Rotation curve fitting and its fatal attraction to cores in realistically simulated galaxy observations

We study the role of systematic effects in observational studies of the cusp-core problem under the minimum disc approximation using a suite of high-resolution (25-pc softening length) hydrodynamical simulations of dwarf galaxies. We mimic realistic kinematic observations and fit the mock rotation curves with two analytic models commonly used to differentiate cores from cusps in the dark matter distribution. We find that the cored pseudo-isothermal sphere (ISO) model is strongly favoured by the reduced $\chi^2_\nu$ of the fits in spite of the fact that our simulations contain cuspy Navarro-Frenk-White profiles (NFW). We show that even idealized measurements of the gas circular motions can lead to the incorrect answer if velocity underestimates induced by pressure support, with a typical size of order $\sim$5 km s$^{-1}$ in the central kiloparsec, are neglected. Increasing the spatial resolution of the mock observations leads to more misleading results because the inner region, where the effect of pressure support is most significant, is better sampled. Fits to observations with a spatial resolution of 100 pc (2 arcsec at 10 Mpc) favour the ISO model in 78-90 per cent of the cases, while at 800-pc resolution, 40-78 per cent of the galaxies indicate the fictitious presence of a dark matter core. The coefficients of our best-fit models agree well with those reported in observational studies; therefore, we conclude that NFW haloes can not be ruled out reliably from this type of analysis.