EDP Sciences
Free Access
Issue
A&A
Volume 566, June 2014
Article Number A143
Number of page(s) 14
Section Planets and planetary systems
DOI https://doi.org/10.1051/0004-6361/201323085
Published online 27 June 2014

© ESO, 2014

1. Introduction

The presence of water vapor in the stratosphere of the outer planets, as established by ISO, has raised the question of the origin of external oxygen in these reducing environments. While the gross similarity of the H2O fluxes into the four giant planets (Feuchtgruber et al. 1997) might have been taken as evidence that micrometeorite ablation is the dominant source, recent observations, especially using the Herschel Space Observatory (Herschel hereafter), have revealed a different picture. These datasets outline the role of recent cometary impacts in delivering H2O, CO and CO2 to Jupiter and CO in Neptune and possibly Saturn and that of Enceladus’ activity in feeding Saturn’s upper atmosphere with water vapor (see Cavalié et al. 2013, and references therein).

Following the original detection by ISO (Coustenis et al. 1998), the presence of water vapor has been recently revived by measurements of the H2O vertical profile by both Cassini/CIRS (Cottini et al. 2012) and Herschel/PACS and Herschel/HIFI (Moreno et al. 2012) at Titan. These studies differed significantly in the amounts of H2O implied by typically a factor of 45 at 115 km. Based on photochemical modeling, Moreno et al. (2012) found that the modeled CO2 abundance at 100200 km is too small by a factor of ~10 compared to the observed value of 1020 ppb when the H2O influx is adjusted to match their water profile. Noting that the atmospheric lifetimes of CO2 and H2O are very different, Moreno et al. (2012) proposed that the discrepancy could be solved by invoking a variable input flux over timescales of tens to hundreds of years and tentatively favored Enceladus’ plume activity as the source of Titan’s external oxygen.

Most recently, Dobrijevic et al. (2014) presented a fully coupled oxygen-nitrogen-hydrocarbon model, in which a number of reactions had been updated or added since the previous models by Hörst et al. (2008) and Moreno et al. (2012); in particular, reactions between N- and O-bearing species were considered. They confirmed the essential conclusion of Moreno et al. (2012) in that the measured H2O profile is inconsistent with the CO2 abundance, although the disagreement was reduced to a factor of 4. Dobrijevic et al. (2014) found that reconciliation was possible if water abundances reported by Cottini et al. (2012) are correct instead; although in this situation and for an Enceladus source, their model tended to overpredict the thermospheric abundance of H2O when compared to the globally averaged upper limit determined by Cui et al. (2009). Dobrijevic et al. (2014) also find that the deposition altitude of the OH/H2O flux (750 km, which is representative of micrometeorite ablation, vs. the top of the atmosphere, which is characteristic of an Enceladus source) influences the flux required to reproduce the observed H2O and CO2 profiles and the abundance of secondary N-O and H-N-O species.

In this work, by means of a time-dependent photochemical model, we explore in more details the scenario of a variable oxygen source at Titan to see whether it is a plausible explanation to the “H2O/CO2 puzzle”. We consider both the H2O profiles derived from Cassini/CIRS (Cottini et al. 2012) and from Herschel (Moreno et al. 2012). In addition, we study a scenario when Titan might have suffered a cometary impact in the past by bringing oxygen species into its atmosphere.

2. Model description

The number density n at altitude z for every constituent i at time t is solved by means of the usual continuity equations in spherical geometry: (1)where Φi can be expressed as (2)The variable ni, Pi, and li are the number density, volumic production rate, and volumic specific loss rate, and r = R0 + z, where R0 = 2575 km and z runs from 34 to 1432 km with an altitude bin size of 1 km. The parameter Di is the molecular diffusion coefficient, T is temperature, Hi and H are the individual and atmospheric scale heights, K(z) is the eddy diffusion coefficient, and, αi is the thermal diffusion coefficient. The equations are solved for methane CH4, methyl radical CH3, acetylene C2H2, ethylene C2H4, ethane C2H6, methyl acetylene CH3C2H, propane C3H8, diacetylene C4H2, atomic hydrogen H, molecular hydrogen H2, carbon monoxide CO, carbon dioxide CO2, O(3P), formyl HCO, formaldehyde H2CO, hydroxyl OH, CH, C2, C4H, C3H5, C2H, 1CH2, 3CH2, C2H3, C2H5, , C4H3, O(1S), O(1D), CH3O, and CH3CO.

We use a fully implicit finite difference scheme (unconditionally stable) with a variable Δt time step to accomodate the large range of characteristic times (i.e., turbulent transport, molecular diffusion, and chemical times for all the species).

The model, which originally derives from Lara et al. (1996), has been updated in several ways. First we include new reaction rates for the hydrocarbons (see Table 1). Second, for the chemical network involving oxygen species, we consider two schemes: (i) the one from (Hörst et al. 2008, hereafter H08), which was also used by (Moreno et al. 2012, see Table 2); and (ii) a modified C-H-O chemical scheme, which results from common reactions in Dobrijevic et al. (2014) and in Hörst et al. (2008) that are updated with rate coefficients in Dobrijevic et al. (2014), and additional reactions from Dobrijevic et al. (2014) that only involve the hydrocarbons and oxygen species listed above. Specifically, this means that we ignore reactions coupling N and O chemistry. This is justified by the fact that we are primarily interested by the profiles of CO2 and H2O and not the abundances of secondary N-O-H species. In particular, the reaction OH + N(4S) in the reaction scheme coupling N and O species (which in the C-H-N-O chemistry by Dobrijevic et al. (2014) is important above 1000 km to produce NO) only represents 0.003% of the OH column integrated loss in the C-H-O chemical network for typical OH and N(4S) vertical profiles. Regarding water, the main additional loss term that involves nitrogen is H2O + N(2D), but this only accounts for 0.85% of the total water loss rate given typical profiles of H2O and N(2D). Reactions for this simplified chemical scheme (hereafter L14), with regard to Dobrijevic et al. (2014) are listed in Table 3.

Table 4

Steady-state models results for an OH and H2 flux at the top of the atmosphere.

Finally, compared to Lara et al. (1996), a more recent treatment of the UV transmission in the haze layer is considered. For this, we have adopted the results shown in Fig. 2 of Krasnopolsky (2009), which in fact do not noticeably differ from the approximation seen in Yung et al. (1984) as used in Lara et al. (1996) and in Moreno et al. (2012).

Here we retain the same treatment for the condensation processes, as in Lara et al. (1996), and adopt the eddy diffusion coefficient (K2) from Moreno et al. (2012), Following Hörst et al. (2008), the O(3P) flux is introduced in the model in a layer with a peak at 1100 km. The magnitude of the O(3P) flux normally drives the CO abundance. However, due to its extremely long lifetime (several 108 yr), reaching a chemical balance on CO needs a long integration time (e.g. Dobrijevic et al. 2014). Instead the CO mixing ratio is prescribed hereat its observed value, 5.1 × 10-5 (Gurwell 2004), at the model’s lower boundary; the abundance vertical profile is then computed in the model, and the O(3P) flux is then unimportant for determining the CO2 and H2O profiles. As detailed below, we investigate the sensitivity of the results to form (OH vs. H2O) and the deposition profile of the water influx.

Boundary conditions at 34 km are set as follows: for condensible species, the mixing ratio is the maximum value allowed by the saturation laws, which is zero supersaturation; for non-condensible species, either they are in local photochemical equilibrium and the number density is computed as the quotient of the production and specific loss, or they have a maximum flux through the lower boundary. At 1432 km, only H and H2 are allowed to escape according to the Jeans formulation, whereas the other species are in diffusive equilibrium (excluding OH/H2O in the case that they have an inward flux due to the Enceladus plume activity).

The thermal profile used for our computation is a combination of (i) the temperatures measured by Huygens/HASI (Fulchignoni et al. 2005) in the troposphere at altitudes between 0–140 km; (ii) the disk-averaged Cassini/CIRS stratospheric temperatures (Vinatier et al. 2010) at altitudes between 140–500 km; (iii) the Cassini/INMS retrieved temperatures (i.e. 155 K as average, de La Haye et al. (2007)) at altitudes between 1000–1500 km; and (iv) a decreasing temperature from 165 K to 155 K at altitudes between 500 and 1000 km.

Our study aims at reproducing (i) the H2O vertical profiles in Moreno et al. (2012) and Cottini et al. (2012) with both chemical schemes, for H08 and L14; and (ii) the CO2 stratospheric abundance from Cassini/CIRS data (de Kok et al. 2007).

3. OH versus H2O external source

Both Hörst et al. (2008) and (Moreno et al. 2012, who considered the H08 chemical scheme) concluded that the OH vs. H2O form of the water input is unimportant when fitting the stratospheric water abundance, since a balance is established between OH and H2O, due to the photolysis of water and reactions between OH and CH3 or OH and CH4 recycling water. They also found that fluxes required to reproduce a given H2O profile are independent on the precise deposition profile (i.e., deposition at the top of the atmosphere as appropriate or in a Chapman layer near 750 km). On the other hand, Dobrijevic et al. (2014) found large variations in the required H2O/OH flux depending on its H2O vs. OH form and on its altitude deposition. For example, Table 2 of Dobrijevic et al. (2014) shows that a given flux produces ~33% more H2O in Titan’s atmosphere for meteoritic ablation near 750 km (cases “IM1” and “IM4”), when it is deposited in the form of H2O compared to the case where it is deposited as OH. The difference becomes larger in the case of water deposition at the top of the atmosphere (cases “IE1” and “IE2”), where a OH flux (compared to H2O flux) that is twice as large is needed to produce the same amount of H2O.

We re-examined these issues with the new treatment of the UV transmission within the haze and the new chemical network (L14). For this, we computed steady-state solutions by fine-tuning the OH/H2O influx to match the available observations (HIFI+PACS in Moreno et al. (2012) and Cassini/CIRS by Cottini et al. (2012)). Table 4 summarizes the required fluxes to match the H2O determinations from Herschel and Cassini/CIRS by using the two sets of chemistry and water influx in the form of either OH or H2O. (Only cases of deposition at the top of the atmosphere are summarized in Table 4.)

Although we do find with our simplified L14 scheme values that are similar to Dobrijevic et al. (2014), Table 4 indicates that an influx in the form of H2O entering Titan’s atmosphere is more “efficient” at producing H2O in Titan’s atmosphere than an OH flux; the difference is only about 20% (vs. a factor ~2 in Dobrijevic et al. 2014). Moreover, for a given form of deposition (OH or H2O), we do not find any significant difference between the required fluxes as a function of deposition profile, as the associated Titan H2O profiles for a given flux and the two scenarios of deposition profiles are identical up to 750 km. In contrast, the profiles start to diverge above this altitude as seen in Figs. 12 and 13 of Moreno et al. (2012), so that measurements of the H2O mole fraction in the upper atmosphere could help constrain the Enceladus in contrast to micrometeoroid ablation origin of the external flux. We are unsure of the cause of the discrepancy with Dobrijevic et al. (2014), and we do not understand why their required fluxes are so dependent on the altitude deposition profile. Indeed, we estimated that the non-inclusion of the N-O coupling has a negligible effect of the fluxes required to match a given H2O profile above, and the latter authors do not explicitly show a case with the N-O chemistry turned off for comparison. Likely reasons of the discrepancy may be related to significantly different profiles of the C-H and C-H-N species profiles computed in (Dobrijevic et al. 2014, not shown therein) and ours.

4. Lifetimes

Moreno et al. (2012) could not simultaneously fit the stratospheric abundance of H2O measured with Herschel and of CO2 (de Kok et al. 2007) with the same OH and O(3P) flux. They proposed that the discrepancy could be solved by invoking a time-variable input flux. They based their argument on the different atmospheric lifetimes of H2O and CO2. This had been already found by Wilson & Atreya (2004), who reported chemical lifetimes of 4.1 and 697 yr at 300 km for H2O and CO2. Moreno et al. (2012) obtained similar numbers (9 yr and 450 yr) for the “column-integrated” lifetime, which is defined by dividing the column density by the vertically-integrated chemical loss including photolysis. For CO2, this lifetime was comparable to the vertical transport time down to the condensation level (360 yr). However, these approaches give either an estimate of the lifetime against chemical loss at some level or a global estimate of the atmospheric residence time of a species in the atmosphere, but they do not handle the fact that the time evolution of the atmospheric mixing ratios depends on both chemical and transport processes, which may show important variations with altitude.

To account for this, we first used our time-dependent model as described, to study the response of oxygen species to an abrupt change in the oxygen source rate. For this, we initialized the oxygen compounds to the steady state solution profiles obtained in the case of the OH Enceladus source (i.e, deposited at the top of the atmosphere) by considering the two variants of the oxygen chemistry (H08 and L14). The steady state OH fluxes required to match the H2O Herschel profile are given in Table 4, and an O(3P) flux of 1.6 × 106 cm-2 s-1 is used. Then, for each case, the oxygen sources are cut to zero and the oxygen species evolve with time. For each species, we define the altitude-dependent “effective lifetime” as the time after which the mixing ratio has decreased by a factor e at the considered altitude. This definition is clearly only approximate since the time evolution does not follow a simple exponential decay. Results for the H08 chemical network are shown in Fig. 1 for all oxygen species but CO (which has a very long lifetime at all levels). It has to be pointed out that the “effective lifetimes” for every species are approximately the same when using the H08 or the L14 chemical network.

For comparison, Fig. 2 shows the altitude-dependent lifetimes associated to the different processes considered in the model for some oxygen species (CO2, H2O, H2CO, O(3P) and OH): photolysis, gas-gas chemical reactions (for which the lifetime is defined at each altitude j as the minimum of , k that represents all of the reactions consuming the species i at altitude j), molecular diffusion, and turbulent transport. For H2O, the photolytic lifetime (which drives the overall chemical lifetime) increases from ~0.5 yr at the top of the atmosphere to ~10 yr at 200 km and further increases at lower levels. The ratio of the chemical lifetime of CO2 to that of H2O is a factor of 100 above 400 km. All these numbers are consistent with the above estimates of the “column-integrated” chemical lifetimes.

Nonetheless, the time evolution of the at a given level is more properly described by the effective lifetimes (Fig. 1). For H2O, it increases regularly from ~0.1 yr at the top to 10 yr at 200 km and about 100 yr at 80 km (at deeper levels, H2O is constrained to very small amounts by condensation, so the apparent “divergence” of the lifetime is not meaningful). For CO2, the effective lifetime increases from 20 yr at the top of the atmosphere to 400 yr at ~80 km before entering in the condensation region. The OH lifetime is very short in the upper atmosphere (>1000 km) but it tracks that of H2O from which it is photochemically produced below this altitude. Similarly, the lifetimes of O(3P) and HCO/H2CO are short below 850 and 450 km and progressively increase to follow that of CO2 below 700 and 400 km, respectively. For these four species, the long lifetimes in the lower atmosphere have, however, little significance because the involved amounts are very small. In addition to the altitude-dependent effective lifetime, it is useful to similarly define the column-averaged effective lifetime as the time after which the column density has decreased by a factor e. These column-average lifetimes are found to be 287 yr, 51 yr, 12 d, 10 d, 5 h, and 1 h for CO2, H2O, H2CO, HCO, OH, and O(3P), respectively. The most important result for our purpose is that the effective lifetimes for CO2 and H2O differ by less than a factor of 6, regardless of the photochemical scheme and the initial profile to which time-evolution is applied.

thumbnail Fig. 1

Effective lifetimes (see text for definition) as a function of altitude for oxygen species. These are calculated for OH and O(3P) input fluxes of 2.4 × 105 and 1.6 × 106 cm-2 s-1, respectively, and the H08 chemical network. The effective lifetime for CO2 for an enhanced input OH flux = 5.1 × 106 cm-2 s-1 (needed to match the CO2 profile) is also shown as a dashed black line.

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thumbnail Fig. 2

Lifetimes for different processes. Solid lines: photolytic lifetime Dotted lines: chemical (gas-gas) lifetime. Dashed lines: molecular diffusion timescale. (). The characteristic time for turbulent transport (H2/K) is also shown. This figure makes use of the H08 chemical scheme, where OH photolysis is not included, and H2CO is only lost via photodissociation.

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5. Evolution of the H2O and CO2 profiles under changes of the input flux

Running the time-dependent model shows that all species except CO, CO2, and H2O decrease to molar fractions <10-12 in less than 10 yr upon an abrupt cut-off of the oxygen input fluxes. While the shape of the CO2 profile is conserved as the CO2 abundance slowly declines with time, the H2O profile strongly evolves. As a consequence of the quick altitude-varying lifetime, the H2O depletion proceeds much more rapidly at upper levels, causing a local maximum (“kink”) of the H2O mixing ratio in the 125160 km altitude range to appear after ~10 yr. This behavior occurs for both the H08 and L14 chemical networks, and initial water profiles in agreement with either Herschel or Cassini/CIRS data. Figure 3 shows the evolution of the CO2 and H2O profiles for initial conditions that match the Sa profile in Moreno et al. (2012) and adopt the H08 chemistry.

thumbnail Fig. 3

Time-evolution of oxygen species 1, 10, 100, 300 and 1000 yr after the oxygen sources have been abruptly cut-off. Profiles are initialized at steady-state conditions for O(3P) and OH input fluxes at 1.6 × 106 and 2.4 × 105 cm-2 s-1, respectively, matching the H2O profile of Moreno et al. (2012). Solid lines refer to H2O, and dashed lines refer to CO2.

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thumbnail Fig. 4

H2O (solid lines) and CO2 (dashed lines) profiles in a time-dependent Enceladus source model, as compared to observations, making use of the H08 chemical scheme. Left panel: results aimed at fitting the H2O observed with Herschel. The profiles are initialized at their steady-state values for a OH flux of 5.1 × 106 cm-2 s-1 (black curves). The different curves correspond to evolution with four different combinations of τ and t0. The red circles show the H2O profile in the (τ = 30 yr, t0 = 96 yr) case calculated in presence of an additional loss of H2O to the haze (see text). Right panel: results aimed at fitting the H2O observed with Cassini/CIRS. The black curves correspond to the steady state profiles obtained with an OH flux of 5.1 × 106 cm-2 s-1. Evolution of these profiles for two different (τ,t0) combinations are shown, as well as the resulting H2O profile, when a loss to the haze is taken into account for the (τ = 30 yr, t0 = 55 yr) case (green dots). Upper limits on H2O thermospheric abundance by Cui et al. (2009) are also shown as arrows.

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5.1. Time-variable input fluxes

Builiding on this, we considered a simple scenario for the time evolution of the oxygen fluxes to test the hypothesis of a time-variable Enceladus source being responsible for the “inconsistent” H2O and CO2 abundances. Essentially, we assume that the input fluxes have been strong enough in the past to explain the observed CO2 and that they have decreased exponentially since some recent time. We describe the history of the OH flux as

  • for t< current epoch–t0: Φ(OH) = Φ0(OH);

  • for t> current epoch–t0: Φ(OH) = Φ0(OH) × exp(-(t/τ)),

where t is the time elapsed since the onset of the flux decline, which is assumed to have started t0 yr before the current epoch. The model thus has three free parameters: (i) t0, the number of years in the past when the input fluxes have started to decrease; (ii) Φ0(OH), the input flux before it started to decrease; and (iii) τ, the characteristic time of the flux decline. Since we are modeling an Enceladus source, we assume that the O(3P) flux follows the same time dependence and fix the O(3P)/OH flux ratio to a constant value.

In the first step, we fixed Φ0(OH) at the value required to match the observed CO2 mole fraction of 1.5 × 10-8 at 100200 km in a steady-state situation. This Φ0(OH) flux depends slightly on the photochemical network, being 5.1 × 106 cm-2 s-1 for H08 and 5.3 × 106 cm-2 s-1 for L14. These values are 16–20 times larger than the steady-state flux needed to match the H2O profile of Moreno et al. (2012) and 4–5.5 times larger than that required to match the H2O profile of Cottini et al. (2012). In the middle/upper atmosphere (say above 300 km), the lifetime of H2O is short, so that the H2O mole fraction reacts to the “instantaneous” flux. This essentially constrains the flux to have declined by the above factors, which implies t0/τ = 2.9 − 3.2 if the water targeted profile is Sa in Moreno et al. (2012) and t0/τ = 1.5 − 1.8 if the H2O abundance to be reproduced is from Cassini/CIRS data (Cottini et al. 2012). The value of τ (and hence t0) remains to be adjusted. However, the CO2 abundance, which reflects the input flux that is “smoothed” over ~300 yr, and the profile of H2O below 300–400 km, tend to provide contradictory constraints. Short values of τ and t0 are favored by CO2, while the steep H2O slope (i.e., the absence of a “kink” near 150 km) would rather point to long values of τ and t0. Figure 4 shows the profiles of H2O and CO2 for various (τ, t0) combinations aimed at reproducing:

In the first case (target H2O profile = Sa from Moreno et al. (2012)), the (τ = 30 yr, t0 = 96 yr) combination permits to reproduce a CO2 profile that closely agrees with its observed value, but the H2O profile shows a marked local maximum and an abundance that is too large below 250 km. Conversely, for (τ = 1000 yr, t0 = 3100 yr), the H2O profile is adequate, but CO2 is underabundant by a factor of 10. Intermediate sets of parameters, such as (τ = 100 yr, t0 = 300 yr) or (τ = 300 yr, t0 = 950 yr), produce unsatisfactory compromises with a poor fit for both species.

thumbnail Fig. 5

H2O (solid lines) and CO2 (dashed lines) profiles in a time-dependent Enceladus source model (H08 chemistry) compared to the observed profile of H2O from (i) left panel: Herschel (Sa profile from Moreno et al. (2012); and (ii) right panel: Cassini/CIRS (Cottini et al. 2012) . Two initial conditions with different and enhanced OH input fluxes (1.0 × 107 in black lines and 2.0 × 107 cm-2 s-1 in red lines) are considered. Evolution times are adjusted so that the H2O mole fraction above 300 km matches observations in the case of Herschel data and at 230 km in the case of Cassini/CIRS. The resulting (i.e., after t0 yr of evolution) H2O and CO2 profiles are plotted with blue and green lines for the initial profiles 1 and 2, respectively (see text for more details). Upper limits on H2O thermospheric abundance by Cui et al. (2009) are also shown as arrows.

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Table 5

Evolution time t0 required to match the Herschel or Cassini/CIRS H2O profiles for both chemical schemes (H08 or L14).

The same general conclusion can be seen in the right panel of Fig. 4, where the target H2O profile is now taken from Cottini et al. (2012). For (τ = 30 yr, t0 = 55 yr), the CO2 stratospheric value is close to the measurements, but the water profile sharply overestimates the H2O mixing ratio near 125 km. For (τ = 300 yr, t0 = 550 yr), H2O is brought into agreement with Cassini/CIRS results, but CO2 is considerably below observations.

As can be seen on the right panel of Fig. 4, the models tuned to match the H2O abundance somewhat overestimate the upper limits (2.8 × 10-6 up to 3.9 × 10-6 in the 1025–1151 km region) from INMS (Cui et al. 2009). A similar problem was encountered by Dobrijevic et al. (2014) for an Enceladus source. We note, however, that Cui et al. (2009) report actual detections of H2O on several inbound spectr with H2O mixing ratios in the range (0.4 − 3.4) × 10-5 with a mean value of 1.2 × 10-5. These mixing ratios would then be consistent with model predictions, so the resolution of this issue must await a clarification of the constraints from INMS. At any rate, we note that the H2O thermospheric abundance is sensitive to the precise OH vs. H2O and vertical deposition profile and might also be affected by reactions (not considered here) that couple the O and N chemistry. In contrast, these effects do not affect the H2O and CO2 stratospheric abundances.

The above models assumed an initial Φ0(OH) equal to the steady-state value needed to fit the CO2 abundance. We explored alternative models with a higher value for Φ0(OH). Specifically with the H08 chemical scheme, we considered two cases with initial fluxes of Φ0(OH) = 1.0 × 107 and 2.0 × 107 cm-2 s-1, respectively, that then declined with a time constant τ = 100 yr. The evolution time t0 needed to match the H2O Herschel abundance above 300 km altitude is 400 yr and 475 yr for the two cases, respectively. As shown in Fig. 5 (left panel), this scenario maintains larger CO2 values compared to the τ = 100 yr case shown in Fig. 4 (which had t0 = 300 yr and Φ0(OH) = 5.1 × 106 cm-2 s-1). The Φ0(OH) = 2.0 × 107 cm-2 s-1 case yields CO2 abundances that are essentially consistent with the observed ~1.5 × 10-8 value at 100200 km. However, the corresponding H2O profile still shows some “kink” below 200 km. Direct comparison of synthetic spectra with data from Moreno et al. (2012) indicates that it still overpredicts the PACS lines (which probe the 90150 km range) by ~50% while the H2O model correctly fits the HIFI observations.

On the other hand, the same approach provides a satisfactory match to the Cassini/CIRS H2O measurements at 115 and 230 km. Continuing with the same chemical scheme, initial Φ0(OH) fluxes, and τ = 100 yr, we find that the Cottini et al. (2012) H2O profile can be reproduced with t0 = 290 yr for Φ0(OH) = 1.0 × 107 cm-2s-1 and t0 = 360 yr for Φ0(OH) = 2.0 × 107 cm-2 s-1 (see Fig. 5, right panel). In both cases, the resulting CO2 stratospheric profile agrees well with observations.

Table 6

Models with H2O loss to the haze.

We performed the same exercise by using the alternate chemical network (L14). Keeping the characteristic time of the flux decline at τ = 100 years, Table 5 summarizes the required values of the evolution time t0 for the different cases. Similar behaviors are obtained with the two sets of chemistry. We conclude that this family of solutions is not satisfactory if the targeted water profile is the one retrieved from Herschel data, whereas a more successful fit of Cassini/CIRS water and carbon dioxide is obtained by assuming considerably OH higher fluxes some centuries ago.

5.2. Loss to the haze

Moreno et al. (2012) speculated that the H2O profile could be affected by an additional non-gaseous chemical loss, which can be a loss to the haze, as it seems to the case for HCN (McKay 1996; Lara et al. 1999; Vinatier et al. 2007). Moreno et al. (2012) found that adding a loss term in the form of L = k[H2O]1.75 cm-3 s-1 restricted to altitudes above 220 km would bring the model to the calculated H2O profile in agreement with the Herschel observations. However, they discarded this option because it does not help reconcile in itself the H2O and CO2 profiles in the steady-state scenario considered in Moreno et al. (2012).

Nonetheless, in this time-dependent scenario, a loss to the haze potentially reduces the H2O mole fraction in the lower stratosphere, as eliminates the H2O “kink” near 150 km and recoves an H2O profile in light with the Herschel observations. To illustrate this, here we come back to the short evolution case of Fig. 4 (left panel) (having Φ0(OH) = 5.1 × 106 cm-2 s-1, τ = 30 yr, t0 = 96 yr), add a loss term of H2O to the haze in the form L = k[H2O]β cm-3 s-1 at z> 300 km, which decreases with a 100 km scale height below 300 km. In a nominal case, we adopt β = 1.75 by analogy to results of HCN (Lara et al. 1999), but solutions with different forms are possible. The red circles in the left panel of Fig. 4 show the resulting H2O profile obtained with k = 2 × 10-14. This profile fully agrees with the empirical Sa profile of Moreno et al. (2012). Alternate functional dependences of L are possible; for example, L = k[H2O]2 cm-3 s-1 with k′ = 5 × 10-16 at z> 300 km and similarly decreases below this altitude produces an identical fit. In these models, the total H2O loss to the haze is ~6 × 105 cm-2 s-1.

For completeness, this study has been extended to the case of the H2O Cassini/CIRS profile and also considers the two chemical schemes. Table 6 shows results of the (k, β) parameters and the total H2O loss to the haze for the different cases.

As a conclusion, including a loss to the haze term in combination on with a time variable flux brings the modeled H2O profile in agreement with available observations (Cottini et al. 2012; Moreno et al. 2012) for both of the chemical schemes used here, which maintains CO2 stratospheric profiles in broad agreement with Cassini/CIRS data (de Kok et al. 2007).

6. Comet impact scenario

In this section, we investigate another alternative for the high CO2/H2O ratio in Titan’s atmosphere: namely, the CO2 that has built up from a relatively recent cometary impact. As shown from the Shoemaker-Levy 9 impacts on Jupiter in 1994, cometary impacts can deliver oxygen compounds to planets. In the Jupiter/SL9 case, shock chemistry at plume re-entry has produced CO and H2O near the 0.1 mbar level (Lellouch et al. 1997, 2002), and both species have since then slowly diffused vertically and horizontally (see Moreno et al. 2003; Cavalié et al. 2013, and references therein). Furthermore, while CO is chemically stable, any newly injected H2O is progressively photolysed to OH and converted to CO2 by reaction with CO. The gas CO2 was observed in 1997 in Jupiter (Lellouch et al. 2002) with a north-south assymetry characteristic of a SL9-derived product (Lellouch et al. 2002). Based on coupled photochemical-horizontal transport modeling, the amount of carbon dioxide and latitudinal distribution could be explained if the material produced by the impacts has a H2O/CO ratio of about 0.11 per volume. In Jupiter’s atmosphere, the model further predicted that CO2 produced in this manner would build up for about 50 yr after the impacts and then begin to decline due to its own photolysis. Comet impacts are also invoked to explain the abundance of CO in Neptune’s stratosphere (Lellouch et al. 2005; Hesman et al. 2007) and possibly Saturn’s (Cavalié et al. 2010).

thumbnail Fig. 6

Evolution of oxygen species after a cometary impact. Initial conditions correspond to deposition of CO and H2O with uniform mixing ratios (with qCO = 10 qH2O) above 300 km. Left panel: models suited to the Herschel H2O profile (Sa from Moreno et al. (2012)). Dashed lines: “small comet” (initial qCO = 6 × 10-5), evolution time tevol = 300 yr. Solid lines: “large comet” (initial qCO = 6 × 10-4), evolution time tevol = 700 yr. The red circles and black squares show the H2O and CO2 for the combination of the “large comet” case with a steady OH influx of 2.4 × 105 cm-2 s-1. Right panel: models suited to the Cassini/CIRS H2O profile Cottini et al. (2012). Dashed lines: “smaller comet” (initial qCO = 3 × 10-5), evolution time tevol = 225 yr. Solid lines: “large comet” (initial qCO = 6 × 10-4), evolution time tevol = 700 yr. The red circles and black squares show the H2O and CO2 for the combination of the “large comet” case with a steady OH influx of 9.0 × 105 cm-2 s-1. Upper limits on H2O thermospheric abundance by Cui et al. (2009) are also shown as arrows.

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We first examine the scenario for Titan in terms of the involved amounts. The CO2 column density in Titan’s atmosphere is 3.6 × 1016 cm-2 which corresponds to 3.0 × 1034 molecules referred to the surface. Assuming full conversion of H2O to CO2 and using an initial H2O/CO ratio of 0.1, this implies that the hypothetical comet delivered 3.0 × 1034 H2O and 3.0 × 1035 CO molecules (i.e, a CO mass of 1.4 × 1013 g). Converting this CO mass into a comet size requires an assumption of the “CO yield” and the comet density. We use a 50% yield (Lellouch et al. 1997, 2005) and a 0.5 g cm-3 mass density. This gives a minimum D = 0.475 km comet diameter.

We then consider the time evolution of a “pure” cometary case, by first considering the constraints from the H2O Herschel profile. The CO and H2O mole fractions are initialized as qCO and qH2O, which are taken as uniform above 300 km (0.1 mbar) and zero below this altitude. These values are considered as constant over the Titan globe. Thus the model is not initialized at comet impact, but a few years after when the species have been mixed horizontally and vertically above the 300 km range (q = qCO). We impose qCO = 10 × qH2O, and these values are adjusted until the CO2 mole fraction matches the observations after some evolution time tevol. Figure 6 (left panel) shows two cases (both of which consider the H08 chemical network): (1) qCO = 6 × 10-5, tevol = 300 yr; and (2) qCO = 6 × 10-4, tevol = 700 yr. These two cases correspond to the deposition of 1.2 × 1036 and 1.2 × 1037 CO molecules implying a cometary diameter of 0.7 and 1.5 km (“small” and “large”), respectively, under the above assumptions on density and CO yield. Both cases produce roughly the same amount of CO2; in contrast, a significantly larger amount of H2O is present in the first case, although this amount of water is importantly below the Herschel observations in both cases. Case (1) represents the maximum amount of cometary H2O that can be accomodated by the observed Herschel H2O profile. This implies that the comet impact occured at least 300 yr ago with a minimum comet diameter of 700 m. Older impacts are possible but require larger impactor sizes to maintain the same amount of CO2.

The right panel of Fig. 6 shows similar models but are tailored to the Cassini/CIRS H2O profile. The “large” comet case is unchanged, but the “small” comet case has values of qCO = 3 × 10-5, tevol = 225 yr. Indeed, the larger stratospheric abundance in the Cassini/CIRS H2O profile can accomodate a larger residual cometary H2O than the Herschel profile. This can be achieved by invoking a smaller and more recent impact (leading to the same CO2 amount but a larger H2O/CO2 ratio after evolution). As it is clear in the right panel of Fig. 6, this case is close to the maximum value of cometary H2O that can be tolerated by the observed Cassini/CIRS H2O profile. This means that if the Cassini/CIRS H2O profile is valid, the impact age could be as young as 225 years with the minimum size of 550 m. Again, older and larger impacts are possible.

We can also combine one of the above models with steady-state production of the oxygen species. This scenario thus depicts the current abundance of oxygen species as a result from the combination of a steady (Enceladus or micrometeorite) source and the evolution of a cometary “spike”. The steady source is primarily responsible for the H2O abundance, while CO2 is mostly the result of the comet impact. The dotted lines in Fig. 6 show the combination of the “large comet” above case with an Enceladus source (with a steady OH source rate of 2.4 × 105 cm-2 s-1 in the left panel and 9.0 × 105 cm-2 s-1 in the right panel). The resulting H2O profiles after 700 yr evolution agree with Herschel and Cassini/CIRS observations, respectively, and the CO2 profile is also fit.

The use of the alternate (L14) oxygen chemical scheme does not noticeably influence the results above. Matching the observations for the same model assumptions in terms of comet size and evolution time only requires a slight (10%) increase of the ΦOH that is provided by the steady Enceladus source. This is to be expected from Table 4, which shows the L14 oxygen chemical scheme to be slightly less efficient in producing atmospheric water.

While these models “technically’ work, their main difficulty is in the plausibility of a recent impact at Titan. Zahnle et al. (2003) find that the number of impacts on Jupiter by 1.5 km or larger ecliptic comets is typically 0.005 per year. They further provide probabilities for ecliptic comet impacts relative to Jupiter for all outer planets and satellites. For Titan, this relative probability is given as 5.4 × 10-5, which means that Titan is hit by a D> 1.5 km comet every ~4 million years on average. The size distribution of the cumulative impact rate is not very steep (slope parameter b = 1 − 1.7 in this size range, according to Zahnle et al. 2003), which means that the occurrence of a 0.5 km comet impact at Titan is only 36 times larger. We are still left with typical impact times of ~1 million years, which is probably fatal for this scenario.

7. Conclusions

We have explored Titan oxygen photochemistry by using a time-variable photochemical model and considering two variants for the oxygen chemical schemes. We find that the effective lifetime of H2O in Titan’s atmosphere exceeds 10 yr below 200 km, which is only a factor of six shorter than that of CO2 when the column densities are averaged. As a consequence, solving the inconsistency between the OH/H2O fluxes required matching the observed H2O and CO2 amounts, which is not straightforward and depends on the magnitude of the flux discrepancy. We find that if the Cottini et al. (2012) measurements are representative of Titan’s true H2O profile, the factor about five in the discrepancy in flux can be solved by invoking a decrease by a factor of ten in the OH/H2O flux (i.e., of Enceladus’ plume activity) over the last ~300 years. While the past activity of Enceladus is unconstrained, the fact that active plumes are currently not emitted along entire tiger stripes fractures and that thermal anomalies are not limited to fractures leaves open the possibility of a more extended and intense activity. If on the other hand, Titan’s water is even less abundant by about another factor of four as found by Moreno et al. (2012), we find that the time-dependent flux scenario is not in itself able to solve the problem and that another loss term for H2O, such as a loss to the haze, has to be invoked.

Acknowledgments

This research has been supported by the Spanish Ministerio de Ciencia e Innovación under contract AyA 2009-08011 and Ministerio de Economía y Competitividad under contract AyA 2012-32237. We thank Ralph D. Lorenz for suggesting the comet impact scenario to us.

References

Online material

Table 1

Hydrocarbon reactions.

Table 2

Hörst et al. (2008) C-H-O reactions.

Table 3

Simplified set of C-H-O reactions derived from Dobrijevic et al. (2014, see text).

All Tables

Table 4

Steady-state models results for an OH and H2 flux at the top of the atmosphere.

Table 5

Evolution time t0 required to match the Herschel or Cassini/CIRS H2O profiles for both chemical schemes (H08 or L14).

Table 6

Models with H2O loss to the haze.

Table 1

Hydrocarbon reactions.

Table 3

Simplified set of C-H-O reactions derived from Dobrijevic et al. (2014, see text).

All Figures

thumbnail Fig. 1

Effective lifetimes (see text for definition) as a function of altitude for oxygen species. These are calculated for OH and O(3P) input fluxes of 2.4 × 105 and 1.6 × 106 cm-2 s-1, respectively, and the H08 chemical network. The effective lifetime for CO2 for an enhanced input OH flux = 5.1 × 106 cm-2 s-1 (needed to match the CO2 profile) is also shown as a dashed black line.

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In the text
thumbnail Fig. 2

Lifetimes for different processes. Solid lines: photolytic lifetime Dotted lines: chemical (gas-gas) lifetime. Dashed lines: molecular diffusion timescale. (). The characteristic time for turbulent transport (H2/K) is also shown. This figure makes use of the H08 chemical scheme, where OH photolysis is not included, and H2CO is only lost via photodissociation.

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In the text
thumbnail Fig. 3

Time-evolution of oxygen species 1, 10, 100, 300 and 1000 yr after the oxygen sources have been abruptly cut-off. Profiles are initialized at steady-state conditions for O(3P) and OH input fluxes at 1.6 × 106 and 2.4 × 105 cm-2 s-1, respectively, matching the H2O profile of Moreno et al. (2012). Solid lines refer to H2O, and dashed lines refer to CO2.

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In the text
thumbnail Fig. 4

H2O (solid lines) and CO2 (dashed lines) profiles in a time-dependent Enceladus source model, as compared to observations, making use of the H08 chemical scheme. Left panel: results aimed at fitting the H2O observed with Herschel. The profiles are initialized at their steady-state values for a OH flux of 5.1 × 106 cm-2 s-1 (black curves). The different curves correspond to evolution with four different combinations of τ and t0. The red circles show the H2O profile in the (τ = 30 yr, t0 = 96 yr) case calculated in presence of an additional loss of H2O to the haze (see text). Right panel: results aimed at fitting the H2O observed with Cassini/CIRS. The black curves correspond to the steady state profiles obtained with an OH flux of 5.1 × 106 cm-2 s-1. Evolution of these profiles for two different (τ,t0) combinations are shown, as well as the resulting H2O profile, when a loss to the haze is taken into account for the (τ = 30 yr, t0 = 55 yr) case (green dots). Upper limits on H2O thermospheric abundance by Cui et al. (2009) are also shown as arrows.

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In the text
thumbnail Fig. 5

H2O (solid lines) and CO2 (dashed lines) profiles in a time-dependent Enceladus source model (H08 chemistry) compared to the observed profile of H2O from (i) left panel: Herschel (Sa profile from Moreno et al. (2012); and (ii) right panel: Cassini/CIRS (Cottini et al. 2012) . Two initial conditions with different and enhanced OH input fluxes (1.0 × 107 in black lines and 2.0 × 107 cm-2 s-1 in red lines) are considered. Evolution times are adjusted so that the H2O mole fraction above 300 km matches observations in the case of Herschel data and at 230 km in the case of Cassini/CIRS. The resulting (i.e., after t0 yr of evolution) H2O and CO2 profiles are plotted with blue and green lines for the initial profiles 1 and 2, respectively (see text for more details). Upper limits on H2O thermospheric abundance by Cui et al. (2009) are also shown as arrows.

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In the text
thumbnail Fig. 6

Evolution of oxygen species after a cometary impact. Initial conditions correspond to deposition of CO and H2O with uniform mixing ratios (with qCO = 10 qH2O) above 300 km. Left panel: models suited to the Herschel H2O profile (Sa from Moreno et al. (2012)). Dashed lines: “small comet” (initial qCO = 6 × 10-5), evolution time tevol = 300 yr. Solid lines: “large comet” (initial qCO = 6 × 10-4), evolution time tevol = 700 yr. The red circles and black squares show the H2O and CO2 for the combination of the “large comet” case with a steady OH influx of 2.4 × 105 cm-2 s-1. Right panel: models suited to the Cassini/CIRS H2O profile Cottini et al. (2012). Dashed lines: “smaller comet” (initial qCO = 3 × 10-5), evolution time tevol = 225 yr. Solid lines: “large comet” (initial qCO = 6 × 10-4), evolution time tevol = 700 yr. The red circles and black squares show the H2O and CO2 for the combination of the “large comet” case with a steady OH influx of 9.0 × 105 cm-2 s-1. Upper limits on H2O thermospheric abundance by Cui et al. (2009) are also shown as arrows.

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In the text

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