The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project (1904.04923v2)

Abstract: Recent developments in compact object astrophysics, especially the discovery of merging neutron stars by LIGO, the imaging of the black hole in M87 by the Event Horizon Telescope (EHT) and high precision astrometry of the Galactic Center at close to the event horizon scale by the GRAVITY experiment motivate the development of numerical source models that solve the equations of general relativistic magnetohydrodynamics (GRMHD). Here we compare GRMHD solutions for the evolution of a magnetized accretion flow where turbulence is promoted by the magnetorotational instability from a set of nine GRMHD codes: Athena++, BHAC, Cosmos++, ECHO, H-AMR, iharm3D, HARM-Noble, IllinoisGRMHD and KORAL. Agreement between the codes improves as resolution increases, as measured by a consistently applied, specially developed set of code performance metrics. We conclude that the community of GRMHD codes is mature, capable, and consistent on these test problems.

• The paper demonstrates that high-resolution GRMHD simulations yield consistent horizon fluxes and accretion rates across nine different codes.
• The paper shows that disk-averaged profiles converge only at higher resolutions, underlining the critical role of spatial detail in capturing accretion physics.
• The paper highlights variations in variability and jet disk interactions at lower resolutions, informing best practices for future astrophysical simulations.

Overview of The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project

The Event Horizon General Relativistic Magnetohydrodynamic (GRMHD) Code Comparison Project addresses the performance and consistency of GRMHD simulations that model the accretion flows near black hole event horizons, a problem of significant interest following discoveries such as the imaging of the black hole in M87 by the Event Horizon Telescope (EHT). This paper, authored by an extensive collaboration including the GRMHD community and the EHTC, comprises a comprehensive evaluation of nine GRMHD codes: Athena++, BHAC, Cosmos++, ECHO, H-AMR, iharm3D, HARM-Noble, IllinoisGRMHD, and KORAL.

Simulation Setup and Methodology

The authors employ a standard setup of radiatively inefficient accretion onto a spinning black hole, where turbulence is driven by the magnetorotational instability (MRI). The initial condition is a hydrodynamic torus threaded by a weak poloidal magnetic field in a Kerr spacetime. The simulation probed the behavior of these codes across low, medium, and high resolutions to evaluate performance metrics effectively. The simulations range from 96 to 192 grid cells cubed, with metrics indicating results' fidelity to high-resolution benchmarks.

Key Findings

1. Horizon-Penetrating Fluxes and Accretion Rates: The codes broadly agree at high resolutions, particularly in the accretion rate ($\dot{M}$), magnetic flux ($\Phi_{\text{BH}}$), angular momentum, and energy fluxes. However, notable deviations appear at lower resolutions, illustrating the importance of adequate spatial resolution in capturing key physical processes.
2. Disk-Averaged Profiles: Metrics like density, plasma beta, magnetic field strength, and velocities exhibit variations among the different codes at lower resolutions, but their convergence improves with higher resolution.
3. Variability and Power Spectral Densities: The codes agree on the general temporal behavior of derived light curves, indicative of realistic accretion-driven variability. There is notable consistency in predicting a red-noise spectrum in these light curves, with a power-law steepening that aligns with observational expectations.
4. Jet Disk Interactions: The codes differ in their handling of low-density regions around the polar axis, influenced by boundary treatments and applied floor models. While qualitative agreement on the jet shape and extent is observed, quantitative discrepancies remain.

Implications

The comparison showcases the maturity of GRMHD codes in reliably modeling black hole accretion physics when sufficient resolution is employed. It underlines critical areas like resolution and magnetic field dynamics where different methodological choices impact results, guiding the development of best practices for future simulations. Achieving consistent results across different computational frameworks is essential for credible multi-code validation of astrophysical phenomena observed by instruments like the EHT.

Conclusion

The paper successfully demonstrates that once adequately resolved, the various GRMHD codes produce consistent and reliable results for black hole accretion systems in the SANE regime. It supports the robustness of these codes in addressing complex astrophysical simulations, paving the way for more detailed studies into alternative accretion scenarios, such as the Magnetically Arrested Disk (MAD) state, and adaptations for non-ideal conditions like radiative and resistive MHD. This project marks a significant step in adopting collaborative code benchmarks that can aid in verifying simulation accuracy and reliability in ongoing astrophysical research.