Probing Stochastic Ultralight Dark Matter with Space-based Gravitational-Wave Interferometers

Ultralight particles are theoretically well-motivated dark matter candidates. In the vicinity of the solar system, these ultralight particles can be described as a superposition of plane waves, resulting in a stochastic field with sizable amplitude fluctuations on scales determined by the velocity dispersion of dark matter. In this work, we systematically investigate the sensitivity of space-based gravitational-wave interferometers to the stochastic ultralight dark matter (ULDM) field within the frequentist framework. We derive the projected sensitivity of a single detector using the time-delay interferometry. Our results show that space-based gravitational-wave interferometers have the potential to probe unconstrained regions in parameter space and improve the current limit on coupling strengths. Furthermore, we explore the sensitivity of a detector network and investigate the optimal configuration for ULDM detection. We introduce the overlap reduction function for ULDM, which quantifies the degree of correlation between the signals observed by different detectors. We find that the configuration, where the signals observed by two detectors are uncorrelated, is the optimal choice for ULDM detection due to a smaller chance of missing signal. This contrasts with the detection of stochastic gravitational-wave background, where the correlated configuration is preferred. Our results may provide useful insights for potential joint observations involving space-based gravitational-wave detectors like LISA and Taiji, as well as other ULDM detection networks operating in the coherence limit.