We investigate the relations between nuclear star clusters (NSCs) and their host galaxies, as well as conduct a comparison 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 galaxies (10^5.5^M_{sun}<M,galaxy_<10^11.5^M_{sun}) for which structural decomposition models and non-parametric morphological measurements are available from our previous work. We determine the nucleation of galaxies based on a combination of visual inspection of galaxy images and residuals from multi-component decomposition models, as well as use a model selection statistic, the Bayesian information criterion (BIC), to avoid missing any faint nuclei. We also test the BIC as an unsupervised method to determine the nucleation of galaxies. We characterise the NSCs using the nucleus components from the multi-component models conducted in the g', r', and i' bands. Overall, we find a dichotomy in the properties of nuclei which reside in galaxies more or less massive than M,galaxy_~10^8.5^M_{sun}. In particular, we find that the nuclei tend to be bluer than their host galaxies and follow a scaling relation of M,nuc_ {prop.to} M_,galaxy_^0.5^ for M_,galaxy_10^8.5^M_{sun} we find redder nuclei compared to the host galaxy which follow M,nuc_ {prop.to} M_*,galaxy_. Comparing the properties of nucleated and non-nuclated 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 ({Delta}(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. However, with the exception of {Delta}(g'-r') and the Gini coefficient (G), we do not find any significant correlations with cluster-centric distance. Yet, 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. Additionally, we find that the observed ultra-compact dwarf (UCD) fraction (i.e. the number of UCDs over the number of UCDs and nucleated galaxies) in Fornax and Virgo peak at the cluster centre, and is consistent with the predictions from simulations. Lastly, we find that the BIC can recover our labels of nucleation up to an accuracy of 97% without interventions. The different trends in NSC properties suggests that different processes are at play at different host stellar masses. A plausible explanation is that the combination of globular cluster in-spiral and in-situ star formation play a key role in the build-up of NSCs. In addition, the environment is clearly another important factor in the nucleation of galaxies, particularly at the centre of the cluster where the nucleation and UCD fractions peak. Nevertheless, the lack of significant correlations with the structures of the host galaxies is intriguing. Finally, our exploration of the BIC as a potential method of determining nucleation have applications for large scale future surveys, such as Euclid.
Cone search capability for table J/A+A/664/A167/table1 (Table of galaxy properties)
