1. Julio Chanamé 10/March/2009 On the Full Exploitation of Discrete Velocity Data: Motivation, Method, and some Applications

2. Julio Chanamé 10/March/2009 A new implementation of Schwarzschild’s method Jan Kleyna Roeland van der Marel On the Full Exploitation of Discrete Velocity Data: Motivation, Method, and some Applications

3. Julio Chanamé 10/March/2009 A new implementation of Schwarzschild’s method dwarf elliptical galaxies in the Local Group dynamics of Galactic globular clusters Jan Kleyna Roeland van der Marel Marla Geha Raja Guhathakurta Justice Bruursema Rupali Chandar Jay Anderson Holland Ford On the Full Exploitation of Discrete Velocity Data: Motivation, Method, and some Applications

4. Mass distribution underlying stellar systems dark halos massive black holes structure formation Detailed dynamical studies

5. ** Detailed ** dynamical studies Mass distribution underlying stellar systems dark halos massive black holes structure formation β = 1 – (σ θ /σ r ) 2

6. ** Detailed ** dynamical studies Mass distribution underlying stellar systems dark halos massive black holes structure formation β = 1 – (σ θ /σ r ) 2

7. ** Detailed ** dynamical studies Mass distribution underlying stellar systems dark halos massive black holes structure formation β = 1 – (σ θ /σ r ) 2 NGC 1407 group

8. Integrated light of unresolved population → long slits → integral field units “Continuous” vs Discrete Data

9. Integrated light of unresolved population → long slits → integral field units LOSVDs “Continuous” vs Discrete Data

10. ω Cen (van de Ven et al. 2006) “Continuous” vs Discrete Data

11. ω Cen (van de Ven et al. 2006) “Continuous” vs Discrete Data

12. Local Group dSph galaxies Walker et al. (2009) Geha et al. (2009)

13. Kinematics of Planetary Nebulae in Elliptical Galaxies Douglas et al. (2007) “Continuous” vs Discrete Data

14. Kinematics of Planetary Nebulae in Elliptical Galaxies Douglas et al. (2007) no dark matter?? binned data! “Continuous” vs Discrete Data

15. Need tools able to exploit these data appropriately globular clusters and PNe around giant E’s red giants in galaxy halos galaxy redshifts in clusters of galaxies ….. “Continuous” vs Discrete Data

16. more general analysis of kinematics ** full ** exploitation of available data → no assumptions about isotropy of velocity ellipsoid → as general as possible regarding geometry → no binning, higher-order moments, …..

17. Modeling the kinematics of stellar systems observations x,y : spatial (light) distribution v : line-of-sight velocity  : tangential velocities (GCs) xy z simplifying assumptions geometry (spherical, axisymmetric,...) shape of velocity ellipsoid simple modeling: Jeans, f(E,L ), …. z phase-space distribution function f (r,v,t) d r d v 33 f(r,v) Integrals of motion spherical system: E, L axisymmetric system: E, L, I z 3

18. Schwarzschild (orbit superposition) models trial gravitational potential Φ orbit library sampling (E,L z,I 3 ) integral space store orbital properties: density and kinematics as a function of (x,y) on sky

19. Cretton et al. (1999) Orbit Library

20. Rix et al. (1997) Cretton et al. (1999) Orbit Library Storing orbital properties

21. credits: SAURON team

22. Schwarzschild (orbit superposition) models trial gravitational potential Φ orbit library sampling (E,L z,I 3 ) integral space store orbital properties: density and kinematics as a function of (x,y) on sky find weighted superposition of (E,L z,I 3 ) orbits that best fits light distribution and kinematics → supermassive black holes; dark halos of galaxies; globular cluster dynamics; ….. → Rix et al. (1997) – Gebhardt et al. (2000) – Valluri et al. (2004) – van de Ven et al. (2008)…. → all set up to handle LOSVDs obtained from “continuous” datasets

23. 3-integral Schwarzschild code for discrete datasets Tests using pseudo-data (axisymmetric) E3 galaxy varying overall rotation inclination on the sky many different input datasets Study the recovery of: distribution function mass-to-light ratio inclination Chanamé, Kleyna, & van der Marel (2008)

24. Recovering the input distribution function (i.e., orbital structure!!) 3-integral Schwarzschild code for discrete datasets Chanamé, Kleyna, & van der Marel (2008)

25. non rotating case rotating case Schwarzschild fit Input model 3-integral Schwarzschild code for discrete datasets Recovering the input distribution function (i.e., orbital structure!!) Chanamé, Kleyna, & van der Marel (2008)

26. proper-motions provide additional information than only-LOS velocities Recovering the input M/L 3-integral Schwarzschild code for discrete datasets Chanamé, Kleyna, & van der Marel (2008)

27. Recovering the input M/L 3-integral Schwarzschild code for discrete datasets Chanamé, Kleyna, & van der Marel (2008) proper-motions provide additional information than only-LOS velocities the more data points the better

28. Recovering the input M/L 3-integral Schwarzschild code for discrete datasets Chanamé, Kleyna, & van der Marel (2008) proper-motions provide additional information than only-LOS velocities the more data points the better

29. Recovering the inclination 3-integral Schwarzschild code for discrete datasets Chanamé, Kleyna, & van der Marel (2008)

30. ongoing applications work in progress!!

31. Classical E's vs dE's M32 E3 NGC 205 dwarf elliptical

32. M32 E3 NGC 205 dwarf elliptical Classical E's vs dE's NGC 4621 E5

33. M32 E3 NGC 205 dwarf elliptical Classical E's vs dE's NGC 4621 E5 Fornax dSph

34. NGC 147 NGC 185 NGC 205 dE's in the Local Group none around Milky Way 3 satellites of M31

35. Low surface brightness at large radii → integrated light measurements too hard → discrete kinematical data dE's in the Local Group ~ 10 arcmin NGC 205

36. dE's in the Local Group NGC 205 Geha, Guhathakurta, Rich, & Cooper (2006) Low surface brightness at large radii → integrated light measurements too hard → discrete kinematical data

37. dE's in the Local Group NGC 205 Geha, Guhathakurta, Rich, & Cooper (2006) Low surface brightness at large radii → integrated light measurements too hard → discrete kinematical data Projected distance ~ 8 kpc from M31 → tidal interaction: isophotal twisting, recent SF → not good for equilibrium dynamical models

38. ~ 13' x 9' dE's in the Local Group NGC 147 de Rijcke et al. (2006) R 90% ┴ ┬ ┴ ┬ Geha et al. (in prep.)

39. dE's in the Local Group Jeans models Simplifying assumptions: axisymmetry, edge on 2-integral DF f(E,L z ) constant M/L

40. Simplifying assumptions: axisymmetry, edge on 2-integral DF f(E,L z ) constant M/L dE's in the Local Group Jeans models

41. 3-integral Schwarzschild code for discrete datasets NGC 147 (constant M/L)

42. van der Marel et al. (2002)

43. M15 Gerssen et al. (2002) van der Marel et al. (2002)

45. ACS/HRC (credits: Jay Anderson, Holland Ford)

46. 4`` x 4`` ACS/HRC (credits: Jay Anderson, Holland Ford)

47. 0.07 mas/yr 0.3 mas/yr 15 km/s @ 10 kpc

48. Search for Intermediate-Mass Black Holes with HST NGC 2808 NGC 6341 NGC 6752 NGC 362 NGC 6624 NGC 6681 NGC 7078 NGC 6266 GTO 10335 GTO 11801 HRC/HRC 2 yr baseline PI Ford GO 10401 GO 10841 GO 11988 HRC/WFPC2 GO 11609 WFC/WFC3 2.5 yr baseline PI Chandar 6 yr baseline PI Chanamé proper motions

49. Search for Intermediate-Mass Black Holes with HST NGC 2808 NGC 6341 NGC 6752 NGC 362 NGC 6624 NGC 6681 NGC 7078 NGC 6266 GTO 10335 GTO 11801 HRC/HRC 2 yr baseline PI Ford GO 10401 GO 10841 GO 11988 HRC/WFPC2 GO 11609 WFC/WFC3 2.5 yr baseline PI Chandar 6 yr baseline PI Chanamé proper motions discrete modeling IMBH ?? no IMBH ??

50. dark halos of dE’s; globular cluster dynamics (IMBHs); ….. globular clusters and PNe in giant ellipticals; ….. galaxies in galaxy clusters; ….. large kinematic surveys of the Milky Way; …. Detailed dynamical models that make the least possible number of simplifying assumptions are crucial to constrain dark halos & BHs. Available data sets need to be exploited to their full extent. dynamical modeling viewpoint: continuous data sets ≠ discrete data sets. Specialized tools are required to do this job adequately. New 3I Schwarzschild code that handles discrete data without loss of information, and works with both LOS velocities and proper motions. Tests show that it recovers the details of the DF, as well as M/L and inclination. Summary

51. END

52. E's classical E's WITH dynamical modeling (van der Marel & van Dokkum 2007; Capellari et al 2006) dE's dE's in the Local Group blue : Virgo dE’s (Geha et al. 2002) green : Local Group dE’s (de Rijcke et al. 2006) red : Jeans model for NGC 147 log σ dSph's dE’s offset from relation for classical E’s → older populations than E’s? → higher proportion of dark matter?

53. E's classical E's WITH dynamical modeling (van der Marel & van Dokkum 2007; Capellari et al 2006) dE's dE's in the Local Group blue : Virgo dE’s (Geha et al. 2002) green : Local Group dE’s (de Rijcke et al. 2006) red : Jeans model for NGC 147 log σ dSph's E's dE's dSph's dE’s offset from relation for classical E’s → older populations than E’s? → higher proportion of dark matter?

54. Classical E's vs dE's Geha, Guhathakurta, & van der Marel (2002;2003) E’s : n ~ 4 (de Vaucouleurs) dE’s: n ~ 1 – 3 I(r) = I 0 exp[(r/r 0 ) 1/n ] Sérsic profile + central nucleus (dE,N)

55. Classical E's vs dE's Geha, Guhathakurta, & van der Marel (2003) E's dE's dSph's GC's Different regions of Fundamental Plane UCD's → different processes of formation? → different evolutionary histories? → ….. dE’s offset from relation for classical E’s → older populations than E’s? → higher proportion of dark matter? → data at large radii to better constrain dark halos → no restrictive assumptions in modeling

56. Classical E's vs dE's dE host vs. nuclei E's dE's dSph's GC's NGC 205 nucleus Virgo dE nuclei

57. Recovering the input distribution function (i.e., orbital structure!!)

58. Recovering the inclination (Chanamé, van der Marel, & Kleyna, in prep.)

59. Verolme et al. (2002) regularization NO YES