Cosmological dark matter annihilation

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1 Cosmological dark matter annihilation Alexander Belikov Department of Physics University of Chicago November 1, 2010 A.Belikov, D. Hooper, Phys.Rev.D 80, (2009) A.Belikov, D. Hooper, Phys.Rev.D 81, (2010) SCIPP, UC Santa Cruz

2 Outline 1 The evidence for dark matter A. Belikov (University of Chicago) Dark matter annihilation. November / 37

3 Outline 1 The evidence for dark matter 2 Observations A. Belikov (University of Chicago) Dark matter annihilation. November / 37

4 Outline 1 The evidence for dark matter 2 Observations 3 The diffuse extragalactic gamma-ray flux from dark matter annihilation Annihilation spectrum Halo parameters A. Belikov (University of Chicago) Dark matter annihilation. November / 37

5 Outline 1 The evidence for dark matter 2 Observations 3 The diffuse extragalactic gamma-ray flux from dark matter annihilation Annihilation spectrum Halo parameters 4 Dark matter effects during reionization epoch A. Belikov (University of Chicago) Dark matter annihilation. November / 37

6 Outline 1 The evidence for dark matter 2 Observations 3 The diffuse extragalactic gamma-ray flux from dark matter annihilation Annihilation spectrum Halo parameters 4 Dark matter effects during reionization epoch 5 Summary A. Belikov (University of Chicago) Dark matter annihilation. November / 37

7 Evidence for Dark Matter. Galaxy rotation curves, velocity dispersion of galaxies Gravitational lensing by galaxy clusters Structure formation (CMB anisotropies and N-body simulations) Big Bang nucleosynthesis Dark Energy Gas, Stars, us Dark Matter A. Belikov (University of Chicago) Dark matter annihilation. November / 37

8 Dark Matter candidates 1 Neutralinos (MSSM, NMSSM, nmssm), gravitinos, etc. 2 Axions. 3 Kaluza-Klein photons/neutrinos. 4 Fourth generation neutrinos. 5 Q-balls, Wimpzillas... 6 Baryonic: black holes, neutron stars, white dwarfs, brown dwarfs - excluded by BBN and microlensing. A. Belikov (University of Chicago) Dark matter annihilation. November / 37

9 The WIMP miracle Y = n X s Γ H Y = const, freeze-out Ω M h cm 3 s 1 /( σv ) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

10 Dark Matter detection 1 Direct detection: looking for collisions with ordinary matter. Cryogenic detection: CDMS, DAMA/LIBRA and others. Noble gases: XENON, ArDM,... 2 Indirect detection: searching for products of annihilation. High energy photons Space telescopes: COMPTEL, Fermi Gamma-Ray Telescope. Imaging Athmospheric Cherenkov Telescopes: HESS, Veritas, Magic. Electrons/positrons: PAMELA, ATIC. Antiprotons: PAMELA, AMS. Neutrinos: ANTARES, IceCube. 3 Indirect 2 : CMB optical depth and anisotropies, IGM temperature and 21 cm - recombination and reionization observables. 4 Collider searches: LHC. A. Belikov (University of Chicago) Dark matter annihilation. November / 37

11 Indirect Detection of Dark Matter Sources of annihilating/decaying Dark Matter. 1 The core of the Sun. 2 Galactic dark matter from the halo and the substructure. 3 The center of galaxy. 4 Cosmological dark matter: Distant halos. Smooth component (Might have been important in early universe.) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

12 Fermi Gamma-Ray Telescope A. Belikov (University of Chicago) Dark matter annihilation. November / 37

13 EGRET,COMPTEL and Fermi Abdo et al. PRL 104, (2010); Oberlack, Physics 3, 21 (2010) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

14 PAMELA Adriani et al., Nature, 458, 607, (2009) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

15 Calculation of the flux 1 The annihilation spectrum: electrons/positrons and prompt photons (PYTHIA) 2 Inverse Compton photons production by high-energy electrons 3 The halo annihilation enhancement factor B(z, M) 4 Halo mass function 5 Optical depth dφ dedtdωda = σv c ρ 2 X 8π H 0 m 2 X dzdm (1+z)3 h(z) B(z,M) dn γ de (z,e)e τ(z,e) dn dm (z,m) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

16 Monochromatic line: forbidden at tree level, but distinct. χ+ χ γ +γ Continuum spectrum: photon is a by-product of annihilation to... Gauge bosons: χ+ χ W + +W γ +... leptons: χ+ χ τ + +τ γ +... quarks: χ+ χ b+ b γ +... Direct annihilation. χ+ χ e + +e For Majorana fermions the amplitude of s-wave annihilation to fermions is suppressed by the square of mass of the final-state fermion. Continuum spectrum: e + e is a by-product of annihilation to... Gauge bosons: χ+ χ W + +W e + +e... leptons: χ+ χ τ + +τ e + +e +... quarks: χ+ χ b+ b e + +e +... A. Belikov (University of Chicago) Dark matter annihilation. November / 37

17 Inverse Compton scattering off abundant CMB photons dn dǫdt = 3σ T cn e (2ǫlnǫ+ǫ+1 ǫ 2 )N(ν 0 )dν 0, where ǫ = ν ( ) 2ECMB h ν 4 Ee 3 m e = (1+z) ( E e 100GeV dn de γ Eγ 3/2, τ H τ IC 4γ 2 ν 0 ) 2 GeV GeV e GeV W + W channel prompt γ e + e IC γ E 2 dn γ /de (GeV) 10 1 E 2 dn γ /de (GeV) E (GeV) 1e-08 1e E (GeV) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

18 The halo annihilation enhancement factor B(z,M) or 2 (z,m) {a,ρ 0 } {c,m} B(z,M) dc P(c ) d 3 rρ 2 (r) P(c ) is a log-normal distribution around c vir (M), σ(log 10 c) = 0.2 Halo density profile ρ(r) = ρ g(r/a) 1 g NFW (x) = x(1+x) 2 1 g Moore (x) = x 1.5 (1+x) g B (x) = (1+x)(1+x 2 ) g Ein (x) = exp [ 2 α (xα 1) ],α = 0.17 c(m) R vir /r 2, M = 4π 3 vir ρ(z)r vir 3, vir 18π2 +82y 39y 2 Ω M (z), y = Ω M (z) 1, r 2 : d/dr(r 2 g(r)) r = 0. ρ(x) x NFW Moore Burkert Einasto A. Belikov (University of Chicago) Dark matter annihilation. November / 37

19 Halo concentration parameter There is a correlation between the mass of the halo M and the concentration parameter c. J. Bullock et al., MNRAS 321, 559 (2001). On average collapse redshift z c is assigned to a halo of mass M through relation M(z c ) = FM, with F = and the typical collapse mass M is defined by σ( M(z)) = δ sc (z). c vir (M,z) = zc 1+z The concentration is cut off at 10 5 solar masses. A. Maccio et al., MNRAS 391, 1940 (2008) logc = log(M/[10 12 h 1 M ))/(1+z) 100 c vir (z=0) 10 Bullock et al. Maccio et al log 10 (M/M Sun ) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

20 Halo mass function. PS universal form: dn dm = ρ 0 M 2 νf(ν) d logν d logm, ν = δ(z)/σ(m). Power spectrum: σ 8 = 0.812, n s = Linear overdensity: δ sc = Sheth-Tormen multiplicity function: νf(ν) = ( ) A 1+ 1 ν 2 ν 2q 2π exp( ν 2 /2 ) with ν = aν, a = 0.75 and q = 0.3. At z = 0 approximately 70% of mass is in halos heavier than 10 6 solar masses. Reed et al., MNRAS 374, 2 (2007) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

21 Optical depth. F.W. Stecker, M.A. Malkan, S.T. Scully, Astrophys.J.648, 774, (2006) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

22 W + W channel: conservative case E 2 dn γ /de (GeV/cm 2 /s/sr) e-05 1e-06 1e-07 1e-08 1e-09 1e-10 W + W channel 100 GeV 200 GeV 400 GeV 800 GeV 1.6 TeV E 2 dn γ /de (GeV/cm 2 /s/sr) 1e-05 1e-06 1e-07 W + W channel 100 GeV 200 GeV 400 GeV 800 GeV 1.6 TeV 1e-11 1e E (GeV) 1e E (GeV) AB, D. Hooper, Phys.Rev.D 81, (2010) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

23 e + e channel: extreme case E 2 dn γ /de (GeV/cm 2 /s/sr) e-05 1e-06 1e-07 1e-08 1e-09 1e-10 e + e channel 100 GeV 200 GeV 400 GeV 800 GeV 1.6 TeV E 2 dn γ /de (GeV/cm 2 /s/sr) 1e-05 1e-06 1e-07 e + e channel 100 GeV 200 GeV 400 GeV 800 GeV 1.6 TeV 1e-11 1e E (GeV) 1e E (GeV) AB, D. Hooper, Phys.Rev.D 81, (2010) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

24 µ + µ channel E 2 dn γ /de (GeV/cm 2 /s/sr) e-05 1e-06 1e-07 1e-08 1e-09 1e-10 µ + µ channel 100 GeV 200 GeV 400 GeV 800 GeV 1.6 TeV E 2 dn γ /de (GeV/cm 2 /s/sr) 1e-05 1e-06 1e-07 µ + µ channel 100 GeV 200 GeV 400 GeV 800 GeV 1.6 TeV 1e-11 1e E (GeV) 1e E (GeV) AB, D. Hooper, Phys.Rev.D 81, (2010) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

25 τ + τ channel E 2 dn γ /de (GeV/cm 2 /s/sr) e-05 1e-06 1e-07 1e-08 1e-09 1e-10 τ + τ channel 100 GeV 200 GeV 400 GeV 800 GeV 1.6 TeV E 2 dn γ /de (GeV/cm 2 /s/sr) 1e-05 1e-06 1e-07 τ + τ channel 100 GeV 200 GeV 400 GeV 800 GeV 1.6 TeV 1e-11 1e E (GeV) 1e E (GeV) S. Profumo, T. E. Jeltema JCAP 0907:020,2009 AB, D. Hooper, Phys.Rev.D 81, (2010) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

26 Required Boost Factor e + e W + W µ + µ τ + τ Boost factor m X (GeV) AB, D. Hooper, Phys.Rev.D 81, (2010) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

Reionization The absence of compete absorption at Lyman-α frequency (Gunn-Peterson trough): H ionized at z 6 UV: He doubly ionized z 3 τ = 0.038 WMAP5: τ = 0.084±0.

27 Reionization The absence of compete absorption at Lyman-α frequency (Gunn-Peterson trough): H ionized at z 6 UV: He doubly ionized z 3 τ = WMAP5: τ = 0.084±0.016 Ly-α forest observations: IGM heating (2 < z < 5) K T igm K at z 4 A. Belikov (University of Chicago) Dark matter annihilation. November / 37

28 The summary of research efforts of dark matter effect on reionization The decay of uniformly distributed DM; E. Pierpaoli (2003), X.Chen, M. Kamionkowski (2003). The annihilation of uniformly distributed DM; Mapelli et al, (2006), Furlanetto et al. (2006). The annihilation of dark matter from halos, L. Chuzhoy (2007), A. Natarajan et al. (2008). The annihilation of dark matter from halos, inverse Compton, AB and D. Hooper (2009), M. Cirelli et al. (2009). Baryonic matter clumping, tracking neutral H and He separately. A. Belikov (University of Chicago) Dark matter annihilation. November / 37

29 The ionized fraction is governed by dx e dz = 1 (1+z)H(z) [R s(z) I s (z) I DM (z)] (1+z) dt b dz = 8σ Ta R TCMB 4 x e 3m ech(z) 1+f He +x e (T b T CMB )+2T b 2 R s = Cα B (T b )x 2 en b (z); I s = Cβ T (1 x e )e E 2s kt b χ i χ e (1 x e )/3, χ h (1+2x e )/3 K(z) 3k b H(z) 1+f He +x e X. Chen, M. Kamionkowski, Phys.Rev.D70 (2004) I DM (z) = Q(z)/n b (z)/e 0, K(z) = Q(z)/n b (z) M χ Q(z) = 1 xe 3 dee dn de γ (E γ,z) [ n A (1+z) 3 (1 x) ] σ(e)c E i z+ z dn de = ( ) dz dt dz (z ) dn 1+z de 1+z E A(z )e τ(z,z,e) z A(z) = σv 2M 2 χρ 2 DM (1+z)6 ((1 f) 2 +B(z)) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

30 The fraction of primary energy deposited as heat, ionization and excitation vs. ionized fraction J. M. Shull and M.E. Steenberg, APJ 298, 268 (1985) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

31 The differential fraction of a 1 TeV photon streaming from z to z deposited as heat, ionization and excitation vs. ionized fraction. Thick lines correspond to z = 1000, thin lines correpond to z = 100. A. Belikov (University of Chicago) Dark matter annihilation. November / 37

32 The ratio annihilation rates of halo vs smooth component of dark matter A(z) = σv 2M 2 χρ 2 DM (1+z)6 ((1 f) 2 +B(z)) 1e NFW Einasto B(z)/(1-f(z)) z A. Belikov (University of Chicago) Dark matter annihilation. November / 37

33 Cross sections of Klein-Nishina, photoionization and pair production photoionization 1e-20 1e-21 Photoionization Klein-Nishina Pair Production Compton scattering on electrons 1e-22 1e-23 production of pairs on atoms production of pairs on free electrons and nuclei scattering/pair production on background photons σ (E) cm 2 1e-24 1e-25 1e-26 1e-27 1e-28 1e E (GeV) A. Zdziarski and R. Svensson, APJ 344, 551 (1989) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

34 A test case. The deposition rate of M X = 2TeV to τ + τ neglecting structure. Neglect the role of halos and set B(z) = 0 and f(z) = 0. ( ) A(z) = σv 2M ρ 2 χ 2 DM (1+z) Mχ 2(1+z) 6 2TeV cm 3 s 1 Set z to 0.1: dn de dn de (E)A(z) dt dz (z) z = dn de (E)(1+z)7/2 ( Mχ 2TeV ) 2cm 3 s 1 GeV 1 With σ(e) = σ T σ(e), where σ T = cm 2, n A = n bar ((1 Y)+0.25Y) = cm 3, Helium Y = 0.25: I(z) = (1+z) 4 ( Mχ 2TeV ) 2 Mχ E i dee dn de (E) σ(e)[gevcm 3 ] A. Belikov (University of Chicago) Dark matter annihilation. November / 37

35 A test case. The deposition rate of m X = 2TeV to τ + τ over z = 0.1 neglecting structure B(z) = 0. M χ dee dn de E i (E) σ(e) - redshift dependent (IC number density) Pair production depends on prompt photons mostly. z Klein-Nishina Photoionization Pair production [GeV] z I KN (z) I photion (z) I pair (z) [GeVcm 3 ] A. Belikov (University of Chicago) Dark matter annihilation. November / 37

36 A test case. The deposition rates for different absorption channels. 2 TeV WIMP τ + τ channel, deposition rates Klein-Nishina Phot-ion Pair-Production I(z) (GeV/cm 3 ) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

37 The deposition rate of M X = 2TeV to τ + τ with attenuation and clumping included. 1e-28 M X = 2 TeV τ + τ 1e-29 I(z) GeV/cm 3 1e-30 1e z A. Belikov (University of Chicago) Dark matter annihilation. November / 37

38 W + W with σv = cm 3 s 1 AB, D. Hooper, Phys.Rev.D 80, (2009) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

39 W + W with σv = cm 3 s 1 AB, D. Hooper, Phys.Rev.D 80, (2009) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

40 e + e with σv = cm 3 s 1, M X = 100 GeV and M X = 600 GeV AB, D. Hooper, Phys.Rev.D 80, (2009) A. Belikov (University of Chicago) Dark matter annihilation. November / 37

41 Summary Inverse Compton photon spectrum is widened by a factor of 2 and shifted down in energies compared to electron spectrum. Inverse Compton scattered photons coming from Dark Matter annihilating primarily in leptophilic channels weakens DM constraints by a factor of two: required boost factor is about a hundred for 100 GeV neutralino annihilating to τ + τ, reminiscent of boost factors required to explain PAMELA. The results from Fermi lower the constraints by a factor of 5 for M X 1TeV for W + W and a factor of few for for M X = GeV for τ + τ. IC photons might have played a role in reionization history: predicted optical depth τ and baryonic temperature T b can become competitive. A. Belikov (University of Chicago) Dark matter annihilation. November / 37

M. Lattanzi. 12 th Marcel Grossmann Meeting Paris, 17 July 2009

M. Lattanzi. 12 th Marcel Grossmann Meeting Paris, 17 July 2009 M. Lattanzi ICRA and Dip. di Fisica - Università di Roma La Sapienza In collaboration with L. Pieri (IAP, Paris) and J. Silk (Oxford) Based on ML, Silk, PRD 79, 083523 (2009) and Pieri, ML, Silk, MNRAS