Numerical simulations of high Lundquist number relativistic magnetic reconnection

We present the results of two-dimensional and three-dimensional magnetohydrodynamical numerical simulations of relativistic magnetic reconnection, with particular emphasis on the dynamics of the plasma in a Petschek-type configuration with high Lundquist numbers, S � 10 5 10 8 . The numerical scheme adopted, allowing for unprecedented accuracy for this type of calculations, is based on high order finite volume and discontinuous Galerkin methods as recently proposed by Dumbser & Zanotti (2009). The possibility of producing high Lorentz factors is discussed, showing that Lorentz factors close to � 4 can be produced for a plasma parameter σm = 20. Moreover, we find that the Sweet-Parker layers are unstable, generating secondary magnetic islands, but only for S > Sc � 10 8 , much larger than what is reported in the Newtonian regime. Finally, the effects of a mildly anisotropic Ohm law are considered in a configuration with a guide magnetic field. Such effects produce only slightly faster reconnection rates and Lorentz factors of about 1% larger with respect to the perfectly isotropic Ohm law.

[1]  A. Klimas,et al.  A simple, analytical model of collisionless magnetic reconnection in a pair plasma , 2009 .

[2]  Miguel A. Aloy,et al.  THE MISSING LINK: MERGING NEUTRON STARS NATURALLY PRODUCE JET-LIKE STRUCTURES AND CAN POWER SHORT GAMMA-RAY BURSTS , 2011, 1101.4298.

[3]  H. C. Spruit,et al.  Efficient acceleration and radiation in Poynting flux powered GRB outflows , 2002, astro-ph/0202387.

[4]  Dmitri A. Uzdensky.  On the Axisymmetric Force-free Pulsar Magnetosphere , 2003 .

[5]  T. Yokoyama,et al.  Magnetic Reconnection Triggered by the Parker Instability in the Galaxy: Two-dimensional Numerical Magnetohydrodynamic Simulations and Application to the Origin of X-Ray Gas in the Galactic Halo , 2002, astro-ph/0209008.

[6]  T. Yokoyama,et al.  Two-dimensional Magnetohydrodynamic Simulations of Relativistic Magnetic Reconnection , 2006, astro-ph/0607285.

[7]  Christos G. Tsagas,et al.  Generalized Ohm's law for relativistic plasmas , 2007, 0711.3573.

[8]  C. Munz,et al.  Hyperbolic divergence cleaning for the MHD equations , 2002 .

[9]  R. Samtaney,et al.  Formation of plasmoid chains in magnetic reconnection. , 2009, Physical review letters.

[10]  Michael Dumbser,et al.  Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws , 2008, J. Comput. Phys..

[11]  Jaap J. W. van der Vegt,et al.  Space-Time Discontinuous Galerkin Method for the Compressible Navier-Stokes , 2006 .

[12]  A. Schekochihin,et al.  Fast magnetic reconnection in the plasmoid-dominated regime. , 2010, Physical review letters.

[13]  Michael Dumbser,et al.  A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes , 2008, J. Comput. Phys..

[14]  O. Zanotti,et al.  ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics , 2007, 0704.3206.

[15]  D. Uzdensky,et al.  Radiative properties of reconnection‐powered minijets in blazars , 2010, 1007.3994.

[16]  Gerhard Zumbusch,et al.  Finite element, discontinuous Galerkin, and finite difference evolution schemes in spacetime , 2009, 0901.0851.

[17]  S. Komissarov,et al.  On the properties of Alfvn waves in relativistic magnetohydrodynamics , 1997 .

[18]  J. V. D. Vegt,et al.  Space--time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows: I. general formulation , 2002 .

[19]  Rudolf A. Treumann,et al.  Relativistic Kinetic Reconnection as the Possible Source Mechanism for High Variability and Flat Spectra in Extragalactic Radio Sources , 2004 .

[20]  Maxim Lyutikov,et al.  Magnetar giant flares and afterglows as relativistic magnetized explosions , 2005 .

[21]  Blackman,et al.  Kinematics of relativistic magnetic reconnection. , 1994, Physical review letters.

[22]  Y. Lyubarsky.  On the relativistic magnetic reconnection , 2005 .

[23]  Magnetic reconnection at the termination shock in a striped pulsar wind , 2007 .

[24]  D. Uzdensky.  The Fast Collisionless Reconnection Condition and the Self-Organization of Solar Coronal Heating , 2007, 0707.1316.

[25]  S. Komissarov,et al.  Multi-dimensional Numerical Scheme for Resistive Relativistic MHD , 2007, 0708.0323.

[26]  D. Uzdensky,et al.  Reconnection in Marginally Collisionless Accretion Disk Coronae , 2008, 0804.4481.

[27]  Michael Hesse,et al.  RESISTIVE MAGNETOHYDRODYNAMIC SIMULATIONS OF RELATIVISTIC MAGNETIC RECONNECTION , 2010, 1005.4485.

[28]  A. A. Schekochihin,et al.  Instability of current sheets and formation of plasmoid chains , 2007 .

[29]  A. Klimas,et al.  RELATIVISTIC TWO-FLUID SIMULATIONS OF GUIDE FIELD MAGNETIC RECONNECTION , 2009, 0909.1955.

[30]  A. Bhattacharjee,et al.  Fast collisionless reconnection in electron-positron plasmas , 2006 .

[31]  M. Heyn,et al.  Relativistic unsteady Petschek-type model of magnetic reconnection , 2007 .

[32]  Oscar Reula,et al.  Beyond ideal MHD: towards a more realistic modelling of relativistic astrophysical plasmas , 2008, 0810.1838.

[33]  O. Skjaeraasen,et al.  The Sigma Problem of the Crab Pulsar Wind , 2003, astro-ph/0309573.

[34]  S. Osher,et al.  Uniformly high order accurate essentially non-oscillatory schemes, 111 , 1987 .

[35]  TWO-FLUID MAGNETOHYDRODYNAMIC SIMULATIONS OF RELATIVISTIC MAGNETIC RECONNECTION , 2009 .

[36]  Michael Hesse,et al.  Two-Fluid MHD Simulations of Relativistic Magnetic Reconnection , 2008 .

[37]  Luciano Rezzolla,et al.  Discontinuous Galerkin methods for general-relativistic hydrodynamics: formulation and application to spherically symmetric spacetimes , 2011, 1103.2426.

[38]  S. Komissarov,et al.  Close binary progenitors of gamma-ray bursts , 2009, 0908.0695.

[39]  T. Di Matteo,et al.  Magnetic reconnection: flares and coronal heating in active galactic nuclei , 1998, astro-ph/9805347.

[40]  G. Kowal,et al.  Fast magnetic reconnection and energetic particle acceleration , 2010, 1003.2637.

[41]  J. Bekenstein,et al.  New conservation laws in general-relativistic magnetohydrodynamics , 1978 .

[42]  Massachusetts Institute of Technology,et al.  Dynamics of Relativistic Reconnection , 2002, astro-ph/0210206.

[43]  Michael Dumbser,et al.  Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations , 2009, J. Comput. Phys..

[44]  Explosive reconnection in magnetars , 2003, astro-ph/0303384.

[45]  Andrei Gruzinov.  Power of an axisymmetric pulsar. , 2005, Physical review letters.