Close-in exoplanets with highly eccentric orbits are subject to large variations in incoming stellar flux between periapse and apoapse. These variations may lead to large swings in atmospheric temperature, which in turn may cause changes in the chemistry of the atmosphere from higher CO abundances at periapse to higher CH4 abundances at apoapse. Here we examine chemical timescales for CO<->CH4 interconversion compared to orbital timescales and vertical mixing timescales for the highly eccentric exoplanets HAT-P-2b and CoRoT-10b. As exoplanet atmospheres cool, the chemical timescales for CO<->CH4 tend to exceed orbital and/or vertical mixing timescales, leading to quenching. The relative roles of orbit-induced thermal quenching and vertical quenching depend upon mixing timescales relative to orbital timescales. For both HAT-P-2b and CoRoT-10b, vertical quenching will determine disequilibrium CO<->CH4 chemistry at faster vertical mixing rates (Kzz > 10^7 cm^2 s^-1), whereas orbit-induced thermal quenching may play a significant role at slower mixing rates (Kzz < 10^7 cm^2 s^-1). The general abundance and chemical timescale results - calculated as a function of pressure, temperature, and metallicity - can be applied for different atmospheric profiles in order to estimate the quench level and disequilibrium abundances of CO and CH4 on hydrogen-dominated exoplanets. Observations of CO and CH4 on highly eccentric exoplanets may yield important clues to the chemical and dynamical properties of their atmospheres.
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