1. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 1 Tales of Dark Matter on Small Scales Niayesh Afshordi Western University Friday, April 13, 2012

2. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 2 Tales of Dark Matter on Small Scales “Friday the 13th is a date considered to be bad luck in Western superstition.” -Wikipedia.

3. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 3 Tales of Dark Matter on Small Scales Outline Introduction: Cold Dark Matter (CDM) Why phase space of CDM haloes is hierarchical Too big to Fail? A Tale of Small Scale Bound Structures & CDM detection Future Prospects for dark matter astronomy

4. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 4 Tales of Dark Matter on Small Scales Roya Mohayaee (IAP, Paris) Ed Bertschinger (MIT) Kathryn Zurek (U-Michigan) Louis Strigari (Stanford) Shant Baghram (U-Waterloo/PI) NA, Mohayaee, Bertschinger: Phys.Rev.D79:083526,2009 NA, Mohayaee, Bertschinger: Phys.Rev.D81:101301, 2010 Baghram, NA, Zurek: Phys.Rev.D84:043511,2011 Baghram, NA, Strigari: in preparation Collaborators

5. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 5 Tales of Dark Matter on Small Scales Outline Introduction: Cold Dark Matter (CDM) Why phase space of CDM haloes is hierarchical Too big to Fail? A Tale of Small Scale Bound Structures & CDM detection Future Prospects for dark matter astronomy

6. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 6 Tales of Dark Matter on Small Scales Bullet Cluster Baryons (X-ray) Matter (lensing) Dark Matter is Collisionless

7. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 7 Tales of Dark Matter on Small Scales Dark Matter is Cold Zaldarriaga & Tegmark 2002

8. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 8 Tales of Dark Matter on Small Scales Indirect Detection Dark Matter can annihilate to – photons (Fermi) – electrons/positrons (PAMELA/Fermi/WMAP…Planck) – Neutrinos (IceCube) Springel, et al. 08

9. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 9 Tales of Dark Matter on Small Scales Directional DM detection Solar system is moving towards the Cygnus constellation in the Milky Way, at 220 km/s  We should see a DM wind coming from Cygnus, which distinguishes it from any other background Sciolla et al 2008 250 km/s

10. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 10 Tales of Dark Matter on Small Scales WIMPs: from gravity to detection Gravitational evidence for DM comes from potential: d 3 x ρ (x)/|x-x’| Direct detection: ρ (x) at solar system Indirect detection (annihilation): d 3 x ρ ( x) 2  WIMP detection is much more sensitive to DM sub- structure: Boost = / 2 -1  Boost to annihilation signal (indirect detection) (e.g., Taylor & Silk 2003)  Variance for direct detection (e.g., Stiff, Widrow, & Frieman 2001)

11. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 11 Tales of Dark Matter on Small Scales Outline Introduction: Cold Dark Matter (CDM) Why phase space of CDM haloes is hierarchical Too big to Fail? A Tale of Small Scale Bound Structures & CDM detection Future Prospects for dark matter astronomy

12. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 12 Tales of Dark Matter on Small Scales Hierarchy in the Phase space CDM is really cold –  v CDM ~ 10 -11 c Phase space density remains constant in lieu of collisions (Liouville’s Theorem): – At CDM freeze out: – Within our Galaxy:  Most of the phase space is empty!  Structures on all scales !!??

13. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 13 Tales of Dark Matter on Small Scales Hierarchical Micro-Structure of the Phase Space time

14. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 14 Tales of Dark Matter on Small Scales Bound sub-haloes (cluster in real/phase space) Tidal debris (cluster in initial conditions) Fundamental discreteness  analogous to galaxy shot noise (NA, Mohayaee, Bertschinger 2009; Vogelsberger & White 2011) Three types of phase structures NGC 3923 Kuhlen, Diemand, et al. Hayashi et al. 2003

15. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 15 Tales of Dark Matter on Small Scales Correlation Functions quantify Hierarchy Large Scale Structure Projected Correlation Function SDSS Masjedi, et al. unbound structure bound substructure Phase Space Correlation Function

16. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 16 Tales of Dark Matter on Small Scales Outline Introduction: Cold Dark Matter (CDM) Why phase space of CDM haloes is hierarchical Too big to Fail? A Tale of Small Scale Bound Structures & CDM detection Future Prospects for dark matter astronomy

17. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 17 Tales of Dark Matter on Small Scales Courtesy of Shant Baghram: http://pirsa.org/12040110/ Too Big to Fail Problem? Baghram, NA, & Strigari, in prep.

18. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 18 Tales of Dark Matter on Small Scales *Binning in the Energy and Angular momentum *Non- smooth phase-space density  Now we can rewrite the observable density of stars, by plugging the phase space density function definition as :  Marginalize over f ab ’s E L Number of binning = number of free parameters Tricks of the Trade!

19. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 19 Tales of Dark Matter on Small Scales Outline Introduction: Cold Dark Matter (CDM) Why phase space of CDM haloes is hierarchical Too big to Fail? A Tale of Small Scale Bound Structures & CDM detection Future Prospects for dark matter astronomy

20. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 20 Tales of Dark Matter on Small Scales 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 the phase space Unlike the halo model, captures the full hierarchy: sub- haloes, sub-sub-haloes, etc. (also much fewer parameters)

21. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 21 Tales of Dark Matter on Small Scales sub-haloes and stable clustering Stable clustering in phase space can be used to describe bound sub n -halo hierarchy Kuhlen, Diemand, et al. Boost » 10 6 ( ½ crit,0 / ½ ) NA, et al. 2010 0.03 Standard deviation of linear overdensity on mass scale M

22. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 22 Tales of Dark Matter on Small Scales DM annihilation profile: stable clustering vs. simulations smooth halo M(<r)/M 200 Bound substructure +tidal cut-off M sub > 10 5 M  M sub > 10 6 M  M sub > 10 7 M  M sub > 10 8 M  Springel, et al. 08 Annihilation Luminosity (<r)

23. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 23 Tales of Dark Matter on Small Scales Massaging the tidal stripping prescription …

24. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 24 Tales of Dark Matter on Small Scales sub-haloes in Direct Detection! Temporal auto-correlation of DM detection in several years…

25. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 25 Tales of Dark Matter on Small Scales Dark Matter Astronomy? From bound subhaloes: 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 unbound structure bound substructure Hansen et al. 2005, Vogelsberger et al. 2009, Kuhlen et al. 2010

26. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 26 Tales of Dark Matter on Small Scales Dark Matter subhaloes may even impact Pulsar Timing Hertzberg, Siegel, Fry 2007

27. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 27 Tales of Dark Matter on Small Scales Dark Matter subhaloes may even impact Pulsar Timing Doppler EffectShapiro Delay Baghram, NA, & Zurek, 2011 log(Pulsar residual power spectrum)

28. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 28 Tales of Dark Matter on Small Scales Lessons CDM has lots of structure on small scales: – Boost in DM annihilation – Time dependence in direct detection signal – Rich structure for directional DM detection – Potentially detectable Pulsar Timing residuals Correlation Function in Phase Space is a Powerful tool (  stable clustering) Measuring Dark Matter masses from stellar kinematics is a tricky business

29. Niayesh Afshordi, Perimeter Institute/U-Waterloo Western University, Apr. 13, 2012 29 Tales of Dark Matter on Small Scales Two Cautionary Notes… What about baryons? – They can enhance CDM structures through adiabatic contraction, or destroy them via gravitational collisions/heating – Real haloes are almost certainly more complicated! Why not just extrapolate simulations? – Simulations are NOT scale-free  tidal limit – Neither is CDM over 10 orders of magnitude!