Wavelength Does Not Equal Pressure: Vertical Contribution Functions and Their Implications for Mapping Hot Jupiters

Multi-band phase variations, in principle, allow us to infer the longitudinal temperature distributions of planets as a function of height in their atmospheres. For example, 3.6 μm emission originates from deeper layers of the atmosphere than 4.5 μm due to greater water vapor absorption at the longer wavelength. Because heat transport efficiency increases with pressure, we expect thermal phase curves at 3.6 μm to exhibit smaller amplitudes and greater phase offsets than at 4.5 μm - yet this trend is not observed. Of the seven hot Jupiters with full-orbit phase curves at 3.6 and 4.5 μm, all of them have greater phase amplitude at 3.6 μm than at 4.5 μm, while four of the seven exhibit a greater phase offset at 3.6 μm. We use a 3D radiative-hydrodynamic model to calculate theoretical phase curves of HD 189733b, assuming thermo-chemical equilibrium. The model exhibits temperature, pressure, and wavelength-dependent opacity, primarily driven by carbon chemistry: CO is energetically favored on the dayside, while CH₄ is favored on the cooler nightside. Infrared opacity, therefore, changes by orders of magnitude between day and night, producing dramatic vertical shifts in the wavelength-specific photospheres, which would complicate eclipse or phase mapping with spectral data. The model predicts greater relative phase amplitude and greater phase offset at 3.6 μm than at 4.5 μm, in agreement with the data. Our model qualitatively explains the observed phase curves, but it is in tension with current thermo-chemical kinetics models that predict zonally uniform atmospheric composition due to the transport of CO from the hot regions of the atmosphere.