Hot Jupiters are a class of Jupiter-mass exoplanets that are characterised by high surface temperatures as they orbit very close to their parent stars. Most hot Jupiters have near-circular orbits with near-zero orbital eccentricities. A perfectly circular orbit is one where the orbital eccentricity is zero. There exist a fraction of hot Jupiters that have non-circular orbits with orbital eccentricities exceeding 0.1. One of the most extreme cases is the exoplanet HD80606b which has an orbital eccentricity of 0.93. Due to its large orbital eccentricity, the amount of flux HD80606b receives from its parent star varies by a factor of over 800.
Superrotation is a common phenomenon in atmospheric circulation models of hot Jupiters. Planetary scale waves in the atmosphere of a hot Jupiters converges angular momentum from the mid-latitudes towards the equator to generate an equatorial superrotating jet. The presence of an equatorial superrotating jet causes an eastward displacement of the hottest spot on the planet from the substellar point. Hot Jupiters in near-circular orbits are expected to be synchronously rotating where the same hemisphere of the planet perpetually facing its parent star like how the same hemisphere of the Moon always faces the Earth. This is due to the fact that the rotational and orbital periods of a synchronously rotating planet are equal. Things are different for hot Jupiters on non-circular eccentric orbits since they are expected to be pseudo-synchronously rotating where the same hemisphere of the planet does not perpetually face its parent star because the planet’s rotational and orbital periods are not equal. Instead, the same hemisphere of an eccentric hot Jupiter approximately faces its parent star only at closest approach during each orbit.
Figure I: Simulations of a hot Jupiter with an orbit-averaged stellar flux of 185691 W/m2 where the orbital eccentricity is increased from zero (top row) to 0.75 (bottom row). Illustrated here are plots of the orbit-averaged zonal wind speeds (left column) and the wind and temperature profiles at 30 millibars in the atmosphere during closest approach (right column). The vertical bars in the right column denote the substellar longitude. (Credit: Tiffany Kataria, et al., 2012)
Models of atmospheric circulation of eccentric hot Jupiters have shown that at closest approach to their parent stars, dayside temperatures, day-night temperature differences and wind speeds all increase with increasing orbital eccentricity. In Figure I shown above, an orbit-averaged stellar flux of 185691 W/m2 is employed for a hot Jupiter to model the effects of increasing orbital eccentricity on atmospheric circulation. As orbital eccentricity varies from 0 to 0.75, the peak temperatures at closest approach increase from 1000 to 1300 degrees Kelvin at the 30 millibar level in the atmosphere. Since the day-night temperature difference increases with increasing orbital eccentricity, the peak wind speed within the equatorial superrotating jet strengthens from 2500 m/s for a circular orbit to 5000 m/s for an orbital eccentricity of 0.75.
A larger orbital eccentricity also results in a shorter rotational period for the hot Jupiter which translates to an increase in rotational rate and a smaller Rossby radius of deformation. This is because the Rossby radius is inversely proportional to the square root of rotational rate. As a result, a hot Jupiter with a larger orbital eccentricity is expected to have a narrower equatorial superrotating jet since the width of the superrotating jet is directly proportional to the Rossby radius of deformation. In Figure I shown above, an orbital eccentricity of zero gives an average jet width of 100 degrees latitude while an orbital eccentricity of 0.75 gives an average jet width of 40 degrees latitude. Apart from the effects of orbital eccentricity, an increase in the orbit-averaged stellar flux shown below in Figure II also leads to strengthening and narrowing of the equatorial superrotating jet. A planet with a higher orbit-averaged stellar flux orbits its parent star at a smaller distance, resulting in a faster rotation rate and a narrower equatorial superrotating jet.
Figure II: Simulations of a hot Jupiter with an orbital eccentricity of 0.25. From top to bottom, the rows illustrate an increase in the orbit-averaged stellar flux. Shown here are plots of the orbit-averaged zonal wind speeds (left column) and the wind and temperature profiles at 30 millibars in the atmosphere during closest approach (right column). The vertical bars in the right column denote the substellar longitude. (Credit: Tiffany Kataria, et al., 2012)
Tiffany Kataria, et al., 2012, “Three-dimensional atmospheric circulation of hot Jupiters on highly eccentric orbits”, arXiv:1208.3795v1 [astro-ph.EP]