Indirect Indirect Detection Of Detection Of Dark MatterDark Matter

D.T. CumberbatchD.T. Cumberbatch

Motivation for Dark Motivation for Dark MatterMatter

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

27 3 1 2CDM3 10 cm s / hσυ − −≈ × Ω characteristic of EW characteristic of EW

interactionsinteractions

What is the Dark Matter What is the Dark Matter made of?made of?

Weakly Interacting Massive Particles (WIMPS)Weakly Interacting Massive Particles (WIMPS)

… … AND MANY MORE!!! AND MANY MORE!!! (e.g. LDM, Gravitinos, Axions, KK bosons, …)(e.g. LDM, Gravitinos, Axions, KK bosons, …)

Stable LSP of SUSY models which conserve R-ParityStable LSP of SUSY models which conserve R-Parity

0214

0113312011

01

01

~~~~~~ HNHNWNBN +++=≡χχ

Lightest NeutralinoLightest Neutralino

DM Detection MethodsDM Detection MethodsTwo Complementary Methods: Two Complementary Methods:

Direct DetectionDirect Detection Measure phonon, charge or light signals produced from elastic scattering Measure phonon, charge or light signals produced from elastic scattering

of WIMPS with a nuclear targetof WIMPS with a nuclear target DAMA, CDMS, EDELWEISS, ZEPLIN, CRESSTDAMA, CDMS, EDELWEISS, ZEPLIN, CRESST

ã

dd,

pp,

e,e

v,v ii

−+ Indirect DetectionIndirect Detection Measure excess in diffuse antiparticle flux from DM Measure excess in diffuse antiparticle flux from DM

annihilationsannihilations HEAT, HESS, EGRET, BESSHEAT, HESS, EGRET, BESS

Astrophysical Sources?Astrophysical Sources?

Supernovae Type 1a Supernovae Type 1a Massive Wolf-Rayet starsMassive Wolf-Rayet stars

Astrophysical sources are Astrophysical sources are insufficient!!!insufficient!!!

A Positron ExcessA Positron Excess

FluxElectron TotalFluxPositron Total

FluxPositron TotalFractionPositron

+=

EXCESS!

Background (Protheroe, 1984)

Positron Production from Positron Production from annihilationannihilation

01

~χ

For For , ,

(solid) (solid) dominates and dominates and (dotted) (dotted)

less soless so

ZW mmm ,<χ

bb→01

01~~ χχ

−+→ ττχχ 01

01

~~

For For : :

(dashed)(dashed)

occur, producing a more occur, producing a more

complicated spectrumcomplicated spectrum

ZW mmm ,>>χ000

101 /~~ ZZWW −+→χχ

0/0 ,, ZWH i−+ f Continuum positrons from cascades involving Continuum positrons from cascades involving

and and Final injection spectrum depends on mass and decay modes:Final injection spectrum depends on mass and decay modes:

annihilation within a annihilation within a smooth halosmooth halo

01

~χ

συρ

χ2

2

m∝Annihilation RateAnnihilation Rate We require We require

Substructure!!!Substructure!!!⇒

Positrons Antiprotons

(Baltz et al. 2001)

Smooth Halo:Smooth Halo: αγβαγρ

ρ/)(

0

])/(1[)/()(

−+=

RrRrr

30Flux HaloSmooth

Flux Observed>=sB

DM SubstructureDM Substructure Standard model assumes that structure originated from quantum fluctuations during inflationStandard model assumes that structure originated from quantum fluctuations during inflation

(Diemand et al. Nature, (Diemand et al. Nature, 433433, , 389 (2005))389 (2005))

Total flux from DMCs strongly depends upon Total flux from DMCs strongly depends upon and and),(),( max Mrrρ minM

3c1.6

pc10)(

107.5

exp)log(

)(

)(

2min200

16min

3/2

min

3

<<≈

×=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎠

⎞⎜⎝

⎛∝

∝

−

−−

−

−

Mr

MhM

MM

MM

MdMdn

kkP

sol

sol

Assuming that the DMC distribution traces the halo density with a halo-to-halo scatter of 4

-3pc500≈)(n Rsol

⇒||)( nkkP −∝ “ “Bottom-upBottom-up” hierarchical structure formation” hierarchical structure formation Subhalo Population = (Constructive Merging) + (Tidal Destruction)Subhalo Population = (Constructive Merging) + (Tidal Destruction)

DM SubstructureDM Substructure

The amplification of the antiparticle flux from clumps is then:

But the simulation was terminated at z=26 We must account for subsequent tidal stripping by stellar encounters during orbits

We adopt NFW profiles for the DMCs (~consistent with We adopt NFW profiles for the DMCs (~consistent with simulation data)simulation data)

tM

Mf

corez

now Δ∝⎟⎟⎠

⎞⎜⎜⎝

⎛≡

= ρ

ρ*

26lnln (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

Cosmic Ray PropagationCosmic Ray Propagation Charged particles diffuse through ISMCharged particles diffuse through ISM Scattering off galactic B-field, CMB radiation and starlight result in energy lossesScattering off galactic B-field, CMB radiation and starlight result in energy losses Diffusion can be well-approximated to a random walkDiffusion can be well-approximated to a random walk

),(),(),( rrr εε

εεε

εε

Qn

bn

Kn

t+⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛∂∂

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛∂∂

∇∇=⎟⎠

⎞⎜⎝

⎛∂∂

∂∂

Diffusion ConstantDiffusion ConstantEnergy loss rateEnergy loss rate

Assuming a constant B-field:Assuming a constant B-field:Source TermSource Term

Proportional to haloProportional to haloannihilation rate per unit vol.annihilation rate per unit vol.

Cosmic Ray PropagationCosmic Ray Propagation We solve for the We solve for the steady-state solutionsteady-state solution

We can solve for by constructing the Green’s function We can solve for by constructing the Green’s function

Manipulate into an inhomogeneous ( “heat” ) equation (Baltz et al. 1998)Manipulate into an inhomogeneous ( “heat” ) equation (Baltz et al. 1998)

Cosmic Ray PropagationCosmic Ray Propagation

[ ] )()(4

)(exp)(4),( 0

00

202/3

0000 υυϑυυτ

υυτπυυ −⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−−=−− −

EEfree K

KGrr

rr

We solve the inhomogeneous equation, using method of Fourier Transforms,We solve the inhomogeneous equation, using method of Fourier Transforms, for a for a mono-energeticmono-energetic, , point sourcepoint source (of energy and position (of energy and position ):):0ε 0r

Boundary Conditions?Boundary Conditions?z Assume uniform cylindrical diffusion zone: Assume uniform cylindrical diffusion zone:

2LDiffusion Zone

Free Escape Zone

Free Escape Zone

)0/( =εddn

)0/( =εddn

)( 0αεKK ≈

BCs require BCs require at at

(Webber et al. 1971)(Webber et al. 1971)

0=haloG kpc4~Lz =

∑∞

−∞=

−−−−−=−−n

nnnfreen

halo zzyyxxGG )',',','()1()','( υυυυ rr

')1(2','','' zLnzyyxx nnnn −+===

Using principle of superposition (Baltz Using principle of superposition (Baltz et al. 1998):et al. 1998):

Cosmic Ray PropagationCosmic Ray Propagation

⎭⎬⎫

⎟⎠

⎞⎜⎝

⎛

Γ⎟⎟⎠

⎞⎜⎜⎝

⎛

Γ+

−+

ΓΓ⎪⎩

⎪⎨⎧

∇−=∂Φ∂

∫

∫ −∞

=

−

==

202

22

02

5

'

)2(0kpc8

kpc80

'2)'(exp

)/'1(

784.0'

),('),(

maxrr

Irr

Rr

Rdr

LHd

ddKcfX

r

E

rz ε

φεετσυ

εεε

αr

[ ] [ ] [ ]{ }∑∞

=

Γ−−Γ++Γ−+Γ=Γ1

/)14(erf2/)14(erf/)34(erf)/(erf),(m

LmLmLmLLH

[ ] 2/10 )'(4 υυτ −=Γ EK

Finally, the solution for the local differential flux (z=0, r=8 kpc) isFinally, the solution for the local differential flux (z=0, r=8 kpc) is

Calculate PF using Calculate PF using for 4 benchmark for 4 benchmark MSSM models MSSM models

/φ ε∂ ∂ Calculate PF forCalculate PF for and 1.6 or 3 and 1.6 or 310 << f =c

συ left as a free parameter left as a free parameter

Positron FractionPositron Fraction

Positron FractionPositron Fraction

However these models However these models require co-require co-annihilations and resonant annihilations and resonant annihilations making them annihilations making them more contrivedmore contrived

Canonical value:Canonical value: 2CDM

1327 /scm103 hΩ×≈ −−συ

We require:We require: (for up to 90% stripping)(for up to 90% stripping)1325 scm10)101( −−×−≈συ

Profumo indicates how Profumo indicates how canonical value can be canonical value can be grossly violated with grossly violated with at at possible possible

1323max

scm10 −−≈συ GeV550≈χm

Conclusion + Further Conclusion + Further WorkWork

Considering the errors in the halo DMC abundance, Considering the errors in the halo DMC abundance, some models are clearly permitted, with preferential some models are clearly permitted, with preferential selection towards selection towards lighterlighter LSPs, even LSPs, evenwhen considering the effects of tidal destructionwhen considering the effects of tidal destruction To improve our analysis we can select LSPs based To improve our analysis we can select LSPs based on a more stringent scan of the entire MSSM on a more stringent scan of the entire MSSM parameter spaceparameter space

2χ

Cross-reference results on PF with an analysis of Cross-reference results on PF with an analysis of cosmic antiprotons,cosmic antiprotons,antideuterons, gamma rays, etc.antideuterons, gamma rays, etc.