Building on decades of effort, a team of computational astrophysicists has achieved a major milestone: developing the most comprehensive model to date of luminous black hole accretion. Leveraging the world's most powerful supercomputers, the researchers have, for the first time, calculated the flow of matter into black holes in full general relativity and in the radiation-dominated regime without using simplifying approximations.
The work, published today in The Astrophysical Journal, was led by researchers from the Institute for Advanced Study and the Flatiron Institute, Center for Computational Astrophysics. It is the first in a series of papers that will present the team's novel computational approach and its applications to several classes of black hole systems.
"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," stated the study's lead author, Lizhong Zhang . Zhang is a joint postdoctoral research fellow in the Institute for Advanced Study's School of Natural Sciences and the Flatiron Institute's Center for Computational Astrophysics, having initiated the project during his first year at IAS (2023–24) before continuing it at Flatiron.
Due to their extreme gravity, no model of black holes would be considered complete without the incorporation of Einstein's theory of general relativity, which describes how the most massive bodies distort the fabric of spacetime. Moreover, when large amounts of matter accrete onto a black hole, a full treatment of how the radiation (light) released moves through that curved spacetime and interacts with surrounding gas is also crucial. However, previous simulations have not been able to take into account these full mathematical complexities. Just as a physics student learns by working with simplified or "toy" models that capture only a subset of the real world's variables, earlier efforts to simulate radiation flows around black holes took necessary shortcuts to simplify the problem.
"Previous methods used approximations that treat radiation as a sort of fluid, which does not reflect its actual behavior," explained Zhang.
Those previous approximations were necessary because the full equations are extremely complex and computationally demanding. But, through joining together insights gained over decades of work, the team developed new algorithms that directly solve them, without approximations. "Ours is the only algorithm that exists at the moment that provides a solution by treating radiation as it really is in general relativity," he added.
Their paper specifically addresses accretion onto stellar mass black holes, which are approximately 10 times the mass of the Sun—relative lightweights compared to Sgr A*, the supermassive black hole at the center of our galaxy. Simulations are essential for understanding such black holes. While high-resolution images have been produced of supermassive black holes, those with stellar mass cannot be observed in the same way, appearing only as pinpoints of light. Instead, researchers must convert the light into a spectrum, which provides the data to map the distribution of energy around a black hole. Compared with supermassive black holes, which evolve over years or even centuries, stellar mass black holes change on human timescales of minutes to hours, making them ideal for studying the evolution of these systems in real time.
Through their simulations, the scholars captured how matter behaves as it spirals toward stellar mass black holes, forming turbulent, radiation-dominated disks, launching powerful winds, and sometimes even producing powerful jets. The team found that their model fit remarkably well with the spectrum obtained from observational data. This agreement between the simulation and observation is crucial, allowing for stronger interpretations of the limited data available for these distant objects.
The Institute for Advanced Study has a long-standing tradition of pioneering computer modeling of complex systems, which has proven vital to the advancement of human knowledge. One early example is the Institute's Electronic Computer Project , led by founding Professor (1933–55) John von Neumann , which provided insight into a variety of fields including fluid dynamics, climate science, and nuclear physics. Building on this legacy, Zhang and his research team were granted access to two of the world's most powerful supercomputers, Frontier and Aurora, housed at Oak Ridge National Laboratory and Argonne National Laboratory, respectively, to model black hole accretion. These "exascale" computers, capable of performing a quintillion operations per second, can occupy thousands of square feet—evoking the room-filling scale of the earliest computers.
To realize the potential of these massive computing resources, the team required complex mathematics and code equal to the task. The team's success in this regard was enabled by Christopher White of the Flatiron Institute and Princeton University, who led the design of the radiation transport algorithm, and Patrick Mullen , Member (2021–22) in the School of Natural Sciences, now based at Los Alamos National Laboratory, who led the implementation of the algorithm in the AthenaK code which is optimized for exascale computing.
In the future, the team will work to determine if their model is applicable to all types of black holes. In addition to stellar mass black holes, their simulations may enhance understanding of supermassive black holes, which drive the evolution of galaxies. The team will continue to evolve its approach to account for the different ways radiation interacts with matter across a wide range of temperatures and densities.
"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," explained James Stone , Professor in the Institute for Advanced Study's School of Natural Sciences and paper co-author. "Now the task is to understand all the science that is coming out of it."
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The Institute for Advanced Study has served as one of the leading independent centers for theoretical research and intellectual inquiry since its establishment in 1930, advancing the frontiers of knowledge across the sciences and humanities. From founding IAS Faculty Albert Einstein, Erwin Panofsky, and John von Neumann to influential figures Emmy Noether, George Kennan, and J. Robert Oppenheimer to the foremost thinkers of the present, IAS is dedicated to enabling independent inquiry and fundamental discovery.
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