Rotation Period Detection for Earth-like Exoplanets

A terrestrial planet's rotation period is one of the key parameters that determines its climate and habitability. Current methods for detecting the rotation period of exoplanets are not suitable for terrestrial exoplanets. Here we demonstrate that, under certain conditions, the rotation period of an Earth-like exoplanet will be detectable using direct-imaging techniques. We use a global climate model that includes clouds to simulate reflected starlight from an Earth-like exoplanet and explore how different parameters (e.g., orbital geometry, wavelength, time resolution) influence the detectability of the planet's rotation period. We show that the rotation period of an Earth-like exoplanet is detectable using visible-wavelength channels with time-series monitoring at a signal-to-noise ratio (S/N) >20 with similar to 5-15 rotation periods of data, while the rotation period of a planet with full ocean coverage is unlikely to be detectable. To better detect the rotation period, one needs to plan the observation so that each individual integration would yield a S/N >10, while keeping the integration time shorter than 1/6 to 1/4 of the rotation period of the planet. Our results provide important guidance for rotation period detection of Earth-like exoplanets in reflected light using future space telescopes.