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Hierarchy in the phase space and dark matter Astronomy

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

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Hierarchy in the phase space and dark matter Astronomy

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  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:0812.2244 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: sd3x½(x)/|x-x’| • Direct detection: ½(x) at solar system • Indirect detection (annihilation): sd3x½2 (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 Hayashi et al. 2002 Kuhlen, Diemand, et al. NGC 3923 • Bound sub-haloes (cluster in real/phase space) • Tidal debris (cluster in initial conditions) • Fundamental discreteness  analogous to galaxy shot noise

  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 time McMilllan & Binney 08 Distribution in action space is a lattice which becomes finer in time

  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 discreteness 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

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

  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 variance @ 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 Astronomywill be just around the corner

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

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