Info

Fig. 7.10 The mass-radius relationship for an ocean planet (top) and a terrestrial-type planet (bottom). The values of M and R are normalized with respect to those for the Earth (After Sotin etal.,2006)

of the temperature conditions in their environment, water is not liquid at their surfaces, but is in the form of ice.

7.3 The Atmospheres of Exoplanets: Their Structure, Evolution and Spectral Characteristics

The observational study of exoplanets is a young science, but, even so, is one that has passed the simple detection stage. The transits of Pegasids - giant exoplanets -when associated with measurement of their mass by velocimetry, will henceforth allow direct comparison of masses and radii of these planets with the models. Thanks to the Hubble Space Telescope, the components of the upper atmospheres of Pegasids could be identified during their transits. More recently, another space observatory, Spitzer, has been able to detect the thermal emission from Pegasids, and thus established extremely tight constraints on their atmospheric composition and circulation. These spectroscopic observations allow us to imagine the potential of future missions, such as the JWST, which will allow us to obtain the infrared spectra of short-period, giant exoplanets. In the longer term, smaller and smaller, and colder and colder planets will be able to be studied through low- and medium-resolution spectra with instruments such as Darwin/TPF-I or TPF-C (Terrestrial Planet Finder), space telescopes dedicated to the detection and description of habitable terrestrial-type planets.

7.3.1 Giant Exoplanets

From a knowledge of the equations of state and opacities of hydrogen and helium at sufficiently high temperature and pressure states (20 000 K, 50 Mbar), and assuming a structure in hydrostatic equilibrium as well as a given initial state at t = 0, we can calculate the evolution of a planet of mass M, and especially predict observable parameters such as the radius or the luminosity. From these observables, the theoretical model thus enable us to deduce the age of the system or set constraints on the composition of the object. We can, in fact, refine this model by adding a solid core of mass Mc, consisting of rocky material or ices, and an enrichment (MZ, env/Menv) of the envelope of mass Menv. This results, for the same overall mass of the planet, in a more compact object. The nature of the solid portion by itself has a limited effect: A core of ice (~3 g/cm3) and a core of rock (~6g/cm3) with the same mass give a similar evolution. Here we assume that the equations of state for the hydrogen/helium mixture, and for the enriched hydrogen/helium mixture are known. In reality, however, this is a vast field of both experimental and theoretical research which is in constant development (see for example Guillot, 2005).

In the earliest stages, the theoretical evolution of a planet of mass M = Menv + Mc strongly depends on the state (radius and temperature) at t = 0, that is, at the moment when accretion ceases, which corresponds to the disappearance of the cir-cumstellar disk of gas. This state at t = 0 may be obtained from formation models (Pollack et al., 1996, Alibert et al., 2005), but the complexity of the accretion phenomenon does not enable us to determine the structure of the planet at the end of accretion with sufficient accuracy. The radius and the temperature at t = 0 are thus very poorly constrained, and it is important to note that for younger objects (less than 10 million years old), which are also the most luminous and the most likely to be detected directly, we do not have a reliable age-mass-luminosity relationship (Chabrier et al., 2006). For these young objects, knowledge of the mass and the luminosity, for example, do not allow us to deduce the age of the system accurately. Similarly, knowledge of the age and the luminosity do not allow the mass to be inferred.

Nevertheless, as Fig. 7.11 shows, this uncertainty no longer affects the evolution after the first 100 million years, and we may predict the evolution of the radius and luminosity of an older planet of given mass. These models have given excellent results for low-mass stars and brown dwarfs. However, strongly irradiated giant planets cannot be modelled as if they were isolated objects, such as brown dwarfs, because the incident solar flux affects both the outer structure of the atmosphere and the evolution of the planet.

Including the effect of irradiation in the calculation of the structure and evolution of a giant planet is not a trivial exercise. In fact, modelling the atmosphere - here, we arbitrarily describe an atmosphere as the outermost portion of the envelope, where

Fig. 7.11 The influence of the initial radius on the evolution of the radius and luminosity of an non-irradiated exoplanet. The continuous-line and dashed curves show the evolution of a planet of 1 Mjup, where the initial radius is set at 3 and 1.3 Jp. In both cases, the planet has a rocky core of 6 Mgarth and an envelope that is enriched with respect to the solar composition (Mz, env/Menv = 0.1). The chain-dotted curve shows the evolution of a planet without a solid core that is of solar composition and with an initial radius of 3 Jp (After Chabrier et al., 2006)

Fig. 7.11 The influence of the initial radius on the evolution of the radius and luminosity of an non-irradiated exoplanet. The continuous-line and dashed curves show the evolution of a planet of 1 Mjup, where the initial radius is set at 3 and 1.3 Jp. In both cases, the planet has a rocky core of 6 Mgarth and an envelope that is enriched with respect to the solar composition (Mz, env/Menv = 0.1). The chain-dotted curve shows the evolution of a planet without a solid core that is of solar composition and with an initial radius of 3 Jp (After Chabrier et al., 2006)

the pressure is less than 103 bar - requires an internal heat flux as a condition for the lower limit. Yet this heat flux depends on the age and should be given by an evolutionary model, because at present there is no complete model that simultaneously treats evolution and detailed radiative transfer in the irradiated zone. Let us consider a non-irradiated planet as the initial evolutionary state: The heat flux at the planet's surface (and thus its luminosity) is calculated by a model of the internal structure, and may be written 4rcR2ffT4ff, where Teff is the temperature of a body equivalent to the object (see Sect. 4.4.2.2). Now let us consider the same planet, but irradiated. Determination of the atmospheric structure requires us to know the incident stellar flux (as an upper limit) and also the internal heat (as a lower limit). The latter is then given by the non-irradiated model for the internal structure. The atmospheric profile obtained may then be reintroduced as an upper limiting condition to calculate the evolution over an interval of time At. The evolution may thus be described in a quasi-static manner. In practice, instead of recalculating the atmospheric structure at each time-step, the atmospheric profile is interpolated on the basis of pre-calculated models with a grid of values for Teff and log g (gravity).

In Fig. 7.12, we may compare a non-irradiated atmospheric profile (night on the figure) with an irradiated profile (day), obtained for the same values of Teff and

Fig. 7.12 Temperature/pressure profiles calculated for a Pegasid. Each profile shown as a continuous line corresponds to a different irradiation geometry, from the substellar point (the point directly facing the star), top, to the non-irradiated profile (terminator and night side), bottom. In this model, no redistribution of the incident stellar flux (f = 1) and no transport are included. The profiles in broken grey lines represent a 'mean dayside' profile with redistribution of the incident flux over one hemisphere (f = 1/2, top) and a mean profile with global redistribution (f = 1/4, bottom). The black dots indicate the separation between the convective and radiative zones for the substellar and night-time profiles. The composition of elements is assumed to be solar, and the equilibrium chemical composition is given by the temperature. Dashed lines indicate the regions in which the principal grains condense. The dotted curve separates the domains where carbon is in the form of CO (hot) or CH4 (cold). The parameters used (mass and irradiation) are those for the planet TrES-1. Modelling carried out by Barman et al. (2005), using the PHOENIX model

Fig. 7.12 Temperature/pressure profiles calculated for a Pegasid. Each profile shown as a continuous line corresponds to a different irradiation geometry, from the substellar point (the point directly facing the star), top, to the non-irradiated profile (terminator and night side), bottom. In this model, no redistribution of the incident stellar flux (f = 1) and no transport are included. The profiles in broken grey lines represent a 'mean dayside' profile with redistribution of the incident flux over one hemisphere (f = 1/2, top) and a mean profile with global redistribution (f = 1/4, bottom). The black dots indicate the separation between the convective and radiative zones for the substellar and night-time profiles. The composition of elements is assumed to be solar, and the equilibrium chemical composition is given by the temperature. Dashed lines indicate the regions in which the principal grains condense. The dotted curve separates the domains where carbon is in the form of CO (hot) or CH4 (cold). The parameters used (mass and irradiation) are those for the planet TrES-1. Modelling carried out by Barman et al. (2005), using the PHOENIX model log g. It will be seen that the strong irradiation produces a hot and quasi-isothermal radiative zone that forces the convective zone to higher pressures and temperatures. Because of this radiative heating from above, the heat flux from the interior towards outer regions becomes less effective, slowing down cooling and the contraction of the planet. At any given age and for the same mass, a non-irradiated planet is thus more compact than an irradiated planet with the same mass and composition.

Once irradiation is included in the modelling, the mass/radius relationship may be compared with observations of Pegasids that transit their parent star, and where we can measure the radius (by the transit) and the mass (from the radial velocity). The theory reproduces the radius for most of the Pegasids that transit in a satisfactory manner (Chabrier et al., 2004), but underestimates the radius of some of them, in particular that of HD 209458b, where the radius is inexplicably large. Figure 7.13 indicates the masses and radii, with their associated errors, of a few Pegasids, known to transit, as well as the theoretical evolution R(t) obtained for the range of masses and irradiation found for these planets. The composition is assumed to be solar (no enrichment of the envelope, and no solid core). Some of these planets have a radius

Fig. 7.13 Comparison between the theoretical and observed radius for Pegasids that transit their star. Each ellipse corresponds to the radius and age of one Pegasid and the associated uncertainties. The dotted curves are the boundaries of the theoretical evolution (using an isolated-planet model) of the radius for the range of masses of the planets shown here. The solid lines are the boundaries for evolution of the radius when irradiation by the central star is included. The theoretical evolutionary curves are those for a planet without a solid core and of solar composition

Fig. 7.13 Comparison between the theoretical and observed radius for Pegasids that transit their star. Each ellipse corresponds to the radius and age of one Pegasid and the associated uncertainties. The dotted curves are the boundaries of the theoretical evolution (using an isolated-planet model) of the radius for the range of masses of the planets shown here. The solid lines are the boundaries for evolution of the radius when irradiation by the central star is included. The theoretical evolutionary curves are those for a planet without a solid core and of solar composition less than that predicted for a planet of solar composition. This may be completely explained by an enrichment in heavy elements or by the presence of a rocky core (or both). For example, the mass of the planet HD 149026b is dominated by heavy elements other than H and He, and it undoubtedly possesses a significant rocky core, which may amount to as much as 80MEarth (Fortney et al., 2006). Although the enrichment of this planet seems to be in qualitative agreement with the star's greater than solar metallicity, it is not easy to explain quantitatively in terms of current planetary formation scenarios. The loss of part of the hydrogen-helium envelope, either by XUV irradiation (Baraffe et al., 2004), or by the collision of two giant planets during the course of their migration (Ikoma et al., 2006) could be the origin of such a 'metallic' planet.

Although planets that are more compact than their theoretical 'solar' model may be explained by significant enrichments, planets that have an even larger radius (^20 per cent in the case of HD 209458b) still defy understanding. This difficulty is all the greater, because Pegasids orbit stars with high metallicity and we would therefore expect them to possess a rocky core and an enriched envelope. The departure from theory may therefore be even more tangible (Guillot et al., 2006). Although the models of the internal structure and the atmosphere suffer from uncertainties linked to the equations of state and opacities (particularly in the case of an envelope with high metallicity), the discrepancy is too great to be ascribed to them. To maintain the radius of HD 209458b, of XO-1, or of HD 189733b at their observed values, it would be necessary to dissipate 1020 Watts (about 1 per cent of the stellar flux intercepted by the planet) in the planet's convective layers, and to maintain this contribution of energy throughout the whole of the planet's evolution. Showman and Guillot (2002) have suggested dynamical mechanisms created by the major asymmetry in the way in which the stellar energy is deposited, which could convert the radiative stellar energy into kinetic energy (winds), transport it, and dissipate it within zones in the interior. Tidal interactions are another means of dissipating the energy within the interior layers but they assume that orbital parameters such as the discrepancy between the orbital period and the period of the rotation, eccentricity or obliquity are not zero. But the orbital evolution of Pegasids should quickly synchronize and circularize the planet's orbit and reduce the obliquity to 0, unless another planet in the system perturbs such evolution. In the case of HD 209458b, the eccentricity could be measured, and has been found to be essentially zero, thus excluding the influence of another planetary body. Another possibility is that the planet might be trapped in a Cassini resonance with non-zero obliquity: the energy dissipated would then be sufficient, but the probability of such a configuration is low and it would be difficult to explain a high proportion of 'inflated' planets (Levrard et al., 2007). A third effect that could affect the radius is atmospheric loss created by the XUV irradiation and interaction with the stellar wind. If the resulting mass loss is very rapid it affects the evolution of the planet (Baraffe et al., 2004). This occurs when the characteristic escape time becomes less than the Kelvin-Helmholtz time, which may be expressed as:

where L is the luminosity of the planet. This condition assumes that a considerable amount of energy is deposited in the outer layers of the atmosphere, which does not seem realistic for a giant planet of MJup. In addition, an increase in the radius requires an even greater amount of energy to be deposited and a more effective escape mechanism. This positive feedback would produce runaway effect leading to the rapid total loss of the hydrogen envelope, and so it is unlikely that we would observe a planet in this phase. Such a dramatic evolution could nevertheless have occurred with less massive planets, such as the hot Neptunes (Baraffe et al., 2005).

So the radius of HD 209458b still remains mysterious. Other exoplanets that transit also seem to have radii greater than predicted by theory, but the error bars accompanying their measurements are very large. In contrast, the radius of HD 209458b has been measured with a far higher accuracy than those of other planets. We must await new measurements with the HST to know the exact number of 'inflated' planets in our sample of transiting exoplanets.

Apart from determination of the radius and the inclination, transits allow us to obtain information about the atmospheres of exoplanets. For a planet with an atmosphere, the planetary radius measured by the decrease in the stellar flux during a transit depends on the wavelength at which the flux is measured. Indeed, if a component present very high in the atmosphere absorbs radiation at a wavelength when the atmosphere is transparent at X2 down to very dense layers, we will measure R(X2) < R(ki). So if we are able measure accurately the difference in depth of a transit in two spectral bands, we will be able to detect the components in the atmosphere (Ehrenreich et al., 2006). This is how sodium has been identified in the upper atmosphere of HD 209458b (Charbonneau et al., 2002), as well as a cloud of neutral gas around the planet, consisting of hydrogen (Vidal-Madjar et al., 2003), and possibly carbon and oxygen (Vidal-Madjar et al., 2004). The interpretation currently accepted for this cloud of neutral atoms is that it represents gas escaping from the atmosphere.

From now on, at last, we are able to detect the infrared thermal emission from Pegasids thanks to the Spitzer space observatory. Such detection was first made for planetary transits (HD 208458b, TrES-1, HD 149026b, and HD 189733b) by measuring the variation in luminosity of the star + planet system during the secondary transit, in the infrared bands with the IRAC, MIPS and IRS instruments (Deming et al., 2005; Charbonneau et al., 2005; and Deming et al., 2006). This variation gives the luminosity of the planet, observed just before and just after the secondary transit (i.e., when the planet passes behind the star), when its day side is turned towards the observer (see Fig. 7.14).

Recently, Spitzer has been able to measure the light-curve at 16 |m, that is the variation in luminosity as a function of orbital phase, for a Pegasid that does not exhibit transits: v Andromedae (Harrington et al., 2006 - Fig. 7.15). The amplitude of the variations is determined by the inclination of the system and by the day-night contrast. This therefore allows us to set constraints on the flux-redistribution parameter (f = 1, 0.5 or 0.25) in theoretical models. In fact, the atmospheric models used to calculate the structure and composition, to construct synthetic spectra, and to calculate the evolution of the radius and the luminosity of exoplanets are, for the most

Fig. 7.14 Secondary transit of HD 189733b (the passage of the planet behind the star), observed by Spitzer/IRS in a band at 16 |m. The Spitzer space observatory has been able to detect the thermal emission from Pegasids during their secondary transits. The flux of the system star + planet decreases when the planet passes behind the star. The difference in the flux before and after, and during the transit therefore gives the thermal emission from the day side of the planet (After Deming et al., 2006)

Fig. 7.14 Secondary transit of HD 189733b (the passage of the planet behind the star), observed by Spitzer/IRS in a band at 16 |m. The Spitzer space observatory has been able to detect the thermal emission from Pegasids during their secondary transits. The flux of the system star + planet decreases when the planet passes behind the star. The difference in the flux before and after, and during the transit therefore gives the thermal emission from the day side of the planet (After Deming et al., 2006)

part, 1-dimensional models (plane-parallel or spherical) in which the irradiation flux at the top of the atmosphere is fixed. Several methods of tackling this problem exist: We may assume that atmospheric dynamics plays a negligible role and that the planet's rotation is very slow, and calculate a 1-dimensional atmospheric profile for a ring around the sub-steller point, defined by its zenith angle (see Fig. 7.12). The overall planetary spectrum is then reconstructed from the individual contributions from each ring. We can calculate a night-time, non-irradiated profile in this way, as well as a day-time profile where the flux at the top of the atmosphere is the stellar flux intercepted by the planetary disk of surface area nR2 and redistributed solely on the day hemisphere, of surface area 2nR2. The redistribution factor f is then equal to 0.5. Finally, we can represent the planet by a single profile, assuming that the flux it intercepts is spread over the whole of the planetary surface (f = 0.25), which may be an acceptable approximation when the planet's rotation is sufficiently rapid.

Because of its significant amplitude, which bears witness to a strong difference in temperature between the day and night sides of the planet, the light-curve of v Andromedae allows us to eliminate the model with global redistribution of the flux (f = 0.25), where atmospheric dynamics and the rotation would create uniform temperature conditions at the levels probed by the thermal emission.

The Spitzer observations of secondary transits have been carried out in different spectral bands, which allows comparison of the measurements with theoretical spectra calculated for the Pegasids. Figure 7.16 shows just such a comparison. The Spitzer measurements provide information at very low resolution and affected by significant noise, which only allows very limited information about the nature of the Pegasids to be obtained. Nevertheless, similar observations, but of better quality

Phase

Fig. 7.15 Infrared radiation curve for a Pegasid as measured by Spitzer. Observed by the MIPS instrument in a band at 24 |m, the flux received from U Andromedae (star + planet) is modulated by the planet's thermal emission, which varies as a function of its orbital phase. The variations observed are the sign of a significant temperature contrast between the day and night sides. The black points are the observations, and the white points correspond to the same observations but offset by one period. The curve is obtained from a model without redistribution of the incident flux (f = 1), similar to that shown in Fig. 7.13 (After Harrington et al., 2006)

Phase

Fig. 7.15 Infrared radiation curve for a Pegasid as measured by Spitzer. Observed by the MIPS instrument in a band at 24 |m, the flux received from U Andromedae (star + planet) is modulated by the planet's thermal emission, which varies as a function of its orbital phase. The variations observed are the sign of a significant temperature contrast between the day and night sides. The black points are the observations, and the white points correspond to the same observations but offset by one period. The curve is obtained from a model without redistribution of the incident flux (f = 1), similar to that shown in Fig. 7.13 (After Harrington et al., 2006)

should be obtained in the future with the JWST (NASA, ESA), and should allow us to set better constraints on the numerous uncertainties that still affect theoretical models (including heavy-element composition, clouds, atmospheric dynamics, and photochemistry).

Currently calculation of synthetic spectra for Pegasids, and for exoplanets in general, rest on the following assumptions:

1. solar abundance of elements,

2. absence of vertical or horizontal transport,

3. molecular composition in chemical equilibrium (determined by temperature),

4. absence of photochemistry (the dissociation of chemical species by incident UV radiation is neglected).

These approximations, although by no means justified, are linked to practical limitations. Regarding point 1, and as may be seen in Figs. 7.16 and 7.18, it should be mentioned that the models will, henceforth, take account of a possible enrichment in heavy elements as characterized by the metallicity of the envelope, Mzienv/Menv. This enrichment has a significant effect on the abundances of molecules and grains formed by condensation.

Atmospheric circulation and the transport of chemical species, and of the heat that is associated with it, are likely to strongly affect thermal atmospheric profiles and their distribution in longitude and latitude, the chemical composition, and thus

Wavelength (^m)

Fig. 7.16 Theoretical spectra for TrES-1 and comparison with Spitzer observations. The curves shown with a continuous line show theoretical spectra of the day hemisphere of TrES-1, the hemisphere that is visible during observations close to secondary transit. These spectra have been obtained by Barman et al. (2005) and correspond to the profiles in Fig. 7.12: without redistribution of the incident stellar flux (f = 1, top), with redistribution over the whole planetary surface (f = 0.25, bottom), and redistribution over the day hemisphere (f = 0.5, centre). The spectra are given as the ratio of planetary to stellar flux. The white squares indicate measurements made by the IRAC instrument on Spitzer in the 3.6, 4.5, 5.8, and 8.0 |m bands for each of the models. The black square in the 4.5 |m band corresponds to a model with f = 0.5 and an enrichment in heavy elements of 10 times the solar value. The observations made with IRAC at 4.5 and 8.0 |m (Charbonneau et al., 2005) are given by the black circles and the associated error bars. The spectrum shown by the dotted line is that of an isolated brown dwarf (Tf = 1150 K)

Wavelength (^m)

Fig. 7.16 Theoretical spectra for TrES-1 and comparison with Spitzer observations. The curves shown with a continuous line show theoretical spectra of the day hemisphere of TrES-1, the hemisphere that is visible during observations close to secondary transit. These spectra have been obtained by Barman et al. (2005) and correspond to the profiles in Fig. 7.12: without redistribution of the incident stellar flux (f = 1, top), with redistribution over the whole planetary surface (f = 0.25, bottom), and redistribution over the day hemisphere (f = 0.5, centre). The spectra are given as the ratio of planetary to stellar flux. The white squares indicate measurements made by the IRAC instrument on Spitzer in the 3.6, 4.5, 5.8, and 8.0 |m bands for each of the models. The black square in the 4.5 |m band corresponds to a model with f = 0.5 and an enrichment in heavy elements of 10 times the solar value. The observations made with IRAC at 4.5 and 8.0 |m (Charbonneau et al., 2005) are given by the black circles and the associated error bars. The spectrum shown by the dotted line is that of an isolated brown dwarf (Tf = 1150 K)

the appearance of the planet's spectrum. In fact, if the molecules are transported in times shorter than the characteristic chemical-reaction times, the composition is no longer a reflection of the local temperature. For example, in a model of partial redistribution (f = 1, or f = 0.5) where the night side is very cold and the day side very hot (at P = 1 bar, Tdciy = 2000 K and T^ght = 300 K, see Fig. 7.16), the CO/CH4 ratio varies strongly from one hemisphere to the other, while such a thermal gradient, even assuming synchronous rotation, should produce violent winds which would tend to equalize the differences. In this case, the CO produced at high temperatures in the day hemisphere is transported to, and survives in, the night hemisphere (Cooper and Showman, 2006 - Fig. 7.20). This phenomenon of quenching also occurs vertically, as observed on Jupiter: the CO formed at high pressures and high temperatures rises towards levels at lower pressures and temperatures, where it is detected, despite predictions made on the basis of equilibrium models. In addition, the temperature itself is evened out horizontally by winds. These dynamical considerations tend to favour models with global redistribution (f = 0.25), which seems, however, to contradict the amplitude of the infrared radiation curve for v Andromedae measured by Spitzer. At any rate, this shows that coupling between radiative transfer, chemistry and dynamics is essential for realistic modelling of the atmospheres of exoplanets and of their spectra.

The dissociation of molecules by UV radiation is an essential element in the chemistry of planetary atmospheres in the Solar System. In the giant planets and on Titan, it initiates (inter alia) the formation of hydrocarbons and clouds of photochemical origin which modify the scattering and absorption properties of the atmosphere. The closer a planet is to its parent star and the hotter the atmosphere, the more justified it is to assume chemical equilibrium. The UV irradiation also increases, however, when the orbital distance decreases, which tends to increase the photochemical effects. Including photochemistry causes the modelling to become very complex, because it presupposes that the chemical composition is calculated from a set of several hundred reactions, the rates of which are often uncertain, in particular when we are dealing with conditions that are far outside the normal range of temperatures. Despite preliminary studies which tend to minimize its role in Pegasids (Liang et al., 2004), photochemistry must eventually be introduced into exoplanet models.

Modelling the atmospheres of exoplanets and their spectra is also rendered uncertain by the tricky treatment of condensation and of cloud formation. The range of temperatures and pressures encountered in the atmospheres of giant exoplanets is vast, and numerous phase transitions are able to occur, causing the formation of mineral grains (silicates and iron), droplets, or ice crystals. The microphysical processes responsible for the nucleation of particles combine with horizontal and vertical motions in the atmosphere (winds, convection, and advection) to form cloud layers. In the atmospheres found in the Solar System, these clouds are generally of finite horizontal extent (they cover only part of the surface), and of variable vertical extent. There properties are only included in the models a posteriori, and in an empirical fashion. Under these conditions, it is clear that we should not expect these one-dimensional models to reproduce the properties of extrasolar clouds in a realistic fashion. The observed spectra will probably reveal a structure intermediate between cloud-free models (where whatever condenses falls down to layers with both elevated pressure and high opacity) and models with clouds (where the particles remain in the layers in which they form). It is, however, important to note that these two types of model give very different results (see Fig. 7.17 for a model with clouds, Fig. 7.18 for spectra with and without clouds, and Fig. 7.19 for spectra without clouds). In Fig. 7.17 it is possible to see the possible effect of clouds as a function of orbital distance. In the case of a Pegasid (a = 0.04 AU, reff = 1440 K), the clouds of silicates and iron at high altitude mask most of absorbing material in the atmosphere, and the spectrum is dominated by the signatures of Na and K. At 0.1 AU (Teff = 870 K), the clouds form at a lower level and allow the most prominent absorptions by gaseous components to be seen. At 0.04 and 0.1 AU, the thermal emission from the planet makes a strong contribution to the spectrum, whereas for more distant and cooler objects it is negligible relative to the reflected starlight. In the hottest objects, carbon is primarily in the form of CO, whereas methane becomes dominant farther out.

Apart from the effect of the clouds themselves, condensation depletes the atmosphere of certain potential absorbents, which may strongly affect the atmospheric structure and the spectrum. This effect is shown in Fig. 7.21: VO and TiO absorb

Fig. 7.17 Synthetic spectra of giant planets as a function of orbital distance. This diagram shows the visible and near-infrared spectra of exoplanets calculated by J. Fortney and M. Marley, for a solar composition and a mass of 1 Mjup. The orbital distance in AU is indicated on each of the spectra. The top spectrum is that of a Pegasid (a = 0.04 AU, Teff = 1440 K). The spectrum at 5.2 AU corresponds with that of Jupiter (After Marley et al., 2007)

Fig. 7.17 Synthetic spectra of giant planets as a function of orbital distance. This diagram shows the visible and near-infrared spectra of exoplanets calculated by J. Fortney and M. Marley, for a solar composition and a mass of 1 Mjup. The orbital distance in AU is indicated on each of the spectra. The top spectrum is that of a Pegasid (a = 0.04 AU, Teff = 1440 K). The spectrum at 5.2 AU corresponds with that of Jupiter (After Marley et al., 2007)

Wavelength (pm)

Fig. 7.18 Sensitivity of synthetic spectra to metallicity and to clouds. Shown here are theoretical spectra for an exo-Jupiter (at 5.2 AU) with different enrichments or depletions in heavy elements, relative to a solar-type composition. (The atmosphere of Jupiter is about 3 x the solar value.) The absorption bands are those of methane (CH4). The bottom curve represents a spectrum without clouds (After Marley et al., 2007)

Wavelength (pm)

Fig. 7.18 Sensitivity of synthetic spectra to metallicity and to clouds. Shown here are theoretical spectra for an exo-Jupiter (at 5.2 AU) with different enrichments or depletions in heavy elements, relative to a solar-type composition. (The atmosphere of Jupiter is about 3 x the solar value.) The absorption bands are those of methane (CH4). The bottom curve represents a spectrum without clouds (After Marley et al., 2007)

in the UV and visible regions, where the incident stellar energy is significant. The addition of these components thus modifies the UV and visible albedo and produces stratospheric heating, which affects the atmospheric structure and the spectrum as far as the thermal infrared. We should not expect these two specific components to occur at high altitudes in sufficient quantities to create such an effect, because

Orbital Phase-Averaged Contrast Ratios (f = 1/4, cloud-free)

Orbital Phase-Averaged Contrast Ratios (f = 1/4, cloud-free)

HD 189733b HD 209458b TrES-1 51 Peg b T Boo b

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