The Effect of Atmospheric Chemistry on the Optical Geometric Albedos of Hot Jupiters

Abstract

We investigate the geometric albedos of hot Jupiters by comparing observational data from space telescopes TESS, Kepler, CoRoT, and CHEOPS against theoretical models. The study aims to understand the distribution of observed geometric albedos across different bandpasses and how these observations align with or deviate from model predictions. We have curated a comprehensive sample of observed geometric albedos, using either existing Spitzer secondary eclipse measurements or a scaling law between the equilibrium and dayside temperature to remove any contaminating thermal planetary emission. We then utilised hierarchical Bayesian modelling to identify trends with planetary properties such as equilibrium temperature, gravity, and stellar metallicity. On a population level, we found no statistical difference in the distributions of geometric albedos measured by TESS compared to those by Kepler, CoRoT and CHEOPS. We confront the geometric albedo sample with a simple, but first principles, model that includes Rayleigh scattering by molecular hydrogen and absorption by sodium, water and titanium oxide and vanadium oxide. We find that the abundance of sodium and water are the key absorbers that influence the geometric albedos of hot Jupiters, whilst the addition of titanium oxide and vanadium oxide (in the absence of condensation) results in vanishing geometric albedos that are inconsistent with the observed distributions.

Figures (12)

• Figure 1: Transmission functions for CHEOPS, Kepler, CoRoT and TESS instruments as a function of wavelength. In this study we group CHEOPS, Kepler and CoRoT together due to their similarity in transmission functions. TESS is kept separate as it transmits more into the red.
• Figure 2: The distribution of observed geometric albedos for both bandpasses (CoRoT-Kepler-CHEOPS (CKC) in blue and TESS in orange), where each observation (from Table \ref{['tab:albedos']}) is treated as a Gaussian distribution with a width given by the 1-sigma uncertainty reported. This histogram plot is made from 10,000 samples of each observation and then normalised. The CKC sample peaks around $A_g = 0.1$ whereas the TESS sample has a wider peak and has a maximum at $A_g = 0$. However, this could be a result of the much wider errorbars in the TESS data, smoothing out any peaks.
• Figure 3: Three panels show the best-fit models (Rayleigh, half-Gaussian and Beta distributions) plotted over the observed geometric albedos, with the shading showing the $1\sigma$ uncertainties in the fits. In orange is the TESS band and in the blue, the CKC band. We find that the best-fit models from the two bandpasses are consistent. We also find that, by calculating the BIC of each fit, that the Rayleigh distribution is the best-fitting model for this data (although not very significantly) and the Beta distribution the worst.
• Figure 4: Geometric albedos and physical parameters for targets observed with CoRoT-Kepler-CHEOPS (blue points) and TESS (orange points). The trend results can be found in Table \ref{['tab:bic']}. We have restricted the y-axis to physical values of the geometric albedo, however it should be noted that some targets (WASP-18b and WASP-33b) have median posterior values below 0.
• Figure 5: Geometric albedo model results, produced by sampling over the input parameter prior distributions (see Table \ref{['tab:chemeq_priors']}) and assuming chemical equilibrium. The wavelength-dependent albedos were then bandpass-integrated to produce the expected albedos in the TESS (orange) and CKC (blue) band. Not shown are the albedos as a function of $T_*$, $T_{\text{planet}}$ and pressure, as these show no discernible correlation. We find that the metallicity (log [M/H]) has the largest impact on the geometric albedo and that from this, water abundance produces slightly tighter constraints on $A_g$ than sodium. We also see very distinct differences between the CHEOPS and TESS bandpasses.