Upper Bound on the Dark Matter Annihilation Cross

Section

Gregory MackCCAPP/The Ohio State University

The self-annihilation cross section

How large can the self-annihilation cross section be?

That’s the question to ask

Most often assumed – “natural scale” 3 x 10-26 cm3/s

Early playing field First: Unitarity Limit from Q.M.

The probabilities for elastic and inelastic scattering must sum to 1

Unitarity of the scattering matrix

Early playing field Second: KKT Take a cuspy profile

and turn it into a core

KKT would need a BR of about 10-10 to not be seen in monoenergetic photons

Say it must be “invisible particles”

No invisible products: essentially two classes of annihilation products PhotonsPhotons (direct or eventual)

Hadrons pions photons Charged leptons radiative loss/internal

brehmsstrahlung Gauge bosons charged leptons Monoenergetic Photons

NeutrinosNeutrinos Sum of probabilities = 100%

Compare background fluxes to theoretical signals

Depends on if you’re looking at: diffuse contribution from all galaxies

Need to integrate over redshift and include the fact that dark matter is clumped in

galaxies

Galactic halo (at some angle from GC) External galaxy (M 31)

DM halo line-of-sight int.

DEPENDS ON PROFILE

Theoretical Signals

Neutrinos

Atmospheric neutrino background.

PhotonsINTEGRAL, COMPTEL, EGRET,

CELESTE, HESS, HEGRA

Regardless, divide background into energy bins to look

Combined constraint for 2 photons

Results for Kravtsov profile (NFW = lighter)

Wide range of masses

Limit takes the most stringent value at each mass

TOTAL cross section limits Wide-ranging

model-indep. limit

Conservative, comprehensive

Gamma limit is comparable to Neutrino

Mack, Beacom, Bell, Jacques, YükselAstro-ph/0803.0157v2 (PRD)

More cross section limits New limits on

photons coming from internal brehmsstrahlung from charged leptons

Bell and Jacques Astro-ph/

0811.0821v1

More cross section limits

We have the capability to make statements about the amount of annihilation dark matter experiences

General, comprehensive limits

Better data means tighter constraints

Conclusions

Extra Slides

Distribution

Different profiles different inner behavior

Moore ρ ~ 1/r1.5

NFW 1/r1.0

Kravtsov 1/r0.4

Moore

NFW

Kravtsov

n2Integral over redshift.The spectrum of neutrinosdepends on the redshift

Theoretical flux calculations – Analysis Methods

Line of sight integral – angular radius ψ

Average over a cone of half-angle ψ

Note: This was done by Yüksel, Horiuchi, Beacom, and Ando to modify our neutrino bound for the Milky Way

AMANDA and SK data support the non-existence of a signal from DM annih.

Atmospheric Neutrino Background

Munich (AMANDA), astro-ph/0509330

Ashie, et al (Super-K)PRD 71, 112005 (2005),Fully-contained events

J dependence on profile

YHBA figure Moore

NFW

Kravtsov

Background subtraction J delta’s minus specific J(psi)

HESS

INTEGRAL