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At the surface of the terrestrial planets, the scale height is 8 km for the Earth, 14 km for Venus, and 10 km for Mars. It is equal to 20 km on Jupiter, and 40 km on Saturn at a pressure level of 0.5 bar, which for Jupiter is close to the NH3 cloud layer.

The temperature structure of a planetary atmosphere mainly depends upon two mechanisms of transport, convection and radiation (see Sect. 5.2.6). Convection, which is dominant in dense atmospheres (P > 0.1 bar), where the temperature decreases as the altitude increases, is caused by density gradients resulting from temperature differences. Using the equation of hydrostatic equilibrium, it may be shown (see e.g., de Pater and Lissauer, 2001) that the temperature gradient follows the dry adiabatic lapse rate:

dT g

dz Cp where Cp is the thermal heat capacity at constant pressure.

The radiation mechanism dominates in the planet's upper troposphere and stratosphere, where the quantity e-T is neither negligible nor equal to 1, with t being the optical depth of the gas:

where kv is the absorption coefficient of the gas and p the density.

The radiative transfer equation is written (see e.g., Encrenaz et al., 2004):

dTv where m = cos 9, 9 being the angle between the line of incidence and the vertical; Iv is the specific intensity (a function of the frequency, v) and Jv is the source function. In planetary atmospheres, for pressures above about 1 mbar, collisions are usually sufficient to produce local thermodynamical equilibrium (LTE): the physical properties of the medium depend only on the temperature; the velocity distributions of the atoms and molecules are Maxwellian; the populations at different energy levels obey Boltzmann's Law; and the source function is the Planck function. Each atmospheric layer radiates like a blackbody, following Kirchhoff's Law:

The temperature at a level z is given by:

The opacity, for a given frequency, depends upon the spectroscopic properties of the atmospheric gases. Condensates are also to be taken into account: NH3 and NH4SH in Jupiter and Saturn, and additionally CH4 and hydrocarbons in Uranus and Neptune.

4.4.2.3 Thermal Emission from a Planetary Atmosphere

The thermal radiance emerging from a planetary atmosphere may be calculated assuming LTE, assuming the radiative transfer equation (see e.g., de Pater and Lissauer, 2001; Encrenaz et al., 2004):

where | is the cosine of the angle of incidence, B(z,v) is the blackbody emission at the altitude z and frequency v, and tv (z, |) is the optical depth above the altitude z, as defined above (Eq. 4.15).

A convenient parameter is the brightness temperature TB(z, v), which is the temperature that a blackbody would emit the same radiance at the given frequency. It may be estimated using the Barbier-Eddington approximation:

• In the case of the specific intensity emitted along the vertical (| = 1), the brightness temperature is, to a first approximation, the temperature of the atmospheric layer for which the optical depth is equal to 1.

• In the case of the flux emitted over the whole planetary disk (integrated over |), the brightness temperature is, to a first approximation, the temperature of the atmospheric layer for which the optical depth is equal to 2/3.

The thermal spectrum of a planetary atmosphere thus depends on two main quantities: the temperature and the optical depth at each level. The optical depth, in turn, depends on the density of the absorber (i.e., the mixing ratio of the atmospheric constituent) and its absorption coefficient. The absorption coefficient is known from spectroscopic data. When an atmosphere has a temperature gradient that changes sign with altitude, the infrared spectrum shows molecular lines either in emission (when the gradient is positive) or in absorption (when the gradient is negative), depending on the intensity of the line, and depending on the abundance an vertical distribution of the absorbing gas. Thermal spectra of Jupiter and Saturn beyond 5 |m typically show a combination of emission features (probing the stratosphere) and absorption features (arising from lower, tropospheric levels), as shown in Fig. 4.21.

4.4.3 The Terrestrial Planets

4.4.3.1 Variation Among the Terrestrial Planets

The four terrestrial planets - Mercury, Venus (Fig. 4.13), Earth, and Mars (Fig. 4.14), in order of their increasing distance from the Sun - are notable for their relatively small size, their high density, and a low number of satellites (or even none). Their surface properties are in sharp contrast. We have seen that Mercury, the planet closest to the Sun, has no stable atmosphere. The other three terrestrial planets have

Fig. 4.13 The planet Venus as observed by the Galileo probe during its fly-by in December 1989 (image credit: courtesy NASA, JPL Galileo Project)

Fig. 4.14 The planet Mars as observed by the Mars Global Surveyor probe (image credit: courtesy NASA, JPL)

atmospheres. On Venus the surface pressure is close to 100 bars at a temperature of 730 K; on Mars, in contrast, it is only 6 millibars on average, with a surface temperature that swings between 150 K (on the southern polar cap) and 300 K at the equator. The Earth occupies a position between these two extremes. The extreme conditions that the terrestrial planets experience, even though the bodies arose under what were essentially neighbouring conditions, pose one of the major challenges to current planetology.

By contrast, from the point of view of their chemical composition, the atmospheres of Venus, the Earth, and Mars have remarkable similarities. For Venus and Mars, carbon dioxide predominates and nitrogen, N2, is present at just a few per cent. The Earth's primitive atmosphere probably had a similar composition, but the presence of abundant liquid water allowed CO2 to be deposited at the bottom of the oceans in the form of calcium carbonate, CaCO3. Oxygen appeared following the development of life, to give the Earth's current atmospheric composition (78 per cent N2, 21 per cent O2).

An important characteristic of the terrestrial planets is their severe depletion of all volatile elements, compared with solar abundances. The properties of their primitive atmospheres were probably strongly affected by massive collisions during their late stages of formation.

4.4.3.2 The Thermal Structure of the Terrestrial Planets

The three terrestrial planets with atmospheres exhibit a layer, near the surface, where the temperature decreases with increasing altitude: this is the troposphere (see Sect. 4.4.2.2). In the case of Venus (Fig. 4.15) and Mars (Fig. 4.16), above this region above about 50 km, there is the mesosphere, a layer that is more-or-less isothermal. On Earth, the tropopause (the upper limit to the troposphere) lies at an average altitude of about 12 km. Above it lies the stratosphere, where the temperature increases with height, thanks to the absorption of ultraviolet solar radiation by molecular oxygen with the formation of the ozone layer.

In most cases, the infrared spectra of the terrestrial planets exhibit atmospheric lines in absorption, because the surface temperature is generally higher than that of the lower atmosphere immediately above it. Because carbon dioxide has the property of absorbing infrared radiation emitted by the surface, the lower atmosphere is correspondingly heated, in turn causing an increase in the temperature of the surface. This is the greenhouse effect, which is particularly strong on Venus. There are regions on Mars and on the Earth where the surface temperature is lower than that of the lower atmosphere: these are the polar caps. Over them, the atmospheric lines appear in emission, with an absorption core because the temperature decreases again in the upper atmosphere. When instrumental methods permit, it will be possible, by observing the thermal spectra of exoplanets, to detect lines in emission or in absorption, and thus determine constraints on their thermal structure.

Atmospheric pressure (mbar)

Thermosphere - 85 km

Mesosphere

Atmospheric pressure (mbar)

Thermosphere - 85 km

Mesosphere

45 km Stratopause

Stratosphere

Troposphere l7O

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