Large-scale circulation and winds

Circulation on hot jupiters

The circulation on hot jupiters is driven by the large dayside–nightside as well as the equator– pole temperature contrasts, and the atmosphere’s tendency of striving towards a global equilibrium. The global circulation pattern can be understood as the interaction between two kinds of waves, namely Rossby waves and Kelvin waves. The large temperature gra- dients in the latitudinal direction (equator vs. pole) create standing Rossby waves, prop- agating longitudinally westwards. Because Rossby waves are transverse waves, they will give rise latitudinal oscillations of the gas, i.e. in the north–south direction. Due to angular momentum conservation the latitudinally oscillating gas has to rotate, which leads to the formation of eddies.2 _{At the same time, the dayside–nightside temperature contrast drives}

Kelvin waves, which propagate into the eastward direction, and the superposition of which onto the Rossby wave pattern leads to a tilting of the Rossby eddies from north-west to the south-east on the northern hemisphere, and from south-west to north-east one the south- ern hemisphere. These wave patterns are depicted in Figure2.1, taken from (Showman & Polvani 2011). The tilted eddies transport angular momentum from the planet’s poles to the equator, giving rise to eastward flowing jets. Because the jet transports gas eastwards, this kind of circulation is also called ‘superrotation’.

As the jet transports heated gas from the day- to the nightside, it causes a dampening of the temperature contrasts between the two hemispheres. Here it is important to appreciate that this occurs in the photosphere of the planets, meaning that the jet can have a direct effect on the planetary emission, by changing its horizontal temperature structure. The analytical criterion of assessing whether or not the winds will have a large impact on the planetary

1_{‘Barotropic’ means that the gas density depends on the pressure only, such as for adiabatic processes.} 2_{An eddy can be thought of as a region of vortex-like rotation.}

spectrum is by comparing the horizontal advection timescale of the jet, ⌧adv, with the radia- tive cooling timescale of the atmosphere, ⌧rad. If

⌧rad> ⌧adv, (2.4)

then the planet transports energy to the nightside more quickly than the atmosphere can cool radiatively, and one expects to see weakened day-night temperature contrasts, and a hot spot offset from the substellar points in phase curves. However, as has been pointed out byHeng & Showman(2015), this analytical relation is non-predictive: without solving for the planetary dynamics the atmospheric advection speed is unknown! Also, the above inequation does not always hold, especially when the dayside heating becomes weaker. In general, and not only in the case of weaker dayside heating, it has been suggested that the vertical advection timescale may provide a better timescale to compare the radiative timescale to (Perez-Becker & Showman 2013).

FIGURE2.1: Dominating circulation pattern on hot jupiters: the equator– pole temperature contrast creates longitudinally propagating, standing Rossby waves traveling in the westward direction. The latitudinal oscil- lation of these waved forms eddies, due to angular momentum conserva- tion. The dayside–nightside temperature forcing creates eastward prop- agating Kelvin waves, which tilt the eddies into the eastward direction, which then transport angular momentum from the high latitudes to the equator, and give rise to the eastward blowing jet on the equator (figure taken fromShowman & Polvani 2011).

Finally, not all is lost when try- ing to predict the atmospheric sus- ceptibility to a smearing out of the temperature gradients by super- rotation: observations, as well as simplified analytical models, indi- cate that the stronger the dayside insolation becomes, the less effi- cient the jets become at equilibrat- ing the dayside–nightside temper- ature gradients, in part because the cooling timescale strongly de- creases as the planets become hotter (Perez-Becker & Showman 2013; Komacek & Showman 2016;

Komacek et al. 2017). Observa- tions show that as the planetary equilibrium temperature increases from 1000 to 2500 K, the day- night relative temperature con- trast (Tday Tnight)/Tday increases

from 0.2 to 0.7, while outliers with contrasts around 1 exist at all temperature ranges (Ko- macek et al. 2017).

40 Chapter 2. Physical properties of planetary atmospheres

Circulation on other planets

Hot jupiters are strongly irradiated, and because they are tidally locked, they rotate com- paratively slowly (multiple days) when compared to the Solar System planets.3 _{A key dif-}

ference is that on the cooler Earth, but also on the Solar System gas giants, the atmospheric radiative timescale is longer than the rotational timescale, which results in the day–night temperature contrasts to be of decreased importance and the equator–pole temperature con- trasts to be dominant (Heng & Showman 2015). On Earth, and on the Solar System gas giants, there exist multiple jet bands, whereas hot jupiters only exhibit a single, broad jet centered on the equator. This can be understood by considering the Rossby deformation radius (Showman & Polvani 2011),

RRoss/ ⌦ 1/2, (2.5)

which gives the typical jet width, and decreases as the planetary spin rate ⌦ increases. It has to be compared to the planetary radius in order to estimate the number and width of the jets which can form, and be qualitatively understood as the length scale over which the Coriolis forces start to overrule the north/southward-motions which would otherwise work towards the broadening of the jet.

I conclusion, the above discussion on atmospheric dynamics merely tried to point out some of the most important features, and is far from being complete. A planet’s circula- tion pattern is influenced by many factors and its size, insolation, rotation period, and the possible presence of magnetic fields may all play a role for the resulting circulation pattern (Batygin et al. 2013;Carone et al. 2015). Also clouds have been conjectured to be able to im- pact the flow pattern of planetary atmospheres (Heng & Showman 2015), either by changing the temperature structure due to their absorption and scattering properties, or even because of their dynamical interaction with the flow itself, if they have a high abundance and are coupled to the gas motions sufficiently well.4