2026ApJ...996L..11H

Observations of transiting hot Jupiters have revealed a mismatch between the values of the Bond versus geometric albedos. In the planetary science literature, the ratio of these quantities is known as the phase integral. It has been extensively measured for the solar system planets and shown to generally be nonunity in value. We use existing Cassini data on Jupiter to derive bandpass-integrated geometric albedos and phase integrals in the CHEOPS, TESS, and Ariel bandpasses, demonstrating that these quantities vary markedly across these different wavelength ranges. By performing a population study of geometric albedos and phase integrals, we demonstrate that atmospheres with partial cloud cover may be identified using measurements of the phase integral if its measured uncertainty is ∼0.1, which corresponds to an uncertainty of ∼3% on the optical/visible secondary eclipse depth. The upcoming Ariel space mission will conduct an unprecedented statistical survey of cloud cover on hot Jupiters via the simultaneous measurement of ∼100 infrared phase curves and optical secondary eclipses. Whenever available, the shape of optical phase curves of reflected light will directly constrain the phase integral, spherical albedo, degree of cloud cover, and scattering asymmetry factor.