LECTURE I

V:

FROM G

ALACTIC

TO

EXTRAGALACTIC

COSMIC

RAYS

Pasq

uale B

lasi

INAF/A

rcetr

i & F

erm

ilab

WHIC

H A

CCELERATED P

ARTICLE

S

BECOME C

OSMIC

RAYS?

WE H

AVE S

EEN T

HAT C

OSMIC

RAYS

ACCELERATED I

N S

NR

HAVE C

ONCAVE S

PECTRA

WE H

AVE A

LSO S

EEN T

HAT T

HE R

ETURN P

ROBABIL

ITY F

ROM

UPS

TREAM I

S U

NIT

Y! ALL P

ARTIC

LES C

OME B

ACK, W

ITH T

HE

POSSIB

LE E

XCEPT

ION O

F T

HOSE A

T P

MAX

WE H

AVE S

EEN T

HAT T

HE S

PECTRUM O

F T

HE E

SCAPI

NG

PARTIC

LES A

T U

PSTREAM I

NFINIT

Y I

S C

LOSE T

O A

DELTA

FUNCTION

SO…W

HIC

H O

NES A

RE T

HE C

OSMIC

RAYS?

ESCAPE

FLU

X I

N T

EST

PARTIC

LE T

HEORY

FO

R D

(E)

PR

OP

OR

TIO

NA

L T

O E

(B

OH

M D

IFF

US

ION

):

*3

1p

r

rp M

AX

−=

DIF

FERENT P

HASES O

F A

SNR

cm/s

M

E 10

M2E

V1/

2- ej

,1/

251

9

ejejs

Θ=

=

MASS O

F T

HE E

JECTA: M

ej

FREE E

XPA

NSIO

N V

ELO

CIT

Y:

TOTAL

KIN

ETIC

ENERGY: E51

THERE I

S A

N I

NIT

IAL P

ERIO

D D

URING W

HICH T

HE S

HELL O

F

THE S

N E

XPA

NDS F

REELY (FREE E

XPA

NSION P

HASE

-BALLIS

TIC

MOTION):

SEDOV P

HASE:

SEDOV P

HASE:

year

s

M n

E 30

0

T5/

6-1

/3-1

/251

Sedo

vΘ

=

The sou

nd spe

ed in

the I

SM is abou

t 106cm

/s

1000

- 10

0

num

ber

Mac

h ≈

STRONG

STRONG

SHOCK

SHOCK

BUT T

HE S

HOCK S

WEEPS

THE M

ATERIA

L I

N F

RONT O

F I

T

AND A

T S

OME P

OINT I

T A

CCUMULATES E

NOUGH M

ATERIA

L

TO S

LOW

DOW

N T

HE E

XPA

NDIN

G S

HELL:

MAX E

NERGY D

URIN

G S

EDOV

THE M

AXIM

UM E

NERGY O

F A

CCELERATED P

ARTIC

LES I

NCREASES

DURING T

HE F

RE E

XPA

NSION P

HASE A

ND R

EACHES A

MAXIMUM

AT T

HE B

EGINNING O

F T

HE S

EDOV P

HASE.

IN T

HE S

EDOV P

HASE:

OVERLAP

OF E

SCAPE

FLUXES: A

SIM

PLE E

STIM

ATE

2/1 )

()

(−

∝t

tt

Ec

MA

Xξ

dE E

dE t

dEdt

dE 4ππ

ρV

21 (t

)F

EQ

(E)d

E1-

1/

2m

ax2 sh

3 ses

c∝

∝≈

BE V

ERY C

AREFUL…THIS I

S J

UST A

WAY T

O S

HOW

HOW

YOU

GET R

OUGHLY A

POW

ER L

AW

BUT S

UMMIN

G N

ON-PO

WER L

AW

S.

MORE D

ETAIL

ED C

ALC’S S

HOW

DEPA

RTURES F

ROM T

HIS

SIM

PLE

TREND

ESCAPE

FLU

X I

N N

ON L

INEAR

REGIME

Caprioli, PB & Amato (2008)

A L

OT O

F P

HYSIC

S I

N

THESE P

LOTS !!!

RECALL T

HAT O

UR I

GNORANCE O

F H

OW

THINGS E

VOLVE W

HEN

THE M

AGNETIC F

IELD B

ECOMES A

MPL

IFIE

D T

O N

ON L

INEAR

LEVELS I

S H

UGE:

�W

E D

O N

OT K

NOW

HOW

B G

ROW

S W

HEN ∆

B/B

>1

�W

E D

O N

OT K

NOW

IF I

T G

ROW

S A

NIS

OTROPI

CALLY

�W

E D

O N

OT K

NOW

HOW

TO E

XTRACT A

DIF

FUSIO

N

COEFFICIE

NT F

ROM I

T (PA

RTICLE-W

AVE I

NTERACTION)

�EVEN T

HE T

RANSPO

RT E

QUATIO

N I

TSELF C

OULD B

E C

HANGED

IN T

HE R

EGIM

E O

F S

TRONG T

URBULENCE

THIS

IGNORANCE R

EFLECTS I

N M

ANY O

F O

UR F

INDINGS W

HIC

H

ARE S

TRONGLY A

FFECTED B

Y A

SSUMING B

OHM D

IFFUSION…

THEREFORE T

HERE I

S A

LOT F

OR Y

OU T

O D

ISCOVER!!!

SOME B

ASIC

ASPE

CTS O

F P

ARTIC

LE

ACCELE

RATIO

N A

T R

ELATIV

ISTIC

SHOCKS

BASIC

S O

F A

CCELE

RATIO

N A

T

RELATIV

ISTIC

SHOCKS

22

21

11

nβ

γ=

nβγ (

)(

)2

22

2 21

11

2 1p

+ε

βγ

=p

+ε

βγ (

)(

)2

22

2 22 2

11

12 1

2 1p

+p

+ε

βγ

=p

+p

+ε

βγ

()

11

2 1p

+ε

4πB<<

11

>>γ

No

equ

ipart

ition

u

ltra

relativist

ic p

ress

ureless

0=

p 1

IN T

HE A

SSUMPT

ION T

HAT:

WE F

IND T

HAT:

31

312

22

==

βε

p

β2=

1/3

τcβ

2

cr L

2

43π

τ≈

LL

rr

cx

>=

=∆

2

31π

τ

UNLESS T

HERE I

S S

TRONG

SCATTERIN

G D

OW

SNTREAM

THE P

ARTIC

LES A

RE T

RAPP

ED

THERE

THE R

ETURN P

ROBABIL

ITY F

ROM D

OW

NSTREAM I

SEXPE

CTED T

O B

E S

MALL

ER T

HAN F

OR N

EW

TONIA

NSHOCKS: STEEPE

R S

PECTRA

ANIS

OTROPY

shγ/1

2 rel

relrel

γ1

41

β+

3

3β+

1+

1=

δµ

≈

−

FIR

ST I

NTERACTION:

ire

lre

li

rel

fre

li

rel

di

EE

EE

EE

22

24

)1(

)1(

γβ

γβ

γ≈

+=

⇒+

=⇒

FURTHER I

NTERACTIO

NS:

Ef≈

2 E

i

EFFECTS O

F A

NIS

OTROPY

6.004.0

≤≤

shsh

βγ

PB &

Vietr

i2005

6.004.0

≤≤

shsh

βγ

51

≤≤

shsh

βγ

EFFECTS O

F T

HE S

PAS

PB &

Vietr

i2005

SOME R

EMARKS

SOME R

EMARKS

�THE S

PECTRUM O

F A

CCELERATED P

ARTIC

LES I

N T

HE

RELATIV

ISTIC

CASE I

S S

TIL

L A

POW

ER L

AW

�THE S

LOPE

OF T

HIS

POW

ER L

OW

IN T

HE U

LTRAREL

CASE I

S A

BOUT 2

.3

�HOW

EVER T

HE S

LOPE

CAN B

ECOME A

PPRECIA

BLY H

ARDER

(FLATTER S

PECTRA) FOR L

ARGE A

NGLE S

CATTERIN

G

�OR A

PPRECIA

BLY S

OFTER (STEEP

SPE

CTRA) DUE T

O

…BASIC

ALLY A

NYTHING E

LSE Y

OU D

O (FOR I

NSTANCE

COMPR

ESSION O

F T

URBULENCE A

T T

HE S

HOCK)

�SHOCK A

CCELERATION A

T R

ELATIV

ISTIC S

HOCKS

DEPE

NDS A

LSO O

N T

HE E

QUATIO

N O

F S

TATE O

F T

HE

DOW

NSTREAM P

LASMA (PR

OTONS, PA

IRS, B-FIE

LDS A

LL

CHANGE T

HE R

ESULTS D

RAMATIC

ALLY)

�THERE I

S N

O N

ON L

INEAR T

HEORY O

F P

ARTIC

LE

ACCELERATION A

T R

ELATIV

ISTIC

SHOCKS

A L

OOK A

T T

HE D

ATA

UNDERSTANDIN

G T

HE O

RIGIN O

F E

XTRAGALACTIC

COSMIC

RAYS R

EQUIR

ES A

N U

NDERSTANDING O

F:

1.W

HAT I

S T

HE O

RIGIN O

F T

HE K

NEE

2.W

HAT I

S T

HE S

PECTRUM O

F T

HE D

IFFERENT C

HEMICAL

SPE

CIE

S

3. W

HERE A

ND H

OW

DOES T

HE G

ALACTIC

SPE

CTRUM E

ND

4. HOW

AND W

HERE D

OES T

HE E

XTRAGALACTIC

SPE

CTRUM

BEGIN

?

5 W

HERE A

ND W

HY D

OES T

HE L

ATTER E

ND

Proton

He

Hör

ande

l‘s m

odel

(20

03)

CREAM d

ata

(2008)

QGSJET

SIB

YLL

Kne

e2

ndkn

ee?

Dip

/Ank

le

G

ZK

?

A P

HYSIC

AL P

ICTURE

Mor

lino

& P

B 2

008

IMPL

ICATIO

NS O

F T

HIS

PICTURE

�THE C

HEMIC

AL

COMPO

SIT

ION O

F C

R B

ECOMES

HEAVIE

R A

T H

IGH E

NERGIE

S

�THE S

PECTRUM O

F P

ROTONS S

HOULD

HAVE A

CUTOFF O

R A

STEEPE

NIN

G A

ROUND (1-5) 106GeV

�THE S

PECTRUM O

F G

ALA

CTIC

COSMIC

RAYS

SHOULD

END W

ITH A

IRON D

OMIN

ATED

COMPO

SIT

ION…

�…

AND S

HOULD

BE C

UT O

FF A

T A

BOUT 1

08GeV

=

1017eV

MORE I

MPL

ICATIO

NS

�THIS

PIC

TURE A

PPEARS C

ONSIS

TENT W

ITH

WHAT W

E S

EEM T

O U

NDERSTAND O

N S

NR

�BUT H

AS P

ROFOUND I

MPL

ICATIO

NS O

N T

HE

ORIG

IN O

F E

XTRAGALA

CTIC

COSMIC

RAYS

�IT

BECOMES O

F T

HE G

REATEST I

MPO

RTANCE

TO M

EASURE A

ND D

ESCRIB

E T

HE E

NERGY

REGIO

N 1

017-1019eV

ANIS

OTROPI

ES

Get

ting

Hea

vier

?

PROPA

GATIO

N O

F E

XTRAGALACTIC

COSMIC

RAYS

−+

++

→+

ee

p γ

p

CM

B

ON C

OSMOLOGICAL T

IME S

CALES T

HERE A

RE T

HREE P

ROCESSES

THAT A

RE R

ELEVANT F

OR P

ROPA

GATION

ADIA

BATIC

LOSSES D

UE T

O

THE E

XPA

NSION O

F T

HE U

NIV

ERSE

BETHE-HEIT

LER P

AIR P

RODUCTION

PHOTOPI

ON P

RODUCTION

++

→+

πγ

nC

MB

p0

CM

Bp

πγ

+→

+p

ENERGY L

OSSES

THE R

ATE O

F E

NERGY L

OSSES F

OR P

HOTOPI

ON P

RODUCTION

AND P

AIR

PRODUCTION A

T R

EDSHIF

T Z

ERO C

AN B

E W

RIT

TEN

AS:

WHERE A

T T

HRESHOLD:

IN T

ERMS O

F R

EDSHIF

T D

EPE

NDENCE:

100 M

pc

GZK

LOSS T

IME

LOSS L

ENGTH

THE S

PECTRUM

CONSERVATION O

F T

HE N

UMBER O

F P

ARTICLES I

N T

HE

COMOVING V

OLUME R

EADS:

IMPL

YING T

HAT T

HE F

LUX I

S:

WHERE E

gIS

THE G

ENERATIO

N E

NERGY, OBTAIN

ED F

ROM E

BY S

OLVIN

G T

HE E

QUATIO

N F

OR L

OSSES O

UT T

O A

REDSHIF

TZ

THE M

ODIF

ICATIO

N F

ACTOR

ONE M

AY D

EFIN

E T

HE S

O C

ALLED M

ODIF

ICATIO

N F

ACTOR A

S:

ADIA

BATIC

LOSSES O

NLY

PAIR

SONLY

ALL

THE M

ODIF

ICATIO

N F

ACTOR

HAS T

HE A

DVANTAGE O

F

SHOW

INGTHE S

PECTRAL

MODIF

ICATIO

N I

N A

WAY

WEAKLY

DEPE

NDENT U

PON

INJECTIO

N S

PECTRUM

DIF

FUSE S

PECTRUM A

ND S

INGLE

SOURCE S

PECTRUM

BACK T

O T

HE M

ODIF

ICATIO

N

FACTOR

HOW

DOES T

HE S

PECTRUM L

OOK

LIKE? T

HE D

IP

ACCID

ENT O

R P

HYSIC

S?

ALT

ERNATIV

E I

NTERPR

ETATIO

N O

F

THE T

RANSIT

ION: THE A

NKLE

ALTERNATIVE I

NTERPR

ETATION O

F T

HE

TRANSIT

ION: MIX

ED C

OMPO

SIT

ION

Allard

et al. 2

005-2008

UNDERSTANDIN

G T

HE D

IFFERENCE:

DIP

VS M

IXED

UNDERSTANDIN

G T

HE D

IFFERENCE:

DIP

VS A

NKLE

Aloisio

et al. 2

007

DIP

ANKLE

THE R

MS O

F X

MAX

THE R

MS O

F X

MAX

Spe

ctru

m o

f UHECRs: c

ase

of

prot

ons

Solid: γ=

2.6

m=0 Emax=1021eV

Dash

ed: γ=

2.6

m=0 E

max=1020eV

Dot

ted: γ=

2.4

m=4 E

max=1021eV

Q(E,z)~E-γ(1+z)m

exp(-E/E

max)

Prot

ons or

Nuc

lei?

Alla

rd e

t al.

2008

PHOTODIS

INTEGRATIO

N L

OSS

LENGTH A

T Z

=0

SPE

CTRUM F

ROM M

IXED

COMPO

SIT

ION

CR A

stro

nomy w

ith P

AO

CORRELATION OF THE ARRIVAL DIRECTIONS

WITH THE LOCAL DIS

TRIBUTIO

N OF MATTER

LOCAL DIS

TRIBUTIO

N OF MATTER

FIR

ST D

ETECTIO

N O

F A

NIS

OTROPI

ES !!!

FIR

ST D

ETECTIO

N O

F A

NIS

OTROPI

ES !!!

UHECR are extragalactic after all !

UHECR are extragalactic after all !

Aniso

trop

y a

nd C

hemical Com

position

•Xmax

compatible with anisotropies?

•May be there is something new to learn on

cross section/multiplicity at ~300 TeVc.m.

•A proton dom

inated com

position at the

highest energies is com

mon to all models of

UHECR, but…

AGN a

s so

urce

s?

Imagecourtesy

of NRAO/A

UI

Let’s do

the n

umbers

Gau

ss

cmE

103.

3

L B

20

17kn

ot×

≈1k

pc

Lkn

ot≈

mG

1-0.

1B

≈

A sim

ple e

stim

ate

of th

e con

ditions

in

the k

nots

The P

oynt

ing

flux

wou

ld b

e

erg/

s10

8c

L 4πB

442 kn

ot

2

×≈

≈π

l

Mpc

78

@ /

105

)10

(40

7.19

sing

let

ser

geV

×≈

>l

Aug

er Nor

th

•T

he U

HE

cos

mic

ray

sky

may

be

anis

otro

pic

on a

larg

e sc

ale:

FU

LL S

KY

CO

VE

RA

GE

•D

ISC

OV

ER

TH

E S

OU

RC

ES

req

uire

s ev

en la

rger

ex

posu

res:

7 ti

mes

Aug

er S

outh

is th

e pl

an

•M

easu

ring

the

spec

trum

of o

ne s

ourc

e is

a b

reak

thro

ugh

to

look

forw

ard

to

•U

HE

Neu

trin

os

A N

ew T

ype o

f Ast

rono

my

PB &

De M

arco

2003

E>10

20eV

CR

ITIC

AL

EX

PO

SU

RE

…

Sou

rce

Spe

ctru

m

The shape

of

the G

ZK f

eatu

re

De M

arc

o, P

B &

Olint

o2006

15 y

ears

of

Aug

er Sou

th

INDIR

ECT W

AYS T

O L

OOK F

OR

SOURCES

Sou

rce

Ele

ctro

mag

netic

ca

scad

e

Fer

rigno

, PB

& D

e M

arco

200

5

CT

A

CT

A

Ferr

igno

, PB

& D

e M

arc

o 2005

CONCLU

SIO

NS (1)

•THE S

NR P

ARADIGM I

S N

OT P

ROVED Y

ET, BUT I

T H

AS

RECENTLY B

EEN C

OMPL

ETED W

ITH T

HE T

ANTALIZ

ING

DIS

COVERY O

F B

AMPL

IFICATIO

N

•W

ITH T

HIS

NEW

INGREDIE

NT, W

HIC

H I

S P

ART O

F T

HE

NON L

INEAR B

EHAVIOUR O

F A

CCELERATORS, IT

IS

POSSIB

LE F

OR P

ROTONS T

O R

EACH T

HE K

NEE…

•AND F

OR H

EAVIE

R N

UCLEI

TO G

O H

IGHER

•IN

THIS

PICTURE I

RON W

OULD R

EACH A

BOUT 1

017eV

AND

SIG

NS T

HE E

ND O

F T

HE G

ALACTIC S

PECTRUM

CONCLU

SIO

NS (2)

•EXTRAGALACTIC

CR S

HOULD T

HEREFORE K

ICK I

N A

T

ABOUT T

HE S

AME E

NERGY

•ONLY T

HE D

IP

AND M

IXED C

OMPO

SIT

ION S

ATIS

FY

THIS

CONDIT

ION

•CHEMICAL C

OMPO

SIT

ION W

ILL (I

HOPE

) SAY W

HIC

H

INTERPR

ETATIO

N I

S T

RUE

•AT T

HE H

IGHEST E

NERGIE

S W

E S

EEM T

O S

EE A

SPE

CTRAL F

EATURE T

HAT R

ESEMBLES T

HE G

ZK

•ANIS

OTROPI

ES I

N T

HE O

VERALL D

ISTRIBUTIO

N H

AVE

BEEN O

BSERVED

CONCLU

SIO

NS (3)

•…BUT I

T A

PPEARS A

T O

DDS W

ITH T

HE M

EASURED

COMPO

SIT

ION (NEW

PARTIC

LE P

HYSICS O

R N

EW

MIS

TAKE?)

•THE W

ORRYSOME C

ONCLUSION I

S T

HAT T

HE K

NEE, THE

TRANSIT

ION, THE E

ND O

F T

HE S

PECTRUM A

ND T

HE

ANIS

OTROPI

ES A

LL D

EPE

ND O

N T

HE Q

UANTITY T

HAT

WE A

RE W

ORST A

T M

EASURIN

G: THE C

HEMICAL

COMPO

SIT

ION…