A team of astrophysicists from the Institute for Advanced Study and the Flatiron Institute has created the most detailed computer model yet of how matter falls into black holes. Their study, published in The Astrophysical Journal, is the first to calculate these flows in full general relativity and in the radiation-dominated regime without relying on shortcuts.
Lead author Lizhong Zhang explained, “This is the first time we’ve been able to see what happens when the most important physical processes in black hole accretion are included accurately. These systems are extremely nonlinear—any over-simplifying assumption can completely change the outcome. What’s most exciting is that our simulations now reproduce remarkably consistent behaviors across black hole systems seen in the sky, from ultraluminous X-ray sources to X-ray binaries. In a sense, we’ve managed to ‘observe’ these systems not through a telescope, but through a computer.”
The team ran a survey of radiation-dominated accretion flows across different mass accretion rates, two values of black hole spin, and varying magnetic field setups. Their models used a new algorithm that directly solves the radiation transport equation in general relativity, made possible by access to modern exascale supercomputers.
The results showed that when black holes accrete (or accumulate) matter at rates above the so-called Eddington limit, the flows form thick, radiation-pressure-supported disks that push out strong equatorial winds. In this regime, a narrow funnel-shaped photosphere near the center leads to very low radiative efficiency, meaning much of the energy is trapped rather than released as light.
The Eddington limit is the maximum luminosity an accreting black hole (or star) can sustain before radiation pressure pushes material away, halting further accretion. For black holes, it sets a theoretical cap on how fast they can grow.
For accretion near or below the Eddington limit, the structure depended on magnetic flux: with net vertical flux, the disk formed a thin, dense midplane layer surrounded by a magnetically dominated corona; without flux, the disk remained magnetically dominated throughout. None of the models reached the magnetically arrested disk state, but those with net flux and rapidly spinning black holes still produced powerful relativistic jets.
The study focused on stellar mass black holes, about ten times the mass of the Sun. These are harder to observe directly than supermassive black holes, which can be imaged, so researchers rely on spectra to understand them. Because stellar mass black holes evolve on timescales of minutes to hours, they are useful for studying how these systems change in real time. The team’s simulations matched well with observational data, including spectra from X-ray binaries and ultraluminous X-ray sources such as Cyg X-3 and SS433. They also suggested that their super-Eddington models might help explain the “little red dots” recently spotted by the James Webb Space Telescope.
The work was powered by two of the world’s fastest computers, AMD-powered Frontier at Oak Ridge National Laboratory and Intel-based Aurora at Argonne National Laboratory. These exascale machines can perform a quintillion operations per second, allowing the team to handle equations that were previously too complex. Christopher White designed the radiation transport algorithm, while Patrick Mullen implemented it in the AthenaK code optimized for exascale computing.
Looking ahead, the researchers plan to extend their approach to supermassive black holes, which shape the evolution of galaxies, and other types of black holes too. They aim to refine their models to capture how radiation interacts with matter under different conditions. Co-author James Stone summed up the achievement: “What makes this project unique is, on the one hand, the time and effort it has taken to develop the applied mathematics and software capable of modeling these complex systems, and, on the other hand, having a very large allocation on the world’s largest supercomputers to perform these calculations. Now the task is to understand all the science that is coming out of it.”
Source: Institute for Advanced Study, IOP Publishing
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