Why the Northern Hemisphere Needs a 30-40 m Telescope and the Science at Stake: Mapping formation pathways of nuclear star clusters across galaxies

Nuclear star clusters (NSCs) are dense, compact stellar systems only a few parsecs across, located at galaxy centers. Their small sizes make them difficult to resolve spatially. NSCs often coexist with massive black holes, and both trace the dynamical state and evolution of their host galaxies. Dense stellar environments such as NSCs are also ideal sites for forming intermediate-mass black holes (IMBHs). To date, spatially resolved NSC properties, crucial for reconstructing dynamical and star-formation histories, have only been obtained for galaxies within 5 Mpc, using the highest-resolution instruments on the current class of very large telescopes. This severely limits spectroscopic studies, and a systematic, unbiased survey has never been accomplished. Because the vast majority of known NSCs are located in the Northern Hemisphere, only a 30-m-class telescope in the North can provide the statistical power needed to study their physical properties and measure the mass of coexisting central black holes. We propose leveraging the capabilities of a 30-m-class Northern telescope to obtain the first comprehensive, spatially resolved survey of NSCs, finally allowing us to unveil their formation pathways and their yet unknown connection with central massive black holes.