H Tran

M Turbet

P Chelin

X Landsheere

Measurements and modeling of absorption by CO 2 + H 2 O mixtures in the spectral region beyond the CO 2 ν 3 -band head

In this work, we measured the absorption by CO 2 + H 2 O mixtures from 2400 to 2600 cm -1 which corresponds to the spectral region beyond the ν 3 band head of CO 2 . Transmission spectra of CO 2 mixed with water vapor were recorded with a high-resolution Fourier-transform spectrometer for various pressure, temperature and concentration conditions. The continuum absorption by CO 2 due to the presence of water vapor was determined by subtracting from measured spectra the contribution of local lines of both species, that of the continuum of pure CO 2 as well as of the self-and CO 2 -continua of water vapor induced by the H 2 O-H 2 O and H 2 O-CO 2 interactions. The obtained results are in very good agreement with the unique previous measurement (in a narrower spectral range). They confirm that the H 2 O-continuum of CO 2 is significantly larger than that observed for pure CO 2 . This continuum thus must be taken into account in radiative transfer calculations for media involving CO 2 + H 2 O mixture. An empirical model, using sub-Lorentzian line shapes based on some temperature-dependent correction factors χ is proposed which enables an accurate description of the experimental results.

Introduction

Properly modeling the absorption spectrum of CO 2 + H 2 O mixtures under various temperature and pressure conditions as well as for different gas concentrations is of great importance for planetary sciences. For instance, this is needed to explain the effect of CO 2 on the water vapor runaway greenhouse limit for Earth and other planets [START_REF] Goldblatt | Low simulated radiation limit for runaway greenhouse climates[END_REF][START_REF] Popp | Transition to a moist greenhouse with CO 2 and solar forcing[END_REF][START_REF] Ramirez | Can increased atmospheric CO 2 levels trigger a runaway greenhouse[END_REF][START_REF] Turbet | The habitability of Proxima Centauri b II. Possible climates and observability[END_REF], a crucial point to understand why Venus and Earth had different fates. This also contributes to understand the future of Earth under the brightening Sun and more generally the habitability of extrasolar planets. For instance, water-rich extrasolar planets may lack the capability to regulate atmospheric CO 2 , potentially leading to dense CO 2 H 2 O atmospheres [START_REF] Wordsworth | Water loss from terrestrial planets with CO 2 -rich atmospheres[END_REF][START_REF] Kitzmann | The unstable CO 2 feedback cycle on ocean planets[END_REF][START_REF] Marounina | Constraining the habitable zone boundaries for water world exoplanets[END_REF][START_REF] Kite | Habitability of exoplanet water worlds[END_REF]. Following Ref. [START_REF] Haberle | The Early Mars climate system[END_REF], extreme events on early Mars could explain the geology of Mars (e.g. dry river beds and lakes) and mineralogy (e.g. clays). In particular, it has been proposed that meteoritic impact-generated steam atmosphere (made of large amounts of CO 2 and H 2 O) could have induced episodic precipitations responsible for the formation of the Martian valley networks [START_REF] Segura | An impact-induced, stable, runaway climate on Mars[END_REF][START_REF] Segura | Modeling the environmental effects of moderate-sized impacts on Mars[END_REF][START_REF] Segura | Environmental effects of large impacts on Mars[END_REF]Turbet et al., 2017). In this case, it is obvious that an accurate knowledge of the absorption spectrum of CO 2 + H 2 O is essential. Such knowledge is ⁎ Corresponding author.

Email address: ha.tran@lmd.jussieu.fr (H. Tran) also crucial to accurately model the evolution and observability of magma ocean planets, e.g. telluric planets that have surface temperatures high enough for their mantle to be in a liquid state, and that are expected to have outgassed large amounts of volatiles dominated by H 2 O and CO 2 [START_REF] Abe | Atmosphere and formation of a hot proto-ocean on Earth[END_REF][START_REF] Elkins-Tanton | Linked magma ocean solidification and atmospheric growth for Earth and Mars[END_REF][START_REF] Hamano | Emergence of two types of terrestrial planet on solidification of magma ocean[END_REF][START_REF] Lebrun | Thermal evolution of an early magma ocean in interaction with the atmosphere[END_REF][START_REF] Lupu | The atmospheres of Earth-like planets after giant impact events[END_REF][START_REF] Marcq | A simple 1-D radiative-convective atmospheric model designed for integration into coupled models of magma ocean planets[END_REF][START_REF] Marcq | Thermal radiation of magma ocean planets using a 1-D radiative-convective model of H 2 O-CO 2 atmospheres[END_REF], assuming mantles relatively oxidizing as on present-day Earth and Venus. Modeling them properly serves to understand the early stage of the evolution of the Solar System rocky planets, as well as to anticipate and prepare future observations of young rocky extrasolar planets, or planets that recently suffered from a collision with a giant impactor.

Despite these potential applications for planetary-atmospheres studies, practically all studies devoted to spectra of CO 2 + H 2 O mixtures are limited to spectroscopic parameters of isolated lines or local absorption. In fact, the infrared absorption spectrum of a CO 2 + H 2 O mixture contains two different contributions. The first, called local absorption, is due to absorption in the center and near wings of the ro-vibrational lines of the monomer of each species. The second contribution is due to absorption by the stable and metastable dimers, to absorption induced by collisions and to absorption in the far wings of monomers lines. This contribution is often called "continuum absorption" in spectroscopy because of its smooth and slowly varying behavior with wavenumber [START_REF] Hartmann | Collisional effects on molecular spectra[END_REF]. For local absorption by the monomers, half-width at half-maximum (HWHM) of several H 2 O lines broadened by CO 2 were measured and/or calculated in various studies [e.g. [START_REF] Brown | CO 2 -broadened water in the pure rotation and ν 2 fundamental regions[END_REF][START_REF] Gamache | A spectral line list for water isotopologues in the 1100-4100 cm -1 region for application to CO 2 -rich planetary atmospheres[END_REF][START_REF] Lu | CO 2 pressure shift and broadening of water lines near 790 nm[END_REF][START_REF] Poddar | Measurement and analysis of rotational lines in the (2ν 1 +ν 2 +ν 3 ) overtone band of H 2 O perturbed by CO 2 using near infrared diode laser spectroscopy[END_REF][START_REF] Sagawa | Pressure broadening coefficients of H 2 O induced by CO 2 for Venus atmosphere[END_REF]] while H 2 O-broadening coefficient of CO 2 lines were measured in [START_REF] Delahaye | Broadening of CO 2 lines in the 4.3 µm region by H 2 O[END_REF]; [START_REF] Sung | Fourier transform infrared spectroscopy measurements of H 2 O-broadened half-widths of CO 2 at 4.3 µm[END_REF]. Local absorption by the monomers can then be computed using these broadening coefficients together with other spectroscopic line parameters such as the line positions and integrated intensities, which are provided in various spectroscopic databases [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF][START_REF] Jacquinet-Husson | The 2015 edition of the GEISA spectroscopic database[END_REF][START_REF] Rothman | HITEMP, the high-temperature molecular spectroscopic database[END_REF]. For continuum absorption, while several studies were devoted to the continua of pure H 2 O (or CO 2 ) as well as of H 2 O (or CO 2 ) in air [see [START_REF] Baranov | The continuum absorption in H2O+N2 mixutres in the 2000-3250 cm -1 spectral region at temperatures from 326 to[END_REF]; [START_REF] Baranov | Water-vapor continuum absorption in the 800-1250 cm-1 spectral region at temperatures from 311 to[END_REF]; [START_REF] Clough | Line shape and the water vapor continuum[END_REF]; [START_REF] Hartmann | Measurements and calculations of CO 2 room-temperature high-pressure spectra in the 4.3 µm region[END_REF]; [START_REF] Hartmann | Molecular dynamics simulations for CO 2 absorption spectra. I. Line broadening and the far wing of the ν 3 infrared band[END_REF][START_REF] Hartmann | The infrared continuum of pure water vapor: calculations and high-temperature measurements[END_REF]; [START_REF] Hartmann | Measurements of pure CO 2 absorption beyond the ν 3 bandhead at high temperature[END_REF]; [START_REF] Mlawer | Recent developments in the water vapor continuum observations and the CKD continuum model[END_REF]; [START_REF] Mondelain | Temperature dependence of the water vapor self-continuum by cavity ring-down spectroscopy in the 1.6 µm transparency window[END_REF]; [START_REF] Perrin | Temperature-dependent measurements and modeling of absorption by CO 2 -N 2 mixtures in the far line-wings of the 4.3 µm CO 2 band[END_REF]; [START_REF] Tran | Measurements and modelling of high pressure pure CO 2 spectra from 750 to 8500 cm-1. I-central and wing regions of the allowed vibrational bands[END_REF][START_REF] Tretyakov | Water dimer rotationally resolved millimeter-wave spectrum observation at room temperature[END_REF] and [START_REF] Mlawer | Development and recent evaluation of the MT_CKD model of continuum absorption[END_REF], for instance], to the best of our knowledge, Ref. [START_REF] Baranov | On the significant enhancement of the continuum-collision induced absorption in H 2 O+CO 2 mixtures[END_REF] is the unique study dedicated to the measurement of the continuum absorption by CO 2 + H 2 O mixtures. Using a Fourier-transform spectrometer and a multi-path cell, Y. I. Baranov [START_REF] Baranov | On the significant enhancement of the continuum-collision induced absorption in H 2 O+CO 2 mixtures[END_REF] measured transmission spectra of CO 2 + H 2 O mixtures for various pressure, temperature and concentration conditions in the infrared. He established that at about 1100 cm -1 , the continuum absorption of H 2 O in CO 2 is nearly twenty times larger than that of H 2 O in N 2 . This observation seems to be consistent with the theoretical results of Ma and Tipping [START_REF] Ma | A far wing line shape theory and its application to the foreign-broadened water continuum absorption[END_REF] where continuum absorption due to the far wings of H 2 O lines broadened by CO 2 and N 2 were calculated at room temperature between 0 and 10,000 cm -1 . In Ref. [START_REF] Baranov | On the significant enhancement of the continuum-collision induced absorption in H 2 O+CO 2 mixtures[END_REF], it was also observed, for a limited spectral range in the far wing of the CO 2 ν 3 band (from 2500 to about 2575 cm -1 ) that the absorption of CO 2 in H 2 O is about one order of magnitude stronger than that of pure carbon dioxide. These results show that the CO 2 + H 2 O continuum must be taken into account in the radiative transfer models for the various applications mentioned previously. Since continuum absorption strongly depends on the considered wavelength and absorption by CO 2 in H 2 O cannot be extrapolated from that of pure CO 2 , a much larger spectral range for the CO 2 ν 3 band wing is thus investigated in this work. The large spectral range considered also enables the development of an empirical model for the H 2 O-continuum absorption of CO 2 in the ν 3 band wing which could be easily used for planetary atmospheres applications.

In this paper, we first present an experimental study of the continuum absorption by CO 2 due to interaction with H 2 O in a region beyond the CO 2 ν 3 band, from 2400 to 2600 cm -1 , much broader than that investigated in Ref. [START_REF] Baranov | On the significant enhancement of the continuum-collision induced absorption in H 2 O+CO 2 mixtures[END_REF]. For this, we used a high-resolution Fourier-transform spectrometer and a White-type cell which can be heated to record about twenty CO 2 + H 2 O spectra for various pressure, temperature and concentration conditions. The continuum absorption by CO 2 due to the presence of water vapor was then determined by subtracting from measured spectra the contribution of local lines of both species, that of the continuum of pure CO 2 as well as of the self-and CO 2 -continua of H 2 O. The obtained results are then compared with the previous measurements of Ref. [START_REF] Baranov | On the significant enhancement of the continuum-collision induced absorption in H 2 O+CO 2 mixtures[END_REF]. In a second step, an empirical model is built in order to represent these experimentally determined values. It is based on a set of χ-factors correcting the Lorentzian shape in the wings of the H 2 O-broadened absorption lines of CO 2 . This paper is organized as follows: the measurement procedure and data analysis are described in Section 2, the obtained results and the empirical model are presented and discussed in Section 3 while the main conclusions are drawn in Section 4.

Measurements procedure and data analysis

The high-resolution Fourier-transform spectrometer at LISA (Bruker IFS 120 HR) was used to record all spectra. The spectrometer was configured with a globar as the broad-band light source, a KBr beam splitter and an InSb detector. The unapodized spectral resolution of 0.1 cm -1 , corresponding to a maximum optical path difference of 9 cm, was used for all measured spectra. The diameter of the FTS iris aperture was set to 2 mm. A White-type absorption cell, made of Pyrex glass and equipped with wedged CaF 2 windows was connected to the FTS with a dedicated optical interface inside the sample chamber of the FTS. Its base length is 0.20 m and, for the experiments described here, an optical path of 7.20 m was used. This cell can be heated to temperatures up to 100 °C with a variation of 0.5 °C along the cell, as measured with a type-K thermocouple ( ± 1.5 °C). In order to avoid condensation and to be able to work with significant H 2 O pressures, the cell and the entire gas-handling system (including the pressure gauges) were enclosed inside a thermally insulated Plexiglas box. The temperature inside the box is regulated by an air heating system at a temperature of about 60 °C. The gas pressure was measured using three capacitive pressure transducers with 100 and 1000 Torr (1 Torr = 1.333 mbar) full scales, with a stated accuracy of ± 0.12%. The spectral coverage from 1000 to 4500 cm -1 was recorded for all measurements. The experiments were carried out as follows: Firstly, the temperature in the cell and that in the box were set to the desired values. Then when these temperatures were stabilized (after about 1 h for the box and 5 hours for the cell), a spectrum was first recorded with the empty cell to provide the 100% transmission. The cell was then filled with about 760 Torr of CO 2 and a pure CO 2 spectrum was recorded. After being pumped out again, the cell was filled with water vapor, purified by several distillations, at the desired pressure (varying from 40 to 110 Torr). Then, CO 2 was introduced until the total pressure reaches a given value (from 380 to 760 Torr). Once the sample was well mixed, a spectrum was recorded using an averaging of 200 scans providing a signal-to-noise ratio of about 500 (RMS) for a recording duration of 16 minutes. The temperature and pressure in the cell were simultaneously recorded every 5 s. This showed that the temperature and pressure variations during the recording of a spectrum remained lower than 0.2 K and 0.5 Torr, respectively. The pressure and temperature conditions for all measurements are summarized in Table 1. Transmission spectra were obtained by dividing the spectra recorded with the gas sample by that obtained with the empty cell. The total absorption coefficient (i.e. α in cm -1 ) at wavenumber σ (cm -1 ) of a CO 2 H 2 O mixture of temperature T (in Kelvin), total density ρ tot (in amagat) and mole fractions xCO 2 and xH 2O can be written as:

where denotes the absorption due to local lines of the monomer X whose extensions are limited to ± Δσ X around the line center and is the continuum absorption due to species X interacting with species Y.

Provided that Δσ X is much greater than the widths of the lines of species X under the considered T and P conditions, one can write [START_REF] Hartmann | Collisional effects on molecular spectra[END_REF]:

where CAX -Y (in cm -1 /amagat 2 ) is the squared-density normalized continuum absorption due to molecule X "influenced" by the presence of molecule Y. The possible origin of the continua will be discussed in the next section.

In order to deduce CACO 2 -H2O from the measured spectra, the following procedure was used: (i) and were calculated by using spectroscopic data given in the 2012 version of the HI-TRAN database [START_REF] Rothman | The HITRAN2012 molecular spectroscopic database[END_REF] for the line positions and integrated intensities, the energies of the lower levels of the transitions and the self-broadening coefficients (i.e. the pressure-normalized HWHMs). The H 2 O-broadening coefficients of CO 2 lines as well as their temperature dependences were calculated following the analytical formulation proposed in Ref. [START_REF] Sung | Fourier transform infrared spectroscopy measurements of H 2 O-broadened half-widths of CO 2 at 4.3 µm[END_REF]. The CO 2 -broadening coefficients of H 2 O lines were scaled from those of air, as done in Ref. [START_REF] Baranov | On the significant enhancement of the continuum-collision induced absorption in H 2 O+CO 2 mixtures[END_REF], their temperature dependences being fixed to those of air [START_REF] Rothman | The HITRAN2012 molecular spectroscopic database[END_REF]. In the absence of available data, the needed CO 2 and H 2 O pressure shifts were assumed to be the same as the air-induced ones, provided by the HITRAN database [START_REF] Rothman | The HITRAN2012 molecular spectroscopic database[END_REF]. The temperature dependences of the self-broadening coefficients for CO 2 and H 2 O lines were also set to be the same as those of the air-broadening coefficients. Since the relative contribution of the local lines is quite small, these approximations lead to very small changes of the total absorptions and do not affect the deduced values of CACO 2 -H2O. The influence of the apparatus line-shape function was also taken into account by convolving the calculated transmission (i.e.

)

with an instrument line shape accounting for the finite maximum optical path difference as well as the iris radius. The contribution of each H 2 O line to was calculated between -25 and 25 cm -1 away from the line center (i.e. = 25 cm -1 ), in order to be consistent with the choice adopted for the water vapor continua CAH 2O -H2O [START_REF] Clough | Line shape and the water vapor continuum[END_REF][START_REF] Mlawer | Development and recent evaluation of the MT_CKD model of continuum absorption[END_REF] and CAH 2O -CO2 [START_REF] Ma | A far wing line shape theory and its application to the foreign-broadened water continuum absorption[END_REF][START_REF] Pollack | Near-infrared light from Venus' Nightside: a spectroscopic analysis[END_REF].

For CO 2 lines, ΔσCO 2 = 5 cm -1 was used in the computation of . The contributions of the continua of pure H 2 O and H 2 O in CO 2 were calculated as follows. Absorption by the self-continuum ( CAH 2O -H2O) of H 2 O was taken from the MT_CKD 3.0 database [START_REF] Mlawer | Development and recent evaluation of the MT_CKD model of continuum absorption[END_REF], available on http://rtweb.aer.com/. The CO 2 -continuum of H 2 O (CAH 2O -CO2) was calculated with the line shape correction functions χ of Ref. [START_REF] Ma | A far wing line shape theory and its application to the foreign-broadened water continuum absorption[END_REF] using line positions and intensities from the 2012 version of the HITRAN database [START_REF] Rothman | The HITRAN2012 molecular spectroscopic database[END_REF] with a cut-off at 25 cm -1 to remove the local line contribution. Its temperature dependence was empirically derived using data provided in Ref. [START_REF] Pollack | Near-infrared light from Venus' Nightside: a spectroscopic analysis[END_REF].

The absorption due to the self-continuum of CO 2 , i.e. CACO 2 -CO2 , was taken from Ref. [START_REF] Tran | Measurements and modelling of high pressure pure CO 2 spectra from 750 to 8500 cm-1. I-central and wing regions of the allowed vibrational bands[END_REF] in which absorption of pure CO 2 beyond the ν 3 band head was measured at temperatures from 260 to 473 K. The values of CACO 2 -CO2 under the temperature conditions considered in the present study were then deduced from those of [START_REF] Tran | Measurements and modelling of high pressure pure CO 2 spectra from 750 to 8500 cm-1. I-central and wing regions of the allowed vibrational bands[END_REF] using a linear interpolation in temperature. The obtained values were compared with those directly deduced from the present measurements (i.e. Spectra number 1, 8 and 15 in Table 1) for pure CO 2 showing very good agreements.

Results

Fig. 1 presents an example of the absorption coefficient (black) of a CO 2 H 2 O mixture measured at 325.18 K and for a total pressure of 761.8 Torr, the molar fraction of H 2 O in the mixture being 0.1037 (spectrum 16 as referred in Table 1). The (1)

(2) that of absorption due to the self-continuum of CO 2 (i.e. cyan) are also plotted on this figure. Following Eqs. ( 1) and ( 2), the difference between the measured absorption coefficient and the sum of all these contributions directly yields the absorption due to the continuum of CO 2 in H 2 O (i.e. , olive). As can be seen on this figure, the relative contribution of the self-and CO 2 -continua of H 2 O to the total absorption is small and absorption is mainly due to the self-and H 2 O-continua of CO 2 . Therefore, uncertainties of the selfand CO 2 -continua of H 2 O [START_REF] Shine | The water vapour continuum in near-infrared windows -Current understanding and prospects for its inclusion in spectroscopic databases[END_REF] will not significantly affect the obtained result. The local lines contribution is correctly reproduced by the calculation leading to a smooth behavior of the values of obtained from the above-described procedure. This treatment was applied to all measured spectra, yielding a set of values of for various mixtures and pressure and temperature conditions of the recorded spectra (see Table 1).

Fig. 2 shows examples of the dependence of on the product of the H 2 O and CO 2 densities, i.e.

for two wavenumbers 2461.57 and 2508.99 cm -1 . As can be observed, nice linear dependences are obtained, in agreement with Eq. ( 2). The slope of a linear fit thus directly yields CACO 2 -H2O [see Eq. ( 2)], leading to 6.32 × 10 -4 ( ± 0.05 × 10 -4 ) and 2.03 × 10 -4 ( ± 0.08 × 10 -4 ) cm -1 /amagat 2 for σ = 2461.57 and 2508.99 cm -1 , respectively.

Experimental values of CACO 2 -H2O, deduced as explained above in all the investigated spectral region are plotted in Fig. 3 (black points). These values were averaged over all measured temperatures since no temperature dependence could be observed within the studied temperature range, as it was the case in Ref. [START_REF] Baranov | On the significant enhancement of the continuum-collision induced absorption in H 2 O+CO 2 mixtures[END_REF]. This indicates that the temperature dependence, if any, must be small as it was shown to be the case, for a 50 K broad temperature interval, for the self- [START_REF] Hartmann | Measurements of pure CO 2 absorption beyond the ν 3 bandhead at high temperature[END_REF], N 2 [START_REF] Perrin | Temperature-dependent measurements and modeling of absorption by CO 2 -N 2 mixtures in the far line-wings of the 4.3 µm CO 2 band[END_REF]) and Ar- [START_REF] Boissoles | Collisionally induced population transfer effect in infrared absorption spectra. II. The wing of the Ar-broadened ν 3 band of CO 2[END_REF]) continua of CO 2 in the same region. The plotted uncertainties (Fig. 3) correspond to the standard deviation of the linear fits (Fig. 2) and of the temperature average. For comparison, the values measured in Ref. [START_REF] Baranov | On the significant enhancement of the continuum-collision induced absorption in H 2 O+CO 2 mixtures[END_REF] were also plotted (red points) in this figure, showing a very good agreement. The values of CACO 2 -H2O are listed in the supplementary material file. for two wavenumbers, deduced from measurements at 325.2 K and their linear fits. The origin of the continuum absorption by CO 2 in the region beyond the ν 3 band head is not fully clear. Indeed, the contributions of the far wing of the lines due to the intrinsic (vibrating) dipole of the CO 2 molecules, of the collision-induced dipole and of stable and meta-stable dimers all show a linear dependence versus the squared total density (or ρ X ρ Y product), as the observed one (see Fig. 2). In fact, while it was though for a long time [START_REF] Boissoles | Collisionally induced population transfer effect in infrared absorption spectra. II. The wing of the Ar-broadened ν 3 band of CO 2[END_REF][START_REF] Hartmann | Measurements of pure CO 2 absorption beyond the ν 3 bandhead at high temperature[END_REF][START_REF] Perrin | Temperature-dependent measurements and modeling of absorption by CO 2 -N 2 mixtures in the far line-wings of the 4.3 µm CO 2 band[END_REF][START_REF] Tipping | for high-temperature[END_REF] that only the first mechanism was involved, it was recently shown that the transient dipoles induced in interacting molecular pair, plays a role [START_REF] Hartmann | Molecular dynamics simulations for CO 2 spectra. III. Permanent and collision-induced tensors contributions to light absorption and scattering[END_REF]. Solving this issue in the case of CO 2 H 2 O is a vast and complex problem that is currently under study. However, there is a need for computational tools suitable for applications such as the ones mentioned in the introduction of this paper. Within this frame, and although this may not be fully rigorous from the point of view of physics, the widely-used χ-factor approach [see Refs. [START_REF] Perrin | Temperature-dependent measurements and modeling of absorption by CO 2 -N 2 mixtures in the far line-wings of the 4.3 µm CO 2 band[END_REF][START_REF] Tran | Measurements and modelling of high pressure pure CO 2 spectra from 750 to 8500 cm-1. I-central and wing regions of the allowed vibrational bands[END_REF]Turbet and Tran, 2017) for instance] seems to be a good compromise. It connects the observed absorption to contributions of the lines due to the intrinsic dipole of the monomer and allows to accurately represent the observations as shown in the above-mentioned references and by the results below. Besides, it can be used to model the contribution of local lines and for extrapolations to other spectral regions, which may be risky but is the only solution in many cases due to the absence of any other model or data. Within this approach, the absorption from the centers to the far wings of the lines of species X in a mixture with species Y, is calculated using the following equation:

(3) where x X and x Y are the molar fractions of species X and Y, respectively. The sums extend over all the lines of species X contributing to the absorption at the current wavenumber σ. The term is the quantum asymmetry factor resulting from the so-called fluctuation-dissipation theorem [START_REF] Hartmann | Collisional effects on molecular spectra[END_REF]. and are respectively the unperturbed line position (cm -1 ), integrated line intensity (cm -2 .amagat -1 ), the line width and shift (both in cm -1 ) due to collisions of the active molecule X with the perturbator Pert. The term is related to spontaneous emission at wavenumber σ. The line-shape correction factor χ X -Pert (T,|σ -σi|) is assumed to be independent of the transition. From this general equation, the continuum absorption of CO 2 in H 2 O (i.e. absorption in the far wings of CO 2 lines broadened by H 2 O within this approach) can be expressed as:

where the sum is now restricted to the lines centered outside the [ (σ -5) and (σ + 5)] cm -1 range and is the H 2 O-broadening coefficient (cm -1 /amagat) of CO 2 lines. The temperature-dependent χ CO2 -H2O factors were thus determined by fitting this equation to the measured values of CACO 2 -H2O (Fig. 3). A functional form for the χ CO2 -H2O factors, similar to what was constructed for pure CO 2 in Refs. [START_REF] Hartmann | Measurements of pure CO 2 absorption beyond the ν 3 bandhead at high temperature[END_REF]; [START_REF] Perrin | Temperature-dependent measurements and modeling of absorption by CO 2 -N 2 mixtures in the far line-wings of the 4.3 µm CO 2 band[END_REF]; [START_REF] Tran | Measurements and modelling of high pressure pure CO 2 spectra from 750 to 8500 cm-1. I-central and wing regions of the allowed vibrational bands[END_REF] was adopted in this work, i.e.:

The temperature dependences of the parameters B i were determined such that the density-squared normalized absorption coefficients [i.e.

in Eq. ( 1)] in the entire region 2400-2600 cm -1 are temperature-independent. This was done for the 200-500 K temperature range. The values of σ 1 , σ 2 and σ 3 as well as B 1 , B 2 and B 3 were determined by fitting Eqs. ( 4) and ( 5) on the measured values of CACO 2 -H2O(Fig. 3), i.e.:

The quality of the fit is demonstrated in Fig. 3 where the absorption coefficients calculated using Eqs. (4-6) (blue line) are in very good agreement with the experimental values (black points). These temperature-dependent χ-factors [Eqs. (5,6)] can now be used to model H 2 O-broadened CO 2 far line wings in applications such as those mentioned in Section 1.

In Ref. [START_REF] Baranov | On the significant enhancement of the continuum-collision induced absorption in H 2 O+CO 2 mixtures[END_REF], it was shown that CACO 2 -H2O is about one order of magnitude stronger than that in pure CO 2 between 2500 and 2575 cm -1 . Since the present study covers a significantly broader spectral range, we verify this by comparing CACO 2 -H2O with CACO 2 -CO2 for the whole considered spectral region. For that, we plot in Fig. 3 the values of CACO 2 -CO2, measured at room temperature by Tran et al., 2011 (green points). This figure confirms that the values of CACO 2 -H2O are indeed significantly larger than those of CACO 2 -CO2, but their ratio is not constant and increases with the wavenumber. This may be qualitatively explained by the effect of incomplete collisions. In fact, in Ref. [START_REF] Tran | Super-and sub-Lorentzian effects in the Ar-broadened line wings of HCl gas[END_REF] it was shown that incomplete collisions (i.e. collisions that are ongoing or start at time zero) lead to an increase of absorption in the line wings. Since the CO 2 H 2 O intermolecular potential involves much larger long-range contributions than that of CO 2 CO 2 , the effect of incomplete collisions must be stronger for CO 2 in H 2 O than for pure CO 2 . This explanation is also consistent with the observed relative magnitudes of the continua of CO 2 in N 2 [START_REF] Perrin | Temperature-dependent measurements and modeling of absorption by CO 2 -N 2 mixtures in the far line-wings of the 4.3 µm CO 2 band[END_REF], Ar [START_REF] Boissoles | Collisionally induced population transfer effect in infrared absorption spectra. II. The wing of the Ar-broadened ν 3 band of CO 2[END_REF] and He [START_REF] Ozanne | Line mixing and nonlinear density effects in the ν3 and 3ν3 infrared bands of CO 2 perturbed by He up to 1000 bar[END_REF] [see also Fig. 6 of Ref. [START_REF] Baranov | On the significant enhancement of the continuum-collision induced absorption in H 2 O+CO 2 mixtures[END_REF]]. However, since line-mixing effects [START_REF] Tran | Measurements and modelling of high pressure pure CO 2 spectra from 750 to 8500 cm-1. I-central and wing regions of the allowed vibrational bands[END_REF] [but likely also the collision-induced dipole moment [START_REF] Hartmann | Molecular dynamics simulations for CO 2 spectra. III. Permanent and collision-induced tensors contributions to light absorption and scattering[END_REF]] contribute to absorption in this spectral region, explaining its behavior as well as analyzing its origin are beyond the scope of this paper and will be carried out in a future study.

Conclusion

Absorption in the spectral region beyond the 4.3 µm (ν 3 ) band of CO 2 broadened by H 2 O was measured with a high-resolution Fourier-transform spectrometer under various pressure and temperature conditions. The measured values are in very good agreement with the unique previous measurement but extend the investigated spectral range. The results show that the CO 2 + H 2 O absorption continuum in this spectral region is significantly larger than the pure CO 2 continuum. Therefore, this continuum must be taken into account in radiative transfer calculations for media involving CO 2 + H 2 O mixture. An empirical model, using sub-Lorentzian line shapes based on temperature-dependent χ-factors was then deduced from the measured values, enabling easy calculations of absorption in the ν 3 band wing of CO 2 broadened by H 2 O. The measurements presented in our manuscript are part of a broader project aiming at characterizing several absorption properties of CO 2 + H 2 O mixtures (Turbet et al., 2017). The effect of these new measurements on various planetary environments will be quantitatively investigated in a future dedicated study.

Fig. 1 .

 1 Fig. 1 presents an example of the absorption coefficient (black) of a CO 2 H 2 O mixture measured at 325.18 K and for a total pressure of 761.8 Torr, the molar fraction of H 2 O in the mixture being 0.1037 (spectrum 16 as referred in Table 1). The calculated contributions of local H 2 O and CO 2 lines, (red line), of the self-(green) and CO 2 -(blue) continua of H 2 O (i.e. and and

Fig. 2 .

 2 Fig. 2. Dependences of on the product of the H 2 O and CO 2 densities (i.e.

Fig. 3 .

 3 Fig. 3. Continuum absorption of CO 2 broadened by H 2 O, CACO 2 -H2O, beyond the CO 2 ν 3 band head region measured in this work (black rectangles) and those measured by Ref. Baranov (2016) (red circles). Values of CACO 2 -H2O calculated from the sub-Lorentzian empirical model [Eqs. (4-6)] are represented by the blue line. The self-continuum of CO 2[START_REF] Tran | Measurements and modelling of high pressure pure CO 2 spectra from 750 to 8500 cm-1. I-central and wing regions of the allowed vibrational bands[END_REF] are also plotted (green) for comparison. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).

Table 1

 1 Experimental conditions of the measured spectra. The path length (L) used for all measurements was fixed to 7.20 m.

	Spectrum	Temperature (K)	H 2 O pressure (Torr)	CO 2 pressure (Torr)
	1	367.15	0	760.6
	2	366.65	108.78	760.25
	3	366.45	86.78	606.6
	4	366.55	54.54	381.3
	5	366.35	109.90	608.9
	6	366.35	68.95	380.9
	7	364.65	108.90	381.45
	8	344.95	0	761.55
	9	344.65	103.90	764.55
	10	344.64	82.65	608.15
	11	344.65	52.15	382.95
	12	344.58	105.60	607.90
	13	344.60	66.19	380.55
	14	344.50	105.10	381.55
	15	325.15	0	759.4
	16	325.18	79.00	761.8
	17	325.19	63.19	609.1
	18	325.15	39.47	380.6
	19	325.35	80.20	610.3
	20	325.25	50.17	382.4
	21	325.15	80.30	382.9

Acknowledgment

The authors thank Dr. Q. Ma for providing his calculated data of the CO 2 -continuum of water vapor at various temperatures. J.-M. Hartmann is acknowledged for helpful discussions.

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Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.icarus.2018.02.009.