  Infrared lightcurves of transiting hot Jupiters present a trend in which the
atmospheres of the hottest planets are less efficient at redistributing the
stellar energy absorbed on their daysides---and thus have a larger day-night
temperature contrast---than colder planets. No predictive atmospheric model has
been published that identifies which dynamical mechanisms determine the
atmospheric heat redistribution efficiency on tidally locked exoplanets. Here
we present a two-layer shallow water model of the atmospheric dynamics on
synchronously rotating planets that explains the observed trend. Our model
shows that planets with weak friction and weak irradiation exhibit a banded
zonal flow with minimal day-night temperature differences, while models with
strong irradiation and/or strong friction exhibit a day-night flow pattern with
order-unity fractional day-night temperature differences. To interpret the
model, we develop a scaling theory that shows that the timescale for gravity
waves to propagate horizontally over planetary scales, t_wave, plays a dominant
role in controlling the transition from small to large temperature contrasts.
This implies that heat redistribution is governed by a wave-like process,
similar to the one responsible for the weak temperature gradients in the
Earth's tropics. When atmospheric drag can be neglected, the transition from
small to large day-night temperature contrasts occurs when t_wave ~
sqrt(t_rad/Omega), where t_rad is the radiative relaxation time and Omega is
the planetary rotation frequency. Alternatively, this transition criterion can
be expressed as t_rad ~ t_vert, where t_vert is the timescale for a fluid
parcel to move vertically over the difference in day-night thickness. These
results subsume the commonly used timescale comparison for estimating heat
redistribution efficiency between t_rad and the global horizontal advection
timescale, t_adv.
