摘要：Aims. We aim to investigate the relations between nuclear star clusters (NSCs) and their host galaxies and to offer 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. Methods. We selected 557 galaxies (105.5 M < M∗,galaxy < 1011.5 M) for which structural decomposition models and non-parametric morphological measurements are available from our previous work. We determined the nucleation of galaxies based on a combination of visual inspection of galaxy images and residuals from multi-component decomposition models, as well as using a model selection statistic, the Bayesian information criterion (BIC), to avoid missing any faint nuclei. We also tested the BIC as an unsupervised method to determine the nucleation of galaxies. We characterised the NSCs using the nucleus components from the multi-component models conducted in the g 0 , r 0 , and i 0 bands. Results. Overall, we find a dichotomy in the properties of nuclei that reside in galaxies more or less massive than M∗,galaxy ≈ 108.5 M. In particular, we find that the nuclei tend to be bluer than their host galaxies and follow a scaling relation of M∗,nuc ∝ M∗,galaxy 0.5 for M∗,galaxy < 108.5 M. In galaxies with M∗,galaxy > 108.5 M, we find redder nuclei compared to the host galaxy, which follows M∗,nuc ∝ M∗,galaxy. Comparing the properties of nucleated and non-nucleated early-type galaxies, we find that nucleated galaxies tend to be redder in global (g 0 − r 0 ) colour, have redder outskirts relatively to their own inner regions (∆(g 0 − r 0 )), are less asymmetric (A), and exhibit less scatter in the brightest second-order moment of light (M20) than their non-nucleated counterparts at a given stellar mass. However, with the exception of ∆(g 0 − r 0 ) 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 peaks 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. Conclusions. The different trends in NSC properties suggest 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.
