SUPERSYMMETRYORSTELLAR
PHYSICS:COSMICRAYELECTRONS
ANDPOSITRONEXCESSES
PeterL.Biermann
1
,
2
,
3
,
4
,
5
,JuliaK.Becker
6
,
7
,Athina
Meli
8
,WolfgangRhode
7
,Eun-SukSeo
9
,&Todor
Stanev
10
1
MPIforRadioastronomy,Bonn,Germany
2
Dept.ofPhys.&Astron.,Univ.ofBonn,Germany
3
Dept.ofPhys.&Astr.,Univ.ofAlabama,Tuscaloosa,
AL,USA
4
Dept.ofPhys.,Univ.ofAlabamaatHuntsville,AL,
USA
5
FZKarlsruhe,andPhys.Dept.,Univ.Karlsruhe,
Germany
1
6
Institutionf¨orFysik,G¨oteborgsUniv.,Sweden
7
Dept.ofPhys.,Univ.Dortmund,Dortmund,Germany
8
ECAP,Friedrich-AlexanderUniversit¨at
Erlangen-Nu¨rnberg,Germany
9
Dept.ofPhysics,Univ.ofMaryland,CollegePark,
MD,USA
10
BartolResearchInst.,Univ.ofDelaware,Newark,
DE,USA
www.mpifr-bonn.mpg.de/div/theory
2
Cosmicrayelectronsandpositrons:newdata
•
Pamela:0810.4995:positronfractionincreasingwith
energy
•
ATIC:Nature
456
,362(2008):“flat”featureincosmic
rayelectrons
•
H.E.S.S.:0811.3894:“steep”featureincosmicrayelec-
trons
3
Figure1Pameladataonpositronfraction,2008
4
Figure2ATICdataoncosmicrayelectrons,2008;opentrianglesbackground
5
Figure3H.E.S.S.dataoncosmicrayelectrons,2008
6
Somesuggestions
•
L.Bergstr¨ometal.,0808.3725:PositronsfromSUSY
darkmatter
•
V.Bargeretal.,0809.0162:Darkmatterlighterthan
thetopquark
•
J.H.Huhetal,0809.2601,2008:TwoDMcomponents
andMSSM
•
Yukse¨
letal.,0810.2784:TeVgammaraysfromGeminga...
7
Figure4L.Bergstr¨ometal.,0808.3725,2008:Neutralinoannihilation
8
Figure5V.Bargeretal.,0809.0162,2008:DMannihilationlighterthantopquark
9
Figure6V.Bargeretal.,0809.0162,2008:DMannihilationlighterthantopquark
10
Figure7J.H.Huhetal,0809.2601,2008:annihilationbetweentwodifferentcomponentsofDM
11
Figure8Yuksel¨
etal.,0810.2784,2008:GemingaTeVpulsarwindnebula
12
Massivestars
•
Starsbetween8and15
M
?
explodeintotheISM
•
Starsabove15
M
?
explodeintotheirownstellarwind
•
Stellarwindshave
B
r
∼
r
?
2
,and
B
φ
∼
(sin
θ
)
/r
(Parker1958)
•
ExplosionsintotheISMgive
E
?
2
.
42
,thepredictedin-
jectionlimit
•
Diffusivelossesaddfactor
E
?
1
/
3
,soaspectrumof
E
?
2
.
75
,thediffusionlimit
•
Theoryerrorbarstypically
±
0
.
04inthespectrum
13
Figure9Maeder&MeynetASP388,3,2006,herelowerpanelofFig.5
14
Figure10Maeder&MeynetASP388,3,2006,Fig.9
15
Figure11Hegeretal.ApJ591,288(2003),Fig.1
16
Figure12Hegeretal.ApJ591,288(2003),Fig.3
17
Figure13Hegeretal.ApJ591,288(2003),Tab.4
18
RedSupergiantandWolfRayetstar
environments
•
Starsaboveabout15
M
?
explodeasredsuper-giant
stars,shortRSGstars
•
Starsaboveabout25
M
?
explodeasbluesuper-giant
stars,orWolfRayetstars,shortWRstars
•
Explosionsintothewindgivepredicted
E
?
7
/
3
,with
diffusionlimit
E
?
8
/
3
•
Theoryerrorbarstypically
?
0
.
02
±
0
.
02inthespec-
trum,asymmetricerrordistribution
19
Thepolarcapcomponent
•
Polarcapcomponent
E
?
2
.
00
,rightuptoknee(about
Z
10
15
eV)
•
atinjectionenergiesonlyafewpercentoftotalCR
power
•
Electronsbeyondabout20GeVinlosslimit(Karda-
shev1962):sospectrum
E
?
3
.
00
•
Electronsinjectedfromabout30MeV(Protheroe&
Biermann1996)
•
Thereforecosmicrayelectronpolarcapcomponentap-
pearsearlierinparticleenergybytheratioofthemass,
say,ofFe,andthe30MeV,soaboutafactorof4000
totheleft,inthehundredsofGeV
20
Figure14Spectralandchemicalstructureattheknee,toberepeatedathighenergy?ElementgroupsareH,
He,CNO,Ne-S,Cl-Mn,andFe.Herethespectraareinthediffusionlimit,andweneedtheinjectionlimit;this
impliesmultiplyingallcurvesby(
A/Z
)
1
/
3
?
10
0
.
1
.Source:Stanevetal.,paperCR-IV1993
21
InjectionI
•
Weconsidertheexcitationinashockedregion
•
Cascadeequation:
d
dt
I
(
k
)
4
πk
2
?
1
k
2
∂
∂k
(
k
4
3
τ
k
∂
∂k
(
I
(
k
)
4
πk
2
))=
Aδ
(
k
?
k
0
)
•
τ
k
isthetimescaleofdiffusionofturbulentenergy:
τ
k
=
1
k
(
γ
eff
I
(
k
)
k/ρ
)
1
/
2
•
ρ
matterdensity,
γ
eff
eff.adiab.index.Source
k
0
.
SolutionKolmogorov(1941)cascade:
•
I
(
k
)
∼
k
2
for
k
≤
k
0
,and
I
(
k
)
∼
k
?
5
/
3
for
k
≥
k
0
22
InjectionII
•
Sourcetermincascadeequation:
σ
excit
I
(
k
)
4
πk
2
with
σ
excit
=
4
π
3
v
A
I
(
k
)
k
p
4
v
∂f
∂x
•
v
particlevelocity,
f
particledistributionfunctionin
p
phasespace,
x
localcoordinate
•
Distributionfunctionhasastepatashock!
•
Balancecascadingwithexcitation,usingaspectrumof
thephasespacedistributionfunction(e.g.windshock)
of
p
?
7
/
3
?
2
23
InjectionIII
•
Turbulenceisexcitedbya)cosmicrays,andb)irregu-
laritiesduetotheinstabilitiesinthewind-driving
•
CRexcitedturbulencespectrum,
I
(
k
)
∼
k
?
13
/
9
•
Irregularitiesinherentinwind-driving,
I
(
k
)
∼
k
?
2
•
Concept:inWRstarstheCRdrivingdominates,and
inRSGstarstheinstabilitydrivingdominates
•
Diffusioncoefficientthen
p
5
/
9
•
Secondaryspallationproductsrunas
E
?
5
/
9
steeper
N
sec
N
prim
∼
E
?
5
/
9
•
ThisisconsistentwiththelowenergyPameladata
24
InjectionIV
•
ForRSGstarexplosionsturbulencedominatedbyir-
regularmotion,so
•
I
(
k
)
∼
k
?
2
:secondaryspallationnoenergydepen-
dence
N
sec
N
prim
∼
1
•
•
Test:
γ
-rayspectrumoftheinnerGalaxy,sameasin-
jection
E
?
7
/
3
•
ModifiedbySolarwindmodulation
•
ThisisconsistentwithMilagrodataforinnerGalaxy
25
Figure15Ptuskinetal.,ICRC1999,vol.
4,p.
291,Fig.
1:column11
.
3
β
g
/
cm
2
for
R<
5GVand11
.
3
β
(
R/
5GV)
?
0
.
54
g
/
cm
2
for
R>
5GV;
R
isrigidity,i.e.momentum
×
c
/charge
26
Figure16Casanovaetal.,IntegralMeeting,0403661,2004,Fig.3
27
Figure17Casanovaetal.,IntegralMeeting,0403661,2004,Fig.5a,theinnerGalaxy
28
Figure18Casanovaetal.,IntegralMeeting,0403661,2004,Fig.5b,theouterGalaxy
29
Cosmicrayelectronsandpositrons
•
Biermann,P.L.,
Astron.&Astroph.
271
,649(1993)
•
Biermann,P.L.,&
Cassinelli,J.P.
,
Astron.&As-
troph.
277
,691(1993)
•
Stanev,T.,Biermann,P.L:,&Gaisser,T.K.,
Astron.
&Astroph.
274
,902(1993)
•
Biermann,P.L.,Gaisser,T.K.,&Stanev,T.,
Phys.
Rev.
D51
,3450-3454(1995)
•
Biermann,P.L.,inv.lectureattheNuclearAstro-
physicsmeetingatHirschegg,inProc.,GSI,Darm-
stadt,p.211-222(1998)
•
Biermann,P.L.,
Langer,N.
,Seo,E.-S.,&Stanev,
T.,
Astron.&Astroph.
369
,269-277(2001)
30
InjectionV
•
Injectionofsecondariesdependsonproductionrate
•
Accelerationfasterforperpendicularshocks,soover
mostof4
π
,soreducedproductionofsecondariesrela-
tivepolarcap
•
By
c/
(3
V
sh
),soafactorlessthan10,probablymore
like2-3effectively(seeMeli&Biermann2006)
•
Thistranslatesintoaparticleenergy,wherethepo-
larcapcomponentbecomesdominant,conservatively
between2
3
to3
3
lowerthanforelectrons.
•
Thisimpliesthenanenergyof500GeVdividedbythis
factor,so60to16GeV.30GeVcompatiblewithdata.
•
Thereforetheratioofthepositrontoelectronfluxes
shouldscaleas
E
+1
/
3
•
ThisisconsistentwiththehigherenergyPameladata.
31
InjectionVI
•
Integratingpastinjectionatsynchrotronlosslimitgives
N
(
E
)
∼
E
?
7
/
3
?
1
•
Randomwalkfromnearbyregionswith
r
?
∆
r
√
N
•
Correspondingtoatime
t
?
∆
r
c
N
•
r
?
∆
r
?
tc
∆
r
?
√
tc
∆
r
(1)
•
∆
r
∼
E
1
/
3
,and
t
∼
1
/E
,so
r
∼
E
?
2
/
3
•
Flatdisksourcedistribution
πr
2
?
E
?
4
/
3
•
SoCR-ehighenergyspectrumpredictedtobe
?
E
?
3
?
4
/
3
•
ThisisconsistentwiththeH.E.S.S.data
32
log10(E/GeV)
E
3
*dN/dE
e
[
GeV
2
cm
-2
sr
-1
s
-1
]
10
2
10
3
1
1.5
2
2.5
3
3.5
4
Figure19ModelpredictionwithATICandH.E.S.Sdataforcosmicrayelectrons:
E
?
10
/
3
,
E
?
3
,and
E
?
13
/
3
33
log(E/GeV)
Φ
e
+
/(
Φ
e
+
+
Φ
e
-
)
10
-1
-0.5
0
0.5
1
1.5
2
Figure20ModelpredictionwithPameladataforcosmicraypositrons,matching
E
?
5
/
9
atlowerenergy,and
E
+1
/
3
athigherenergy.
34
Consequencesofmassivestarphysics
•
Cosmicrayelectronsatlowenergiessumof
E
?
2
.
75
and
E
?
8
/
3
•
Wigglesinspectrumattributabletoadiabaticlosses,
adiabaticcompression,andcatastrophiclossesinmag-
neticbottles
•
Thecosmicrayelectronspectrum
E
?
10
/
3
atmoderate
energies,
E
?
3
athigherenergy,
•
andatthehighestenergies
E
?
13
/
3
•
Thecosmicraypositron/electronratiowillapproacha
E
?
5
/
9
atlowerrelativisticenergy,
•
and
E
+1
/
3
athigherenergy
35
Acknowledgement
WorkwithPLBwassupportedbycontractAUGER05
CU5PD1/2viaDESY/BMBandbyVIHKOSviaFZ
Karlsruhe;byErasmus/SokratesEU-contractswithethe
universitiesinBucharest,Cluj-Napoca,Budapest,Szeged,
Cracow,andLjubljana;bytheHumboldtFoundation;and
byresearchfoundationsinKorea,China,Australia,India
andBrazil.
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