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1 4

2

3 3 1 Introduction Fokker-Planck

4 A BSS-S

5 ev ev GHz (C.L.Carili.et al 1992) r 0 =(0, 0, 5kpc) F (E,R E 0, r 0 ) r 0 =(0, 0, 5kpc) r 0 =(0, 0, 5kpc) r 0 =(0, 0, 5kpc) E 0 =1TeV κ =10 29 (E/GeV) 0.3 cm 2 /s κ =10 29 (E/GeV) 0.5 cm 2 /s F (E,R E 0, r 0 ) r 0 =(0, 0, 5kpc) κ =10 29 (E/GeV) 0.3 cm 2 /s κ =10 29 (E/GeV) 0.5 cm 2 /s r 0 =(0, 0, 5kpc)

6 3.9 r 0 =(0, 0, 5kpc) ( ) ( ) F (E,R E 0, r 0 ) (3.2.12) r 0 = (0, 0, 5kpc) µ =0.5 µ =0.3 (3.2.13) r 0 =(0, 0, 5kpc) r 0 =(0, 0, 9kpc) TeV Bohm Diffusion Bohm Diffusion Bohm Diffusion κ B 100 1TeV Bohm Diffusion κ B GeV κ = (E/GeV) 0.6 cm 2 /s κ = (E/GeV) 0.6 cm 2 /s 1TeV κ = (E/GeV) 0.6 cm 2 /s 10GeV

7 4.2 κ com = (E/GeV) 0.6 cm 2 /s r 0 =(0, 0, 5kpc) F (E,R E 0, r 0 ) κ com = (E/GeV) 0.6 cm 2 /s r 0 =(0, 0, 10kpc) F (E,R E 0, r 0 ) κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 5kpc) F (E,R E 0, r 0 ) κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 10kpc) F (E,R E 0, r 0 ) κ com = (E/GeV) 0.6 cm 2 /s r 0 =(0, 0, 5kpc) F (E,R E 0, r 0 ) κ com = (E/GeV) 0.6 cm 2 /s r 0 =(0, 0, 5kpc) r 0 =(0, 0, 5kpc) κ com = (E/GeV) 0.6 cm 2 /s r 0 =(0, 0, 10kpc) r 0 =(0, 0, 10kpc)

8 4.9 κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 5kpc) r 0 =(0, 0, 5kpc) κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 10kpc) r 0 =(0, 0, 10kpc) κ = (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 5kpc) κ = (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 10kpc) Bohm Diffusion 100 r 0 =(0, 0, 5kpc) Bohm Diffusion 100 r 0 =(0, 0, 10kpc) κ = (E/GeV) 0.6 cm 2 /s (10GeV 1TeV) Bohm Diffusion κ B 100 (10GeV 1TeV) A.1 BSS-S

9 Ginzburg Stecker ( 10kpc) NGC4631 NGC891 NGC253 CANGAROO (Collaboration of Australia and Nippon for a GAmma Ray Observatory in the Out back) NGC253 [Itoh,Enomoto,Yanagita,Yoshida,and Tsuru 2003] π 0 X 1

10 Fokker-Planck Fokker-Planck 2

11 1 Introduction ( ) 1eV/cm 3 0.3eV/cm 3 RXJ π 0 SN pc Ginzburg Stecker Ginzburg Stecker ( 10kpc) 3

12 10kpc 5g/cm 2 n 1atom/cm 3 5g/cm ( 10 Be) Be n 1atom/cm 3 NGC4631 NGC891 NGC253 NGC253 CANGAROO 4

13 ( ) X π 0 3 Fokker-Planck Fokker-Planck 5

14

15 Hess ( ) MeV GeV (> ev) (< MeV) 7

16 2.1.1 (2.1) 10 5 ev ev [Jokipii & Kota,1988] (2.1) ev E ev knee ev ev 3.0 knee ev/n ev ev ev 10 9 ev (path length) Fe MeV/n GeV/n (2.2) IMP

17 2.1: 10 5 ev ev 9

18 (1) (Li Be B(L )) Z (2) H He H He (1) L sub-fe C, N, O L (Path Length) erg/s ev [Yanagita,Nomoto,Hayakawa 1990,Yanagita Nomoto 1999] 10

19 2.2: : ( MeV/n) : ( MeV/n) simpson[1983] 11

20 X ASCA TeV CANGAROO (the Collaboration of Australia and Nippon for a GAmma-Ray Observatory in the Outback) SN TeV [Koyama et al.1995;tanimori et al.,1998] CANGAROO RXJ π 0 [H.Muraishi et al2000] ( ) de = N(3 ln γ +19.8) dt i ev s 1 12

21 γ =(1 v 2 /c 2 ) 1/2 N τ = E (de/dt) i = E(eV) N(3 ln γ +19.8) X 1 E ( de dt ) brems =4NZ 2 r 2 e αcḡ r e α ḡ Gaunt Factor Gaunt Factor ḡ =ln(2γ) 1 3 =lnγ Gaunt Factor ḡ = ln(183z 1 3 )

22 2.2.3 ( ) de dt ad = 1 3 ( v)e ( ) de = 4 dt 3 σ T cγ 2H2 8π sync σ T Thomson γ H 2 /8π X 14

23 ( de dt ) IC = 4 3 σ T cγ 2 U ph σ T Thomson γ U ph ( ) 0.6eV/cm eV/cm 3 (T 2.728K) 3µG (de/dt) IC (de/dt) sync = U rad U mag 1 τ = E de/dt = E 4 3 σ = T cγ 2 U CMBR γ U CMBR 0.262eV/cm 3 15

24

25 3 3.1 Ginzburg Stecker ( 10kpc) NGC4631 NGC891 NGC253 CANGAROO (Collaboration of Australia and Nippon for a GAmma Ray Observatory in the Out back) NGC253 [Itoh,Enomoto,Yanagita,Yoshida,and Tsuru 2003] NGC253 (3.1) [Carili,Holdaway,Ho,and De Pree 1992] 0.33GHz NGC Mpc 19kpc(16 ) 17

26 π 0 X Fokker-Planck Fokker-Planck 3.2 E E

27 ApJ...399L 3.1: 0.33GHz (C.L.Carili.et al 1992) 19

28 Fokker-Placnk (3.2) 10kpc 1kpc 1µG 0.262eV/cm 3 (T=2.728K) 250km/s E E Fokker-Planck 1 [Yamada,1999] Full 20

29 Z I.C. Synchrotron Galactic Wind 250km/s Electron radius:10kpc thickness:1kpc Y Galactic Disk X Magnetic Field : 1 ug Photon Density : 0.262eV/cc 3.2: 21

30 Zhang [Zhang,1999] Fokker-Placnk 2 1 Fokker-Placnk Brown Fokker-Placnk f t = ( κ f Vf)+ 1 3 ( V ) 1 p 2 p (p3 f) (3.2.1) f( r, p, t) κ V Fokker-Planck Full- 22

31 (3.2.1) Fokker-Placnk dx i = V i dt + 2κdW i (i x,y,z) (3.2.2) dp = (dp adi + dp IC + dp syn ) (3.2.3) dx i 1 dp 1 V i 250km/s κ (E/GeV) µ cm 2 /s dp adi dp IC dp syn dw Gauss Wiener P (dw )= ( ) 1 2πdt exp dw 2 2dt (3.2.4) 3 ( ) de = 1 dt 3 ( V )E ad (3.2.5) ( de dt ( de dt ) ) IC sync = 4 3 σ T cγ 2 U ph (3.2.6) = 4 3 σ T cγ 2B2 8π (3.2.7) 23

32 E V 250km/s γ σ T cm 2 U ph 0.262eV/cm 3 B 1µG c cm/s (3.2.2)(3.2.3) Euler t i+1 x i+1 p i+1 x i+1 = x i + V i δt + 2κ(p i )δw (3.2.8) p i+1 = p i + dp adi (t i )+dp IC (t i )+dp syn (t i ) (3.2.9) t i (x i,p i ) δw (3.2.4) Gauss Fokker-Placnk (3.2.1) (3.2.2)(3.2.3) 2 [Yamada 1999] (3.3) 2 ( ) 24

33 Forward in Time Z Final State Fixed Initial Condition Y Galactic Disk X Backward in Time Z Fixed FinalCondition E0,r0 Galactic Disk Y Initial State EnergyDistribution : F(E,R E0,r0) X 3.3: 25

34 (3.2.2)(3.2.3) (3.2.2)(3.2.3) V V dp syn dp IC dp syn dp IC dx i = V i dt + 2κdW i (i x,y,z) (3.2.10) dp = dp adi + dp IC + dp syn (3.2.11) (3.2.10)(3.2.11) r 0 E 0 E F (E,R E 0, r 0 ) r 0 E 0 (3.2.10)(3.2.11) Euler R R (3.2.10)(3.2.11) E (E 0, r 0 ) r 0 E 0 r 0 (3.4) E 0 =1TeV r 0 =(0, 0, 5kpc) E 0 =1TeV r 0 =(5kpc, 0, 5kpc) 2 z x y z (0,0,5kpc) 26

35 : (5kpc,0,5kpc) (0,0,5kpc) (5kpc,0,5kpc) (3.5) r 0 =(0, 0, 5kpc) E 0 =10GeV 100GeV 1TeV 10TeV F (E,R E 0, r 0 ) κ =10 29 (E/GeV ) 0.5 cm 2 /s F (E,R E 0, r 0 ) E <E 0 F (E,R E 0, r 0 )=0 r 0 =(0, 0, 5kpc) E 0 r 0 =(0, 0, 5kpc) E 0 (3.2.11) r 0 =(0, 0, 5kpc) (3.5) ( r 0 =(0, 0, 5kpc) E 0 =10GeV 100GeV 1TeV 10TeV) r 0 =(0, 0, 5kpc) (3.6) (3.2.10)(3.2.11) 27

36 0.3 F(E,R E0,R0) (0,0,5kpc) Kinetic Energy (GeV) 3.5: r 0 =(0, 0, 5kpc) F (E,R E 0, r 0 ) 28

37 0.25 Arrival Time Distribution (0,0,5kpc) Arrival Time (Year) 3.6: r 0 =(0, 0, 5kpc) r 0 = (0, 0, 5kpc) 29

38 0.14 F(E,R 1TeV,5kpc) Kinetic Energy (GeV) 3.7: r 0 = (0, 0, 5kpc) E 0 =1TeV κ =10 29 (E/GeV) 0.3 cm 2 /s κ =10 29 (E/GeV) 0.5 cm 2 /s F (E,R E 0, r 0 ) 30

39 0.25 Arrival Time Distribution(0,0,5kpc) Arrival Time (Year) 3.8: r 0 =(0, 0, 5kpc) κ =10 29 (E/GeV) 0.3 cm 2 /s κ =10 29 (E/GeV) 0.5 cm 2 /s r 0 =(0, 0, 5kpc) 31

40 (3.5) (3.6) r 0 =(0, 0, 5kpc) r 0 =(0, 0, 5kpc) 10GeV 100GeV 1TeV 10TeV (3.7) r 0 =(0, 0, 5kpc) E 0 =1TeV κ =10 29 (E/GeV) 0.3 cm 2 /s κ =10 29 (E/GeV) 0.5 cm 2 /s F (E,R E 0, r 0 ) 3000 µ µ =0.3 µ =0.5 µ =0.3 (3.8) (3.7) κ =10 29 (E/GeV) 0.3 cm 2 /s κ =10 29 (E/GeV) 0.5 cm 2 /s r 0 =(0, 0, 5kpc) µ =0.3 µ = TeV (3.5) (3.7) F (E,R E 0, r 0 ) r 0 =(0, 0, 5kpc) 32

41 r 0 =(0, 0, 5kpc) E 0 r 0 f r0 (E 0 ) F (E,R E 0, r 0 )( (3.5) (3.7)) f R (E) f r0 (E 0 )= E 0 f R (E)F (E,R E 0,r 0 )de (3.2.12) f R (E) f R (E) E 2.2 (3.2.13) (3.9) r 0 =(0, 0, 5kpc) κ =10 29 (E/GeV) 0.3 cm 2 /s κ =10 29 (E/GeV) 0.5 cm 2 /s ( ) ( ) (3.2.12) E 0 =10GeV 32GeV 100GeV 320GeV 1TeV 3.2TeV 10TeV κ =10 29 (E/GeV) 0.3 cm 2 /s κ = (E/GeV) 0.5 cm 2 /s (3.2.13) (3.9) 2 µ =0.3 µ =0.5 µ =0.3 z (3.10) (3.9) 33

42 κ =10 29 (E/GeV) 0.5 cm 2 /s ( ) r 0 =(0, 0, 5kpc) E 0 =10GeV 32GeV 100GeV 320GeV 1TeV 3.2TeV 10TeV ( ) r 0 =(0, 0, 9kpc) E 0 =10GeV 32GeV 100GeV 320GeV 1TeV 3.2TeV 10TeV (3.9) r 0 =(0, 0, 5kpc) r 0 =(0, 0, 9kpc) r 0 =(0, 0, 9kpc) kpc <x<20kpc 20kpc <y<20kpc 20kpc <z<20kpc (3.11) 2kpc yz (3.11) x (3.12) κ =10 29 (E/GeV) 0.5 cm 2 /s (3.12) 10GeV 100GeV 1TeV 10TeV kpc 34

43 Energy Spectrum (0,0,5kpc) GeV 3.9: r 0 =(0, 0, 5kpc) ( ) ( ) F (E,R E 0, r 0 ) (3.2.12) r 0 =(0, 0, 5kpc) µ =0.5 µ =0.3 (3.2.13) 35

44 10-7 Energy Spectrum GeV 3.10: r 0 =(0, 0, 5kpc) r 0 =(0, 0, 9kpc) ( ) ( ) F (E,R E 0, r 0 ) (3.2.12) r 0 =(0, 0, 5kpc) r 0 =(0, 0, 9kpc) (3.2.13) 36

45 1 10GeV GeV TeV TeV GeV z 10kpc 10GeV GeV z 10kpc 100GeV 5 1TeV z 10kpc 10TeV z 10kpc 1 z 10kpc R L 2(κt cool ) 1/2 [C.Ito,R.Enomoto,S.yanagita,T.Yoshida,T.G.Tsuru 2003] t cool Gauss Gauss (κt cool ) 1/2 2(κt cool ) 1/ z 10GeV 100GeV 1TeV 10TeV 12.1kpc 6.8kpc 3.8kpc 2.2kpc 37

46 0.1 z 10GeV 100GeV 1TeV 10TeV 13kpc 8kpc 4kpc 3kpc (3.13) 1TeV µ (3.12) (3.13) µ =0.4 µ =0.5 µ =0.6 µ =0.7 (3.12) µ =0.4 µ =0.5 µ = µ = µ =0.4 z 10kpc 1TeV 1 µ =0.5 µ =0.6 1TeV 1 µ = µ z 10kpc µ z 10kpc (3.12) R L 2(κt cool ) 1/2 0.1 z R L 1TeV µ =0.4 µ =0.5 µ =0.6 µ = kpc 3.83kpc 5.41kpc 7.64kpc 1TeV 0.1 z µ =0.4 µ =0.5 µ =0.6 µ =0.7 3kpc 4kpc 4.5kpc 9kpc R L (3.13) 38

47 z x 2kpc 2kpc y 3.11: 39

48 kpc kpc kpc kpc kpc kpc 3.12: 10GeV 100GeV 1TeV 10TeV κ =10 29 (E/GeV) 0.5 cm 2 /s 40

49 20 20 kpc kpc kpc kpc kpc kpc kpc kpc 3.13: 1TeV µ =0.4 µ =0.5 µ =0.6 µ =0.7 41

50 3.3 (3.12) (3.13) Ginzburg Stecker TeV 10kpc κ =10 29 (E/GeV) µ cm 2 /s 2 λ r L ξ ξ = λ r L (3.3.1) ξ [Terasawa 2002] Bohm Diffusion Bohm Diffusion κ B 42

51 v κ B = 1 3 r Lv (3.3.2) (3.14) (3.15) Bohm Diffusion κ B z 5kpc Bohm Diffusion κ B 1µG 10GeV 100GeV 1TeV 10TeV cm 2 /s cm 2 /s cm 2 /s cm 2 /s κ =10 29 (E/GeV) µ cm 2 /s Bohm Diffusion κ B ( (3.14)) (3.9) 10GeV 100GeV GeV 10 9 (0,0,5kpc) 100GeV 1000 κ B ( (3.15)) (3.16) (3.17) Bohm Diffusion κ B 100 1TeV 10GeV (3.16) 1TeV (3.17) 10GeV (3.16) z 2kpc 1TeV 0.1 Bohm Diffusion κ B kpc 1TeV 43

52 (3.17) z 6kpc 10GeV 1 Bohm Diffusion κ B 100 6kpc 10GeV Bohm Diffusion κ B 100 Ginzubulg Stecker TeV 10 Be 26 Al 36 Cl 54 Mn Be/B Al/Mg Cl/Ar Mn/Fe B/C κ = (E/GeV) 0.6 cm 2 /s [Webber and Soutoul 1997] (3.18) z 5kpc 3000 (3.18) ( ) κ = (E/GeV) 0.6 cm 2 /s κ =10 29 (E/GeV) 0.6 cm 2 /s ( ) κ = (E/GeV) 0.6 cm 2 /s κ =10 29 (E/GeV) µ cm 2 /s 1/5 (3.19) κ = (E/GeV) 0.6 cm 2 /s κ =10 29 (E/GeV) 0.6 cm 2 /s 1/5 44

53 10-7 Electron Energy Spectrum (0,0,5kpc) GeV 3.14: Bohm Diffusion

54 10-7 Electron Energy Spectrum (0,0,5kpc) GeV 3.15: Bohm Diffusion

55 20 10 kpc kpc 3.16: Bohm Diffusion κ B 100 1TeV

56 20 kpc kpc 3.17: Bohm Diffusion κ B GeV

57 10-7 Electron Energy Spectrum (0,0,5kpc) GeV 3.18: κ = (E/GeV)cm 2 /s ( ) κ =10 29 (E/GeV) 0.6 cm 2 /s 49

58 6kpc TeV (3.20) κ = (E/GeV) 0.6 cm 2 /s 10GeV (3.19) 1TeV (κ = (E/GeV) 0.6 cm 2 /s) 10GeV z 10kpc kpc 10GeV κ = (E/GeV) 0.6 cm 2 /s Ginzbrug Stecker 6kpc TeV 50

59 20 kpc kpc 20 kpc kpc 3.19: κ = (E/GeV) 0.6 cm 2 /s 1TeV κ =10 29 (E/GeV) 0.6 cm 2 /s 1TeV 51

60 20 kpc kpc 3.20: κ = (E/GeV) 0.6 cm 2 /s 10GeV 52

61 Bohm Diffusion κ B B/C κ = (E/GeV) 0.6 cm 2 /s (4.1) 3 10kpc 1kpc xyz 1µG 300km/s E E

62 Z Adiabatic Loss Galactic Wind 300km/s Proton radius:10kpc thickness:1kpc Y Galactic Disk X Magnetic Field : 1uG 4.1: 54

63 4.2 Fokker- Planck Full- dx i = V i dt + 2κdW i (i x,y,z) (4.2.1) dp = dp adi (4.2.2) dx i 1 dp 1 V i 300km/s κ 2 2 κ Bs = 100 κ B cm 2 /s κ com = (E/GeV) 0.6 cm 2 /s κ B Bohm Diffusion (dp adi ) dw Gauss Wiener (3.2.4) (4.2) κ com = (E/GeV) 0.6 cm 2 /s r 0 =(0, 0, 5kpc) E 0 =10GeV 100GeV 1TeV 10TeV F (E,R E 0, r 0 ) (4.4) κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 5kpc) E 0 =10GeV 100GeV 1TeV 10TeV F (E,R E 0, r 0 ) (4.6) (4.2) r 0 =(0, 0, 5kpc) E 0 =10GeV 100GeV 1TeV 10TeV F (E,R E 0, r 0 ) κ Bs 55

64 κ com (4.2) (4.6) κ com (4.3) κ com r 0 =(0, 0, 10kpc) E 0 =10GeV 100GeV 1TeV 10TeV F (E,R E 0, r 0 ) (4.3) r 0 =(0, 0, 10kpc) (4.4) (4.2) κ com (10GeV 100GeV) (4.4) κ Bs r 0 =(0, 0, 5kpc) E 0 =10GeV 100GeV 1TeV 10TeV F (E,R E 0, r 0 ) (4.2) (4.4) µ 1 µ (4.4) 4 5 κ Bs κ com kpc 56

65 0.9 F(E,R E0,R0) (0,0,5kpc) Kinetic Energy (GeV) 4.2: κ com = (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 5kpc) F (E,R E 0, r 0 ) 57

66 0.7 F(E,R E0,R0) (0,0,10kpc) Kinetic Energy (GeV) 4.3: κ com = (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 10kpc) F (E,R E 0, r 0 ) 58

67 0.7 F(E,R E0,R0) (0,0,5kpc) Kinetic Energy (GeV) 4.4: κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 5kpc) F (E,R E 0, r 0 ) 59

68 0.7 F(E,R E0,R0) (0,0,10kpc) Kinetic Energy (GeV) 4.5: κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 10kpc) F (E,R E 0, r 0 ) 60

69 0.2 Electron F(E,R E0,R0) (0,0,5kpc) Kinetic Energy (GeV) 4.6: κ com = (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 5kpc) F (E,R E 0, r 0 ) 61

70 (4.5) κ Bs r 0 =(0, 0, 10kpc) E 0 =10GeV 100GeV 1TeV 10TeV F (E,R E 0, r 0 ) r 0 =(0, 0, 10kpc) (4.5) (4.2) (4.4) κ Bs (4.7) (4.2) r 0 =(0, 0, 5kpc) τ r 0 =(0, 0, 5kpc) (4.8) (4.3) r 0 =(0, 0, 10kpc) (4.9) (4.4) r 0 =(0, 0, 5kpc) (4.4) µ 1 r 0 =(0, 0, 5kpc) (4.10) (4.5) r 0 =(0, 0, 10kpc) 62

71 0.1 Arrival Time Distribution (0,0,5kpc) Arrival Time (Year) 4.7: κ com = (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 5kpc) r 0 =(0, 0, 5kpc) 63

72 0.1 Arrival Time Distribution (0,0,10kpc) Arrival Time (Year) 4.8: κ com = (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 10kpc) r 0 =(0, 0, 10kpc) 64

73 0.8 Arrival Time Distribution (0,0,5kpc) Arrival Time (Year) 4.9: κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 5kpc) r 0 =(0, 0, 5kpc) 65

74 1 Arrival Time Distribution (0,0,10kpc) Arrival Time (Year) 4.10: κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 10kpc) r 0 =(0, 0, 10kpc) 66

75 4.3 (4.2) (4.5) F (E,R E 0, r 0 ) r 0 =(0, 0, 5kpc) r 0 =(0, 0, 10kpc) r 0 =(0, 0, 5kpc) r 0 =(0, 0, 10kpc) E 0 r 0 f r0 (E 0 ) F (E,R E 0, r 0 )( (4.2) (4.5)) f R (E) (3.2.12) E E 2.2 (4.11) (4.2) κ com r 0 =(0, 0, 5kpc) (4.12) (4.3) κ com r 0 =(0, 0, 10kpc) r 0 =(0, 0, 5kpc) (4.12) (4.11) (4.12) κ com (4.13) (4.4) κ Bs r 0 =(0, 0, 5kpc) (4.14) (4.5) κ Bs 67

76 r 0 =(0, 0, 10kpc) κ com (4.11) (4.13) κ Bs κ com 10 4 (4.13) (4.13) (4.13) E 2.2 (4.13) 1TeV 10TeV (4.4) µ 1 µ (4.13) (4.14) (4.14) κ Bs 4.4 (4.15) κ com (4.15) 10GeV 1TeV 1 10GeV ( ) TeV ( ) 10GeV z 10kpc GeV z 10kpc 1TeV z 10kpc 68

77 10-7 Proton Energy Spectrum (0,0,5kpc) GeV 4.11: κ = (E/GeV)cm 2 /s r 0 =(0, 0, 5kpc) 69

78 10-7 Proton Energy Spectrum (0,0,10kpc) GeV 4.12: κ = (E/GeV)cm 2 /s r 0 = (0, 0, 10kpc) 70

79 10-7 Proton Energy Spectrum (0,0,5kpc) GeV 4.13: Bohm Diffusion 100 r 0 =(0, 0, 5kpc) 71

80 10-7 Proton Energy Spectrum (0,0,10kpc) GeV 4.14: Bohm Diffusion 100 r 0 =(0, 0, 10kpc) 72

81 TeV z 10kpc 10GeV 1TeV 1TeV (3.12) κ = (E/GeV) 0.6 cm 2 /s TeV 10kpc (4.16) κ Bs (4.16) 10GeV 1TeV 1 10GeV ( ) TeV ( ) GeV z 10kpc 1 10GeV z 10kpc 1TeV z 10kpc 2 1TeV z 10kpc Bohm Diffusion κ B 100 TeV 10kpc 73

82 kpc kpc kpc kpc 4.15: κ = (E/GeV) 0.6 cm 2 /s 10GeV κ = (E/GeV) 0.6 cm 2 /s 1TeV 74

83 kpc kpc kpc kpc 4.16: Bohm Diffusion κ B GeV Bohm Diffusion κ B 100 1TeV 75

84

85 5 Ginzburg Stecker ( 10kpc) ( ) Fokker-Placnk Fokker-Placnk (3.12) (3.13) (3.12) 2 (3.13) µ (3.12) (3.13) κ =10 29 (E/GeV) µ cm 2 /s Bohm Diffusion 77

86 100 κ Bs = 100 κ B B/C κ com = (E/GeV) 0.6 cm 2 /s (3.16) (3.19) κ Bs κ com 1TeV (3.16) κ Bs 10kpc TeV κ com (3.19) 10kpc TeV NGC253 TeV CANGAROO [Itoh,Enomoto,Yanagita,Yoshida,and Tsuru 2003] 10kpc TeV TeV TeV 10kpc TeV NGC253 κ com (3.17) (3.20) κ Bs κ com 10GeV (3.17) κ Bs 10GeV (3.20) 10kpc 10GeV µg GHz (3.1) 10kpc 78

87 µg κ com 10GeV TeV NGC253 κ com κ com Ginzburg Stecker TeV NGC253 10kpc π 0 10kpc (4.15) (4.16) κ com κ Bs 10GeV 1TeV Ginzburg Stecker 79

88 ( 10kpc) 80

89 A BSS-S [Neill,Olinto,Blasi 2001] (A.1) (A.1) bisymmetric even-parity field model(bss-s) (z=0) 0 6µG 3µG B sp = B 0 (r)cos(θ β ln(r/r 0 )) (A.0.1) B 0 (r) = 3ρ 0 r tanh3 ( r )µg r 1 (A.0.2) B(r, θ, z =0)=B sp (sin pˆρ +cospˆθ) (A.0.3) ( B S (r, θ, z) =B(r, θ, z =0) 1 2cosh( z z 1 ) + 1 2cosh( z z 2 ) ) (A.0.4) r 0 =10.55kpc β =1/ tan p p = 10 ρ 0 =8.5kpc r 1 =2kpc z 1 =0.3kpc z 2 =4kpc (κ ) (κ ) 2 d x = ( κ V V d )dt + α σ dw σ (t) (A.0.5) dp = dp adi + dp IC + dp syn (A.0.6) 81

90 A.1: BSS-S z 0 kpc 82

91 (A,0,5) κ x x y z (A,0,7) κ 0 0 κ = 0 κ κ (A.0.7) (A,0,6) dw σ Gauss Wiener (3.2.4) α σ dw σ ασ dw σ (t) = α 1 dw 1 + α 2 dw 2 + α 3 dw 3 (A.0.8) = 2κ dw 1 + 2κ dw 2 + 2κ dw 3 (A.0.9) (r, θ, z) ê r cos χ sin χ 0 ê θ = sin χ cos χ ê φ ê b ê ê z (A.0.10) ê x cos θ sin θ 0 ê r ê y = sin θ cos θ 0 ê θ (A.0.11) ê z ê x cos θ cos χ sin θ sin χ cos θ sin chi sin θ cos χ 0 ê b ê y = cos θ sin chi +sinθcos χ cos θ cos χ sin θ sin χ 0 ê ê z ê z (A.0.12) ê z 83

92 dw x cos θ cos χ sin θ sin χ cos θ sin chi sin θ cos χ 0 2κ dw 1 dw y = cos θ sin chi +sinθcos χ cos θ cos χ sin θ sin χ 0 2κ dw 2 dw z κ dw 3 (A.0.13) χ cos χ = B r B r (A,0,5) V d ( ) V d = pv B 3q B 2 (A.0.14) (A.0.15) (A,0,1) (A,0,4) V dx = pv 2coth 3 ( r r 1 )sec(θ β ln( r r 0 ))(x cos p + y sin p)(z 2 sin( z z 1 )+z 1 sin( z z 2 )) 3q 3r 0 z 1 z 2 (cos( z z 1 )+cos( z z 2 )) 2 (A.0.16) V dy = pv 2coth 3 ( r r 1 )sec(θ β ln( r r 0 ))(y cos p x sin p)(z 2 sin( z z 1 )+z 1 sin( z z 2 )) 3q 3r 0 z 1 z 2 (cos( z z 1 )+cos( z z 2 )) 2 (A.0.17) V dz = pv 3q coth2 ( r )csch 2 ( r )sec 2 (θ β ln( r ))( 12r cos p cos(θ β ln( r )) r 1 r 1 r 0 r 0 +r 1 (3 cos(p + θ β ln( r )) 2β cos p sin(θ β ln( r ))) sinh( 2r )) r 0 r 0 r 1 /6r 0 r 1 (cos( z z 1 )+cos( z z 2 )) (A.0.5) κ (A.0.7) (r, θ, z) κ 84

93 κ 0 0 κ = 0 κ κ = κ ê θ ê θ + κ ê ê + κ ê b ê b (A.0.18) κ cos 2 χ + κ sin 2 χ (κ κ )cosχsin χ 0 κ = (κ κ )cosχsin χ κ cos 2 χ + κ sin 2 χ κ (A.0.19) κ xx κ xy 0 κ = κ yx κ yy κ zz (A.0.20) κ xx = (κ cos 2 χ + κ sin 2 χ)cos 2 θ +(κ cos 2 χ + κ sin 2 χ)sin 2 θ (κ κ )sin2χ κ xy = (κ κ )cosχsin χ(cos 2 θ sin 2 θ)+(κ κ )cos2χ κ yx = (κ κ )cosχsin χ(cos 2 θ sin 2 θ)+(κ κ )cos2χ κ yy = (κ cos 2 χ + κ sin 2 χ)cos 2 θ +(κ cos 2 χ + κ sin 2 χ)sin 2 θ +(κ κ )sin2χ κ zz = κ (A.0.20) κ κ 85

94

95 NGC253 87

96

97 [1] Andrew W. Strong,and Igor V.Moskalenko,Astrophys.J,509, ,1998 [2] C.Itoh.,et al,a&a,396,l1-l4,2002 [3] C.Itoh,R.Enomoto,S.Yanagita,T.Yoshida,and T.G.Tsuru,Astrophys.J,584,L000- L000,2003 [4] D.Breitschwerdt,J.F.McKenzie,and H.J.Volk,A&A,269,54-66,1993 [5] F.W.Stecker,IAUS,84, ,1979 [6] Jokipii,J.R.,and J.Kota,J.Geophys.Res.91, ,1986 [7] Koyama,K.,et al.,nature 378, ,1995 [8] Ming Zhang,Astrophys.J 513, ,1999 [9] R.Enomoto.,et al,nature,416, ,2002 [10] Simpson,J.A.,Ann.Rev.Nucl.Part.Sci.,33, ,1983. [11] S.O Neill,A.Olinto,and P.Blasi,ICRC2001 [12] V.L.Ginzburg,IAUS,84, ,1979 [13] W.R.Webber,and A.Soutoul,Astrophys.J,506, ,1998 [14] Yamada,Y.,S.Yanagita,and T.Yoshida,Adv.Space Res.in press 1999 [15] Yanagita,S.,and N.Nomoto,Proc.3rd Integral Workshop, The Extreme Universe,pub.Kluwer Academic Publishers,in press [16], 10,

98 [17], 12,2000 [18], 14,2002 [19],,,, (1983) [20],, (2002) [21] M.S.Longair,High Energy Astrophysics Second Edition Vol.1 [22] M.S.Longair,High Energy Astrophysics Second Edition Vol.2 [23] Thomas K.Gaisser,Cosmic Rays and Particle Physics, (1997) 90

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Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e 7 -a 7 -a February 4, 2007 1. 2. 3. 4. 1. 2. 3. 1 Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e z

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