  I study the process of dark matter capture by the Sun, under the assumption
of a Weakly Interacting Massive Particle (WIMP), in the framework of
non-relativistic effective field theory. Hypothetically, WIMPs from the
galactic halo can scatter against atomic nuclei in the solar interior, settle
to thermal equilibrium with the solar core and annihilate to produce an
observable flux of neutrinos. In particular, I examine the thermalization
process using Monte-Carlo integration of WIMP trajectories. I consider WIMPs in
a mass range of 10--1000 GeV and WIMP-nucleon interaction operators with
different dependence on spin and transferred momentum. I find that the density
profiles of captured WIMPs are in accordance with a thermal profile described
by the Sun's gravitational potential and core temperature. Depending on the
operator that governs the interaction, the majority of the thermalization time
is spent in either the solar interior or exterior. If normalizing the
WIMP-nuclei interaction strength to a specific capture rate, I find that the
thermalization time differs at most by 3 orders of magnitude between operators.
In most cases of interest, the thermalization time is many orders of magnitude
shorter than the age of the solar system.
