  Annihilating dark matter particles in nearby subhalos could generate
potentially observable fluxes of gamma rays, unaccompanied by emission at other
wavelengths. Furthermore, this gamma-ray emission is expected to be spatially
extended, providing us with a powerful way to discriminate dark matter subhalos
from other astrophysical gamma-ray sources. Fermi has detected two dark matter
subhalo candidates which exhibit a statistically significant degree of spatial
extension (3FGL J2212.5+0703 and 3FGL J1924.8-1034). It has been argued that
the most likely non-dark matter interpretation of these observations is that
they are each in fact multiple nearby point sources, too close to one another
on the sky to be individually resolved. In this study, we consider the ability
of next generation gamma-ray telescopes to spatially resolve the gamma-ray
emission from subhalo candidates, focusing on the proposed e-ASTROGAM mission.
We find that such an instrument could significantly clarify the nature of
Fermi's dark matter subhalo candidates, and provide an unprecedented level of
sensitivity to the presence of annihilating dark matter in nearby subhalos.
