The many reasons that the rotation curves of low-mass galaxies can fail as tracers of their matter distributions

It is routinely assumed that galaxy rotation curves are equal to their circular velocity curves (modulo some corrections) such that they are good dynamical mass tracers. We take a visualisation-driven approach to exploring the limits of the validity of this assumption for a sample of $33$ low-mass galaxies ($60<v_{\mathrm{m}\mathrm{a}\mathrm{x}}\mathrm{/}\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}<120$) from the APOSTLE suite of cosmological hydrodynamical simulations. Only $3$ of these have rotation curves nearly equal to their circular velocity curves at $z=0$, the rest are undergoing a wide variety of dynamical perturbations. We use our visualisations to guide an assessment of how many galaxies are likely to be strongly perturbed by processes in several categories: mergers/interactions (affecting $6$/$33$ galaxies), bulk radial gas inflows ($19$/$33$), vertical gas outflows ($15$/$33$), distortions driven by a non-spherical DM halo ($17$/$33$), warps ($8$/$33$), and winds due to motion through the IGM ($5$/$33$). Most galaxies fall into more than one of these categories; only $5$/$33$ are not in any of them. The sum of these effects leads to an underestimation of the low-velocity slope of the baryonic Tully-Fisher relation ($\alpha \sim 3.1$ instead of $\alpha \sim 3.9$, where $M_{\mathrm{b}\mathrm{a}\mathrm{r}}\propto v^{\alpha }$) that is difficult to avoid, and could plausibly be the source of a significant portion of the observed diversity in low-mass galaxy rotation curve shapes.