Cosmological dark matter annihilation

Cosmological dark matter annihilation Alexander Belikov Department of Physics University of Chicago November 1, 2010 A.Belikov, D. Hooper, Phys.Rev.D 80, 035007 (2009) A.Belikov, D. Hooper, Phys.Rev.D 81, 043505 (2010) SCIPP, UC Santa Cruz

Outline 1 The evidence for dark matter A. Belikov (University of Chicago) Dark matter annihilation. November 2010 2 / 37

Outline 1 The evidence for dark matter 2 Observations A. Belikov (University of Chicago) Dark matter annihilation. November 2010 2 / 37

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 2010 2 / 37

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 2010 2 / 37

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 2010 2 / 37

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 2010 3 / 37

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 2010 4 / 37

The WIMP miracle Y = n X s Γ H Y = const, freeze-out Ω M h 2 3 10 27 cm 3 s 1 /( σv ) A. Belikov (University of Chicago) Dark matter annihilation. November 2010 5 / 37

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 2010 6 / 37

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 2010 7 / 37

Fermi Gamma-Ray Telescope A. Belikov (University of Chicago) Dark matter annihilation. November 2010 8 / 37

EGRET,COMPTEL and Fermi Abdo et al. PRL 104, 101101 (2010); Oberlack, Physics 3, 21 (2010) A. Belikov (University of Chicago) Dark matter annihilation. November 2010 9 / 37

PAMELA Adriani et al., Nature, 458, 607, (2009) A. Belikov (University of Chicago) Dark matter annihilation. November 2010 10 / 37

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 2010 11 / 37

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 2010 12 / 37

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 = 3.4 10 2 (1+z) ( E e 100GeV dn de γ Eγ 3/2, τ H τ IC 4γ 2 ν 0 ) 2 GeV 100 100 GeV e + 100 GeV 20 18 16 W + W channel prompt γ e + e IC γ E 2 dn γ /de (GeV) 10 1 E 2 dn γ /de (GeV) 14 12 10 8 6 4 2 0.1 0.0001 0.001 0.01 0.1 1 10 100 E (GeV) 1e-08 1e-06 0.0001 0.01 1 100 E (GeV) A. Belikov (University of Chicago) Dark matter annihilation. November 2010 13 / 37

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) 1.5 1 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) 1000 100 10 1 0.1 0.01 0.01 0.1 1 10 x NFW Moore Burkert Einasto A. Belikov (University of Chicago) Dark matter annihilation. November 2010 14 / 37

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 = 0.015 and the typical collapse mass M is defined by σ( M(z)) = δ sc (z). c vir (M,z) = 4.4 1+zc 1+z The concentration is cut off at 10 5 solar masses. A. Maccio et al., MNRAS 391, 1940 (2008) logc = 0.971 0.094log(M/[10 12 h 1 M ))/(1+z) 100 c vir (z=0) 10 Bullock et al. Maccio et al. 1-5 0 5 10 15 log 10 (M/M Sun ) A. Belikov (University of Chicago) Dark matter annihilation. November 2010 15 / 37

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 = 0.96. Linear overdensity: δ sc = 1.686. 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 2010 16 / 37

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 2010 17 / 37

W + W channel: conservative case E 2 dn γ /de (GeV/cm 2 /s/sr) 0.001 0.0001 1e-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-12 0.0001 0.001 0.01 0.1 1 10 100 1000 E (GeV) 1e-08 0.0001 0.001 0.01 0.1 1 10 100 1000 E (GeV) AB, D. Hooper, Phys.Rev.D 81, 043505 (2010) A. Belikov (University of Chicago) Dark matter annihilation. November 2010 18 / 37

e + e channel: extreme case E 2 dn γ /de (GeV/cm 2 /s/sr) 0.001 0.0001 1e-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-12 0.0001 0.001 0.01 0.1 1 10 100 1000 E (GeV) 1e-08 0.0001 0.001 0.01 0.1 1 10 100 1000 E (GeV) AB, D. Hooper, Phys.Rev.D 81, 043505 (2010) A. Belikov (University of Chicago) Dark matter annihilation. November 2010 19 / 37

µ + µ channel E 2 dn γ /de (GeV/cm 2 /s/sr) 0.001 0.0001 1e-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-12 0.0001 0.001 0.01 0.1 1 10 100 1000 E (GeV) 1e-08 0.0001 0.001 0.01 0.1 1 10 100 1000 E (GeV) AB, D. Hooper, Phys.Rev.D 81, 043505 (2010) A. Belikov (University of Chicago) Dark matter annihilation. November 2010 20 / 37

τ + τ channel E 2 dn γ /de (GeV/cm 2 /s/sr) 0.001 0.0001 1e-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-12 0.0001 0.001 0.01 0.1 1 10 100 1000 E (GeV) 1e-08 0.0001 0.001 0.01 0.1 1 10 100 1000 E (GeV) S. Profumo, T. E. Jeltema JCAP 0907:020,2009 AB, D. Hooper, Phys.Rev.D 81, 043505 (2010) A. Belikov (University of Chicago) Dark matter annihilation. November 2010 21 / 37

Required Boost Factor 10000 e + e W + W µ + µ τ + τ Boost factor 1000 100 100 1000 m X (GeV) AB, D. Hooper, Phys.Rev.D 81, 043505 (2010) A. Belikov (University of Chicago) Dark matter annihilation. November 2010 22 / 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±0.016 Ly-α forest observations: IGM heating (2 < z < 5) 5 10 3 K T igm 2 10 4 K at z 4 A. Belikov (University of Chicago) Dark matter annihilation. November 2010 23 / 37

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 2010 24 / 37

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) 043502 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 2010 25 / 37

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 2010 26 / 37

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 2010 27 / 37

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+06 100000 NFW Einasto 10000 1000 B(z)/(1-f(z)) 2 100 10 1 0.1 0.01 0.001 0 20 40 60 80 100 z A. Belikov (University of Chicago) Dark matter annihilation. November 2010 28 / 37

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-06 0.0001 0.01 1 100 E (GeV) A. Zdziarski and R. Svensson, APJ 344, 551 (1989) A. Belikov (University of Chicago) Dark matter annihilation. November 2010 29 / 37

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)6 6.4 10 45 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 = 5.2 10 28 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 = 6.6524 10 25 cm 2, n A = n bar ((1 Y)+0.25Y) = 2.09 10 7 cm 3, Helium Y = 0.25: I(z) = 1.7 10 31 (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 2010 30 / 37

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] 1 30.88 2.05 10 5 29.02 10 14.47 8.727 10 4 30.77 100 5.16 2.88 10 4 32.04 1000 2.02 1.08 10 4 32.5 z I KN (z) I photion (z) I pair (z) [GeVcm 3 ] 1 8.4 10 29 5.6 10 25 7.9 10 29 10 3.6 10 26 2.2 10 22 7.7 10 26 100 9.1 10 23 5.6 10 19 5.9 10 22 1000 3.5 10 19 5.6 10 15 5.6 10 18 A. Belikov (University of Chicago) Dark matter annihilation. November 2010 31 / 37

A test case. The deposition rates for different absorption channels. 2 TeV WIMP τ + τ channel, deposition rates 10 15 Klein-Nishina Phot-ion Pair-Production I(z) (GeV/cm 3 ) 10 20 10 25 10 30 0.1 1 10 100 1000 A. Belikov (University of Chicago) Dark matter annihilation. November 2010 32 / 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-31 0 50 100 150 200 z A. Belikov (University of Chicago) Dark matter annihilation. November 2010 33 / 37

W + W with σv = 3 10 26 cm 3 s 1 AB, D. Hooper, Phys.Rev.D 80, 035007 (2009) A. Belikov (University of Chicago) Dark matter annihilation. November 2010 34 / 37

W + W with σv = 4.5 10 24 cm 3 s 1 AB, D. Hooper, Phys.Rev.D 80, 035007 (2009) A. Belikov (University of Chicago) Dark matter annihilation. November 2010 35 / 37

e + e with σv = 3 10 26 cm 3 s 1, M X = 100 GeV and M X = 600 GeV AB, D. Hooper, Phys.Rev.D 80, 035007 (2009) A. Belikov (University of Chicago) Dark matter annihilation. November 2010 36 / 37

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 = 100 400GeV 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 2010 37 / 37