Cosmic Ray Helium Hardening

0.23 MB·

by  Yutaka Ohira

Accepted: January19,2011
PreprinttypesetusingLATEXstyleemulateapjv.8/13/10
COSMIC RAY HELIUM HARDENING
Yutaka Ohira and Kunihito Ioka
TheoryCenter,Institute ofParticleandNuclearStudies,KEK(HighEnergyAccelerator ResearchOrganization),1-1Oho,Tsukuba
305-0801, Japan;[email protected]
Accepted: January 19, 2011
ABSTRACT
1 Recent observations by CREAM and ATIC-2 experiments suggest that (1) the spectrum of cosmic
1 ray (CR) helium is harder than that of CR proton below the knee 1015 eV and (2) all CR spectra
0 become hard at & 1011 eV/n. We propose a new picture that higher energy CRs are generated in
2 more helium-rich region to explain the hardening (1) without introducing different sources for CR
helium. The helium to proton ratio at ∼ 100 TeV exceeds the Big Bang abundance Y = 0.25 by
n
several times, and the different spectrum is not reproduced within the diffusive shock acceleration
a
J theory. We argue that CRs are produced in the chemically enriched region, such as a superbubble,
and the outward-decreasing abundance naturally leads to the hard spectrum of CR helium if CRs
1
escape from the supernova remnant (SNR) shock in an energy-dependent way. We provide a simple
2
analytical spectrum that also fits well the hardening (2) because of the decreasing Mach number in
] the hot superbubble with ∼ 106 K. Our model predicts hard and concave spectra for heavier CR
E elements.
H Subject headings: accelerationof particles — cosmic rays — shock waves — supernova remnants
.
h
p 1. INTRODUCTION ular clouds emit gamma-rays (e.g. Abdo et al. 2009;
- Tavani et al.2010)andthegamma-rayobservationssup-
o Recently, the Cosmic Ray Energetics And Mass
port that SNRs produce the bulk of Galactic CRs (e.g.,
r (CREAM) has directly observed the CR compositions
st with high statistics in the wide energy range up to Ohira et al. 2011; Li & Chen 2010).
a about 1014 eV. Interestingly, CREAM shows N (E) ∝ Accordingto DSA theory, the spectrum ofaccelerated
[ E−2.66±0.02 for CR proton and N (E) ∝ E−2p.58±0.02 particles at a shock does not depend on CR elements,
He but depends only on the velocity profile of the shock.
3 for CR helium in the energy region 2.5 × 1012 eV– Thus,naively,recentCRobservationsseemtoshowthat
v 2.5 × 1014 eV, that is, the spectrum of CR helium is the acceleration site of CR helium is different from that
5 harder than that of CR proton (Ahn et al. 2010). Al- of CR proton (Biermann et al. 2010). However, in this
0 though the difference of the spectral index ∆s ≈ 0.08
differentsitescenario,itshouldbebychancethattheob-
4 appears small, the implications are of great importance servedratioofCRheliumandproton,N /N ,at109eV
4 asshownbelow. Inaddition,the spectralindex becomes He p
is similar to the cosmic abundance (Y = 0.25). Fur-
. hard by ∼0.12 for CR proton and by ∼0.16 for CR he-
1 thermore, the difference of the spectral index ∆s≈0.08
1 liumat&2×1011eV/nbecausetheAlphaMagnetSpec- means that N /N at 1014 eV is about 3 times higher
0 trometer(AMS)showsNp(E)∝E−2.78±0.009 fortheCR thanthatat1H09e eVp. Thisenhancementisamazingsince
1 proton(Alcaraz et al.2000a)andN (E)∝E−2.74±0.01
He the mean helium abundance in the universe is virtually
v: for CR helium (Alcaraz et al. 2000b) in the low-energy maintained constant. The stellar nucleosynthesis never
i range 1010 eV–1011 eV. These results have been already enhancesthe meanheliumabundanceby afactor,which
X obtainedbytheAdvancedThinIonizationCalorimeter-2 is the essential reason that the big bang nucleosynthesis
r (ATIC-2) (Panov et al. 2009). is indispensable for the cosmic helium abundance. To
a For CR electrons, the Fermi gamma-ray space tele- make the enhancement, we should consider inhomoge-
scope has recently observed the spectrum of CR elec- neous abundance regions. We show that this leads to
trons in the wide energy range from 7 × 109 eV to the different spectrum of CR proton and helium when
1012 eV (Ackermann et al. 2010). Fermi shows that the escaping from SNRs.
observed date can be fitted by a power law with spec- In this letter, considering the inhomogeneous abun-
tral index in the interval 3.03 − 3.13 and the spectral dance region, we provide a new explanation about (1)
hardening at about 1011 eV, which may have the same the different spectrum of CR proton and helium, even
origin as that of the CR nuclei. (For other models, see, if CR protonand helium are acceleratedsimultaneously.
e.g., Kashiyama et al. 2010; Kawanaka et al. 2010; Ioka OurideausesthefactthatCRsescapingfromSNRsgen-
2010, and references therein). Note that we do not dis- erally have a different spectrum than that of the accel-
cuss CR positrons in this letter. eration site (Ptsuskin & Zirakashvili 2005; Ohira et al.
Supernova remnants (SNRs) are thought as the ori- 2010; Caprioli et al. 2010). The runaway CR spectrum
gin of the Galactic CRs. The most popular acceleration dependsonnotonlytheaccelerationspectrumatshocks
mechanism at SNRs is the diffusive shock acceleration but also the evolution of the maximum energy and the
(DSA) (Axford et al. 1977; Krymsky 1977; Bell 1978; number of accelerated CRs (Ohira et al. 2010). We also
Blandford & Ostriker 1978). In fact, Fermi and AG- suggestthat (2) the spectralhardening of CRs is caused
ILE show that middle-age SNRs interacting with molec- by the decreasing Mach number in the high tempera-
2 Ohira and Ioka
-s low-energy CRs. Then, the number of runaway CRs be-
E
tween χ and χ+dχ is
Runaway CR dpmax
F (χ,p ) dχ , (1)
er N ∝χβ SNR max dχ
b -(s+α/β)
m E which corresponds to the number of runaway CRs be-
u E-s tween p = pmax(χ) and p = pmax(χ) + dp, Fesc(p)dp.
N Hence, F (p) is
esc
F (p)=F (p−1 (p),p) , (2)
esc SNR max
χ-α
E m a x ∝ wherep−1 (p)istheinversefunctionofp (χ). Assum-
max max
ing F (χ,p) ∝ χβp−s and p (χ) ∝ χ−α, we obtain
SNR max
Energy the runaway CR spectrum as
soFliidg,.d1a.—shedSchaenmdadtoicttpedictluinreesofshtohwe rtuhneawruanyaCwRaysCpeRctrsupmec.trTumhe, Fesc(p)∝p−(s+αβ) , (3)
CR spectrum inside an SNR at an early epoch and CR spectrum
where α and β are parameters to describe the evolution
insidetheSNRatalaterepoch,respectively. Thesolidlineofthe
runaway CR spectrum represents the equation (3). A variable χ ofmaximumenergyandthe number ofacceleratedCRs,
(e.g.,theshockradius)describestheSNRevolution. respectively. (We use α∼6.5andβ ∼1.5later.) There-
ture medium. Both the inhomogeneous abundance and
fore,therunawayCRspectrumF isdifferentfromthat
esc
thehightemperaturecanberealizedinthesuperbubbles in the SNR F ∝ p−s. Figure 1 shows the schematic
SNR
with multiple supernovae. Our conclusions are summa-
picture of the runaway CR spectrum. In this Letter, we
rized as follows.
use the shock radius, R , as χ.
sh
The evolution of the maximum energy of CRs at
• Runway CR spectra depend on not only CR spec-
the SNR has not been understood. This strongly de-
tra inside the SNR but also the evolution of the
pends on the evolution of the magnetic field around
maximum energy and the number of accelerated
the shock (e.g. Ptsuskin & Zirakashvili 2003). Although
CRs. Therefore, taking account of the inhomoge-
some magnetic field amplifications have been proposed
neous abundance region, runaway CR spectra of
(e.g., Lucek & Bell 2000; Bell 2004; Giacalone & Jokipii
different CR elements have different spectra (sec-
2007;Ohira et al.2009b)andinvestigatedbysimulations
tion 2 and 3.1).
(e.g., Niemiec et al. 2008; Riquelme & Spitkovsky 2009;
• Our model is in excellentagreementwith observed Ohira et al.2009a;Gargat´e et al.2010),the evolutionof
spectra of CR proton and helium. Harder spec- the magnetic field has not been completely understood
trum of CR helium is due to the enhancement of yet. Here we assume that CRs with the knee energy es-
theheliumabundancearoundtheexplosioncenter. cape at R = RSedov, where RSedov is the shock radius
On the other hand, the concave spectra of all CR at the beginning of the Sedov phase. Furthermore, we
elementsareduetothedecreasingMachnumberin use the phenomenological approach with the power-law
thehotgaswith∼106K. Theconcavespectramay dependence (Gabici et al. 2009; Ohira et al. 2010),
bealsoproducedbytheCRnonlineareffect,theen-
−α
ergy dependent effects on the accelerated CRs (on Rsh
p (R )=p Z , (4)
α or β), the propagation effect (γ), and/or multi max sh knee R
(cid:18) Sedov(cid:19)
components with differentspectralindices (section
3.2 and 4). where pknee = 1015.5 eV/c is the four momentum of the
knee energy. Note that α does not depend on the CR
• Within the single component scenario, the hard composition because the evolution of the maximum en-
helium spectrum suggests that the origin of the ergy depends only on the evolutionof the magnetic field
Galactic CR is SNRs in superbubbles, although and the shock velocity.
wearenotexcludingthemulticomponentscenario The evolution of the number of CRs inside the SNR
(section 5). has not been also understood. This depends on the
injection mechanism (Ohira et al. 2010) and the den-
• Our model predicts that heavier (at least volatile)
sity profile around the SNR. We here adopt the ther-
CR elements also have harder spectra than that of
mal leakage model (Malkov & Vo¨lk 1995) as an injec-
CR proton and have concave spectra (section 5). tion model. For the total density profile, ρ (R ) ≈
tot sh
2. RUNAWAYCRSPECTRUM mp(np(Rsh)+4nHe(Rsh)) where np and nHe are the
numberdensity ofprotonandhelium andm is the pro-
p
Inthissection,webrieflyreviewtherunawayCRspec- ton mass, the shock velocity of the Sedov phase is
trum(seeAppendix ofOhira et al.(2010)). We hereuse
aagvea)rtioabdleescχri(bfeortheexaemvopluletitohneosfhaonckSNraRd.iuLsetoFr the(SχN,pR) ush(Rsh)∝ρtot(Rsh)−21Rs−h23 . (5)
SNR
andp (χ) be the CRmomentumspectrum[(eV/c)−1] In the thermal leakage model, the injection momentum
max
andthemaximumfourmomentumofCRinsidetheSNR ofelementiisproportionaltothe shockvelocity,pinj,i ∝
atacertainepochlabeledbyχ,respectively. CRsescape ush,andthenumberdensityofCRwithmomentumpinj,i
in order,from the maximum energy CR because the dif- is proportional to the density, p3inj,ifi(pinj,i) ∝ ni(Rsh),
fusion length of high-energy CRs is larger than that of where f is the distribution function of CR element i.
i
Cosmic Ray Helium Hardening 3
Early shock Late shock runaway CR spectra (See Section 4 for more details).
Figure 2 shows the schematic picture of our idea.
n High-energy proton Low-energy proton 3.2. Spectral hardening of all CRs at the same energy
y p per nucleon
t
i
s Inthissubsection,wediscussthespectralhardeningof
n
the observed CRs. The Galactic CR spectrum observed
e High-energy helium
D at the Earth, F , is obtained by the simple leaky box
obs
model
n Low-energy helium
He F ∝F (p)/D(p)∝F (p)p−γ , (9)
obs esc esc
where D(p) ∝ pγ is the diffusion coefficient (e.g.
Strong et al. 2007). Hence, the index of the observed
Radius spectrum is
β
Fig.2.—Schematicpictureoftheformationofthedifferentspec- sobs =s+ +γ . (10)
α
trum. Thesolidanddashed lineshow the protondensity andthe
heliumdensity,respectively. Thedottedlinesshowtheshockfront. The deviation from a single power law means that at
Inearlyphase,high-energyCRprotonandCRheliumescape,and
least one of s, α, β, and γ has an energy dependence
inlate phase, low-energy CR proton and CR helium escape. The
ratioofCRheliumtoCRprotonincreaseswiththeCRenergy. or that the origin of low energy CRs below 1011 eV is
different from that of high energy CRs above 1011 eV.
Hence,the numberofCRelementiwithareferencemo- Althoughthe multi componentscenariomay be the case
mentum p=m c, F (R ,m c) is because there are many types of SNRs, we discuss the
p SNR,i sh p
single component scenario in this letter.
FSNR,i(Rsh,mpc)∝Rs3hfi(mpc) Firstly, we discuss the energy dependence of s. From
∝R3 pslow+2f (p ) equation (7), s depends on the shock radius because the
sh inj,i i inj,i Mach number M decreases with the shock radius. Then
∝R3 n (R )pslow−1 we can expect the spectral harding of all CR compo-
sh i sh inj,i
sitions at the same rigidity cp/Ze, that is, at approxi-
∝ni(Rsh)ρtot(Rsh)1−s2lowRs3h(3−2slow) (6,) matelythe sameenergyper nucleon. Fromequation(5),
the Mach number is
where fi(p)p2 ∝ p−slow and slow is the spectral index −1 −1 −3
in the non-relativistic energy region. For the nonlinear M ≈103 ρtot(Rsh) 2 T 2 Rsh 2 ,
DSA, the spectral index in the non-relativistic energy ρ (R ) 104 K R
(cid:18) tot Sedov (cid:19) (cid:18) (cid:19) (cid:18) Sedov(cid:19)
regionis different from that in the relativistic energy re- (11)
gion (Berezhko & Ellison 1999). To understand the es- where T is the surrounding temperature and we assume
sentialfeatureoftherunawayCRspectrum,weherecon- that the ejecta mass and the energy of supernova explo-
sider only the test-particle DSA, that is, slow = s. Be- sion are 1 M⊙ and 1051 erg, respectively. From equa-
cause ni(Rsh)ρtot(Rsh)1−2s is not always a single power- tions (4), (7) and (11), we can obtain s as a function of
lawform,theevolutionofthenumberofacceleratedCRs p (see § 4).
can not be always described by a constant β. Alternatively the spectralhardening can be also inter-
preted as the CR nonlinear effect (e.g., Drury & Vo¨lk
3. BASICIDEA 1981; Malkov & Drury 2001). This issue will be ad-
3.1. Different spectrum of CR proton and helium dressed in the future work.
Next, we discuss the energy dependence of β that is
Accordingto the test particleDSA theory,the index s
the parameter to describe the evolution of the number
of relativistic CR energy spectrum depends only on the
of accelerated CRs. In Section 3.1, we consider different
velocity jump at the shock,
power-law forms for n (R ) and n (R ) to make the
p sh He sh
u +2u M2+1 differentspectrum of the CR protonand helium. There-
1 2
s= =2 , (7) fore,ρ (R )≈m [n (R )+4n (R )]is notasingle
u −u M2−1 tot sh p p sh He sh
1 2 power law form, and β has an energy dependence (see
where we use the Rankine-Hugoniot relation at the sec- § 4).
ond equation and M is the Mach number. Then, the The energy dependence of γ will be soon precisely de-
index of the runaway CR spectrum, s , is termined by AMS-02 (Pato et al. 2010). We do not dis-
esc
cuss the energy dependence of α because the complete
β
s =s+ , (8) physicsofthe CRescape andmagneticturbulence is be-
esc
α yond the scope of this Letter.
inequation(3). Therefore,ifβ/α(inparticularβ,thein- 4. COMPARISONOFOURMODELWITHOBSERVATIONS
dexfortheacceleratedCRnumberevolution)isdifferent,
Inthissection,specifyingmodelparameters,wecalcu-
the runaway CR spectrum is different between the CR
late the Galactic CR spectrum. For simplicity, we here
compositions. This is our main idea to explain the he-
assume the number densities of proton and helium as
liumhardeningobservedbyCREAMandATIC-2. From
follows,
equation (6), β depends on the ambient number density
n . Therefore, different density profiles make different n (R )=n
i p sh p,0
4 Ohira and Ioka
where F and ǫF are normalization factors of
P (AMS) p,knee p,knee
P (ATIC-2) CRprotonandheliumandZ =2forhelium, ands(p)is
-2-1-1m s sr ] HPHHe e( e(C C((RAARTEMEIACSAM-)M2 ) )) oabllFtpaigainureardemfe3rtoemsrhsoeaqwruesaαtti,hoeγn,scδ(o4,m)ǫ,,p(Ta7r),isFaonpn,dkno(e1fe1.o).urInmthoidseml owdiethl,
1.75eV otibosnerevffaetciotsnsw.itWh ethteakmeodinutloataiocncopuonttenthtiealsΦola=r m45o0dMulaV-
G
2.75E [ 104 (aGgrleeeemsoennt&wAixthfortdhe19o6b8s)e.rveOdusrpemctordae,lwisithinαex=cell6e.n5t,
ux * γ = 0.43, δ = 0.715, ǫ = 0.31, T = 106 K. The dif-
Fl ferent spectra of CR proton and helium originate from
the different density profiles in equations (12). Figure 4
101 102 103 104 105 106 shows the evolution of the maximum energy of CRs and
Kinetic energy per particle [GeV] the spectral index of CRs inside the SNR. In the early
Fig.3.— Comparison of our model (solid and dashed line) phase, the spectral index s is 2 and after then, the spec-
with AMS (triangle) (Alcarazetal. 2000a,b), ATIC-2 (square) tral index decreases with the shock radius because the
(Panovetal. 2009) and CREAM (circle) (Ahnetal. 2010) obser-
Mach number decreases with shock radius. The change
vations for Galactic CRs. Filled symbols and the solid line show
CRproton. OpensymbolsandthedashedlineshowCRhelium. ofspectralindex s is about0.1 whichis almostthe same
as the observed hardening. The observed hardening is
not the result of the change of the injection history, β,
107 Emax 2.48 but the result ofspectralchange of CRs inside the SNR.
106 s 2.4 The high temperature T ∼ 106 K is necessary for the
spectral hardening ∆s∼0.1.
105 2.32 Inaddition, ourmodel also makes a concavespectrum
V] of CR electrons as observed (Ackermann et al. 2010).
e
[Gmax104 2.24 s Htroownsevhears,tnhoetebveoelnutuionndeorfsitnojoedctiwoenlle.ffiScoiewnecyneoefdCfRuretlheecr-
E
103 2.16 studies to discuss the CR electron spectrum in detail.
102 2.08 5. DISCUSSION
To make the different spectrum, our model requires
101 2
1 2 3 4 5 6 7 that the helium abundance around the explosion cen-
Rsh / RSedov ter is higher than that of the solar abundance. SNRs
in superbubbles are one of candidates. Higdon et al.
Fig. 4.— The evolution of the maximum energy Emax/Z (solid (1998) show that supernova ejecta can dominate the
line)andthespectralindexsoftestparticleDSA(dashedline)in
equations (4),(7)and(11)asfunctionsofRsh. superbubble mass within a core radius of one third of
the superbubble radius. In the stellar wind and the
supernova explosion, the stellar hydrogen envelope has
R −δ lower density and higher velocity than that of helium.
n (R )=ζn sh , (12) Then we expect that the helium fraction in the cen-
He sh p,0
(cid:18)RSedov(cid:19) ter of superbubbles is higher than that in the outer re-
gion. Furthermore, to make the concave spectrum, our
where n is the number density of proton at R =
p,0 sh model requires an ambient medium with high temper-
RSedov, and ζnp,0 is the normalization factor of the he- ature, T = 106 K. This is also consistent with su-
lium density. We set ζ =106.5(δ/α)−1 so that the helium perbubbles. According to the CR composition study,
abundance is that of the solar abundance, nHe/np =0.1 SNRs in superbubbles have been considered as the ori-
(i.e., Y ≈ 0.25), when cpmax = Z GeV with equation gin of Galactic CRs (e.g., Lingenfelter & Higdon 2007;
(4). Note that the power-law dependence is a first step Ogliore et al. 2009). Particle accelerations in super-
approximation for the mean value. Then, from equa- bubbles have been also investigated by intensive stud-
tions (2), (4), (6), (9), observed spectra of CR proton ies (e.g., Bykov & Fleishman 1992; Parizot et al. 2004;
and helium are Dar & De Ru´jula 2008; Ferrand & Marcowith 2010).
Wehereconsideredasphericallysymmetricsystem. The
1−s(p)
1+ζ(p/pknee)αδ 2 off-center effects may be important for the initial phase
Fobs,p=Fp,knee and thereby for the high energy spectrum, because the
1+ζ
( ) shock radius at the beginning of the Sedov phase R
Sedov
p −[s(p)+3{3−2αs(p)}+γ] is about 20 pc which is comparable to the typical size
× , (13) of OB association, 35 pc (Parizot et al. 2004), and the
(cid:18)pknee(cid:19) shockradiusRsh isabout200pcatthe endofthe Sedov
1−s(p) phase. This is an interesting future problem.
1+ζ(p/Zpknee)αδ 2 Note that the spectral hardening can be also made by
F =ǫF
obs,He p,knee 1+ζ the nonlinear model, the energy dependence of the CR
( )
diffusion coefficient and/or multi components with dif-
p −[s(p)+3{3−s2(αp)}−2δ+γ] ferentspectralindices. Sothehightemperaturemaynot
× (14), be absolutelynecessary. The stellarwindofredgiantsis
Zp
(cid:18) knee(cid:19)
Cosmic Ray Helium Hardening 5
one of candidates for the cold and helium rich ambient. velocity is not fast enough to accelerate refractory ele-
Still, the dominant core-collapse supernovae is type II ments to the knee energy when the refractory elements
(e.g.,Smartt et al.2009)whichhasnoheliumrichwind, areinjectedbecausethesputteringtimescaleistoolong.
sothatthe superbubblescenariolooksmorelikelyasthe Therefore,refractoryCRsaroundthekneeenergyshould
origin of the Galactic CRs above 1011 eV. For the CRs be injected by the standard manner similar to volatile
below 1011 eV, the spectral difference between CR pro- CRs. In this case, the refractory CRs also have harder
ton and helium may be caused by the solar modulation spectra than protons, although we need further studies
and the inelastic interactions (Putze et al. 2010). of the injection of refractory CRs at the knee energy.
The spatial variation of the helium ionization degree IfCRstrappedinsidetheSNRandreleasedattheend
can also change the injection history. The injection effi- of the SNR’s life outnumber runaway CRs (see figure
ciency of the large rigidity is thought to be higher than 3 in Caprioli et al. (2010)), our scenario does not work
thatoflow rigiditysince particleswith largerigidity can for producing hard and concave spectra. In our model
easily penetrate through the shock front fromthe down- with α∼6.5 in Eq. (4), trapped CRs have energy below
streamregion. Iftheionizationdegreeincreaseswiththe 1 GeV when they are released, that is, p . Zm c
max p
SNR radius, the CR helium spectrum becomes harder when R & 10R , and are not relevant for our in-
sh Sedov
thantheCRprotonone,β <β . However,therigidity terest. Higher energy CRs escape from the SNR even
He p
dependenceoftheinjectionefficiencyhasnotbeenunder- after advectedto the downstreamsince the CR diffusion
stood completely. Moreover, the injection from neutral isfasterthanthe expansionoftheSNR.Ourcaseissim-
particles should also be understood (Ohira et al. 2009b, ilar to the right figure 7 in Caprioli et al. (2010) where
2010). trapped CRs are released below 100 GeV. The energy
Accordingtoourmodel,CRspectraofheaviervolatile boundary between trapped CRs and runaway CRs de-
elements than helium is also harderthan that of proton. pends on the evolution of the maximum energy (α).
Low-energyCRsofrefractoryelementsarethoughttore-
sultfromsuprathermalinjectionby sputteringoffpreac-
We thank the referee, T. Suzuki, T. Terasawa and A.
celerated, high-velocity grains (Ellision et al. 1997). To
Bamba for comments. This work is supported in part
be accelerated to the relativistic energy, the refractory
by grant-in-aid from the Ministry of Education, Cul-
elements shouldbe sputtered because the grainscannot
ture,Sports,Science,andTechnology(MEXT)ofJapan,
be acceleratedto the relativisticenergy. The SNR shock
No.21684014(Y.O.andK.I.),Nos.19047004,22244019,
22244030(K. I.).
REFERENCES
Abdo,A.A.,etal.,2009,ApJ,706,L1 Kashiyama,K.,Ioka,K.,&Kawanaka, N.,2010, arXiv:1009.1141
Ackermann,M.,etal.,2010,Phys.Rev.D,82,092004 Kawanaka,N.,Ioka,K.,&Nojiri,M.N.,2010,ApJ,710,958
Ahn,H.S.,etal.,2010,ApJ,714,L89 Krymsky,G.F.,1977,Doki.Akad.NaukSSSR,234,1306
Alcaraz,J.,etal.,2000a, Phys.Lett. B,490,27 Li,H.,&Chen,Y.,2010,MNRAS,409,L35
Alcaraz,J.,etal.,2000b, Phys.Lett.B,494,193 Lingenfelter,R.E.,&Higdon,J.C.,2007,ApJ,660,330
Axford,W.I.,Leer,E.,&Skadron,G.,1977,Proc.15thInt. Lucek,S.G.,&Bell,A.R.2000, MNRAS,314,65
CosmicRayConf.,Plovdiv,11,132 Malkov,M.A.,&V¨olk,H.J,1995, A&A,300,605
Bell,A.R.1978,MNRAS,182,147 Malkov,M.A.,&Drury,L.O’C.,2001,Rep.Prog.Phys.,64,429
Bell,A.R.,2004,MNRAS,353,550 Niemiec,J.,Pohl,M.,&Nishikawa,K.,2008, ApJ,684,1174
Berezhko,E.G.,&Ellison,D.C.,1999,ApJ,526,385 Ogliore,R.C.etal.,ApJ,695,666
Biermann,P.L.,Becker,J.K.,Dreyer,J.,Meli,A.,Seo,E.,& Ohira,Y.,Reville,B.,Kirk,J.G.,&Takahara, F.2009a, ApJ,
Stanev, T.,2010,ApJ,725,184 698,445
Blandford,R.D.,&Ostriker,J.P.,1978,ApJ,221,L29 Ohira,Y.,Terasawa,T.&Takahara,F.,2009b, ApJ,703,L59
Bykov,A.M.,&Fleishman,D.G.,1992,MNRAS,255,269 Ohira,Y.,&Takahara, F.,2010, ApJ,721,L43
Caprioli,D.,Amato,E.,&Blasi,P.,2010,Astropart.Phys.,33, Ohira,Y.,Murase,K.&Yamazaki,R.,2010,A&A,513,A17
160 Ohira,Y.,Murase,K.&Yamazaki,R.,2011,MNRAS,410,1577
Dar,A.,&DeRu´jula,A.,2008,Phys.Rep.,466,179 Riquelme,M.A.&Spitkovsky, A.,2009, ApJ,694,626
Drury,L.O’C.,&V¨olk,H.J.1981,ApJ,248,344 Panov,A.D.etal.,2009,BulletinoftheRussianAcademyof
Ellision,D.C.,Drury,L.O’C.,&Meyer,J.-P.,1997,ApJ,487, Sciences: Physics,73,564
197 Parizot,E.,Marcowith,A.,vanderSwaluw,E.,Bykov,A.M.,&
Ferrand,G.,&Marcowith,A.,2010,A&A,510,A101 Tatischeff, V.,2004, A&A,424,747
Gabici,S.,Aharonian,F.A.,&Casanova,S.,2009,MNRAS,369, Pato,M.,Hooper,D.,&Simet,M.,2010,JCAP,06,022
1629 Ptuskin,V.S.,&Zirakashvili,V.N.,2003,A&A,403,1
Gargat´e,L.,Fonseca, R.A.,Niemiec,J.,Pohl,M.,Bingham,R., Ptuskin,V.S.,&Zirakashvili,V.N.,2005,A&A,429,755
&Silva,L.O.,2010,ApJ,711,L127 Putze,A.,Maurin,D.,&Donato, F.2010,A&A,526,A101
Giacalone,J.,&Jokipii,J.R.,2007,ApJ,663,L41 Smartt,S.J.,Eldridge,J.J.,Crockett, R.M.,&Maund,J.R.
Gleeson,L.J.,&Axford,W.I.,ApJ,154,1011 2009,MNRAS,395,1409
Higdon,J.C.,Lingenfelter,R.E.,&Ramaty, R.,1998,ApJ,509, Strong,A.W.,Moskalenko,I.V.,&Ptuskin,V.S.,2007,Annual
L33 ReviewofNuclearandParticleScience, 57,285
Inoue,T.,Yamazaki,R.&Inutsuka, S.,2009,ApJ,695,825 Tavani,M.etal.,2010,ApJ,710,L151
Ioka,K.,2010,Prog.Theor.Phys.,123,743