2. Spatial Structure Evolution of Open Star Clusters W. P. Chen and J. W. Chen Graduate Institute of Astronomy National Central University IAU-APRM2002.7.03 Tokyo

3. Open Clusters What we have learned/taught in AST101: irregularly and sparsely shaped. How irregular are they anyway? IC 348 by 2MASS

4. Globular Clusters Stars concentrate progressively toward the center. The King model (1962) is understood as a combination of an isothermal sphere; i.e., dynamically relaxed in the inner part of the cluster, and tidal truncation by the Milky Way in the outer part. Surface brightness of M3 (Da Costa and Freeman, 1976)

5. King Model (1962) r c : core radius r t : tidal radius k  central number density

6. Structure of an Open Cluster The initial stellar distribution in a star cluster is dictated perhaps by the structure in the parental molecular cloud. (Initial) As the cluster evolves, the distribution is modified by gravitational interaction among member stars. (Internal) Eventually stellar evaporation and external disturbances --- Galactic tidal force, differential rotation, and collision with molecular clouds --- would dissolve the cluster. (External)

7. Spatial Structure by Star Counting in 2MASS Stellar density within concentric annuli Center too crowded to resolve by 2MASS; outer part follows well a King model Background uniform out to large angular extents K lim (3-  )=15.6 --- not deep enough to reach MS, for distant and old globular clusters Projected radial stellar density of a GC, M55

8. 2MASS 3-sigma limit

9. Open cluster NGC 2506 (1.9 Gyr; 3.3 kpc) mosaiced from 2MASS data

10. Sources toward NGC2506 and the surface density

12. Locations of sample galactic open clusters. http://www.ipac.caltech.edu/2mass/

13. Radial density profile of NGC 2506

14. Cumulative stellar density profiles for NGC 2506 (1.9 Gyr; 3.3 kpc) shows apparent evidence of mass segregation …… in contrast to that in M11 found by Mathieu (1984)

15. Stars in the young (5 Myr) star cluster IC 348 are centrally concentrated, and seem to segregate  star formation processes more than subsequent dynamic evolution

16. The old (9 Gyr) open cluster Berkeley 17 shows no evidence of mass segregation.

17. Clusterl,b  (Myr) N*N* M/M ⊙ D (kpc) R s (‘) R (pc)  re (Myr) τ/τ re Segr. Young NGC1893 174, -02 44983094.46.58.92910.01? IC348 160, -18 53222000.3216.51.6140.2Y Intermediate NGC1817 186, -13 8002361462.112.57.91396N? NGC2506 231, +10 1,9001,0386433.317.517.36053Y NGC2420 198, +20 2,2004502792.512.59.422310Y Old NGC6791 070, +11 8,0001,0956794.210.513.254315? Be17 176, -04 9,0003702292.59.57.114263N

18. Relaxation Time τ cross = R/V ; τ relax ~τ cross ． N cross N cross = 0.1 N / ln N τ evap ~ 100 τ relax R: radius V: velocity dispersion N: number of member stars

19. NGC 1893 --- 4 Myr

20. IC 348 --- 5 Myr

21. NGC1817 --- 800 Myr

22. NGC 6791 --- 8,000 Myr

23. Be 17 --- 9,000 Myr

24. Summary 2MASS good for study of open clusters - Full data release expected end of 2002 - Deep IR images to differentiate the MS (IR camera with Nagoya U & PMO) Stars in an open cluster, regardless of masses, are concentrated progressively toward the center. The youngest star clusters show evidence of luminosity (mass) segregation - cf. molecular cloud structure (SMA)

25. Summary --- II By a few Gyr (several relaxation times), clusters become highly relaxed, until dynamical disruptions dominate. Tidal distortions (age, location, massive vs low-mass stars)  Open clusters (scattering around the galactic disk) as probes of galactic mass distribution e.g., disk vs volume potential - galactic disk and (dark) halo models

26. Our knowledge, or even recognition, of galactic open clusters is highly incomplete, most biased toward the ones that are nearby and with bright stars.

27. Open clusters are distributed widely around the galactic disk.

28. Open Cluster Study at NCU Luminosity Function Evolution  age and star formation history (e.g., coeval vs periodic bursts) done Structural Evolution  dynamics  probing galactic mass distribution (e.g., disk vs volume potential) ½ done Variability and [rotation vs magnetic activity] doing

29. Open Clusters/NCU --- cont. Lulin 1 m telescope (Taiwan) August 2002 Maidanak Observatory (Uzbekistan) 1.5 m and 1 m Moletai Obs. 1.65 m (Lithuania) YALO 1 m (Chile) Imaging plus CORAVEL high- resolution spectroscopy Kentucky-Yunnan-Taiwan Telescope (KYTT) to lift off by 2004-2005?

30. Fast rotating stars P(rot) < 12 d (BLUE) are distinguished from slow rotators (RED) by their X-ray luminosity (normalized to solar – in yellow. The Rossby number gives the rotation period in units of the eddy's lifetime. (http://www.aip.de/groups/turbulence/star_t.html)