Particle Acceleration by Shocks Brian Reville, Klara Schure, Tony Bell with Brian Reville, Klara Schure, Gwenael Giacinti University of Oxford http://hubblesite.org/newscenter/archive/releases/2006/30/image/a/format/xlarge_web/

Cassiopeia A Radio (VLA) Infrared (Spitzer) NASA/JPL NASA/JPL Optical chandra.harvard.edu/photo/ 0237/0237_radio.jpg NASA/ESA/ Hubble Heritage (STScI/AURA)) NASA/CXC/MIT/UMass Amherst/ M.D.Stage et al. NASA/JPL NASA/JPL NASA/JPL-Caltech/ O Krause(Steward Obs) Optical (Hubble) X-ray (Chandra)

Historical shell supernova remnants Chandra observations Kepler 1604AD Tycho 1572AD SN1006 Cas A 1680AD HESS observation SNR RX J1713.7-3946 Aharonian et al Nature (2004) 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.

Cosmic Ray (CR) acceleration This talk: How do CR escape SNR? Can SNR accelerate CR to 1 PeV – and when? Importance of magnetic field amplification for the above Observations: TeV emission outside SNR For related discussion : Drury (2011) MNRAS 415 1807 Malkov, talk on Weds Reville, talk on Weds

Cosmic ray acceleration High velocity plasma Low velocity B2 B1 CR track Due to scattering, CR recrosses shock many times Gains energy at each crossing

CR acceleration time shock u ncr upstream L=D/ushock L~R/8 R Time needed for acceleration (Lagage & Cesarsky) D increases with CR energy L~R/8 Max CR energy set by t = R/ushock R Shock moves distance R = 8L during CR acceleration time t SNR CR precursor If so, CR never escape upstream shock Theory is simplistic

Maximum CR energy Conclusion: Need amplified magnetic field, Magnitude of the problem: CR Larmor radius: parsec Max CR energy set by t = R/ushock Bohm is minimum diffusion coefficient: Maximum CR energy: Young SNR: age=300yrs, B=3mG, ushock=5000 km s-1 Max CR energy = 1013eV Tycho Conclusion: Need amplified magnetic field, D varies with time, space, CR energy

Streaming CR excite instabilities L~R/8 CR precursor Streaming CR excite instabilities R SNR shock Shock CR streaming ahead of shock Excite instabilities Amplify magnetic field upstream downstream Amplify magnetic field Lucek & Bell (2000)

Conditions for PeV acceleration Equipartition magnetic field Maximum CR energy: 20PeV Theoretical saturation, matches observation (Vink 2006,2008) h = CR efficiency factor Maximum CR energy: 0.5 PeV (young SNR) Within error bars, but tough! Are Tycho, Kepler already too old and too slow?

Time for magnetic field amplification? Growth rate of fastest growing mode: CR electric current density: Upstream energy fluxes: Energy of CR carrying current Shortest growth time: CR efficiency/0.03 Density in cm-3 ushock in 10,000 km s-1 Cannot assume instability reaches saturation

The scalelength issue CR Larmor radius: Wavelength of fastest growing mode: for ushock=10,000 km s-1 and n =1 cm-3 Fortunately: instability grows non-linearly by spatial expansion Routes to large-scale structure with CR response included: 1) Filamentation (Brian Reville) 2) Include scattering (Klara Schure)

Numerical simulation of interacting physics Coupled questions: Does the instability have time to grow? Does the instability saturate? How large is the magnetic field? What is the maximum CR energy? Do CR escape upstream of the shock? Simulation code: MHD background plasma coupled to kinetic CR treatment through jxB Include shock, precursor & escape Self-consistent magnetic field generation CR respond to magnetic field (not diffusion model) 2D or 3D with momentum-dependent beyond-diffusion CR treatment Time-dependent CR model: isotropic drift off-diagonal part of stress tensor CR distribution defined in local fluid rest frame See Schure & Bell (2011) for instability analysis with stress tensor

Flow into reflecting wall (2D simulation) Parallel magnetic field 370rg (3104 cells) Flow at 0.1c 7.7rg (64 cells) shock wall Thermal pressure expansion CR free CR energy density B0 Magnetic energy density Perpendicular magnetic field

Section near shock Thermal pressure shock CR energy density Magnetic energy density 7.7rg 61rg

Momentum dependence Two populations at low CR energy Confined by magnetic field Freely escaping, excite instability High energy CR escape freely: Large mean free path Generated once low energy CR confined

Escape and confinement (t=2t0/3) 3D simulation 240rg 7.7rg shock Thermal pressure Confined CR escaping CR CR energy density Perpendicular magnetic field Perpendicular field Perpendicular slices

Instability growth CR only confined if enough CR escaped upstream CR energy density Perpendicular magnetic field Stationary box in upstream plasma Max growth rate Number of e-foldings: Number of CR passed through box (times charge) CR only confined if enough CR escaped upstream

How many e-foldings Condition for CR confinement: (Fixed current simulations 2004) Condition for CR confinement:

Instability growth Make a guess: c = 3 CR energy density Perpendicular magnetic field (matches simulation) Condition for CR confinement: Upstream energy fluxes: Mean energy of escaping CR: in 300 yrs Max CR energy a few times larger: in 10,000 km s-1 Make a guess: c = 3 in cm-3

Compare with saturation limit on CR energy Instability growth time (depends on CR escaping upstream) emax = cej c = 3 Instability saturation + acceleration time in 300 yrs in cm-3 in 10,000 km s-1 Suggests: PeV acceleration lies on limit for both growth times and saturation High energy CR escape upstream (with efficiency ~h almost by definition) Growth time limit Saturation limit

Evolution of max CR energy as limited by growth times assume c = 3 1987A after 6 years Cas A During Sedov phase Blast wave energy in 1044J

Conclusions Instability growth/saturation limits acceleration Some CR must escape/get ahead of main precursor to excite magnetic field Energy of escaping CR determined by Pre-Sedov SNR reach PeV, but only just Max CR energy drops during Sedov Young high velocity SNR into high density might exceed PeV