1. Cold Dark Matter Flows and Caustics
Pierre Sikivie (U. of Florida)
IDM 2004
Edinburgh, September 8, 2004

2. Elucidating the structure of galactic halos is important for
understanding galactic dynamics
predicting signals for dark matter searches

3. Caustics in cold dark matter. . x x x x
Dark matter particles are red and,
on this page, they are free. d d x x

4. 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

5. 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

6. Phase space structure of spherically symmetric halos

7. Implications:
At every point in physical space, the distribution of velocities is discrete, each velocity corresponding to a particular flow at that location.
2. At some locations in physical space, where the number of flows changes, there is a caustic, i.e. the density of dark matter is very high there.

8. but do not destroy the sheet structure in phase space
- the number of flows at our location in the Milky Way halo is of order 100
- small subhalos from hierarchical structure formation produce an effective velocity dispersion
but do not destroy the sheet structure in phase space
the known inhomogeneities in the distribution of matter are insufficient to diffuse the flows by gravitational scattering
present N-body simulations do not have enough particles to resolve the flows and caustics
(see however: Stiff and Widrow, Bertschinger and Shirokov)

9. Hierarchical clustering introduces effective velocity dispersion

10. A shell of particles, part of a continuous flow
A shell of particles, part of a continuous flow. The shell has net angular momentum. As the shell falls in and out of the galaxy, it turns itself inside out. . . . . . .

11. A caustic forms where the particles with the most angular momentum are at their closest approach to the galactic center.

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

13. On the basis of the self-similar infall model, 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 (I. Tkachev, Y. Wang +
PS, astro-ph/ )

14. 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

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

16. Spiral Arms vs. Caustic Rings of DM
What causes the rises in the inner rotation curve of the Milky Way?
Both spiral arms and caustic rings may contribute
However, here are some reasons to believe that caustic rings of dark matter are the main cause:
- the number of rises between 3 and 8.5 kpc is approximately 10, which
is the expected number of caustic rings, whereas only 3 spiral arms are
known in that range (Scutum, Sagittarius, and Local)
- the rises are sharp transitions in the rotation curve, both where they start
and where they end. The sharpness of the rises is consistent with the fact
that the dark matter density diverges on caustic surfaces
- bumps and rises are present in rotation curves at galactocentric distances
much larger than the disk radius, where there are no spiral arms seen.

17. from W.B. Burton and W.W. Shane, 1970

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

19. The Big Flow density velocity velocity dispersion
previous estimates of the total local halo density range from to gr/cm
-24 3
in the direction of galactic rotation
in the direction away from the galactic center

20. Experimental implications
for dark matter axion searches
- peaks in the energy spectrum of microwave photons
from conversion in the cavity detector
- high resolution analysis of the signal yields a more sensitive search (see talk by Darin Kinion)
for dark matter WIMP searches
- plateaux in the recoil energy spectrum from elastic WIMP collisions with target nuclei
- the flux is largest around December
(Vergados; Green; Gelmini and Gondolo; Ling, Wick &PS)

21. Conclusions Cold Dark Matter forms discrete flows and caustics.
The minimum set of caustics in a galactic halo is a
series of simple folds located on topological spheres
surrounding the galaxy plus a series of caustic rings
(elliptic umbilics) in the galactic plane.
There is evidence that the locations of caustics are
correctly predicted by the self-similar infall model.
That evidence implies that the dark matter in
our neighborhood is dominated by a Big Flow.

23. Caustics of light at the bottom of a swimming pool on a sunny breezy day
water
surface
pool
bottom
light
intensity
position

24. Caustics are common in the
propagation of light (rainbows,
the twinkling of stars, shimmering
of the sea, gravitational lenses … )
because
1. light is collisionless
2. in many cases, the flow of light
has small velocity dispersion

25. Caustics are rare in the propagation of ordinary matter because of collisions. On the other hand, cold dark matter 1. is collisionless 2. has negligible primordial velocity dispersion.