  Dark matter could be captured in the Sun and self-annihilate, giving rise to
an observable neutrino flux. Indirect searches for dark matter looking for this
signal with neutrino telescopes have resulted in tight constraints on the
interaction cross-section of dark matter with ordinary matter. We investigate
how robust limits are against astro-physical uncertainties. We study the effect
of the velocity distribution of dark matter in our Galaxy on capture rates in
the Sun. We investigate four sources of uncertainties: orbital speed of the
Sun, escape velocity of dark matter from the halo, dark matter velocity
distribution functions and existence of a dark disc. We find that even extreme
cases currently discussed do not decrease the sensitivity of indirect detection
significantly because the capture is achieved over a broad range of the
velocity distribution by integration over the velocity distribution. The effect
of the uncertainty in the high-velocity tail of dark matter halo is very
marginal as the capture process is rather inefficient at this region. The
difference in capture rate in the Sun for various scenarios is compared to the
expected change in event rates for direct detection. The possibility of
co-rotating structure with the Sun can largely boost the signal and hence makes
the interpretation of indirect detection conservative compared to direct
detection.
