Multi-orbital-phase and multi-band characterization of exoplanetary atmospheres with reflected light spectra

Direct imaging of widely separated exoplanets from space will obtain their reflected light spectra and measure atmospheric properties. Previous calculations have shown that a change in the orbital phase would cause a spectral signal, but whether this signal may be used to characterize the atmosphere has not been shown. We simulate starshade-enabled observations of the planet 47 Uma b, using the to-date most realistic simulator SISTER to estimate the uncertainties due to residual starlight, solar glint, and exozodiacal light. We then use the Bayesian retrieval algorithm ExoReL$^\Re$ to determine the constraints on the atmospheric properties from observations using a Roman- or HabEx-like telescope, comparing the strategies to observe at multiple orbital phases or in multiple wavelength bands. With a $\sim20\%$ bandwidth in 600 - 800 nm on a Roman-like telescope, the retrieval finds a degenerate scenario with a lower gas abundance and a deeper or absent cloud than the truth. Repeating the observation at a different orbital phase or at a second $20\%$ wavelength band in 800 - 1000 nm, with the same integration time and thus degraded S/N, would effectively eliminate this degenerate solution. Single observation with a HabEx-like telescope would yield high-precision constraints on the gas abundances and cloud properties, without the degenerate scenario. These results are also generally applicable to high-contrast spectroscopy with a coronagraph with a similar wavelength coverage and S/N, and can help design the wavelength bandwidth and the observation plan of exoplanet direct imaging experiments in the future.