Pasquale BlasiINAF/Arcetri Astrophysical Observatory

4th School on Cosmic Rays and Astrophysics UFABC - Santo André - São Paulo – Brazil

WHAT NEXT?We have found the elegant results of the theory of DIFFUSIVE SHOCKACCELERATION in the TEST PARTICLE approximation and also foundsome of its limitations:

1.TOO LARGE EFFICIENCIES TO EXPECT TEST PARTICLES

2.THE EXPECTED DIFFUSION COEFFICIENT LEADS TO TOO LOW EMAX

3.IF PARTICLES DIFFUSE THEY ALSO LEAD TO WAVE GROWTH

ALL THESE PHENOMENA SUGGEST THAT WE NEED TO MOVE BEYONDTHE TEST PARTICLE APPROXIMATION

NON LINEAR THEORY OF DIFFUSIVE SHOCK ACCELERATION

Dynamical Reaction of Accelerated Particles

PRECURSOR

Un

dis

turb

ed M

ediu

m

Sh

ock

Fro

nt v

subshock Precursor

Conservation of Momentum

Transport equationfor cosmic rays

SU

BS

HO

CK Velocity Profile

€

∂f∂t

=∂

∂xD∂f

∂x

⎡ ⎣ ⎢

⎤ ⎦ ⎥− u

∂f

∂x+

1

3

du

dxp∂f

∂p+Q(x, p, t)

€

ρ0u02 + Pg,0 = ρ (x)u2(x) + Pg (x) + PCR (x)

WHAT SHOULD BE EXPECT?

High p

UPSTREAM

Velocity

SUBSHOCK

PRECURSOR

1. PARTICLES WITH HIGH P FEEL LARGER COMPRESSION FACTOR THEN LOW P PARTICLES

2. THE TOTAL COMPRESSION BECOMES LARGER THAN 4

3. THE SPECTRUM SHOULD BE NO LONGER A POWER LAW!

4. AT HIGH P THE SLOPE SHOULD BE FLATTER THAN 2 !!!

5. THE GAS BEHIND THE SHOCK SHOULD BE COOLER THAN FOR AN ORDINARY SHOCKRtot Rsub

INJECTION

Ideal Collisionless Shock (More) Real Collisionless Shock

rL

WHICH PARTICLES AND HOW MANY PARTICLESENTER THE ACCELERATION CYCLE?

THIS IS THE LEAST UNDERSTOOD ASPECTS OF ALL !

INJECTION…cont’d

f(p)

p

Maxwellian for the Downstream gas

Pinj = pth,2

2321

13

4 ξsb/

eξRπ

η= Relation between

Rsub, ξ and η

T2

T1

OUTPUT OF THECALCULATIONS

SHOCK HEATING and SPECTRA

PB, Gabici & Vannoni 2005

SHOCKMODIFICATION

REDUCEDHEATING

Particle Diffusion Wave Growth

Remember that we showed that a particle diffuses along a direction z wherethere is an ordered magnetic field B0 because of a small perturbation B perpendicular to B0.

In this process the particles lose momentum in the z direction and this p Is transferred to the B waves.

This equals the momentum gained by the waves:

And imposing a perfect balance:

€

nCRmvD → nCRmvw ⇒dPCRdt

=nCRm(vD − vw )

τ

€

dPw

dt= γW

δB2

8π

1

vw

€

γW = 2nCRngas

vD − vwvw

Ωcyc

In the ISM this is ~10-3 yr-1 butclose to a shock front the growcan be even larger!!!B IS AMPLIFIED BY PARTICLES

SMALL PERTURBATIONS IN THE LOCAL B-FIELD CAN BE AMPLIFIED BY THE SUPER-ALFVENIC STREAMING OF THEACCELERATED PARTICLES

Particles are accelerated because there isHigh magnetic field in the acceleration region

High magnetic field is present because particlesAre accelerated efficiently

Without this non-linear process, no acceleration of cr to High energies (and especially not to the knee!)

Bell 2004, Amato & PB 2009

Successes of the SNR paradigm1. Observation of X-ray rims

TYPICAL THICKNESS OF FILAMENTS: ~ 10-2 pc

The synchrotron limited thickness is:

€

B ≈100 μGauss

ChandraCassiopeia A

ChandraSN 1006

Successes of the SNR paradigm

2. Max energy and the knee

pm

ax/m

c

107

106

105

104 50 100 150 200

M0

MAXIMUM MOMENTUMMAXIMUM MOMENTUM

PROTONKNEE

Bohm Diff withoutB-amplification

PB, Amato & Caprioli, 2007

Magnetic fieldamplification leadsto higher values of theMaximum energy

Observed proton spectrum

Data from Bertaina et al. 2008

Successes of the SNR paradigm

3. evidence for a CR precursor ?

PRECURSORREGION RIM

Morlino, Amato, PB & Caprioli 2010

Successes of the SNR paradigm

4. Balmer dominated shocksDOWNSTREAM

ION Temperature LOWER because of CR acceleration

NEUTRAL Temperature HIGHER because of charge exchange

+ +

BROAD BALMER LINE IS NARROWER

NARROW BALMER LINE IS WIDER

Observations of Balmer dominated shocks

Helder et al. 2009

INFERRED EFFICIENCY of CR ACCELERATION 50-60% !!!

Observation of Balmer dominated shocksbroader narrow Balmer line Sollerman et al. 2003

Broadening of the narrow line hints to a mechanism for heating of the neutrals upstreamon scales shorter than ionization scales TURBULENT HEATING

CHARGE EXCHANGE UPSTREAM

Observation of Balmer dominated shocks:

Possible evidence for a CR precursor in the narrow Balmer line

A broadened narrow Hline from upstream shows that the neutrals and ions have some level of charge exchange different bulk velocities and/or T’s between the two components

CR precursor

HADRONIC

LEPTONIC

Morlino, Amato & PB 2009

RXJ1713

RX

J17

13

RXJ1713 with fermi data

1. e/p Equilibration downstream? (Morlino et al. 2009)2. Very low value of Kep at given time 3. Lines from non-equilibrium ionization ? (Ellison et al. 2010)4. What are those Fermi data points telling us?

A Puzzling situationCourtesy of S. Funk

• Most SNR detected by Fermi have steep spectra (some exceptions, such as RXJ1713)

• The predicted spectra would naively require steep diffusion D(E)~E0.7 in conflict with anisotropy measurements

A small print in the theory of DSA: a point as important as poorly known

Velocity of scattering centers in the shock frame NOT velocity of the plasma

In general the velocity of scattering centers is small and there is no problem

BUT AMPLIFIED MAGNETIC FIELD high velocity ???

VERY MACROSCOPIC CONSEQUENCES ON SPECTRA!

€

vw =δB

4πρ>> vA,0

ROLE OF NUCLEI

Caprioli, PB, Amato 2010

The dynamical reaction of nuclei on the shock structureturns out to be VERY IMPORTANT

ROLE OF NUCLEI: The knee

Caprioli, PB, Amato 2010

WHERE DO GALACTIC CR end?1. The SNR paradigm hints to a galactic CR spectrum

ending at ~a few 1017 eV

2. Observations of chemical composition also suggest the same trend

?

PROPAGATION OF PROTONS from extragalactic sources

100 Mpc

GZK

DIP

HOW DOES THE SPECTRUM LOOK LIKE? THE DIP

Berezinsky et al. 2005Aloisio et al. 2007

Dip structure

HISTORICAL INTERPRETATION OF THE TRANSITION: THE ANKLE

ALTERNATIVE INTERPRETATION OF THE TRANSITION: MIXED COMPOSITION

Allard et al. 2005-2008

UNDERSTANDING THE DIFFERENCE:

DIP VS MIXED

From Kampert 2008

UNDERSTANDING THE DIFFERENCE:

DIP VS ANKLE

Aloisio, Berezinsky, PB & Ostapchenko 2008

DIP ANKLE

XMAX and RMS OF XMAX

Auger

HiRes