Structure and Scale of Cosmic Ray Modified Shocks

POSTER

Abstract

Astrophysical shocks, diffusively accelerating cosmic rays (CR) ought to develop CR precursors. The length of the precursor $L_{p}$ is believed to be set by the ratio of the CR mean free path $\lambda$ to the shock speed, $L_{p}\sim c\lambda/V_{sh}\sim cr_{g}/V_{sh}$, which is independent of the CR pressure $P_{c}$. However, the X-ray observations of supernova remnant shocks suggest that the precursor scale may be significantly shorter than $L_{p}$ which would question the above estimate unless the magnetic field is strongly amplified and the gyroradius $r_{g}$ is strongly reduced. We argue that while the CR pressure builds up ahead of the shock, the acceleration enters into a strongly nonlinear phase in which an acoustic instability, driven by the CR pressure gradient, dominates other instabilities (for $\beta < 1$ ). In this regime the precursor steepens into a strongly nonlinear front whose size scales with \emph{the CR pressure }as $L_{f}\sim L_{p}\cdot\left(L_{s}/L_{p}\right)^{2}\left(P_{c}/P_{g}\right)^{2 }$, where $L_{s}$ is the scale of the developed acoustic turbulence, and $P_{c}/P_{g}$ is the ratio of CR to gas pressure. Since $L_{s}\ll L_{p}$, the precursor scale reduction may be strong in the case of even a moderate gas heating by the CRs through the acoustic and (possibly also) the other instabilities driven by the CRs.

Authors

  • Patrick Diamond

    UCSD

  • Mikhail Malkov

    UCSD

  • Antony Valentini

    CITA, MIT, Caltech/JPL, Academia Sinica, Dong Hwa Univ., Soochow Univ., Nanticoke High School, UT, Maverick Systems Corp., RIS Corp., LSU, Shimadzu Corp., UNIRIB, ORAU/ORISE, Physics Division, Oak Ridge National Laboratory, Oak Ridge Associated Universities, Los Alamos National Laboratory, University of South Dakota, RIKEN BNL Research Center, University of Wisconsin-Milwaukee, Brown University, University of Maryland, Jet Propulsion Laboratory - California Institute of Technology, Center for Relativistic Astrophysics, Georgia Tech, University of Rochester, University of Idaho, Texas A\&M University, Universit\&#039;e Paris Diderot-Paris 7, Washington University in St. Louis, Harvard-Smithsonian Center for Astrophysics, University of California, Berkeley, Massachusetts Institute of Technology, Rockwell Collins Inc., Northwestern University, N IST, Indiana Unviersity, Harvard University, University of Notre Dame, Fachbereich Theoretische Physik, Institut fur Physik, Karl-Franzens-Universitat Graz, Austria, Instituto de Estructura de la Materia, CSIC, Spain, Physics Department, University of Wisconsin-Barron, Orion Foundation, Physics Dept, University of West Florida, Pensacola, Florida, 32514, TUNL, Duke University, James Madison University, University of New Mexico, Photonics CoE, Idaho State University, Pocatello, ID 83209, Los Alamos National Laboratory, Los Alamos, NM 87545, Argonne National Laboratory, University of Washington, National Institute of Standards and Technology, National Institute of Standards and Technology (and West Virginia University), NRAO, University of Florida, LLNL / NPS, LLNL, UC Berkeley, LLNL/NPS, Univerity of Washington, CNRS-IN2P3, Marseille, FR, CERN and King&#039;s College, London UK, Brookhaven National Laboratory, ICTP, Trieste, IT, Fermi National Accelerator Laboratory, University of Wisconsin Milwaukee, Princeton University, North Carolina Central U. (NCCU), Triangle Universities Nuclear Laboratory (TUNL), University of California, Riverside, NSCL/MSU, Triangle Universities Nuclear Laboratory, Duke University, University of North Carolina, Duke University, University of North Carolina at Chapel Hill, Triangle Universities Nuclear Laboratory, KVI Groningen, APS Director of Public Affairs, Perimeter Institute, Caltech, Rutgers, U. Tenn., ORNL, Stanford School of Medicine, Radiation Oncology and Molecular Imaging Program, Stanford Applied Physics Department, Stanford School of Medicine, Radiation Oncology, Boston University, BNL, Rutgers University, Purdue University, Penn. State University, UCSD, Lawrence Livermore National Laboratory, University of Richmond, University of Massachusetts-Lowell, Mississippi State University, University of Tennessee, Argonne National Lab, Florida State University, US Naval Academy, ANL, Univ. of Maryland, Univ. of Massachusetts (Lowell), Univ. of Tennessee, Univ. of Manchester, UK, NBI, Danmark, Mississippi State Univ., Physics Division, Argonne National Laboratory, Argonne, IL 60439, Mississippi State University, Mississippi State, MS 39762, UGC-DAE Consortium for Science Research, Kolkata, India, Department of Physics, University of Notre Dame, Notre Dame, IN 46556, San Jose State University, Pacific Northwest National Laboratory, University of Chicago, Fermilab, Program Director, US LHC Accelerator Research Program (LARP), Montana State University, Department of Astrophysical Sciences, Princeton University, School of Mathematics, University of Southampton, CCT, Louisiana State University, CSIC-IEEC Barcelona, TAPIR, California Institute of Technology, University of Texas at Brownsville, Royal Military College of Canada, California State University, Sacramento, Norfolk State University, Oak Ridge National Laboratory, Utah State University, Executive Producer \& Co-Creator of The Big Bang Theory, University of California, Los Angeles, Cyclotron Institute, Texas A\&M University, Hope College, NSCL, Augustana College, Clemson University