1. Indirect Detection Of Dark Matter
D.T. Cumberbatch

2. Motivation for Dark Matter
Rotation Curves of spiral galaxies:
M/L ratio
Abell 1689, HST
Galaxy clusters:
Proper motion
X-ray emissions from hot gas
Gravitational lensing
Large-scale structure
2dFGRS
WMAP
Anisotropies in the CMB

3. What is the Dark Matter made of?
Weakly Interacting Massive Particles (WIMPS)
Lightest Neutralino
Stable LSP of SUSY models which conserve R-Parity
characteristic of EW interactions
… AND MANY MORE!!! (e.g. LDM, Gravitinos, Axions, KK bosons, …)

4. DM Detection Methods Two Complementary Methods: Direct Detection
Measure phonon, charge or light signals produced from elastic scattering of WIMPS with a nuclear target
DAMA, CDMS, EDELWEISS, ZEPLIN, CRESST
Indirect Detection
Measure excess in diffuse antiparticle flux from DM annihilations
HEAT, HESS, EGRET, BESS

5. A Positron Excess Astrophysical sources are insufficient!!!
Background (Protheroe, 1984)
EXCESS!
Astrophysical Sources?
Supernovae Type 1a
Massive Wolf-Rayet stars
Astrophysical sources are insufficient!!!

6. Positron Production from annihilation
Continuum positrons from cascades involving and
Final injection spectrum depends on mass and decay modes:
For ,
(solid) dominates and (dotted)
less so
For :
(dashed)
occur, producing a more
complicated spectrum

7. annihilation within a smooth halo
Positrons
Antiprotons
(Baltz et al. 2001)
Annihilation Rate
We require Substructure!!!

8. DM Substructure
Standard model assumes that structure originated from quantum fluctuations during inflation
“Bottom-up” hierarchical structure formation
Subhalo Population = (Constructive Merging) + (Tidal Destruction)
Total flux from DMCs strongly depends upon and
(Diemand et al. Nature, 433, 389 (2005))
Assuming that the DMC distribution traces the halo density with a halo-to-halo scatter of 4

9. DM Substructure
But the simulation was terminated at z=26
We must account for subsequent tidal stripping by stellar encounters during orbits
(Zhao et al. 2005)
We assume that all clumps will currently possess a fraction f (0< f <1) of its mass at z=26, since
We adopt NFW profiles for the DMCs (~consistent with simulation data)
The amplification of the antiparticle flux from clumps is then:

10. Cosmic Ray Propagation
Charged particles diffuse through ISM
Scattering off galactic B-field, CMB radiation and starlight result in energy losses
Diffusion can be well-approximated to a random walk
Diffusion Constant
Energy loss rate
Assuming a constant B-field:
Source Term
Proportional to halo
annihilation rate per unit vol.

11. Cosmic Ray Propagation
We solve for the steady-state solution
Manipulate into an inhomogeneous ( “heat” ) equation (Baltz et al. 1998)
We can solve for by constructing the Green’s function

12. Cosmic Ray Propagation
We solve the inhomogeneous equation, using method of Fourier Transforms,
for a mono-energetic, point source (of energy and position ):
Boundary Conditions? z
Assume uniform cylindrical diffusion zone: 2L
Diffusion Zone
Free Escape Zone
BCs require at
(Webber et al. 1971)
Using principle of superposition (Baltz et al. 1998):

13. Cosmic Ray Propagation
Finally, the solution for the local differential flux (z=0, r=8 kpc) is
Calculate PF using for 4 benchmark MSSM models
Calculate PF for and or 3
left as a free parameter

14. Positron Fraction

15. Positron Fraction We require: (for up to 90% stripping)
Canonical value:
Profumo indicates how canonical value can be grossly violated with at possible
However these models require co-annihilations and resonant annihilations making them more contrived

16. Conclusion + Further Work
Considering the errors in the halo DMC abundance, some models are clearly permitted, with preferential selection towards lighter LSPs, even
when considering the effects of tidal destruction
To improve our analysis we can select LSPs based on a more stringent scan of the entire MSSM parameter space
Cross-reference results on PF with an analysis of cosmic antiprotons,
antideuterons, gamma rays, etc.