Simulating intermediate black hole mass measurements for a sample of galaxies with nuclear star clusters using ELT/HARMONI high spatial resolution integral-field stellar kinematics

Understanding the demographics of intermediate-mass black holes (IMBHs, $M_{\rm BH} \approx 10^2-10^5$ M$_\odot$) 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 ELT/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 \hst\ imaging, stellar population models, and Jeans Anisotropic Models (JAM), assuming IMBH masses up to 1\% of the NSC mass. We simulated observations across six NIR gratings at 10 mas resolution. Analyzing the mock data with standard kinematic extraction (pPXF) and JAM models in a Bayesian framework, we demonstrate that HARMONI can resolve the IMBH SOI and accurately recover masses down to $\approx 0.5\%$ of the NSC mass within feasible exposure times. These results highlight HARMONI's potential to revolutionize IMBH studies.