In late 2021, Salvatore Torquato, of Princeton’s Chemistry Department, reached across the aisle and invited a young astrophysicist at the Institute for Advanced Study to apply the tools of statistical mechanics to his own work on the distribution of galaxies.
The astrophysicist, Oliver Philcox, now a postdoctoral fellow at the Simons Foundation, was thrilled. A year-long collaboration followed.
The questions at the heart of their unusual collaboration were clear: can the statistical descriptors that Torquato has worked with throughout his career find application in unlikely places like cosmology, and can they accurately characterize the complexity in the distribution of galaxies? The answer to both questions: yes, indeed.
Their collaboration took place this week with an article Physical Review X, “The Disordered Heterogeneous Universe: Galaxy and Cluster Distribution on Length Scales.” In it, the researchers demonstrate that they can reveal useful information about the spatial distribution of galaxies from some descriptors most commonly used to classify the microstructure of materials.
Astrophysicists have long explored questions about the large-scale structure of the Universe through the standard tools of physical cosmology. What Torquato and Philcox did was provide proof that a new set of descriptors can be used to characterize structural data on length scales, from the atomic scale to the largest scales in the Universe…including the Universe.
Torquato uses the word “zoology” to capture the range of theoretical and computational techniques he uses in his work. What he means is: application of statistical descriptors that describe complex microstructures of materials to determine their physical and chemical properties on a macroscale.
Applying these techniques to the largest scale to detect similarities, Torquato and Philcox treated galaxies as a cloud of individual points similar to particles in a material.
“So, okay, I have two regions of space: it could be the galaxies, and then everything outside the galaxies. Among other things, you can study the holes between galaxies similar to how you would study the structure of materials,” he said. . Torquato, a theoretical chemist and Lewis Bernard Professor of Natural Sciences, Princeton Professor of Chemistry and Institute of Materials..
“If I say, I want to put a ball between the galaxies that doesn’t touch any of the galaxies, how big a ball do I need? You could apply this statistical question to any complex structure, whether it’s the distribution of galaxies or the distribution of atoms. That’s the beauty of it.
“Interestingly,” he added, “the unique structure of the Universe provides new challenges for ascertaining even better descriptions for describing terrestrial materials.”
Philcox, a former graduate student in Princeton’s Department of Astrophysical Sciences, embraced this “zoology” to expand his own toolbox. A key example was the use of the pair bond function, which Philcox defines as a special way of characterizing materials by looking at the distribution of point pairs.
“Going deep into zoology with Sal certainly led to some interesting discoveries of statistics used in materials science that could be used in cosmology but hadn’t yet, the pair-linking function being the most notable,” Philcox said. “Conventional cosmological statistics answer the question: if I pick two points at random, what is their separation, probabilistically?
“The pair link function does something similar, but includes topological information. Essentially, it groups the particles in a material into connected structures and then looks at the distribution of separations between two points within that structure, rather than globally.”
Using this and other functions, the researchers were able to create tables of numbers that served as a measure of order or disorder in length scales. When applied to questions of spatial relationships between galaxies, the tools highlighted a kind of correlated disorder — a complex structural property that is “definitely” not random.
“We’re asking exactly the same questions about large-scale structure that cosmologists have always asked using more formal descriptors: how do we describe that structure, how do we characterize it, how do we quantify it, what can we get from it in terms of physics,” Torquato said. . “We’re just using some new theoretical tools to do it.”
Philcox added: “I think it’s an important message that there are some conceptually very simple tools that can allow us to extract new information about the Universe, particularly about its accretion, that is quite orthogonal to what has already been used. We are excited to see how they can be used in practice.”