We use mock interferometric HI measurements and a conventional tilted-ring modelling procedure to estimate circular velocity curves of dwarf galaxy discs from the APOSTLE suite of {Lambda}CDM cosmological hydrodynamical simulations. The modelling yields a large diversity of rotation curves for an individual galaxy at fixed inclination, depending on the line-of-sight orientation. The diversity is driven by non-circular motions in the gas; in particular, by strong bisymmetric fluctuations in the azimuthal velocities that the tilted-ring model is ill-suited to account for and that are difficult to detect in model residuals. Large misestimates of the circular velocity arise when the kinematic major axis coincides with the extrema of the fluctuation pattern, in some cases mimicking the presence of kiloparsec-scale density cores, when none are actually present. The thickness of APOSTLE discs compounds this effect: more slowly-rotating extra-planar gas systematically reduces the average line-of-sight speeds. The recovered rotation curves thus tend to underestimate the true circular velocity of APOSTLE galaxies in the inner regions. Non-circular motions provide an appealing explanation for the large apparent cores observed in galaxies such as DDO 47 and DDO 87, where the model residuals suggest that such motions might have affected estimates of the inner circular velocities. Although residuals from tilted ring models in the simulations appear larger than in observed galaxies, our results suggest that non-circular motions should be carefully taken into account when considering the evidence for dark matter cores in individual galaxies.
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