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Rotation curves of galaxies show a wide range of shapes, which can beparamaterized as scatter in Vrot(1kpc)/Vmax i.e.the ratio of the rotationvelocity measured at 1kpc and the maximum measured rotation velocity. Weexamine whether the observed scatter can be accounted for by combining scattersin disc scale-lengths, the concentration-halo mass relation, and the M*-Mhalorelation. We use these scatters to create model galaxy populations; when housedwithin dark matter halos that have universal, NFW density profiles, the modeldoes not match the lowest observed values of Vrot(1kpc)/Vmax and has too littlescatter in Vrot(1kpc)/Vmax compared to observations. By contrast, a model usinga mass dependent dark matter profile, where the inner slope is determined bythe ratio of M*/Mhalo, produces galaxies with low values of Vrot(1kpc)/Vmax anda much larger scatter, both in agreement with observation. We conclude that thelarge observed scatter in Vrot(1kpc)/Vmax favours density profiles that aresignificantly affected by baryonic processes. Alternative dark matter coreformation models such as SIDM may also account for the observed variation inrotation curve shapes, but these observations may provide important constraintsin terms of core sizes, and whether they vary with halo mass and/or mergerhistory.

The Variation of Rotation Curve Shapes as a Signature of the Effects of Baryons on Dark Matter Density Profiles