Groundbreaking simulations show how black holes glow bright

Surprisingly, some of the universe’s brightest objects are black holes. As scorching gas and dust flow around and into a black hole, they glow with fierce intensity across the light spectrum. Now, a team of computational astrophysicists has developed the most comprehensive simulations ever made of how black holes create these dazzling light shows.

Using supercomputers, the researchers calculated the behavior of material zipping around black holes. Unlike all previous studies that relied on simplifying approximations, the researchers utilized a full treatment of how light moves and interacts with matter within Albert Einstein’s general relativity.

Their results could help explain the hundreds of strange, faintly luminous objects known as little red dots (LRDs) spotted in the early universe by the James Webb Space Telescope. A leading theory, supported by the new results, proposes that these dots are black holes that are consuming material through a process called ‘super-Eddington accretion’ in the hearts of primordial galaxies.

The researchers present their groundbreaking simulations in a paper published December 3 in The Astrophysical Journal.

“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,” says Lizhong Zhang, lead author of the study and a research fellow at the Simons Foundation’s Flatiron Institute in New York City. “Any oversimplifying 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.”

Zhang is a joint postdoctoral research fellow in the Institute for Advanced Study (IAS) in Princeton, New Jersey, and the Flatiron Institute’s Center for Computational Astrophysics (CCA). Zhang co-authored the new study with collaborators at IAS, the CCA, Los Alamos National Laboratory and the University of Virginia. The study 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.

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 space-time. That space-time distortion shapes how the light created by the infalling material moves and interacts with the surrounding material.

Those full general relativistic equations are tough to solve, even for powerful computers. Previous simulations took shortcuts by simplifying the calculations of radiation. “Previous methods used approximations that treat radiation as a sort of fluid, which does not reflect its actual behavior,” Zhang explains.

By combining insights gained over decades of work, the team developed new algorithms that can directly solve the equations without sacrificing accuracy or requiring unreasonable amounts of computational power. “Ours is the only algorithm that exists at the moment that provides a solution by treating radiation as it really is in general relativity,” says Zhang.

Their paper addresses accretion onto stellar mass black holes, which are approximately 10 times the mass of the sun, though relative lightweights compared to Sagittarius A*, the supermassive black hole at the center of our galaxy, which has a mass more than 4 million times that of our sun.

Simulations are essential for understanding stellar mass 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 light spectrum obtained from observational data. This agreement between the simulation and observation is crucial, allowing for improved interpretations of the limited data available for these distant objects.

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 are capable of performing a quintillion operations per second.

Even with all that computational power, the researchers still needed clever code and complex mathematics to get accurate results. Christopher White of the CCA and Princeton University led the design of the radiation transport algorithm. Patrick Mullen of Los Alamos National Laboratory helmed the implementation of the algorithm in code optimized for exascale computing. The simulations were built on top of an algorithm developed by the CCA’s Yan-Fei Jiang that combines an angle-dependent algorithm that tracks the way radiation interacts and moves with a model of how fluid flows around a rotating sphere in the presence of a strong magnetic field. (Jiang’s work is now widely used across the astrophysics community for objects such as black holes and massive stars.)

In the future, the team behind the new simulations will work to determine if the model applies 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, as well as further investigate the identity of the James Webb Space Telescope’s little red dots. The simulations indicate that these objects may be producing more light than the Eddington limit — a balance between the gravitational force pulling material inward and the outward pressure of radiation released by the infalling matter, assuming a perfect spherical flow. In this case, the black holes are radiating more energy than can be balanced by the inward pull of gravity.

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.

“Now the task is to understand all the science that is coming out of it,” says James Stone, an IAS professor and co-author of the new paper.

About the Flatiron Institute

The Flatiron Institute is the research division of the Simons Foundation. The institute's mission is to advance scientific research through computational methods, including data analysis, theory, modeling and simulation. The institute's Center for Computational Astrophysics creates new computational frameworks that allow scientists to analyze big astronomical datasets and to understand complex, multi-scale physics in a cosmological context.