The Albedo Problem and Cloud Cover on Hot Jupiters

TL;DR

The paper addresses the albedo discrepancy for hot Jupiters by reframing it through the phase integral $q = A_S/A_g$, linking observable reflected-light properties to cloud characteristics. It derives bandpass-integrated quantities $\bar{A}_g$ and $\bar{q}$ from Cassini Jupiter data across CHEOPS, TESS and Ariel bandpasses, and performs a population analysis using homogeneous and inhomogeneous reflectors with Henyey-Greenstein scattering to connect $q$ to cloud cover and particle size. The results show substantial wavelength dependence in bandpass-integrated albedos and phase integrals; $q$ commonly requires inhomogeneous cloud coverage with nonzero $g$, with Kepler-7b’s $\bar{q}=1.77 \pm 0.07$ well-reproduced by the ensemble approach, and a precision of $\delta \bar{q} \approx 0.1$ on the optical phase integral enabling constraint of cloud properties. The Ariel mission is projected to enable a large statistical survey of cloud cover on hot Jupiters by combining optical eclipses with infrared phase curves, allowing robust inferences on $A_B$, $\bar{A}_g$, and $q$ across a population and informing models of cloud formation in highly irradiated atmospheres.

Abstract

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 non-unity in value. We use existing Cassini data of 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 $\sim 0.1$, which corresponds to an uncertainty of $\sim 3\%$ 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 $\sim 100$ 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.

Figures (3)

• Figure 11: Left panel: Previously measured Cassini phase integral, spherical albedo and geometric albedo of Jupiter as functions of wavelength (from li18). Right panel: Bandpass-integrated geometric albedos computed using the respective filter response functions and the geometric albedo spectrum measured by the Cassini spacecraft. For comparison, we plot the Cassini geometric albedo spectrum across the JWST NIRISS SOSS wavelength range and the spectral response functions for Ariel, CHEOPS and TESS.
• Figure 22: Bandpass-integrated phase integrals versus geometric albedos for both real targets and synthetic populations. The real targets include the Solar System gas/ice giants and exoplanets both in the pre-JWST era and using JWST (curated data listed in Table 1). As the data are only for display purposes, we plot symmetric error bars using the larger of the uncertainties when they are asymmetric. For the synthetic population (5000 random draws), we have computed $q$ using the mathematical solutions of heng21 as described in the text. The left panel shows a synthetic population of homogeneous reflectors (2 parameters), while the right panel shows one of inhomogeneous reflectors (5 parameters). In both cases, a Henyey-Greenstein scattering phase function is assumed and only the randomly generated population of scattering asymmetry factors ($g$) is displayed in color.
• Figure 33: Population study of the phase integral using the same synthetic population of inhomogeneous reflectors generated in Figure \ref{['fig:pop']}, but plotted as functions of the scattering asymmetry factor and degree of cloud cover. For display purposes, we have restricted the color range for $q=1$ to $3$. Shown are the measured degree of cloud cover and scattering asymmetry factor for Kepler-7b (see text for details).