1. Star Clusters Ay 16 Lecture 11 March 6, 2008

2. Star Clusters Types Distances (Space Motions, Parallax ++) Dynamics Relaxation Masses (Virial Theorem) Stellar Populations HR Diagrams Pop I and II

3. Star Clusters Four Basic Types: Globular (round & bound) Open (irregular & bound) Association (irregular, not bound) HII Region (very young, irregular) (  other young eg. GMC clusters)

4.  Cen

5. G1

6. Palomar 1

8. NGC 188

9. h &  Per

10. CYG OB2

11. ORION Trapezium

12. NGC2237

13. M87 David Malin AAT Globulars (15-20,000)

14. Spatial Distribution of Globular Clusters

15. Distribution of HII Regions in The Milky Way

16. M31 UV

18. Stars Move…. v = total velocity v R = radial vel v T = tangential velocity v T = v sin  tan  = v T /v R

19. Proper Motion  (radians/s) = v T (km/s)/d(km) but radians/sec is a “bad” unit, never mind km! So convert km/s to parsecs/yr and radians to arcsec: multiply by 3.156x10 7 s/yr / 3.086x10 13 km/pc and by 206265”/radian v T = 4.74  (arcsec/yr) d(pc) or d = v T /4.74  or, if we know , d = v R tan  / 4.74 

20. Moving Cluster Method Compare the proper motion of a cluster with the rate at which its size changes. Clusters appear to be heading towards particular points on the sky.

21. We need the radial velocity, vr, the proper motion, , and the angle to the convergent point, .

22. Today --- Hipparcos High Precision Parallax Collecting Satellite 2.4 million stars measured, ~118,000 with high precison parallaxes better than 0.001 arcsec Hyades distance = 46.34 +/- 0.27 pc ESA 1993

23. Also, get distances from HR diagrams. Magnitudes --> apparent luminosity is proportional to 1/d2 Color is essentially distance independent (except when dust gets in the way) So --- slide HR diagrams for similar clusters to get offset between a cluster of a known distance and an unknown.

24. Cluster Timescales Stars still move! How fast/long? Cluster dynamics can be described in terms of two important parameters:

25. Timescales: Size r (pc) Stellar Velocity or velocity dispersion (the distribution of velocities w.r.t. the cluster mean)  (km/s) Simplest time scale = crossing time t C = r/  = 10 6 years r(in pc)/  ( in km/s)

26. Relaxation Time t r = relaxation time, = time to establish dynamical equilibrium Estimate by “collision” time for stars in the cluster. If n = the stellar density v = average stellar velocity r = “impact parameter” By geometry n (  r 2 ) v t r = 1  t r = 1/n  r 2 v

27. The Virial Theorem For a “relaxed” system, i.e. one that is (1)bound, time invariant on average (2)With well defined kinetic and potential energies = -1/2

29. HR Diagrams Ejnar Hertzsprung & Henry Norris Russell 1906/1913 Studied star clusters and nearby stars

33. HR Diagrams Complete Color-Magnutide diagrams can give you cluster distances cluster ages cluster metallicities