5 Simulations and results

We present successively our results on the humid ${\rm CO}_{2}$-dominated, dry ${\rm CO}_{2}$-dominated and water-rich atmospheres. For each atmospheric case under study, we give its description in terms of parameters of the model, the past or present Solar System situation it may correspond to, and/or its theoretical interest for the "maximization'' of the false positive detection risk with Darwin. The results are then presented, compared with other existing observational or theoretical work, and their effective significance for the false positive problem is analyzed. The robustness of the results to model changes is explored in more details for case A. An overview of all cases is summarized in Table 3.

Figure 2: Photodissociation cross sections of ${\rm H}_{2}$O, ${\rm CO}_{2}$ and ${\rm O}_{2}$.

   
5.1 Humid CO $\mathsf{_2}$-dominated atmospheres

We made four different runs. In all of them water vapor abundances were close to the saturation value. The ${\rm CO}_{2}$ pressure increased from 6 mbar (case A) to 1 bar (case B) and 3.2 bar (case C); the last case D ( $P_{{\rm CO}_{2}}$ = 0.2 bar) "maximizes'' the risk of a false positive detection of life. In cases A and B, the atmosphere was pure ${\rm CO}_{2}$, whereas cases C and D included also 0.8 bar of ${\rm N}_{2}$, leading respectively to total pressures $P_{{\rm tot}}$ of 4 bar and 1 bar. Beside their representativity of humid ${\rm CO}_{2}$-dominated atmospheres, these cases were also studied for themselves as representing A) Mars today; B) a possible terraforming (McKay et al. 1991) or ancient state of Mars; C and D) two plausible stages of the early Earth atmosphere; see Selsis (2000b) for more details.

   
5.1.1 Case A ( $\mathsfsl{P}\mathsf{_{tot}}$ = $\mathsfsl{P}\mathsf{_{CO_{2}} = 6}$ mbar)

All input parameters for this run correspond to present-day Mars; the set of values is the same as used by Nair et al. (1994). The mean chemical atmospheric composition is that determined from Viking data (Owen et al. 1997): 95.3%  ${\rm CO}_{2}$, 2.7%  ${\rm N}_{2}$, 1.6% Ar. We adopted the thermal profile recommended by Seiff (1982) up to 100 km and the one by Nair between 100 and 220 km. Ground-level humidity has been adjusted to obtain a column density of 3.1 $\mu$m precipitable water, which is within the range observed on Mars (Clancy et al. 1992); a run with 8.2 $\mu$m has also been performed. The law for the turbulent diffusion coefficient K as a function of altitude has been fitted from the data compiled by Krasnopolsky (1993). The variation of the surface albedo with $\lambda$ has been parametrized according to Lindner (1985). When included, H and ${\rm H}_{2}$ escape and ${\rm O}_{2}$ sink on the surface are supposed to correspond to the stationary state (loss of 2 H atoms for one O atom), as result e.g. of the regulation mechanism proposed by Yung & DeMore (1999).

Simulations were first conducted for a basic set of conditions: constant solar flux, 3.1 $\mu$m-pr ${\rm H}_{2}$O, H and O escape. The set of chemical reactions and reaction rates has been optimized, leading to a database we called "MARS'' (Selsis 2000b), different from the JPL97 database (DeMore et al. 1997) by taking into account the specific role of ${\rm CO}_{2}$ as a third body in the association reactions. The production of ${\rm O}_{2}$ and ${\rm O}_{3}$ through photolysis is shown in Fig. 3. After a growth for 100 000 yr the abundances reach a constant value close to present day values for Mars, which are respectively about 10^-3and 10^-8 in mixing ratio.

Figure 3: Evolution of the ${\rm O}_{2}$ and ${\rm O}_{3}$ column densities as a function of time for a humid ${\rm CO}_{2}$ dominated Mars-like atmosphere at low pressure ( $P_{{\rm CO}_{2}}$ = 6 mbar) . The ${\rm H}_{2}$O column density corresponds to 3.1 $\mu$m precipitable water (solid line); a more humid atmosphere (8.2 $\mu$m-pr) is also shown (dotted line). Note that more water results in less ${\rm O}_{2}$ and ${\rm O}_{3}$ (see text). A steady state is reached after 100 000 yr. The grey areas represent the abundance range deduced from observations for these two compounds nowadays.

The effects of suppressing the O and H escape, increasing the humidity, changing the chemistry database, and night/day alternance versus mean solar flux have been also investigated; the results are summarized in Table 3. The observations (see Table 1) are best reproduced by cases using the optimized "MARS'' chemical database, and including H and O escape. This shows that standard chemical databases (like the JPL97 database, developed for terrestrial applications) need to be adapted according to the nature of the background gas(es) (e.g. carbon dioxide).

The ${\rm O}_{2}$ abundance changes but ${\rm O}_{2}$ remains a minor component (<0.3%): we notice that even the twofold increase in ${\rm O}_{2}$ from case A-1a to case A-1c results in only an ${\rm O}_{3}$ increase of 25%.

Note that more water results in less ${\rm O}_{2}$ and ${\rm O}_{3}$, illustrating the mechanism alluded to above (Sect. 3.4): the increase of radicals H, OH and HO₂ diminishes the ${\rm O}_{2}$ production (by catalyzing the CO and O recombination to ${\rm CO}_{2}$) and efficiently destroys ${\rm O}_{3}$. We also tested whether the mean abundances of the various compounds are affected when taking into account the diurnal variation of the insolation. As our model is time dependent, we can simulate the evolution with small time steps (10 min maximum). This mode of simulation however does not allow long integration times. Starting from the steady state found in case A we note that the mean ${\rm O}_{2}$ content is slightly sensitive to the day/night alternance and evolves from the initial state: an increase of 0.2% is seen for 250 days. Longer term effects have still to be checked.

We conclude that in a Martian-like, low pressure, pure ${\rm CO}_{2}$ atmosphere, the abiotic production of ${\rm O}_{2}$ and ${\rm O}_{3}$ is marginal ( $2\times 10^{-3}$ and 10^-7 at most); this result is robust with respect to uncertainties in the modelling process. Such a low ${\rm O}_{3}$ content would not show up in the IR spectrum taken by Darwin, which will not be able to detect an absorption or emission feature less intense than about one fifth of the terrestrial ${\rm O}_{3}$ band (Léger, private communication).

 

 

Table 2: Case A (present Mars). This Table shows the dependence of the results for ${\rm O}_{2}$ and ${\rm O}_{3}$ on some of the input parameters. The observations (see Table 1) are best reproduced by cases A-1a and A-2, which use the optimized "MARS'' chemical database, and include H and O escape.

	A-1a	A-1b	A-1c	A-1d	A-2
$N_{\rm H2O}$ ($\mu$m-pr)	3.1	3.1	3.1	3.1	8.2
Chemistry	MARS	MARS	JPL	JPL	MARS
Escape	yes	no	yes	no	yes
$\times$( ${\rm O}_{2}$) ( $\times 10^{-3}$)	1.1	0.5	2.4	0.5	1.0
$N_{{\rm O}_{2}}$ (1020cm-2)	2.5	1.1	5.3	1.0	2.3
$N_{{\rm O}_{3}}$ (1015cm-2)	6.5	2.5	8.0	0.5	5.0

  
5.1.2 Case B ( $\mathsfsl{P}\mathsf{_{tot}}$ = $\mathsfsl{P}\mathsf{_{CO_{2}}} = 1$ bar)

How does the previous result change for a denser humid ${\rm CO}_{2}$ atmosphere? Let us consider now a 1 bar atmosphere made of  ${\rm CO}_{2}$, with water present. This case can be seen as the Martian atmosphere some time in the past (see Sect. 3.3.2). It may also represent an eventual future of the planet, according to the "terraforming'' scenario proposed by McKay et al. (1991), where the introduction of an efficient greenhouse gas (e.g. CFC) in small quantities initiates an increase in the temperature and leads to the sublimation of ${\rm CO}_{2}$ and ${\rm H}_{2}$O, which themselves generate a runaway greenhouse effect liberating more of those gases. In a 1 bar atmosphere, a partial pressure of 1 mbar for ${\rm O}_{2}$ is the minimum for growing plants (McKay et al. 1991).

 

 

Table 3: Model parameters and results for each case. The parameters were chosen to favour, under realistic conditions, an O₂/O₃ abiotic enrichment. However none of the surveyed cases presented the triple signature of Earth-like oxygenic photosynthesis: no false positive case. The weak triple signature in case G appears in an unlikely extreme situation (see text). Notes: (1) Adjusted to obtain the column density measured on Mars (i.e. 3.1 and 8.2 microns precipitable of ${\rm H}_{2}$O). (2) Surface humidity: $H_{{\rm surf}}$ = 1%, so that $X_{{\rm H}_{2}{\rm O}}$(surface)/ $X_{{\rm saturated}} = 0.01$. (3) In units of present mean solar flux at Earth distance. Case A, B: present solar flux at Mars distance; cases C, D: solar flux at 1 AU 4.2 Gy ago according to standard evolutionnary models; Cases E, F: flux set to have a mean surface temperature of about 300 K (a false positive detection has to be in the habitable zone). (4) Results for no NO flux nor ${\rm O}_{2}$ sink. For the effect of these, see text. (6) Computation of the thermal profile was done only for the initial state of the atmosphere, no iterations were made after photochemical calculations. (5) Left column: results with the initial fixed thermal profile; right column results with the computed thermal profile. (7) The range of values given for ${\rm O}_{2}$ and ${\rm O}_{3}$ in cases C and D accounts for the presence or not of NO production by lightnings (Navarro-Gonzalez et al. 1998). The others influences we have tested ( ${\rm O}_{2}$ sinks and volcanic emission of reducing species) are not included here because they make the abundances of ${\rm O}_{2}$ and ${\rm O}_{3}$ completely negligeable compare to detectable levels. (8) The triple signature required for Darwin to suspect a biologic activity consists in the simultaneous presence of mid-IR bands of all three species ${\rm O}_{3}$, ${\rm H}_{2}$O and CO₂. This takes into account the resolution and sensitivity of the instrument.

	${\bf CO_2}$ humid					${\bf CO_2}$ dry		${\bf H_2O}$ influx
Cases	A	B		C	D	E	F	G
$P_{{\rm tot}}$ (mbar)/ $P_{{\rm CO}_{2}}$ (mbar)	6/6	1000/1000		4000/3200	1000/200	4000/4000	1000/50	1000/traces
$X_{{\rm CO}{\footnotesize 2}}$	0.957	1		0.8	0.2	1	0.05	$3\times 10^{-4}$
${\rm H}_{2}$O	$N_{{\rm H}_{2}{\rm O}}$ (1) - 3.1/8.2	$H_{{\rm surf}}$ (2) - 1%		$H_{{\rm surf}}~100\%$	$H_{{\rm surf}}~100\%$	no	no	constant input
$P_{{\rm N}_{2}}$ (mbar)	0.16	0		800	800	0	950	1000
solar flux (3)	0.43	0.43		0.73	0.73	0.5	0.7	1
gravity	Mars	Mars		Earth	Earth	Earth	Earth	Earth
${\rm O}_{2}$ surface losses	no	no		no (4)	no (4)	no	no	yes, < ${\rm H}_{2}$ losses
thermal profile	observed	arbitrary (B1)	computed (B2)	educated guess	educated guess	computed (6)		computed
influences	chemistry, day/night	thermal profile		${\rm O}_{2}$ loss,	${\rm O}_{2}$ loss,			high stellar UV
tested	H/O escape, moisture			volcanism	volcanism
$P_{{\rm O}_{2}}$ (mbar)	$6\times 10^{-3}$	0.5 (5)	20 (5)	[0.4-4] (7)	[0.01-0.1] (7)	27	3.5	decrease
${\rm O}_{2}$ column density (cm-2)	$2.5\times 10^{20}$	$1.3\times 10^{22}$	$8.8\times 10^{23}$	[1022-1023]	[1020-1021]	$2.7\times 10^{24}$	$9\times 10^{22}$
${\rm O}_{2}$ mixing ratio	10-3	$5\times 10^{-4}$	0.02	[10-4-10-3]	[10-5-10-4]	2.7%	0.35%	<1%
${\rm O}_{3}$ column density (cm-2)	$6.5\times 10^{15}$	$5\times 10^{17}$	$1.8\times 10^{19}$	<1017	<1016	$3.4\times 10^{18}$	$1.7\times 10^{18}$
${\rm O}_{3}$ mixing ratio	$\approx 10^{-8}$	$2\times 10^{-8}$	$5\times 10^{-7}$	<10-9	<10-10	$3\times 10^{-8}$	$7\times 10^{-8}$	<10-7
comments	Mars today	early or terraformed		early Earth I	early Earth II			comet or hydrated
& Figures	3	Mars / 4-5-6		7	8	9-10	11-12	IDPs infall / 13
Triple signature? (8)	no	no		no	no	no	no	marginal

Such an atmosphere has already been modelled by Chassefière & Rosenqvist (1995a), who obtained a partial pressure $P_{{\rm O}_{2}}$ of 1 mbar, assuming a "terrestrial thermal profile without stratosphere'', to take into account the a priori absence of heating by  ${\rm O}_{3}$. But, as noted by these authors, the water vapor profile critically influences the  ${\rm O}_{2}$ production, and this profile itself relies heavily on the thermal profile.

Figure 4: Photochemistry in a 1 bar ${\rm CO}_{2}$ atmosphere (case B). This graphs show the iterative procedure used to calculate the thermal and chemical profiles. The first step consists in calculating the chemical evolution using an initial guess of the thermal profile (it was taken from Rosenqvist & Chassefière 1995) and corresponds to a modified terrestrial profile, isothermal above the tropopause). Once a steady state reached, a new thermal profile, T1 is computed in radiative-convective equilibrium with this composition (step 2). Photochemical computation and temperature retrieval are repeated once again (steps 3 and 4). This iterative procedure should be proceeded until reaching stable conditions but this highly time-consuming task was not completed. Anyway, the photochemical states called B2 and B1 can be shown respectively as an upper limit and an extreme lower limit for the O2 and O3 contents. Indeed, the cold trap that leads to a water vapor depletion above 30-40 km will still be efficient with the thermal profile T1: ${\rm H}_{2}$O abondance in the stratosphere will increase, but not above 10-7. This will lower slightly the O2-O3 production but then, a lower O3 abundance would lead to a colder stratosphere and to less water vapor. From this result we suggest an equilibrium state close to B2with a temperature profile between T1 and T2. For the resulting infrared emission, see Fig. 6.

The different steps of our modelling of this case B are shown in Fig. 4. We started the simulation with the same thermal profile as Rosenqvist and Chassefière and obtained a first photochemical equilibrium (step 1). This case (B₁) reproduces approximately the case studied by these authors, with a partial pressure $\mbox{$P_{{\rm O}_{2}}$ } \approx 0.5$ mbar . Then we computed the temperature profile (T₁ in Fig. 4) in radiative-convective equilibrium with this chemical composition (step 2). This new profile displays a strong decrease in temperature with increasing altitudes due to the low level of ozone and the absence of stratospheric warming. We let then the chemistry evolve from the state B₁ to a new steady state B₂ (step 3). The ${\rm O}_{2}$ abundance is considerably higher (40 times) , with $\mbox{$P_{{\rm O}_{2}}$ }\ \approx 20$ mbar leading to a "super ozone layer'', which is compared to the terrestrial case in Fig. 5. This ozone layer, in turn, heats the upper atmosphere, giving the next thermal profile T₂ (step 4). As the thermal effects are not directly coupled with the photochemical evolution, one should proceed with such iterations until reaching a final self-consistent state. This very time consuming task has not been undertaken in the present work. However, from these calculations, we can show that the final solution is bracketed allowing the estimation of the false positive risk. The thermal structure T₂ still provides a cold trap, limiting the vertical transport of ${\rm H}_{2}$O, and the level of water vapor in the hot stratosphere cannot exceed 10^-8-10^-7. This is enough to diminish slightly the production of ${\rm O}_{2}$ and ${\rm O}_{3}$ which, in turn, lowers the stratospheric warming and moisture, providing a negative feedback. Hence, the chemical equilibrium cannot differ much from state B₂. This one and the thermal profile T₂can be seen as upper limits respectively for the ${\rm O}_{2}$ and ${\rm O}_{3}$ contents and the temperature.

Figure 5: Super ozone layer produced in a 1-bar humid ${\rm CO}_{2}$ atmosphere (solid line, case B2). Terrestrial ozone is shown for comparison (dashed line).

The existence of an ozone layer as dense as on Earth, or even denser, is thus not necessarily a by-product of biological activity. But does this super ozone layer lead to an observable ${\rm O}_{3}$ IR band for Darwin, and hence to a "false positive''? The infrared emission calculated for the chemical composition B₂ is shown in Fig. 6. Synthetic spectra were computed for both the thermal structure T₁ and T₂, in order to display the ${\rm O}_{3}$ feature for both extreme cases. Despite the relatively high abundance of ${\rm O}_{2}$ and ${\rm O}_{3}$,the latter molecule will not be detected in this case with Darwin: the large quantity of ${\rm CO}_{2}$ present in the atmosphere completely masks its signature (see Fig. 6). The sensitivity and resolution required to reveal the ${\rm O}_{3}$ feature is far beyond the capability of the first generation of instruments that will be dedicated to the spectroscopic study of extrasolar planets. Moreover, in the further perspective of high performance instruments able to resolve this weak ${\rm O}_{3}$ contribution from ${\rm CO}_{2}$ features, the presence of high pressure ${\rm CO}_{2}$ bands would warn the observer about the possible abiotic origin of this signature.

In this case B, the non-detectability of ${\rm O}_{3}$ eliminates any "false positive'' risk for the Darwin strategy based on the ${\rm O}_{3}$ criterium; it however points out the opposite risk of false negative (see Sect. 6.2.3).

Figure 6: IR emission of an 1 bar ${\rm CO}_{2}$ humid atmosphere. This case B may for example be representative of an early Mars, or a terraformed Mars. Synthetic spectra have been computed for the maximum ${\rm O}_{3}$ content and the two extreme temperature profiles. The shaded grey area indicates the ozone feature, which is embedded within ${\rm CO}_{2}$ bands. At Darwin resolution and signal-to-noise ratio ( $\Delta \lambda \sim 0.5~\mu$m, SNR<10, Volonte et al. 2000), the presence of ${\rm O}_{3}$ cannot be inferred, for any temperature profiles contained between these ones. There is no false postive risk even at higher resolution as the high ${\rm CO}_{2}$ pressure features (within the 9-11 $\mu$m and also 7-8 $\mu$m ranges) will warn about the possible abiotic origin of ${\rm O}_{2}$ and ${\rm O}_{3}$.

   
5.1.3 Case C ( $\mathsfsl{P}{\mathsf{_{tot} = 4}}$ bars, $\mathsfsl{P}{\mathsf{_{CO_{2}} = 3200}}$ mbar, $\mathsfsl{P}{\mathsf{_{N_{2}} = 800}}$ mbar)

This case and the following one are ${\rm CO}_{2}$-rich humid atmospheres, with the same ${\rm N}_{2}$ content as in the present Earth atmosphere, but high ( $P_{{\rm CO}_{2}}$ = 0.2 bar) to very high ( $P_{{\rm CO}_{2}}$ = 3.2 bar) ${\rm CO}_{2}$ abundance. These neutral atmospheres are possible states of the early Earth atmosphere (Case C has been investigated as such by Navarro-Gonzalez et al. 1998).

We first discuss the most extreme case (C). The temperature profile is taken similar to the present one on Earth but for the stratospheric ozone heating which is suppressed. The solar flux is 73% of the present one (Gough 1981), which corresponds to 4.2 Gyr BP according to standard evolution models of the Sun; the surface temperature remains high due to the greenhouse effect of ${\rm CO}_{2}$. The relative humidity at surface level is assumed to be 100%.

After about 10⁵ yr a chemical steady state is reached (Fig. 7), with a mixing ratio of photochemically-produced ${\rm O}_{2}$ of about 10^-3 ( $P_{{\rm O}_{2}}$ $\approx 4$ mbar) and only 10^-7 for ${\rm O}_{3}$.

Figure 7: Case C: dense ${\rm CO}_{2}$-dominated humid atmosphere (4 bars, 80% ${\rm CO}_{2}$, 20% ${\rm N}_{2}$). This atmosphere contains as much ${\rm N}_{2}$ as present day Earth atmosphere and may represent a very early stage of the early Earth atmophere. Chemical relative abundances are ploted as a function of altitude. No NO flux nor ${\rm O}_{2}$ surface sink included (see text).

To provide a better representation of the early Earth, simulations have been conducted for both cases C and D where a gas production linked to volcanic activity and a ${\rm O}_{2}$ sink by oxydation of surface rocks are included; these simulations also address the problem of the NO/ ${\rm O}_{2}$ ratio, crucial for some prebiotic reaction (Commeyras et al. 2002). The volcanic gas sources include NO, produced by lightnings in volcanic plumes, and reducing species ( ${\rm H}_{2}$, CO or ${\rm CH}_{4}$) released in the case of a more reducing upper mantle. In all cases the volcanic gases decrease the oxygen and ozone contents. We conclude that in the high $P_{{\rm CO}_{2}}$ humid atmosphere of case C no ozone IR feature would thus be seen by Darwin, due to the low ozone content, and the masking by ${\rm CO}_{2}$ lines.

   
5.1.4 Case D ( $\mathsfsl{P}{\mathsf{_{tot} = 1}}$ bars, $\mathsfsl{P}{\mathsf{_{CO_{2}} = 200}}$ mbar, $\mathsfsl{P}{\mathsf{_{N_{2}} = 800}}$ mbar)

The previous case C may not correspond to a long-lasting stage of the planet evolution in the presence of abundant liquid water and continental crust, as weathering will efficiently pump atmospheric ${\rm CO}_{2}$ into carbonates (Pollack et al. 1987; Sleep & Zahnle 2001). Furthermore, on the Earth itself geological evidence suggests a maximum $P_{{\rm CO}_{2}}$ of $\approx$40 mbar since 2.8 Gyr BP (Rye et al. 1995); note however that we have no constraints from rocks on $P_{{\rm CO}_{2}}$ for earlier times. The minimum ${\rm CO}_{2}$ pressure needed for maintaining the temperature above the water freezing point at early times ($\approx$4 Gyr ago) is 200 mbar in the absence of methane (Pavlov et al. 2000). We thus conducted a simulation for this value, which is more likely to represent a substantial fraction of the evolution of the Earth's early atmosphere than case C.

The vertical profiles of some species, at steady state, are shown in Fig. 8. The ${\rm O}_{2}$ production appears less efficient than in the previous case, with a relative abundance between 10^-6(ground) and 10^-3 (at $\approx$60 km). The ground level value for ${\rm O}_{2}$ decreases even further if a NO volcanic source and ${\rm O}_{2}$ surface sink are included.

As in case C, we conclude that no infrared ${\rm O}_{3}$ feature will be seen by Darwin. Thus dense humid ${\rm CO}_{2}$-rich atmosphere have a low photochemical production of ${\rm O}_{2}$ and will not display any "false positive'' ${\rm O}_{3}$ signature for Darwin.

Figure 8: Case D: medium density ${\rm CO}_{2}$-dominated humid atmosphere (1 bar, 20% ${\rm CO}_{2}$, 80% ${\rm N}_{2}$). This atmosphere also contains as much ${\rm N}_{2}$ as present day Earth atmosphere, but seems a more likely representation of the early Earth atmosphere. Chemical relative abundances are ploted as a function of altitude. The grey area between solid and dashed lines indicates the variability of the profiles with or without oxygen surface sink and with low or high NO production (see text).

   
5.2 Dry CO $\mathsf{_2}$ atmospheres

In the humid ${\rm CO}_{2}$-rich atmospheres studied above, HO_x radicals produced by ${\rm H}_{2}$O photolysis limit the production of ${\rm O}_{2}$. What happens in a dry ${\rm CO}_{2}$ atmosphere? Nair et al. (1994) have used their photochemical model of Mars to study the equilibrium state of such an atmosphere when water is absent. They obtain a mixing ratio of $3.9\times 10^{-2}$ for ${\rm O}_{2}$ (and $7.7\times 10^{-2}$ for CO), with ${\rm CO}_{2}$ remaining the main atmospheric constituents. This contradicts Atreya & Gu (1994), who estimate that ${\rm CO}_{2}$ should be fully converted to CO and ${\rm O}_{2}$ in less than 6000 yr. An equilibrium model like that used by Nair et al. seems inappropriate to handle the problem, as the physical conditions are strongly modified during the conversion of ${\rm CO}_{2}$ to CO and ${\rm O}_{2}$: increase of the density (by a factor 1.5 when the conversion is complete), modification of the hydrostatic equilibrium, surface warming and mid atmosphere cooling due to ${\rm CO}_{2}$. We study here a 4 bar ${\rm CO}_{2}$ atmosphere (case E), which leads to a large ${\rm O}_{2}$ and ${\rm O}_{3}$ content, and a 50 mbar ${\rm CO}_{2}$ atmosphere (case F), which is a compromise between the ${\rm O}_{2}$ production and the detectability of the ${\rm O}_{3}$ IR bands.

   
5.2.1 Case E: 4 bar pure CO $\mathsf{_2}$ atmosphere

We consider a pure ${\rm CO}_{2}$ very dense atmosphere with Earth's gravity. To handle the evolution of the physical parameters, we make a stepwise computation, readjusting the physical parameters after each step. We made simulations up to 300 000 yr only due to computation time limitations. After 300 000 yr, ${\rm O}_{2}$ reaches a level of 2.7%; this stage is not yet fully stationary, but further ${\rm O}_{2}$ evolution appears extremely slow, as ${\rm O}_{2}$ absorbs the very same photons which dissociate ${\rm CO}_{2}$. It seems thus that ${\rm CO}_{2}$ remains the main constituent of such an atmosphere, as predicted, despite its limitations, by the equilibrium model of Nair et al. In Fig. 9 we show the ${\rm O}_{3}$ concentration. The upper atmosphere is richer than the Earth's atmosphere; this is due to the absence of the hydrogen compounds responsible for catalytic destruction of ${\rm O}_{3}$. The concentration of ${\rm O}_{3}$ at low altitude is low: production is limited due to the high ${\rm CO}_{2}$ column density which severely limits the number of dissociating ( $\lambda < 242$ nm) photons there, whereas ${\rm O}_{3}$ produced at higher altitudes is photodissociated by longer wavelength photons before reaching the lower atmosphere.

Figure 9: Case E: ozone layer produced in a 4 bar dry pure ${\rm CO}_{2}$ atmosphere; the terrestrial profile is shown for reference (heavy solid line).

The simulated IR Darwin spectrum for this atmosphere is shown in Fig. 10. No ${\rm O}_{3}$ signature is present, due to the high ${\rm CO}_{2}$ content which masks the ${\rm O}_{3}$ lines between 9 and 10 $\mu$m (900 and 1100 cm^-1).

Figure 10: Case E: IR Darwin spectrum simulated for a 4 bar dry pure ${\rm CO}_{2}$ atmosphere. Despite of the important ${\rm O}_{3}$ layer (see Fig. 9) the ${\rm O}_{3}$ signature is completely masked by ${\rm CO}_{2}$ lines between 900 and 1100 cm-1.

   
5.2.2 Case F: 1 bar dry low CO $\mathsf{_2}$ (50 mbar or 5%) N $\mathsf{_2}$ (95%) atmosphere

Now we try to maximize the risk of having an ${\rm O}_{3}$ signature in a ${\rm CO}_{2}$ -rich atmosphere: we consider a case where $P_{{\rm CO}_{2}}$ is $\sim$50 mbar, which is just below the 100 mbar ${\rm CO}_{2}$ pressure threshold above which the masking of ${\rm O}_{3}$ bands by ${\rm CO}_{2}$ takes place, while keeping a high photochemical production of ${\rm O}_{2}$, and hence the possibility of an ${\rm O}_{3}$ 9.6 $\mu$m band. The ${\rm N}_{2}$ content is 20% higher than on Earth just to have a 1 bar atmosphere. The presence of ${\rm N}_{2}$ as a background gas simplifies the numerical treatment without significantly affecting the chemistry ( ${\rm N}_{2}$ does not absorb at the wavelengths important for the dissociation of ${\rm CO}_{2}$ and ${\rm O}_{2}$, nor is chemically active). An equilibrium is reached after 50 000 yr; Fig. 11 displays the corresponding abundance profiles.

The partial pressure of photochemically produced ${\rm O}_{2}$ reaches 3.5 mbar. If ${\rm O}_{2}$ is consumed by surface oxydation processes, the photochemical ${\rm O}_{2}$ production must proceed continuously, and the atmosphere needs a constant ${\rm CO}_{2}$ supply, e.g. from comets or volcanoes. But, in both cases, other compounds are also injected (water, and in the second case, sulfur and chlorine compounds), both reducing the efficiency of the ${\rm O}_{2}$ and ${\rm O}_{3}$ accumulation, either by chemical reduction or by catalysing the CO and ${\rm O}_{2}$ recombination to ${\rm CO}_{2}$. In the atmosphere of Venus, chlorine and sulfur compounds oxidize CO to ${\rm CO}_{2}$ (e.g. Yung & DeMore 1999); this explains why, in this ${\rm CO}_{2}$-rich atmosphere, the ${\rm O}_{2}$ abundance is so low (cf. above , Sect. 3.1.1).

As seen in Fig. 12, the ${\rm O}_{3}$ band can only barely be detected in the IR spectrum; only a very good signal to noise and a very precise knowledge of the ${\rm CO}_{2}$ abundance and of the thermal profile would allow one to infer the presence of ${\rm O}_{3}$ from this spectrum.

Figure 11: Case F: steady state computed from an initial dry atmosphere of 95% ${\rm N}_{2}$, 5% ${\rm CO}_{2}$. ${\rm O}_{2}$ mixing ratio reaches 0.3%. The middle atmosphere ${\rm O}_{3}$ profile shows the logarithmic dependance of ${\rm O}_{3}$ on the ${\rm O}_{2}$ content predicted by Léger et al. (1993) but the lower atmosphere is very depleted in ${\rm O}_{3}$ as compared to the Earth. The thermal spectrum obtained is shown in Fig. 12.

Figure 12: Case F: IR Darwin spectrum computed for a 1 bar ${\rm N}_{2}$ dry atmosphere with 5% (50 mbar) of ${\rm CO}_{2}$. The $9.6~\mu$m ozone signature (in grey) is mixed with the ${\rm CO}_{2}$ bands at 9 and $11~\mu$m. Even with the capability to separate the two features this would not be consider as a "false-positive'' case because the ${\rm O}_{3}$- ${\rm CO}_{2}$ absorption is not associated to an ${\rm H}_{2}$O signature. The triple criterium is not gathered here.

  
5.3 Case G: Humid atmosphere with permanent water supply

Water is dissociated into ${\rm OH} + {\rm H}$ or ${\rm O} + \mbox{${\rm H}_{2}$ }$ in the upper atmosphere; as H and ${\rm H}_{2}$ escape, the atmosphere is enriched in oxygen. Such an accumulation however can proceed if, and only if, the ${\rm O}_{2}$ consumption (oxydation of rocks, reactions with volcanic gases, ...) is less efficient than hydrogen escape. On Venus, for example, the H escape on a short time scale may have produced a ${\rm O}_{2}$-rich atmosphere, but for a limited time only (Kasting 1988).

To have such a phenomenon for a longer time, one may consider a constant supply of water, for example by a constant influx of comets, or of small ice particles of cometary origin (this case was suggested to us by J. Schneider). Another case of interest is an ${\rm H}_{2}$O-dominated atmosphere with an initial ${\rm H}_{2}$O reservoir but no permanent influx; such a situation might have occurred e.g. on a warmer early Europa. Case G can be used to set upper limits for the ${\rm O}_{2}$ photochemical production in the latter case.

We thus consider here a planet of Earth size and gravity with a humid atmosphere, a constant ${\rm H}_{2}$O influx, high hydrogen escape rate, low ${\rm O}_{2}$ consumption by surface oxidation, 1 bar of ${\rm N}_{2}$ and low level of minor species which would act as catalysts of H and O recombination to ${\rm H}_{2}$O. We include however 0.03% of ${\rm CO}_{2}$ (its abundance on Earth): without such traces there would not be the "triple ${\rm CO}_{2}$- ${\rm H}_{2}$O- ${\rm O}_{3}$ signature'' in Darwin spectra, and hence no "false positive'' risk. The ${\rm H}_{2}$O influx of 10¹⁰ cm^-2 s^-1is high enough to ensure a very high ${\rm H}_{2}$O stratospheric abundance of about 10^-3 (as opposed to 10^-6 in the present Earth's stratosphere). Note that this flux is 1000 times higher than the estimated delivery flux required to explain the water vapor observed in the atmosphere of giant planets (Feuchtgruber et al. 1997). Due to the strong ${\rm H}_{2}$O influx, such an atmosphere leads to specific numerical problems like imposing small time steps. This limits in practice the duration of the numerical integration to $\approx$100 years, which is low compared to time required to have a significant O₂build up. We tackle the problem in a different way, including in the initial atmosphere a small quantity of ${\rm O}_{2}$, and studying its variation with time. We have thus included 1% ${\rm O}_{2}$. For higher contents, UV photons are largely absorbed by ${\rm O}_{2}$ and ${\rm H}_{2}$O is no longer efficiently photodissociated. Our computations show that the ${\rm O}_{2}$ content tends to decrease, and thus that 1% ${\rm O}_{2}$ (10 mbar) represents an extreme upper limit of the possible oxygen content of this kind of humid atmosphere. Figure 13 shows the vertical ${\rm O}_{3}$ profile (as compared with the terrestrial one). ${\rm O}_{3}$ is present with a very low mixing ratio (<10^-7). This is lower than expected from extrapolating from the 20% ${\rm O}_{2}$ standard terrestrial atmosphere to a 1% ${\rm O}_{2}$ following the logarithmic behaviour established by Paetzold (1962) and Léger et al. (1993); this is due to the specific nature of the humid atmosphere under study: the catalytic destruction of ${\rm O}_{3}$ by H and HO_x species is strongly enhanced compared to the Earth.

Figure 13: Case G: ozone layer produced in a humid atmosphere (1 bar ${\rm N}_{2}$, 0.1% ${\rm H}_{2}$O) with constant ${\rm H}_{2}$O influx and little ${\rm CO}_{2}$ (0.03%). There is a strong destruction of ozone in the stratosphere catalysed by HOx compounds (whereas in the terrestrial case NOx and chlorine compounds are the main species responsible for that). The terrestrial profile is shown for reference (heavy solid line).

Figure 14: Case G: IR Darwin spectrum simulated for a humid atmosphere (1 bar ${\rm N}_{2}$, 0.1% ${\rm H}_{2}$O) with constant ${\rm H}_{2}$O influx and little ${\rm CO}_{2}$ (0.03%). The ${\rm O}_{3}$ line is barely detectable at present (R=25, left) and improved (R=100, right) Darwin resolution. Despite the presence of ${\rm CO}_{2}$ and ${\rm H}_{2}$O line, the risk to detect such case as a "false positive'' is marginal.

This catalytic destruction follows these three main cycles:

OH + O	$\longrightarrow$	H + ${\rm O}_{2}$
H + ${\rm O}_{3}$	$\longrightarrow$	OH + ${\rm O}_{2}$
O + O$_{\bf 3}$	$\longrightarrow$	2O$_{\bf 2}$
OH + ${\rm O}_{3}$	$\longrightarrow$	${\rm HO}_{2}$ + ${\rm O}_{2}$
${\rm HO}_{2}$ + O	$\longrightarrow$	OH + ${\rm O}_{2}$
O + O$_{\bf 3}$	$\longrightarrow$	2O$_{\bf 2}$
OH + ${\rm O}_{3}$	$\longrightarrow$	${\rm HO}_{2}$ + ${\rm O}_{2}$
${\rm HO}_{2}$ + ${\rm O}_{3}$	$\longrightarrow$	OH + 2 ${\rm O}_{2}$
2O$_{\bf 3}$	$\longrightarrow$	3O$_{\bf 2}$

An efficient production of O₂ in a humid atmosphere requires a very high rate of ${\rm H}_{2}$O photolysis driven by strong UV radiations in the water-rich upper atmosphere. H and HO_x radicals are then much more abundant and also chemically efficient in a wider range of altitudes. The ozone destruction is then amplified by the very same process that produces ${\rm O}_{2}$, even in the absence of the main species responsible for the ozone destruction on Earth: the NO_x (these radicals come from the photolysis of ${\rm N}_{2}$O which is a by-product of biological activity and therefore are not present in the abiotic cases we considered.) For Darwin nominal (R=25) and improved (R=100) resolutions, there is only a marginal signature of ${\rm O}_{3}$ in the IR spectrum (Fig. 14), despite the fact that lower ${\rm O}_{3}$ means less warming of the atmosphere, and an enhanced contrast of the absorbing band (Selsis 2000a). Although ${\rm CO}_{2}$ and ${\rm H}_{2}$O bands are present in this spectrum, we consider that, with planned Darwin resolution and sensitivity, the weakness of the ${\rm O}_{3}$ band makes extremely low the risk of identifying a humid atmosphere with constant ${\rm H}_{2}$O influx as a false positive case. Moreover, the necessity of matching, for the planet, the many ad hoc conditions quoted at the beginning of this paragraph makes this risk even more marginal (see discussions, Sect. 6.2.2).