Mapping the Skies of Ultracool Worlds: Detecting Storms and Spots with Extremely Large Telescopes

Extremely large telescopes (ELTs) present an unparalleled opportunity to study the magnetism, atmospheric dynamics, and chemistry of very low mass stars (VLMs), brown dwarfs, and exoplanets. Instruments such as the Giant Magellan Telescope - Consortium Large Earth Finder (GMT/GCLEF), the Thirty Meter Telescope's Multi-Objective Diffraction-limited High-Resolution Infrared Spectrograph (TMT/MODHIS), and the European Southern Observatory's Mid-Infrared ELT Imager and Spectrograph (ELT/METIS) provide the spectral resolution and signal-to-noise (S/N) necessary to Doppler image ultracool targets' surfaces based on temporal spectral variations due to surface inhomogeneities. Using our publicly-available code, $Imber$, developed and validated in Plummer & Wang (2022), we evaluate these instruments' abilities to discern magnetic star spots and cloud systems on a VLM star (TRAPPIST-1); two L/T transition ultracool dwarfs (VHS J1256$-$1257 b and SIMP J0136+0933); and three exoplanets (Beta Pic b and HR 8799 d and e). We find that TMT/MODHIS and ELT/METIS are suitable for Doppler imaging the ultracool dwarfs and Beta Pic b over a single rotation. Uncertainties for longitude and radius are typically $\lesssim 10^{\circ}$, and latitude uncertainties range from $\sim 10^{\circ} \ \rm{to} \ 30^{\circ}$. TRAPPIST-1's edge-on inclination and low $\upsilon \sin i$ provide a challenge for all three instruments while GMT/GCLEF and the HR 8799 planets may require observations over multiple rotations. We compare the spectroscopic technique, photometry-only inference, and the combination of the two. We find combining spectroscopic and photometric observations can lead to improved Bayesian inference of surface inhomogeneities and offers insight into whether ultracool atmospheres are dominated by spotted or banded features.