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

We investigate the relations between nuclear star clusters (NSCs) and their host galaxies, and between the structural properties of nucleated and non-nucleated galaxies. We also address the environmental influences on the nucleation of galaxies in the Fornax main cluster and the Fornax A group. We select 557 Fornax galaxies ($10^{5.5} M_{\odot} < M_{\rm *,galaxy} < 10^{11.5} M_{\odot} $) for which structural decomposition models and non-parametric indices are available. We determine galaxy nucleation based on a combination of visual inspection and a model selection statistic, the Bayesian information criterion (BIC). We also test the BIC as an unsupervised method to determine nucleation labels. We find a dichotomy in the properties of nuclei which reside in 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 galaxies and 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 compared to the host and follow $M_{\rm *,nuc} \propto M_{\rm *,galaxy}$. Comparing early-type galaxies, we find that nucleated galaxies tend to be redder in global ($g'-r'$) colour, have redder outskirts relative to their own inner regions ($Δ(g'-r')$), be less asymmetric ($A$) and exhibit less scatter in the brightest second order moment of light ($M_{20}$) than their non-nucleated counterparts at a given stellar mass. Additionally, we find the nucleation fractions to be typically higher in the Fornax main cluster than in the Fornax A group, and that the nucleation fraction is highest towards the centre of their respective environments. We also find that the BIC can recover our labels of nucleation up to an accuracy of 97\%. (abridged)