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.
