  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.
