  The cold dark matter (CDM) structure formation model predicts that about 5-10
percent of a typical galactic halo of mass $\sim 10^{12} \ms$ is in
substructures with masses $\lesssim 10^8 \ms$. To directly detect such
substructures, we propose to observe dust continuum emission from a strongly
lensed QSO-host galaxy using a large submillimeter interferometer array with a
high angular resolution of $\sim 0.01$arcsec such as the planned Atacama Large
Submillimeter Array (ALMA). To assess their observational feasibility, we
numerically simulate millilensing of an extended circular source by a CDM
substructure modeled as a tidally truncated singular isothermal sphere (SIS)
embedded in a typical QSO-galaxy lens system, B1422+231, modeled as a singular
isothermal ellipsoid (SIE) with an external constant shear and a constant
convergence. Assuming an angular resolution of 0.01arcsec, we find that the
angular positions of $\sim 10^8 \ms$ substructures at several kpc from the
center of the macrolens halo can be directly measured if the size of the dust
continuum emission region and the gradient of the surface brightness at the
position of the perturber are sufficiently large. From the astrometric shift on
a scale of a few times $10~$mas of an image perturbed by a subhalo with respect
to an unperturbed macrolensed image, we can break the degeneracy between
subhalo mass and distance provided that macrolensing parameters are determined
from positions and fluxes of multiple images.

Astrophysics