Enormous disks of stars or debris can operate under the same rules as subatomic particles, changing based on the Schrodinger equation, which physicists use to model quantum-mechanical systems.

Viewing space structures with that equation can lend new insights into how galaxies evolve, as well as reveal clues about the mechanics of the early solar system and the action of rings circling distant planets, a new study reports. science of universe space science

California Institute of Technology researcher Konstantin Batygin, author of the new study, hadn’t expected to find that particular equation when studying those astrophysical disks. “At the time, I was completely floored,” Batygin told Space.com. “I was expecting the regular wave equation to appear, something like the wave of a string or something like that. And instead, I get this equation, which is really the cornerstone of quantum mechanics.” science of universe space science

Using the Schrodinger equation, physicists can interpret the interactions of systems on atomic and subatomic scales in terms of waves as well as particles — a key concept in quantum mechanics that describes those systems’ sometimes unintuitive behavior. It turns out, the warping of astrophysical disks can act like particles, too. science of universe space science

“In retrospect, when I look at the problem now, I’m surprised at how I didn’t just guess that that’s what it was going to be,” said Batygin, who’s perhaps best known (to laypeople, anyway) for co-authoring a 2016 study with fellow Caltech researcher Mike Brown that found evidence for a possible undiscovered “Planet Nine” in the dark depths of our outer solar system. science of universe space science

## Blast from the past

Batygin came across the connection when teaching a class. He was trying to explain how waves travel through the broad disks that are a staple of space architecture — for instance, such disks are built of stars around supermassive black holes at a galaxy’s center, and made of dust and debris in a newborn star system. The disks bend and warp in a complex way that current modeling can’t handle on all timescales. Scientists can calculate their actions over very short time spans, like what happens over a few orbits, as well as how they will disperse over an entire lifetime, but not how and why they will change on the order of hundreds of thousands of years. science of universe space science

“Things might happen, and you don’t really know why — it’s a complicated system, so you just see stuff unfold, see some kind of dynamical evolution unfold,” Batygin said. “Unless you have this monstrously complicated physical intuition, you just don’t understand what’s going on in your simulation.” science of universe space science

To follow a disk’s development, Batygin borrowed a trick from the 1770s: calculating the way mathematicians Joseph-Louis Lagrange and Pierre-Simon Laplace modeled the solar system as a series of giant loops following the planets’ orbits. While the model wasn’t helpful on short timescales of a few circuits around the sun, it could accurately depict the orbits’ interactions with one another over time. science of universe space science

Instead of modeling individual planets’ orbits, Batygin used a series of thinner and thinner rings to represent different pieces of the astrophysical disk, like layers of an onion, each tied to the mass of the orbiting bodies within that region.The rings’ gravitational interactions with one another could model how the disk would warp and change. science of universe space science

And when the system got too complicated to calculate by hand or on the computer as he added more rings, he used a mathematical shortcut to convert to describing an infinite number of infinitely thin rings. science of universe space science

“This is just a broadly known mathematical result which is used in physics left and right,” Batygin said. But yet, somehow, nobody had taken the leap to model an astrophysical disk that way. science of universe space science

“What is truly remarkable to me is that nobody has blurred [the rings] into a continuum ever before,” he said. “It seems so obvious in retrospect, and I don’t know why I didn’t think of it sooner.” science of universe space science