New Method Catalogs the Faint 'Ringing' Overtones of Merging Black Holes

When two black holes collide and merge, the newly formed, larger black hole does not settle down immediately — it continues to "ring" as it relaxes into a stable shape. Because a black hole cannot produce sound, it instead sends out gravitational waves, ripples in spacetime first predicted by Albert Einstein. The frequencies of these vibrations, known as quasinormal modes, depend on the merged black hole's mass and spin and act like a fingerprint, letting scientists test general relativity under some of the most extreme gravitational conditions in the universe.

Researchers at the University of Cambridge have developed a technique, described in a study in Physical Review Letters, that can identify and catalog these modes more accurately by analyzing computer simulations of black hole mergers. The method relies on Bayesian analysis, a statistical approach that weighs competing evidence to find the most probable explanation for a dataset. It detected not only the loudest fundamental "note" produced during the ringdown but also fainter "overtones" — weaker harmonics that fade more quickly and are much harder to detect.

"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 of Cambridge's Institute of Astronomy, the study's first author. "Our method provides a systematic, data-driven way to resolve this uncertainty." Beyond the fundamental notes and overtones, Dyer and coauthor Christopher Moore also identified unusual "nonlinear modes" that arise when two or more fundamental frequencies interact, producing signals resembling the tones of an electric guitar played with heavy distortion.

Dyer and Moore tested their method on a publicly available catalog of high-precision simulations covering a wide range of black hole mass ratios and spin configurations, recording which modes could be detected and when. The results could help interpret observations from current gravitational wave detectors such as LIGO and Virgo, as well as future instruments, and could sharpen tests of whether a merged black hole's properties match what Einstein's equations predict.