Constraining the radius and atmospheric properties of directly imaged exoplanets through multi-phase observations

Context. The theory of remote sensing shows that observing a planet at multiple phase angles (α ) is a powerful strategy to characterize its atmosphere. Here, we study this observing strategy as applied to future disc-integrated direct imaging of exoplanets in reflected starlight.Aims. We analyse how the information contained in reflected-starlight spectra of exoplanets depends on the phase angle and the potential of multi-phase measurements to better constrain the atmospheric properties and the planet radius (R p ).Methods. We simulate spectra (500−900 nm) at α = 37°, 85°, and 123° with a spectral resolution of R ~ 125−225 and signal-to-noise ratio (S ∕N ) = 10, consistent with the expected capabilities of future direct-imaging space telescopes. Assuming a H2 -He atmosphere, we use a seven-parameter model that includes the atmospheric methane abundance ( ), the optical properties of a cloud layer and R p . All these parameters are assumed to be unknown a priori and are explored with a Markov chain Monte Carlo retrieval method.Results. No single-phase observation can robustly identify whether the atmosphere has clouds or not. A single-phase observation at α = 123° and S ∕N = 10 can constrain R p with a maximum error of 35%, regardless of the cloud coverage. We find that combining small (37°) and large (123°) phase angles is a generally effective strategy to break multiple parameter degeneracies. This enables us to determine the presence or absence of a cloud and its main properties, and R p , with higher confidence in all the explored scenarios. Other strategies, such as doubling S ∕N to 20 for a single-phase observation or combining small (37°) and moderate (85°) phase angles, fail to achieve this. We show that the improvements in multi-phase retrievals are associated with the shape of the scattering phase function of the cloud aerosols and that the improvement is more modest for isotropically scattering aerosols. We finally discuss that misidentifying the background gas in the retrievals of super-Earth observations leads to systematic underestimation of the absorbing gas abundance.Conclusions. Exoplanets with wide ranges of observable phase angles should be prioritized for atmospheric characterization in reflected starlight.