  The scattering rate at dark-matter direct-detection experiments should
modulate annually due to the Earth's orbit around the Sun. The rate is
typically thought to be extremized around June 1, when the relative velocity of
the Earth with respect to the dark-matter wind is maximal. We point out that
gravitational focusing can alter this modulation phase. Unbound dark-matter
particles are focused by the Sun's gravitational potential, affecting their
phase-space density in the lab frame. Gravitational focusing can result in a
significant overall shift in the annual-modulation phase, which is most
relevant for dark matter with low scattering speeds. The induced phase shift
for light O(10) GeV dark matter may also be significant, depending on the
threshold energy of the experiment.
