  Rotation curves of galaxies show a wide range of shapes, which can be
paramaterized as scatter in Vrot(1kpc)/Vmax i.e.the ratio of the rotation
velocity measured at 1kpc and the maximum measured rotation velocity. We
examine whether the observed scatter can be accounted for by combining scatters
in disc scale-lengths, the concentration-halo mass relation, and the M*-Mhalo
relation. We use these scatters to create model galaxy populations; when housed
within dark matter halos that have universal, NFW density profiles, the model
does not match the lowest observed values of Vrot(1kpc)/Vmax and has too little
scatter in Vrot(1kpc)/Vmax compared to observations. By contrast, a model using
a mass dependent dark matter profile, where the inner slope is determined by
the ratio of M*/Mhalo, produces galaxies with low values of Vrot(1kpc)/Vmax and
a much larger scatter, both in agreement with observation. We conclude that the
large observed scatter in Vrot(1kpc)/Vmax favours density profiles that are
significantly affected by baryonic processes. Alternative dark matter core
formation models such as SIDM may also account for the observed variation in
rotation curve shapes, but these observations may provide important constraints
in terms of core sizes, and whether they vary with halo mass and/or merger
history.
