[Paper Review] Numerical simulations of black hole accretion flows

Agnieszka Janiuk, Kostas Sapountzis+2 more|arXiv (Cornell University)|May 29, 2018

Gamma-ray bursts and supernovae25 references3 citations

TL;DR

This paper presents a general relativistic magnetohydrodynamics (GRMHD) numerical simulation framework to model black hole accretion disks and jet formation in extreme astrophysical environments such as gamma-ray bursts (GRBs) and blazars. It demonstrates that magnetically driven winds from hyper-accreting disks, combined with neutrino processes and the Blandford–Znajek mechanism, can power relativistic jets and explain kilonova emission, with Lorentz factors reaching ~100 and X-ray emission from radioactive isotopes like $^{44}$Ti and $^{57}$Co.

ABSTRACT

We model the structure and evolution of black hole accretion disks, and their neighboring regions, using numerical simulations. The numerics is governed by the equations of general relativistic magneto-hydrodynamics (GRMHD). In particular, such disks and outflows can be found at the base of very energetic ultra-relativistic jets produced by cosmic explosions, so called gamma-ray bursts (GRBs). Another, more persistent type of the jet phenomena, are blazars, emitted from the centers of galaxies. Long-lasting, detailed computations are essential to properly determine the physics of these explosions, and confront the theoretical models with any potential observables. From the point of view of numerical methods and computational techniques, three ingredients need to be considered. First, the numerical scheme must work in a conservative manner, which is achieved by solving a set of non-linear equations at each time-step, to advance the conserved quantities from one time step to the next. Second, the efficiency of computations intrinsically depends on the code parallelization methods, which may use various techniques. Third, the analysis of results is possible via the post-processing of the computed time-dependent physical quantities, and visualization of the flow properties. This is done via implementing various packages and libraries that are standardized in the field of computational astrophysics and supported by community developers. In the present paper, we discuss the physical picture of the cosmic sources which are modeled using numerical framework. We also describe several technical issues, in the particular context of our own experience with the performance of the GRMHD code which we develop. We also present a suite of performance tests, done on the High-Performance Computer cluster (HPC) in the Center for Mathematical Modeling of the Warsaw University.

Motivation & Objective

• To model the structure and evolution of magnetized accretion disks around black holes in extreme environments such as gamma-ray bursts (GRBs) and blazars.
• To investigate the role of general relativistic magnetohydrodynamics (GRMHD) in driving ultra-relativistic jets from black hole engines.
• To examine the impact of microphysics—particularly nuclear reactions, equation of state (EOS), and neutrino transport—on disk structure and ejecta composition.
• To connect simulated disk properties with observable signatures, including X-ray emission from radioactive decay and kilonova light curves.
• To validate the model against multi-messenger observations, including GW170817 and GRB 130603B, to constrain disk-jet system properties.

Proposed method

• Numerical simulations are performed using a conservative finite-volume GRMHD code solving the full set of relativistic MHD equations in curved spacetime.
• The simulation framework incorporates a realistic equation of state (EOS) for hot, dense, and degenerate plasma relevant to GRB and kilonova environments.
• Nuclear reaction networks are implemented to compute the synthesis of r-process isotopes, including $^{44}$Ti, $^{57}$Co, and $^{65}$Zn, under non-equilibrium conditions.
• Post-processing tools are used to compute synthetic X-ray and optical emission from radioactive decay, enabling comparison with observations.
• The code is parallelized using MPI and optimized for high-performance computing (HPC) clusters, with performance benchmarks reported.
• Boundary conditions and numerical stability are carefully treated to ensure accurate long-term evolution of turbulent, magnetized accretion disks.

Experimental results

Research questions

• RQ1 How do GRMHD simulations of hyper-accreting disks reproduce the observed properties of short gamma-ray bursts and kilonovae?
• RQ2 What is the relative contribution of the Blandford–Znajek process versus neutrino-driven winds in powering relativistic jets in GRB engines?
• RQ3 To what extent does the microphysics—specifically the nuclear reaction network and EOS—determine the composition and energy budget of disk ejecta?
• RQ4 Can the simulated X-ray emission from radioactive isotopes match the observed flux in GRB afterglows, such as GRB 130603B?
• RQ5 How do the timescales of disk turbulence and jet variability relate to the observed short-timescale variability in blazar and GRB emission?

Key findings

• The simulations show that magnetically driven, low electron fraction ($Y_{\rm e}$) winds from the accretion disk can power kilonova emission, consistent with observations of GW170817.
• The ultimate Lorentz factors of the jets reach values on the order of 100, consistent with observations of ultra-relativistic GRB outflows.
• X-ray emission from radioactive isotopes such as $^{44}$Ti, $^{57}$Co, and $^{65}$Ga is predicted in the 12–80 keV energy band, matching the excess NIR flux observed in GRB 130603B.
• The Blandford–Znajek mechanism and neutrino processes are found to contribute comparably to jet power in GRB engines.
• The dynamical ejecta from the disk, with mass $M_{\rm ej} \sim 0.01 M_{\odot}$, can emit $10^{40}-10^{41}$ erg/s in optical and near-infrared bands over a timescale of ~1 week.
• The lightcurve of the electromagnetic counterpart to GW170817 is well reproduced by the model, with fast-fading, reddish emission consistent with r-process nucleosynthesis.