2025A&A...694A..42L

The coexistence of nuclear star clusters (NSCs) and supermassive black holes (SMBHs) in galaxies with stellar masses of ∼10¹⁰ M_⊙, scaling relations between their properties and the properties of the host galaxy (e.g., ${M_{{\rm{NSC}}}^{{\rm{stellar }}} - M_{{\rm{galaxy }}}^{{\rm{stellar }}}}$ and ${{M_{{\rm{BH}}}} - M_{{\rm{galaxy }}}^{{\rm{stellar }}}}$), and the fact that NSCs seem to take on the role of SMBHs in less massive galaxies (and vice versa in the more massive ones) suggest that the origin of NSCs and SMBHs is related. In this study we implemented an 'in situ' NSC formation scenario in which NSCs are formed in the center of galaxies due to star formation in the accumulated gas. We explored the impact of the free parameter A_res, which regulates the amount of gas transferred to the NSC reservoir and thus plays a crucial role in shaping the cluster's growth. Simultaneously, we included a black hole (BH) seed formation recipe based on stellar collisions within NSCs in the semi-analytic model GALACTICUS to explore the resulting population of SMBHs. We determined the parameter space of the NSCs that form a BH seed and find that in initially more compact NSCs, the formation of these BH seeds is more favorable. This leads to the formation of light, medium, and heavy BH seeds, which eventually reach masses of up to ∼10⁹ M_⊙ and is comparable to the observed SMBH mass function at masses above 10⁸ M_⊙ . Additionally, we compared the resulting population of NSCs with a NSC mass function derived from the stellar mass function of galaxies from the GAMA survey at ɀ < 0.06, finding a good agreement in terms of shape. We also find a considerable overlap in the observed scaling relations between the NSC mass, the stellar mass of the host galaxy, and the velocity dispersion, which is independent of the value of Ares . However, the chi-square analysis suggests that the model requires further refinement to achieve better quantitative agreement.