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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 Shock acceleration energy spectrum Krymsky (1977), Axford Leer & Skadron (1977), Blandford & Ostriker (1978), Bell (1978) B1 Cosmic Ray B2 shock Low velocity High velocity plasma plasma At each shock crossing, shock velocity = u s Fractional energy gain Fraction of CR lost u n s n c us c Differential energy spectrum N ( ) 2 Acceleration time limits CR energy shock ushock ncr upstream L rg For acceleration to high energy Bohm diffusion: mfp = Larmor radius Max CR energy u shock E 13 3 10 1 eV 5000 km s 2 B t D 3G 300 yr DBohm Lagage & Cesarsky 1983 1) Need large magnetic field 2) Structured on scale of CR Larmor radius 1 Electric currents carried by CR and thermal plasma R jcr L CR pre-cursor Density of 1015eV CR: ~10-12 cm-3 Current density: jcr ~ 10-18 Amp m-2 jcrxB force acts on plasma to drive instabilities Non-resonant hybrid (NRH) instability B jxB jxB Bell, MNRAS 353, 550 (2004) CR current jxB expands loops stretches field lines more B more jxB Cavity/wall structure Historical shell supernova remnants (Vink & Laming, 2003; Völk, Berezhko, Ksenofontov, 2005) Tycho 1572AD Kepler 1604AD SN1006 Cas A 1680AD 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. Maximum CR energy: need time to amplify magnetic field Max instability growth rate max jCR 1 2 0 SNR For magnetic field amplification need max shock X dt 5 CR precursor CR not confined until CR electric charge passed upstream QCR jCR dt X Cm-2 Shock upstream precursor downstream Maximum CR energy: need time to amplify magnetic field CR 230 ne1/ 2 u72 Rpc TeV Cas A u7 0.6, R pc 2, ne 1 CR 160 TeV Already too slow Sedov phase 1/ 3 1/ 6 4 / 3 CR 20 E44 ne u6 TeV shock vel in 1000 km s-1 Blast wave energy in 1044J SN expansion into circumstellar wind 7u wind mass loss in 10-5 solar masses yr-1 2 30 M 5 PeV u4 shock vel in 30,000 km s-1 wind vel in 10 km s-1 CR need to escape efficiently into ISM 90% of CR energy confined with 400 u74 / 3 TeV Low energy CR cool adiabatically as SNR expands Energy drives blast wave Given to new generation of CR Etotal 0.05 ln max min 4R03 0u02 3 10% of CR energy escapes with escape 400 u74 / 3 TeV Two escape routes from SNR – structure of CR spectrum Released when SNR disperses Escaped during Sedov expansion CR ,max 230 ne1/ 2 u72 Rpc TeV 10GeV 100GeV 1TeV 10TeV 100TeV Spectral bend at ~200GeV (PAMELA, AMS) Tomassetti (2012) Hydrogen/Helium knee at 640TeV? (ARGO-YBJ/LHAAASO) Bartoli et al 2015 Particle acceleration in radio galaxies Image Credit: X-ray: NASA/CXC/SAO; Optical: NASA/STScI; Radio: NSF/NRAO/AUI/VLA Quasar jet 4C74.26 Beamwidth: 15” Flux density (Jy) Riley & Warner (1990) Erlund et al 2010 Erlund et et al al2010 Erlund 2010 Araudo, Blundell & Bell (2015) Radio IR optical X-ray Frequency Turnover in IR/optical:~200 GeV electrons Consistent with Weibel turbulence: Small scale, rapidly damped Weibel instability: counter-streaming beams Spitkovsky, 2008 1) Perturbed beam density 2) Magnetic field Problem: small scalelength n 7 s 2 10 -4 -3 pi 10 cm c 3) Focus currents 1/ 2 m Relativistic shocks are ~perpendicular In upstream rest frame In shock rest frame, G = 4 u shock c 1 G 2 In shock rest frame, G = 16 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 shock Plasma flow at c/3 Perpendicular relativistic shocks Shock Monte Carlo with fixed scattering downstream, no scattering upstream In downstream rest frame (not shock frame) n/g = 0 No energy gain Energy gain = 2.34 n/g = 0.1 Energy gain = 4.44 n/g = 1 Need n/g >1 for reasonable energy gain Energy gain = 31.5 n/g = 10 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 Characteristic scalelength s ( s rg ) s rg Larmor radius n s 1 g rg n s 2 107 -4 -3 pi 10 cm c 1 Larmor radius 1/ 2 m E B 3.3 1019 m rg EeV G Non-resonant hybrid (NRH) instability – can this help? Expands non-linearly, 1 E Bamplified 3 1011 m s TeV 100 G max Condition for CR confinement: max dt 5 1 2 j 0 Disordered amplified magnetic field dominates initial field Maximum CR energy capable of exciting turbulence (assuming ~E-2.4 CR spectrum) ENRH n 9/ 4 Gshock 4 -3 10 cm 5/ 4 B0 G 5 / 2 700 GeV Turbulence can accelerate CR to higher energy Emax n 5/ 2 Gshock 4 -3 10 cm 3/ 2 3 B0 100 TeV G Guideline energy scale at relativistic shocks Hillas energy R B0 EeV EHillas cBR kpc G Max energy to which CR are accelerated CR energy Emax n 5/ 2 Gshock 4 -3 10 cm 3/ 2 3 B0 100 TeV G Max energy at which CR excite non-resonant turbulence ENRH n 9/ 4 Gshock 4 -3 10 cm 5/ 4 B0 G 5 / 2 700 GeV n & B0 are upstream values defined in shock/downstream rest frame Energy at which CR are injected E0 Gshock GeV Predictions • Historical SNR (Cas A, Tycho, Kepler, SN1006) accelerate to few 100TeV Emax ne1/ 2 u72 Rpc 200 TeV 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 1/ 3 1/ 6 4 / 3 Enon rel E44 ne u6 20 TeV • Interiors of Sedov SNR contain unseen CR bubble • Relativistic shocks (eg jet termination shocks) accelerate to Erel • n 5/ 2 Gshock 4 -3 10 cm 3/ 2 3 B0 100 TeV G Relativistic shocks do not accelerate UHECR (probably)