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3 1 Introduction 3 2 7 2.1.................................. 7 2.1.1..................... 8 2.1.2............................. 8 2.1.3.......................... 10 2.2............................... 12 2.3..................... 14 2.3.1............................. 14 2.3.2............................. 15 2.3.3............................. 15 2.3.4...................... 16 2.3.5........................ 16 3 19 3.1............................. 19 3.2............................. 20 3.2.1........................... 22 3.2.2 Fokker-Planck............ 22 3.2.3................. 34 3.2.4.................... 36 3.3............... 44 4 55

4.1..................... 55 4.2.................. 57 4.3..................... 69 4.4.................. 70 5 79 A BSS-S 83................................... 87...................................... 89

5 2.1 10 5 ev 10 20 ev.................................. 9 2.2.. 11 2.3....................... 13 3.1 0.33GHz (C.L.Carili.et al 1992)................... 21 3.2.................. 23 3.3 27 3.4... 29 3.5 r 0 =(0, 0, 5kpc) F (E,R E 0, r 0 )......... 30 3.6 r 0 =(0, 0, 5kpc) r 0 =(0, 0, 5kpc)....... 31 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 )................ 32 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)........... 33

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).............. 37 3.10 r 0 =(0, 0, 5kpc) r 0 =(0, 0, 9kpc).......................... 38 3.11..................... 41 3.12........................ 42 3.13 1TeV........ 43 3.14 Bohm Diffusion 100.................. 47 3.15 Bohm Diffusion 1000.................. 48 3.16 Bohm Diffusion κ B 100 1TeV................. 49 3.17 Bohm Diffusion κ B 100 10GeV................ 50 3.18 κ =2.2 10 28 (E/GeV) 0.6 cm 2 /s........................ 51 3.19 κ =2.2 10 28 (E/GeV) 0.6 cm 2 /s 1TeV......................... 53 3.20 κ =2.2 10 28 (E/GeV) 0.6 cm 2 /s 10GeV........................ 54 4.1.................. 56

4.2 κ com =2.2 10 28 (E/GeV) 0.6 cm 2 /s r 0 =(0, 0, 5kpc) F (E,R E 0, r 0 )................. 59 4.3 κ com =2.2 10 28 (E/GeV) 0.6 cm 2 /s r 0 =(0, 0, 10kpc) F (E,R E 0, r 0 )................ 60 4.4 κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 5kpc) F (E,R E 0, r 0 ).......................... 61 4.5 κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 10kpc) F (E,R E 0, r 0 ).......................... 62 4.6 κ com =2.2 10 28 (E/GeV) 0.6 cm 2 /s r 0 =(0, 0, 5kpc) F (E,R E 0, r 0 )................. 63 4.7 κ com =2.2 10 28 (E/GeV) 0.6 cm 2 /s r 0 =(0, 0, 5kpc) r 0 =(0, 0, 5kpc)............... 65 4.8 κ com =2.2 10 28 (E/GeV) 0.6 cm 2 /s r 0 =(0, 0, 10kpc) r 0 =(0, 0, 10kpc)............. 66

4.9 κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 5kpc) r 0 =(0, 0, 5kpc)........................ 67 4.10 κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 10kpc) r 0 =(0, 0, 10kpc)........................ 68 4.11 κ =2.2 10 28 (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 5kpc)......... 71 4.12 κ =2.2 10 28 (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 10kpc)........ 72 4.13 Bohm Diffusion 100 r 0 =(0, 0, 5kpc)... 73 4.14 Bohm Diffusion 100 r 0 =(0, 0, 10kpc)... 74 4.15 κ =2.2 10 28 (E/GeV) 0.6 cm 2 /s (10GeV 1TeV)................... 76 4.16 Bohm Diffusion κ B 100 (10GeV 1TeV).......... 77 A.1 BSS-S.............................. 84

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

Fokker-Planck Fokker-Planck 2

1 Introduction 1912 40 ( ) 1eV/cm 3 0.3eV/cm 3 RXJ1713.7-3946 π 0 SN1006 100 150pc Ginzburg Stecker Ginzburg Stecker ( 10kpc) 3

10kpc 5g/cm 2 n 1atom/cm 3 5g/cm 2 3 10 6 ( 10 Be) 2 10 7 3 10 6 10 Be n 1atom/cm 3 NGC4631 NGC891 NGC253 NGC253 CANGAROO 4

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

2 2.1 1912 Hess ( ) 1948 1 MeV GeV (> 10 18 ev) (< MeV) 7

2.1.1 (2.1) 10 5 ev 10 20 ev [Jokipii & Kota,1988] (2.1) 10 10 ev E 10 15 ev knee 10 15 ev 2.6 2.7 10 15 ev 3.0 knee 10 15 ev/n 10 20 10 21 ev 10 18 ev 10 10 ev 10 9 ev 2.1.2 (path length) Fe MeV/n GeV/n (2.2) IMP8 1973 1 1978 9 8

2.1: 10 5 ev 10 20 ev 9

(1) (Li Be B(L )) Z (2) H He H He (1) L sub-fe C, N, O L (Path Length) - 2.1.3 10 46 erg/s 10 15 ev [Yanagita,Nomoto,Hayakawa 1990,Yanagita Nomoto 1999] 10

2.2: : (70 280 MeV/n) : (1000 2000 MeV/n) simpson[1983] 11

X ASCA TeV CANGAROO (the Collaboration of Australia and Nippon for a GAmma-Ray Observatory in the Outback) SN1006 100TeV [Koyama et al.1995;tanimori et al.,1998] CANGAROO RXJ1713.7-3946 π 0 [H.Muraishi et al2000] 2.2 2.2.1 ( ) de =7.64 10 15 N(3 ln γ +19.8) dt i ev s 1 12

γ =(1 v 2 /c 2 ) 1/2 N τ = E (de/dt) i = E(eV) 7.64 10 15 N(3 ln γ +19.8) 2.2.2 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 +0.36 Gaunt Factor ḡ = ln(183z 1 3 ) 1 18 13

2.2.3 ( ) de dt ad = 1 3 ( v)e 2.2.4 1 ( ) de = 4 dt 3 σ T cγ 2H2 8π sync σ T Thomson γ H 2 /8π 2.2.5 X 14

( de dt ) IC = 4 3 σ T cγ 2 U ph σ T Thomson γ U ph ( ) 0.6eV/cm 3 0.262eV/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 2.3 1012 γ U CMBR 0.262eV/cm 3 15

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 NGC253 2.5Mpc 19kpc(16 ) 17

π 0 X Fokker-Planck Fokker-Planck 3.2 E E 2.2 3 18

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

Fokker-Placnk 3.2.1 (3.2) 10kpc 1kpc 1µG 0.262eV/cm 3 (T=2.728K) 250km/s E E 2.2 3.2.2 Fokker-Planck 1 [Yamada,1999] Full 20

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

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

(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 10 29 (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

E V 250km/s γ σ T 6.67 10 25 cm 2 U ph 0.262eV/cm 3 B 1µG c 3.00 10 10 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

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

(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

5 4 3 2 1 4 2 0-2 -40 4 2 0-2 -4 3.4: (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 3000 1 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

0.3 F(E,R E0,R0) (0,0,5kpc) 0.25 0.2 0.15 0.1 0.05 0 1 10 10 2 10 3 10 4 10 5 10 6 Kinetic Energy (GeV) 3.5: r 0 =(0, 0, 5kpc) F (E,R E 0, r 0 ) 28

0.25 Arrival Time Distribution (0,0,5kpc) 0.225 0.2 0.175 0.15 0.125 0.1 0.075 0.05 0.025 0 10 4 10 5 10 6 10 7 10 8 10 9 Arrival Time (Year) 3.6: r 0 =(0, 0, 5kpc) r 0 = (0, 0, 5kpc) 29

0.14 F(E,R 1TeV,5kpc) 0.12 0.1 0.08 0.06 0.04 0.02 0 10 3 10 4 10 5 10 6 10 7 10 8 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

0.25 Arrival Time Distribution(0,0,5kpc) 0.225 0.2 0.175 0.15 0.125 0.1 0.075 0.05 0.025 0 10 4 10 5 10 6 10 7 10 8 10 9 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

(3.5) (3.6) r 0 =(0, 0, 5kpc) r 0 =(0, 0, 5kpc) 10GeV 100GeV 1TeV 10TeV 10 8 10 7 10 6 10 5 (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 =0.5 2 10 6 1TeV 10 6 3.2.3 (3.5) (3.7) F (E,R E 0, r 0 ) r 0 =(0, 0, 5kpc) 32

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 = 10 29 (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

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) 3.2.4 20kpc <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

10-7 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10-16 10-17 10-18 10-19 10-20 Energy Spectrum (0,0,5kpc) 10-21 10-2 10-1 1 10 10 2 10 3 10 4 10 5 10 6 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

10-7 Energy Spectrum 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10-16 10-17 10-18 10-19 10-20 10-21 10-2 10-1 1 10 10 2 10 3 10 4 10 5 10 6 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

1 10GeV 0.1 0.1 100GeV 0.05 0.05 1TeV 0.01 0.05 0.05 10TeV 0.01 0.03 10GeV z 10kpc 10GeV 15 100GeV 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 ) 1/2 95 0.1 z 10GeV 100GeV 1TeV 10TeV 12.1kpc 6.8kpc 3.8kpc 2.2kpc 37

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 =0.6 0.01 0.05 0.05 µ =0.7 0.10 0.1 µ =0.4 z 10kpc 1TeV 1 µ =0.5 µ =0.6 1TeV 1 µ =0.7 10 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 =0.7 2.71kpc 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

z x 2kpc 2kpc y 3.11: 39

20 20 10 0 0.1 0.2 0.3 0.4 0.5 kpc 10 0 0.05 0.10 0.15 0.20 0.25 0.30 0.40-10 -10-20 -20-10 0 10 20 20-20 -20-10 0 10 20 kpc 20 10 0.01 10 kpc 0 0.05 0.10 0.15 0.35 kpc 0 0.01 0.04 0.07 0.16-10 -10-20 -20-10 0 10 20 kpc -20-20 -10 0 10 20 kpc 3.12: 10GeV 100GeV 1TeV 10TeV κ =10 29 (E/GeV) 0.5 cm 2 /s 40

20 20 kpc 10 0 0.01 0.05 0.1 0.15 0.25 kpc 10 0 0.01 0.05 0.10 0.15 0.35-10 -10-20 -20-10 0 10 20 kpc 20-20 -20-10 0 10 20 kpc 20 10 0.01 10 0.1 kpc 0 0.05 0.10 0.15 0.20 0.35 kpc 0 0.2 0.3 0.4 0.5-10 -10-20 -20-10 0 10 20 kpc -20-20 -10 0 10 20 kpc 3.13: 1TeV µ =0.4 µ =0.5 µ =0.6 µ =0.7 41

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 30 300 [Terasawa 2002] Bohm Diffusion 30 300 Bohm Diffusion κ B 42

v κ B = 1 3 r Lv (3.3.2) (3.14) (3.15) Bohm Diffusion κ B 100 1000 z 5kpc Bohm Diffusion κ B 1µG 10GeV 100GeV 1TeV 10TeV 3.3 10 23 cm 2 /s 3.3 10 24 cm 2 /s 3.3 10 25 cm 2 /s 3.3 10 26 cm 2 /s κ =10 29 (E/GeV) µ cm 2 /s Bohm Diffusion 100 1000 10 4 10 3 100 κ B ( (3.14)) (3.9) 10GeV 100GeV 10 2 100GeV 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 1 0.002 0.001 (3.17) 10GeV 1 0.05 0.03 0.01 (3.16) z 2kpc 1TeV 0.1 Bohm Diffusion κ B 100 10kpc 1TeV 43

(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 =2.2 10 28 (E/GeV) 0.6 cm 2 /s [Webber and Soutoul 1997] (3.18) z 5kpc 3000 (3.18) ( ) κ =2.2 10 28 (E/GeV) 0.6 cm 2 /s κ =10 29 (E/GeV) 0.6 cm 2 /s ( ) κ =2.2 10 28 (E/GeV) 0.6 cm 2 /s κ =10 29 (E/GeV) µ cm 2 /s 1/5 (3.19) κ =2.2 10 28 (E/GeV) 0.6 cm 2 /s 1 0.01 0.03 κ =10 29 (E/GeV) 0.6 cm 2 /s 1/5 44

10-7 Electron Energy Spectrum (0,0,5kpc) 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10-16 10-17 10-18 10-19 10-20 10-21 10-2 10-1 1 10 10 2 10 3 10 4 10 5 10 6 GeV 3.14: Bohm Diffusion 100 45

10-7 Electron Energy Spectrum (0,0,5kpc) 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10-16 10-17 10-18 10-19 10-20 10-21 10-2 10-1 1 10 10 2 10 3 10 4 10 5 10 6 GeV 3.15: Bohm Diffusion 1000 46

20 10 kpc 0 0.001 0.002-10 -20-20 -10 0 10 20 kpc 3.16: Bohm Diffusion κ B 100 1TeV 1 0.002 0.001 47

20 kpc 10 0 0.01 0.03 0.05-10 -20-20 -10 0 10 20 kpc 3.17: Bohm Diffusion κ B 100 10GeV 1 0.01 0.03 0.05 48

10-7 Electron Energy Spectrum (0,0,5kpc) 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10-16 10-17 10-18 10-19 10-20 10-21 10-2 10-1 1 10 10 2 10 3 10 4 10 5 10 6 GeV 3.18: κ =2.2 10 28 (E/GeV)cm 2 /s ( ) κ =10 29 (E/GeV) 0.6 cm 2 /s 49

6kpc TeV (3.20) κ =2.2 10 28 (E/GeV) 0.6 cm 2 /s 10GeV 1 0.10 0.10 (3.19) 1TeV (κ = 2.2 10 28 (E/GeV) 0.6 cm 2 /s) 10GeV z 10kpc 1 0.10 10kpc 10GeV κ =2.2 10 28 (E/GeV) 0.6 cm 2 /s Ginzbrug Stecker 6kpc TeV 50

20 kpc 10 0 0.01 0.04 0.07 0.22-10 -20-20 -10 0 10 20 kpc 20 kpc 10 0 0.01 0.05 0.10 0.15 0.20 0.35-10 -20-20 -10 0 10 20 kpc 3.19: κ =2.2 10 28 (E/GeV) 0.6 cm 2 /s 1TeV κ =10 29 (E/GeV) 0.6 cm 2 /s 1TeV 51

20 kpc 10 0 0.10 0.20 0.30 0.40 0.50-10 -20-20 -10 0 10 20 kpc 3.20: κ =2.2 10 28 (E/GeV) 0.6 cm 2 /s 10GeV 52

4 3 2000 Bohm Diffusion 100 100 κ B B/C κ =2.2 10 28 (E/GeV) 0.6 cm 2 /s 2 4.1 (4.1) 3 10kpc 1kpc xyz 1µG 300km/s E E 2.2 53

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

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 =2.2 10 28 (E/GeV) 0.6 cm 2 /s κ B Bohm Diffusion (dp adi ) dw Gauss Wiener (3.2.4) (4.2) κ com =2.2 10 28 (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

κ com 3000 1 (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 10 4 5kpc 56

0.9 F(E,R E0,R0) (0,0,5kpc) 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1 10 10 2 10 3 10 4 10 5 10 6 Kinetic Energy (GeV) 4.2: κ com =2.2 10 28 (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 5kpc) F (E,R E 0, r 0 ) 57

0.7 F(E,R E0,R0) (0,0,10kpc) 0.6 0.5 0.4 0.3 0.2 0.1 0 1 10 10 2 10 3 10 4 10 5 10 6 Kinetic Energy (GeV) 4.3: κ com =2.2 10 28 (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 10kpc) F (E,R E 0, r 0 ) 58

0.7 F(E,R E0,R0) (0,0,5kpc) 0.6 0.5 0.4 0.3 0.2 0.1 0 1 10 10 2 10 3 10 4 10 5 10 6 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

0.7 F(E,R E0,R0) (0,0,10kpc) 0.6 0.5 0.4 0.3 0.2 0.1 0 1 10 10 2 10 3 10 4 10 5 10 6 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

0.2 Electron F(E,R E0,R0) (0,0,5kpc) 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 1 10 10 2 10 3 10 4 10 5 10 6 Kinetic Energy (GeV) 4.6: κ com =2.2 10 28 (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 5kpc) F (E,R E 0, r 0 ) 61

(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 2 10 7 r 0 =(0, 0, 5kpc) (4.8) (4.3) r 0 =(0, 0, 10kpc) (4.9) (4.4) r 0 =(0, 0, 5kpc) 2 10 7 (4.4) µ 1 r 0 =(0, 0, 5kpc) (4.10) (4.5) r 0 =(0, 0, 10kpc) 62

0.1 Arrival Time Distribution (0,0,5kpc) 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 10 4 10 5 10 6 10 7 10 8 10 9 Arrival Time (Year) 4.7: κ com =2.2 10 28 (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 5kpc) r 0 =(0, 0, 5kpc) 63

0.1 Arrival Time Distribution (0,0,10kpc) 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 10 5 10 6 10 7 10 8 10 9 10 10 Arrival Time (Year) 4.8: κ com =2.2 10 28 (E/GeV) 0.6 cm 2 /s r 0 = (0, 0, 10kpc) r 0 =(0, 0, 10kpc) 64

0.8 Arrival Time Distribution (0,0,5kpc) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 10 7 10 8 10 9 Arrival Time (Year) 4.9: κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 5kpc) r 0 =(0, 0, 5kpc) 65

1 Arrival Time Distribution (0,0,10kpc) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 10 7 10 8 10 9 Arrival Time (Year) 4.10: κ Bs = 100 κ B cm 2 /s r 0 =(0, 0, 10kpc) r 0 =(0, 0, 10kpc) 66

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

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 ( ) 0.1 0.1 1TeV ( ) 10GeV z 10kpc 14 15 10GeV z 10kpc 1TeV z 10kpc 68

10-7 Proton Energy Spectrum (0,0,5kpc) 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10-16 10-17 10-18 10-19 10-20 10-21 10-2 10-1 1 10 10 2 10 3 10 4 10 5 10 6 GeV 4.11: κ =2.2 10 28 (E/GeV)cm 2 /s r 0 =(0, 0, 5kpc) 69

10-7 Proton Energy Spectrum (0,0,10kpc) 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10-16 10-17 10-18 10-19 10-20 10-21 10-2 10-1 1 10 10 2 10 3 10 4 10 5 10 6 GeV 4.12: κ = 2.2 10 28 (E/GeV)cm 2 /s r 0 = (0, 0, 10kpc) 70

10-7 Proton Energy Spectrum (0,0,5kpc) 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10-16 10-17 10-18 10-19 10-20 10-21 10-2 10-1 1 10 10 2 10 3 10 4 10 5 10 6 GeV 4.13: Bohm Diffusion 100 r 0 =(0, 0, 5kpc) 71

10-7 Proton Energy Spectrum (0,0,10kpc) 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10-16 10-17 10-18 10-19 10-20 10-21 10-2 10-1 1 10 10 2 10 3 10 4 10 5 10 6 GeV 4.14: Bohm Diffusion 100 r 0 =(0, 0, 10kpc) 72

34 35 1TeV z 10kpc 10GeV 1TeV 1TeV (3.12) κ =2.2 10 28 (E/GeV) 0.6 cm 2 /s TeV 10kpc (4.16) κ Bs (4.16) 10GeV 1TeV 1 10GeV ( ) 0.01 0.02 1TeV ( ) 0.01 0.01 10GeV z 10kpc 1 10GeV z 10kpc 1TeV z 10kpc 2 1TeV z 10kpc Bohm Diffusion κ B 100 TeV 10kpc 73

20 0.10 10 kpc 0 0.20 0.30 0.40 0.50-10 -20-20 -10 0 10 20 kpc 20 0.20 0.30 10 0.40 0.50 0.60 kpc 0-10 -20-20 -10 0 10 20 kpc 4.15: κ =2.2 10 28 (E/GeV) 0.6 cm 2 /s 10GeV κ =2.2 10 28 (E/GeV) 0.6 cm 2 /s 1TeV 74

20 10 0.01 kpc 0 0.03 0.05 0.09-10 -20-20 -10 0 10 20 kpc 20 0.02 10 0.03 0.04 0.05 0.10 kpc 0-10 -20-20 -10 0 10 20 kpc 4.16: Bohm Diffusion κ B 100 10GeV Bohm Diffusion κ B 100 1TeV 75

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

100 κ Bs = 100 κ B B/C κ com =2.2 10 28 (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

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

( 10kpc) 80

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

10 5 0-5 -10-10 -5 0 5 10 A.1: BSS-S z 0 kpc 82

(A,0,5) κ x x y z (A,0,7) κ 0 0 κ = 0 κ 0 0 0 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 0 0 0 1 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) 0 0 1 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 0 0 1 ê z (A.0.12) ê z 83

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 0 0 1 2κ 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

κ 0 0 κ = 0 κ 0 0 0 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 0 0 0 κ (A.0.19) κ xx κ xy 0 κ = κ yx κ yy 0 0 0 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

NGC253 87

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