"Fundamental acceleration processes and CTA"
From CTA observations to fundamental acceleration mechanisms... a difficult task:
• many different acceleration mechanisms: Fermi 1, Fermi 2, shear, ...
(Fermi acceleration at shock: most standard, nice powerlaw, few free parameters)
• main signatures to be determined:
Emin , Emax [Ã timescale tacc(E) ], spectral slope h®i, running d ®/ d ln E
• only secondary photon spectra are observed, reconstruction process is difficult and source
physics dependent ...
Fermi at mildly relativistic
internal shocks
• different ways of addressing this problem:
- acceleration physics: idealized source configurations ) calculate tacc(E), ®(E)
- data interpretation: most effort on source modelling ( tacc » tL , ® » best fit
Martin Lemoine - IAP
Fermi acceleration
shock front
rest frame
Simple view of Fermi acceleration:
• test particle approximation: particles get
accelerated as they bounce back and forth on
magnetic inhomogeneities on both sides of
the shock front
Modern view of Fermi acceleration:
•relativistic regime: vsh » c, how well does Fermi acceleration operate?
•test particle approximation is not a good approximation: cosmic ray energy
density/pressure represents a sizeable contribution...
) modification of the shock jump conditions, non-linear Fermi acceleration
•theory and observations suggest that the coupling between accelerated particles and e.m.
waves is of fundamental importance, for both non-relativistic and relativistic shocks
• there exists an intimate link between the physics of (relativistic or not) collisionless shock
waves, accelerations mechanisms, source physics, hence observational data at VHE
• a new numerical tool to probe acceleration physics: Particle-In-Cell (PIC) simulations...
• astrophysical objects probe different physical conditions...
SNR: non-relativistic, weakly magnetised
IGM shock waves: non-relativistic, unmagnetized ?
GRB: moderately to ultra-relativistic, weakly magnetised?
PWNe: ultra-relativistic, strongly magnetised?
Acceleration at IGM shock waves and magnetic fields
IGM shock waves:
acceleration can proceed if the unshocked medium is magnetized: gamma-ray observations
would allow to measure this unshocked (primeval?) magnetic field and/or constrain the
amplication mechanisms...
Keshet et al. 03
filament, 16£ 16±, ±µ =0.4±
above 1GeV
cluster, 16£ 16±, ±µ =0.4±
log10(J/J0) (>1 GeV)
J0' 10-7 cm-2 s-1 sr-1
cluster, 16£ 16±, ±µ =0.2±
above 10 GeV
log10(J/J0) (>10 GeV)
J0' 10-9 cm-2 s-1 sr-1
Relativistic Fermi acceleration
• the ambient magnetic field inhibits Fermi
acceleration: B?down » ¡ shB?up, therefore B
is mostly perpendicular, particle is trapped on
B line and advected away from the shock far
in the shocked region
shock front
rest frame
) Fermi acceleration requires energy transfer between shock and magnetic field...
... accelerated particles are the likely agent of transfer via e.m. beam-plasma instabilities
) particles do not radiate via synchrotron, but via jitter radiation on small scale e.m. fluctuations
• if the ambient magnetic field is too strong, accelerated particles cannot propagate far enough
into the unshocked plasma (penetration length » rL / ¡sh 3 !), hence instabilities cannot grow,
hence Fermi acceleration is inhibited:
) Fermi acceleration should not operate at strongly magnetized PWNe terminal shocks,
in magnetized GRB external shocks (?) ... much to be learned from VHE observations...
(some) Open questions:
• spectral slope, running and maximal energy still unknown...
• Fermi acceleration at moderately relativistic shock waves (ex. GRB internal shocks)...
• time dependence of the shock structure and Fermi acceleration...
Relativistic Fermi acceleration: an example
Observations of GRB 080916C:
• Fermi LAT detection of high energy
emission >1 GeV, delayed by several
seconds with respect to lower energy
• various interpretations, among which:
o Wang et al. 09: inverse Compton,
E° as high as 70GeV implies
tacc ' tL and offers a lower limit on
unshocked magnetic field
o Razzaque et al. 09: VHE emission is proton synchrotron radiation, delay » proton cooling time;
implies acceleration of p to & 1020 eV, but requires huge magnetic energy content
Acceleration mechanism vs energy
Cosmic ray all-sky all-particle spectrum (x E3):
very small flux at UHE:
»1/km2/century at 1020eV
sources: GRBs, blazars??
Galactic supernovae remnants
...Sources of ultra-high energy cosmic rays are the most powerful accelerators known in Nature...
Main questions:
• which source, which acceleration mechanism to reach E » 1020 eV?
• are secondaries (gamma-rays/ neutrinos) expected...?
Secondaries of ultra-high energy cosmic ray sources
Assumptions: sources of UHE protons and nuclei embedded in magnetized clusters
Kotera et al. 09
) detection of gamma-rays from UHE sources in galaxy clusters in unlikely even for CTA, even with
optimistic assumptions
Other possibilities:
• Gabici & Aharonian 05 suggest to detect the >GeV synchrotron light of 1018eV e+ e- pairs produced by
UHE protons interacting with the CMB: unlikely for 'modern' source luminosities...
• secondaries emitted in the source itself: also unlikely for reasons of temporal coincidences between
arrival of UHE protons and VHE gamma-rays (magnetic fields...)

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