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Cosmic rays: origin and physics

Cosmic rays: origin and physics. Richard Lieu Dept. of Physics University of Alabama, Huntsville. Inscription at Erice Sicily, about VICTOR HESS. Here in the Erice maze Cosmic rays are all the craze Just because a guy named Hess When ballooning up found more not less.

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Cosmic rays: origin and physics

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  1. Cosmic rays: origin and physics Richard Lieu Dept. of Physics University of Alabama, Huntsville

  2. Inscription at Erice Sicily, about VICTOR HESS Here in the Erice maze Cosmic rays are all the craze Just because a guy named Hess When ballooning up found more not less

  3. Relativistic Particles • ISM component that can be directly measured (dust, local ISM also) • Low mass fraction, but energy close to equipartition with field, turbulence • Composition includes H+, e-, and heavy ions • Elemental distribution allows measurement of spallation since acceleration: pathlength

  4. The all-particle CR spectrum Galactic: Supernovae Galactic?, Neutron stars, superbubbles, reacceleratedheavy nuclei --> protons ? Extragalactic?; source?, composition? Cronin, Gaisser, Swordy 1997

  5. Wilkes

  6. Origin of cosmic rays • The high degree of isotropy of Galactic CRs (~ one part per 10^3) suggests that they do not originate from one or two very energetic sources. .

  7. Fermi acceleration • Ball  charged particle • Racket  “magnetic mirrors” B B V B • Magnetic “inhomogeneities” or plasma waves

  8. Trivial analogy... • Tennis ball bouncing off a wall • No energy gain or loss v v rebound = unchanged velocity v v same for a steady racket... How can one accelerate a ball and play tennis at all?!

  9. Moving racket • No energy gain or loss... in the frame of the racket! V v Guillermo Vilas v + 2V unchanged velocity with respect to the racket  change-of-frame acceleration

  10. Wave-particle interaction • Magnetic inhomogeneities ≈ perturbed field lines Adjustement of the first adiabatic invariant: p2 / B ~ cst rg<<l Nothing special... rg>>l Pitch-angle scattering:Da ~ B1/B0Guiding centre drift:r ~ rgDa rg ~ l

  11. Origin of cosmic rays • Fermi: stochastic acceleration • When a particle is reflected off a magnetic mirror coming towards it in a head-on collision, it gains energy • When a particle is reflected off a magnetic mirror going away from it, in an overtaking collision, it loses energy • Head-on collisions are more frequent than overtaking collisions  net energy gain, on average (stochastic process)

  12. E2, p2 q1 q2 V E1, p1 Second Order Fermi Acceleration • Direction randomized by scattering on the magnetic fields tied to the cloud

  13. Finally... second order in V/c

  14. Mean rate of energy increase Mean free path between cloudsalong a field line: L Mean time between collisions L/(c cos f) = 2L/c Acceleration rate dE/dt = 2/3 (V2/cL)E  E/tacc Energy drift function b(E)  dE/dt = E/tacc

  15. Energy spectrum • Diffusion-loss equation Injection rate diffusion term Flux in energy space Escape • Steady-state solution (no source, no diffusion)  power-law x = 1 + tacc/tesc

  16. Problems of Fermi’s model • Inefficient • L ~ 1 pc  tcoll ~ a few years • b ~ 10-4  b2 ~ 10-8 (tCR ~ 107 yr) tacc > 108 yr !!! • Power-law index • x = 1 + tacc/ tesc • Why do we see x ~ 2.7 everywhere ?  smaller scales

  17. Origin of cosmic rays • Zwicky proposed acceleration by supernova e.

  18. Orign of Cosmic rays • Fred Hoyle was probably the first to have asked the question whether shock acceleration by a supernova remnant is responsible.

  19. Seminal papers on diffusive shock acceleration • Axford, Leer, and Skadron 1977. • Krimsky 1978. • Bell 1978. • Blandford and Ostriker 1978,

  20. Add one player to the game... • “Converging flow”... Marcelo Rios Guillermo Vilas V V

  21. u1 u2 k2/u2 k1/u1 Diffusive shock acceleration downstream upstream • Time to complete one cycle: • Confinement distance: k/u • Average time spent upstream: t1 ≈ 4k / cu1 • Average time spent upstream: t2 ≈ 4k / cu2 • Bohm limit: k = rgv/3 ~ Eb2/3qB • Proton at 10 GeV: k ~ 1022 cm2/s •  tcycle ~ 104 seconds ! • Finally, tacc ~ tcycle Vs/c ~ 1 month !

  22. First order acceleration On average: • Up- to downstream: < cos q1 > = -2/3 • Down- to upstream: < cos q2 > = 2/3 Finally...  first order in V/c

  23. Cosmic rays beyond the `knee’ Origin could be GRBs, pulsars, AGNs, or clusters Beware the extragalactic origin of the VHE CRs GRBs and AGNs have relativistic shocks Turbulent acceleration in clusters

  24. Central soft excess (no background issues) for Coma

  25. GZK cutoff • At R ~ 10^19 eV a cosmic ray particle undergoes pion production with the cosmic microwave background. • Prediction of an absolute cutoff in the CR spectrum. • Problems with Lorentz invariance.

  26. Conclusion • Cosmic rays with energy below the `knee’ are probably accelerated by strong shocks in SNRs. • Above the `knee’: a mixture of Galactic and extragalactic origin. Sources can range from 2nd order Fermi processes to relativistic shocks. • GZK cutoff appears to be `semi-confirmed’. • Reason could either be local origin or Lorentz invariance violation.

  27. Energy spectrum • At each cycle (two shock crossings): • Energy gain proportional to E: En+1 = kEn • Probability to escape downstream: P = 4Vs/rv • Probability to cross the shock again: Q = 1 - P • After n cycles: • E = knE0 • N = N0Qn • Eliminating n: • ln(N/N0) = -y ln(E/E0), where y = - ln(Q)/ln(k) • N = N0 (E/E0)-y x = 1 + y = 1- ln Q/ln k

  28. Universal power-law index with • We have seen: • For a non-relativistic shock • Pesc << 1 • DE/E << 1 • … where D = g+1/g-1 for strong shocks is the shock compression ratio • For a monoatomic or fully ionised gas, g=5/3 x = 2, compatible with observations

  29. The standard model for GCRs • Both analytic work, simulations and observations show that diffusive shock acceleration works! • Supernovae and GCRs • Estimated efficiency of shock acceleration: 10-50% • SN power in the Galaxy: 1042 erg/s • Power supply for CRs: eCR Vconf/ tconf ~ 1041 erg/s ! • Maximum energy: • tacc ~ 4Vs/c2  (k1/ u1 + k2/ u2) • kB = Eb2/3qB E •  acceleration rate is inversely proportional to E… • A supernova shock lives for ~ 105 years • Emax ~ 1014 eV  Galactic CRs up to the knee...

  30. Drop shot V v v - 2V Particle deceleration

  31. Resonant scattering with Alfven (vA2 = B2/m0r) and magnetosonic waves: w - kv = nW (W = qB/gm = v/rg : cyclotron frequency) • Magnetosonic waves: • n = 0 (Landau/Cerenkov resonance) • Wave frequency doppler-shifted to zero •  static field, interaction of particle’s magnetic moment with wave’s field gradient • Alfven waves: • n = ±1 • Particle rotates in phase with wave’s perturbating field •  coherent momentum transfer over several revolutions...

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