We present new observations of the nebula around the Magellanic candidate Luminous Blue Variable S61. These comprise high-resolution data acquired with the Australia Telescope Compact Array (ATCA), the Atacama Large Millimetre/Submillimetre Array (ALMA), and VISIR at the Very Large Telescope (VLT). The nebula was detected only in the radio, up to 17 GHz. The 17 GHz ATCA map, with 0.8 arcsec resolution, allowed a morphological comparison with the H$alpha$ Hubble Space Telescope image. The radio nebula resembles a spherical shell, as in the optical. The spectral index map indicates that the radio emission is due to free-free transitions in the ionised, optically thin gas, but there are hints of inhomogeneities. We present our new public code RHOCUBE to model 3D density distributions, and determine via Bayesian inference the nebulas geometric parameters. We applied the code to model the electron density distribution in the S61 nebula. We found that different distributions fit the data, but all of them converge to the same ionised mass, ~0.1 $rm Modot$, which is an order of magnitude smaller than previous estimates. We show how the nebula models can be used to derive the mass-loss history with high-temporal resolution. The nebula was probably formed through stellar winds, rather than eruptions. From the ALMA and VISIR non-detections, plus the derived extinction map, we deduce that the infrared emission observed by space telescopes must arise from extended, diffuse dust within the ionised region.
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