Magnetic-Field Amplification and Cosmic-Ray Acceleration in Turbulent MHD Shocks

1. Magnetic-Field Amplification and Cosmic-Ray Acceleration in Turbulent MHD Shocks Joe Giacalone and Randy Jokipii University of Arizona Aspen 2007

2. Galactic cosmic-rays and SNR’s • The power law, up to the “knee” at 1015 eV, is explained by diffusive shock acceleration at supernovae blast waves • Lagage and Cesarsky (1983) estimated the maximum energy to be less than 1014 eV • assuming Bohm diffusion and a hydrodynamic (parallel) shock. • It has been shown that a higher maximum energy is achieved for a quasi-perpendicular shock Aspen 2007

3. The importance of the magnetic-field angle • A SNR blast waves moves into a B with a preferred direction • The angle between B and shock normal varies • The physics of acceleration at parallel and perpendicular shocks is different Parallel shocks  slow Perpendicular shocks  fast (K┴ < K║) • for a given time interval, a perpendicular shock will yield a larger maximum energy than a parallel shock. Aspen 2007

4. Maximum EnergyAssumes Sedov solution for SNR blast wave Perpendicular Shock (Hard-sphere scattering) Bohm Diffusion Aspen 2007

5. There is no “injection” problem • Large scale turbulent magnetic field leads to “field-line random walk” • This enhanced the trapping of low-energy particles near the shock • Low-rigidity electrons are also efficiently accelerated Aspen 2007

6. CME – Interplanetary Space CME – Solar Corona Termination Shock (blunt) Supernova remnants Aspen 2007

7. Berezhko et al., 2003 • Berezhko et al. (2003) compared a model of shock acceleration of electrons (Ee ~ 100 TeV) including synchrotron losses and concluded that the observed fine-scale x-ray emissions could only result if the field were very strong (B > 100μG) Bamba et al, 2003 Aspen 2007

8. What enhances B near the shock? • Bell and Lucek (2001) proposed that a cosmic-ray current drives an instability (because of a JcrxB force) leading to a large magnetic-field amplification “There is no alternative process without ad hoc-assumptions in the literature, or a new one which we could reasonably imagine, that would amplify the MF in a collisionless shock without particle acceleration” (Berezhko et al., 2003) Aspen 2007

9. Is the physics of shock-accelerated particles and coupled hydromagnetic waves well understood? Self-consistent plasma simulations of a parallel shock The self-generated waves are generally weaker than expected from theory Wave growth rate depends on shock-normal angle – need to examine the effects of large-scale background fluctuations Theory (dashed line) Aspen 2007

10. Enhanced B downstream of a shock moving through a plasma containing density turbulence(without cosmic-ray excited waves!) Aspen 2007

11. New MHD Simulations of Strong Shocks Moving Through Turbulence Density 12Lc • Numerical simulation of a shock wave moving into a turbulent plasma • Solves the MHD equations for a fluid reflected off of a rigid wall • Shock moves from right to left • The upstream medium contains turbulent density fluctuations • log-normal statistics, Kolmogorov spectrum • The fluctuations do not suffer much numerical dissipation because they are continually injected at the upstream boundary. 8Lc 4Lc 0 Aspen 2007 0 2Lc 4Lc 6Lc

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13. Tycho seen at 3 different X-ray energies Aspen 2007

14. Note that Ellison and Blondin (2001) assume r > 4 (due to efficient particle acceleration). If this is the case, the distance above may be shorter. Aspen 2007

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19. Conclusions • New results from MHD simulations of shocks moving through a medium containing density fluctuations indicate that B is significantly amplified • For parameters typical of supernovae shocks B > 100 μG within a coherence scale of the shock • This can be understood in terms of the vortical/turbulent downstream flow forcing together and stretching B • This is a natural explanation of the enhanced B at SNRs without relying on cosmic-ray generated fluctuations Aspen 2007

20. Extra slides Aspen 2007

21. Simulation Art Aspen 2007

22. Is there another way to enhance B without relying on the cosmic rays to excite waves? • Ellison and Blondin pointed out that strong shocks that accelerate particles very efficieenty have higher compression rations which shirinks the region betgween forward and recerse shocks. Thus, material associated with the ejecta can penetragte near the forward shock (as in the Richtmeyer-Meshkov instability) • Balsara does something similar to us … Aspen 2007

23. Recent simulations including pre-existing waves Large 1D simulations of a parallel shock moving into a turbulent medium Transverse magnetic field Zooming in on the region near the shock reveals the existence of “SLAMS” → Ion density Ion-inertial length Ion-inertial length Aspen 2007