  We present a semi-analytic model atmosphere for close-in exoplanets that
captures the essential physics of phase curves: orbital and viewing geometry,
advection, and re-radiation. We calibrate the model with the well-characterized
transiting planet, HD 189733b, then compute light curves for seven of the most
eccentric transiting planets. We present phase variations for a variety of
different radiative times and wind speeds. In the limit of instant
re-radiation, the light curve morphology is entirely dictated by the planet's
eccentricity and argument of pericenter: the light curve maximum leads or
trails the eclipse depending on whether the planet is receding from or
approaching the star at superior conjunction, respectively. For a planet with
non-zero radiative timescales, the phase peak occurs early for super- rotating
winds, and late for sub-rotating winds. We find that for a circular orbit, the
timing of the phase variation maximum with respect to superior conjunction
indicates the direction of the dominant winds, but cannot break the degeneracy
between wind speed and radiative time. For circular planets the phase minimum
occurs half an orbit away from the phase maximum -despite the fact that the
coolest longitudes are always near the dawn terminator- and therefore does not
convey any additional information. In general, increasing the advective
frequency or the radiative time has the effect of reducing the peak-to-trough
amplitude of phase variations, but there are interesting exceptions to these
trends. Lastly, eccentric planets with orbital periods significantly longer
than their radiative time exhibit "ringing" whereby the hot spot generated at
periastron rotates in and out of view. The existence of ringing makes it
possible to directly measure the wind speed (the frequency of the ringing) and
the radiative time constant (the damping of the ringing).
