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Hierarchy in the phase space and dark matter Astronomy
Niayesh Afshordi
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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.????
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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
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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
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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!
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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
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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
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Hierarchical Micro-Structure of the Phase Space
time
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Phase mixing in action-angle space
Evolution of tidal debris is simple in action-angle space time
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Lattices in action space Fundamental discreteness
Distribution in action space is a lattice which becomes finer in time time McMilllan & Binney 08
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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
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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
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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)
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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
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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.
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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.
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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
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sub-haloes in Direct Detection!
Temporal auto-correlation of DM detection in several years…
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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
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tidal debris
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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
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Local vs. Total Boost in NFW haloes
Total boost Local Boost
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