Loss of Water on the Young Venus: The Effect of a Strong Primitive Solar Wind

ICARUS

126, 229–232 (1997) IS975677

ARTICLE NO.

NOTE Loss of Water on the Young Venus: The Effect of a Strong Primitive Solar Wind E. CHASSEFIE` RE Laboratoire de Me´te´orologie Dynamique, Universite´ Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France E-mail: [email protected] Received October 16, 1996; revised January 2, 1997

An enhanced primitive solar wind, such as may have prevailed during the first few 100 million years of the solar system history, is shown to have had the potential to stimulate strong thermal atmospheric escape from the young Venus. Due to heating by solar wind bombardment of an extended dense planetary corona, typically 10 times more extensive than the solid planet, an escape flux of pure atomic hydrogen as large as 3 3 1014 cm22 sec21 is found to be possible, provided the solar wind was P103 –104 more intense than now. Even if escape was diffusion-limited, an enhanced primitive solar UV flux (a factor of P5 above present level), absorbed by P0.3 mbar of thermospheric water vapor, was able to supply the flow at the required rate. For these high escape rates, oxygen was massively dragged off along with hydrogen, and water molecules could be lost at a rate of P6 3 1013 molecules cm22 sec21. Because, at this rate, a terrestrial-type ocean was completely lost in P10 million years, short compared to typical accretion and outgassing times, water was lost ‘‘as soon’’ as it was outgassed. This mechanism could explain the present lack of oxygen in the Venus atmosphere. Because it is expected to affect all sunlike stars in the early phase of planet formation, abiotic oxygen atmospheres could be rare in the universe.  1997 Academic Press

Would the telescopic observation of oxygen, and more particularly ozone, in substantial amounts on an extrasolar planet be a reliable clue to the presence of life (Owen, 1980; Le´ger et al. 1993)? The Earth is the only planet of the Solar System to have an oxygen atmosphere, and this oxygen is known to be of biological origin. Venus is free of oxygen but it is thought to have contained a primordial water ocean, giving rise to a dense steam atmosphere and a subsequent strong greenhouse effect (Rasool and De Bergh, 1970). The present lack of water is supposed to be due to photodissociation of H2O followed by thermal escape of H at an early stage (see, e.g., Kasting and Pollack, 1983). Following Kasting (1995), the oxygen left behind can in principle accumulate and give rise to a massive abiotic oxygen atmosphere. The lack of oxygen on Venus is puzzling, and might imply a low initial endowment of Venus with water. An alternate hypothesis is the loss of oxygen by oxidation of the crust, but it was shown by Lewis and Prinn (1984) that the trapping of P100 bars of O2 over geological times should impose a permanent extrusion

of nonoxidized material with a rate much larger than on Earth, which seems implausible. By considering that H primitive escape is limited by available solar EUV energy, we have confirmed the finding by Kasting (Chassefie`re, 1996a), showing that planets like Venus or Mars are unlikely to have lost an important fraction of their oxygen, swept away together with hydrogen (see Hunten et al, 1989, for the theory). From a new hydrodynamic model (Chassefie`re, 1996b), which takes into account the transition from a fluid to a noncollisional regime at the exobase level, we have shown that only a small part of the available EUV is consumed in escape. In a companion paper (Chassefie`re, submitted to Geophys. Res. Lett., referred to as CP here), this model is applied to primitive EUV conditions, but present solar wind conditions, and it is shown that the consequent oxygen flux is virtually zero, as already found from our previous simpler approach (Chassefie`re, 1996a). On the other hand, the model shows that the solar wind (SW) is an important source of energy, through the action of energetic neutrals formed by charge exchange between escaping neutrals and SW protons. The effect of an enhanced solar wind at early times therefore deserves to be examined. The aim of the present paper is to provide a first estimate of the effect of an enhanced primitive SW on escape by establishing a budget of incoming and outgoing energy fluxes at the exobase. The planetocentric altitude of the exobase, which is the only free parameter of the study, is denoted by rex . At low values of the SW flux, of the order of its present value, the obstacle, that is the boundary between the SW plasma and the planetary wind plasma, is located above the exobase. The atmosphere is heated by energetic neutrals (ENs) produced by charge exchange between escaping H atoms and SW protons above the obstacle (Chassefie`re, 1996b). Some of them intercept the fluid corona, with substantial heating of its outer regions. At high values of the SW flux, the SW ram pressure is in excess of the plasma pressure in the corona and direct interaction between SW protons and fluid corona H atoms is expected in the case of a non-magnetized planet like Venus. Because the H–H1 charge exchange cross-section sex and the H–H collision cross section sc are of similar magnitudes, 2 3 10215 and 3 3 10215 cm2, respectively, the fate of incoming SW protons is to be transformed to neutral atoms near the exobase level. The ENs created in this way enter the fluid corona to a depth of a few mean collisional free paths (typically P104 km). This mechanism can be compared to the sputtering of neutral species by picked-up planetary ions. Similarly, it works only in the case of weakly magnetized planets. Luhman and Kozyra (1991) have shown that atmospheric loss from accelerated oxygen ions in the Venus atmosphere is two orders of magnitude above the loss from direct SW pickup ions in present solar conditions. As shown by Jakosky et al. (1994, and references therein), many species, including carbon, oxygen, nitrogen and noble

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` RE E. CHASSEFIE

230

gases, could be efficiently removed from the martian atmosphere over geological times. The mechanism we invoke here is of the same nature, although the energy carriers are not picked-up ions, but neutrals formed by charge exchange between SW ions and escaping neutrals. For this mechanism to be efficient, a large escape flux is required, as it could have been the case in the primitive water-rich Venus atmosphere. Let us denote by m the mass of a H atom (or proton), N the density of the SW (N 5 aN0 , where the present value N0 is P20 cm23 at the distance of Venus), V the velocity of SW protons (V P 400 km sec21). In a one-dimensional approach, the SW flux is NV/4 (the factor 4 is the ratio of the spherical area to the cross-sectional area of the planet). The energy flux carried by the SW is P(N/4) 3 V 3 (mV2 /2), if the SW thermal energy is neglected. For a given value of rex , the SW energy flux intercepted by the planet is therefore FEN 5 kAr2exNmV 3,

(1)

where rex , as any other radial distance in this study, is expressed in units of 1 planetary radius r0 (P6000 km for Venus). In order to quantify the balance between the inward energy flux FEN and the outward energy flux carried by escaping atoms, we make the assumption that the escape energy is entirely provided by ENs. This assumption is not necessarily true at low SW levels (see CP). But at the very high SW levels which might have existed in the young solar system (a 5 1000 or even more; see, e.g., Henney and Ulrich, 1995), this assumption is justified. The outward energy flux may be calculated by introducing the thermal kinetic energy sA mv 2 of escaping atoms in the Jeans integral, which yields an average escaping energy E per atom of E (tex) 5 2tex 1

lex 1 1 tex / lex

(2)

in units of kT0 . T0 is the temperature at the base of the expansion (at P200 km altitude), P250 K. We use a normalized temperature t 5 T/T0 and the position is described by the distance parameter l 5 rc /r (where rc P 25 for Venus), which is proportional to the gravitational potential energy. For lex $ tex , E Q lex : the value of the energy is exactly that required to overcome the gravitational barrier. In the other extreme case, E Q 2tex : the mean energy lost is the thermal energy of particles (much in excess of their gravitational energy), obtained for the value of the thermal velocity (2kT/m)1/2 corresponding to the maximum of the Maxwellian distribution. For very large exospheric temperatures particles do not ‘‘feel’’ gravity anymore. The particle flux fex , given by Jeans’ law (Eqs. 19–21 in Chassefie`re, 1996b), depends on both the density nex at the exobase and the exospheric temperature tex . The energy balance can be written FEN 5 fex(nex , tex) E(tex).

FIG. 1. Escape flux as a function of exobase planetocentric altitude (in units of planetary radius) for a 5 1 (a), a 5 30 (b), a 5 500, 2000 (c), and a 5 100,000 (d).

(3)

tex is imposed since the product of the scale height Hex 5 tex r 2exkT0 /mg0 with nex and with the collisional cross-section sc must be equal to unity, where g0 is the acceleration of gravity at the surface (r 5 1). In fact, the effective scale height H9ex must take into account the partition function z(lex/tex ,l), introduced and tabulated by Chamberlain (1963). Above the exobase, the vertical distribution of the density is not barometric and z is the corrective factor to be applied. For r R y, i.e., l R 0, the H atom density n(l) 5 z(lex/tex ,l) 3 nbar(l) tends toward zero, where nbar is the barometric distribution. znbar varies asymptotically as l2 because of mass conservation. The effective scale height H e9x(lex/tex) has been calculated and tabulated. Whereas H is unrealistically large at high exospheric temperatures, H e9x may be shown to be smaller than rex from a simple calculation using its asymptotical value. By replacing nex by (H e9xsc)21 in Eq. (3), tex is obtained as a function of lex . nex(lex) can be deduced and the

value of the escape flux fex(lex) obtained, as well as FEN(lex). For low values of the SW (a , P 10), the obstacle may be in some cases above the exobase, and there is no direct contact between the SW and the fluid corona. ENs are created outside the planetosphere, above the exobase, and the calculation of FEN is possible but more complicated (Eqs. 30–34 in Chassefie`re, 1996b). fex is plotted versus rex in Fig. 1 for four cases. (1) Present solar conditions (a 5 1, obstacle above the exobase; at rex P 2, fex P 1011 cm22 sec21, which agrees reasonably well with the results of Chassefie`re (1996b). (2) SW enhancement by a factor of P30: the analysis of the volatile content of the lunar regolith shows a three-fold excess of SW nitrogen with respect to that expected from the present-day flux (Clayton and Thiemens, 1980). Such an excess suggests a time dependence similar to the one of the EUV flux (Zahnle and Walker, 1982) : a 5 30 (for t P 108 yr). Nevertheless, the analysis of the lunar regolith does not provide reliable information on early times because of later melting. (3) Models of the young sun explaining, at least partly, the present solar lithium depletion, with early mass loss rates of 5.7 3 10212 Ms /year (a P 500; Ms is the solar mass) and 2.0 3 10211 Ms /year (a P 2000) (Henney and Ulrich, 1995). (4) Very large early mass loss rate of 1029 Ms /year (a Q 100,000), following Graedel et al. (1991) and the somewhat controversial suggestions of Willson (1987, and references therein). The decrease of the collisional cross-section with temperature as t20.2 (Chassefie`re, 1996b), resulting in an increase of nex at high temperatures, is taken into account. A marked increase of fex is observed for rex varying from 1 (ground level) up to P5. This increase is more moderate at higher exobase levels. The response of the escape flux to an increase of the SW is strongly nonlinear. As shown in Fig. 2, the exospheric temperature becomes so high that E is much in excess of the minimum required energy lex . By assuming a P 2000 and a large exobase radius rex P 10 (see CP), fex P 1014 cm22 sec21 (Fig. 1) and FEN P 4 3 104 erg cm22 sec21. The value of the minimum energy required for escape is only 87 erg cm22 sec21, i.e., P2/1000 of the incoming SW energy.

231

NOTE Although the major result of our companion paper (CP) is that a large collisional corona can be formed under primitive EUV conditions, the question of the location of the exobase needs to be discussed more thoroughly in the present context. Indeed, it is relatively easy to obtain solutions of hydrodynamic equations for which t regularly increases from 1 at the base to P104 at the exobase (at rex P 10) by using the hydrodynamical part of our model (Chassefie`re, 1996b). Nevertheless, for this type of solution, energy is transported by diffusion inward of heat deposited at the exobase entirely by SW, and not at all by EUV. For such a regime to be possible, the flow must remain subsonic everywhere, because any transition to a supersonic flow would inhibit inward diffusion of heat. This condition requires an atomic density at the base larger than P3 3 1011 cm23. The problem is that, in this case, the altitude of the exobase, as calculated by comparing the collisional mean free path and the scale height, becomes infinite, which is of course unphysical. In fact, because the bulk velocity decreases as the inverse square of the radial distance, an evaporation level, above which the very hot medium is no more confined by bulk flow, necessarily exists. This may be defined as the level above which the atomic diffusion velocity uD becomes larger than the bulk velocity u. A simple calculation can be performed. The diffusion coefficient D for a H/O mixture, D5A

Ts , n

(4)

can be calculated by using, as an average, the H–O binary diffusion value (A 5 6 3 1017 if D is expressed in units of cm2 sec21; the values of A for H–H and O–O are P3 times smaller and P1.5 times larger, respectively) and s P 0.7 (Banks and Kockarts, 1973, pp. 39–41). The diffusion velocity uD is PD/H, where H is the density scale height. For a given temperature (here, t P 104, i.e., T P 2.5 million K), uD is therefore inversely proportional to n 3 H. For very high temperatures, H becomes unrealistically high if it is calculated in the classical way, and it must be replaced by the radius r of the sphere, as previously. In this case we say

FIG. 2. Same as Fig. 1 for the exospheric temperature.

that evaporation occurs if the time for an atom to traverse the whole sphere by diffusion is equal to the time required to traverse it at the bulk velocity. This is a reasonable assumption. By replacing H by r (because, at t P 104, H . r), and by using the equation of mass conservation, which permits n to be expressed as a function of u and f, one obtains the following numerical relationship: uD 1 P r. u 6

(5)

The numerical factor is obtained by assuming an escape flux of the H 1 H 1 O mixture of P1.8 3 1014 cm22 sec21 (see hereafter). Evaporation is therefore expected to occur at rev P 6 planetary radii. Above this level, there is a sharp increase of the expansion velocity and a subsequent decrease of the density over, say one scale height, that is Prev . The exobase level is therefore expected to be located near rex P 2rev P 12. Thus, our approach is self-consistent, at least in first approximation. The consequence is that a hydrogen escape flux as high as P1014 –1015 cm22 sec21 is in principle possible during the first 108 yr of the solar system, provided the SW was P103 –104 stronger than today, which does not seem unrealistic. The crossover mass, that is the minimum mass at which a constituent can be swept away with hydrogen, is mc P 210 amu for fex 5 3 1014 cm22 sec21, obtained e.g., for (a, rex) 5 (104,10) or (a, rex) 5 (103, 25) (see Fig. 1), and T 5 250 K (see Chassefie`re, 1996a, for details). Oxygen, of mass 16, can therefore escape. If we assume a ratio O : H 5 1 : 2, the mean atomic mass of escaping atoms is 6. It is easy to show that fex varies as m21/3, which results in a somewhat reduced flux, P1.8 3 1014 cm22 sec21, that is P1.2 3 1014 H atoms cm22 sec21. The value of mc is therefore somewhat reduced (mc P 85), but remains large enough to produce massive escape of oxygen. More than 80% of the oxygen is removed. Note that, at an escape rate of 6 3 1013 H2O molecules cm22 sec21, the equivalent of one terrestrial ocean would be lost in only P10 myr, that is in a time short compared to the accretion time (P100 myr); water is removed ‘‘as soon’’ as it is outgassed. A major point is that, for an exospheric temperature in the range t 5 103 –104 (P1 3 106 K), as expected for a .P 1000, sc (P3–10 3 10216 cm2) is P3 times smaller than sex . SW protons are transformed to neutral atoms by charge exchange about P1 scale height (i.e., H e9x P rex at high temperature) above the exobase. For example, for rex P 10, ENs are created at r P 20. It follows that even a magnetized planet such as Earth, with a magnetosphere of size P10 planetary radii, could efficiently lose its oxygen. In fact, the Earth did not lose its water because a runaway greenhouse did not develop (Rasool and De Bergh, 1970). The present work suggests that either oxygen is lost with hydrogen in O : H Q 1 : 2 proportions, or water is not lost at all. In neither case can a massive abiotic oxygen atmosphere be formed. Is the photodissociation of water vapor in the primitive Venus atmosphere able to provide 6 3 1013 H2O molecules per square centimeter each second? Let us assume a UV enhancement in the range P150–250 nm by a factor b P 2 during the first few 108 yr (Zahnle and Walker, 1982). By using Table 7.3 in Banks and Kockarts (1973, p. 141), it may be found that the wavelength value llim such as the flux of solar photons seen by Venus at l , llim is 6 1013 cm22 sec21, is P210 nm. The photodissociation cross-section of H2O at llim is slim P 10224 cm2. A column of pure water vapor of P1024 cm22, that is P30 mbar, is therefore required. This is much less than the pressure expected in the case of a runaway greenhouse. Nevertheless, if escape if diffusion-limited, this quantity must be present in the thermosphere, above the cold trap. It corresponds to a H2O density nw of P1018 cm23 (rw P 3 3 1025 g cm23) at the cold trap level. This value seems unrealistically large (Kasting and Pollack, 1983), but note that by assuming b 5 5, the picture drastically changes : in this case, llim P 200 nm, slim P 10222 cm2, and rw P 3 3 1027 g cm23, which is more reasonable. This brief calculation shows that the limiting factor for primitive escape of oxygen could have been set by transport and/or photochemistry rather than by solar conditions.

` RE E. CHASSEFIE

232 ACKNOWLEDGMENTS

This study was supported by the Programme National de Plane´tologie of the Institut National des Sciences de l’Univers. I am grateful to Olivier Gupta and Michae¨l Peigney from Ecole Polytechnique for their help in implementing the numerical part of this work. I thank Dr D. Grinspoon and an anonymous referee for their constructive opinions and help in improving the form of this note.

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