「 Cosmic-rays and diffused gamma-rays」

Aoyama-gakuin University

T. Shibata

Is the diffused γ-ray data in harmony with the cosmic-ray data ?

Status of Galactic Cosmic-ray Observation

physics:

origin, source, accel. limit

path length, anisotropy

r-process, s-process, source spectrum

2-ry products + novel sources

nearby source

C.R. life time, accel. period

C.R. density, gas density, novel source

　 Observables:

◎ 1-ry nucleus(p,He,C, …)

◎ 2-ry nucleus(Li,Be,B, …)

◎ ultra heavy (Z 　 30)

◎ anti-proton, positron

◎ primary electron

◎ isotope(10Be, …,59Co, …)

◎ diffused gamma-rays

2hh2hg

拡散係数　ガス密度　

2R

Dh

nh

Dg

ng

Dh

nh

:

:

:

:

:

:

ガス密度　

ガス密度　

拡散係数　

拡散係数　

一定( )

一定( )

一定( )

halo

halo

disk

　 Ginzburg-Ptuskin の銀河モデル（１９７６、１９９０）

( 300pc)

( 30kpc)

( a few kpc?)～

～

～

×

× :源 r z0 0( , )

：太陽系 z 0～r 10kpc～ , ）(

r0

r

Propagation of Cosmic-rays in Our Galaxy

×： source r0 　

(r0,z0)

●： solar system r 　 (r 10kpc, 　z 0)

Ⅰ］ Our Model● Gas density : )(exp)(

nn/z|z|r/r

0nrn

with

● Source density : )(exp)()(QQ

zzrrRR /||/ r0

QQ ;

RR00

QQ )(

● Boundaryless Galaxy :

,r,(N |z|→∞ 0);R 0);Rz,(N →∞r

with

● Diffusion coefficient : )/(exp)()(DD

zzrrRR /||D rD0

;

vDD00

R )( αR

0 20 40 60 80 100 1200.0001

0.001

0.01

0.1

1

101

10

10

10

10

10

101

0

-1

-2

-3

-4

Radial distance from galactic center; r (kpc)

N(r

, 0)/

N(r

=10

kp

c, 0

)L = 20 d 40 60 80 100 kpc

z = z = z = 2 kpcD n Q

r = r = r =D n Q 20 kpc

0.0001

0.001

0.01

0.1

1

101

0 20 40 60 80 100 120

nnn5 16:07:57 2002/12/28

D

D

CL d ∞= (no radial boundary in Galaxy)

Ⅱ］ Important parameters

● average scale height : r

Dn rrr

11

2

11Longitudinal dist. of diff. γ

● average scale height : z

Dn zzz

11

2

11Latitudinal dist. of diff. γ

●

＝

0

2

1

1

:

:

: ≪

≫

ν

nz

nz

nzDz

Dz

Dz

nzzD

1

1

● 2.2 2.4～ γ γR Q：

● : Kraichnan - type

: Kolmogorov- type

2

1

3

1α αRD

(source)

● σ ＝ 2

D0

0

czn

D

σ ＝ mb34.9 ) ( σ

:,/ xx1 average path length (

for

0D ＝ 2810 seccm2

＝

＝ kpc1

0n 3cm1

Dz

: 銀河中心でのガス密度

: 拡散係数の scale height

σ

for R = 1 GV at G.C.( )

0 0,0 pp

)0

( )● ＝Dτ

zD

＝ 733.

: life time of unstable nuclei

for

＝ 2810 seccm2

＝

＝

kpc 1Dz

y 10 2.18 6 for Be10

D

0η

0η

τ0

τ0

0,0η

for R = 1 GV at G.C.( )

: 拡散係数の scale height

0 0

0

∫ v σ γp[ ]E0 , ) dLn r ( )N4π

1

Ⅲ］ Gamma-ray Spectrum

Proton density-3cm ) (

γ ray prod. prob.

0

-1sec )(

(dl ) ( b sind

dI ○・

∫ dE0minE

E0 ( )r ;γE ( )θ;

γEγ

p

2Lπ4

dVσvn )(r

z

x

y0

l

Earth

line of sight

L

b

γγp)(rpN

Ⅲ-１］ Proton-spectrum

Intensity at solar system

Relative proton intensity

1 10 100 1000

(Galactic center)

(Solar system)

r (kpc) 0

5

10

15

20

.5

.2

kinetic energy E0(GeV/nucleon)

I p(r

; E

0)/I

p(0

; E

0)

.1

1

.05

Ⅲ-２］ γ- ray production cross section

anything　 　　 　 　 　　 　 　 　 　　 　 pp

③　 400 ~ 2000 GeV

① 　　　　　　　　　　　　 ~ 1 GeV ：　　 Bugg et al. (1964)

② 　 10 ~ 300 GeV ：　　 Jaeger et al. (1975)

：　　 Neuhofer et al. (1972)　

σ γp E γE0 ,( )