Exploring Ultralight Dark Matter Self-Coupling via the Gravitational Wave Background

Supermassive black hole binary mergers serve as prominent sources of the stochastic gravitational wave background (SGWB), detectable by pulsar timing arrays (PTAs). If dark matter-induced friction is present in the vicinity of these mergers, it can lead to suppression in the nanohertz frequency range of the SGWB spectrum. In particular, ultralight dark matter (ULDM) forming compact solitonic cores around supermassive black holes can imprint signatures in PTA observations. Our analysis places limits on the mass and self-interaction strength of ULDM, demonstrating that soliton-induced dynamical friction can significantly alter the SGWB spectrum. PTAs have the potential to exclude certain ULDM mass ranges while probing the effects of self-interactions, offering a novel avenue to investigate the fundamental properties of ULDM.