The improved estimates will enable scientists to calculate the fundamental properties of the universe more accurately, the astrophysicists reported March 17, 2023, in the Proceedings of the National Academy of Sciences.

“It’s such a simple thing; that’s the beauty of this,” says study co-author Francisco Villaescusa-Navarro, a research scientist at the Flatiron Institute’s Center for Computational Astrophysics (CCA) in New York City. “Even though it’s so simple, nobody before found this term. People have been working on this for decades, and still they were not able to find this.”

The work was led by Digvijay Wadekar of the Institute for Advanced Study in Princeton, New Jersey, along with researchers from the CCA, Princeton University, Cornell University and the Center for Astrophysics | Harvard & Smithsonian.

Understanding the universe requires knowing where and how much stuff there is. Galaxy clusters are the most massive objects in the universe: A single cluster can contain anything from hundreds to thousands of galaxies, along with plasma, hot gas and dark matter. The cluster’s gravity holds these components together. Understanding such galaxy clusters is crucial to pinning down the origin and continuing evolution of the universe.

Perhaps the most crucial quantity determining the properties of a galaxy cluster is its total mass. But measuring this quantity is difficult — galaxies cannot be ‘weighed’ by placing them on a scale. The problem is further complicated because the dark matter that makes up much of a cluster’s mass is invisible. Instead, scientists deduce the mass of a cluster from other observable quantities.

In the early 1970s, Rashid Sunyaev, current distinguished visiting professor at the Institute for Advanced Study’s School of Natural Sciences, and his collaborator Yakov B. Zel’dovich developed a new way to estimate galaxy cluster masses. Their method relies on the fact that as gravity squashes matter together, the matter’s electrons push back. That electron pressure alters how the electrons interact with particles of light called photons. As photons left over from the Big Bang’s afterglow hit the squeezed material, the interaction creates new photons. The properties of those photons depend on how strongly gravity is compressing the material, which in turn depends on the galaxy cluster’s heft. By measuring the photons, astrophysicists can estimate the cluster’s mass.

However, this ‘integrated electron pressure’ is not a perfect proxy for mass, because the changes in the photon properties vary depending on the galaxy cluster. Wadekar and his colleagues thought an artificial intelligence tool called ‘symbolic regression’ might find a better approach. The tool essentially tries out different combinations of mathematical operators — such as addition and subtraction — with various variables, to see what equation best matches the data.

Wadekar and his collaborators ‘fed’ their AI program a state-of-the-art universe simulation containing many galaxy clusters. Next, their program, written by CCA research fellow Miles Cranmer, searched for and identified additional variables that might make the mass estimates more accurate.

AI is useful for identifying new parameter combinations that human analysts might overlook. For example, while it is easy for human analysts to identify two significant parameters in a dataset, AI can better parse through high volumes, often revealing unexpected influencing factors.

“Right now, a lot of the machine-learning community focuses on deep neural networks,” Wadekar explained. “These are very powerful, but the drawback is that they are almost like a black box. We cannot understand what goes on in them. In physics, if something is giving good results, we want to know why it is doing so. Symbolic regression is beneficial because it searches a given dataset and generates simple mathematical expressions in the form of simple equations that you can understand. It provides an easily interpretable model.”

The researchers’ symbolic regression program handed them a new equation, which was able to better predict the mass of the galaxy cluster by adding a single new term to the existing equation. Wadekar and his collaborators then worked backward from this AI-generated equation and found a physical explanation. They realized that gas concentration correlates with the regions of galaxy clusters where mass inferences are less reliable, such as the cores of galaxies where supermassive black holes lurk. Their new equation improved mass inferences by downplaying the importance of those complex cores in the calculations. In a sense, the galaxy cluster is like a spherical doughnut. The new equation extracts the jelly at the center of the doughnut that can introduce larger errors, and instead concentrates on the doughy outskirts for more reliable mass inferences.

The researchers tested the AI-discovered equation on thousands of simulated universes from the CCA’s CAMELS suite. They found that the equation reduced the variability in galaxy cluster mass estimates by around 20 to 30 percent for large clusters compared with the currently used equation.

The new equation can provide observational astronomers engaged in upcoming galaxy cluster surveys with better insights into the mass of the objects they observe. “There are quite a few surveys targeting galaxy clusters [that] are planned in the near future,” Wadekar noted. “Examples include the Simons Observatory, the Stage 4 CMB experiment and an X-ray survey called eROSITA. The new equations can help us in maximizing the scientific return from these surveys.”

Wadekar also hopes that this publication will be just the tip of the iceberg when it comes to using symbolic regression in astrophysics. “We think that symbolic regression is highly applicable to answering many astrophysical questions,” he said. “In a lot of cases in astronomy, people make a linear fit between two parameters and ignore everything else. But nowadays, with these tools, you can go further. Symbolic regression and other artificial intelligence tools can help us go beyond existing two-parameter power laws in a variety of different ways, ranging from investigating small astrophysical systems like exoplanets, to galaxy clusters, the biggest things in the universe.”

Nuclear astrophysics research has shown elements including and heavier than carbon in the universe are produced in stars. But the first stars, stars born soon after the Big Bang, did not contain such heavy elements, which astronomers call ‘metals’. The next generation of stars contained only a small amount of heavy elements produced by the first stars. To understand the universe in its infancy, it requires researchers to study these metal-poor stars.

Luckily, these second-generation metal-poor stars are observed in our Milky Way Galaxy, and have been studied by a team of Affiliate Members of the Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU) to close in on the physical properties of the first stars in the universe.

The team, led by Kavli IPMU Visiting Associate Scientist and The University of Tokyo Institute for Physics of Intelligence Assistant Professor Tilman Hartwig, including Visiting Associate Scientist and National Astronomical Observatory of Japan Assistant Professor Miho Ishigaki, Visiting Senior Scientist and University of Hertfordshire Professor Chiaki Kobayashi, Visiting Senior Scientist and National Astronomical Observatory of Japan Professor Nozomu Tominaga, and Visiting Senior Scientist and The University of Tokyo Professor Emeritus Ken’ichi Nomoto, used artificial intelligence to analyze elemental abundances in more than 450 extremely metal-poor stars observed to date. Based on the newly developed supervised machine learning algorithm trained on theoretical supernova nucleosynthesis models, they found that 68 per cent of the observed extremely metal-poor stars have a chemical fingerprint consistent with enrichment by multiple previous supernovae.

The team’s results give the first quantitative constraint based on observations on the multiplicity of the first stars.

“Multiplicity of the first stars were only predicted from numerical simulations so far, and there was no way to observationally examine the theoretical prediction until now,” said lead author Hartwig. “Our result suggests that most first stars formed in small clusters so that multiple of their supernovae can contribute to the metal enrichment of the early interstellar medium,” he said.

“Our new algorithm provides an excellent tool to interpret the big data we will have in the next decade from on-going and future astronomical surveys across the world” said Kobayashi, also a Leverhulme Research Fellow.

“At the moment, the available data of old stars are the tip of the iceberg within the solar neighborhood. The Prime Focus Spectrograph, a cutting-edge multi-object spectrograph on the Subaru Telescope developed by the international collaboration led by Kavli IPMU, is the best instrument to discover ancient stars in the outer regions of the Milky Way far beyond the solar neighborhood.,” said Ishigaki.

The new algorithm invented in this study opens the door to make the most of diverse chemical fingerprints in metal-poor stars discovered by the Prime Focus Spectrograph.

“The theory of the first stars tells us that the first stars should be more massive than the Sun. The natural expectation was that the first star was born in a gas cloud containing the mass million times more than the Sun. However, our new finding strongly suggests that the first stars were not born alone, but instead formed as a part of a star cluster or a binary or multiple star system. This also means that we can expect gravitational waves from the first binary stars soon after the Big Bang, which could be detected future missions in space or on the Moon,” said Kobayashi.

In their study, the researchers took a close look at a species that has long been studied at the University of Bonn — the resurrection plant Craterostigma plantagineum. It bears its name quite rightly: In times of drought, one might think it is dead. But even after months of drought, a little water is enough to revive it. “At our institute, we have been studying how the plant does this for many years,” explains Prof. Dr. Dorothea Bartels from the Institute of Molecular Physiology and Biotechnology of Plants (IMBIO) at the University of Bonn.

Her interests include the genes that are responsible for drought tolerance. It became increasingly clear that this ability is not the result of a single “miracle gene.” Instead, a great many genes are involved, most of which are also found in species that do not cope so well with drought.

The plant has eight copies of each chromosome

In the current study, Bartel’s team, together with researchers from the University of Michigan (USA), analyzed the complete genome of Craterostigma plantagineum. And this is built quite complex: While most animals have two copies of each chromosome — one from the mother, one from the father — Craterostigma has eight. Such an “eightfold” genome is also called octoploid. We humans, in contrast, are diploid.

“Such a multiplication of genetic information can be observed in many plants that have evolved under extreme conditions,” Bartels says. But why is that? A probable reason: If a gene is present in eight copies instead of two, it can in principle be read four times as fast. An octoploid genome can therefore enable large quantities of a required protein to be produced very quickly. This ability also appears to be important for the development of drought tolerance.

In Craterostigma, some genes associated with greater tolerance to drought are even further replicated. These include the so-called ELIPs — the acronym stands for “early light inducible proteins,” as they are rapidly switched on by light and protect against oxidative stress. They occur in high copy numbers in all drought-tolerant species. “Craterostigma has close to 200-ELIP genes that are nearly identical and are located in large clusters of ten or twenty copies on different chromosomes,” Bartels explains. Drought-tolerant plants can therefore presumably draw on an extensive network of genes that they can rapidly upregulate in the event of drought.

Drought-sensitive species usually have the same genes — albeit in lower copy numbers. This is also not surprising: The seeds and pollen of most plants are often still able to germinate after long periods without water. So they also have a genetic program to protect against drought. “However, this program is normally switched off at germination and cannot be reactivated afterwards,” the botanist explains. “In resurrection plants, in contrast, it remains active.”

Most species “can do” drought tolerance

Drought tolerance, then, is something that the vast majority of plants “can do.” The genes that confer this ability probably emerged very early in the course of evolution. However, these networks are more efficient in drought-tolerant species and, moreover, are not active only at certain stages of the life cycle.

That said, not every cell in Craterostigma plantagineum has the same “drought program” either. This was shown by researchers from the University of Düsseldorf, who were also involved in the study. For instance, different drought network genes are active in roots during desiccation than in leaves. This finding is not unexpected: Leaves, for instance, need to protect themselves against the damaging effects of the sun. They are helped in this by ELIPs, for example. With sufficient moisture, the plant forms photosynthetic pigments that at least partially absorb radiation. This natural protection largely fails during drought. Roots, in contrast, do not have to worry about sunburn.

The study improves understanding of why some species suffer so little from drought. In the long term, it could therefore contribute to the breeding of crops such as wheat or corn that cope better with drought. In times of climate change, these are likely to be in greater demand than ever in the future.

Participating institutions and funding:

In addition to the University of Bonn, Michigan State University (USA) and Heinrich Heine University Düsseldorf were involved in the study. The work was funded by the US National Science Foundation (NSF) and the German Research Foundation (DFG).