1. Bose-Einstein Condensationof Dark Matter Axions Pierre Sikivie ASK2011 Conference Seoul, Korea April 11, 2011

2. Outline Dark matter Axions Bose-Einstein Condensation Caustics

3. Fritz Zwicky 1898 - 1974

4. COMA cluster of galaxies COMA, a cluster of galaxies

5. cluster mass Virial Theorem cluster radius velocities of galaxies in the cluster Using the virial theorem, Zwicky (1933) showed that the Coma cluster contains roughly 100 times more mass than accounted for by the luminous matter in the cluster.

6. Vera Rubin and Kent Ford

7. Galactic rotation curves galactic mass rotation speed

8. Rubin and Ford (1970) found that the rotation speed of M31 is constant at large radii implying that the total galactic mass increases proportionately to the radius. Galaxies are surrounded by halos of dark matter.

9. the bullet cluster (D. Clowe, A. Gonzales and M. Markevitch. 2004)

10. WMAP

11. Concurring data from: Boomerang, Maxima, South Pole, Saskatoon, DASI, VSA, …

12. Cosmological Parameters -29 3 Age of the universe 13.7 Gigayear Spatial curvature none Energy density 0.95 10 gr/cm Energy fractions vacuum energy atoms and molecules dark matter

13. What is thedark matter ?

14. The candidates the axion the WIMP the sterile neutrino others

15. The Strong CP Problem Because the strong interactions conserve P and CP,. The Standard Model does not provide a reason for to be so tiny, but a relatively small modification of the model does provide a reason …

16. If a symmetry is assumed, relaxes to zero, and a light neutral pseudoscalar particle is predicted: the axion.

17. f f a a = 0.97 in KSVZ model 0.36 in DFSZ model

18. The remaining axion window laboratory searches cosmology stellar evolution

19. There are two axion populations: hot and cold. When the axion mass turns on, at QCD time,

20. Cold axion properties if decoupled number density velocity dispersion phase space density

21. Bose-Einstein Condensation if identical bosonic particles are highly condensed in phase space and their total number is conserved and they thermalize then most of them go to the lowest energy available state

22. why do they do that? by yielding their energy to the non-condensed particles, the total entropy is increased. BEC preBEC

23. PS + Q. Yang, PRL 103 (2009) 111301 Thermalization occurs due to gravitational interactions at time

24. Gravitational interactions thermalize the axions and cause them to form a BEC when the photon temperature After that

25. DM forms caustics in the non-linear regime . . x x DM particles in phase space x x x x

26. . z Phase space distribution of DM in a homogeneous universe z for WIMPs for axions (preBEC) for sterile neutrinos

27. The dark matter particles lie on a 3-dimensional sheet in 6-dimensional phase space . z the physical density is the projection of the phase space sheet onto position space z

28. The cold dark matter particles lie on a 3-dimensional sheet in 6-dimensional phase space . z the physical density is the projection of the phase space sheet onto position space z

29. Phase space structure of spherically symmetric halos

30. (from Binney and Tremaine’sbook)

32. Phase space structure of spherically symmetric halos

33. Galactic halos have inner caustics as well as outer caustics. If the initial velocity field is dominated by net overall rotation, the inner caustic is a ‘tricusp ring’. If the initial velocity field is irrotational, the inner caustic has a ‘tent-like’ structure. (Arvind Natarajan and PS, 2005).

34. simulations by Arvind Natarajan

35. The caustic ring cross-section D -4 an elliptic umbilic catastrophe

36. Galactic halos have inner caustics as well as outer caustics. If the initial velocity field is dominated by net overall rotation, the inner caustic is a ‘tricusp ring’. If the initial velocity field is irrotational, the inner caustic has a ‘tent-like’ structure. (Arvind Natarajan and PS, 2005).

38. On the basis of the self-similar infall model(Filmore and Goldreich, Bertschinger) with angular momentum (Tkachev, Wang + PS), the caustic rings were predicted to be in the galactic plane with radii was expected for the Milky Way halo from the effect of angular momentum on the inner rotation curve.

39. Effect of a caustic ring of dark matter upon the galactic rotation curve

40. Composite rotation curve(W. Kinney and PS, astro-ph/9906049) • combining data on 32 well measured extended external rotation curves • scaled to our own galaxy

41. Inner Galactic rotation curve Inner Galactic rotation curve from Massachusetts-Stony Brook North Galactic Pane CO Survey (Clemens, 1985)

42. IRAS

43. IRAS

44. Outer Galactic rotation curve R.P. Olling and M.R. Merrifield, MNRAS 311 (2000) 361

45. Monoceros Ring of stars H. Newberg et al. 2002; B. Yanny et al., 2003; R.A. Ibata et al., 2003; H.J. Rocha-Pinto et al, 2003; J.D. Crane et al., 2003; N.F. Martin et al., 2005 in the Galactic plane at galactocentric distance appears circular, actually seen for scale height of order 1 kpc velocity dispersion of order 20 km/s may be caused by the n = 2 caustic ring of dark matter (A. Natarajan and P.S. ’07)

46. Rubin and Ford (1970) found that the rotation speed of M31 is constant at large radii implying that the total galactic mass increases proportionately to the radius. Galaxies are surrounded by halos of dark matter.

47. from L. Chemin, C. Carignan & T. Foster, arXiv: 0909.3846 Rotation curve of Andromeda Galaxy

48. 15.4 29.2 kpc 10.3 10 arcmin = 2.2 kpc

49. The caustic ring halo model assumes net overall rotation axial symmetry self-similarity

50. The specific angular momentum distribution on the turnaround sphere Is it plausible in the context of tidal torque theory?