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
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
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
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