Cosmic Rays andDiffuse Galactic Gamma-Ray Emission

Igor Moskalenko & Andrew StrongNRC & NASA GSFC MPE, Garching

• Introduction• Modelling approach• Nuclei in CR & propagation parameters• Diffuse gamma rays & tests of the nucleon spectrum• An application (WIMP search)

Main references:ApJ 1998, 493, 694 (positrons & electrons)A&A 1998, 338, L75 (antiprotons & test of the nucleon spectrum)ApJ 1998, 509, 212 (nuclei & numerical scheme)Phys.Rev.D 1999, 60, 063003 (positrons from the dark matter)ApJ 2000, 528, 357 (anisotropic inverse Compton scattering)ApJ 2000, 537, in press (diffuse continuum gamma rays)

Overviews:ASP Conf. Ser. 1999, 171, 162Proc. 5th Compton Symp. 2000, AIP, in press

Our results and software are available on WWW:

http://www.gamma.mpe-garching.mpg.de/~aws/aws.html

seminar 2/28/2000

Introduction Interactions in the ISM Links between branches of CR physics Modelling approach Galprop model Isotope table Equation Interstellar radiation field & anisotropic IC scattering An effect of anisotropic IC scattering 3D distribution GALPROP parameters & constraints Nuclei in CR & propagation parameters B/C diffusion/convection no break B/C diffusion/convection with break B/C with reacceleration 10Be reacceleration 10Be convection Other recent estimates B/C and subFe/Fe Some other ratios Isotopic abundances Gradients SNR distribution (Case & Bhattacharya 1996) Diffuse gamma rays & tests of the nucleon spectrum Conventional model Unidentified sources Hard Nucleons model Electrons & synchrotron index Hard Electrons model Hard Electrons & Modified Nucleons model Synchrotron profiles Longitude and latitude profiles High latitudes Electron spec. + Baring An application (WIMP search) Green's functions WIMP positrons Some other pictures Interstellar radiation field Reacceleration formalism Interstellar gas distribution SNR distribution (Case & Bhattacharya 1998) pbar/p ratio Enlarged 70-100 MeV profile Parameters & objectives of models

Page 2 of 3Reports

7/5/2002file://C:¥Download¥Galprop¥Reports.htm

2.6 m

top Time of Flight

top Cherenkov

top Drift Chamber

mid Drift Chamber

Magnet Coil

bot Drift Chamber

mid Time of Flight

bot Cherenkov

bot Time of Flight

e-

BBe

10Be

e+e-πο

synchrotron

sources

acceleration

e-pHe

C,N,O reacceleration

gas

ISRF

bremsstrahlung

inverse Compton

diffusionconvection

HALO

disk: sources, gas

energy losses

spallation

π+π−

escape

p

B

SNRs, shocksSuperbubbles

interstellar

ISOMAX

photon emission

γX,

pHe

C,N,O

gas

mediumChandra

GLAST

ACE

BESS

seminar 2/8/2000

pbar & positron

background

estimates

Supersymmetrical

particle search

LiBeB production

in the ISM

Evolution of

the Universe

Spectra of

p & Hein the Galaxy

Truly diffuse

gamma-ray

emission

Spectrum of

extragalactic

gamma-ray

emission

pbar & positronmeasurements

Gamma & electronmeasurements

Nucleimeasurements

Diffusioncoefficient

Reacceleration/

convection in

the ISM

Halo

size

Fixes the propagation

& allows to studyorigin of CR & their

source abundances

Some links between branches of cosmic ray physics

‘galprop’ model

f( R, z, p ) R

z

gas, ISRF, B

Galactic CR propagation numerically in 3D

realistic gas, radiation fields

propagation of primaries,

source distribution can be chosen

sources

halo boundary

nuclear reaction network

program available on WWW

γ-rays, synchrotron computed consistently

p ,e+, e-, γ−,synchrotron emission

current version includes:

diffusion, convection, reaccelerationenergy losses

+ All 87 stable & long-lived isotopes H-> Ni !

secondaries, tertiaries etc.

Table of Isotopes (1999)

Z=0-28 Part 1 of 2

n1

1/2+614.6 s

β-

H3

1/2+12.33 y

β-

H4

2-

Li4

2-

H5

He5

3/2-0.60 MeV

n

Li5

3/2-1.5 MeV

p

Be5

H6

He6

0+806.7 ms

β-

Be6

0+92 keV

2p

He7

(3/2)-160 keV

n

Be7

3/2-53.12 d

EC

B7

(3/2-)1.4 MeV

He8

0+119.0 ms

β-n

Li8

2+838 ms

β-2α

Be8

0+6.8 eV

2α

B8

2+770 ms

EC2α

C8

0+230 keV

He9

(1/2-)0.30 MeV

n

Li9

3/2-178.3 ms

β-n

B9

3/2-0.54 keV

2pα

C9

(3/2-)126.5 ms

ECp,ECp2α,...

He10

0+0.3 MeV

n

Li101.2 MeV

n

Be10

0+1.51E+6 y

β-

C10

0+19.255 s

EC

N10

Li11

3/2-8.5 ms

β-n,β-2n,...

Be11

1/2+13.81 s

β-α

C11

3/2-20.39 m

EC

N11

1/2+740 keV

p

Li12

Be12

0+23.6 ms

β-

B12

1+20.20 ms

β-3α

N12

1+11.000 ms

EC3α

O12

0+0.40 MeV

2p

Be13

(1/2,5/2)+0.9 MeV

n

B13

3/2-17.36 ms

β-n

N13

1/2-9.965 m

EC

O13

(3/2-)8.58 ms

ECp

Be14

0+4.35 ms

β-n,β-2n,...

B14

2-13.8 ms

β-

C14

0+5730 y

β-

O14

0+70.606 s

EC

F14

(2-)

p

B1510.5 ms

β-

C15

1/2+2.449 s

β-

O15

1/2-122.24 s

EC

F15

(1/2+)1.0 MeV

p

B16

(0-)200 Ps

n

C16

0+0.747 s

β-n

N16

2-7.13 s

β-α

F16

0-40 keV

p

Ne16

0+122 keV

2p

B17

(3/2-)5.08 ms

β-n

C17193 ms

β-n

N17

1/2-4.173 s

β-n

F17

5/2+64.49 s

EC

Ne17

1/2-109.2 ms

ECp,ECα,...

B18

C18

0+95 ms

β-n

N18

1-624 ms

β-n,β-α,...

F18

1+109.77 m

EC

Ne18

0+1672 ms

EC

Na18

B19

C1946 ms

β-n

N19

(1/2-)0.304 s

β-n

O19

5/2+26.91 s

β-

Ne19

1/2+17.22 s

EC

Na19

p

C20

0+14 ms

β-n

N20100 ms

β-n

O20

0+13.51 s

β-

F20

2+11.00 s

β-

Na20

2+447.9 ms

ECα

Mg20

0+95 ms

ECp

C21

N2185 ms

β-n

O21

(1/2,3/2,5/2)+3.42 s

β-

F21

5/2+4.158 s

β-

Na21

3/2+22.49 s

Mg21

(3/2,5/2)+122 ms

ECp

Al21

C22

0+

N2224 ms

β-n

O22

0+2.25 s

β-

F22

4+,(3+)4.23 s

β-

Na22

3+2.6019 y

Mg22

0+3.857 s

EC

Al2270 ms

ECp

Si22

0+6 ms

ECp

N23

O2382 ms

β-n

F23

(3/2,5/2)+2.23 s

β-

Ne23

5/2+37.24 s

β-

Mg23

3/2+11.317 s

EC

Al230.47 s

ECp

Si23

N24

O24

0+61 ms

β-n

F24

(1,2,3)+0.34 s

β-

Ne24

0+3.38 m

β-

Na24

4+14.9590 h

β-*

Al24

4+2.053 s

ECα*

Si24

0+102 ms

ECp

P24

O25

F2559 ms

β-n

Ne25

(1/2,3/2)+602 ms

β-

Na25

5/2+59.1 s

β-

Al25

5/2+7.183 s

EC

Si25

5/2+220 ms

ECp

P25

O26

0+

F26

Ne26

0+197 ms

β-n

Na26

3+1.072 s

β-

Al26

5+7.17E+5 y

EC*

Si26

0+2.234 s

EC

P26

(3+)20 ms

ECp

S26

F27

Ne2732 ms

β-n

Na27

5/2+301 ms

β-n

Mg27

1/2+9.458 m

β-

Si27

5/2+4.16 s

EC

P27

1/2+260 ms

ECp

S2721 ms

ECp,EC2p,...

F28

Ne28

0+17 ms

β-n

Na28

1+30.5 ms

β-n

Mg28

0+20.91 h

β-

Al28

3+2.2414 m

β-

P28

3+270.3 ms

ECp,ECα,...

S28

0+125 ms

ECp

Cl28

F29

Ne290.2 s

β-

Na29

3/244.9 ms

β-n

Mg29

3/2+1.30 s

β-

Al29

5/2+6.56 m

β-

P29

1/2+4.140 s

EC

S29

5/2+187 ms

ECp

Cl29

Ne30

0+

Na30

2+48 ms

β-n,β-2n,...

Mg30

0+335 ms

β-

Al30

3+3.60 s

β-

P30

1+2.498 m

EC

S30

0+1.178 s

EC

Cl30

Ar30

0+20 Ns

p

Ne31

Na31

3/2+17.0 ms

β-n,β-2n,...

Mg31230 ms

β-n

Al31

(3/2,5/2)+644 ms

β-

Si31

3/2+157.3 m

β-

S31

1/2+2.572 s

EC

Cl31150 ms

ECp

Ar3115.1 ms

ECp,EC2p,...

Ne32

0+

Na32

(3-,4-)13.2 ms

β-n,β-2n,...

Mg32

0+120 ms

β-n

Al32

1+33 ms

β-

Si32

0+150 y

β-

P32

1+14.262 d

β-

Cl32

1+298 ms

ECp,ECα,...

Ar32

0+98 ms

ECp

K32

Na338.2 ms

β-n,β-2n,...

Mg3390 ms

β-n

Al33

Si336.18 s

β-

P33

1/2+25.34 d

β-

Cl33

3/2+2.511 s

EC

Ar33

1/2+173.0 ms

ECp

K33

Na345.5 ms

β-n,β-2n,...

Mg34

0+20 ms

β-n

Al3460 ms

β-n

Si34

0+2.77 s

β-

P34

1+12.43 s

β-

Cl34

0+1.5264 s

EC*

Ar34

0+844.5 ms

EC

K34

Ca34

0+

Na351.5 ms

β-n

Mg35

Al35150 ms

β-n

Si350.78 s

β-

P35

1/2+47.3 s

β-

S35

3/2+87.32 d

β-

Ar35

3/2+1.775 s

EC

K35

3/2+190 ms

ECp

Ca3550 ms

EC2p

Mg36

0+

Al36

Si36

0+0.45 s

β-n

P365.6 s

β-

Cl36

2+3.01E+5 y

EC,β-

K36

2+342 ms

ECp,ECα,...

Ca36

0+102 ms

ECp

Sc36

Mg37

Al37

Si37

P372.31 s

β-

S37

7/2-5.05 m

β-

Ar37

3/2+35.04 d

EC

K37

3/2+1.226 s

EC

Ca37

3/2+181.1 ms

ECp

Sc37

Al38

Si38

0+

P380.64 s

β-n

S38

0+170.3 m

β-

Cl38

2-37.24 m

β-*

K38

3+7.636 m

EC*

Ca38

0+440 ms

EC

Sc38

Ti38

0+

Al39

Si39

P390.16 s

β-n

S39

(3/2,5/2,7/2)-11.5 s

β-

Cl39

3/2+55.6 m

β-

Ar39

7/2-269 y

β-

Ca39

3/2+859.6 ms

EC

Sc39

(7/2-)

Ti39

(3/2+)26 ms

ECp

Si40

0+

P40260 ms

β-n

S40

0+8.8 s

β-

Cl40

2-1.35 m

β-

Sc40

4-182.3 ms

ECp,ECα,...

Ti40

0+50 ms

EC

V40

Si41

P41120 ms

β-n

S41

Cl41

(1/2,3/2)+38.4 s

β-

Ar41

7/2-109.34 m

β-

Ca41

7/2-1.03E+5 y

EC

Sc41

7/2-596.3 ms

EC

Ti41

3/2+80 ms

ECp

V41

Si42

0+

P42110 ms

β-n

S42

0+0.56 s

β-n

Cl426.8 s

β-

Ar42

0+32.9 y

β-

K42

2-12.360 h

β-

Sc42

0+681.3 ms

EC*

Ti42

0+199 ms

EC

V42

Cr42

P4333 ms

β-n

S43220 ms

β-n

Cl433.3 s

β-

Ar43

(3/2,5/2)5.37 m

β-

K43

3/2+22.3 h

β-

Sc43

7/2-3.891 h

EC

Ti43

7/2-509 ms

EC

V43

(7/2-)800 ms

EC

Cr43

(3/2+)21 ms

ECp,ECα,...

P44

S44

0+123 ms

β-n

Cl44434 ms

β-n

Ar44

0+11.87 m

β-

K44

2-22.13 m

β-

Sc44

2+3.927 h

EC*

Ti44

0+63 y

EC

V44

(2+)90 ms

ECα*

Cr44

0+53 ms

ECp

Mn44

P45

S4582 ms

β-n

Cl45400 ms

β-n

Ar4521.48 s

β-

K45

3/2+17.3 m

β-

Ca45

7/2-162.61 d

β-

*

Ti45

7/2-184.8 m

EC

V45

7/2-547 ms

EC

Cr4550 ms

ECp

Mn45

Fe45

P46

S46

0+

Cl46223 ms

β-n

Ar46

0+8.4 s

β-

K46

(2-)105 s

β-

Sc46

4+83.79 d

β-*

V46

0+422.37 ms

EC*

Cr46

0+0.26 s

EC

Mn4641 ms

ECp

Fe46

0+20 ms

ECp

S47

Cl47

β-n

Ar47700 ms

β-n

K47

1/2+17.50 s

β-

Ca47

7/2-4.536 d

β-

Sc47

7/2-3.3492 d

β-

V47

3/2-32.6 m

EC

Cr47

3/2-500 ms

EC

Mn47100 ms

ECp

Fe4727 ms

ECp

S48

0+

Cl48

Ar48

0+

K48

(2-)6.8 s

β-n

Sc48

6+43.67 h

β-

V48

4+15.9735 d

EC

Cr48

0+21.56 h

EC

Mn48

4+158.1 ms

ECp,ECα,...

Fe48

0+44 ms

ECp

Co48

S49

Cl49

Ar49

K49

(3/2+)1.26 s

β-n

Ca49

3/2-8.718 m

Sc49

7/2-57.2 m

β-

V49

7/2-330 d

Cr49

5/2-42.3 m

Mn49

5/2-382 ms

EC

Fe49

(7/2-)70 ms

ECp

Co49

Cl50

Ar50

0+

K50

(0-,1,2-)472 ms

β-n

Ca50

0+13.9 s

β-

Sc50

5+102.5 s

β-*

Mn50

0+283.88 ms

EC*

Fe50

0+150 ms

ECp

Co50

(6+)44 ms

ECp

Ni50

Cl51

(3/2+)

Ar51

K51

(1/2+,3/2+)365 ms

β-n

Ca51

(3/2-)10.0 s

β-n

Sc51

(7/2)-12.4 s

β-

Ti51

3/2-5.76 m

β-

Cr51

7/2-27.7025 d

EC

Mn51

5/2-46.2 m

EC

Fe51

5/2-305 ms

EC

Co51

(7/2-)

Ni51

(7/2-)

Ar52

0+

K52105 ms

β-n

Ca52

0+4.6 s

β-

Sc52

3+8.2 s

β-

Ti52

0+1.7 m

β-

V52

3+3.743 m

β-

Mn52

6+5.591 d

EC*

Fe52

0+8.275 h

EC*

Co5218 ms

EC

Ni52

0+38 ms

ECp

Ar53

K53

(3/2+)30 ms

β-n

Ca53

(3/2-,5/2-)90 ms

β-n

Sc53

Ti53

(3/2)-32.7 s

β-

V53

7/2-1.61 m

β-

Mn53

7/2-3.74E+6 y

EC

Fe53

7/2-8.51 m

EC*

Co53

(7/2-)240 ms

EC*

Ni53

(7/2-)45 ms

ECp

K5410 ms

β-n

Ca54

0+

Sc54

Ti54

0+

V54

3+49.8 s

β-

Mn54

3+312.3 d

EC,β-

Co54

0+193.23 ms

EC*

Ni54

0+

EC

K55

Ca55

(5/2-)

β-

Sc55

Ti55

(3/2-)320 ms

β-

V55

(7/2-)6.54 s

β-

Cr55

3/2-3.497 m

β-

Fe55

3/2-2.73 y

EC

Co55

7/2-17.53 h

EC

Ni55

7/2-212.1 ms

EC

Ca56

0+

β-

Sc56

(3+)

β-

Ti56

0+160 ms

β-n

V56

(3+)230 ms

β-

Cr56

0+5.94 m

β-

Mn56

3+2.5785 h

β-

Co56

4+77.27 d

EC

Ni56

0+6.077 d

EC

Ca57

Sc57

(7/2-)

β-

Ti57

(5/2-)180 ms

β-n

V57

(7/2-)320 ms

β-n

Cr57

3/2-,5/2-,7/2-21.1 s

β-

Mn57

5/2-85.4 s

β-

Co57

7/2-271.79 d

EC

Ni57

3/2-35.60 h

Sc58

(3+)

β-

Ti58

0+

V58

(3+)200 ms

β-

Cr58

0+7.0 s

β-

Mn58

1+3.0 s

β-*

Co58

2+70.86 d

EC*

Sc59

Ti59

(5/2-)

β-

V59

(7/2-)130 ms

β-

Cr590.74 s

β-

Mn59

3/2-,5/2-4.6 s

β-

Fe59

3/2-44.503 d

β-

Ni59

3/2-7.6E+4 y

EC

Ti60

0+

β-

V60

(3+)200 ms

β-n

Cr60

0+0.57 s

β-

Mn60

0+51 s

β-*

Fe60

0+1.5E+6 y

β-

Co60

5+5.2714 y

*

Ti61

(1/2-)

β-n

V61

Cr61

(5/2-)270 ms

β-n

Mn61

(5/2-)0.71 s

β-

Fe61

3/2-,5/2-5.98 m

β-

Co61

7/2-1.650 h

β-

V62

(3+)

β-

Cr62

0+190 ms

β-n

Mn62

(3+)0.88 s

β-

Fe62

0+68 s

β-

Co62

2+1.50 m

β-*

V63

(7/2-)

β-

Cr63

(1/2-)110 ms

β-n

Mn630.25 s

β-

Fe63

(5/2)-6.1 s

β-

Co63

(7/2)-27.4 s

β-

Ni63

1/2-100.1 y

β-

V64

β-

Cr64

0+

Mn64

(3+)140 ms

β-n

Fe64

0+2.0 s

β-

Co64

1+0.30 s

β-

Cr65

(1/2-)

β-

Mn65

(5/2-)110 ms

β-n

Fe650.4 s

β-

Co65

(7/2)-1.20 s

β-

Ni65

5/2-2.5172 h

β-

Cr66

0+

β-

Mn6690 ms

β-n

Fe66

0+440 ms

β-

Co66

(3+)0.233 s

β-

Ni66

0+54.6 h

β-

Cr67

(1/2-)

β-

Mn67

β-

Fe67

(1/2-)470 ms

β-n

Co67

(7/2-)0.42 s

β-

Ni67

(1/2-)21 s

β-

Mn68

β-

Fe68

0+0.10 s

β-

Co680.18 s

β-

Ni68

0+19 s

β-

Mn69

(5/2-)

β-

Fe69

(1/2-)170 ms

β-n

Co690.27 s

β-

Ni6911.4 s

β-

Fe70

0+

β-

Co70150 ms

β-n

Ni70

0+

Fe71

(7/2+)

β-

Co71

(7/2-)210 ms

β-n

Ni711.86 s

β-

Fe72

0+

β-

Co7290 ms

β-n

Ni72

0+2.1 s

β-

Co73

(7/2-)

β-

Ni73

(7/2+)0.70 s

β-n

Co74

β-

Ni74

0+0.54 s

β-n

Co75

(7/2-)

β-

Ni75

(7/2+)0.6 s

β-n

Ni76

0+0.24 s

β-n

Ni77 Ni78

0+

β-

H1

1/2+

99.985

H2

1+

0.015

He3

1/2+

0.000137

He4

0+

99.999863

Li6

1+

7.5

Li7

3/2-

92.5

Be9

3/2-

100

B10

3+

19.9

B11

3/2-

80.1

C12

0+

98.90

C13

1/2-

1.10

N14

1+

99.634

N15

1/2-

0.366

O16

0+

99.762

O17

5/2+

0.038

O18

0+

0.200

F19

1/2+

100

Ne20

0+

90.48

Ne21

3/2+

0.27

Ne22

0+

9.25

Na23

3/2+

100

Mg24

0+

78.99

Mg25

5/2+

10.00

Mg26

0+

11.01

Al27

5/2+

100

Si28

0+

92.23

Si29

1/2+

4.67

Si30

0+

3.10

P31

1/2+

100

S32

0+

95.02

S33

3/2+

0.75

S34

0+

4.21

Cl35

3/2+

75.77

S36

0+

0.02

Ar36

0+

0.337

Cl37

3/2+

24.23

Ar38

0+

0.063

K39

3/2+

93.2581

Ar40

0+

99.600

K40

4-1.277E+9 y

EC,β-

0.0117

Ca40

0+

96.941

K41

3/2+

6.7302

Ca42

0+

0.647

Ca43

7/2-

0.135

Ca44

0+

2.086

Sc45

7/2-

100

Ca46

0+

0.004

Ti46

0+

8.0

Ti47

5/2-

7.3

Ca48

0+6E+18 y

β-,β-β-

0.187

Ti48

0+

73.8

Ti49

7/2-

5.5

Ti50

0+

5.4

V50

6+1.4E+17 y

EC,β-

0.250

Cr50

0+1.8E+17 y

ECEC4.345

V51

7/2-

99.750

Cr52

0+

83.789

Cr53

3/2-

9.501

Cr54

0+

2.365

Fe54

0+

5.8

Mn55

5/2-

100

Fe56

0+

91.72

Fe57

1/2-

2.2

Fe58

0+

0.28

Ni58

0+

68.077

Co59

7/2-

100

Ni60

0+

26.223

Ni61

3/2-

1.140

Ni62

0+

3.634

Ni64

0+

0.926

1H

91.0%1.00794

1 -259.34°-252.87°-240.18°

+1-1

2He

8.9%4.002602

2 -272.2°-268.93°-267.96°

0

3Li

1.86×10 -7%6.941

21

180.5°1342°

+1

4Be

2.38×10 -9%9.012182

22

1287°2471°

+2

5B

6.9×10 -8%10.811

23

2075°4000°

+3

6C

0.033%12.0107

24

4492t°3642s°

+2+4-4

7N

0.0102%14.00674

25

-210.00°-195.79°-146.94°

±1±2±3+4+5

8O

0.078%15.9994

26

-218.79°-182.95°-118.56°

-2

9F

2.7×10 -6%18.9984032

27

-219.62°-188.12°-129.02°

-1

10Ne

0.0112%20.1797

28

-248.59°-246.08°-228.7°

0

11Na

0.000187%22.989770

281

97.80°883°

+1

12Mg

0.00350%24.3050

282

650°1090°

+2

13Al

0.000277%26.981538

283

660.32°2519°

+3

14Si

0.00326%28.0855

284

1414°3265°

+2+4-4

15P

0.000034%30.973761

285

44.15°280.5°

721°+3+5-3

16S

0.00168%32.066

286

115.21°444.60°

1041°+4+6-2

17Cl

0.000017%35.4527

287

-101.5°-34.04°143.8°

+1+5+7-1

18Ar

0.000329%39.948

288

-189.35°-185.85°-122.28°

0

19K

0.0000123%39.0983

2881

63.38°759°

+1

20Ca

0.000199%40.078

2882

842°1484°

+2

21Sc

1.12×10 -7%44.955910

2892

1541°2836°

+3

22Ti

7.8×10 -6%47.867

28

102

1668°3287°

+2+3+4

23V

9.6×10 -7%50.9415

28

112

1910°3407°

+2+3+4+5

24Cr

0.000044%51.9961

28

131

1907°2671°

+2+3+6

25Mn

0.000031%54.938049

28

132

1246°2061°

+2+3+4+7

26Fe

0.00294%55.845

28

142

1538°2861°

+2+3

27Co

7.3×10 -6%58.933200

28

152

1495°2927°

+2+3

28Ni

0.000161%58.6934

28

162

1455°2913°

+2+3

2 4 6 8

10 12 14

16

18 20

22 24

26 28

30 32

34

36

38

40 42

44 46

48 50

Decay Q-value RangeQ(??)Q(β−)>0Q(β−)-SN>0Q(β−)>0 + Q(EC)>0Stable to Beta DecayQ(EC)>0Q(EC)-SP>0Q(P)>0Naturally Abundant

�

�t���r� p� t� �

q��r� p�

��r��Dxx�r� � �V ��

��

�p�p�Dpp

�

�p

��p�

p��

��

�p��dp

dt�

�

�p�r�V ���

��

�i�

�

�r

diffusion convection

sources

diffusive reacceleration

energy loss convection

fragmentation radioactive decay

Cosmic Ray Propagation Model

small boost& less collisions

γhead-on:big boost& more collisions

seminar 2/8/2000

Interstellar Radiation Field

Anisotropic Inverse Compton Scattering

e_

Galactic plane

e_

γ γ

electrons in halosee anisotropicradiation:head-on collisionsare seen by observerin plane

8 ANISOTROPIC INVERSE COMPTON SCATTERING IN THE GALAXY

FIG. 5.— Latitude – longitude plot of the anisotropic/isotropic intensity ratio for 11.4 MeV�-rays (ratio of the two sky maps). Halo sizez h = 4 kpc (left) and 10kpc (right).

FIG. 6.— The intensity ratio vs.�-ray energy for some direction as seen from the solar position. The corresponding Galactic coordinates (l�b) are shown near theright scale. Halo sizezh = 4 kpc (left) and 10 kpc (right).

in radius than the stellar component.In practice we calculate the anisotropic/isotropic ratio� for any particular model of the particle propagation (halo size, electron

spectral injection index etc.) on a spatial grid taking into account the difference between stellar and dust contributions to the ISRF,and then interpolate it when integrating over the line of sight (see SMR99).

Fig. 5 shows a Galactic latitude – longitude plot of the intensity ratio for 11.4 MeV�-rays for two Galactic models with halo sizezh = 4 kpc and 10 kpc. This is obtained from the computed sky maps in the anisotropic and isotropic cases. The calculation has beenmade with a ‘hard’ interstellarelectron spectrum (the interstellar electron spectrum is discussed below). It is seen that the enhancementdue to the anisotropic ICS can be as high as a factor�1.4 for the pole direction in models with a large halo,zh � 10 kpc. The maximal

seminar 2/8/2000

Anisotropic/isotropic IC

E = 11.4 MeV

4 kpc halo 10 kpc halo

1.35

1.25

seminar 2/8/2000

Galactic CR distribution of Carbon-12 and Boron-10,11

Table 1: The GALPROP parameters & constraintsParameter Constraints

Gas distribution (H2, HI, HII); He/HGalactic magnetic field model

Observations-”-

Interstellar radiation field (ISRF) Observations + calculations

Particle injection spectra: Nucleons

Electrons

Local spectrum ?Diffuse gamma-ray emissionAntiproton & positron measurements

Local spectrum ?Synchrotron index measurements

Diffusion coefficient, DxxReacceleration: Alfven velocity, VaConvection: break in the diffusion coeff.

convection velocity @ z=0 velocity gradient dV/dz

Secondary/primary ratio (e.g. B/C)-”--”--”--”-

Galactic halo radius, RhGalactic halo height, Zh

= 30 kpc, fixedRadioactive isotopes (e.g. Be-10/Be-9)

Source distribution deduced from EGRET >100 MeV data

seminar 2/28/2000

Standard approach (e.g. ‘leaky box’)

Dxx α v .....R < R0Dxx α vRµ ....R > R0

µ=0.6R0 = 4 GeV/c

fitted from secondary/primary ratios

Diffusive reacceleration

Dxx Dpp = p2VA2 /9

Dxx α vRµ

µ=1/3 (Kolmogorov)

2 free parameters, ad hoc break

1 free parameter, no break

rigidity

momentum diffusion coeff.spatial diffusion coeff.

physical basis

0.5<l< 30.0 , 330.0<l<359.0

-5.0<b< 5.0

seminar 2/8/2000

protons gammas

Tests of the nucleon spectrum

positronsantiprotons

Conventional model

HEAT 98MASS91

IMAX 97

Evaluations:Menn 00Webber 98Seo 91

Hard X-rays -- soft gamma rays:unresolved point sources vs. diffuse emission

RXTE/OSSE (Kinzer et al. 1999; Valinia et al. 2000):• Bright sources contribute 46% at 60 keV and 20% at 100 keV• A variable component dominates at 10 keV-200 keV: exponen-

tially cut off power law• Hard component dominates above 500 keV

Yamasaki et al. 1997- diffuse hard X-rays:• Unresolved point sources ~20%• Young electrons in SNRs - the rest; -- still point sources !

Our result: changeover probably occurs at MeV energies

Diffuse emission + a few dosen of Crab-like sources

seminar 2/28/2000

0.5<l< 30.0 , 330.0<l<359.0

-5.0<b< 5.0

0.5<l< 30.0 , 330.0<l<359.0

-5.0<b< 5.0

seminar 2/8/2000

Hard Electrons model

0.5<l< 30.0 , 330.0<l<359.0

-5.0<b< 5.0

seminar 2/8/2000

protons gammas

Tests of the nucleon spectrum

positronsantiprotons

Hard Nucleons model

HEAT 98MASS91

IMAX 97

Evaluations:Menn 00Webber 98Seo 91

Synchrotron spectral index

C

Hard

injectionindex 2.0-2.4

seminar 2/8/2000

Interstellar electron spectra

0.5<l< 30.0 , 330.0<l<359.0

-5.0<b< 5.0

seminar 2/8/2000

protons gammas

Tests of the nucleon spectrum

positronsantiprotons

Hard Electrons & Modified Nucleons model

MASS91HEAT 98

IMAX 97

Evaluations:Menn 00Webber 98Seo 91

0

5

10

15

20

25

0 5 10 15 20

Bto

t, m

kG

R, kpc

Magnetic field in the Galactic plane

Broadbent et al. 1990

present paper

seminar 2/8/2000

Magnetic field distribution

Intensity profiles of synchrotron emission @ 408 MHz

408 MHz

10.0<l<60.0/300.0<l<350.0

408 MHz

-5.0<b<5.0

1000-2000MeV

1.0<l<180.0/181.0<l<359.0

1000-2000MeV

-5.0<b<5.0

γ-ray profiles from EGRET Phase 1-4compared to model with hard electron spectrum and modified nucleon spectrum

IC

bremss

πo

πo

ICbremss

TOTAL

EGRET

EGRET

TOTAL

0.5<l<179.0 , 180.5<l<359.0

70.0<b< 89.0

HIGH GALACTIC LATITUDE GAMMA RAYSshowing effect on inverse Compton scattering

of anisotropic interstellar radiation field

Anisotropic ICS

Isotropic ICS

Electron spectra based on γ-raysand

SNR acceleration from Baring et al. 1998

interstellar

injection

yr�1 GeV�1, �0�107 yr; G2 : � � 1.52�10�9 yr�1

GeV�1,��2�108 yr GeV. It is clear that the leaky-boxmodel does not work here, moreover a resonable fit to our Gfunctions is impossible for any combination of � and �0 �or�). The difference in the normalization at maximum (E��) is mainly connected with our accurate calculation of theISRF which is responsible for the energy losses.

Figure 3 shows our calculated G functions for differentmodels of the dark matter distribution: ‘‘isothermal,’’Evans,and alternative. The curves are shown for two halo sizes zh�4 and 10 kpc and several energies ��1.03, 2.06, 5.15,10.3, 25.8, 51.5, 103.0, 206.1, 412.1, 824.3 GeV. At highenergies, increasing positron energy losses due to the ICscattering compete with the increasing diffusion coefficient,while at low energies increasing energy losses due to theCoulomb scattering and ionization �10� compete with energygain due to reacceleration. The first effect leads to a smallersensivity to the halo size at high energies. The second onebecomes visible below �5 GeV and is responsible for theappearance of accelerated particles with E�� .

It is interesting to note that for a given initial positronenergy all three dark matter distributions provide very simi-lar values for the maximum of the G function �on theE2G(E ,�) scale�, while their low-energy tails are different.This is a natural consequence of the large positron energylosses. Positrons contributing to the maximum of the G func-tion originate in the solar neighborhood, where all modelsgive the same dark matter mass density �see Eq. �4 for thedefinition of the G function�. The central mass density inthese models is very different �Fig. 1, and therefore theshape of the tail is also different since it is produced bypositrons originating in distant regions. As compared to theisothermal model, the Evans model produces sharper tails,while the alternative model gives more positrons in the low-energy tail. At intermediate energies (�10 GeV) where theenergy losses are minimal, the difference between zh�4 and

10 kpc is maximal. Also at these energies positrons fromdark matter particle annihilations in the Galactic center cancontribute to the predicted flux. This is clearly seen in thecase of the alternative model with its very large central massdensity �Fig. 3�c, zh�10 kpc�.

To provide the Green’s function for an arbitrary positronenergy, which is necessary for prediction of positron fluxesin the case of continuum positron source functions �as willbe required if one considers secondary, tertiary, etc., decayproducts, we made a fit to our numerical results. Since aresonable fit using the leaky-box Green’s functions is impos-sible we have chosen the function

G�E ,��1025

E210a log2E�b logE�c����E

�10w log2E�x logE�y��E���

�cm sr�1 GeV�1� , �10

which allows us to fit our numerical functions with accuracybetter than 10% over a decade in magnitude �on theE2G(E ,�) scale�. Here the first term fits the low energy tail,the second term fits the right-hand-side part of the G func-

FIG. 2. Calculated G functions for the uniform dark matter dis-tribution, zh�4 kpc and 10 kpc, for ��25.76, 103.0, 412.1 GeV�solid lines. The leaky-box functions G1 and G2 are shown bydashed and dotted lines, respectively. The units of the abscissa are1025 GeV cm sr�1.

FIG. 3. Calculated G functions for different models of the darkmatter distribution: �a ‘‘isothermal,’’ �b Evans, �c alternative.Upper curves zh�10 kpc, lower curves zh�4 kpc, ��1.03,2.06, 5.15, 10.3, 25.8, 51.5, 103.0, 206.1, 412.1, 824.3 GeV. Theunits of the abscissa are 1025 GeV cm sr�1.

IGOR V. MOSKALENKO AND ANDREW W. STRONG PHYSICAL REVIEW D 60 063003

063003-4

Positron signal & background estimates, data: HEAT’98.

* cross section: Kamionkowski & Turner 1991

• A significant detection of a signal requires favorableconditions and precise measurements

• A correct interpretation of measurements requires fur-ther developments in modelling production and propa-gation of CR species in the Galaxy

1e-08

1e-07

1e-06

1e-05

0.0001

10 100

E^2

Flu

x, G

eV/c

m^2

/s/s

r

E, GeV

C

HEMN χχ->ee

χχ->WW(ZZ)->ee

C HEMN

103 GeV

206 GeV

412 GeV

26 GeV

10 GeV

5 GeV

seminar 2/8/2000

Positrons from neutralino annihilations in the Galactic halo

Interstellar radiation �eld

Figure �� Di�erential energy density �u� ��m eV cm�� �m��� of ISRFin the Galactic plane �z � �� at R � � �top�� kpc �center�� and kpc�bottom�� Shown are the contributions of stars �dashed�� dust �dash�dot��CMB �dash���dots�� and total �full line��

Standard approach (e.g. ‘leaky box’)

Dxx α v .....R < R0Dxx α vRµ ....R > R0

µ=0.6R0 = 4 GeV/c

fitted from secondary/primary ratios

Diffusive reacceleration

Dxx Dpp = p2VA2 /9

Dxx α vRµ

µ=1/3 (Kolmogorov)

2 free parameters, ad hoc break

1 free parameter, no break

rigidity

momentum diffusion coeff.spatial diffusion coeff.

physical basis

No. 2, 1998 NEW &-D RELATION 771

SNRs are observed, and therefore observational incom-pleteness is still a problem for regions 1 and 3, where thecompleteness factors are lower. The scaled total number ofshell SNRs in region 2 is where the error on the(56 ^ 4)/f

z,

number of SNRs represents the uncertainty in the &-D rela-tion and represents the incompleteness due to the lack off

zselection e†ects compensation for the zero bins. For region2, If region 2 is considered representative of thef

zB 0.96.

entire Galaxy, then the total number of shell remnants forr ¹ 16 kpc and & [ 5 ] 10~23 W m~2 Hz~1 sr~1 is esti-mated to be The Monte Carlo simulation shows that336/f

z.

this estimate is not very sensitive to the uncertainty in the&-D relation.

A weighted Ðt of the shell SNR surface density distribu-tion in region 2, normalized to the surface density at thesolar circle, was performed using the functional formemployed by & JonesStecker (1977) :

f (r) \A r

r_

Baexp

A[b

r [ r_

r_

B, (14)

where kpc is the SunÈGalactic center distance. Wer_

\ 8.5Ðnd that a \ 2.00 ^ 0.67 and b \ 3.53 ^ 0.77 ; the radialscale length of the distribution is B7.0 kpc. The shape of thedistribution is similar to that obtained by Kodiara (1974).The two distributions are shown in Figure 7a.

implies that the surface density is zero atEquation (14)r \ 0. However, our data suggest that the surface density isnot zero near the Galactic center. Therefore, we have usedthe following functional form to obtain a weighted Ðt to theunnormalized surface density distribution :

f (r) \ A sinAnr

r0] h0

Be~br , (15)

where A \ 1.96 ^ 1.38 kpc~2, kpc,r0 \ 17.2 ^ 1.9 h0 \0.08 ^ 0.33, and b \ 0.13 ^ 0.08 kpc~1. This Ðt is valid for

i.e., 16.8 kpc ; f (r) \ 0 beyond that. Ther \ r0(1 [ h0/n),data and Ðt are shown in Figure 7b.

The scale length of 7.0 kpc is consistent with that deter-mined by previous studies. used a simpleGreen (1996b)model with SNRs distributed as a Gaussian in Galacticradius and compared the resulting longitudinal distributionwith the observed SNR longitudinal distribution, obtaininga scale length of B7.0 kpc. However, no attempt was made

to compensate for selection e†ects other than to use a &-limited sample. et al. used a more sophisticatedLi (1991)model distributing SNRs in an exponential disk as well as inspiral arms. They incorporated a 1/d2 selection bias,assuming completeness out to d \ 3 kpc. They then com-pared the longitudinal distribution given by the model withthe observed SNR longitudinal distribution, obtaining ascale length of B5È9 kpc, depending on the model param-eters. As Li et al. point out, the scale length of the Galacticstellar disk is D5 kpc, suggesting that the SNR scale length,as derived in this work and by and et al.Green (1996b) Li

would indicate that the SNR distribution is not(1991),associated with the stellar disk population.

5. CONCLUSION

The catalog of known SNRs has continued to grow insize. The number of SNRs with reasonably determined dis-tances has also increased. However, most distances given inthe literature were calculated using older rotation curves.We have recalculated the distances, where necessary, usinga modern rotation curve and used the updated distances toderive a new &-D relation for shell SNRs. This &-D relation,using a sample of 36 shell SNRs (37 including Cas A), yieldsa slope of [2.38 excluding Cas A and [2.64 with Cas A.When the 41 shell SNRs in the LMC and SMC are added tothe sample, the slope is [2.41 with a smaller error. Usingthe &-D relation to estimate distances to individual rem-nants is viable only with the assumptions that all shellSNRs have the same radio luminosity dependence on lineardiameter, have the same supernova explosion mechanismand energy, and are evolving into identical environments.We Ðnd that, on average, the error in the distance estima-tion to an individual SNR to be D40% when using our &-Drelation. However, the error in deriving ensemble character-istics of SNRs such as the SNR surface density can be lower(D10%È20% for the mid-Galactic region). We attempt tocompensate for observational selection e†ects inherent inSNR searches by employing a scaling method based on thesensitivity, angular resolution, and sky coverage of actualradio surveys. Using the updated distances, the new &-Drelation, and the scale factors, the shell SNR surface densityradial distribution was derived. The distribution peaks atD5 kpc and has a scale length of D7.0 kpc.

FIG. 7.ÈThe SNR density radial distribution for region 2 using the new distances and compensation for selection e†ects. (a) The distribution derived inthis work (solid line and data points) and that of (dashed line), both normalized to the density at the radius of the solar circle. (b) TheKodaira (1974)unnormalized data points and the Ðt to eq. (15).

p/p for various nucleon spectra

hard nucleons

modified nucleons

options for diffuse γ-rays

Hof et al. 1996 HEAT

normal

70-100MeV

1.0<l<180.0/181.0<l<359.0

Latitude profile of γ-rays

for model with 4 kpc halo

HEMN

IC

bremss πo

TOTAL

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6" = 9�� �. ����8% 527 Æ ; ��/( �� ��������������%

�2������� ��������� ��� �'�,� �� 4���,��4��� � �=%

.)����� ������)� �������3����� �� %# �������� �� ���� �%

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�2������� ��������� ��� �'�,� �� 4���,��4��� & ��=%

�Æ ; � �$ � �$ 4���,��4��� " =( �� ����������%