Extending the Frontier of Spatially-Resolved Supermassive Black Hole Mass Measurements to at $1\lesssim z\lesssim2$: Simulations with ELT/MICADO High-Resolution Mass Models and HARMONI Integral-Field Stellar Kinematics

Abstract

Current spatially resolved kinematic measurements of supermassive black hole (SMBH) masses are largely confined to the local Universe (distances $\lesssim100$ Mpc). We investigate the potential of the Extremely Large Telescope's (ELT) first-light instruments, MICADO and HARMONI, to extend these dynamical measurements to galaxies at redshift $1\lesssim z\lesssim2$. We select a sample of five bright, massive, quiescent galaxies at these redshifts, adopting their S\'ersic profiles from HST photometry as their intrinsic surface brightness distributions. Based on these intrinsic models, we generate mock MICADO images using SimCADO and mock HARMONI integral-field spectroscopic data cubes using HSIM. The HARMONI simulations utilize input stellar kinematics derived from Jeans Anisotropic Models (JAM). We then process these mock observations: the simulated MICADO images are fitted with Multi-Gaussian Expansion to derive stellar mass models, and stellar kinematics are extracted from mock HARMONI cubes with pPXF. Finally, these derived stellar mass models and kinematics are used to constrain JAM dynamical models within a Bayesian framework. Our analysis demonstrates that SMBH masses can be recovered with an accuracy of $\sim$10%. We find that MICADO can provide detailed stellar mass models with $\sim$1 hour of on-source exposure. HARMONI requires longer minimum integrations for reliable stellar kinematic measurements of SMBHs. The required on-source time scales with apparent brightness, ranging from 5-7.5 hours for galaxies at $z\approx1$ (F814W, 20-20.5 mag) to 5 hours for galaxies at $1<z\lesssim2$ (F160W, 20.8 mag). These findings highlight the ELT's capability to push the frontier of SMBH mass measurements to $z\approx2$, enabling crucial tests of SMBH-galaxy co-evolution at the top end of the galaxy mass function.