A numerical simulation study of an astrometry case for MORFEO at the ELT

Abstract: We report results from numerical simulations assessing astrometry measurements with the Multiconjugate Adaptive Optics Relay for ELT Observations (MORFEO) instrument on the Extremely Large Telescope (ELT). Using the Advanced Exposure Time Calculator (AETC), we evaluate MORFEO astrometric accuracy in moderately crowded fields. Our simulations account for spatially variable Point Spread Function (PSF), geometric distortion, and rotation-dependent variations. We computed focal plane coordinates using observed stellar distribution and computed population synthesis with the SPISEA tool, generating stellar magnitude distributions for MICADO filters at selected metallicities and stellar ages. Our analysis shows that MORFEO can achieve high-precision astrometry in the galaxy neighborhood (within $\mu < 24$ mag) by minimizing PSF enlargement and optimizing calibration strategies. These results inform future observational campaigns and contribute to the development of astrometric science cases for the ELT.