1. Hierarchy in the phase space and dark matter Astronomy
Niayesh Afshordi

2. Collaborators Roya Mohayaee (IAP, Paris) Ed Bertschinger (MIT)
Hierarchical Phase Space Structure of Dark Matter Haloes: Tidal debris, Caustics, and Dark Matter annihilation:  arXiv:
Hierarchy in the Phase Space and Dark Matter Astronomy: arXiv:0906.????

3. Outline Why phase space of DM haloes is hierarchical
Unbound Structures & hierarchy in action space
Bound Structures & stable clustering
Future Prospects for dark matter astronomy

4. WIMPs: from gravity to detection
Gravitational evidence for DM comes from potential: sd3x ½(x)/|x-x’|
Direct detection: ½(x) at solar system
Indirect detection (annihilation): s d3x ½2 (x)
WIMP detection is much more sensitive to DM sub-structure:
(local) Boost ´ h½2i/h½i2-1
Boost to annihilation signal (indirect detection)
Variance for direct detection

5. Hierarchy in the Phase space
CDM is really cold
vCDM » 10-11c
Phase space density remains constant in lieu of collisions (Liouville Theorem):
At CDM freeze out:
Within our Galaxy:
Most of the phase space is empty!

6. Three types of phase structures
Bound sub-haloes (cluster in real/phase space)
Tidal debris (cluster in initial conditions)
Fundamental discreteness
 analogous to galaxy shot noise
Hayashi et al. 2002
Kuhlen, Diemand, et al.
NGC 3923

7. Outline Introduction Why phase space of DM haloes is hierarchical
Unbound Structures & hierarchy in action space
Bound Structures & stable clustering
Future Prospects for dark matter astronomy

8. Hierarchical Micro-Structure of the Phase Space
time

9. Phase mixing in action-angle space
Evolution of tidal debris is simple in action-angle space
time

10. Lattices in action space  Fundamental discreteness
Distribution in action space is a lattice which becomes finer in time
time
McMilllan & Binney 08

11. Catastrophes in the CDM Structure
Discrete/cold structures in action space project into catastrophes into real space
Catastrophes of light ray distribution
cusp
fold (caustic)
Catastrophes in stellar distribution
NGC 3923

12. Annihilation Boost in DM haloes
Tidal debris: hf(J1)f(J2)i/|J1-J2|-1.6
Fundamental discreteness: hf(J1)f(J2)i/ ±3(J1-J2)
Boost = h½2i/h½i2-1 » O(1) + 3x105 (½/½crit)-3/2
tidal debris
discreteness

13. Summary I
Action space correlation provides a good description of unbound substructure
Tidal remnants boost annihilation by O(1)
The boost due to caustics is only significant beyond 20% of rvir (hence negligible at solar system)

14. Outline Why phase space of DM haloes is hierarchical
Unbound Structures & hierarchy in action space
Bound Structures & stable clustering
Future Prospects for dark matter astronomy

15. Bound Substructures
Small sub-haloes become resilient to tidal stripping
Stable clustering hypothesis:
# of pairs at small physical separation remains constant (Davis & Peebles 77)
We extend this to phase space
Unlike the halo model, captures the full hierarchy: sub-haloes, sub-sub-haloes, etc.

16. sub-haloes and stable clustering
Stable clustering in phase space can be used to describe bound subn-halo hierarchy
Boost » 106 (½crit,0/½)
Boost » 106 (½crit,0/½)
Kuhlen, Diemand, et al.

17. DM annihilation profile: stable clustering vs. simulations
Msub > 105M¯
Msub > 106M¯
Msub > 107M¯
Msub > 108M¯
smooth halo
M/M200
Annihilation Luminosity (<r)
Bound substructure
+tidal cut-off
Springel, et al. 08

18. sub-haloes in Direct Detection!
Temporal auto-correlation of DM detection in several years…

19. Dark Matter Astronomy? From bound sub-haloes:
Boost = O(1) = density solar radius
Local DM wind may NOT come from the direction of Cygnus!
Phase space correlation will be probed by directional DM detection

20. tidal debris

21. Conclusions
Phase space of CDM haloes is mostly empty, and has a rich structure:
Hierarchy of tidal debris and subn-haloes
Fundamental discreteness/Action lattices
The structures can yield:
Boost in DM annihilation
Time dependence in direct detection signal
Rich structure for directional DM detection
If/when we detect Dark Matter particles, Dark Matter Astronomy will be just around the corner

22. Local vs. Total Boost in NFW haloes
Total boost Local Boost