Diurnal thermal tides in a non-synchronized hot Jupiter

Abstract

We perform a linear analysis to investigate the dynamical response of a non‐synchronized hot Jupiter to stellar irradiation. In this work, we consider the diurnal Fourier harmonic of the stellar irradiation acting at the top of a radiative layer of a hot Jupiter with no clouds and winds. In the absence of the Coriolis force, the diurnal thermal forcing can excite internal waves propagating into the planet's interior when the thermal forcing period is longer than the sound crossing time of the planet's surface. When the Coriolis effect is taken into consideration, the latitude‐dependent stellar heating can excite weak internal waves (g modes) and/or strong baroclinic Rossby waves (buoyant r modes) depending on the asynchrony of the planet. When the planet spins faster than its orbital motion (i.e. retrograde thermal forcing), these waves carry negative angular momentum and are damped by radiative loss as they propagate downwards from the upper layer of the radiative zone. As a result, angular momentum is transferred from the lower layer of the radiative zone to the upper layer and generates a vertical shear. We estimate the resulting internal torques for different rotation periods based on the parameters of HD 209458b.

Semidiurnal thermal tides in asynchronously rotating hot Jupiters

“…Goldreich & Soter 1966) be enhanced by several orders of magnitude. This reinforces the conclusions of Arras & Socrates (2010) for the semidiurnal tide, and of Gu & Ogilvie (2009) who demonstrated that the diurnal thermal tide could drive the upper layers of the atmosphere into asynchronous rotation by transporting angular momentum upward. Moreover, it emphasizes the necessity to consider the possibility of tidally-driven asynchronous zonal flows in the modeling of the general circulation of hot Jupiters beyond a critical orbital radius, which is approximately r ≈ 0.03 AU in the treated case.…”

“…Thermal tides have been examined before in different ways (Gu & Ogilvie 2009;Arras & Socrates 2010;Leconte et al 2015). Here, we use the formalism developed by Auclair-Desrotour et al (2017a) with the physical setup of Arras & Socrates (2010).…”

“…Indeed, this change of coordinates expands the domain of the stably stratified atmosphere (see Ioannou & Lindzen 1993a,b, 1994, for gravitational atmospheric tides in Jovian planets), which allows us to increase the vertical resolution in this region. Another way to expand the heated radiative zone would be to choose the optical depth z op measured from r = +∞ as radial coordinate, as done by Gu & Ogilvie (2009). With this coordinate, the upper limit of the atmosphere corresponds to z op = 0 and the center of the planet to z op = +∞.…”

“…These arguments invoke the transport of angular momentum between the planet's orbit and its atmosphere or interior Showman & Guillot (2002), the forcing of a fast superrotating equatorial jet in the atmosphere by the strong day-night heating contrast (Showman et al 2015), and the ability of thermal tides to generate asynchronous zonal flows (Gu & Ogilvie 2009;Arras & Socrates 2010). This later mechanism was first introduced by Gold & Soter (1969) through an ad hoc approach to explain the locking of Venus at the observed retrograde rotation rate.…”

“…However, as discussed by Gu & Ogilvie (2009), there is no solid surface in hot Jupiters to support the load of a mass surplus in the atmosphere of the planet as in telluric Venus-like planets. As a consequence, it would seem that no net tidal bulge could appear and the tidal torque exerted on the atmosphere should be negligible.…”