We present observations and models of the kinematics and the distribution of the neutral hydrogen (HI) in the isolated dwarf irregular galaxy, Wolf-Lundmark-Melotte (WLM). We observed WLM with the Green Bank Telescope (GBT) and as part of the MeerKAT Early Science Programme, where 16 dishes were available. The HI disc of WLM extends out to a major axis diameter of 30 arcmin (8.5 kpc), and a minor axis diameter of 20 arcmin (5.6 kpc) as measured by the GBT. We use the MeerKAT data to model WLM using the TiRiFiC software suite, allowing us to fit different tilted-ring models and select the one that best matches the observation. Our final best-fitting model is a flat disc with a vertical thickness, a constant inclination and dispersion, and a radially-varying surface brightness with harmonic distortions. To simulate bar-like motions, we include second-order harmonic distortions in velocity in the tangential and the vertical directions. We present a model with only circular motions included and a model with non-circular motions. The latter describes the data better. Overall, the models reproduce the global distribution and the kinematics of the gas, except for some faint emission at the 2-sigma level. We model the mass distribution of WLM with a pseudo-isothermal (ISO) and a Navarro-Frenk-White (NFW) dark matter halo models. The NFW and the ISO models fit the derived rotation curves within the formal errors, but with the ISO model giving better reduced chi-square values. The mass distribution in WLM is dominated by dark matter at all radii.
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