1. What mass are the smallest protohalos in thermal WIMP dark-matter models? Kris Sigurdson Institute for Advanced Study Space Telescope Science Institute Hubble Fellows Symposium April 20, 2006

2. Outline Thermal WIMPs and Chemical Decoupling WIMP Kinetic Decoupling Small-Scale Cutoff in the Matter Power Spectrum My Results: The Kinetic Decoupling Temperature The Mass of the Smallest Protohalos in Viable Particle Physics Models

3. Standard Model of the Universe Galaxy Surveys BBN Hubble Space Telescope Supernovae Surveys CMB “The Standard Model”

4. Nonbaryonic Dark Matter ≠

5. Thermal WIMPs 1)Cosmologically stable due to a conserved quantum number. 2)In thermal equilibrium at early times (high temperatures) and relic abundance fixed by the total annihilation cross section of pairs to all lighter species. Weakly Interacting Massive Particles (particle-antiparticle pairs have no net “charge”)

6. WIMP Chemical Decoupling Eventually the annihilation rate drops below the expansion rate of a FRW Universe. Pairs of WIMPs can no longer find each other efficiently in a Hubble time and the relic abundance is fixed Expansion Rate Annihilation Rate Freeze-Out

7. WIMP Relic Abundance Relic Abundance from Freeze-Out Relic Abundance from Cosmology  We now know the total annihilation cross section for thermal WIMP dark matter! Are the any other astrophysical indicators of the particle physics?

8. WIMP Chemical Decoupling Eventually the annihilation rate drops below the expansion rate of a FRW Universe. Pairs of WIMPs can no longer find each other efficiently in a Hubble time and the relic abundance is fixed Expansion Rate Annihilation Rate Freeze-Out

9. The End of Dark-Matter Interactions? NOT The end of: Same Conserved Quantum Number The end of: Elastic Scattering Inelastic Scattering Few Many Annihilation (Number Changing) Photons, Neutrinos, Charged Leptons, Quarks

10. WIMP Kinetic Decoupling Eventually the scattering rate drops below the expansion rate of a FRW Universe. WIMPs no longer scatter off the thermal bath efficiently in a Hubble time and start to cool, free-stream, and then gravitationally cluster Expansion Rate Scattering Rate Oscillates with plasma

11. Evolution of Perturbations Plasma Decoupled Dark Matter

12. WIMP Kinetic Decoupling From A. Loeb and M. Zaldarriaga, Phys. Rev. D 71, 103520 (2005) [arXiv:astro-ph/0504112].

13. WIMP Kinetic Decoupling From A. Loeb and M. Zaldarriaga, Phys. Rev. D 71, 103520 (2005) [arXiv:astro-ph/0504112]. Small-Scale Cutoff

14. The Mass of the Smallest Protohalos The temperature of kinetic decoupling sets the small-scale cutoff in the matter power spectrum. In turn, the small-scale cutoff sets the mass of the smallest protohalos that form when these scales go nonlinear at What value is T kd ?

15. What Value is T kd ? S. Hofmann, D. Schwarz, and H.Stöcker, Phys. Rev. D 64, 083507 (2001) [arXiv:astro-ph/0104173]. A. Green, S. Hofmann, and D. Schwarz, Mon. Not. Roy. Astron. Soc 353, L23 (2004) [arXiv:astro-ph/0309621]. A. Green, S. Hofmann, and D. Schwarz, JCAP 0508, 003 (2005) [arXiv:astro-ph/0503387]. Estimate in “generic” supersymmetric (SUSY) models. Predict power spectra and that an earth mass cutoff is expected in SUSY models.

17. An Earth Mass from SUSY? S. Profumo, KS, M. Kamionkowski, “What mass are the smallest protohalos?” [arXiv:astro-ph/0603373]. Q: Is an earth mass cutoff really generic in WIMP models that produce the cosmological abundance of dark matter? NO

18. Our Approach Kinetic-decoupling temperature for WIMPs in supersymmetric models of dark-matter. Must account for the dark matter abundance from cosmology and be compatible with present constraints from particle physics. Include detailed model (with correct cross sections) of the particle physics for both chemical and kinetic decoupling. S. Profumo, KS, M. Kamionkowski, [arXiv:astro-ph/0603373].

19. Scattering Cross Section S. Profumo, KS, M. Kamionkowski, [arXiv:astro-ph/0603373]. Only Z Boson (Heavy Scalars) Z Boson +Sleptons (Light Scalars) Resonant Scattering Same Relic Abundance

20. Kinetic Decoupling Temperature S. Profumo, KS, M. Kamionkowski, [arXiv:astro-ph/0603373]. Scan over SUSY Parameter Space. Maximum Minimum

21. Minimum Protohalo Mass S. Profumo, KS, M. Kamionkowski, [arXiv:astro-ph/0603373]. Scan over SUSY Parameter Space. Maximum Minimum

22. Conclusions of our Paper Earth mass protohalos are possible but are NOT a generic prediction of SUSY. A wide range of M c between 10 -6 and 100 M  are possible. We expect the range derived here to be characteristic of other particle physics models of thermal WIMPS beyond SUSY. S. Profumo, KS, M. Kamionkowski, [arXiv:astro-ph/0603373].

23. Observational Signatures? S. Profumo, KS, M. Kamionkowski, [arXiv:astro-ph/0603373]. Q: Can protohalos survive to the present day and be important in our Galaxy? A1: For small (M c < 10 -7 M  ?), probably No. (Green and Goodwin 2006) Stellar disruption time less than age of the Galaxy. A2: For larger M c   Maybe. Could amount to as much as 0.1% of dark matter in the Galaxy by mass (neglecting disruption). At M  : ( Diemand et al. 2005) 100% survive at R Sun (Zhao et al. 2005) 0% (Berezinsky 2005) 17% Must survive mergers, accretion processes, tidal stripping, and tidal disruption by stars. Bright Side: Even if disrupted can produce tidal streams. Bottom Line: Tough Astrophysical Problem. Simulation of orbits of minihalos in realistic galaxies.

24. Observational Signatures Enhanced Gamma Ray Annihilation Signal? 1)Protohalos within our Galaxy could be bright gamma sources. 2)Clumpiness may enhance total gamma ray flux from nearby extragalactic systems. Enhanced Direct Detection Rates. 1) If a protohalo or the tidal stream of a disrupted protohalo passes through the Solar neighborhood then direct detection rates will be enhanced by perhaps a factor 10. 2)If the smooth dark-matter component is reduced then direct detection rates at other times will be slightly decreased. S. Profumo, KS, M. Kamionkowski, [arXiv:astro-ph/0603373].

25. Particle Physics/Astrophysics Observation Feedback Loop!

26. Summary Kinetic Decoupling of WIMPs sets the minimum mass of dark-matter protohalos. Earth mass protohalos are NOT a generic prediction of SUSY CDM models. Perhaps: Another window onto the particle physics of dark matter! The Challenge: Relate the physics of dark matter to the astrophysics of dark matter and ultimately to observations of dark matter! Can’t just ignore it.