  The shape distortion of the presumed Milky Way dark matter halo can impact
the local density of dark matter and thus the direct detection program. We
examine the population of galactic rotation curves measured by SPARC and fit
them to dark matter haloes that are distorted with a multipole density
distribution, finding a significantly better fit with prolate haloes over
spherically symmetric ones. This is to be expected since the long-distance
Rubin flattening v(r)= constant is the natural Kepler law due to a filamentary
rather than a spherical source. Then, elongating the distribution brings about
a smaller squared chi, all other things being equal, including the use of
several different radial dark matter profiles. The ellipticities that we fit to
rotation curve data seem to be much more significant than those computed in
cosmological simulations of dark matter haloes. If the Milky Way's halo would
be typical of the spiral-galaxy SPARC sample (which we presently ignore), the
local dark matter density might currently be overestimated by a factor 2. This
would carry on into dark-matter cross-section bounds.
