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Using a shallow water model with time-dependent forcing we show that the peakof an exoplanet thermal phase curve is, in general, offset from secondaryeclipse when the planet is rotating. That is, the planetary hot-spot is offsetfrom the point of maximal heating (the substellar point) and may lead or lagthe forcing; the extent and sign of the offset is a function of both therotation rate and orbital period of the planet. We also find that the systemreaches a steady-state in the reference frame of the moving forcing. The modelis an extension of the well studied Matsuno-Gill model into a full sphericalgeometry and with a planetary-scale translating forcing representing theinsolation received on an exoplanet from a host star.  The speed of the gravity waves in the model is shown to be a key metric inevaluating the phase curve offset. If the velocity of the substellar point(relative to the planet's surface) exceeds that of the gravity waves then thehotspot will lag the substellar point, as might be expected by consideration offorced gravity wave dynamics. However, when the substellar point is movingslower than the internal wavespeed of the system the hottest point can lead thepassage of the forcing. We provide an interpretation of this result byconsideration of the Rossby and Kelvin wave dynamics as well as, in the veryslowly rotating case, a one-dimensional model that yields an analytic solution.Finally, we consider the inverse problem of constraining planetary rotationrate from an observed phase curve.

The thermal phase curve offset on tidally- and non-tidally-locked exoplanets: A shallow water model