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, (2002) (astro-ph/ ) astro-ph/

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

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

Solar wakes

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

b

Impact parameter vs. polar angle

Flows velocity  From energy and angular momentum conservation  with

Flows velocity modulation (on Earth)

Flows velocity modulation Distortion near the spike Flow 4+

Flows density    

Flow density modulation (on Earth) Flow 10+

Axion Signal Modulation

Axion detection  Principle: Photoconversion in a strong magnetic field Photon energy:  Frequency resolution of ADMX 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.

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

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

WIMP Signal Modulation

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

The function T(E) June December Isothermal Cold static

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).

List of flows nv (km/s) v_X (km/s) v_Y (km/s) v_Z (km/s) d (10^-26 gr/cm^3) ~ ~ or or or or or or or or

T(E) in the caustic ring halo model

Predicted event rate DAMA in the range 2 – 6 keV

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.

 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.