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AMS-02 Kazunori Nakayama (University of Tokyo) 2015/5/16, Current situation Excess in Positron and Electron flux : PAMELA/AMS-02 and Fermi No excess in gamma-rays : Fermi,

  1. 宇宙線観測と暗黒物質 AMS-02 による反陽子 Kazunori Nakayama (University of Tokyo) 2015/5/16, 神戸大学

  2. Current situation • Excess in Positron and Electron flux : PAMELA/AMS-02 and Fermi • No excess in gamma-rays : Fermi, HESS, ... • No excess in neutrinos : SK, IceCube • Strong constraint from CMB and BBN • Excess in Anti-Proton ? : AMS-02

  3. Indirect detection of dark matter DM + DM → e ± , γ , ¯ p, ν , . . . e ± ¯ p γ ν We are here

  4. 日木曜日 年 月 日木曜日 年 月 Positron/electron Excess )) - 0.4 (e � )+ 0.3 + (e 0.2 � ) / ( + (e � Positron fraction 0.1 Muller & Tang 1987 MASS 1989 TS93 HEAT94+95 CAPRICE94 AMS98 HEAT00 0.02 Clem & Evenson 2007 PAMELA 0.01 0.1 1 10 100 Fermi Energy (GeV) PAMELA

  5. Positron by AMS-02

  6. Anti-proton by AMS-02

  7. Astrophysics ? G.Giesen et al, 1504.04276

  8. Astrophysics ? Kohri, Ioka, Fujita, Yamazaki, 1505.01236

  9. Dark Matter ！？ + - Conventional, W W PAMELA2014 AMS-02 4 10 − background DM+background DM /P P 5 − 10 6 − 10 3 1 2 4 − 10 10 10 10 1 10 Energy[GeV] Jin, Wu, Zhou, 1504.04604

  10. Diffusion Equation ∂ x ) + ∂ x ) = K ( E ) ∇ 2 f i ( E, � ∂ tf i ( E, � ∂ E [ b ( E ) f i ( E, � x )] + Q i ( E, � x ) x )] − f i ( E, � x ) P ji − ∂ � ∂ z [ V c ( z ) f i ( E, � + f j ( E, � x ) , τ i τ j j>i x ) : Distribution function of species i f i ( E, � K 0 (kpc 2 /Myr) Model R (kpc) L (kpc) MIN 20 1 0.0016 MED 20 4 0.0112 MAX 20 15 0.0765 L ) V c (km/s) δ 0.85 13.5 0.70 12 0.46 5 R

  11. Diffusion Equation ∂ x ) + ∂ x ) = K ( E ) ∇ 2 f i ( E, � ∂ tf i ( E, � ∂ E [ b ( E ) f i ( E, � x )] + Q i ( E, � x ) x )] − f i ( E, � x ) P ji − ∂ � ∂ z [ V c ( z ) f i ( E, � + f j ( E, � x ) , τ i τ j j>i x ) : Distribution function of species i f i ( E, � Diffusion due to tangled magnetic field K 0 (kpc 2 /Myr) Model R (kpc) L (kpc) MIN 20 1 0.0016 MED 20 4 0.0112 MAX 20 15 0.0765 L ) V c (km/s) δ 0.85 13.5 0.70 12 0.46 5 R

  12. Diffusion Equation ∂ x ) + ∂ x ) = K ( E ) ∇ 2 f i ( E, � ∂ tf i ( E, � ∂ E [ b ( E ) f i ( E, � x )] + Q i ( E, � x ) x )] − f i ( E, � x ) P ji − ∂ � ∂ z [ V c ( z ) f i ( E, � + f j ( E, � x ) , τ i τ j j>i x ) : Distribution function of species i f i ( E, � Diffusion due to Energy loss due to tangled magnetic field I.C. and synchrotron K 0 (kpc 2 /Myr) Model R (kpc) L (kpc) MIN 20 1 0.0016 MED 20 4 0.0112 MAX 20 15 0.0765 L ) V c (km/s) δ 0.85 13.5 0.70 12 0.46 5 R

  13. Diffusion Equation ∂ x ) + ∂ x ) = K ( E ) ∇ 2 f i ( E, � ∂ tf i ( E, � ∂ E [ b ( E ) f i ( E, � x )] + Q i ( E, � x ) x )] − f i ( E, � x ) P ji − ∂ � ∂ z [ V c ( z ) f i ( E, � + f j ( E, � x ) , τ i τ j j>i x ) : Distribution function of species i f i ( E, � Diffusion due to Energy loss due to Source (Supernova, tangled magnetic field I.C. and synchrotron Dark Matter) K 0 (kpc 2 /Myr) Model R (kpc) L (kpc) MIN 20 1 0.0016 MED 20 4 0.0112 MAX 20 15 0.0765 L ) V c (km/s) δ 0.85 13.5 0.70 12 0.46 5 R

  14. Diffusion Equation ∂ x ) + ∂ x ) = K ( E ) ∇ 2 f i ( E, � ∂ tf i ( E, � ∂ E [ b ( E ) f i ( E, � x )] + Q i ( E, � x ) x )] − f i ( E, � x ) P ji − ∂ � ∂ z [ V c ( z ) f i ( E, � + f j ( E, � x ) , τ i τ j j>i x ) : Distribution function of species i f i ( E, � Diffusion due to Energy loss due to Source (Supernova, tangled magnetic field I.C. and synchrotron Dark Matter) K 0 (kpc 2 /Myr) Model R (kpc) L (kpc) MIN 20 1 0.0016 Convective wind MED 20 4 0.0112 MAX 20 15 0.0765 L ) V c (km/s) δ 0.85 13.5 0.70 12 0.46 5 R

  15. Diffusion Equation ∂ x ) + ∂ x ) = K ( E ) ∇ 2 f i ( E, � ∂ tf i ( E, � ∂ E [ b ( E ) f i ( E, � x )] + Q i ( E, � x ) x )] − f i ( E, � x ) P ji − ∂ � ∂ z [ V c ( z ) f i ( E, � + f j ( E, � x ) , τ i τ j j>i x ) : Distribution function of species i f i ( E, � Diffusion due to Energy loss due to Source (Supernova, tangled magnetic field I.C. and synchrotron Dark Matter) K 0 (kpc 2 /Myr) Model R (kpc) L (kpc) Collision of nucleus MIN 20 1 0.0016 Convective wind MED 20 4 0.0112 of i species MAX 20 15 0.0765 L ) V c (km/s) δ 0.85 13.5 0.70 12 0.46 5 R

  16. Diffusion Equation ∂ x ) + ∂ x ) = K ( E ) ∇ 2 f i ( E, � ∂ tf i ( E, � ∂ E [ b ( E ) f i ( E, � x )] + Q i ( E, � x ) x )] − f i ( E, � x ) P ji − ∂ � ∂ z [ V c ( z ) f i ( E, � + f j ( E, � x ) , τ i τ j j>i x ) : Distribution function of species i f i ( E, � Diffusion due to Energy loss due to Source (Supernova, tangled magnetic field I.C. and synchrotron Dark Matter) K 0 (kpc 2 /Myr) Model R (kpc) L (kpc) Production of i Collision of nucleus MIN 20 1 0.0016 Convective wind MED 20 4 0.0112 from collision of j of i species MAX 20 15 0.0765 L ) V c (km/s) δ 0.85 13.5 0.70 12 0.46 5 R

  17. Diffusion Equation for Positron ∂ x ) + ∂ x ) = K ( E ) ∇ 2 f i ( E, � ∂ tf i ( E, � ∂ E [ b ( E ) f i ( E, � x )] + Q i ( E, � x ) x )] − f i ( E, � x ) P ji − ∂ � ∂ z [ V c ( z ) f i ( E, � + f j ( E, � x ) , τ i τ j j>i x ) : Distribution function of species i f i ( E, � Diffusion due to Energy loss due to Source (Supernova, tangled magnetic field I.C. and synchrotron Dark Matter) K 0 (kpc 2 /Myr) Model R (kpc) L (kpc) Production of i Collision of nucleus MIN 20 1 0.0016 Convective wind MED 20 4 0.0112 from collision of j of i species MAX 20 15 0.0765 L ) V c (km/s) δ 0.85 13.5 0.70 12 0.46 5 R

  18. Diffusion Equation ∂ x ) + ∂ x ) = K ( E ) ∇ 2 f i ( E, � ∂ tf i ( E, � ∂ E [ b ( E ) f i ( E, � x )] + Q i ( E, � x ) x )] − f i ( E, � x ) P ji − ∂ � ∂ z [ V c ( z ) f i ( E, � + f j ( E, � x ) , τ i τ j j>i x ) : Distribution function of species i f i ( E, � Diffusion due to Energy loss due to Source (Supernova, tangled magnetic field I.C. and synchrotron Dark Matter) K 0 (kpc 2 /Myr) Model R (kpc) L (kpc) Production of i Collision of nucleus MIN 20 1 0.0016 Convective wind MED 20 4 0.0112 from collision of j of i species MAX 20 15 0.0765 L ) V c (km/s) δ 0.85 13.5 0.70 12 0.46 5 R

  19. Diffusion Equation for Anti-Proton ∂ x ) + ∂ x ) = K ( E ) ∇ 2 f i ( E, � ∂ tf i ( E, � ∂ E [ b ( E ) f i ( E, � x )] + Q i ( E, � x ) x )] − f i ( E, � x ) P ji − ∂ � ∂ z [ V c ( z ) f i ( E, � + f j ( E, � x ) , τ i τ j j>i x ) : Distribution function of species i f i ( E, � Diffusion due to Energy loss due to Source (Supernova, tangled magnetic field I.C. and synchrotron Dark Matter) K 0 (kpc 2 /Myr) Model R (kpc) L (kpc) Production of i Collision of nucleus MIN 20 1 0.0016 Convective wind MED 20 4 0.0112 from collision of j of i species MAX 20 15 0.0765 L ) V c (km/s) δ 0.85 13.5 0.70 12 0.46 5 R

  20. DM source term r ) dN ¯ p ( T ) Q ( T, � r ) = q ( � dT � ρ DM ( | � � 2 r ) = 1 r | ) q ( � 2 � σ v � for annihilating DM , m DM � ρ DM ( | � � 1 r | ) q ( � r ) = for decaying DM . m DM τ DM r ) dN ¯ p ( T ) : energy spectrum of anti-p from DM decay � dT ) = τ DM : DM annihilation cross section, lifetime 1 � , 2 � σ v � � ρ DM ( | � : DM density profile in the Galaxy r | )

  21. Propagation of charged particle in tangled magnetic field � δ � λ = K ( E ) E ∼ 10 17 cm ∼ 0 . 1pc 1GeV c � δ � 1 � 2 � t E 2 � K ( E ) t ∼ 1kpc r ∼ 10 8 yr 1GeV r Charged particle escapes from diffusion zone after 10^7~10^8 yr. ≡ t esc Electron/positron loses energy before escape due to inverse Compton and synchrotron: � � ( δ − 1) / 2 � 1 GeV EK ( E ) r loss loss = ∼ 1 . 8 kpc b ( E ) E

  22. Primary/Secondary ratio f prim Primary: Produced at Source (Proton, Carbon, ...) Secondary: Produced by primary CR-intersteller f sec medium interaction (Anti-proton, Boron, ...) f sec ∼ t int f prim t esc Prim/Sec ratio determines escape time, but there is a degeneracy on K and L. K 0 [kpc 2 / Myr] K 0 [cm 2 / s] R [kpc] L [kpc] V c [km / s] δ 2 . 31 × 10 28 MAX 20.0 15 0.46 0.0765 5 3 . 38 × 10 27 MED 20.0 4 0.70 0.0112 12 4 . 83 × 10 26 MIN 20.0 1 0.85 0.0016 13.5 Donato et al. (2004) Anti-p of DM origin is Primary, not Secondary, hence anti-p flux of DM origin significantly depend on L.

  24. B/C B/C -1 10 AMS-02 Conventional MIN MED MAX 3 -2 -1 2 10 10 10 10 1 10 Kinetic Energy[GeV/n] Jin, Wu, Zhou, 1504.04604

  25. P /P, Background -4 10 /P P -5 10 PAMELA2014 AMS-02 Conventional MIN MED MAX -6 10 3 -1 2 10 10 10 1 10 Energy[GeV] Jin, Wu, Zhou, 1504.04604

  26. Anti-proton flux from DM : diffusion model dependence

  27. Comparison with AMS-02 data Astro BG Astro BG tted), 10 (das long-dashed), while th 1 d 2 × 10 27 sec, d 6 × 10 − 25 cm 3 / sec, τ DM ) = 2 � σ v � ) = m DM = 1 , 3 , 10 , 30TeV � m DM = 0 . 5 , 1 , 2 , 10TeV Hamaguchi, Moroi, KN, 1504.05937

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