Modeling Spitzer 3.6 and 4.5 $\mu$m Eclipse Depths for the Inflated Hot Jupiter in the Evolved Binary System HD 202772

As an inflated Hot Jupiter orbiting an early-type primary star in the evolved binary HD 202772 system, HD 202772 A b's presence invites a study of how such a planet forms and evolves. As a prelude to potential atmospheric characterization with the latest generation of observatories, we present a reduction and analysis of eclipse light curve observations of HD 202772 A b acquired with the Spitzer Space Telescope using the 3.6 and 4.5 $\mu$m channels. We find eclipse depths of $680\pm68$ and $1081^{+54}_{-53}$ ppm, respectively, corresponding to day-side effective temperatures of $2130^{+102}_{-91}$ and $2611^{+46}_{-49}$ K. The corresponding Bond albedos are consistent with the distribution of albedos for Hot Jupiters observed with both Spitzer and TESS. The heat redistribution efficiencies consistent with the Bond albedo range predicted by 1-D atmospheric models in radiative-convective equilibrium are $0.71\pm0.10$ and $0.03^{+0.03}_{-0.02}$, respectively, indicating a weak day-night contrast for the former and a strong contrast for the latter. Given this, and the unique environment in which this planet resides, we recommend follow-up observations with JWST to more precisely constrain its atmospheric composition and structure, as well as its host stellar environment, to elucidate if and how the atmospheres of these close-in giants evolve with host stars in binaries past the main sequence.