al. (2003)] NGC 6752: HST/WFPC2 5 yr baseline Error Median:0.31 mas/yr Mode: 0.17 mas/yr Error Median:0.31 mas/yr Mode: 0.17 mas/yr

23. [Drukier et al. (2003)] NGC 6752: HST/WFPC2 5 year baseline

24. Velocity Dispersion Profile C.f. 3.5 to 6.3 km/s central radial velocity dispersion from the integrated spectrum [Dubath et al. (1997)] ⇒ (M/L) V ~ 9(M/L) ☉

25. Have a good evening.