1. Diurnal and Annual Modulation of Cold Dark Matter Signals Ling Fu-Sin IDM2004, Edinburgh, Sept. 8th 2004 in collaboration with Pierre Sikivie & Stuart Wick, Phys. Rev. D66, 023504 (2002) (astro-ph/0203448) astro-ph/0405231

2. Outline  Motivations  Solar wakes  Axion signal modulation  WIMP signal modulation  Conclusions

3. Motivations  Quest for DM: we need an accurate description of the potential signature.  DM is characterized by two essential properties: It is collisionless It has negligible velocity dispersion  Axions  WIMPs

4. Solar wakes

5. Effect of the Sun’s gravity on the structure of cold DM flows  Solar wakes: 1 flow upstream, 3 flows downstream  Appearance of caustics: Spike: line caustic on the axis of symmetry, downstream Skirt: conical surface near with opening close to the maximum scattering angle

6. b

7. Impact parameter vs. polar angle

8. Flows velocity  From energy and angular momentum conservation  with

9. Flows velocity modulation (on Earth)

10. Flows velocity modulation Distortion near the spike Flow 4+

11. Flows density    

12. Flow density modulation (on Earth) Flow 10+

13. Axion Signal Modulation

14. Axion detection  Principle: Photoconversion in a strong magnetic field Photon energy:  Frequency resolution of ADMX detector @ LLNL (in search mode) for Cavity bandwidth set by the quality factor of the cavity. If one octave is to be covered in one year, the time spent at each frequency is about 100 sec.

15. Frequency modulation Relativistic effects Jupiter & other planets Earth’s gravity Earth’s rotation Earth’s orbital rotation Earth’s eccentricity Frequency shift on the measurement time scale

16. Density modulation  Away from spike  Near spike  Near skirt

17. WIMP Signal Modulation

18. WIMP direct detection formulas  Detection by elastic scattering with nuclei Differential event rate Total rate with,,  Cold flow with,

19. The function T(E) June December Isothermal Cold static

20. The WIMP Signal modulation for the Caustic ring halo model and the DAMA result Caustic ring halo model: self similar infall halo model with a large number of flows corresponding to particles falling in and out for the n th time P. Sikivie et al., PRD56(1997)1863. P. Sikivie, PLB567(2003).

21. List of flows nv (km/s) v_X (km/s) v_Y (km/s) v_Z (km/s) d (10^-26 gr/cm^3) 1+62048020-3950.3 1-605-570202100.3 2+52045010-2550.8 2- 3+ 3- 4+ 4- 5+ 5- 6+ 6- 7+ 7- 8+ 8-... 505 435 420 350 340 265 255 300 280 330 310 330 315... -440 415 -310 350 -165 130 120 100 75 70 35 55 20... 10 ~0 -10 85 -120 230 -245 300 -305 320 -310... 250 -130 285 ~0 295 210 195 160 120 110 50 80 20... 0.8 1.4 3.4 15 or 170 170 or 15 3.4 or 6.5 6.5 or 3.4 1.3 or 4.1 4.1 or 1.3 1.1 or 2.0 2.0 or 1.1...

22. T(E) in the caustic ring halo model

23. Predicted event rate modulation @ DAMA in the range 2 – 6 keV

24. Conclusions  DM is collisionless and has negligible velocity dispersion. These features determine the shape of its signal in a detector. Axion: narrow peak in frequency WIMP: plateau in the differential event rate  The presence of caustics is potentially crucial for DM discovery.

25.  Axions: Diurnal modulation enables to reconstruct the velocity of the DM flow. It is therefore crucial to include all effects to a precision.  WIMPs: Event rate modulation is very sensitive to thresholds, and can therefore be different with different targets. Caustic ring halo model not incompatible with DAMA: large WIMP masses are favored.