  The orbit of the Earth about the Sun produces an annual modulation in the
WIMP direct detection rate. If the local WIMP velocity distribution is
isotropic then the modulation is roughly sinusoidal with maximum in June,
however if the velocity distribution is anisotropic the phase and shape of the
signal can change. Motivated by conflicting claims about the effect of
uncertainties in the local velocity distribution on the interpretation of the
DAMA annual modulation signal (and the possibility that the form of the
modulation could be used to probe the structure of the Milky Way halo), we
study the dependence of the annual modulation on various astrophysical inputs.
We first examine the approximations used for the Earth's motion about the Sun
and the Sun's velocity with respect to the Galactic rest frame. We find that
overly simplistic assumptions lead to errors of up to ten days in the phase and
up to tens of per-cent in the shape of the signal, even if the velocity
distribution is isotropic. Crucially, if the components of the Earth's velocity
perpendicular to the motion of the Sun are neglected, then the change in the
phase which occurs for anisotropic velocity distributions is missed. We then
examine how the annual modulation signal varies for physically and
observationally well-motivated velocity distributions. We find that the phase
of the signal changes by up to 20 days and the mean value and amplitude change
by up to tens of per-cent.
