      

 dN/dE ∝ E-2.7(E<1015.5eV)
dN/dE ∝ E-3.0(1015.5eV<E<1018.5eV)
dN/dE ∝ E-2.6(1018.5eV<E)  ,, 2012


6(.

4)>EM@N
109 eV-1020 eV

51"65>EM@N 6*
1eV/cm3+%55O/

nCR ~ 10-9 /cm3 @ ~GeV
nth ~ 100 /cm3 @ ~ eV
6?A5'&=7-;*
10B325 50,<+

4:<IJLN5FBC548$P0GKHBD9#=!

Eknee=1015.5eV(1particle /m2/yr)
Gaisser 2006

~10Jà,,, 2012)
()

())

())

(rL = Emax/ZeB

Kotera & Olinto 2011= Rsize
à rL / c = Rsize / cà tgyro = tdyn) ) 


C(Kotera & Olinto 2011

(10)

6(10)

6C

E>

5à

MH

R

Pierre Auger

TA

Matthews et al. 2017

= 2R

H=

15
12P KPFenu et al. 2017

AZ/=2UG33
H2 EVCPierre Auger

TAHanlon et al 2018   Bellido et al. 2017   

AugerTA

E > 57 EeV

E > 8 EeV

Matthews et al. 2017!
àGora et al. 2018?
!
àr3,naVlTothSe,
mgIcPn N
ESnIEu)i
A < &LuE
3.

0kN

6A < &1 << Ax
9k2A&NS)&A
2<A& )< &4E(Tà

2Aumr

INnAà24H

HZZK,

INPHeG
TcAbAxP
Timmermans et al. 2018

ZgiCLDàR,,, 2012&# -/0'!"+($*)%

$ ,.)radio(X-ray

Cassam-Chenai et al. 2008

R ~ 1018 – 1020 cm v/c ~ 10-2 – 10-3

TeV g-ray

Acero et al. 2010  GeV  (~300 SNRs)
X  TeV  (~14 SNRs)
GeV-g  TeV  (~35 SNRs)
TeV-g  or  10TeV  (~16 SNRs)

(!"+%BISM

Shocked ISM
B (ISM)

CR" +,#+-
'$ *)* &%

dN/dE ∝E-s , s = ( r + 2 ) / ( r – 1 ),r ~ 4 à dN/dE ∝E-2

Axford 1977, Krymsky 1977, Blandford&Ostriker 1978, Bell 1978',;%0<3":*(=17-;8.

(9 :-8.745*
Lsize (9 83 ":645/7+ (Leaky box)

d2NCR
dtdE

=dNCR/dEtesc(E)+ Qsour(E)tesc(E) = Lsize2 / Ddiff(E)Ddiff(E) = D0Ed
Qsour(E) = Q0E-s

dNCR= tesc(E) Qsour(E)dE

dNCR Lsize2Q0 -(s+d)=E
D0dE@F>H-2#)!

:2AD?CG=&.

$,; s + d = 2.8 à EBG:*s = 2, d = 0.8 =&  

PC, N, O

Energy flux

Fe

Ep,knee ~ 3 PeV,EFe,knee = ZEp,knee~ 100 PeV,Energy(1)

Ohira et al. 2016

ProtonHelium
Carbon x10

 AMS-02
 CREAMP, He, C  R ~ 300GV  

 





B/C


Aguilar et al. 2018

Aguilar et al. 2016

+dE-r=r rd=r rbr

3rà =r rl VRrGne0.1

à
a9raCr 2 B
kmoBc p
LB/r r48

aK,) M?
? -DN))-)

0+ 162.

(

Ackermann et al. Science 2013p)(0)(

Ahnen et al. 2017Cas A

UCR ~ 1050 erg
Emax ~ 10 TeV
dN/dE ∝ E-2.4
7e

82

8a7I

7 7KI

OK7. ,K,1 &) 0,(,1 &trhr

2t5r
5hl

7rhl

i2ti2tV
V

8e2
7ritt

2
( type Ia, Ib/c, IIp, type IIb, ...)
72r
V?

tr

25t
7O5((V(7( ) .01a7TC,S,20DCV-DAXCT1DCVCTPI

VC 2030 à 300-1000 ?

LMKCeCRE

rz,imch

89 1 85 1=yiteu oOFXv

MFOFXMrzrz
sa.

00&: 082 015( &ch&)

F

B
•

G•
•sse

•

s
R

PG1 ra B
NGPuN BNAB
1p µG1 sA

j

11t
G1+0,lGeA aB/C):,
3 C &">@3!
;+9(/."
3 B &8:9/ 3 >@63.4"B45/<01$3." B&):9(/4%1'-7$2

+950"C à B 3

B/ C 33=AB?C 4"
 L2/D 3=AB?C ;%-':9#&*9

nsyn,max!" #tacc = tcool,syn 

tacc = x tgyro Emax ∝x-1/2B-1/2  hnsyn,max ∝x-1B0= x-1mec2 / a~ 160 x-1 MeV

Mrk421
Blazarhnsyn,max ~ 1 - 103 eV
à x %105 - 108

Inoue & Takahara, ApJ, 1996

  UHECR$Vsh /cos q > c "!

#'&

Lemoine ("*,)+$%'& 

Superluminal shock  ldB < rg
3=JILK?E4:6;@@+"?9C-! >=20EGF.
&1EAF9C>@->7=JILK?!
?E42'et al. 2006,
ldB < rL,CR (Niemiec
Lemoine et al. 2006)

à lmfp ~ rgyro2/ldB ∝E2
Not Bohm

Niemiec et al. 2006
!

B0+dB?E4 H;&%

ldB < rgyro <=FE4H)8<-#@*7GF(&@
$H
1020eVB;*;3=/(e.g. Lemoine&Pelletier 2010)
ldB < rgyro ?E4?E4?2 35=F<power law ,D2F.(e.g. Pelletier et al. 2009)

PIC simulations of relativistic shocks
Particle in cell simulation
A=>;<C3 5'

5&:",dN/dE∝E-2.4

Spitkovsky 20085+* #!26(
5@B?A6Weibel
4701%-98)
ldB ~ c/wp << rgyro à  $5:/.)Spectral index ~ 2.4

Emax of Weibel mediated shocks
PIC simulations show
ldB ~ c/wpp ( << rgyro).
à Small angle scatteringà Dqq ~ (dq)2 / dt~ (ldB/rgyro)2 / (ldB/c)
à Dxx ~ clmfp ~ c (c/Dqq)~ crgyro2/ldB ∝E2

Rturb ~ rgyro,shNot Bohm

à Emax is limited byRturb ~ Rdiff ~ Dxx/cSironi et al. 2013

à Emax ~1017eV for GRB

Abeysekara et al 2018


Aguilar et al. 2016

Aguilar et al. 2015

P, He

B/C∝E-0.3330.019

~2.8 (p @100GeV)

d = 0.333

2.7 (He @100GeV)

s+d~2.7- 2.8 à s~2.37-2.47

%(#&"CR
Rigidity'$)**2 !







Aguilar et al. PRL, 2018

p, He, C, O 
R~200GVhardening !
  "(2)



1"/'-0)3EB

K8

,//0MJ :2
/!&#00=3EBPG<K8%".(-"/0MJKF

/%// =3EBD5<K8+/!-(PG<HA?>(D5<1950I

C;O9)

C;O9)$*/LQ4@

N13%3EB67

1

Svensmark & Friis-Christensen 1997, Svensmark PRL 1998   

Svensmark
A&G 20072Shaviv, PRL, 2002, Shaviv & Veizer, GSA Today, 2003
10" $!##Svensmark A&G 2007

JAXAHP&   ! (%#"' $Li et al. Nature, 2017(B)
"G &6 :/G3AB

M*/G3A.)P 'NF JG7GLG >O"G6
"G8U
!%H;

RT"7K909VQCM@9,=?2S
5-(+<D #<D$# ("4+EI1)


Tanaka et al. GRL 2008  HP)E?C0B.;J G9T9D=9%&V9BW

D=9MI@K#!"NF(/ $"'5Intel1978S H2B-)E?41:HP)E?6BW
+GV9QG UL>

%&V9*7KO,RX<A83 P*

Proton and Helium spectra (E<0.2PeV)
NUCLEON

CREAM

Ahn et al. ApJL 2010

Atkin et al. arXiv:1702.02352

   E ~ 0.1PeV !

P+He spectrum (E~1PeV)
ARGO-YBJ

Montini et al.
arXiv:1608.01251

   E ~ 3 PeV   .
P+He   E ~ 1 PeV  .
E ~ 1 PeV He  E ~ 0.5 PeV  

P+He spectrum (E>1PeV)KASKADE + KASKADE-Grande

D. KangarXiv:1702.08743

E>10PeV  .

P+He .

E>1PeVTotal CR spectrum (IceTop)

Breaks at ~ 3PeV and ~ 100PeV
Dip structure at 10PeVRawlins et al. 2016

Total CR spectrum (Tale)

From slide of Tareq AbuZayy

Breaks at ~ 3PeV and ~ 100PeV
Dip structure at 10PeV

Total CR spectrum (Tunka-HiSCORE, Tunka-133)

Breaks at ~ 3PeV and ~ 100PeV
Dip structure at 10PeV

E ~ 100PeV .

LOFAR(E=100PeV-300PeV)
Buitink et al. Nature 2016a = (<Xproton> - Xmax ) / (<Xproton> - Xiron )The cumulative Xmax distribution shows thatthe total fraction of p+He at 100PeV is in the range [0.38,0.98]
at a 99% confidence level, with a best-fit value of 0.8.

E ~ 100PeV .

Summary of CR observations
There are some unexpected results and tensions.
CR He dominates at ~ 0.1PeV. (CREAM, NUCLEON)
The p+He spectrum breaks at ~ 1PeV < 3PeV. (ARGO-YBG)
The p+He spectrum does not fall off exponentially above 3PeV. (KASKADE+KASKADE-Grande)
Heavy CRs dominate over the CR p+He at ~ 100 PeV. (KASKADE+KASKADE-Grande)

The total CR spectrum breaks at 3PeV and 100PeV, and dips at 10PeV.
(IceTop, TALE, Tunka-133)
CR p+He dominates over heavy CRs at ~ 100PeV. (LOFAR)

Emax of DSA
1



, Δp


c,p




u1



u
Δp = 2 pcuu21$ Dp

Δp =1

4(u1- u2)3c

u1
p=pc!, Δt = (lmfp,1/u1 + lmfp,2/u2) ~ Tgyro,1(c/u1) + Tgyro,2(c/u2)
tacc = p Δt/Δp ~ Tgyro,1(c/ush)2 + 4Tgyro,2(c/ush)2 ( Krymsky et al. 1979,tacc = tSedov ~ 200yr, and Tgyro,1 >> Tgyro,2Drury 1983)

à Emax ~ 0.03PeV Bup,1µG (lmfp/rg)(ush/3000km/s)2"3PeV 
3µG à 100µG # , #B >~100µG!.
 .

RX J1713.7-3946

If g-rays are due to IC, we can measure Bdown.
nFnsyn/nFnIC ~ 16 à Bdown ~ 12 µG

If g-rays are due to the pion decay, we can estimate Ep,max.
Eg,max ~ 0.01PeV à Ep,max ~ 0.1 PeV

Abdalla+2017

Ohira&Yamazaki17SN1006
Acero+2010

If g-rays are due to IC, we can measure Bdown.
nFnsyn/nFnIC ~ 100 à Bdown ~ 30 µG

If g-rays are due to the pion decay, we can estimate Ep,max.
Eg,max ~ 0.008PeV à Ep,max ~ 0.08 PeVXing+2016

RCW86
Abramowski+2016

If g-rays are due to IC, we can measure Bdown.
nFnsyn/nFnIC ~ 50 à Bdown ~ 22 µG

If g-rays are due to the pion decay, we can estimate Ep,max.
Eg,max ~ 0.0035PeV à Ep,max ~ 0.035 PeV

RX J0852.0-4622(Vela Junior)
Abdalla+2016

If g-rays are due to IC, we can measure Bdown.
nFnsyn/nFnIC ~ 4 à Bdown ~ 7 µG

If g-rays are due to the pion decay, we can estimate Ep,max.
Eg,max ~ 0.0055PeV à Ep,max ~ 0.055 PeV







Spectral index of radio synchrotron flux, fn∝n - aReynolds et al., 2011, SSR

a = (s-1)/2dN/dE∝E-saThe standard DSA predicts s = 2(a = 0.5)

Abdalla et al. 2016

X (Ohira & & Yamazaki 2017)