The Sun’s activity in the young solar system

7.2 The Sun’s activity in the young solar system

Stellar magnetic activity strongly influences planetary surfaces and atmospheres in at least two ways:

The solar wind and high-energy particle streams interact with ions and neutrals in the upper planetary atmospheres, but also with the solid surfaces in the absence of atmospheres. Electron impact ionization, charge exchange, and other processes lead to important alterations of atmospheric or surface materials and to their erosion (e.g., Chassefière and Leblanc, 2004 ; Kulikov et al., 2007 ).
High-energy (XUV) radiation affects planetary atmospheres through ionization, heating, dissociation and recombination and induced chemistry (e.g., Canuto et al., 1982 ). Hard radiation also interacts with solid surfaces.

The evolution of planetary surfaces and atmospheres can therefore be understood only in the context of the evolution of the enhanced high-energy solar particle and photon fluxes. For this reason, the past, much higher solar XUV and particle fluxes are crucial elements in our understanding of planet evolution, in particular questions on evaporation of their atmospheres and the loss of water reservoirs. After a short summary of relevant physical effects, I address key issues related to solar-system planets and Saturn’s moon Titan, and conclude with aspects related to “hot Jupiters” around solar analogs.

The evolution of the Earth’s atmosphere is sketched in Figure 39 . It indicates a large water reservoir at the earliest times, part of which is thought to have subsequently escaped from Earth (see also Section 7.2.6 below). Note also the rapid increase of biologically produced O₂ starting around 2.2 Gyr before present.

Figure 39:

Evolution of the constituents of the Earth’s atmosphere in time (adapted from

http://science.nasa.gov/headlines/y2002/10jan_exo-atmospheres.htm?list161037, after D. Des Marais and K.J. Zahnle).

7.2.1 Planetary atmospheric chemistry induced by high-energy radiation

The young Sun’s elevated ultraviolet flux had considerable impact on the photochemistry of planetary atmospheres. Ayres (1997 ) estimated the photoionization rates based on the evolution of ionizing flux of solar analogs. He concluded that photorates scale approximately as t^–1, implying rates that were nearly 100 times stronger at a solar age of 100 Myr than at present (Figure 40 ).

Figure 40:

Photoionization rates for H, O, O₂, and N₂ for different ages of the Sun, derived from the level of ionizing flux of solar analogs. The thick solid lines give the best estimates, the shaded areas give the allowed ranges based on uncertainties in the rotation-activity relationship (from Ayres, 1997 , reprinted with permission).

UV radiation initiated the photochemical processes leading to the formation of O₂ and O₃ in the prebiotic terrestrial atmosphere (Canuto et al., 1982 ). Ozone absorbs strongly in the 200–300 nm band and therefore protects life from lethal doses of UV radiation.

UV radiation produces oxygen by photolysis of water and CO₂:

H2O + hν → OH + H; λ ≤ 240 nm , (26 ) OH + OH → O + H2O , (27 ) CO2 + hν → CO + O; λ ≤ 230 nm , (28 )

after which O₂ is formed (Canuto et al., 1982 ). The atomic H can escape into space (see Section 7.2.3 below). Ozone is formed through

(M stands for other molecules; there are also several reactions that destroy O₂ and O₃; see Canuto et al. 1982 ). Atmospheric chemical models subject to enhanced UV irradiation show that the surface mixing ratio of O₂ increases by a factor of 10⁴–10⁶ above the standard pre-biotic value of 10^–15 due to enhanced levels of solar UV radiation (corresponding to 1–300 times the present-day Sun).

The UV irradiation of the young Earth was particularly strong during the Sun’s T Tauri phase, up to factors of 10³ above the present solar values. The potential influence on planet formation and the subsequent generation of planetary atmospheres should therefore have been very significant at those epochs – if any of the planetary atmospheres were indeed forming at such early times already. The UV irradiation could increase the total column of O₃ by 1–3 orders of magnitude (Canuto et al., 1983 ), thus shielding incoming solar UV radiation efficiently and protecting early forms of life.

7.2.2 High-energy radiation and the planetary biospheres in habitable zones

Ionizing radiation is of crucial importance also for the evolution of life. While high doses are lethal for life, modest doses are important drivers of genetic mutations and therefore biological evolution. Although at present most high-energy radiation is absorbed in the high atmosphere of the Earth, significant effects may be found in thinner atmospheres (e.g., Mars) or in the environment of the young Sun where the irradiation by XUV photons was hundreds of times stronger. Smith et al. (2004 ) have computed the propagation of ionizing radiation through model atmospheres of terrestrial-like planets.

The incident spectra are those of supernovae explosions, gamma-ray bursts and, relevant for us, coronal X-ray flares that occurred at a much higher rate and up to much higher total energies in the young Sun compared to the present (Telleschi et al., 2005 ; Audard et al., 2000 ). Monte Carlo methods were used to calculate the transfer of incident X-ray and gamma-ray photons via Compton scattering and photoabsorption. The incident high-energy photons ionize molecules, thereby creating primary electrons, which collide further to produce secondary photoelectrons. These excite molecules and create aurora-like emission. A single incident photon can cause ionization of tens of thousands of molecules. For a neutral gas, most of the secondary-electron energy, however, goes into molecule excitation rather than ionization (different from ionized gas; Smith et al. 2004 ).

Strong re-radiation of the energy will occur in the N₂ bands in the UV region (Smith et al., 2004 ), and at this point, the composition of the atmosphere becomes relevant as a variety of opacity sources and Rayleigh scattering will redistribute the radiation. Smith et al. (2004 ) studied in particular “habitable” atmospheres, requiring column densities of at least 30–100 g cm^–2 for Earth-like planet (the Earth atmosphere’s column density is 1024 g cm^–2). Their principal results can be summarized as follows:

While the direct transmission of stellar flare X-ray photons to a planetary surface is negligible, in a thin atmosphere with column density of 30–100 g cm^–2, pure atmospheric Rayleigh scattering (appropriate for a young terrestrial atmosphere) would transmit $≈$ 10% of the incident energy flux as UV radiation; about 1–3% are transmitted as UV photons if only a terrestrial-like O₃/O₂ molecular absorption screen is present.
In denser, Earth-like atmospheres ( $> ∼$ 100 g cm^–2), direct transmission of X-ray photons is essentially zero, but still of order 2 $×$ 10^–3 of the incident flux reaches the surface as UV radiation even in the presence of an O₃/O₂ shield. In a pure Rayleigh-scattering atmosphere (important for the young Earth), the transmission is of order 5%.

Even planets with thick atmospheres that shield evolving life from direct ionizing radiation will shower their surfaces with UV radiation owing to stochastic flares occurring on the host star. The present-day Sun produces about one flare every 100 yr with a transmitted UV surface flux equal to or larger than the continuous solar UV flux in the 200–320 nm band (Smith et al., 2004 ). Whether the UV irradiation effect is of prime importance for a planet around a young solar-like star is not clear, but it appears to be important for planets orbiting lower-mass M dwarf flare stars (Smith et al., 2004 ).

7.2.3 Planetary atmospheric loss and high-energy radiation and particles

Various mechanisms induced by solar magnetic activity can lead to escape of planetary atmospheric species, both neutrals and ions. The principal losses strongly depend on the magnetic activity of the host star. Thermal escape processes relate to a Maxwellian particle distribution and are consequently determined by the temperature of the respective atmospheric layer, and therefore by its heating rate. Thermal escape is predominantly controlled by photon irradiation from the host star. Non-thermal escape is due to other processes in which energization and escape are related to microscopic non-thermal processes (e.g., particle acceleration; Lundin and Barabash 2004 ; Lundin et al. 2007 ). Key factors are high-energy particle streams from the central star, i.e., the solar/stellar winds, and the magnetic environment of the planet itself.

The heating of planetary upper atmospheres and the generation of ionospheres is primarily due to the solar XUV radiation. The thermosphere is the layer in which most of this radiation is absorbed and is transformed to heat, leading to a positive (upward) temperature gradient. In the exosphere, the mean free path of atmospheric species is large, so that collisions are negligible. The lighter species may escape from this layer into space if their thermal velocity exceeds the gravitational escape velocity. The base of the exosphere, the exobase, is located at the height where the mean free path is equal to the local scale height, H = kT_exo/mg, where k is the Boltzmann constant, T_exo is the exobase temperature, m is the mass of the main atmospheric species, and g is the gravitational acceleration (Kulikov et al., 2007 ).

Let us define the thermal escape parameter

as the ratio between the potential energy of a particle and the thermal energy kT_exo, where M is the planet’s mass, m is the particle mass (in the following: mostly atomic hydrogen), r is the planetocentric distance, and T_exo is the exospheric temperature. Let us now assume a Maxwellian distribution for a given species. If X $>$ 1.5, e.g. for low temperatures, only the particles in the tail of the Maxwellian have kinetic energies sufficient for escape. The particle loss through a spherical surface at radius r is given by the Jeans formula (“Jeans escape”, e.g., Jeans 1925 ; Öpik 1963 ; Kulikov et al. 2006 ),

Here, v₀ = (2kT_exo/m)^1/2 is the most probable velocity of the particle (see, e.g., Chassefière and Leblanc, 2004 ; Kulikov et al., 2006 ).

If the mean thermal energy of the particles (3kT_exo/2) exceeds the gravitational energy, i.e., for X $>$ 1.5 or analogously for temperatures T_exo $>$ 2GMm / 3kr or kT $> ∼$ mv_esc²/2, the exosphere becomes unstable and hydrostatic equilibrium does not apply. The top of the atmosphere “blows off”, i.e., moves radially away from the planet with a velocity near its thermal velocity. To produce sufficiently high temperatures, a high level of EUV irradiation is required. The incoming EUV energy is then no longer converted into thermal energy but directly into kinetic energy. “Hydrodynamic escape” calculations are required (Öpik, 1963 ; Hunten, 1973 ; Watson et al., 1981 ).

The most important heating and cooling processes in the upper atmosphere of the Earth are, following Kulikov et al. (2007 ) and references therein,

heating of the thermosphere due to photoionization of CO₂, N₂, O₂, and O by solar XUV irradiation,
heating due to photodissociation of O₂ and O₃ by solar UV irradiation,
chemical heating in exothermic binary and 3-body reactions,
molecular heat conduction in neutral gas,
cooling by infrared emission in the ro-vibrational bands of CO₂, NO, O₃, OH, NO⁺, ¹⁴N¹⁵N, CO, O₂, and others,
heating and cooling by contraction and expansion of thermosphere,
turbulent energy dissipation and heat conduction.

Models of XUV heating of the present-day Earth’s thermosphere predict an average exospheric temperature of $≈$ 1000 K (Kulikov et al., 2007 , and references therein), in agreement with measurements. For Venus, T_exo = 270 K (Kulikov et al., 2006 , 2007 ) where the low value is due to efficient cooling by CO₂. And for Mars, T_exo = 220–240 K (Kulikov et al., 2007 ).

Non-thermal processes are also relevant in outer planetary atmospheres. There are several main types of non-thermal escape processes (Chassefière and Leblanc, 2004 ; Lundin et al., 2007 ):

Dissociative recombination (photochemical escape): After UV photoionization, ions recombine by forming energetic neutrals that may escape. Dissociative recombination of ionospheric molecular ions and photodissociation of molecular neutrals are sources of suprathermal H, C, N, O, and CO in the exosphere of (present) Venus (Kulikov et al., 2007 , and references therein). These atoms are eventually thermalized through collisions, or are lost if they reach the exobase with energies exceeding the escape energy.
Ion pick-up escape: Ions are produced by photo-ionization, electron impact, or charge exchange and are dragged along by the magnetic field; a fraction of the particles escape in the solar wind.
Ionospheric outflow: Ionospheric matter is accelerated away by the electric field in the solar wind.
Ion sputtering: A fraction of the ions produced by photo-ionization, electron impact, or charge exchange re-impact the neutral atmosphere (owing to their large gyroradii) and eject neutral particles. This process is particularly important in the absence of a strong planetary magnetic field.

I now discuss results from applications to solar-system bodies and extrasolar planets.

7.2.4 Mercury: Erosion of atmosphere and mantle?

Mercury stands out among solar-system planets by showing the largest average density, and its core is large compared to other terrestrial planets (60% of its radius). It is possible that strong winds and enhanced XUV irradiation from the young Sun removed much of the early atmosphere and the outer mantle of Mercury (Tehrany et al., 2002 ; Ribas et al., 2005 ). It is thus possible that Mercury started as a planet similar in size to Earth but has lost its mantle as a consequence of interactions with the young, active Sun.

7.2.5 Venus: Where has the water gone?

The atmosphere of Venus is extremely dry when compared to the terrestrial atmosphere (a total water content of 2 $×$ 10¹⁹ g or 0.0014% of the terrestrial ocean, vs. 1.39 $×$ 10²⁴ g on Earth, Kasting and Pollack 1983 ). The similar masses of Venus and Earth and their formation at similar locations in the solar nebula would suggest that both started with similar water reservoirs (Kasting and Pollack, 1983 ). The Venus atmosphere also reveals a surprisingly high deuterium-to-hydrogen (D/H) abundance ratio of (1.6 $±$ 0.2) $×$ 10^–2 or 100 times the terrestrial value of 1.56 $×$ 10^–4 (Donahue et al., 1982 ; Kasting and Pollack, 1983 ). These observations have motivated a basic model in which water was abundantly available on the primitive Venus. Any water oceans would evaporate, inducing a “runaway greenhouse” in which water vapor would become the major constituent of the atmosphere (Ingersoll, 1969 ). This vapor was then photodissociated in the upper atmosphere by enhanced solar EUV irradiation (Kasting and Pollack, 1983 ), followed by the escape of hydrogen (but not deuterium) into space (Watson et al., 1981 ; Kasting and Pollack, 1983 ). Oxygen either (partly) followed the same route or (partly) reacted with reduced atmospheric gases or minerals in the crust (Kasting et al., 1984 ). Judged from the D/H abundance ratio, at least 0.3% of a terrestrial ocean should have been outgassed (Donahue et al., 1982 ). I summarize some of the results and problems discussed in the literature as far as they refer to solar activity and its much higher level in the early Sun.

Detailed atmospheric models have been calculated by, e.g., Watson et al. (1981 ), Kasting and Pollack (1983 ), Kasting et al. (1984 ), Kasting (1988 ), Chassefière (1996b ), and Kulikov et al. (2006 ). These models solve the equations of continuity and diffusion (e.g., constrained to the vertical direction in 1-D approaches) for a number of species, hydrostatic and heat balance equations, and equations of vibrational kinetics for radiating molecules. They include irradiation by solar XUV and UV and their long-term evolution (see Kulikov et al., 2007 , for a review).

Kulikov et al. (2006 ) and Kulikov et al. (2007 ) presented results for Venus, assuming no atmospheric (in particular, hydrogenic) loss, i.e., the upper atmospheres are not hydrogen-rich and not humid (Figure 41 ). For present-day solar XUV irradiation, the calculated exospheric temperature is 270 K, in good agreement with measurements. However, increasing the XUV flux to levels of the young Sun, i.e., a 100fold EUV flux, thermospheric temperatures up to $≈$ 8200 K are reached 4.5 Gyr ago, if the CO₂ content is the same as today (96%). Higher temperatures are obtained for lower CO₂ content.

Figure 41:

Modeled temperature profiles for Venus for various solar XUV levels: 1 = present-day, 10 times (3.8 Gyr ago), 50 times (4.33 Gyr ago), and 100 times (4.5 Gyr ago) present levels, based on a 96% CO₂ thermosphere (from Kulikov et al., 2007

, © Springer Verlag, reprinted with permission.).

The blow-off limit in the exobase is reached at 4000 K, permitting hydrogenic blow-off during the first 250 Myr after the Sun’s arrival on the ZAMS. Detailed hydrodynamic computations by Chassefière (1996b ) show high Jeans escape flux even for present-day solar XUV irradiation for a Venus-like planet with a hydrogen atmosphere.

The question on water on the young Venus then concentrates on the availability of water vapor in the young Venus’ upper atmosphere, that can photodissociate so that H escapes. The critical solar flux leading to complete evaporation of a water ocean (a “runaway greenhouse”, Ingersoll 1969 ) is $≈$ 1.4 S_sun nearly independently of the amount of cooling CO₂ in the atmosphere (Kasting, 1988 ), where S_sun = 1360 Wm^–2 is the present-day solar constant. This critical flux is just about the flux expected from the young Sun at the orbit of Venus (and is about 70% of the present-day value at the same solar distance).

These model calculations suggest that the amount of water in the present terrestrial ocean could have escaped from Venus in only 50 Myr if the H₂O mass fraction (mass mixing ratio) was at least 0.46, and the XUV flux was 70–100 times the present values (Kulikov et al., 2007 ).

The remaining problem then is to explain the extremely low oxygen content in the present-day atmosphere of Venus (Chassefière, 1996a ). In a strong hydrodynamic escape process on young Venus, heavier gases such as O may be dragged with H (Zahnle and Kasting, 1986 ; Zahnle et al., 1990 ) although Chassefière (1996a ) concluded that such loss was modest. Ion pick-up by the solar wind and ionospheric erosion by Kelvin–Helmholtz instabilities may be the dominant O⁺ loss mechanism in the present atmosphere of Venus (Lammer et al., 2006 ; Chassefière, 1997 ). The denser, young solar wind (Wood et al., 2002 ) could in fact easily remove the expected amount of O⁺ from a massive water ocean (Chassefière, 1997 ; Kulikov et al., 2006 ). The equivalent of one terrestrial ocean could be removed in only 10 Myr if the solar wind had been 10³–10⁴ times stronger than today, i.e., the escape would be “instantaneous” compared with outgassing time scales (Chassefière, 1997 ) although it is doubtful whether the young solar wind was indeed as strong as required for such massive losses (Wood et al. 2005 , see Section 5.1).

7.2.6 Earth: A CO₂ atmosphere and magnetic protection

There is evidence for early hydrodynamic escape from the Earth’s atmosphere. Compared to Venus, the lighter noble gases Ne and Ar are depleted in the Earth’s atmosphere with respect to the heavier Kr and Xe; the isotopic composition of the noble gases points in the same direction (Zahnle and Kasting, 1986 ; Zahnle et al., 1990 ; Chassefière and Leblanc, 2004 , and references therein).

The Kulikov et al. (2007 ) model of the terrestrial atmosphere shows that a ten-fold increase of the XUV flux, corresponding to the Sun $>$ 3.8 Gyr ago, leads to exobase temperatures of $>$ 10,000 K, which would imply escape rates not only for H but also for H₂, He, N, O, or C. The hydrogenic blow-off temperature is only about 5000 K. As a consequence of dissociation of H₂O, large amounts of water would thus have been lost unless there was a significantly higher CO₂ content in the early atmosphere, because CO₂ is efficiently cooling the upper atmosphere by radiation in the 15 $μ$ m band (Kulikov et al., 2007 ). Given the high early solar XUV flux, the atmospheric CO₂ content in the young Earth’s atmosphere may have been at similar levels as in the atmospheres of the present-day Venus and Mars ( $≈$ 95%; Kulikov et al. 2007 ). Its reduction and consequently, the rise of T_exo, due to weathering onto the surface and the seafloor during the first 500 Myr was accompanied by a rapid decay of the solar EUV irradiation so that T_exo was kept below blow-off conditions.

An important factor of the young Earth’s atmosphere is the relatively strong (as compared to Venus or evolved Mars) terrestrial magnetosphere that protects the atmosphere from solar-wind pickup erosion. An early on-set of the dynamo was therefore essential to protect the atmosphere and the large water reservoir of the Earth (Kulikov et al., 2007 ; Lundin et al., 2007 ).

7.2.7 Mars: Once warmer and wetter?

There is substantial evidence for a warmer and wetter climate on ancient Mars (Carr, 1986 ). The presence of valley networks in the highlands as well as some crater morphology require the presence of liquid water (e.g., Craddock and Maxwell 1993 ). Using Mars Global Surveyor images and altimeter data, Carr and Head (2003 ) estimated the depth of a primitive Martian ocean at 150 m (over the whole planet). Judged from the near-absence of valleys in the younger northern areas, liquid water disappeared suddenly 3.5–4 Gyr ago (Chassefière and Leblanc, 2004 ). Temperatures above 0 ^oC and a massive atmosphere were required at earlier epochs, with a substantial content of greenhouse gases (Chassefière and Leblanc, 2004 ).

Massive atmospheric loss is relatively easy to explain, given Mars’ low surface gravity and the absence of a global magnetic field protecting the atmosphere from the solar wind after about 700 Myr of the planet’s formation (Acuña et al., 1998 ). Intense erosion by direct interaction between solar wind and the extended atmosphere is thus possible although significant suppression of non-thermal escape by the magnetic field would be possible during the first 200–300 Myr (Hutchins et al., 1997 ; Kulikov et al., 2007 ). In present-day Mars, hydrogen is predominantly lost through thermal escape (five times more efficiently than by non-thermal escape), while loss of oxygen to space requires non-thermal processes (Lammer et al., 2003a ).

Like for other planets, the thermal escape of the young atmosphere of Mars depended strongly on the solar EUV irradiation, and non-thermal escape processes would also have depended on the ancient solar wind strength. Blow-off conditions are reached for an exospheric temperature T_exo $> ∼$ 1000 K (Lammer et al., 2003a ). This requires an EUV flux $≈$ 100 times the present solar value (Kulikov et al. 2007 , see Figure 42 ), i.e., blow-off may apply to the the earliest times of the solar evolution, namely the first few 100 Myr after the Sun’s arrival on the ZAMS (when a strong solar wind would perhaps provide additional support, Chassefière 1996b , 1997 ; Chassefière and Leblanc 2004 ). For solar conditions 2.5 Gyr and 3.5 Gyr ago, Lammer et al. (2003a ) concluded that the exospheric temperature was only T_exo = 350 K and 600 K, respectively (with a 3 times and 6 times higher solar EUV flux, respectively), insufficient for blow-off unless a significantly lower CO₂ mixing ratio applied (Kulikov et al., 2007 ), although Jeans escape and non-thermal escape of H remained operational.

Figure 42:

Modeled temperature profiles for Mars for various solar XUV levels: 1 = present-day, 10 times (3.8 Gyr ago), 50 times (4.33 Gyr ago), and 100 times (4.5 Gyr ago) present levels, based on a 96% CO₂ thermosphere (from Kulikov et al., 2007

Calculations show that in contrast to the situation on Venus and Earth, a considerable fraction of O (from the dissociated H₂O molecules) may have been dragged off by the escaping H in the very young Mars (4–4.6 Gyr ago; Chassefière 1996a ). Non-thermal escape processes (of O) alone may explain the loss of a 12–15 m Martian ocean during the past 3.5 Gyr (Lammer et al. 2003a ; Chassefière and Leblanc 2004 , and further references therein converging to similar numbers). Lammer et al. (2003a ) and Chassefière and Leblanc (2004 ) summarized escape rates for three different epochs (present, 2.5 Gyr and 3.5 Gyr ago) to find that oxygen loss to space in the early epochs is predominantly due to sputtering (and also ion pick-up; see also Luhmann et al. 1992 ; Jakosky et al. 1994 ), in contrast to the present-day situation. During the last 2 Gyr, however, O escape was not sufficient to balance H escape from dissociated water, implying that oxygen must have reacted efficiently with surface material.

7.2.8 Venus, Earth, Mars: Similar start, different results?

Even if Venus, Earth, and Mars might all have started with dense, CO₂ rich atmospheres and a large reservoir of water, the outcome of atmospheric evolution shows three very different planets: a very arid Venus with its dense, greenhouse-effective hot CO₂ atmosphere; a water-rich Earth with a biologically transformed, intermediate-density atmosphere; and a cold Mars with frozen water reservoirs and a greenhouse-ineffective CO₂ atmosphere. Key factors that led to the variations between the present-day planets are, among others: the close distance of Venus to the Sun, potentially allowing for a runaway greenhouse leading to the complete escape of water into space; the Earth’s magnetic field that protected the atmosphere from erosion by the early and stronger solar wind, together with the biological activity unfolding on young Earth; and the low surface gravity of Mars coupled with the absence of a magnetic field that led, except during the initial few 100 Myr, to more efficient erosion of the early atmosphere. Further factors such as continents (allowing for a carbonate-silicate geochemical cycle and thus the removal of CO₂, see Section 7.1.1), plate tectonics (allowing for release of CO₂, see Kasting and Toon 1989 ), or volcanic activity may matter as well. Nevertheless, in all cases, the level of XUV emission and the strength of the solar wind in the early solar system were of prime importance. Figure 43 shows a sketch of the different evolutionary paths of the atmospheres of Venus, Earth, and Mars considering the long-term evolution of the Sun’s XUV radiation and the solar-wind strength (from Kulikov et al. 2007 ; see also Lundin et al. 2007 ).

Figure 43:

Comparison of evolutionary paths of Venus, Earth, and Mars, accounting for the influence of solar XUV and particle radiation (from Kulikov et al., 2007 , © Springer Verlag, reprinted with permission).

7.2.9 Titan: Early atmospheric blow-off?

The same atmospheric methodology as described for Venus and Mars can be applied to other solar-system atmospheres. There is a particularly interesting isotopic anomaly in the atmosphere of Titan, namely a ¹⁵N enrichment with respect to ¹⁴N by a factor of 3.9–4.5 (Penz et al., 2005 , and references therein). Non-thermal escape processes alone cannot account for the enrichment unless an unrealistically strong solar wind is assumed for the first 500 Myr after the origin of the solar system (Lammer et al., 2000 ; Penz et al., 2005 ).

It is important to note that present-day Titan’s orbit resides entirely within Saturn’s magnetosphere, i.e., its atmosphere is protected from the solar wind. Because the latter has decayed during the Sun’s evolution (Section 5.1), Titan spent most of its time outside Saturn’s magnetosphere at ages of about 100 Myr, and still more than half of the time at an age of 1 Gyr; its atmosphere was therefore subject to direct solar-wind interactions. Nevertheless, sputtering and ion pick-up are not sufficient to explain the anomalous ¹⁵N/¹⁴N ratio (Penz et al., 2005 ).

Thermal escape is an alternative. The present exospheric temperature is in the range of T_exo $≈$ 150–180 K, while for blow-off, T_exo $>$ 8040 K is required (see Penz et al., 2005 , and references therein). Scaling the present T_exo by using the XUV flux decay law derived for solar analogs (Section 5.6), one finds blow-off conditions for Titan during the first 200 Myr. Only 50 Myr would in fact suffice to remove 30 Titan atmospheres, needed to explain the anomalous ¹⁵N/¹⁴N isotopic ratio (Penz et al. 2005 ; see also Lunine et al. 1999 ).

7.2.10 Hot Jupiters: Mass evolution by evaporation?

The discovery of extrasolar, Jupiter-class planets very close to their parent stars (Mayor and Queloz, 1995 ) immediately brought up the question on the stability of such objects. Gaseous planets close to a solar-like star will efficiently evaporate. However, as discussed above, it is not the radiative effective temperature, T_eff, that is relevant for evaporation, but rather the exospheric temperature, T_exo, which is determined by the stellar XUV flux, and is therefore a consequence of stellar activity.

A “Hot Jupiter” orbiting a star like the present-day Sun at a distance of 0.04 AU is, with regard to solar XUV irradiation, an analog to a Jupiter-like planet in orbit around the ZAMS Sun at a distance of 1.3 AU. The analogy does not hold for the stellar wind, and there may also be a substantial effect due to synchronous (i.e., slow) rotation of hot Jupiters (Grießmeier et al., 2004 ).

Lammer et al. (2003b ) derived the escape rate of a hydrogen atmosphere of a Jupiter-like exoplanet based on exospheric XUV absorption and heating. They used the time-dependent XUV fluxes from the “Sun in Time” program (Section 5.6). Although for Jupiter in its 5.2 AU orbit around the present-day Sun, XUV heating leads to T_exo $≈$ 140 K only, a close-in hydrogen-rich Jupiter at distances $<$ 0.3 AU may suffer blow-off temperatures T_exo $>$ 2 $×$ 10⁴ K. The XUV-absorbing atmospheric layer (the “exobase”) expands to several planetary radii, which has been directly confirmed by a planetary transit observation (Vidal-Madjar et al., 2003 ). The initial calculations by Lammer et al. (2003b ) led to very high mass-loss rates, initially criticized by Yelle (2004 ) who derived 20 times smaller escape rates by also including atmospheric chemistry in their calculations; in particular, they considered thermospheric cooling by H₃⁺ and the lowering of the solar energy deposition rate by ionization of H to H⁺, which either escapes, or recombines by emitting a photon, which escapes as well. In this case, the escape rate will not be large enough to substantially affect the planetary evolution. This was substantially confirmed by new calculations performed by the previous group (see Penz et al., 2007 ) who considered Roche-lobe effects to the hydrodynamic loss, and used realistic heating efficiencies (rather than an energy-limited, 100% efficiency assumption) and IR cooling terms for HD 209458b, a Jupiter-sized planet in orbit around an old, inactive solar analog. The temperatures at 1.5 R_planet then reach 6000–10,000 K (Figure 44 ) which, however, leads to blow-off thanks to gravitational effects by the Roche lobe. Loss rates of 7 $×$ 10¹⁰ g s^–1 are obtained, in agreement with calculations by Yelle (2004 ) and Yelle (2006 ). Extrapolated to young MS ages of the host star (applying elevated XUV irradiation, i.e., a factor of 100 at an age of 0.1 Gyr, see Table 6), the loss rate may exceed 10¹² g s^–1, leading to an integrated mass loss of 1–3.4% of the present mass over the entire MS life time of the host star, a fraction that is not leading to substantial alterations in the planet. However, higher evaporation fractions are possible for planets orbiting closer to the host star.

Figure 44:

Temperature profile through the atmosphere of the “hot Jupiter” HD 209458b in a 0.046 AU orbit around its solar-analog host star, for different XUV radiation levels corresponding to ages of 4, 2, 1, 0.5, 0.2, and 0.1 Gyr (from Penz et al., 2007 , reprinted with permission).

In summary, hot Jupiters around young solar analogs should be in a state of extensive atmospheric loss for four reasons. The first three, close distance, high XUV flux, and strong wind of the host star have been discussed above. The fourth is the lack of a strong planetary dynamo owing to the slow, synchronous rotation of the planet. This prevents the planet from building up an extensive magnetosphere that protects the upper atmospheric layers from erosion by the solar wind. In fact, during the first 500 Myr, the magnetosphere may not protect the atmospheres of hot Jupiters even if tidal locking were ignored (Grießmeier et al., 2004 ). The “hot Jupiter” would therefore interact with the solar/stellar wind in a similar way as present-day Venus. Such interactions are even further enhanced by collisions with coronal mass ejections (CMEs). Given that these were probably much more frequent in the young Sun, significant effects are expected for planets at larger distances. Khodachenko et al. (2007 ) found that in order to prevent atmospheric erosion down to the planetary core, a sufficiently strong planetary magnetic field must be present to deflect CME plasma at stand-off distances of at least 1.3 R_planet for hot Jupiters like HD 209458b. The very existence of numerous Jupiter-mass planets very close to their host stars may indicate that the planets are able to retain substantial magnetic moments (Khodachenko et al., 2007 ).