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 $Λ$CDM, the photon path of each macro-image traverses numerous microhalos, which collectively produce a stochastic centroid motion with a calculable red power spectrum. Halos whose crossing times exceed the survey time impart a relative angular acceleration between image pairs. The response is strongest for subhalos with sizes of 0.01-1 pc (masses of $10^{-6}$-$1~M_\odot$ in $Λ$CDM), extending lensing sensitivity 12 to 14 orders of magnitude below the smallest DM structures detected to date. 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 $μ$as per-epoch precision forecast for extended-path intensity correlation (EPIC), and the wide-separation cluster-lensed triple SDSS J1029+2623 at 1 $μ$as. The angular-acceleration channel reaches the standard $Λ$CDM microhalo population with a variance signal-to-noise ratio of order ten for the galaxy lens and order unity for the cluster under the (optimistic) assumption that half of the projected mass density at the image positions resides in 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 $μ$as light-centroiding precision on multiply imaged quasars. [Abridged]