2025AJ....170..124N

Understanding the demographics of intermediate-mass black holes (IMBHs, M_BH ≈ 10²-10⁵M_⊙) in low-mass galaxies is key to constraining black hole seed formation models, but detecting them is challenging due to their small gravitational sphere of influence (SOI). The upcoming Extremely Large Telescope (ELT) High Angular Resolution Monolithic Optical and Near-infrared Integral Field Spectrograph (HARMONI) instrument, with its high angular resolution, offers a promising solution. We present simulations assessing HARMONI's ability to measure IMBH masses in nuclear star clusters (NSCs) of nearby dwarf galaxies. We selected a sample of 44 candidates within 10 Mpc. For two representative targets, NGC 300 and NGC 3115 dw01, we generated mock HARMONI integral-field data cubes using realistic inputs derived from Hubble Space Telescope imaging, stellar population models, and Jeans anisotropic models (JAM), assuming IMBH masses up to 1% of the NSC mass. We simulated observations across six near-infrared gratings at 10 mas resolution. Analyzing the mock data with standard kinematic extraction and JAM models in a Bayesian framework, we demonstrate that HARMONI can resolve the IMBH SOI and accurately recover masses down to ≈0.5% of the NSC mass within feasible exposure times. These results highlight HARMONI's potential to revolutionize IMBH studies.