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The Physics of Cosmic Ray Acceleration Tony Bell University of Oxford

This study explores the mechanisms and limitations of cosmic ray acceleration in supernova remnants, including shock acceleration and the role of magnetic fields. It examines the energy spectrum, acceleration time limits, and escape routes of cosmic rays in the interstellar medium.

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The Physics of Cosmic Ray Acceleration Tony Bell University of Oxford

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  1. The Physics of Cosmic Ray Acceleration Tony Bell University of Oxford with Brian Reville Klara Schure Gwenael Giacinti Anabella Araudo Katherine Blundell SN1006: A supernova remnant 7,000 light years from Earth X-ray (blue): NASA/CXC/Rutgers/G.Cassam-Chenai, J.Hughes et al; Radio (red): NRAO/AUI/GBT/VLA/Dyer, Maddalena & Cornwell; Optical (yellow/orange): Middlebury College/F.Winkler. NOAO/AURA/NSF/CTIO Schmidt & DSS

  2. Shock acceleration energy spectrum B1 B2 Low velocity plasma High velocity plasma Krymsky (1977), Axford Leer & Skadron (1977), Blandford & Ostriker (1978), Bell (1978) Cosmic Ray shock At each shock crossing, shock velocity = us Fractional energy gain Fraction of CR lost Differential energy spectrum

  3. Acceleration time limits CR energy shock ushock ncr upstream L For acceleration to high energy Bohm diffusion: mfp = Larmor radius Max CR energy Lagage & Cesarsky 1983 • Need large magnetic field • Structured on scale of CR Larmor radius

  4. R L CR pre-cursor shock Electric currents carried by CR and thermal plasma jcr Density of 1015eV CR: ~10-12 cm-3 Current density: jcr ~ 10-18 Amp m-2 jcrxB force acts on plasma to drive instabilities

  5. Non-resonant hybrid (NRH) instability B j x B j x B Bell, MNRAS 353, 550 (2004) Cavity/wall structure CR current jxB expands loops stretches field lines more B more jxB

  6. Tycho 1572AD Kepler 1604AD SN1006 Cas A 1680AD Historical shell supernova remnants (Vink & Laming, 2003; Völk, Berezhko, Ksenofontov, 2005) Chandra observations NASA/CXC/Rutgers/ J.Hughes et al. NASA/CXC/Rutgers/ J.Warren & J.Hughes et al. NASA/CXC/NCSU/ S.Reynolds et al. NASA/CXC/MIT/UMass Amherst/ M.D.Stage et al.

  7. Maximum CR energy: need time to amplify magnetic field Max instability growth rate SNR For magnetic field amplification need shock X CR precursor CR not confined until CR electric charge Cm-2 passed upstream Shock upstream precursor downstream X

  8. Maximum CR energy: need time to amplify magnetic field Cas A Already too slow Sedov phase shock vel in 1000 km s-1 Blast wave energy in 1044J SN expansion into circumstellar wind wind mass loss in 10-5 solar masses yr-1 wind vel in 10 km s-1 shock vel in 30,000 km s-1

  9. CR need to escape efficiently into ISM 90% of CR energy confined with 10% of CR energy escapes with Low energy CR cool adiabatically as SNR expands Energy drives blast wave Given to new generation of CR

  10. Two escape routes from SNR – structure of CR spectrum Released when SNR disperses Escaped during Sedov expansion 10GeV 100GeV 1TeV 10TeV 100TeV Hydrogen/Helium knee at 640TeV? (ARGO-YBJ/LHAAASO) Spectral bend at ~200GeV (PAMELA, AMS) Bartoli et al 2015 Tomassetti (2012)

  11. Particle acceleration in radio galaxies Image Credit: X-ray: NASA/CXC/SAO; Optical: NASA/STScI; Radio: NSF/NRAO/AUI/VLA

  12. Quasar jet 4C74.26 Beamwidth: 15” Riley & Warner (1990) Erlund et al 2010 Erlund et al 2010 Erlund et al 2010 Araudo, Blundell & Bell (2015) Radio IR Flux density (Jy) optical X-ray Frequency Consistent with Weibel turbulence: Small scale, rapidly damped Turnover in IR/optical:~200 GeV electrons

  13. Weibel instability: counter-streaming beams Spitkovsky, 2008 1) Perturbed beam density 2) Magnetic field 3) Focus currents Problem: small scalelength

  14. Relativistic shocks are ~perpendicular In upstream rest frame In shock rest frame, G = 4 In shock rest frame, G = 16 Plasma flow at c/3 Plasma flow at 0.998 c CR penetrate upstream ~ one Larmor radius q Shock velocity = c/10 Perpendicular shock Even at shock velocity = c/10 CR have difficulty getting back from downstream CR density shock

  15. Perpendicular relativistic shocks Monte Carlo with fixed scattering downstream, no scattering upstream Shock In downstream rest frame (not shock frame) n/wg = 0 No energy gain Energy gain = 2.34 n/wg = 0.1 Energy gain = 4.44 n/wg = 1 Need n/wg>1 for reasonable energy gain Energy gain = 31.5 n/wg = 10

  16. Limitations of Weibel instability Well-recognised Lemoine & Pelettier (2010), Sironi, Spitkovsky & Arons (2013), Reville & Bell (2014) Imagine turbulence consisting of random cells of size s Larmor radius Each cell deflects through angle Characteristic scalelength Larmor radius

  17. Non-resonant hybrid (NRH) instability – can this help? Expands non-linearly, Condition for CR confinement: Disordered amplified magnetic field dominates initial field Maximum CR energy capable of exciting turbulence (assuming ~E-2.4CR spectrum) Turbulence can accelerate CR to higher energy

  18. Guideline energy scale at relativistic shocks Hillas energy Max energy to which CR are accelerated Max energy at which CR excite non-resonant turbulence CR energy are upstream values defined in shock/downstream rest frame Energy at which CR are injected

  19. Predictions • Historical SNR (Cas A, Tycho, Kepler, SN1006) accelerate to few 100TeV but may have accelerated to PeV in past • PeV acceleration occurs in very young SNR expanding at high velocity into dense pre-ejected wind • Sedov SNR accelerate to • Interiors of Sedov SNR contain unseen CR bubble • Relativistic shocks (eg jet termination shocks) accelerate to • Relativistic shocks do not accelerate UHECR (probably)

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