Researchers have developed a technique to analyse how black holes 'ring' when they collide and merge: one of the universe's most dramatic events.
When black holes merge, the collision produces a new, larger black hole that 'rings' like a plucked guitar string or a bell while it settles into its final, stable shape. But instead of sound waves, the new black hole rings with gravitational waves: ripples in spacetime first predicted by Albert Einstein.
The new black hole vibrates at a specific set of frequencies, depending on its mass and spin, which helps scientists learn about the object formed in the collision.
These vibrations, known as quasinormal modes, are the fingerprint of a black hole. Detecting them is central to testing Einstein's general theory of relativity in the most extreme gravitational environments in the universe.
Now, researchers from the University of Cambridge have developed a method to identify and catalogue these modes with greater accuracy than before. Writing in the journal Physical Review Letters, they outline how they sifted through computer simulations of black hole mergers and identified not just the fundamental 'note' the black hole rings at, but also the 'overtones', the fainter harmonics that fade away more quickly.
"While the loudest mode is routinely observed in gravitational wave data, many quieter modes are much more difficult to detect, and there has been ongoing debate about which modes are present and when they appear," said Richard Dyer from Cambridge's Institute of Astronomy, the study's first author. "Our method provides a systematic, data-driven way to resolve this uncertainty, and our results provide a reference for both theoretical studies and real observations."
The researchers based their method on Bayesian analysis, a statistical technique that systematically weighs evidence to determine the most probable explanation for a given dataset.
In addition to the fundamental 'notes' and 'overtones', the researchers also found unusual 'nonlinear modes' in the data: vibrations produced when two or more of the fundamental frequencies interact with one another. These are analogous to the complex tones an electric guitar can produce when played with heavy distortion. Detecting these modes requires high-quality data and careful analysis to distinguish them from noise.
"The ringdown is one of the most direct probes of black holes we have," said Dyer. "But extracting all the information it contains is hard. We wanted a principled, data-driven way to do that."
Dyer and his co-author Dr Christopher Moore applied their method to a publicly available catalogue of highly accurate simulations that model gravitational waves to the theoretical boundary where they can be cleanly measured. They recorded which modes were detectable, and when, across a wide range of simulated black hole collisions with different mass ratios and spin configurations.
The researchers say their results will be useful for interpreting data from current gravitational wave detectors such as LIGO and Virgo, and for next-generation detectors. Knowing which frequencies to search for in a given collision could allow researchers to perform even more precise tests of general relativity: for example, checking that the properties of the final black hole are consistent with what Einstein's equations predict.
Reference:
Richard Dyer and Christopher J. Moore. 'Quasinormal mode content of binary black hole ringdowns.' Physical Review Letters (2026). DOI: 10.1103/ptmd-rz1t
