Open Problems with Very High Energy

Cosmic Rays

Pasquale BlasiNational Institute for AstrophysicsArcetri Astrophysical Observatory

Firenze, Italy

TeV Workshop, Madison, August 2006

Outline

• Some observational facts– Spectrum– Chemical Composition– Anisotropies

• Where do CRs become extragalactic?– The dip– The Ankle– Mixed Composition

• Open issues with acceleration of CRs– Non linear Fermi Acceleration– Relativistic shocks

• Help of multifrequency observations

Observations I: SpectrumKnee 2nd Knee Dip GZK?

Observations – I: Spectrum

The actual discrepancy is at 1-2 standard deviations

De Marco, PBand Olinto 2006

Chemical Composition

Proton

knee

Helium

knee

Iron

?

From A. Watson (2006)

KneeRegion

TRANSITION? ?

DIP ANKLE

Anisotropies

Observations – III: Anisotropy

HiRes-I data with E>1019.5 eV with mono (52 events versus 47 of AGASA)The banana-shaped error boxes are [4.9-6.1]x[0.4-1.5] degrees

HiRes stereo data (271 eventswith E>1019 eV versus about 900of AGASA). The error boxes areabout 0.6 degrees wide.Only 27 events above 4 1019 eV

Small Scale AnisotropiesPB & De Marco 2003

10-5 Mpc-3

Statistical Volatility of the SSA signalStatistical Volatility of the SSA signal

De Marco, PB & Olinto 2006

THE SSA AND THE

SPECTRUM OF AGASA

DO NOT APPEAR

COMPATIBLE WITH

EACH OTHER (5 sigma)

De Marco, PBand Olinto 2006

>4 1019 eV

>1020eV

105 km2 sr yr

De Marco, PBand Olinto 2006

15 years ofOperation of Auger South

Transition from Galactic to Extragalactic Cosmic Rays

• The Ankle scenario

• The Dip scenario

• The mixed Composition scenario

Transition 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, Hnatyk2006

Transition at the Dip

1. STILL TRUE that a STEEP GAL spectrum meets a FLAT EX-GAL spectrum

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

Kachelriess and Semikoz 2005Aloisio, Berezinsky, PB, Grigorieva and Gazizov 2006

L (L) max E

Transition due to Mixed Composition

Allard et a. 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

Some Open Problems with Acceleration of Cosmic Rays

The lesson we can learn from galactic cosmic rays…

A CRUCIAL ISSUE: the maximum energymaximum energy of accelerated particles

1. The maximum energy is determined in general by the balance between the

Acceleration time and the shortest between the lifetime of the shock and

the loss time of particles

2. For the ISM, the diffusion coefficient derived from propagation is roughly

For a typical SNR the maximum energy comes out as For a typical SNR the maximum energy comes out as FRACTIONS OF GeV !!!FRACTIONS OF GeV !!!

Similar numbers would be obtained for galactic sources of similar age and in Similar numbers would be obtained for galactic sources of similar age and in

similar conditions. similar conditions.

0.60.310 3 29 αE=ED αGeV

2

2

1

1

21

3

u

ED+

u

ED

uu=Eτacc

PARTICLE ACCELERATION AT ASTROPHYSICAL SHOCKS IS EFFICIENT ONLY IF PARTICLES GENERATE THEIR OWN SCATTERING CENTERS!!!

NON-LINEAR PARTICLE ACCELERATION

Pitch angle scattering and Spatial DiffusionPitch angle scattering and Spatial Diffusion

The Alfven waves can be imagined as small perturbations on top of a

background B-field

B B0B1

The equation of motion of a particle in this field is

10 B+Bvc

Ze=

dt

pd

In the reference frame of the waves, the momentum of the particle remains

unchanged in module but changes in direction due to the perturbation:

mcγZeB=Ωψ+tkvμΩpc

BμZev=

dt

dμ/ cos

10

12/12

pF

pcrvλ=pD L

3

1

3

1

2)/())(( BBkkpF The Diffusion coeff reducesTo the Bohm Diffusion for F(p)~1

Maximum Energy Maximum Energy a la a la Lagage-CesarskyLagage-Cesarsky

In the LC approach the lowest diffusion coefficient, namely the highest energy,

can be achieved when F(p)~1 and the diffusion coefficient is Bohm-like.

For a life-time of the source of the order of 1000 yr, we easily get

Emax ~ 104-5 GeV

secuBE=

u

EDτ μGeV

shockacc

21000

162

3.310

ΓFσF=x

Fu+

t

F

Wave growth HERE IS THE CRUCIAL PART!

Wave damping

Bell 1978

pF

pcrvλ=pD L

3

1

3

1

z

PCR

Av

Maximum Level of Turbulent Self- Generated Field

σF=x

Fu+

t

F

Stationarity

z

Pv

z

F u CR

A

Integrating

1222

0

2

u

PM

B

B CRA

Breaking of LinearTheory…

For typical parameters of a SNR one has δB/B~20.

UPSTREAM

SHOCK

B

SHOCK

B

Possible Observational Evidence for Amplified Magnetic FieldsPossible Observational Evidence for Amplified Magnetic Fields

240 µG

360 G

Volk, Berezhko & Ksenofontov (2005)

Rim 1

Rim 2

Lower

Fields

Add to all this, the enourmous Predictions of Non-linear Diffusive Shock Acceleration!!!1. Curved spectra2. Heating suppression downstream3. B-field amplification

Bell 2004

Hybrid Simulations (PIC+MHD) used to follow the field Hybrid Simulations (PIC+MHD) used to follow the field

Amplification when the linear theory starts to failAmplification when the linear theory starts to fail

2CR2

A20

2

ρu

P

c

uM

B

δB For typical parameters of a

SNR we get δB/B~300

The Max energy for a SNR becomes ~1017 eV for protons and 3 1018 eV for Iron nuclei (for Bohm diffusion)

General lesson and concerns

• The max energy as estimated through Hillas-like plots may well be incorrect by orders of magnitude if the ambient field is used instead of the self-generated field

• δB/B>>1 is predicted by a quasi-linear approach, though confirmed by PIC

• PIC carried out in very simple approach. No nonlinear effects taken into account in these PIC simulations…

• THERE ARE NO such calculations in the case of RELATIVISTIC SHOCKS

Particle Acceleration At Relativistic Shocks

Peculiar Aspects of Particle Acceleration at relativistic

shocks222111 nβγ=nβγ

22222111

21 p+εβγ=p+εβγ

22222

22111

21

21 p+p+εβγ=p+p+εβγ

we find that p2 = (1/3) 2 and 2 = 1/3

11

21

4p+ε

π

B 11 γ

No equipartition ultrarelativistic pressureless

01 =p

c

πr=τ B

larmor2

13/2/ >πrΔL B

For a homogeneous magneticfield downstream NO PARTICLEis expected to return back to the shock.

The turbulent structure of theB-field is crucial!

L

Taub’srelations

E

~42 E

Reflection at the relativisticmirror works ONLY at the first interaction.

After that

2 / EE

Relativistic mirror vs Fermi Relativistic mirror vs Fermi accelerationacceleration

Universal or non-universal…

1 for 2.3-2.2 p )( - pf

Most calculations of particle acceleration at relativistic shocks leadto the so-called UNIVERSAL SPECTRUM

This important result is obtained by solving the same equation:

f

)1( z

)(u 2 Df

ASSUMPTIONS: the scattering is diffusive and in the so-called Small Pitch Angle Scattering (SPAS) regime (Dµµ is constant ONLYfor the isotropic case)

μ'fμ'μ,w+μfμd=z

fμ+uγ

The transport equation in the most general case is

Vietri 2003PB & Vietri 2005

Arbitrary Scattering Function

For instance, in the case of Large Angle Scattering:

Blasi & Vietri 2005

/1Universal

More non-universality…

0B

B

Isotropic turbulence

AnisotropicTurbulence

Lemoine et al. 2006

Again, one ends up again in a situation of quasi-coherent perpendicularField downstream: PARTICLES DO NOT RETURN → SPECTRUM STEEPENS

Caveat: what if the field upstream does not have a coherence length? (e.g.Scale invariant spectrum 1/k)

The role of multifrequency observations

• For Galactic CRs the role of Multi-ν observations is obvious (e.g. gamma, X, radio from SNR,…)

• A similar role would be desirable for UHECRs– Interactions inside the source during the acceleration– Interactions during the propagation from source to observer

• The sources of UHECRs might be identified through the SSA of the arrival directions, but this depends on Extra-Gal B-field, chemical composition, Gal B-field, etc...

• Correlations with Large Scale Structures (Longo et al. 2006) would also be helpful.

A simulated Auger South Sky

De Marco

CONCLUSIONS• A lot of indirect evidence is accumulating in favor of SNRs

being sources of CRs in the Galaxy, up to <1018 eV…but no iron solid proof

• The transition between Gal to Extra-Gal CRs takes place either at the second knee or at the ankle (very important for the origin of UHECRs; crucial the composition)

• Acceleration at shock fronts presents us with exciting new developments and challenges to reach high Emax even of relevance for UHECRs

• The spectrum of UHECRs is being investigated by Auger…just some patience is needed. It would be precious to gather information about the composition in the transition region

• UHECRs are still orphans…may be something even bigger than Auger South will be needed to “see” the sources (Auger North, Super Auger, EUSO-like?)