ACCELERATION AND ACCELERATION AND TRANSPORT OF HIGH ENERGY TRANSPORT OF HIGH ENERGY

COSMIC RAYS: COSMIC RAYS: A REVIEWA REVIEW

PASQUALE BLASIPASQUALE BLASIINAF/Osservatorio Astrofisico di INAF/Osservatorio Astrofisico di

ArcetriArcetri

The all-particle spectrum of CR’sThe all-particle spectrum of CR’s

Knee 2nd knee Dip/Ankle GZK?

TEST PARTICLES THEORY OF SHOCK TEST PARTICLES THEORY OF SHOCK ACCELERATIONACCELERATION

1 upP

2

2

2

2DW u 4-1

u1

u1P

SHOCK

DOWNSTREAM UPSTREAM

RETURN PROBABILITY FROM UP

RETURN PROBABILITY FROM DOWN

ENERGY GAIN PER CYCLE

21 uu 3

4 /

cycleEE

IMPLICATIONS OF T-P THEORYIMPLICATIONS OF T-P THEORY

The spectrum of accelerated particles is a The spectrum of accelerated particles is a power law Epower law E--γγ with with γγ=(r+2)/(r-1) ->2 for r->4=(r+2)/(r-1) ->2 for r->4

The spectrum is independent of the The spectrum is independent of the diffusion coefficientdiffusion coefficient

The spectrum is universal and independent The spectrum is universal and independent of all details. of all details.

What does depend on details is the What does depend on details is the maximum energy!maximum energy!

THE NEED FOR A NON LINEAR THEORYTHE NEED FOR A NON LINEAR THEORY

Energetic argument: Energetic argument:

The few particles that leave from upstream carry out The few particles that leave from upstream carry out energy which make the shock radiative and thereby energy which make the shock radiative and thereby more compressive (r>4) -> even flatter spectramore compressive (r>4) -> even flatter spectra

If the pressure accumulated in CRs is large, then If the pressure accumulated in CRs is large, then γγ=5/3 =5/3 approaches 4/3 and again the shock becomes more approaches 4/3 and again the shock becomes more compressive (r>4) -> even flatter spectracompressive (r>4) -> even flatter spectra

energy totaln thelarger tha becan /ln minmaxCR EEEENdE=E

A crucial point that makes A crucial point that makes shock acceleration nonlinearshock acceleration nonlinear

0.60.310 3 29 αE=ED αGeV

The case of SNR shocks is a useful example here:

ASSUMPTION: The diffusion coefficient experienced by particlesis the same as in the ISM

The ACCELERATION TIME is then

2

2

1

1

21

3

u

ED+

u

ED

uu=Eτacc

For a typical SNR the maximum energy comes For a typical SNR the maximum energy comes

out as out as

FRACTIONS OF GeV !!!FRACTIONS OF GeV !!!

NONLINEAR SHOCK ACCELERATION IS NONLINEAR SHOCK ACCELERATION IS NEEDED TO ACCOUNT FOR:NEEDED TO ACCOUNT FOR:

The dynamical reaction of the The dynamical reaction of the accelerated particles onto the shock accelerated particles onto the shock structurestructure

Describe the magnetic field Describe the magnetic field amplification induced by cosmic rays amplification induced by cosmic rays themselves themselves [SELF GENERATION [SELF GENERATION THROUGH COSMIC RAY INDUCED THROUGH COSMIC RAY INDUCED INSTABILITIES]INSTABILITIES]

The Basic Physics of Modified Shocks

Un

dis

turb

ed

Med

ium

Sh

ock F

ron

t v

subshock Precursor

00 uρ=xuxρ

xP+xP+xuxρ=P+uρ CRgg,2

02

00

tp,x,Q+p

fp

dx

du+

x

fu

x

fD

x=

t

f

3

1

Conservation of Mass

Conservation of Momentum

Equation of DiffusionConvection for theAccelerated Particles

Spectra at Modified ShocksSpectra at Modified Shocks

Very Flat Spectra at high energyAmato and PB (2005)

LinearSpectrum

4

3.2

4.5

Efficiency of Acceleration (PB, Gabici & Vannoni

(2005))

Note that only thisFlux ends up DOWNSTREAM!!!(CURVED SPECTRA)

This escapes out To UPSTREAM(DELTA FUNCTION)

Advected and escaping spectraAdvected and escaping spectra

ESCAPINGESCAPINGSPECTRUMSPECTRUM

pmax

PB, Gabici and Vannoni 2005

Depends on the temporal evolution of the SNR

Ptuskin and Zirakashvili 2005

E-2

TIME

NEED FOR LARGE TURBULENT NEED FOR LARGE TURBULENT MAGNETIC FIELDSMAGNETIC FIELDS

LARGE B IS NOT ENOUGH: SCATTERING MUST OCCUR AT ROUGHLY THE BOHM RATE!!! -> STRONG TURBULENCE

POSSIBLE EVIDENCE FOR B-FIELD POSSIBLE EVIDENCE FOR B-FIELD AMPLIFICATIONAMPLIFICATION

Cutoff

Figure from Berezhko & Volk 2006

THE PHYSICS IS IN THE CUTOFFS !!!

THE PHYSICS IS IN THE CUTOFFSTHE PHYSICS IS IN THE CUTOFFS

The position of the X-ray cutoff is The position of the X-ray cutoff is independent of the strength of B (for independent of the strength of B (for Bohm diffusion)Bohm diffusion)

The way the flux goes to zero tells us The way the flux goes to zero tells us about the spectrum of accelerated about the spectrum of accelerated electronselectrons

The cutoff in the gammas tells us about The cutoff in the gammas tells us about the cutoff in the proton spectrum or in the the cutoff in the proton spectrum or in the electron spectrumelectron spectrum

MAGNETIC FIELD MAGNETIC FIELD AMPLIFICATIONAMPLIFICATION

Resonant Streaming Instability Resonant Streaming Instability (Achterberg 1983, Zweibel 1978, Bell 1978)(Achterberg 1983, Zweibel 1978, Bell 1978)

Non-resonant Streaming Instability Non-resonant Streaming Instability (Bell 2004)(Bell 2004)

Firehose InstabilityFirehose Instability

……

BASIC ASPECTS OF B-FIELD BASIC ASPECTS OF B-FIELD AMPLIFICATION BY CR’sAMPLIFICATION BY CR’s

)v(v ADCR mn

dtdP CRCR

A

W

vB

WdtdP 1

8

2

vSRATE OF MOMENTUM LOST BY CR

BUT THIS MUST EQUAL THE RATEOF MOMENTUM GAIN BY THE WAVES

GROWTHRATE OFWAVES

BY REQUIRING EQUILIBRIUM:

A

AD

gas

CR

vvv

nn cycW

Shock

Maximum Energy in the Proton Maximum Energy in the Proton SpectrumSpectrum

11stst effect: the effect: the magnetic field is magnetic field is amplified thereby amplified thereby leading to higher leading to higher EmaxEmax

22ndnd effect: the effect: the precursor slows down precursor slows down the upstream plasma the upstream plasma thereby reducing the thereby reducing the pmaxpmax

PB, Amato & Caprioli 2007

Self-Generated

Bohm modified

Bohm unmodified

knee

IF SNR ACCELERATE GALACTICCOSMIC RAYS WE SHOULDDETECT GAMMA RAY SPECTRA WITH CUTOFFS AROUND 10-100 TeV

Max E

nerg

y in

GeV

Shock Mach number

RESONANT AND NON-RESONANT RESONANT AND NON-RESONANT UNSTABLE MODESUNSTABLE MODES

The upstream plasma is made of :

and COSMIC RAYS:

Each component is described through a Vlasov equation (collision-less plasmas):

Cold protons

Cold electrons

Cold isotropic electrons which Compensate the CR charge!!!

0][)(

p

fBv

c

qfv

t

f

Perurbation of the Vlasov equations together with theEquation of conservation of charge provide a dispersion relation:

If CR acceleration is efficient (PCR~ρu2):

Im[ω]

Re[ω]

Bell 2004Blasi & Amato2007

RELATIVISTIC SHOCKS IN 1 SLIDERELATIVISTIC SHOCKS IN 1 SLIDE

The standard prediction in the SPAS regime The standard prediction in the SPAS regime is a universal spectrum Eis a universal spectrum E-2.3-2.3

BUT many violations: LAS (<2), B-field BUT many violations: LAS (<2), B-field compression at the shock (>>2)compression at the shock (>>2)

In general, need strong turbulence. In general, need strong turbulence.

(1/3) c

Concluding remarks on Concluding remarks on accelerationacceleration

Most physics concepts discussed so far are fully general: Most physics concepts discussed so far are fully general: both dynamical reaction and B-field amplification are both dynamical reaction and B-field amplification are crucial in all CR accelerators: crucial in all CR accelerators: NONLINEAR EFFECTS ARE NONLINEAR EFFECTS ARE NOT CORRECTIONS. THEY ARE THE REASON WHY IT NOT CORRECTIONS. THEY ARE THE REASON WHY IT WORKS!WORKS!

We limited our discussion to non-relativistic shocks We limited our discussion to non-relativistic shocks because a theory of modified relativistic shocks has not because a theory of modified relativistic shocks has not been developed yetbeen developed yet

If the magnetic field amplification due to streaming If the magnetic field amplification due to streaming instability takes place, also acceleration to UHE in some instability takes place, also acceleration to UHE in some sources could be made easiersources could be made easier

Many issues still unclear: injection, nonlinear Many issues still unclear: injection, nonlinear development of turbulence, diffusion coefficient when development of turbulence, diffusion coefficient when δδB/B>>1,…B/B>>1,…

THE TRANSITION FROM THE TRANSITION FROM GALACTIC TO EXTRAGALACTIC GALACTIC TO EXTRAGALACTIC

COSMIC RAYSCOSMIC RAYSConsequences of the previous Consequences of the previous

points:points: If protons are accelerated If protons are accelerated

to about the knee, and to about the knee, and scattering is at the Bohm scattering is at the Bohm rate, then the knees in the rate, then the knees in the other elements are at Z other elements are at Z times the proton kneetimes the proton knee THE GALACTIC CR SPECTRUM MUST END

SOMEWHERE AROUND 1017 eV

Transition at the AnkleTransition at the Ankle1. A steep GAL spectrum encounters a flat EX-GAL spectrum

2. The GAL spectrum should extend to >1019 eV and is

expected to be Fedominated

3. The chemical composition of the EX-GAL part can

have heavy nuclei

Aloisio, Berezinsky, PB, Gazizov, Grigorieva, Hnatyk 2006

Transition at the DipTransition at the Dip

1. STILL TRUE that a STEEP GAL spectrum meets a FLAT EX-GAL spectrum (Second knee)

2. The Low energy flattening due to either pair prod. or most likely magnetic horizon

3. The GAL spectrum is expected to END at <1018 eV (mainly Fe)

4. The EX-GAL spectrum is predicted to be mainly protons

at E>1018 eV (No more that 15% He allowed)

5. Steep injection spectrum unless complex injection

Aloisio, Berezinsky, PB, Gazizov, Grigorieva, Hnatyk 2006

A DIP IS GENERATED DUE ONLY TO PAIR PRODUCTION. ITS POSITIONIS FIXED BY PARTICLE PHYSICS INTERACTIONS

Transition due to Mixed Transition due to Mixed CompositionCompositionAllard et al. 2006

1. Particles at injection have an arbitrary chemical composition2. Relatively flat spectra at injection are required3. The inferred galactic spectrum has a cutoff at energies about the same as in the DIP scenario4. At 1019 eV there is still an appreciable fraction of heavy elements5. At 1020 eV, as in all other models, there are mainly protons

ELONGATION RATESELONGATION RATES

Aloisio, Berezinsky, PB and Ostapchenko, 2007

DIP ANKLE

Stars: Fly’s EyeSquares: HiRes-MIACircles: HiResTriangles: Auger

SHARPRISE

Elongation rate (Mixed Elongation rate (Mixed Composition)Composition)

Allard et al. 2007

DISTRIBUTION OF XDISTRIBUTION OF XMAX MAX (Fly’s Eye)(Fly’s Eye)A

lois

io,

Bere

zin

sky,

PB

an

d O

sta

pch

en

ko,

2007

DISTRIBUTION OF XDISTRIBUTION OF XMAX MAX (HiRes-MIA)(HiRes-MIA)A

lois

io,

Bere

zin

sky,

PB

an

d O

sta

pch

en

ko,

2007

CONCLUSIONSCONCLUSIONS ACCELERATION BY SHOCKS IS BECOMING SELF-ACCELERATION BY SHOCKS IS BECOMING SELF-

CONSISTENTCONSISTENT

THE PICTURE WE ARE GETTING FROM SNR IS THAT THE PICTURE WE ARE GETTING FROM SNR IS THAT ACCELERATION OCCURS IN A NONLIN REGIME AND ACCELERATION OCCURS IN A NONLIN REGIME AND IMPLIES STRONG B AMPLIFICATIONIMPLIES STRONG B AMPLIFICATION

THE IMPLICATION IS THAT THE GALACTIC COSMIC THE IMPLICATION IS THAT THE GALACTIC COSMIC RAY SPECTRUM SHOULD END AT A FEW 10RAY SPECTRUM SHOULD END AT A FEW 101717 Ev Ev (MAINLY IRON)(MAINLY IRON)

THE TRANSITION REGION IS THEREFORE UNDER THE TRANSITION REGION IS THEREFORE UNDER DEBATE (ANKLE, DIP or MIXED?) Consistency with DEBATE (ANKLE, DIP or MIXED?) Consistency with the standard model?the standard model?

THE CHEMICAL COMPOSITION IS THE BEST TOOL THE CHEMICAL COMPOSITION IS THE BEST TOOL TO EXPLORE THIS PHENOMENON, BUT NO TO EXPLORE THIS PHENOMENON, BUT NO ANSWER YETANSWER YET