Probing Dark Matter Subhalos in Galaxy Clusters Using Highly Magnified Stars

Luminous stars in background galaxies straddling the lensing caustic of a foreground galaxy cluster can be individually detected due to extreme magnification factors of $\sim 10^2$--$10^3$, as recently observed in deep HST images. We propose a direct method to probe the presence of dark matter subhalos in galaxy clusters by measuring the astrometric perturbation they induce on the image positions of magnified stars or bright clumps: lensing by subhalos breaks the symmetry of a smooth critical curve, traced by the midpoints of close image pairs. For the giant arc at $z = 0.725$ behind the lensing cluster Abell 370 at $z = 0.375$, a promising target for detecting image pairs of stars, we find that subhalos of masses in the range $10^6$--$10^8\,M_\odot$ with the abundance predicted in the cold dark matter theory should typically imprint astrometric distortions at the level of $20$--$80\,{\rm mas}$. We estimate that $\sim 10\,$hr integrations with JWST at $\sim 1$--$3\,\mu{\rm m}$ may uncover several magnified stars whose image doublets will reveal the subhalo-induced structures of the critical curve. This method can probe a dynamic range in the subhalo to cluster halo mass ratio $m/M \sim 10^{-7}$--$10^{-9}$, thereby placing new constraints on the nature of dark matter.