  The search for weakly interacting massive particles (WIMPs) by direct
detection faces an encroaching background due to coherent neutrino-nucleus
scattering. For a given WIMP mass the cross section at which neutrinos
constitute a dominant background is dependent on the uncertainty on the flux of
each neutrino source from either the Sun, supernovae or atmospheric cosmic ray
collisions. However there are also considerable uncertainties with regard to
the astrophysical ingredients to the predicted WIMP signal. Uncertainties in
the velocity of the Sun with respect to the Milky Way dark matter halo, the
local density of WIMPs, and the shape of the local WIMP speed distribution all
have an effect on the expected event rate in direct detection experiments and
hence will change the region of the WIMP parameter space for which neutrinos
are a significant background. In this work we extend the WIMP+neutrino analysis
to account for the uncertainty in the astrophysics dependence of the WIMP
signal. We show the effect of uncertainties on projected discovery limits with
an emphasis on low WIMP masses (less than 10 GeV) when Solar neutrino
backgrounds are most important. We find that accounting for astrophysical
uncertainties changes the shape of the neutrino floor as a function of WIMP
mass but also causes it to appear at cross sections up to an order of magnitude
larger, extremely close to existing experimental limits - indicating that
neutrino backgrounds will become an issue sooner than previously thought. We
also explore how neutrinos hinder the estimation of WIMP parameters and how
astrophysical uncertainties impact the discrimination of WIMPs and neutrinos
with the use of their respective time dependencies.
