Probing the Variation of the Inner-Surface-Brightness Profile of Nuclear Star Clusters on the Intermediate-Mass Black Hole Mass Measurements Using Mock Observations of ELT/MICADO and HARMONI

Simulations of intermediate-mass black holes (IMBHs) in dwarf galaxies within 10 Mpc that host bright nuclear star clusters (NSCs), prime candidates for IMBH formation, using the High Angular Resolution Monolithic Optical and Near-infrared Integral (HARMONI) field spectrograph on the Extremely Large Telescope probes black hole formation in the early Universe. Our approach combines observed surface brightness profiles from the Hubble Space Telescope (HST), synthetic stellar population spectra, and Jeans Anisotropic Modeling (JAM) for stellar dynamics. Mock HARMONI observations were generated with the HSIM simulator and analyzed in a Bayesian framework to infer IMBH masses down to 0.5% of the NSC mass. In this work, we extend these simulations by constructing improved stellar-mass models using SimCADO to simulate imaging with the Multi-AO Imaging Camera for Deep Observations (MICADO). The MICADO data are jointly analyzed with HARMONI kinematics via JAM to reassess IMBH masses and uncertainties. This combined framework enables us to examine how variations in the NSC inner surface-brightness slope influence IMBH mass estimates, providing tighter constraints on low mass black holes and advancing models for IMBH detection in NSCs.