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Relativistic magnetohydrodynamics in dynamical spacetimes: Improved electromagnetic gauge condition for adaptive mesh refinement grids

Zachariah B. Etienne*, Vasileios Paschalidis, Yuk Tung Liu, and Stuart L. Shapiro†

  • Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

  • *zetienne@illinois.edu
  • †Also at Department of Astronomy and NCSA, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
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Phys. Rev. D 85, 024013 – Published 11 January, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.024013

Abstract

We recently developed a new general relativistic magnetohydrodynamic code with adaptive mesh refinement that evolves the electromagnetic (EM) vector potential Ai instead of the magnetic fields directly. Evolving Ai enables one to use any interpolation scheme on refinement level boundaries and still guarantee that the magnetic field remains divergenceless. As in classical EM, a gauge choice must be made when evolving Ai, and we chose a straightforward “algebraic” gauge condition to simplify the Ai evolution equation. However, magnetized black hole–neutron star (BHNS) simulations in this gauge exhibit unphysical behavior, including the spurious appearance of strong magnetic fields on refinement level boundaries. This spurious behavior is exacerbated when matter crosses refinement boundaries during tidal disruption of the neutron star. Applying Kreiss-Oliger dissipation to the evolution of the magnetic vector potential Ai slightly weakens this spurious magnetic effect, but with undesired consequences. We demonstrate via an eigenvalue analysis and a numerical study that zero-speed modes in the algebraic gauge, coupled with the frequency filtering that occurs on refinement level boundaries, are responsible for the creation of spurious magnetic fields. We show that the EM Lorenz gauge exhibits no zero-speed modes, and as a consequence, spurious magnetic effects are quickly propagated away, allowing for long-term, stable magnetized BHNS evolutions. Our study demonstrates how the EM gauge degree of freedom can be chosen to one’s advantage, and that for magnetized BHNS simulations the Lorenz gauge constitutes a major improvement over the algebraic gauge.

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Phys. Rev. D 85, 024013– Published 11 January, 2012
  • Received 12 October 2011
Article part of CHORUS

© 2012 American Physical Society

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