Accurate astrometry is a key deliverable for the next generation of multi-conjugate adaptive optics (MCAO) systems. The MCAO Visible Imager and Spectrograph (MAVIS) is being designed for the Very Large Telescope Adaptive Optics Facility and must achieve 150 $mu$as astrometric precision (50 $mu$as goal). To test this before going on-sky, we have created MAVISIM, a tool to simulate MAVIS images. MAVISIM accounts for three major sources of astrometric error, high- and low-order point spread function (PSF) spatial variability, tip-tilt residual error and static field distortion. When exploring the impact of these three error terms alone, we recover an astrometric accuracy of 50 $mu$as for all stars brighter than $m=19$ in a 30s integration using PSF-fitting photometry. We also assess the feasibility of MAVIS detecting an intermediate mass black hole (IMBH) in a Milky Way globular cluster. We use an N-body simulation of an NGC 3201-like cluster with a central 1500 M$_{odot}$ IMBH as input to MAVISIM and recover the velocity dispersion profile from proper motion measurements. Under favourable astrometric conditions, the dynamical signature of the IMBH is detected with a precision of ~0.20 km/s in the inner ~4 of the cluster where HST is confusion-limited. This precision is comparable to measurements made by Gaia, HST and MUSE in the outer ~60 of the cluster. This study is the first step towards building a science-driven astrometric error budget for an MCAO system and a prediction of what MAVIS could do once on sky.
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