Can proper motions of dark-matter subhalos be detected?

One of the goals of NASA's Fermi Gamma-ray Space Telescope (formerly GLAST) will be detection of gamma rays from dark-matter annihilation in the Galactic halo. Theoretical arguments suggest that dark matter may be bound into subhalos with masses as small as 10^{-4}--10^2 Earth mass. If so, it may be possible to detect individual subhalos as point sources in the Fermi Telescope. It has further been argued that some of these point sources may exhibit proper motions. Here we show that upper limits to the diffuse gamma-ray background constrain the number of subhalos close enough to exhibit proper motions to be less than one.