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Transcript of Cosmic Rays and Diffuse Galactic Gamma-Ray · PDF fileCosmic Rays and Diffuse Galactic...
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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