The Physics of Cosmic Ray Acceleration Tony Bell University of Oxford 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 with Brian Reville Klara Schure Gwenael Giacinti Anabella Araudo Katherine Blundell

Fractional energy gain Fraction of CR lost Shock acceleration energy spectrum Differential energy spectrum High velocity plasma Low velocity plasma B2B2 B1B1 shock Cosmic Ray At each shock crossing, shock velocity = u s Krymsky (1977), Axford Leer & Skadron (1977), Blandford & Ostriker (1978), Bell (1978)

Acceleration time limits CR energy shock upstream n cr u shock L Max CR energy For acceleration to high energy Bohm diffusion: mfp = Larmor radius Lagage & Cesarsky )Need large magnetic field 2)Structured on scale of CR Larmor radius

Electric currents carried by CR and thermal plasma Density of eV CR: ~ cm -3 Current density: j cr ~ Amp m -2 L R shock CR pre-cursor j cr j cr x B force acts on plasma to drive instabilities

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

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

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

Blast wave energy in J Sedov phase Cas A SN expansion into circumstellar wind wind mass loss in solar masses yr -1 wind vel in 10 km s -1 Already too slow shock vel in 30,000 km s -1 shock vel in 1000 km s -1

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

100GeV10TeV1TeV100TeV10GeV Escaped during Sedov expansion Released when SNR disperses Two escape routes from SNR – structure of CR spectrum Spectral bend at ~200GeV (PAMELA, AMS) Hydrogen/Helium knee at 640TeV? (ARGO-YBJ/LHAAASO) Tomassetti (2012) Bartoli et al 2015

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

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

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

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

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

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 Each cell deflects through angle Larmor radius Characteristic scalelength Larmor radius

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

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

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)