astrophysical signals of dark matter...

Astrophysical Signals of Dark

Matter Annihilation

Positrons and Gamma-Rays

Sheldon Campbell

Texas A&M University PAC Lunch Seminar

September 10, 2008

Outline

1. Why dark matter (in astrophysics, cosmology, and particle physics)?

2. Galactic dark matter annihilation signal: positrons and gamma-rays.positrons and gamma-rays.

3. The importance of halo substructure and some recent results.

4. Extragalactic dark matter annihilation gamma-rays.

5. Conclusions.

Dark Matter in Astronomy

• Spiral galaxy rotation curves

• Velocity dispersions of:

– Matter in elliptical galaxies

– Matter in dwarf galaxies– Matter in dwarf galaxies

– Galaxies in galaxy clusters

Abell 2029

70-90% dark matterM�1014 M�

Dark Matter in Astronomy

• Gravitational Lensing– dark matter maps: subtract visible matter from

observed mass distribution

• Cosmic Microwave Background FluctuationsFluctuations– consistent with ΛCDM cosmology with 23%

cold dark matter energy content

• Large scale structure formation requires cold dark matter

Dark Matter in Astronomy

• Gravitational Lensing– dark matter maps: subtract visible matter from

observed mass distribution

• Cosmic Microwave Background FluctuationsFluctuations– consistent with ΛCDM cosmology with 23%

cold dark matter energy content

• Large scale structure formation requires cold dark matter

Any alternative to dark matter has a lot of work to do.

Dark Matter Properties

Cold dark matter is:

• non-relativistic

• electrically neutral

• massive• massive

• stable

• weakly interacting

• does not form compact objects

– EROS-2 experiment sees very few compact objects in

the galactic halo (Tisserand et al ’07)

Dark Matter in Particle Physics

• Standard Model contains no such matter.

– What about massive neutrinos?

• relativistic (bad for structure formation)

• not abundant enough (small part of DM content)

• Particle candidates found in Extensions to the • Particle candidates found in Extensions to the

Standard Model such as

– supersymmetry with R-parity

– extra dimensions (Kaluza-Klein)

• Models constructed to give correct dark matter

relic density in big bang scenarios.

Particle Physics Prediction

Dark matter particles annihilate.

etc.

ν

γ

e+

p-

etc.

Annihilation products and

their spectra per annihilation

depend on interaction properties.

Astrophysical Signal of Dark Matter

Annihilation

Intensity profile of products depend on:

– particle physics properties of dark matter

• annihilation cross section determines the rate of

annihilation for a given density of dark matterannihilation for a given density of dark matter

• spectrum per annihilation

– dark matter distribution

• intensity traces density squared

– interactions of products with astronomical

background

Signals to look for:

• positrons

– HEAT

– PAMELA

– AMS-02– AMS-02

• gamma-rays

– EGRET

– Fermi Gamma-Ray Space Telescope

Positron Signal

DM+

e- + e+

µ+ + …τ+ + …

e+ + …e+ + …e+ + …

+DM q + …

W + …

e+ + …e+ + …

etc.

Positron Propagation

Tangled magnetic fields randomize the particle motion.

Modeled as a random walk via a diffusion equation. (Lavalle et. al. ’08)equation. (Lavalle et. al. ’08)

)(2

0

0 EQE

n

dt

dE

EE

n

E

EK =

∂

∂

∂

∂+

∂

∂∇

−

δ

diffusion

coefficient

energy

losses

positron

source

3 Main Sources of Energy Loss

• synchrotron emission

B�� µG ⇒ ε���������

� ���������� ����� ������� �������������������� �������������������

��������

� ������ ������� ���������� �����������

3 Main Sources of Energy Loss

• synchrotron emission

B�� µG ⇒ ε���������

� ���������� ����� ������� �������������������� �������������������

��������

� ������ ������� ���������� �����������

EE

E

dt

dE

τ0

2−=

Myrs 3001016 ≈≈Eτ

GeV10 ≡E

Diffusion Equation

Boundary Conditions

Diffusion zone is a pillbox of height 2L.

L ~ distance cosmic ray

travels before escapingtravels before escaping

the galactic disk

2L

0=∂

∂

E

non the boundary

Allowed Diffusion Model

Parameters

Lavalle, et. al. allowable parameter range

– consistent with observed B/C flux ratios in

cosmic rays (Maurin,Trillet,Donato ’02)

δ K0 (kpc2/Myr) L (kpc)

max 0.46 0.0765 15

med 0.70 0.0112 4

min 0.85 0.0016 1

Positron Propagation Length

– emitted at energy ES

– detected at energy E

−

=

−− 11

04δδ

τλ

EEK SE

−

−=

00

0

1

4

δ

τλ

E

E

E

EK SE

D

Positron Propagation Length

– emitted at energy ES

– detected at energy E

−

=

−− 11

04δδ

τλ

EEK SE

−

−=

00

0

1

4

δ

τλ

E

E

E

EK SE

D

Example:−“med” diffusion model

− ES = 200 GeV

E = 190 GeV ⇒ λD = 0.4 kpc

E = 1 GeV ⇒ λD = 5.7 kpc (galactic centre is 7.6 kpc away)

⇒ 2.09.6

3.0

−

≅

−

GeVkpc

EDλ

Barger, Keung, Marfatia, Shaughnessy (2008)

PAMELA Results and

Generic Annihilation Models

Smooth NFW halo profile

γγ

ρρ

−

+

=

3

1

)(

ss

s

r

r

r

r

r

with inner slope γ = 1.Mode Model MDM B · ⟨σ v⟩ · 1025 χ2/dof

(GeV) (cm3/s)

WLWL med 150 6.6 1.2

med 85 2.3 2.8

WTWT med 150 7.3 1.7

med 85 2.1 2.1

e+e- min 150 17.0 5.0

med 150 5.9 0.9

max 150 3.7 1.1

min 85 4.1 5.0

med 85 2.0 1.0

max 85 1.3 1.7

Halo substructures contribute a signal boost B.

PAMELA and mSUGRA

Such a dramatic rise in flux is seen in models in the coannihilation region where mχ ≈ m

ẽ.

The branching ratio for

χ e-

becomes greatly enhanced in this parameter space.

χ

χ

ẽ

e-

γ

e+

GeV

GeV

240

233

~ =

=

em

mχ

PAMELA and mSUGRA

GeV

GeV

240

233

~ =

=

em

mχ

PAMELA and mSUGRA

GeV

GeV

240

233

~ =

=

em

mχ

PAMELA and mSUGRA

Require boost factors of ~104

Substructures boost the

annihilation signal

The cores of NFW haloes become more

dense for smaller mass objects.

0)(

<∂ rρ

0)(

<∂

∂

rM

rρ

profiles halo matter dark smooth to dueIntensity

ressubstructu withondistributi to dueIntensity =B

Boost Factor:

Assumed to be energy independent.

Inside a smooth halo

Siegal-Gaskins (2008)

Subhaloes with Mmin=107 M�

Siegal-Gaskins (2008)

Subhaloes with Mmin=10 M�

Siegal-Gaskins (2008)

Substructure in Simulations

Aquarius Simulations (Virgo Collaboration)

– Springel, et. al. (2008)

– presented by Carlos Frenk at IDM 2008

– 6 galaxy size haloes at various resolutions– 6 galaxy size haloes at various resolutions

Via Lactea Simulations

– Diemand, et. al. (2007)

– Diemand, et. al. (2008)

– presented by Michael Kuhlen at IDM 2008

Resolution of the Simulations

Simulation

Particle

number in

halo

# of resolved

substructures

Mass resolution (M��

Aq-A-5 808,479 299 3.14 x 106

Aq-A-4 6,424,399 1,960 3.92 x 105

Aq-A-3 51,391,468 13,854 4.91 x 104

Aq-A-2 184,243,536 45,024 1.37 x 104

Aq-A-1 1,473,568,512 297,791 1.71 x 103

Via Lactea I 84,700,000 ~10,000 2.18 x 104

Via Lactea II 470,000,000 ~100,000 3.92 x 103

z = 1.5

•N200=3×106

4003

run

Aquarius

z = 1.5

•N200=94×106

12003 run

Aquarius

z = 1.5

N200=750×106

24003 run

Aquarius

z = 1.5

N200=750×106

24003 run

Aquarius~10% halo mass in substructures

Via Lactea II inner 40 kpc

Subhalo abundances:

in agreement

Does spherically averaged

simulated halo profile agree with

NFW profile?

Aquarius shows excellent convergenceat all resolutions.

Profile is approximatelyProfile is approximatelyfit by an NFW profile.

Check the logarithmicslope of the profile.

Logarithmic slope of Aquarius’

spherically averaged density profile

NFW profile

dlo

g r

Shallower than NFWat small radii.

No obviousconvergence to apower law at small

Moore et al

Navarro et al. (2004)

(Einasto profile; α=.19)

dlo

g ρ

/dlo

g r

r [kpc]

power law at smallradius.

Einasto halo profileprovides a better fit.

( )[ ]12 −−=

α

αρρ srr

es

Via Lactea II shows similar results

A sampling of 8 largesubhaloes shows cuspyinteriors, but smaller densitythan main halo.

Red: best fit NFW profilewith γ = 1.24.

Blue: best fit Einasto profilewith α = 0.170.

How scale dependent is the structure?

From Diemand, et. al. (2008):

“Via Lactea II predicts a remarkable self-similar

pattern of clustering properties…. [A] simple pattern of clustering properties…. [A] simple

explanation: subhalo density profiles were

modified by tidal mass loss, which removes

material from the outside in, but does not

change the inner cusp nature.”

How scale dependent is the structure?

“Via Lactea II demonstrates the fractal-like appearance of the dark matter by resolving the second generation of surviving sub-structures from the merging hierarchy. This suggests that at infinite hierarchy. This suggests that at infinite resolution one would find a long nested series of halos within halos etc., reminiscent of a Russian Matryoshka doll, all the way down the first and smallest earth mass haloes that form.”

Carlos Frenk offered a different view at IDM 2008

“The hierarchy is clearly NOT self-similar and is heavily is heavily dependent on the degree of tidal stripping of the subhalo.”

Via Lactea II estimate of boost factors

Assumptions:

– inner profile slope of subhaloes evenly distributed

between 1.0-1.5.

– extrapolate simulation resolution down to earth-size

microstructures.

Positron signal:Positron signal:

– assumed detectable anti-particles produced within

1 kpc.

– average boost B = 1.4.

– 1% of locations (near a large substructure) had B > 10.

Gamma-ray signal:

– estimated B ≈ 4–14.

Aquarius’ prediction for gamma-rays from milky way dark matter annihilation

…and from Via Lactea II

Can you see it? FGST 4-day exposure

Some issues currently being debated in

the substructure community

• Is halo dark matter comprised mostly of small earth sized clumps?

• Do small earth sized clumps dominate the annihilation signal?annihilation signal?

• Are dwarf subhalos the best targets for detecting a signal? (Better than a diffuse signal?)

• Are subhalo emissions boosted by sub-substructure?

Now let us considerextragalactic darkmatter annihilationmatter annihilationsignals.

Extragalactic gamma-rays due to

dark matter annihilation

• Subtraction of the modeled galactic sources reveals isotropic extragalactic gamma-rays.

Ando, Komatsu (2006)Ando, Komatsu (2006)

),(3

2

2

)1(8

),(

1

),]1([)()(

zEe

dE

dNz

m

vzEW

zEzWrdrEI

γτ

γ

γ

γ

ρ

ρ

ρ

γργγ

ρ

π

σ

δ

δ

−+

=

−≡

+= ∫

DM

DM

Spherical halo model provides good

descriptions of dark matter distribution

Cooray, Sheth (2002)

)(

),|(),()(

2

2

z

zMrdV

dM

zMdndMz

Mρ

ρδ ρ

∫∫∞

=

min

Halo mass function well constrained by

simulations at large mass scalesJenkins, et. al. (2001)

Intensity profile contains

unconstrained boost factor

• The signal is again expected to be boosted due to halo substructures.– Can a galactic positron signal provide some

constraint to an extragalactic gamma-ray signal boost factor?signal boost factor?

• Idea: if the boost factor is independent of the gamma-ray energy, then it does not contribute to the angular power spectrum.– angular power spectrum therefore provides a

more robust signal prediction.

Possibility of intensity boosts due to

large velocity effects?

• When the comoving velocity of annihilating particles is relativistic, the annihilation cross section increases with velocity.

( )2)( vbavv +≈σ

• For neutralino dark matter, b/a ≈ mχ / me .

• Velocity effects become important approximately when the maximum circular velocity of a halo satisfies

( )2)(

c

vbavv +≈σ

1

2

≥

c

v

a

b

Conclusions

• The realization that one may learn about particle

interactions through astronomical observation is

remarkable.

• Resolution of a dark matter annihilation signal may

requirerequire

– a stronger understanding of the distribution of dark

matter (particularly small scale structure and

substructures),

– strong propagation models of the annihilation

products,

– an understanding of background processes that

produce high energy particles, and the distribution

and abundance of these processes.

Conclusions

• Current models seem to require very large boost factors

to explain preliminary excesses as dark matter

annihilation.

• These indirect detection experiments, along with direct

detection experiments and collider experiments will detection experiments and collider experiments will

provide independent, complementary constraints that will

provide directions to the correct physics that lies beyond

the standard model.