Discovering Substellar Dark Matter Halos with Astrometric Weak Lensing of Multiply Imaged Quasars

Abstract

We propose time-domain astrometric weak lensing of multiply imaged quasars as a probe of substellar dark matter (DM) halos. In $\Lambda$CDM, each macro-image's light traverses many microhalos, producing a stochastic centroid motion with a calculable red power spectrum. Halos with crossing times longer than the survey impart a relative angular acceleration between image pairs. The response peaks at subhalo scale radii 0.005-2 pc and masses $3\times10^{-6}$-$10^2\,M_\odot$, 12-14 orders of magnitude below the smallest detected DM structures, down to the damping cutoffs of a 100 GeV thermal relic. We forecast the sensitivity of ten-year campaigns with 300 epochs for two benchmark systems: the galaxy-lensed quadruple B1422+231 at a 0.1 $\mu$as per-epoch precision forecast for extended-path intensity correlation, and the cluster-lensed triple SDSS J1029+2623 at 1 $\mu$as. The angular-acceleration channel reaches the standard $\Lambda$CDM microhalo population with a variance signal-to-noise ratio of order ten for the galaxy lens (order unity after stellar microlensing subtraction) and 0.35 for the cluster under the optimistic assumption that 10% of the projected mass density at the image positions resides in surviving microhalos. A positive detection would: raise universal lower bounds on the DM particle mass to $\gtrsim400$ keV for fermions and $\gtrsim10^{-12}$ eV for bosons; constrain the DM kinetic decoupling temperature to $\gtrsim 10$ MeV; and be sensitive to the running of the spectral tilt at the 0.01 level over 15-20 e-folds of the primordial curvature power spectrum. A robust null result across well-characterized lenses would constrain microhalo survival and/or imply violations of the above inequalities. These signatures motivate differential astrometric observations with extreme 0.1-1 $\mu$as light-centroiding precision on multiply imaged quasars. [Abridged]