Towards realistic modelling of the astrometric capabilities of MCAO systems: Detecting an intermediate-mass black hole with MAVIS

Accurate astrometry is a key deliverable for the next generation of multiconjugate adaptive optics (MCAO) systems. The MCAO-Assisted Visible Imager and Spectrograph (MAVIS) is being designed for the Very Large Telescope Adaptive Optics Facility and must achieve 150 μas astrometric precision (50 μas goal). To test this before going on-sky, we have created MAVIS Image Simulator (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 μas for all stars brighter than m = 19 in a 30 s 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 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-1 in the inner ∼4 arcsec of the cluster where Hubble Space Telescope (HST) is confusion limited. This precision is comparable to measurements made by Gaia, HST, and Multi Unit Spectroscopic Explorer (MUSE) in the outer ∼60 arcsec 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.