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General relativistic force-free electrodynamics with a discontinuous Galerkin-finite difference hybrid method (2404.01531v2)

Published 1 Apr 2024 in astro-ph.IM, astro-ph.HE, gr-qc, and physics.plasm-ph

Abstract: Relativistic plasmas around compact objects can sometimes be approximated as being force-free. In this limit, the plasma inertia is negligible and the overall dynamics is governed by global electric currents. We present a novel numerical approach for simulating such force-free plasmas, which allows for high accuracy in smooth regions as well as capturing dissipation in current sheets. Using a high-order accurate discontinuous Galerkin method augmented with a conservative finite-difference method, we demonstrate efficient global simulations of black hole and neutron star magnetospheres. In addition to a series of challenging test problems, we show that our approach can-depending on the physical properties of the system and the numerical implementation-be up to 10x more efficient than conventional simulations, with a speedup of 2-3x for most problems we consider in practice.

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References (70)
  1. Y. Lyubarsky, Fast radio bursts from reconnection in a magnetar magnetosphere, Astrophys. J.  897, 1 (2020), arXiv:2001.02007 [astro-ph.HE] .
  2. C. Thompson and R. C. Duncan, The soft gamma repeaters as very strongly magnetized neutron stars - 1. Radiative mechanism for outbursts, Mon. Not. Roy. Astron. Soc. 275, 255 (1995).
  3. A. M. Beloborodov, On the mechanism of hard X-ray emission from magnetars, Astrophys. J. 762, 13 (2013), arXiv:1201.0664 [astro-ph.HE] .
  4. A. Y. Chen and A. M. Beloborodov, Particle-in-cell simulations of the twisted magnetospheres of magnetars. i., The Astrophysical Journal 844, 133 (2017).
  5. T. Uchida, Theory of force-free electromagnetic fields. I. General theory, Phys. Rev. E 56, 2181 (1997).
  6. A. Gruzinov, Stability in force-free electrodynamics (1999), arXiv:astro-ph/9902288 [astro-ph] .
  7. A. Tchekhovskoy, A. Spitkovsky, and J. G. Li, Time-dependent 3D magnetohydrodynamic pulsar magnetospheres: Oblique rotators, Monthly Notices of the Royal Astronomical Society: Letters 435, L1–L5 (2013).
  8. A. Bransgrove, A. M. Beloborodov, and Y. Levin, A quake quenching the Vela pulsar, Astrophys. J.  897, 173 (2020), arXiv:2001.08658 [astro-ph.HE] .
  9. K. Parfrey, A. M. Beloborodov, and L. Hui, Dynamics of strongly twisted relativistic magnetospheres, Astrophys. J. 774, 92 (2013), arXiv:1306.4335 [astro-ph.HE] .
  10. A. Nathanail, E. R. Most, and L. Rezzolla, Gravitational collapse to a Kerr–Newman black hole, Mon. Not. Roy. Astron. Soc. 469, L31 (2017), arXiv:1703.03223 [astro-ph.HE] .
  11. E. R. Most, A. Nathanail, and L. Rezzolla, Electromagnetic emission from blitzars and its impact on non-repeating fast radio bursts, Astrophys. J. 864, 117 (2018), arXiv:1801.05705 [astro-ph.HE] .
  12. S. S. Komissarov, Electrodynamics of black hole magnetospheres, Mon. Not. Roy. Astron. Soc. 350, 407 (2004), arXiv:astro-ph/0402403 .
  13. A. Spitkovsky, Time-dependent force-free pulsar magnetospheres: Axisymmetric and oblique rotators, The Astrophysical Journal 648, L51 (2006).
  14. J. C. McKinney, Relativistic force-free electrodynamic simulations of neutron star magnetospheres, Mon. Not. Roy. Astron. Soc. 368, L30 (2006a), arXiv:astro-ph/0601411 .
  15. A. Y. Chen, Y. Yuan, and G. Vasilopoulos, A numerical model for the multiwavelength lightcurves of PSR J0030+0451, Astrophys. J. Lett. 893, L38 (2020), arXiv:2002.06104 [astro-ph.HE] .
  16. F. Carrasco and M. Shibata, Magnetosphere of an orbiting neutron star, Phys. Rev. D 101, 063017 (2020), arXiv:2001.04210 [astro-ph.HE] .
  17. C. Palenzuela, L. Lehner, and S. L. Liebling, Dual jets from binary black holes, Science 329, 927 (2010b), arXiv:1005.1067 [astro-ph.HE] .
  18. C. Palenzuela, L. Lehner, and S. Yoshida, Understanding possible electromagnetic counterparts to loud gravitational wave events: Binary black hole effects on electromagnetic fields, Phys. Rev. D 81, 084007 (2010c).
  19. F. Carrasco, M. Shibata, and O. Reula, Magnetospheres of black hole-neutron star binaries, Phys. Rev. D 104, 063004 (2021), 2106.09081 [astro-ph.HE] .
  20. E. R. Most and A. A. Philippov, Electromagnetic precursors to gravitational wave events: Numerical simulations of flaring in pre-merger binary neutron star magnetospheres, Astrophys. J. Lett. 893, L6 (2020), arXiv:2001.06037 [astro-ph.HE] .
  21. E. R. Most and A. A. Philippov, Electromagnetic precursor flares from the late inspiral of neutron star binaries, Monthly Notices of the Royal Astronomical Society 515, 2710 (2022).
  22. E. R. Most and A. A. Philippov, Reconnection-powered fast radio transients from coalescing neutron star binaries, Phys. Rev. Lett. 130, 245201 (2023a).
  23. E. R. Most and A. A. Philippov, Electromagnetic precursors to black hole–neutron star gravitational wave events: Flares and reconnection-powered fast radio transients from the late inspiral, Astrophys. J. Lett. 956, L33 (2023b), arXiv:2309.04271 [astro-ph.HE] .
  24. C. Kalapotharakos and I. Contopoulos, Three-dimensional numerical simulations of the pulsar magentoshere: Preliminary results, Astron. Astrophys. 496, 495 (2009), arXiv:0811.2863 [astro-ph] .
  25. F. Carrasco and O. Reula, Novel scheme for simulating the force-free equations: Boundary conditions and the evolution of solutions towards stationarity, Phys. Rev. D 96, 063006 (2017), arXiv:1703.10241 [gr-qc] .
  26. J. Cho, Simulation of relativistic force-free magnetohydrodynamic turbulence, Astrophys. J. 621, 324 (2005), arXiv:astro-ph/0408318 .
  27. E. Asano, T. Uchida, and R. Matsumoto, Time evolution of relativistic force-free fields connecting a neutron star and its disk, Publ. Astron. Soc. Jap. 57, 409 (2005), arXiv:astro-ph/0502371 .
  28. J. C. McKinney, General relativistic force-free electrodynamics: a new code and applications to black hole magnetospheres, Mon. Not. Roy. Astron. Soc. 367, 1797 (2006b), arXiv:astro-ph/0601410 .
  29. C. Yu, A high-order WENO-based staggered Godunov-type scheme with constrained transport for force-free electrodynamics, Monthly Notices of the Royal Astronomical Society 411, 2461 (2011), https://academic.oup.com/mnras/article-pdf/411/4/2461/3050165/mnras0411-2461.pdf .
  30. K. Parfrey, A. M. Beloborodov, and L. Hui, Introducing PHAEDRA: A new spectral code for simulations of relativistic magnetospheres, Mon. Not. Roy. Astron. Soc. 423, 1416 (2012), 1110.6669 [astro-ph.HE] .
  31. J. Petri, The pulsar force-free magnetosphere linked to its striped wind: Time-dependent pseudo-spectral simulations, Mon. Not. Roy. Astron. Soc. 424, 605 (2012), arXiv:1205.0889 [astro-ph.HE] .
  32. G. Cao, L. Zhang, and S. Sun, Spectral simulations of an axisymmetric force-free pulsar magnetosphere, Monthly Notices of the Royal Astronomical Society 455, 4267 (2015), https://academic.oup.com/mnras/article-pdf/455/4/4267/4094642/stv2577.pdf .
  33. M. Lombart and G. Laibe, Grain growth for astrophysics with discontinuous Galerkin schemes, Monthly Notices of the Royal Astronomical Society 501, 4298 (2020).
  34. J. Pétri, General-relativistic monopole magnetosphere of neutron stars: a pseudo-spectral discontinuous Galerkin approach, Mon. Not. Roy. Astron. Soc. 447, 3170 (2015), arXiv:1412.3601 [astro-ph.HE] .
  35. J. Petri, General-relativistic force-free pulsar magnetospheres, Mon. Not. Roy. Astron. Soc. 455, 3779 (2016), arXiv:1511.01337 [astro-ph.HE] .
  36. F. Vilar, A posteriori correction of high-order discontinuous Galerkin scheme through subcell finite volume formulation and flux reconstruction, Journal of Computational Physics 387, 245 (2019).
  37. J. Núñez-de la Rosa and C.-D. Munz, Hybrid DG/FV schemes for magnetohydrodynamics and relativistic hydrodynamics, Computer Physics Communications 222, 113 (2018).
  38. A. M. Rueda-Ramírez, W. Pazner, and G. J. Gassner, Subcell limiting strategies for discontinuous Galerkin spectral element methods, Computers & Fluids 247, 105627 (2022).
  39. L. Pareschi and G. Russo, Implicit–Explicit Runge–Kutta schemes and applications to hyperbolic systems with relaxation, Journal of Scientific Computing 25, 129 (2005).
  40. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman, 1973).
  41. C. Palenzuela, Modelling magnetized neutron stars using resistive magnetohydrodynamics, Monthly Notices of the Royal Astronomical Society 431, 1853 (2013).
  42. A. Schoepe, D. Hilditch, and M. Bugner, Revisiting hyperbolicity of relativistic fluids, Phys. Rev. D 97, 123009 (2018), arXiv:1712.09837 [gr-qc] .
  43. D. Hilditch and A. Schoepe, Hyperbolicity of divergence cleaning and vector potential formulations of general relativistic magnetohydrodynamics, Phys. Rev. D 99, 104034 (2019), arXiv:1812.03485 [gr-qc] .
  44. C. R. Evans and J. F. Hawley, Simulation of magnetohydrodynamic flows: A constrained transport model, Astrophys. J. 332, 659 (1988).
  45. S. S. Komissarov, Multidimensional numerical scheme for resistive relativistic magnetohydrodynamics, Monthly Notices of the Royal Astronomical Society 382, 995 (2007).
  46. P. Goldreich and W. H. Julian, Pulsar electrodynamics, Astrophys. J. 157, 869 (1969).
  47. H. P. Pfeiffer and A. I. MacFadyen, Hyperbolicity of force-free electrodynamics, arXiv e-prints , arXiv:1307.7782 (2013), arXiv:1307.7782 [gr-qc] .
  48. V. Paschalidis and S. L. Shapiro, A new scheme for matching general relativistic ideal magnetohydrodynamics to its force-free limit, Physical Review D 88, 104031 (2013), publisher: American Physical Society.
  49. D. A. Kopriva, Implementing Spectral Methods for Partial Differential Equations (Springer Dordrecht, 2009).
  50. S. A. Teukolsky, Formulation of discontinuous Galerkin methods for relativistic astrophysics, Journal of Computational Physics 312, 333 (2016).
  51. S. A. Teukolsky, Short note on the mass matrix for Gauss–Lobatto grid points, Journal of Computational Physics 283, 408 (2015).
  52. B. Cockburn and C.-W. Shu, Runge–Kutta discontinuous Galerkin methods for convection-dominated problems, Journal of Scientific Computing 16, 173 (2001).
  53. E. Hairer, S. Nørsett, and G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Solving Ordinary Differential Equations II: Stiff and Differential-algebraic Problems (Springer, 1993).
  54. C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, Journal of Computational Physics 77, 439 (1988).
  55. C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, II, Journal of Computational Physics 83, 32 (1989).
  56. E. R. Most, L. J. Papenfort, and L. Rezzolla, Beyond second-order convergence in simulations of magnetized binary neutron stars with realistic microphysics, Monthly Notices of the Royal Astronomical Society 490, 3588–3600 (2019).
  57. V. Rusanov, The calculation of the interaction of non-stationary shock waves and obstacles, USSR Computational Mathematics and Mathematical Physics 1, 304 (1962).
  58. T. Nonomura and K. Fujii, Robust explicit formulation of weighted compact nonlinear scheme, Computers & Fluids 85, 8 (2013), international Workshop on Future of CFD and Aerospace Sciences.
  59. Y. Chen, G. Tóth, and T. I. Gombosi, A fifth-order finite difference scheme for hyperbolic equations on block-adaptive curvilinear grids, Journal of Computational Physics 305, 604 (2016).
  60. P.-O. Persson and J. Peraire, Sub-cell shock capturing for discontinuous Galerkin methods, in 44th AIAA Aerospace Sciences Meeting and Exhibit, https://arc.aiaa.org/doi/pdf/10.2514/6.2006-112 .
  61. R. M. Wald, Black hole in a uniform magnetic field, Phys. Rev. D 10, 1680 (1974).
  62. S. S. Komissarov and J. C. McKinney, Meissner effect and Blandford-Znajek mechanism in conductive black hole magnetospheres, Mon. Not. Roy. Astron. Soc. 377, L49 (2007), arXiv:astro-ph/0702269 .
  63. A. R. King, J. P. Lasota, and W. Kundt, Black holes and magnetic fields, Phys. Rev. D 12, 3037 (1975).
  64. K. Parfrey, A. Philippov, and B. Cerutti, First-principles plasma simulations of black-hole jet launching, Phys. Rev. Lett. 122, 035101 (2019), arXiv:1810.03613 [astro-ph.HE] .
  65. A. Nathanail and I. Contopoulos, Black hole magnetospheres, Astrophys. J. 788, 186 (2014), arXiv:1404.0549 [astro-ph.HE] .
  66. I. Contopoulos, D. Kazanas, and C. Fendt, The axisymmetric pulsar magnetosphere, Astrophys. J. 511, 351 (1999), arXiv:astro-ph/9903049 .
  67. S. S. Komissarov, Simulations of the axisymmetric magnetospheres of neutron stars, Monthly Notices of the Royal Astronomical Society 367, 19–31 (2006).
  68. F. Carrasco, C. Palenzuela, and O. Reula, Pulsar magnetospheres in general relativity, Phys. Rev. D 98, 023010 (2018), arXiv:1805.04123 [astro-ph.HE] .
  69. P. Grete, F. W. Glines, and B. W. O’Shea, K-Athena: a performance portable structured grid finite volume magnetohydrodynamics code, IEEE Transactions on Parallel and Distributed Systems 32, 85 (2021), arXiv:1905.04341 .
  70. B. Szilágyi, Key elements of robustness in binary black hole evolutions using spectral methods, International Journal of Modern Physics D 23, 1430014 (2014), publisher: World Scientific Publishing Co.
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