Extragalactic Astronomy

1. Extragalactic Astronomy Lecture 4: Kinematics & Mass Distribution of Spirals and Dwarfs

2. Dynamics of Disks • A disk is a system in equilibrium between: • Gravity (inward) • Rotation (outward) • A disk is supported by rotation in r • Vrot ~ 200 km/sec • A disk is supported by the velocity dispersion in z • s ~ 10 km/sec • So, V (r) allow to deduce the gravitational potentiel f (r)

3. Dynamics of Disks • From Poisson equation: • Until the 70s, the method of flattened spheroids was used. The mass distribution was modeled by a succession of flattened shells with r(a), where a was the major axis of the shell

4. Dynamics of Disks • The flattening of the shell is given by (1 – k2)1/2, where k is the axis ratio • The advantage of this model is that V (r) depends only of r (a < r) beause the potential f inside the shell is constant

5. Dynamics of Disks Parametrization: Brandt (1960) n = parameter of the form Determines where the curve starts to be Keplerian Mtot = (3/2)3/n V2max rmax / G

6. Dynamics of Disks Infinitely thin disk: Freeman (1970)

7. Dynamics of Disks Exponential disk

8. Dynamics of Disks Solid body (e.g. dwarf) Flat (e.g. spiral)

9. Dynamics of Disks Infinitely thin c/a ~ 0.2 Carignan 1983

10. Optical Rotation Curves Rubin et al. 1980, ApJ, 238, 471

11. Optical Rotation Curves bulge disk Kent 1986, AJ, 91, 1301

12. Radio Rotation Curves Bosma 1981, AJ, 86, 1825

13. Radio Rotation Curves M(r) ~ r sM ~ sHI Bosma 1981, AJ, 86, 1825

14. HI Rotation Curve Rogstad 1974, AJ, 193, 309

15. HI Rotation Curves Sicotte & Carignan 1997, AJ, 113, 1585

16. HI Rotation Curves Sicotte & Carignan 1997, AJ, 113, 1585

17. HI Rotation Curves Bosma 1981, AJ, 86, 1791

18. HI Rotation Curves warp Bosma 1981, AJ, 86, 1791

19. Mass Models Carignan & Freeman 1985, ApJ, 294, 494

20. Mass Models Carignan & Freeman 1985, ApJ, 294, 494

21. Mass Models Disk Halo NGC 3109 Carignan 1985, ApJ, 299, 59

22. Mass Models NGC 3109 Jobin & Carignan 1980

23. Mass Models • Halo formalism (Kent 1986)

24. Mass Models

25. Mass Models van Albada et al. 1985, ApJ, 295, 305

26. Mass Models

27. Vc observed Vc    R Vc calculated for a disk Fit of rotation curves Département de physique

28. Mass Models Kent 1987, AJ, 93, 816

29. Mass Models

30. Mass Models

31. Mass Models • MOND: Modified Newtonian Dynamics • Milgrom (1983) proposed that the law of gravity must be modified in presence of small accelerations • For large R, V2 = (GMa0)1/2 • where a0 = const. Begeman et al. 1991

32. Mass Models Sanders et al. 1991

33. Mass Models Blais-Ouellette et al. 2001

34. Mass Models - Dwarfs Carignan & Beaulieu 1989 Carignan & Freeman 1988

35. Mass Models - Dwarfs Carignan & Purton 1998

36. Mass Models - Dwarfs

37. Mass Models - Dwarfs Keplerian decline

38. Mass Models - Dwarfs DDO 154

39. Mass Models - Dwarfs Carignan et al. 1990

40. Mass Models - Dwarfs

41. Mass Models – Beam Smearing Blais-Ouellette et al. 1999

42. Mass Models – Beam Smearing Example of Beam Smearing for DDO 88 with the VLA

43. Mass Models – Beam Smearing Blais-Ouellette et al. 1999

44. Mass Models

45. Mass Models

46. Mass Models

47. Mass Models (cusp vs core) Blais-Ouellette et al. 2001

48. Mass Models (cusp vs core)

49. Mass Models (cusp vs core) LSB LSB & dwarfs de Blok & Bosma 2002 Swaters et al. 2003

50. Mass Models (cusp vs core) De Naray et al. 2006