Dark Photon Dark Matter and Low-Frequency Gravitational Wave Detection with Gaia-like Astrometry

Astrometric surveys offer us a method to search for elusive cosmic signatures, such as ultralight dark photon dark matter and gravitational waves, by observing the deflection to the apparent positions of the stars. The detection capabilities of such surveys rapidly decrease at low frequencies, because the signals become hardly distinguishable from the background motion of stars. In this work, we find that the background motion can be well described by a linear model over time, based on which we propose a linear background subtraction scheme. Compared to the conventional quadratic subtraction, the advantage of linear subtraction emerges within the frequency range below $6 \times 10^{-9}~{\rm Hz}$. Taking dark photons with purely gravitational interactions, dark photons with additional $U(1)_{B}$ or $U(1)_{B-L}$ gauge interactions, and low-frequency gravitational waves as examples, we illustrate that the linear subtraction scheme can result in an enhancement of more than one order of magnitude in the exclusion limits of Gaia-like experiments in the low-frequency range.