The galaxy is not a smooth lake but a pond with ripples. These ripples are created by ultralight dark matter (particles billions of billions of times lighter than an electron). The oscillations of its field slightly disrupt the rhythm of distant pulsars — cosmic lighthouses whose signals are picked up by Earth-based radio telescopes.

Until now, dark matter hunters worked with two extremes. Either they assumed the ripples are the same everywhere, as if the whole pond were waving in sync. Or they assumed each pulsar has its own independent swell. But real ripples are more complex: they have spatial correlations. Nearby points on the water oscillate similarly, distant ones differently. New work by a group of astrophysicists for the first time builds an analysis where the field amplitude of dark matter smoothly transitions from full coherence to full independence — depending on the distance between pulsars.

The authors applied the method to two interaction scenarios between dark matter and ordinary matter: linear and quadratic. In the latter case, they also accounted for a universal gravitational signal from pressure oscillations of ultralight matter. To handle uncertainties in pulsar distances, they used an augmented latent field and a surrogate based on normalizing flows. The method was tested on synthetic data, including blind signal injection tests, and it performed correctly.