Astrometric Detection of Ultralight Dark Matter

Ultralight dark matter induces time-dependent perturbations in the spacetime metric, enabling its gravitational direct detection. In this work, we propose using astrometry to detect dark matter. After reviewing the calculation of the metric in the presence of scalar dark matter, we study the influence of the perturbations on the apparent motion of astrophysical bodies. We apply our results to angular position measurements of quasars, whose vast distances from Earth present an opportunity to discover dark matter with a mass as low as $10^{-33} \, \mathrm{eV} $. We explore the prospects of very long baseline interferometry and optical astrometric survey measurements for detecting ultralight relics, finding that for the smallest masses, current astrometric surveys can detect dark matter moving locally with a velocity of $10^{-3}$ with energy density as low as $10 ^{ - 4} ~{\rm GeV} / {\rm cm} ^3 $.