Structure and Evolution of an Exoplanet

We have seen that the process of formation (or evolution) of exoplanets seems to be very different from the planets in the Solar System, because giant exoplanets are discovered in close proximity to their stars. What about their internal structure and their atmospheres? We know the principal external factors responsible for the structure of planetary atmospheres (solar radiation, magnetic field, and interaction with the surface). In addition, the temperature and cloud structures of planetary atmospheres depend upon their composition, which determines, at each level, the opacities of the gaseous and solid phases (Sect. 4.4.2.2). We can also model a synthetic exoplanet spectrum that corresponds to each model in terms of comparing it with experimental data, when instrumental methods allow us to observe the spectra.

Modelling the internal structure of a sub-stellar object requires determining the temperature gradient and thus knowing the energy-transfer mechanism. Three mechanisms may be involved: radiation, conduction, and convection. A complete description of these processes may be found, in particular, in de Pater and Lissauer (2001) and Guillot (2006). A key parameter involved in all cases is the opacity, which depends on the atmospheric composition, pressure, and temperature, and determines how much energy is absorbed at each level. At pressures higher than a few bars, the collision-induced absorption caused by H2-H2 and H2-He collisions must be taken into account. In addition, molecules present in planetary atmospheres (CH4, NH3, H2O ...) contribute to the opacities through their rotational and vibration-rotation bands. As a result, the spectrum of a planetary atmosphere is strongly dependent upon the wavelength (see Sect. 4.4.2.2.). Finally, condensates may play an important role by contribution to the opacity; their abundances mostly depend on the temperature (see e.g., Pollack et al., 1994).

Radiation transfer typically dominates in planetary stratospheres and upper tropospheres, at pressures lower than 0.1 bar. In the conduction regime, energy is transferred by collisions between particles. This mechanism is efficient, in particular, near the surface of the terrestrial planets. Finally convection is the energy transport caused by large-scale motions induced by density gradients resulting from temperature differences. It may be shown (Guillot, 2006) that convection dominates in isolated sub-stellar objects (weakly irradiated exoplanets or brown dwarfs). It is

M. Ollivier et al., Planetary Systems. Astronomy and Astrophysics Library, DOI 978-3-540-75748-1.7, © Springer-Verlag Berlin Heidelberg 2009

also the case for dense atmospheres (with pressure higher than 1 bar) and molten interiors of planets.

We can also model a synthetic exoplanet spectrum that corresponds to each model in terms of comparing it with experimental data, when instrumental methods allow us to observe the spectra.

In this chapter we shall discuss the internal structure of exoplanets (giant ex-oplanets, ocean-type exoplanets, and terrestrial-like exoplanets), and then the atmospheric structure of giant exoplanets. The atmospheric models may be tested by comparing them with synthetic spectra that correspond to existing observations. A specific section is devoted to the case of habitable planets (these being defined as planets where the surface is at least partially covered in liquid water), and their spectral characteristics. The problem of searching for life on planets in the habitable zone is discussed in Appendix.

7.1 The Internal Structure of Giant Exoplanets

Giant exoplanets are considered to be analogous to the giant planets in the Solar System as far as their formation and evolution are concerned. We believe that they formed by accretion of a massive core of ices (about 10 Earth masses at least) and through the collapse of the surrounding nebula, which primarily consisted of hydrogen and helium (see Sect. 4.3.2.3). Subsequently they cooled and contracted gravi-tationally. A more comprehensive review may be found in Guillot (2006).

7.1.1 The Observable Features

In the case of exoplanets, we have only two observable features at our disposal: the minimum mass and, in a few cases, the exact mass and the radius. For the planets in the Solar System, we have a considerable number of far more significant data. In particular, several types of observational data allow us to put constraints on the internal structure of the giant planets in the Solar System:

a) the mass (determined very accurately thanks to the motion of satellites);

b) the equatorial radius, Re, and the polar radius, Rp (these being measured in the visible region);

c) the rate of rotation (the internal rotation, defined from the magnetic field; it is slightly different from the period derived from surface features);

d) the gravitational moments J2, J4 and J6, determined from the paths of space-probes; these are defined as follows:

where V is the gravitational potential, Pi Legendre polynomials, and Ji the gravitational moments of order i. The giant planets are close to hydrostatic equilibrium and only even-ordered coefficients cannot be neglected;

e) the atmospheric composition, in particular the abundance ratios of helium and heavy elements (carbon for the four giant planets, as well as S, N, and the rare gases for Jupiter, following the measurements made by the Galileo probe);

f) the thermal profile, determined down to a pressure-level of several bars by measurements of the radio occultations of the Voyager probes and, more accurately, down to 22 bars on Jupiter, thanks to the Galileo probe;

g) the energy balance for the giant planets, determined from measurements of the overall infrared emission by the IRIS experiment on the Voyager probes. An internal source was discovered for Jupiter, Saturn and Neptune. These three planets emit significantly more energy than they receive from the Sun. the intrinsic fluxes are 5500, 2000, and 430 ergs_1cm~2, respectively, for Jupiter, Saturn, and Neptune.

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