PARTICLE ACCELERATION IN
SUPERNOVA REMNANTS:
IMPLICATIONS FOR THE ORIGIN
OF GALACTIC COSMIC RAYS
Pasquale Blasi
INAF/Arcetri Astrophysical Observatory
Geneva, 28/03/2012
OUTLINE
1. GENERAL COSMIC RAY FACTS
1. BASICS OF PARTICLE ACCELERATION IN THE NON LINEAR REGIME
2. MAGNETIC FIELD AMPLIFICATION
3. WHAT ARE GAMMA RAY OBSERVATIONS TELLING US ?
4. PARTICLE ACCELERATION IN PARTIALLY IONIZED MEDIA
THE BASIC PROBLEM OF COSMIC RAY PHYSICS CONSISTS IN FIGURING
OUT THE PHYSICS OF ACCELERATION AND PROPAGATION GIVEN
BASICALLY THREE OBSERVABLES:
1)SPECTRUM OF CHEMICALS (protons, He, CNO, MgAlSi, Fe)
2)SECONDARY/PRIMARY RATIOS
3)ANISOTROPY
SOURCES  MULTIFREQUENCY OBSERVATION vs MODELS
THE PROPAGATION OF COSMIC RAYS BOTH INSIDE THE SOURCES AND IN
THE GALAXY IS DIFFUSIVE IN NATURE, AND IS USUALLY DESCRIBED BY
USING A DIFFUSION COEFFICIENT D(E) (ALTHOUGH A DIFFUSION TENSOR
SHOULD BE USED)
CR move diffusively in the Galaxy
ALL THESE MEASUREMENTS TELL US
THAT ON AVERAGE CR STAY IN THE
GALAXY FOR A FEW TENS MILLION
YEARS BEFORE ESCAPING THE GALAXY
DIFFUSIVE MOTION
H
Rd
disc
2h
Halo
Particle escape
THE DIFFUSIVE MOTION LEADS TO ESCAPE TIMES ~H2/D(E) >> H/c
D(E)=(1/3) v l(E) is the diffusion coefficient and l(E) is the scattering
Length as a function of energy E
Secondary/Primary ratios
D(E) E
Primary/Primary
 1/ 3

  0.7


CREAM 2008

Simple scaling relations
IN ORDER FOR INJECTION AND ESCAPE TO LEAD TO A STATIONARY
SITUATION ONE HAS TO REQUIRE:
n(E)  q(E) esc (E) ~ E
 
DURING PROPAGATION CR PRODUCE SECONDARY NUCLEI AT A
RATE
qsec (E)  Ysp n(E) sp ngas c
AND AGAIN IN A STATIONARY REGIME:
nsec (E)  qesc (E) esc (E)
nsec (E)
1
~ x(E) ~
n(E)
D(E)
PAMELA
CREAM
The B/C ratio as a diffusion indicator
IN PRINCIPLE B/C ~ 1/D(E) IN
THE HIGH RIGIDITY REGIME
BUT UNCERTAINTIES ARE STILL
LARGE
NOT EASY TO DISCRIMINATE
AMONG DIFFERENT DIFFUSION
COEFFICIENTS
Adapted from Obermeier et al. 2011
BASICS of the SNR PARADIGM
Zwicky (mid 30s) and Ginzburg & Sirovatsky (mid 60s) realized that
On energetic grounds SNR are the only viable source of CR in the
Galaxy
TOTAL CR LUMINOSITY OF THE GALAXY ~ 3x1040 erg/s
LSN  R SN Ekin  3  1041 erg s -1
IN PRINCIPLE AN EFFICIENCY OF ORDER 10% PER SN IS SUFFICIENT TO
ACCOMMODATE THE COSMIC RAY ENERGETICS
THE BIG QUESTION IS HOW DOES NATURE PERFORM
THE ENERGY CONVERSION?
ACCELERATION MECHANISM
SUPERNOVA BLAST WAVE
FREE EXPANSION VELOCITY: Vs 
2Eej
M ej
-1/2
 109 E1/2
M
51
ej, cm/s
THE EXPANSION SPEED DROPS DOWN DURING THE SEDOV-TAYLOR
PHASE, BUT THE MACH NUMBER IS ~100
A STRONG SHOCK WAVE DEVELOPS
THEORY OF CR ACCELERATION
IN SNRs
Diffusive Shock Acceleration
PB 2002, 2004, Amato & PB 2005, 2006, Caprioli +, 2007-2011, Morlino + 2007-2012
The first order FERMI ACCELERATION
Test particle theory
Downstream
DIFFUSION OF CHARGED PARTICLES
BACK AND FORTH THROUGH THE
SHOCK LEADS TO
Upstream
E 4
 (U1 U2 )
E 3
PARTICLES ARE ACCELERATED TO A
POWER LAW SPECTRUM
U2
U1
SHOCK FRONT

THE SLOPE OF THE SPECTRUM ONLY
DEPENDS ON THE COMPRESSION
NOT ON THE DIFFUSION COEFFICIENT
FOR STRONG SHOCKS:
E-2
NON LINEAR THEORY
A theory of particle acceleration that allows one
to describe:
1. Dynamical reaction of accelerated particles
2. CR-induced B-field and their reaction
3. Recipe for injection (self-regulation)
4. Escape of particles (Cosmic Rays)
DIFFUSIVE ACCELERATION AT COLLISIONLESS
NEWTONIAN SHOCKS
non linear theory: BASIC PHYSICAL ASPECTS
COMPRESSION FACTOR BECOMES
FUNCTION OF ENERGY
VELOCITY
PROFILE
SPECTRA ARE NOT PERFECT
POWER LAWS (CONCAVE)
0
1
2
GAS BEHIND THE SHOCK IS
COOLER FOR EFFICIENT SHOCK
ACCELERATION
SYSTEM SELF REGULATED
EFFICIENT GROWTH OF B-FIELD
IF ACCELERATION EFFICIENT
Basics of CR streaming instability
+ +
+++++
+ + + + ++
++++++++
++++++++
++++++++
+ + + ++
++ ++
SHOCK
FRONT
JCR=nCRVs q
B0
THE UPSTREAM PLASMA REACTS TO
THE UPCOMING CR CURRENT BY
CREATING A RETURN CURRENT TO
COMPENSATE THE POSITIVE CR CHARGE
THE SMALL INDUCED PERTURBATIONS
ARE UNSTABLE (ACHTERBERG 1983, ZWEIBEL
1978, BELL 1978, BELL 2004, AMATO & PB 2009)
CR MOVE WITH THE SHOCK SPEED (>> VA). THIS UNSTABLE SITUATION
LEADS THE PLASMA TO REACT IN ORDER TO SLOW DOWN CR TO <VA
BY SCATTERING PARTICLES IN THE PERP DIRECTION (B-FIELD GROWTH)
Particle Diffusion  Wave Growth
dPCR nCR m(vD VA )
nCR mvD  nCR mVA 

dt

dPw
B 1
 W
dt
8 VA
2
nCR vD VA
W  2
cyc
ngas VA
In the ISM
this is ~10-3 yr-1 but close to a shock front the
growth can be much larger!!!

dB IS AMPLIFIED BY PARTICLES
MAGNETIC FIELD AMPLIFICATION
SMALL PERTURBATIONS IN THE LOCAL B-FIELD CAN BE
AMPLIFIED BY THE SUPER-ALFVENIC STREAMING OF THE
ACCELERATED PARTICLES
Particles are accelerated because there is
High magnetic field in the acceleration region
High magnetic field is present because particles
are accelerated efficiently
Without this non-linear process, no acceleration of CR
to High energies (and especially not to the knee!)
X-ray rims and B-field amplification
TYPICAL THICKNESS OF FILAMENTS: ~ 10-2 pc
The synchrotron limited thickness is:
B  100 Gauss
In some cases the strong fields are confirmed
by time variability of X-rays
Uchiyama & Aharonian, 2007
SPECTRA
THE SPECTRA OF ACCELERATED PARTICLES ARE IN GENERAL
CONCAVE AND FLATTER THAN E-2 AT HIGH ENERGY
THE MAXIMUM ENERGY WITH B-FIELD AMPLIFICATION REACHS
UP TO ~1015 eV FOR PROTONS (Z TIMES HIGHER FOR NUCLEI)
THESE SPECTRA SHOULD REFLECT IN THE GAMMA RAY SPECTRA
(IF DUE TO PP SCATTERING) AND OF NEUTRINOS
BUT THE OBSERVED SPECTRA OF GAMMAS
ARE TYPICALLY ~ E-2.3
CLEARLY INCOMPATIBLE WITH LEPTONIC MODELS! BUT ALSO NOT
COMPATIBLE WITH THE SIMPLEST PREDICTION OF NLDSA: E-2
THE EFFECT OF THE VELOCITY OF WAVES
One should remember that the compression factor that counts in shock
acceleration is not that of fluid velocity, but that of the scattering centers velocity
When the magnetic field is amplified the Alfven speed is not well defined and one
may argue that it should be calculated in the amplified field (it depends on helicity!):
THIS EFFECT LEADS TO STEEPER SPECTRA WHEN
ACCELERATION IS EFFICIENT (BUT VERY MODEL
DEPENDENT)
TROUBLE WITH SLOPES ?
VERY SURPRISING TO SEE THAT THE
REQUIRED ACCELERATION EFFIC. ARE
HIGH BUT THE SPECTRA ARE STEEP
Caprioli 2011
Caprioli 2011
The case of RX J1713
Morlino et al. 2009
Morlino, Amato & PB 2009
The case of Tycho
Morlino&Caprioli 2011
STEEP SPECTRUM
BASICALLY IMPOSSIBLE TO
EXPLAIN WITH LEPTONS
CR spectra and SNRs
Blasi & Amato 2011
Deficit compensated
by extragalactic CRs
Chemicals and the KNEE
Blasi & Amato 2011
d=1/3
He
p
Fe
ONLY FOR d=1/3 SPECTRUM OF He HARDER THAN SPECTRUM OF PROTONS
AS A RESULT OF SPALLATION
Large Scale CR Anisotropy
Naïve expectation:
proportional to Ed
d=1/3
d=0
.6
Blasi & Amato 2011
EFFECT OF SPIRAL ARMS
PB and Amato 2011
Broad Arms
Tight Arms
DEPENDENCE OF HALO SIZE
PB and Amato 2011
EFFECT OF EXTRAGALACTIC CR
WITHOUT EXTRAGALACTIC
COMPONENT
WITH EXTRAGALACTIC
COMPONENT
SOME NEW DIRECTIONS
COLLISIONLESS SNR SHOCKS IN
PARTIALLY IONIZED MEDIA
SUBTLE ASPECTS OF ACCELERATION
AT A COLLISIONLESS SHOCK
NEUTRALS
AND IONS
PB+, 2012
SHOCK VELOCITY
v

CHARGE EXCHANGE  BROAD
BALMER LINE (NEUTRALS
THAT MADE CHARGE
EXCHANGE) REFLECTING
THE TEMPERATURE OF IONS…
+
+
Hot
ion
Cold
ion
Cold neutral
hot neutral
BUT THE LATTER AFFECTED BY EFFICIENT CR ACCELERATION
BROAD BALMER LINES NARROWER THAN FOR
UNMODIFIED SHOCKS
Wbroad  8 ln 2
kT2
 1.02 vsh
m
INFERRED EFFICIENCY of CR ACCELERATION 50-60% !!! (BUT model
dependent)
Helder et al. 2009
NARROW BALMER LINES BROADER THAN FOR
UNMODIFIED SHOCKS
Sollerman et al. 2003
NEUTRALS
VELOCITY
PROFILE
v
IONS

CHARGE EXCHANGE OCCURS
NOW IN THE CR INDUCED
PRECURSOR
Wbroad

NARROW BALMER LINE BROADER
THAN FOR AN UNMODIFIED SHOCK
 T0 1/2
kT0
 8 ln 2
 21 km/s  4 
10 K 
m
The neutral return flux
NEUTRALS
AND IONS
PB + 2012
SHOCK VELOCITY
A NEUTRAL ATOM CAN CHARGE
EXCHANGE WITH AN ION WITH
V<0, THEREBY GIVING RISE TO
A NEUTRAL WHICH IS NOW FREE
TO RETURN UPSTREAM
THIS NEUTRAL RETURN FLUX
LEADS TO ENERGY AND
MOMENTUM DEPOSITION
UPSTREAM OF THE SHOCK!
Vperp=0
V<0
1
v/(Vs/4)
Neutrals as collisionless particles
Neutrals are describing through the Vlasov equation:
Stationary
+ charge exch
- Charge exch and
ionization
Relevant cross sections
n=1
n=2
Ions as a plasma
Mass conservation
Momentum Conservation
Energy Conservation
Mass flux of neutrals
Momentum flux of neutrals
Energy flux of neutrals
Distribution Functions in phase space
PB+2012
UPSTREAM
DOWNSTREAM
NEUTRAL
RETURN
FLUX
THE DISTRIBUTION FUNCTIONS OF NEUTRALS ARE
NOT MAXWELLIAN IN SHAPE BUT APPROACH SUCH
SHAPE AT DOWNSTREAM INFINITY
EFFECT of
IONIZATION
NEUTRAL INDUCED
PRECURSOR
SHOCK MODIFIED BY THE
NEUTRAL RETURN FLUX
PB+2012
NEUTRAL INDUCED PRECURSOR
PB+2012
EVEN FOR A STRONG SHOCK (M>>1) THE EFFECTIVE MACH NUMBER OF
THE PLASMA IS DRAMATICALLY REDUCED DUE TO THE ACTION OF THE
NEUTRAL RETURN FLUX
ACCELERATION OF TEST PARTICLES
PB+ 2012
1 GeV
10 GeV
100 GeV
1 TeV
CONCLUSIONS
THE SN PARADIGM EXPLAINS THE ROUGH OBSERVATIONAL PICTURE OF
THE ORIGIN OF COSMIC RAYS
BUT MISSING PIECES: STEEP SPECTRA, ANISOTROPY, SPECTRAL FEATURES
IN THE NUCLEAR SPECTRA
MAGNETIC FIELD AMPLIFICATION INDUCED BY CR IS NOW ONE OF THE HOT
TOPICS IN EXPLAINING X-RAY MORPHOLOGY AND REACH THE KNEE
THE KNEE CAN BE EXPLAINED REASONABLY WELL IN TERMS OF CHANGE OF
CHEMICAL COMPOSITION, BUT TRANSITION AT THE DIP (NOT ANKLE)
PRESENCE OF NEUTRALS EXTREMELY IMPORTANT DIAGNOSTIC TOOL FOR
CR ACCELERATION AS WELL AS POSSIBLE CAUSE FOR SPECTRAL
STEEPENING