Ultralight Dark Matter Constraints from NanoHertz Gravitational Waves

Abstract: We investigate the impact of ultralight dark matter (ULDM) on the mergers of supermassive black holes (SMBH) and the resulting stochastic gravitational wave background. ULDM is based on exceptionally light particles and yields galactic halos with dense central solitons. This increases the drag experienced by binary SMBH, decreasing merger times and potentially suppressing gravitational radiation from the binary at low frequencies. We develop semi-analytic models for the decay of SMBH binaries in ULDM halos and use current pulsar timing array (PTA) measurements to constrain the ULDM particle mass and its fractional contribution to the dark matter content of the universe. We find a median ULDM particle mass of $7. \times 10^{-22}$ eV and show that scaling relations suggest that the drag remains effective at relatively low ULDM fractions, which are consistent with all other constraints on the model. Consequently, future pulsar timing measurements will be a sensitive probe of any ULDM contribution to the overall dark matter content of the universe.