1. The Case for Axion Dark Matter
Pierre Sikivie
`The Dark Matter Connection:
Theory and Experiment'
Firenze, May 21, 2010

2. Outline The inner caustics of galactic halos
Axions form a Bose-Einstein condensate
Tidal torque theory with ordinary CDM
and with axion BEC
- magnitude of angular momentum
- net overall rotation
- self-similarity
Conclusion

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

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

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

6. 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

7. 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

8. Phase space structure of spherically symmetric halos

9. (from Binney and Tremaine’s book)

11. Phase space structure of spherically symmetric halos

12. 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).

13. simulations by Arvind Natarajan

14. The caustic ring cross-sectionD -4
an elliptic umbilic catastrophe

15. 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).

17. On the basis of the self-similar infall model (Fillmore 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.

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

19. 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

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

21. IRAS

22. IRAS

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

24. 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)

25. from L. Duffy and PS, Phys. Rev. D78 (2008) 063508

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

27. Self-similar ansatz
entire phase space structure is time-independent except for a rescaling of
all length scales by
all velocities by
all densities by

28. Self-similarity happens if the initial overdensity has a power law profile
Fillmore and Goldreich, 1984
with
is related to the slope of the evolved spectrum of density
perturbations on galactic scales

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

30. Tidal torque theory neighboring protogalaxy
Stromberg 1934; Hoyle 1947; Peebles 1969, 1971

31. Magnitude of angular momentum
G. Efstathiou et al. 1979, 1987
from caustic rings
fits perfectly ( )

32. Tidal torque theory with ordinary CDM
neighboring
protogalaxy
the velocity field remains irrotational

33. For collisionless particles
If initially,
then for ever after.

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

36. 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

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

38. Gravitational interactions thermalize the axions and cause them to form a BEC when the photon temperature
(PS and Q. Yang, 2009)

39. Tidal torque theory with axion BEC
net overall rotation is obtained because, in the lowest energy state,
all axions fall with the same angular momentum

40. is minimized for given when .
For axion BEC
is minimized for given
when

42. Tidal torque theory with axion BEC
net overall rotation is obtained because, in the lowest energy state,
all axions fall with the same angular momentum

43. Self-Similarity
a comoving volume

44. Self-Similarity (yes!)
time-independent axis of rotation
provided

45. Conclusions If the dark matter is axions, the phase space
structure of galactic halos predicted by tidal torque
theory is precisely, and in all respects, that of the
caustic ring model proposed earlier on the basis
of observations.
The other candidates (WIMPs, sterile neutrinos, ...)
predict a different phase space structure for
galactic halos.