We study the feasibility of observationally constraining the rotation rate of hot Jupiters, planets that are typically assumed to have been tidally locked into synchronous rotation. We use a three-dimensional General Circulation Model to solve for the atmospheric structure of two hot Jupiters (HD 189733b and HD 209458b), assuming rotation periods that are 0.5, 1, or 2 times their orbital periods (2.2 and 3.3 days, respectively), including the effect of variable stellar heating. We compare two observable properties: 1) the spatial variation of flux emitted by the planet, measurable in orbital phase curves, and 2) the net Doppler shift in transmission spectra of the atmosphere, which is tantalizingly close to being measurable in high-resolution transit spectra. Although we find little difference between the observable properties of the synchronous and non-synchronous models of HD 189733b, we see significant differences when we compare the models of HD 209458b. In particular, the slowly rotating model of HD 209458b has an atmospheric circulation pattern characterized by westward flow and an orbital phase curve that peaks after secondary eclipse (in contrast to all of our other models), while the quickly rotating model has a net Doppler shift that is more strongly blue-shifted than the other models. Our results demonstrate that the combined use of these two techniques may be a fruitful way to constrain the rotation rate of some planets, and motivate future work on this topic.
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