1. Upper Bound on the Dark Matter Annihilation Cross Section Gregory Mack CCAPP/The Ohio State University

2. 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 cm 3 /s

3. 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

4. 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”

5.  No invisible products: essentially two classes of annihilation products Photons Photons (direct or eventual)  Hadrons  pions  photons  Charged leptons  radiative loss/internal brehmsstrahlung  Gauge bosons  charged leptons  Monoenergetic Photons Neutrinos Neutrinos  Sum of probabilities = 100% Compare background fluxes to theoretical signals

6.  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

7. Neutrinos Atmospheric neutrino background. Photons INTEGRAL, COMPTEL, EGRET, CELESTE, HESS, HEGRA Regardless, divide background into energy bins to look

8. Combined constraint for 2 photons  Results for Kravtsov profile (NFW = lighter)  Wide range of masses  Limit takes the most stringent value at each mass

9. TOTAL cross section limits  Wide-ranging model-indep. limit  Conservative, comprehensive  Gamma limit is comparable to Neutrino Mack, Beacom, Bell, Jacques, Yüksel Astro-ph/0803.0157v2 (PRD)

10. More cross section limits  New limits on photons coming from internal brehmsstrahlung from charged leptons  Bell and Jacques  Astro- ph/0811.0821v1

11. More cross section limits

12.  We have the capability to make statements about the amount of annihilation dark matter experiences  General, comprehensive limits  Better data means tighter constraints Conclusions

13. Extra Slides

14. Distribution  Different profiles  different inner behavior  Moore ρ ~ 1/r 1.5  NFW 1/r 1.0  Kravtsov 1/r 0.4 Moore NFW Kravtsov

15. n2n2 Integral over redshift. The spectrum of neutrinos depends on the redshift

16. 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

17.  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

18. J dependence on profile  YHBA figure Moore NFW Kravtsov

19. Background subtraction  J delta’s minus specific J(psi) HESS INTEGRAL