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We investigate the relations between nuclear star clusters (NSCs) and theirhost galaxies, and between the structural properties of nucleated andnon-nucleated galaxies. We also address the environmental influences on thenucleation of galaxies in the Fornax main cluster and the Fornax A group. Weselect 557 Fornax galaxies ($10^{5.5} M_{\odot} < M_{\rm *,galaxy} < 10^{11.5}M_{\odot} $) for which structural decomposition models and non-parametricindices are available. We determine galaxy nucleation based on a combination ofvisual inspection and a model selection statistic, the Bayesian informationcriterion (BIC). We also test the BIC as an unsupervised method to determinenucleation labels. We find a dichotomy in the properties of nuclei which residein galaxies more or less massive than $M_{\rm *,galaxy} \approx 10^{8.5}M_{\odot}$. Specifically, the nuclei tend to be bluer than their host galaxiesand follow a scaling relation of $M_{\rm *,nuc} \propto {M_{\rm*,galaxy}}^{0.5}$ for $M_{\rm *,galaxy} < 10^{8.5} M_{\odot}$. In galaxies with$M_{\rm *,galaxy} > 10^{8.5} M_{\odot}$ we find that nuclei are redder comparedto the host and follow $M_{\rm *,nuc} \propto M_{\rm *,galaxy}$. Comparingearly-type galaxies, we find that nucleated galaxies tend to be redder inglobal ($g'-r'$) colour, have redder outskirts relative to their own innerregions ($\Delta (g'-r')$), be less asymmetric ($A$) and exhibit less scatterin the brightest second order moment of light ($M_{20}$) than theirnon-nucleated counterparts at a given stellar mass. Additionally, we find thenucleation fractions to be typically higher in the Fornax main cluster than inthe Fornax A group, and that the nucleation fraction is highest towards thecentre of their respective environments. We also find that the BIC can recoverour labels of nucleation up to an accuracy of 97\%. (abridged)

Photometric properties of nuclear star clusters and their host galaxies in the Fornax cluster