WALLABY pre-pilot survey: ultra-diffuse galaxies in the Eridanus supergroup

We present a pilot study of the atomic neutral hydrogen gas (H I) content of ultra-diffuse galaxy (UDG) candidates. In this paper, we use the pre-pilot Eridanus field data from the Widefield ASKAP L-band Legacy All-sky Blind Survey to search for H I in UDG candidates found in the Systematically Measuring Ultra-diffuse Galaxies survey (SMUDGes). We narrow down to 78 SMUDGes UDG candidates within the maximum radial extents of the Eridanus subgroups for this study. Most SMUDGes UDGs candidates in this study have effective radii smaller than 1.5 kpc and thus fail to meet the defining size threshold. We only find one H I detection, which we classify as a low-surface-brightness dwarf. Six putative UDGs are H I-free. We show the overall distribution of SMUDGes UDG candidates on the size-luminosity relation and compare them with low-mass dwarfs on the atomic gas fraction versus stellar mass scaling relation. There is no correlation between gas-richness and colour indicating that colour is not the sole parameter determining their H I content. The evolutionary paths that drive galaxy morphological changes and UDG formation channels are likely the additional factors to affect the H I content of putative UDGs. The actual numbers of UDGs for the Eridanus and NGC 1332 subgroups are consistent with the predicted abundance of UDGs and the halo virial mass relation, except for the NGC 1407 subgroup, which has a smaller number of UDGs than the predicted number. Different group environments suggest that these putative UDGs are likely formed via the satellite accretion scenario.