General relativistic force-free electrodynamics with a discontinuous Galerkin-finite difference hybrid method (2404.01531v2)
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.
- Y. Lyubarsky, Fast radio bursts from reconnection in a magnetar magnetosphere, Astrophys. J. 897, 1 (2020), arXiv:2001.02007 [astro-ph.HE] .
- 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).
- A. M. Beloborodov, On the mechanism of hard X-ray emission from magnetars, Astrophys. J. 762, 13 (2013), arXiv:1201.0664 [astro-ph.HE] .
- A. Y. Chen and A. M. Beloborodov, Particle-in-cell simulations of the twisted magnetospheres of magnetars. i., The Astrophysical Journal 844, 133 (2017).
- T. Uchida, Theory of force-free electromagnetic fields. I. General theory, Phys. Rev. E 56, 2181 (1997).
- A. Gruzinov, Stability in force-free electrodynamics (1999), arXiv:astro-ph/9902288 [astro-ph] .
- 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).
- 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] .
- 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] .
- 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] .
- 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] .
- S. S. Komissarov, Electrodynamics of black hole magnetospheres, Mon. Not. Roy. Astron. Soc. 350, 407 (2004), arXiv:astro-ph/0402403 .
- A. Spitkovsky, Time-dependent force-free pulsar magnetospheres: Axisymmetric and oblique rotators, The Astrophysical Journal 648, L51 (2006).
- J. C. McKinney, Relativistic force-free electrodynamic simulations of neutron star magnetospheres, Mon. Not. Roy. Astron. Soc. 368, L30 (2006a), arXiv:astro-ph/0601411 .
- 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] .
- F. Carrasco and M. Shibata, Magnetosphere of an orbiting neutron star, Phys. Rev. D 101, 063017 (2020), arXiv:2001.04210 [astro-ph.HE] .
- C. Palenzuela, L. Lehner, and S. L. Liebling, Dual jets from binary black holes, Science 329, 927 (2010b), arXiv:1005.1067 [astro-ph.HE] .
- 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).
- 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] .
- 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] .
- 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).
- E. R. Most and A. A. Philippov, Reconnection-powered fast radio transients from coalescing neutron star binaries, Phys. Rev. Lett. 130, 245201 (2023a).
- 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] .
- 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] .
- 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] .
- J. Cho, Simulation of relativistic force-free magnetohydrodynamic turbulence, Astrophys. J. 621, 324 (2005), arXiv:astro-ph/0408318 .
- 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 .
- 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 .
- 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 .
- 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] .
- 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] .
- 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 .
- M. Lombart and G. Laibe, Grain growth for astrophysics with discontinuous Galerkin schemes, Monthly Notices of the Royal Astronomical Society 501, 4298 (2020).
- 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] .
- J. Petri, General-relativistic force-free pulsar magnetospheres, Mon. Not. Roy. Astron. Soc. 455, 3779 (2016), arXiv:1511.01337 [astro-ph.HE] .
- 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).
- J. Núñez-de la Rosa and C.-D. Munz, Hybrid DG/FV schemes for magnetohydrodynamics and relativistic hydrodynamics, Computer Physics Communications 222, 113 (2018).
- A. M. Rueda-Ramírez, W. Pazner, and G. J. Gassner, Subcell limiting strategies for discontinuous Galerkin spectral element methods, Computers & Fluids 247, 105627 (2022).
- L. Pareschi and G. Russo, Implicit–Explicit Runge–Kutta schemes and applications to hyperbolic systems with relaxation, Journal of Scientific Computing 25, 129 (2005).
- C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman, 1973).
- C. Palenzuela, Modelling magnetized neutron stars using resistive magnetohydrodynamics, Monthly Notices of the Royal Astronomical Society 431, 1853 (2013).
- A. Schoepe, D. Hilditch, and M. Bugner, Revisiting hyperbolicity of relativistic fluids, Phys. Rev. D 97, 123009 (2018), arXiv:1712.09837 [gr-qc] .
- 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] .
- C. R. Evans and J. F. Hawley, Simulation of magnetohydrodynamic flows: A constrained transport model, Astrophys. J. 332, 659 (1988).
- S. S. Komissarov, Multidimensional numerical scheme for resistive relativistic magnetohydrodynamics, Monthly Notices of the Royal Astronomical Society 382, 995 (2007).
- P. Goldreich and W. H. Julian, Pulsar electrodynamics, Astrophys. J. 157, 869 (1969).
- H. P. Pfeiffer and A. I. MacFadyen, Hyperbolicity of force-free electrodynamics, arXiv e-prints , arXiv:1307.7782 (2013), arXiv:1307.7782 [gr-qc] .
- 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.
- D. A. Kopriva, Implementing Spectral Methods for Partial Differential Equations (Springer Dordrecht, 2009).
- S. A. Teukolsky, Formulation of discontinuous Galerkin methods for relativistic astrophysics, Journal of Computational Physics 312, 333 (2016).
- S. A. Teukolsky, Short note on the mass matrix for Gauss–Lobatto grid points, Journal of Computational Physics 283, 408 (2015).
- B. Cockburn and C.-W. Shu, Runge–Kutta discontinuous Galerkin methods for convection-dominated problems, Journal of Scientific Computing 16, 173 (2001).
- 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).
- C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, Journal of Computational Physics 77, 439 (1988).
- C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, II, Journal of Computational Physics 83, 32 (1989).
- 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).
- V. Rusanov, The calculation of the interaction of non-stationary shock waves and obstacles, USSR Computational Mathematics and Mathematical Physics 1, 304 (1962).
- 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.
- 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).
- 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 .
- R. M. Wald, Black hole in a uniform magnetic field, Phys. Rev. D 10, 1680 (1974).
- 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 .
- A. R. King, J. P. Lasota, and W. Kundt, Black holes and magnetic fields, Phys. Rev. D 12, 3037 (1975).
- 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] .
- A. Nathanail and I. Contopoulos, Black hole magnetospheres, Astrophys. J. 788, 186 (2014), arXiv:1404.0549 [astro-ph.HE] .
- I. Contopoulos, D. Kazanas, and C. Fendt, The axisymmetric pulsar magnetosphere, Astrophys. J. 511, 351 (1999), arXiv:astro-ph/9903049 .
- S. S. Komissarov, Simulations of the axisymmetric magnetospheres of neutron stars, Monthly Notices of the Royal Astronomical Society 367, 19–31 (2006).
- F. Carrasco, C. Palenzuela, and O. Reula, Pulsar magnetospheres in general relativity, Phys. Rev. D 98, 023010 (2018), arXiv:1805.04123 [astro-ph.HE] .
- 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 .
- 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.