Hierarchy in the phase space and dark matter detection

1. Hierarchy in the phase space and dark matter detection 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:0812.2244 • Hierarchy in the Phase Space and Dark Matter Detection: in preparation

3. Dark Matter detection • 22% of density of Universe consist of DM • No clear non-gravitational detection • Tentative anomalies may come from WIMP’s: • PAMELA, positron excess • ATIC e+-e-excess • WMAP haze at Galactic center • INTEGRAL 511 keV excess • DAMA/LIBRA direct detection signal • ?????

4. WIMPs: from gravity to detection • Gravitational evidence for DM comes from potential: sd3x½(x)/|x-x’| • Direct detection: ½(x) at solar system • Indirect detection (annihilation): sd3x½(x)2 WIMP detection is much more sensitive to DM sub-structure: Boost ´h½2i/h½i2-1

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. Conclusions • Phase space of CDM haloes is mostly empty, and has a rich structure: • Hierarchy of tidal debris and subn-haloes • Fundamental discreteness • Boost in DM annihilations • DM direct detection can show signs of sub-structure

7. 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 Kuhlen, Diemand, et al. NGC 3923

8. Hierarchical Micro-Structure of the Phase Space

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

10. Lattices in action space • Distribution in action space is a lattice which becomes finer in time Afshordi et al. 08 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 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. Local vs. Total Boost in NFW haloes Total boost Local Boost

14. sub-haloes and stable clustering • Stable clustering in phase space can be used to describe bound subn-halo hierarchy within virial radius Boost »106 (½crit,0/½) at solar system Kuhlen, Diemand, et al. Afshordi et al. in prep.

15. sub-haloes in Direct Detection! • Temporal auto-correlation of DM detection in several years… Afshordi et al. in prep.

16. Conclusions • Phase space of CDM haloes is mostly empty, and has a rich structure: • Hierarchy of tidal debris and subn-haloes • Fundamental discreteness • Boost in DM annihilations • DM direct detection can show signs of sub-structure