We fit galactic rotation curves obtained by SPARC from dark matter haloes that are not spherically symmetric, but allowed to become prolate or oblate with a higher-multipole density distribution. This is motivated by observing that the flattening of v(r)=constant is the natural Kepler law due to a filamentary rather than a spherical source, so that elongating the distribution could bring about a smaller chi squared, all other things being equal. We compare results with several different dark matter profiles and the extracted best fits to the ellipticity computed in cosmological simulations of dark matter haloes. The shape distortion can impact our understanding of the local density of dark matter and thus be of interest for the direct detection program.
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