Cosmic antimatter from dark matter annihilation: effects of cosmological subhalos and uncertainties Julien Lavalle (Dept of Theoretical Physics, University of Turin) Refs (arXiv) : 0603796, 0712.0468, 0709.3634, 0704.2543, 0808.0332, 0809.5268, 0902.3665 Collab: Delahaye, Salati, Taillet (LAPTH) – Maurin (LPNHE) – Nezri (LAM) Ling (Brussels) – Donato, Fornengo, Lineros (Turin) – Bi, Yuan (Beijing) – Bringmann (Stockholm) 1 st Tango in Paris — IAP Tuesday, May 5 th 2009 Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 1
Requirements from PAMELA e + background (Delahaye et al, arXiv:0809.5268) ] ) -1 - + +e .GeV Secondary e flux + -2 10 - + /(e e fraction (med e spectrum) IS -1 .s + -1 positron fraction e .sr φ = 600 MV -2 /dE [cm -3 10 MS98 (IS) φ d 3.5 -1 10 + e ∈ = 600 MV) Propagation -4 10 MIN φ CAPRICE 94 TOA ( Propagation MED -5 MIN 10 HEAT 94-95 HEAT 94-95 MAX MED HEAT 00 AMS 01 MAX -2 AMS1 07 10 Full allowed MS98 PAMELA 08 -6 10 -1 2 2 10 1 10 10 1 10 10 E [GeV] E [GeV] Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 2
Requirements from PAMELA e + background Orders of magnitude for χχ → e + e − (for E → m χ = 100 GeV). (Delahaye et al, arXiv:0809.5268) From PAMELA, the excess is � 5 × φ bg (100 GeV) ∼ 1 . 5 · 10 − 9 cm − 2 . s − 1 . GeV − 1 . sr − 1 . « − 3 . 5 ] „ E ) -1 - + 3 · 10 − 10 +e cm − 2 . s − 1 . GeV − 1 . sr − 1 .GeV Secondary e flux φ bg (100 GeV) ≃ + -2 100 GeV 10 - + /(e e fraction (med e spectrum) IS -1 .s „ ρ ⊙ + -1 « 2 positron fraction e .sr δβc τE 0 � σv � φ = 600 MV -2 φ χχ ( E → m χ ) ≃ /dE [cm E 2 4 π 2 m χ -3 10 « „ 100 GeV MS98 (IS) « 4 „ τ ” „ ρ ⊙ � σv � « φ 3 · 10 − 10 “ d ≃ 3.5 -1 10 + e 3 · 10 − 26 cm 3 / s 10 16 s 0 . 3 GeV / cm 3 ∈ m χ = 600 MV) Propagation -4 10 For m χ ≃ 100 GeV, need for an amplification of: B ≃ 5 . MIN φ CAPRICE 94 TOA ( Propagation MED -5 MIN 10 HEAT 94-95 HEAT 94-95 MAX MED HEAT 00 AMS 01 MAX -2 AMS1 07 10 Full allowed MS98 PAMELA 08 -6 10 -1 2 2 10 1 10 10 1 10 10 E [GeV] E [GeV] Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 2
Smooth NFW halo and generic predictions CAPRICE 94 -2 10 HEAT 94-95 AMS 01 Boost to get ∼ 5 × φ bg at ∼ 100 GeV : -3 10 ] -1 100 GeV .sr -4 10 -1 WIMP mass 100 GeV 500 GeV 1 TeV .s 500 GeV -1 .GeV final state -5 10 -2 1000 GeV /dE [cm e + e − 5 100 350 -6 10 W + W − 80 500 1000 φ d -7 10 3.5 b ¯ + b 250 500 1000 e from WIMPs E + e line -8 10 + - W W b b -9 10 Bg Del08 -10 10 3 -1 2 10 1 10 10 10 E [GeV] Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 3
Smooth NFW halo and generic predictions Baltz & Edsjö, 98 Boost factor of 55 E.A. Baltz and J. Edsjö, 1998 CAPRICE 94 Positron fraction, e + / (e + + e - ) -2 10 HEAT 94-95 Signal + bkg. HEAT 94+95 Bkg. AMS 01 Boost to get ∼ 5 × φ bg at ∼ 100 GeV : Signal -3 10 Bkg. only fit -1 ] -1 10 100 GeV .sr -4 10 -1 WIMP mass 100 GeV 500 GeV 1 TeV (d) Example 4 .s 500 GeV -1 .GeV final state -5 10 -2 1000 GeV /dE [cm e + e − 5 100 350 -6 10 W + W − 80 500 1000 φ d -7 10 3.5 b ¯ + b 250 500 1000 e from WIMPs E -2 m χ = 130.3 GeV 10 + e line -8 10 k s = 54.6 + - W W χ 2 /7 = 1.35 b b -9 10 Bg Del08 2 3 1 10 10 10 Positron energy (GeV) -10 10 3 -1 2 10 1 10 10 10 E [GeV] Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 3
Inhomogeneous halo and boosted annihilation rate Though the topic is still controversial, clumps are predicted by theory and simulations of hierarchical formation of structures (in the frame of Λ CDM) Annihilation rate is increased in a characteristic volume, because < n 2 dm > ≥ < n dm > 2 (Silk & Stebbins ApJ’93) The boost factor to the annihilation rate is related to the statistical variance via <n 2 dm > B ann ∼ <n dm > 2 There is some scatter in N-body experi- ments: how to translate theoretical un- certainties to flux uncertainties ? what and where are the less ambiguous sig- natures, if so ? (Fig. from Diemand et al, MNRAS’04) Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 4
Inhomogeneous halo and boosted annihilation rate Though the topic is still controversial, Minimal mass from free streaming ∼ 10 − 6 M ⊙ clumps are predicted by theory and (e.g. Bringmann arXiv:0903.0189). simulations of hierarchical formation of . structures (in the frame of Λ CDM) Nbody resolution: ∼ 10 5 M ⊙ — ∼ 10 5 subhalos Annihilation rate is increased in a in the MW (e.g. Diemand et al 08, Springel et al characteristic volume, because 08). < n 2 dm > ≥ < n dm > 2 .. (Silk & Stebbins ApJ’93) Mass distribution ∼ M − 1 . 9 , various concentra- tion models. ⇒∼ 10 15 Earth-mass objects in the The boost factor to the annihilation rate is MW! related to the statistical variance via <n 2 .. dm > B ann ∼ <n dm > 2 Antibiased spatial distribution. (What for small objects ?) There is some scatter in N-body experi- .. ments: how to translate theoretical un- Limits: spatial and mass resolutions (numerical) certainties to flux uncertainties ? what + NO BARYONS (physical)! and where are the less ambiguous sig- natures, if so ? (Fig. from Diemand et al, MNRAS’04) Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 4
Gamma-rays versus antimatter cosmic rays Courtesy P . Salati The annihilation signal is integrated : over a small solid angle around the line of sight for γ − rays and neutrinos = ⇒ Boost factors are not the same ! over a rather small volume around the Earth for antimatter CRs, due to diffu- sion processes Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 5
Boost from few objects 0.16 ) - m = 50 GeV Primary contribution +e LZP (m = 6 TeV) + Background from MS98 KK /(e 0.14 Total + positron fraction e Few massive subhalos are expected in the HEAT data 0.12 MW: Closest clump at ~0.5 kpc 0.1 ” − 1 “ M ∼ 100 × 10 8 M ⊙ 0.08 0.06 By chance , one or few could wander close to 0.04 the Earth ... 0.02 Predictions: move a single (or few) object(s) 2 1 10 10 E (GeV) Lavalle, Pochon, Salati & Taillet around astro-ph/0603796 Very small probability: fine tuned models 1 + e from WIMPs -1 10 smooth !!! ( ∼ O (10 3 − 4 )objects / MW volume ) Clump at 2 kpc -2 ] 10 -1 .sr -1 -3 .s 10 -1 .GeV Multimessenger analysis : check radio, γ -ray -4 10 -2 /dE [cm -5 10 and antiproton constraints -6 φ 10 d 3.5 E -7 10 Not a clean prediction of clumpiness ⇒ -8 10 What about global effects? . -9 10 -10 10 -1 2 10 1 10 10 E [GeV] Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 6
Boost from few objects 0.16 ) - m = 50 GeV Primary contribution +e LZP (m = 6 TeV) + Background from MS98 KK /(e 0.14 Total + positron fraction e Few massive subhalos are expected in the HEAT data 0.12 MW: Closest clump at ~0.25 kpc 0.1 ” − 1 “ M ∼ 100 × 10 8 M ⊙ 0.08 0.06 By chance , one or few could wander close to 0.04 the Earth ... 0.02 Predictions: move a single (or few) object(s) 2 1 10 10 E (GeV) Lavalle, Pochon, Salati & Taillet around astro-ph/0603796 Very small probability: fine tuned models 1 + e from WIMPs -1 10 smooth !!! ( ∼ O (10 3 − 4 )objects / MW volume ) Clump at 1 kpc -2 ] 10 -1 .sr -1 -3 .s 10 -1 .GeV Multimessenger analysis : check radio, γ -ray -4 10 -2 /dE [cm -5 10 and antiproton constraints -6 φ 10 d 3.5 E -7 10 Not a clean prediction of clumpiness ⇒ -8 10 What about global effects? . -9 10 -10 10 -1 2 10 1 10 10 E [GeV] Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 6
Boost from few objects 0.16 ) - m = 50 GeV Primary contribution +e LZP (m = 6 TeV) + Background from MS98 KK /(e 0.14 Total + positron fraction e Few massive subhalos are expected in the HEAT data 0.12 MW: Closest clump at ~0.12 kpc 0.1 ” − 1 “ M ∼ 100 × 10 8 M ⊙ 0.08 0.06 By chance , one or few could wander close to 0.04 the Earth ... 0.02 Predictions: move a single (or few) object(s) 2 1 10 10 E (GeV) Lavalle, Pochon, Salati & Taillet around astro-ph/0603796 Very small probability: fine tuned models 1 + e from WIMPs -1 10 smooth !!! ( ∼ O (10 3 − 4 )objects / MW volume ) Clump at 0.5 kpc -2 ] 10 -1 .sr -1 -3 .s 10 -1 .GeV Multimessenger analysis : check radio, γ -ray -4 10 -2 /dE [cm -5 10 and antiproton constraints -6 φ 10 d 3.5 E -7 10 Not a clean prediction of clumpiness ⇒ -8 10 What about global effects? . -9 10 -10 10 -1 2 10 1 10 10 E [GeV] Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 6
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