Effect of the Sun’s gravity on the distribution and detection of dark matter near the Earth

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Abstract
The effect of the Sun’s gravity on the distribution of dark-matter (DM) particles in the vicinity of the Earth is considered. The event rate in a cryogenic detector is found and the annual modulation of the signal due to this effect is compared to the annual modulation due to the relative velocities of the Sun and Earth. The effect is order 1% and probably too small to be seen experimentally. The effect of this distribution function on the capture rate of DM particles into the Earth is also considered. The rate could be suppressed for DM particles not well matched in mass to common elements in the Earth. Finally, the density of DM particles in bound orbits around the Sun is estimated and, contrary to earlier work, no way of generating an enhancement over ‘‘equilibrium’’ density is found; in fact, a general argument shows the density to be very nearly the ‘‘equilibrium’’ density. The inclusion of an ‘‘equilibrium’’ density of bound particles has negligible effect on direct detection, but removes the capture rate suppression.