The Unified Model: a journey beyond the solar system
January 2014 - In an exciting development led by astrophysicists from the University of Exeter, the Met Office's Unified Model has been used to start investigating the atmospheres of planets which lie beyond our own solar system - exoplanets.
Of the current set of over 1000 confirmed exoplanets and around a further 3500 unconfirmed candidates from the Kepler mission, current instrumentation offers us a glimpse of the atmospheres of a subset of these. Termed hot Jupiters, these planets are Jovian in size but orbit within 0.1 AU of their star, closer than Mercury is to our Sun. The large gravitational tidal forces felt by these objects are expected to force them into a synchronised rotation-orbit state, resulting in permanent 'day' and 'night' sides.
Using the Hubble Space Telescope astronomers have made measurements and inferences that give the basic ingredients to form an idealised model of the atmosphere of one of these distant, exotic worlds. These include the driving temperature gradient, rotation rate and information about the size, gravity and composition of the atmosphere. Perhaps most impressively, astronomers have been able to make tentative estimates of the wind speeds in the upper atmospheres of the hot Jupiter HD 209458b. They estimate the wind speeds to reach a staggering 1000 ms-1, i.e. about the current air speed record for a jet aircraft!
What makes the Unified Model useful for studying the atmospheres of hot Jupiters?
As well as being a leading model for simulating the Earth's weather and climate, the Unified Model relaxes some approximations that are often made in other models and which are probably not applicable to the more extreme atmospheres of the exoplanets. In particular, it is often assumed that the depth of the atmosphere is small compared to the radius of the planet (the shallow-atmosphere approximation). With the Even Newer Dynamics for General atmospheric modelling of the environment (ENDGame) version of the Unified Model this approximation can be made or not and hence the impact of the deep-/shallow-approximation can be investigated.
What makes studying the atmospheres of hot Jupiters useful for the Unified Model?
For those back on Earth, running the Unified Model in such extreme conditions stress tests the numerical basis of the model and increases confidence in the robustness of its formulation. This is especially important when the model is used to simulate changing climates of the future (though hopefully they will not be as extreme as those of a hot Jupiter!). Additionally, the developments that are emerging from this work, particularly on the radiation scheme, will inform us about some of the issues, and hopefully also the solutions, that will be encountered in using the model to simulate Space Weather.
The results of the research performed with the university team have been presented in two recent publications:
- Mayne et al. (2013a) (Using the UM dynamical cores to reproduce idealised 3-D flows) performed several idealised tests of Earth-like systems demonstrating a consistency of the results with others from the literature. The tests included a hypothetical tidally-locked Earth with a permanent day and night side. This work provided confidence in the set-up of the model and its basic ability to perform well in more extreme conditions than it is usually used for.
- In the second paper, Mayne et al. (2013b) (The UM, a fully-compressible, non-hydrostatic, deep atmosphere GCM, applied to hot Jupiters) present some initial idealised simulations of a hot Jupiter. Calculations have been performed for a thin layer of atmosphere (down to a pressure of 1 hPa) as well as a deeper test case down to 200 hPa of the planet HD 209458b.
Figure 1 shows the simulated temperature (colour scale) and horizontal wind (vector arrows) at heights of 10 000 km (about 1 hPa) and 5 000 km (about 100 hPa) above the inner boundary (top and bottom panels respectively). For the upper height layer the irradiation from the parent star is extremely intense (about a million times that received by Jupiter) and the day side temperature is forced very quickly to that of radiative equilibrium i.e. it is very hot! Additionally, the night side air cools very rapidly, creating large contrasts in temperature, about 1000 K, between the day and night side, or equator and pole (c.f. 40 K difference between the average equatorial and polar temperatures on Earth). This temperature gradient leads to a large pressure gradient. The hot day side is 'pumped up', with orders of magnitude larger pressures, at a given altitude, than the night side, driving winds of around 5 kms-1 around the planet. The terminator, which delineates the day and night side, can be thought of as a huge 'waterfall' as the gas plummets down the potential onto the night side. The feature eastward of the hot spot is a convergence of the winds that have circumnavigated the globe colliding and causing gas to descend rapidly adiabatically heating the air below. Deeper into the atmosphere much of the radiation has been attenuated by the layers above and therefore does not penetrate to this layer. Here, the advection, most significantly a prograde equatorial jet, can alter the temperature profile. This leads to a smearing of the hot spot and an offset in the hottest part of the atmosphere from the substellar point, or closest point to the parent star.
When the shallow-atmosphere approximation is made, the results match previous work solving similar equations. However, given that such atmospheres and their circulation patterns are expected to be large scale (i.e. not shallow) it is unsurprising that when the shallow-atmosphere approximation is relaxed the results begin to depart from the literature (which solve the primitive equations assuming a shallow-atmosphere). The slow rotation and fast advection speeds lead to Rossby deformation radii and Rhines scales, i.e. the scale of vortices and jets, that are approximately planetary in scale. The deep-atmosphere equations more accurately model the larger scale circulations which lead to `activation' of the deeper atmospheric layers via transfer of momentum between the upper lower pressure and deeper higher pressure regions. The resulting energy and momentum balance is then different for the deep-atmosphere solution, compared to that of the shallow-atmosphere case, and the atmospheric flow changes. Because the timescales for the deeper atmosphere and the momentum exchange are of order >500 days, these changes are only observed towards the end of the 1200 Earth days of simulation. Work is under way at the University of Exeter to understand how this evolution occurs, in terms of the underlying mechanisms driving the atmospheric dynamics, and the findings will be presented in a future work.
There are several immediate puzzles revealed by the observations of hot Jupiters. For instance, some of these planets appear much larger than predicted by evolutionary models (even taking into account heating via tidal effects and the irradiation). This is indicative of heating deep in the atmosphere, requiring a mechanism to either transport or deposit energy at depths greater than the radiation is expected to penetrate. Also, the presence of thermal inversions and aerosols in the atmospheres of some hot Jupiters has been suggested by observations, the presence of which require an understanding of the 3D circulations within these atmospheres. Given the depth of hot Jupiter atmospheres and the role that vertical winds are expected to have (for instance in supporting aerosols against settling) the UM is excellently equipped to tackle the scientific puzzles.
The existing radiative transfer scheme within the Unified Model is being developed and adapted, by the university team, to provide coupled models, helping to explore the deposition of heat as a function of depth in hot Jupiter atmospheres. Additionally, a chemical network is also being developed to address problems associated with the effect of the complex photochemical reactions expected at the top of the heavily irradiated atmospheres of hot Jupiters. The tools that are being developed as part of this work will allow the study of the climate of the young Earth, in a collaboration between the astrophysics team and members of the Earth Systems Science group at the University of Exeter. In particular this will allow the long-standing scientific puzzle termed the faint-young Sun paradox to be investigated. Due to the evolution of the Sun, the early Earth received around 20% less flux than today. Simple 1D radiative transfer models predict that the water should have been completely frozen, in contradiction to evidence from the fossil record. Some missing source of opacity (i.e. a greenhouse gas) or effects due to photochemistry, or 3D circulation could be responsible for keeping temperatures higher.