F Gobet

B Farizon

M Farizon

M J Gaillard

J P Buchet

M Carré

T D Märk

Caloric curve for the liquid-to-gas transition of the H 25 + hydrogen cluster ion

Keywords: Phase transition, Caloric curve, Hydrogen cluster ions, Cluster fragmentation

High energy collisions (60 keV/amu) of the H 25 + hydrogen cluster ions with an helium target have been completely analyzed on an event-by-event basis in a recently developed multi-coincidence experiment. By selecting specific decay reactions we can start after the energizing collision with a microcanonical cluster ion ensemble of fixed excitation energy. From the respective fragment distributions for these selected decay reactions we derive corresponding temperatures of the decaying cluster ions. The relation between this temperature and the excitation energy (caloric curve) exhibits the typical prerequisites (plateau region) of a first order phase transition in a finite system, in the present case signaling the transition from a bound cluster to the free gas phase type situation.

Introduction

Phase transitions are universal properties of matter in interaction. They have been extensively studied in the thermodynamical limit of infinite system. However in many physical situations this limit cannot be accessed and so phase transitions should be reconsidered from a more general point of view. This is for example the case of matter under long range forces like gravitation [1]. Even if these self gravitating systems are very large they cannot be considered as infinite system because of the nonsaturating nature of * Corresponding author. E-mail: bfarizon@ipnl.in2p3.fr the force. Other cases are provided by microscopic or mesoscopic systems consisting of matter which is known to exhibit phase transitions. Metallic clusters can melt before being vaporized [2,3]. Quantum fluid may undergo Bose condensation or super-fluid transition [START_REF]Proceedings of "Quark Matter 1997[END_REF]. Dense hadronic matter should merge in a quark-gas phase transition [5]. One of the great challenges in cluster physics in the last years was the identification and characterization of critical behavior and the observation of phase transitions, including solid-to-liquid and liquid-to-gas phase transitions. Since clusters are particles of finite size one is confronted with the general question of how to detect and/or characterize such a transition in a finite system.

It has been proposed that phase transitions in finite systems within the microcanonical ensemble [1,6] may be detected by a characteristic functional relationship between the temperature and the excitation energy, the so-called caloric curve, i.e., a first order phase transition should correspond to a negative branch for the heat capacity [7][8][START_REF] Chomaz | Proceedings of the XXXVIII International Winter Meeting on Nuclear Physics[END_REF].

In a strict sense, sharp second order phase transitions can only occur in the thermodynamic limit that is critical singularities are only present for a system with a large number of particles [START_REF] Chomaz | [END_REF]. In small systems such as two colliding nuclear or molecular systems fluctuations may wash out the signature of the phase transition [8,11]. Nevertheless, it has been demonstrated theoretically (see [11] and references therein) and also experimentally (see [12] and references therein) that finite systems may indeed exhibit a critical behavior to be seen when studying inclusive fragment size distributions, scaled factorial moments, and anomalous fractal dimensions. For instance recent heavy ion collision experiments around the Fermi energy (see ref. [START_REF] Chomaz | Proceedings of the XXXVIII International Winter Meeting on Nuclear Physics[END_REF] in [11]) and cluster collision experiments around the Bohr energy (see [13] and references therein) have shown the formation of many different fragments in the exit channel of the reaction exhibiting a power law in total fragment size distributions. Such a power law, as described by the Fisher droplet model [14,15] is expected to hold for droplet condensation/evaporation near the critical temperature, indicating a liquid-to-gas second order phase transition. However, recent work on the lattice gas model [8] demonstrates that a critical behavior is compatible with a first order phase transition because of the finite size effects. As concluded by Gross and coworkers [6,16] on the basis of extensive theoretical modeling the best signature, however, of a phase transition of first or second order in a finite system is the specific shape of the caloric curve (see [7,[START_REF] Chomaz | Proceedings of the XXXVIII International Winter Meeting on Nuclear Physics[END_REF]) or according to the theoretical work of Berry and coworkers [17][18][19] the specific dependence of the thermodynamic temperature on the total energy in the system.

Pochodzolla et al. [20] were the first to determine experimentally a relation between the temperature of hot decaying nuclei resulting from Au + Au collisions at 600 MeV/amu and their excitation energy, the shape of this relation exhibiting the characteristic plateau expected for a phase transition. The validity of this first experimental observation of a caloric curve for a liquid-to-gas phase transition for nuclear systems (in particular the determination of the temperature) was later questioned [8] because follow-up experiments arrived at different shapes (see [21,22] and references therein). On the other hand, Haberland and coworkers [2,3,23] reported the first experimental determination of a caloric curve for the solid-to-liquid like transition (melting) of a small cluster temperature, i.e., a sodium cluster consisting of 139 atoms [2]. A beam of cluster ions was generated with a canonical distribution of internal energy thus fixing the temperature. One cluster size was selected (thus switching to microcanonical system), irradiated by photons and the photofragmentation pattern (which can be related to the energy) was measured as a function of this cluster temperature. Moreover, Bachels et al. [24] reported recently a caloric curve for the melting of a free tin cluster distribution (without mass selection) employing a sensitive pyroelectric foil, the interpretation of their experiment was, however, later questioned [25]. Very recently Schmidt et al. [26] reported a caloric curve for Na 139 + measured from 100 K up to the temperature where the clusters are boiling and spontaneously emit atoms thereby allowing them to construct the caloric curve across the liquid to gas change for a sodium cluster ion. Moreover, we were recently able, employing an advanced accelerator mass spectrometry experiment [27], to derive for the first time the relation between the temperature and the excitation energy (caloric curve) for a molecular cluster ion (e.g., the H 27 + ion). This relation exhibited the typical prerequisites of a first order phase transition in a finite system signaling the transition from a bound cluster to the gas phase [27]. In the present paper we extend our previous study to another cluster ion, i.e., the H 25 + ions. It has to be noted that the sizes of these hydrogen cluster ions are much smaller than the previously studied metal cluster ions and thus we are probing here the lower limit of the underlying statistical concept.

The protonated hydrogen cluster ions represent in contrast to the previously studied metal cluster ions [23][24][25][26] a quite different class of systems where a quantum solute is solvated by a quantum solvent; the added proton becomes trapped and a tightly localized H 3 + core is surrounded by solvating H 2 molecules, H 3 + (H 2 ) m=11 [28]. Moreover, after the energizing collisions between 60 keV/amu ions with a helium target we select a microcanonical ensemble of cluster ions with a given energy (by selecting specific decay reactions from a host of possible decay channels) and determine from the (partial) fragment size distribution the corresponding temperature of the ensemble of decaying cluster ions. This experiment involves the complete event-by-event analysis of 11,685 collisions using a recently developed [12,13] multi-coincidence technique for the simultaneous detection of the correlated, ionized and neutral, collision fragments thus allowing us to obtain an experimental caloric curve for the transition from a bound cluster to the gas phase.

Experimental set-up

Mass selected hydrogen cluster ions with an energy of 60 keV/amu are prepared in a high-energy cluster ion beam facility [12] consisting of a cryogenic cluster jet expansion source combined with a high performance electron ionizer and a two step ion accelerator (consisting of an electrostatic field and a RFQ post-accelerator). After momentum analysis by a magnetic sector field, the mass selected high energy projectile pulse (pulse length 100 ms, repetition + (H 2 ) m=11 cluster ions is crossed perpendicularly by a helium target beam effusing from a cylindrical capillary tube (see Fig. 1). Prior to this the ion beam is collimated by two apertures ensuring an angular dispersion of about ±0.8 mrad. One meter behind this collision region the high energy hydrogen collision products (neutral and ionized) are passing a magnetic sector field analyzer. The undissociated primary H 3

+ (H 2 ) m=11 cluster projectile ion or the neutral and charged fragments resulting from reactive collisions are then detected approximately 0.3 s after the collision event with a multi-detector device consisting of an array of passivated implanted planar silicon surface barrier detectors located at different positions at the exit of the magnetic analyzer.

With this instrument we are able to record for each event simultaneously the number (multiplicity) of each mass-identified fragment ion resulting from the interaction (for more experimental details, see [12,13,29]). In addition, for each event we can also monitor in coincidence with the detected ions the sum of the masses of all the neutral fragments. Moreover, by probing the angular distribution of these neutrals in front of the detector by using a movable aperture (0.5 mm of diameter) and additional information (as described later) about the reaction probability of H 2 and H 3 + projectiles we can conclude that the neutral products observed consist only of hydrogen atoms and hydrogen molecules [START_REF] Gobet | Analysis of the neutral fragments[END_REF] with no larger neutral clusters present. As an example, we report in Fig. 2a the spectrum corresponding to the detection of all the neutral fragments produced by collisions of H 15 + cluster ions with helium target atoms without using this moveable collimator. The number associated with each peak in this figure corresponds to the measured total neutral mass being produced in a single collision by one fragmenting cluster ion H 15 + . We observe 15 separate peaks (as described in detail in reference [START_REF] Farizon | [END_REF]) the peak at the lowest mass corresponding to an hydrogen atom with mass 1 amu and the peak at the highest mass corresponding to a total mass of 15 amu. Without further measurements we cannot at this point identify the identity of the neutrals causing these peaks, e.g., the peak at mass 4 could be due to four hydrogen atoms, two hydrogen molecules, two hydrogen atoms plus one hydrogen molecule or to one hydrogen dimer (H 2 ) 2 . One way to obtain more information is to measure the neutral fragments under the same experimental condition however with the movable collimator positioned in front of the dectector for the neutral fragments thereby limiting the acceptance angle for neutral fragments being produced in the collision region by a single collisional event.

In this case (see Fig. 2b) only two major peaks can be observed in the spectrum one at mass 1 and one at mass 2, respectively, corresponding to the detection of H, H + HorH 2 . This immediately excludes the possibility that neutral fragments larger than H 2 are being produced by these collisions. The reason that we do see larger peaks when removing this collimator is due to the fact that in this case we can detect several neutral fragments from one collision event even if these fragments are produced with initial kinetic energy and thus have spread over a large area at the point of detection (with the collimator we will detect only the central part of the beam, and if we do not detect larger masses than 2 we can safely conclude that no larger molecules are present in the beam). Nevertheless, we also observe in Fig. 2b a few events corresponding to mass 3 and 4. The diameter aperture has been chosen in such a way that the probability to detect simultaneously two fragments originating from the same fragmenting cluster (e.g., one leaving the fragmenting cluster ion in forward and one in backward direction) is very small. But this probability cannot be reduced to zero and thus we are expecting a few events with larger masses even if the largest fragment is H 2 . Thus mass 3 may be interpreted as being due to the simultaneous detection of one hydrogen atom and one hydrogen molecule (there exists no neutral hydrogen trimer) and mass 4 may be interpreted as being mainly due to the simultaneous detection of two hydrogen molecules. One additional reason why the peak at mass 4 cannot be interpreted as evidence for the existence of bound neutral fragment (H 2 ) 2 is the rather high multiplicity observed for the neutral fragments produced (see the large signal for the higher mass numbers in Fig. 2a).

So far we have therefore determined that fragments produced (and detected with the collimator) have mass 1 or 2. In order to obtain information about the identity of the detected signal at mass 2 one needs further information. This may be obtained by using a movable grid in front of the detector and studying the reaction probabilities for H 2 and H 3 + projectiles interaction with a He target. This allows us to distinguish whether a resulting signal at a mass of 2 amu is due to one hydrogen molecule, due to two hydrogen atoms or due to a certain mixture of these two cases (for details of this rather involved analysis see [START_REF] Gobet | Analysis of the neutral fragments[END_REF]32]). For larger clusters this technique cannot be directly applied and therefore additional information on relative cross sections for the various product channels needs to be used for a complete analysis of the neutral mass peak [START_REF] Gobet | Analysis of the neutral fragments[END_REF].

Thus without going here into further experimental detail we can state that we are able to analyze on an event-by-event basis the identity of all correlated fragments produced in a single collision event between the H 3 + (H 2 ) 11 cluster ion and the He target atom, the fragmentation reactions having the general form

H 3 + (H 2 ) 11 +He → aH 3 + (H 2 ) k + bH 3 + + cH 2 + + dH + + e(H 2 ) + f H with a-f = 0, 1,... . (1)
The validity of single collision conditions has been ascertained by measurements at different He target pressures and allows us to derive also absolute cross sections for the occurrence of specific reaction channels (partial cross sections, for details see [33]). This complete analysis allows us to go beyond the straightforward determination of total fragment size distributions as reported previously ( [13] and references therein), since we are able to generate for the first time partial fragment size distributions for selected decay reactions or classes of decay reactions.

Construction of the caloric curve

As we need for the construction of a caloric curve the simultaneous determination of the energy and the temperature of the system, we use the ability to select certain classes of reactions to group our analyzed events into a number of different subgroups each representing collisions in which a certain amount of energy is deposited into the cluster. Thus we are generating from our large set of collisions various subsets containing only cluster ions with a certain energy (or energy range) in a microcanonical sense. The basic idea behind this is to analyze each decay reaction in terms of the energy required for all the particles produced in such a decay reaction (taking into account the well known potential energy curves for the hydrogen molecule when calculating the energy for the Franck-Condon transitions from quasi-isolated cold ground state H 2 molecules to the various excited states involved) and to use the total energy value obtained as a measure for the internal energy prior to the decay.

For instance, analyzing the identity of the neutrals the observed decay reactions of H 3 + (H 2 ) 11 ions into H 9

+ + H 2 + plus a neutral mass totaling 14 amu shows that 86.1% of the cases correspond to the production of seven hydrogen molecules. In this case the necessary energy for the reaction is 15.7 eV (the ionization energy for the hydrogen molecule) neglecting the much smaller binding energy of the hydrogen molecules. Similarly, 13% of these events correspond to the production of six hydrogen molecules and two hydrogen atoms necessitating an additional energy input of about 10.3 eV to dissociate one molecule into two atoms (thus yielding a total energy of 26 eV), 0.8% correspond to five molecules and four atoms (total energy of 36.3 eV) and 0.1% to four molecules and six atoms (total energy of 46.6 eV).

Fig. 3 shows for the H 3 + (H 2 ) m=11 cluster ion projectile the corresponding measured partial fragment mass distribution for eight selected subsets each of which includes reactions of a certain energy range, e.g., 2-12 eV, 15-25 eV, etc. It is interesting to note that the shape of these distributions changes significantly as a function of the energy deposited, i.e., from a U-shaped form at low energy which is due to the occurrence of a mixture of evaporation and multi-fragmentation processes, to a pure power law at intermediate energies due to the presence of only multi-fragmentation reactions to finally a regime at high energies which is dominated by complete disintegration processes. So far these different regimes could only be observed by different experiments with widely different collision parameters ranging from low energy mass spectrometer collision experiments [34], to high Fig. 3. Partial fragment mass distributions for different subsets of reaction channels (selected according to the energy deposited in the collision complex, i.e., 2-12 eV, 15-25 eV, etc.) occurring in collisions of 60 keV/amu H 25 + ions with He. Solid lines: fits using Fisher's formula (see text). energy cluster/atom or nuclear collision experiments (see [13] and references therein) and to beam foil experiments with clusters yielding only atomic fragment ions [35]. This is the first time (see also recent results reported for the H 27 + cluster ion [27]) that this characteristic change of the mass distribution as a function of energy deposited has been determined in only one experiment over the whole range of possible shapes and thus possible decay mechanisms.

Returning now to the construction of the caloric curve we need in a second step to determine for each subset of known energy the corresponding temperature of the cluster ions prior to the decay. Here we use a relationship between the characteristic shape of a fragment mass distribution and the temperature of the decaying nuclei at around the critical point reported recently by Belkacem et al. [11]. They were able to fit quite differing numerical mass distributions obtained by classical MD calculations for a nucleus with 100 constituents (see the distributions shown in Fig. 4)a t Fig. 4. Mass distributions obtained for the expansion of a nuclear system consisting of 100 constituents (A = 100) for eight different initial temperatures ranging from 2 to 20 MeV. The dots in the plot show the results of the MD calculations and solid lines the fits using Fisher's formula (adapted from Belkacem et al. [11]). different initial canonical temperatures (by generating 2000 events per temperature) very well with Fisher's droplet formula [14]

dN dA = Y 0 A -τ (X A ) 2/3 Y A , (2)
with Y 0 , X, Y and τ fitting parameters and A the atomic mass number, thus demonstrating a direct relationship between the shape of the mass distribution (as described by (2) and in particular by the parameter Y which is related to the temperature approaching the value 1 at the critical temperature) and the initial temperature of the decaying system (see also [36]). In Fig. 4 we show the mass distributions and the corresponding fits obtained in this way for the expansion of the nuclear system with 100 constituents (A = 100) for eight different initial temperatures ranging from 2 to 20 MeV (from Belkacem et al. [11]). It is interesting to note at this point that these mass distributions exhibit a similar evolution of the fragment size distribution with increasing temperature as the present ones (see Fig. 3) with increasing amount of excitation energy. Thus, following the methodology of Belkacem et al. [11] in fitting their mass distribution, i.e., first fixing the parameter τ using a rather pure power law distribution (e.g., the one at an energy of 47 eV in Fig. 4) and then fitting the other parameters by using all distributions (and doing this in an iterative way several times), we also succeeded to fit the presently obtained (partial) fragment mass distributions with Eq. (2). With a slope of -3.16 (as compared to -2.23 in the calculation of Belkacem et al. [11]; previous experimentally determined values for total fragment mass distribution for clusters and nuclei having values of about -2.6 [14]) we obtain a very good agreement between our experimental points and the fits (solid lines in Fig. 3; the corresponding values of the fitting parameters Y 0 , X, Y and τ entering in the formula Eq. ( 2) are given in Table 1). In the case of the H 3 + (H 2 ) m=12 [27] Table 1 Values of the fitting parameters Y 0 , X, Y, and τ entering in the Fisher formula Eq. ( 2) as derived from the experimental data for H we used a slope of -3.38 and the fits obtained were equally convincing. This then allows us by comparison with the results of Belkacem et al. [11] (Fig. 4)to designate for each of the subsets considered a relative measure for the temperature due to the characteristic shape of its fragment mass distribution (as expressed by the fitted parameters, in particular the parameter Y).

Thus the major overriding conclusion for these results is that for small energies the distribution is quickly changing with increasing energy from a U-shaped form to a single power law fall off. Moreover, this power law, containing fragments of all sizes, is sustained over a broad energy range and thus this is direct evidence for a constant temperature in this energy range. Finally, at very large energies this power law is replaced by a shape which is falling off much faster than this power law signaling a sudden change (increase) in temperature. It is interesting to note that in a similar fashion, though in a different context and by different theoretical means, temperatures of decaying carbon cluster ions have been determined by measuring either the microcanical decay rate constants for monomer evaporation [37] (see also results for aniline-argon clusters [38], the kinetic energy release distributions for monomer evaporation [39] or the fragmentation pattern in surface-induced dissociations [40]). Using this 'temperature' which is only a relative measure (due to the comparison with MD calculations applied to the nuclear matter), we plot in Fig. 5 the temperature derived in reduced units vs. the energy deposited. As a matter of fact we have for this purpose considered more data subsets than shown in Fig. 3. Moreover, similar results have also been obtained for other cluster ion as shown in Fig. 5. Caloric curve for cluster fragmentation: temperature (given in reduced value (T/T 0 ), with T 0 the temperature in the plateau part of the curve) vs. the energy deposited in the H 25 + cluster ion. The error bars given for one of the experimental points comprises on the one hand the maximum error in assigning the energy including the unknown extent of vibrational excitation in the one hydrogen molecule hit on average by the He atom during the collision and on the other hand the maximum error in assigning the temperature using various fitting procedures. In practice as we are using the best fit method for all the points the relative error in the temperature is much smaller and this is also mirrored by the rather small deviations of the experimental points from each other in the plateau region. This interpretation is confirmed by similar observations for other cluster sizes.

reference [27] thus confirming independence of this characteristic result from the finite particle size.

Results and conclusion

This caloric curve can be clearly divided into three parts, after an initial increase a distinct plateau is present before the curve is rising again. This curve therefore agrees qualitatively with the typical prerequisites of a first order phase transition [7] (see also Fig. 7 in [START_REF] Chomaz | Proceedings of the XXXVIII International Winter Meeting on Nuclear Physics[END_REF]) in a finite system. It thus constitutes a strong signature for a liquid-to-gas like phase transition in a fragmenting cluster and thus confirms and replaces the other fingerprints such as the power law in mass distributions and factorial moment analyses [16]. As in the calculations discussed by Gross et al. [6] using microcanonical metropolis sampling for hot atomic metal clusters the transition occurs and is characterized by the interplay and transition from monomer evaporation reactions (see also Fig. 4)t o multi-fragmentation reactions and complete vaporization events in this bound-free transition regime. The particular long plateau (indicating a relatively large apparent specific heat involved in this transition also observed for the melting of sodium cluster ions by Haberland and coworkers [2,3,23,26]) may be attributed to the many different degrees of freedom available in this special type of cluster being bound by a mixture of dispersion force (intermolecular binding) and covalent binding with more intramolecular excited states available than in atomic clusters.

Fig. 1 .

 1 Fig. 1. Schematic view of the experimental set-up.

frequency 1

 1 Hz) consisting in the present study of H 3

Fig. 2 .

 2 Fig. 2. Mass spectrum for the neutral fragments for decaying H 15 + ions: (a) without movable collimator in front of the detector and (b) with movable collimator in front of the detector.

Acknowledgements

Work supported by the FWF, Wien, Austria, the Amadee program of the French and Austrian governments and the EU Commission, Brussels.


Denis A Belyaev
email: dbelyaev@iki.rssi.ru

Anna A Fedorova

Alexander Trokhimovskiy

Juan Alday

Franck Montmessin

Oleg I Korablev

Franck Lefèvre

Andrey S Patrakeev

Kevin S Olsen

Alexey V Shakun

Revealing a High Water Abundance in the Upper Mesosphere of Mars with ACS onboard TGO

 For the first time, water relative abundances are reported in a previously unexplored altitude range: from 100 to 120 km  Both the global dust storm (MY34) and the two perihelion seasons (MY34, 35) observed reveal 10-50 parts of H 2 O per million by volume at 100-120 km  Contributions of a single GDS and perihelion into the H escape from Mars are nearly equivalent, suggesting the repeatable seasonal effect dominates in the long term

Introduction

The vertical distribution of water vapor (H 2 O) on Mars is an indicator of the intricate coupling of distinct phenomena: temperature variations, cloud formation, sublimation, turbulent and convective mixing, etc. H 2 O is usually expected to be confined below the hygropause, which is the level where the saturation condition is met and where water ice clouds may form, as occurs on Earth. For the first time, this layer was established on Mars by ground-based microwave soundings of [START_REF] Clancy | Water vapor saturation at low altitudes around Mars aphelion: A key to Mars climate?[END_REF] with a saturation level between 10-20 km around the aphelion, i.e., Solar Longitudes (L S ) 70°, and 40-60 km around perihelion (L S 250°). In parallel, [START_REF] Rodin | Vertical distribution of water in the nearequatorial troposphere of Mars: water vapor and clouds[END_REF] reported water vapor profiles retrieved from the solar occultations made by Auguste on Phobos-2 in 1989. The existence of a hygropause at 30-35 km (with a mixing ratio of 3 ppm) in the northern spring (L S =0°-20°) near the equator was claimed. The first climatology of water vapor profiles was derived from SPICAM-IR solar occultations on Mars Express (MEx) (Fedorova et al., 2009;2018;2021;[START_REF] Maltagliati | Annual survey of water vapor vertical distribution and wateraerosol coupling in the martian atmosphere observed by SPICAM/MEx solar occultations[END_REF], covering eight Martian years. The hygropause level was found to vary from 40 to 80 km depending on season, latitude, and dust events.

The observation of large amounts of water vapor in and above the middle atmosphere (>40 km) was accompanied by the discovery of fast variations of the hydrogen corona over several weeks (Chaffin et al., 2014;Clarke et al., 2014). This variability suggested a new paradigm in the perception of how water escapes from Mars [START_REF] Chaffin | Elevated atmospheric escape of atomic hydrogen from Mars induced by high-altitude water[END_REF]. So far, water escape was thought to be controlled by a slow process involving H 2 , formed from the catalytic manuscript submitted to Geophysical Research Letters recombination of carbon dioxide with odd hydrogen [START_REF] Mcelroy | Stability of the Martian atmosphere[END_REF][START_REF] Krasnopolsky | Mars' upper atmosphere and ionosphere at low, medium, and high solar activities: implications for evolution of water[END_REF]. The non-condensable H 2 can overcome the hygropause and reach the mesosphere (80-120 km) transported by turbulent mixing or circulation. There it can dissociate and release H atoms that will escape the planet once above the exobase.

Long-term observations revealed that water vapor transport from the troposphere into the lower mesosphere of Mars occurs during major dust storms. In particular, a significant H 2 O enhancement in the middle atmosphere was observed during the global dust storm (GDS) in 2007 (MY28) with a rise of the hygropause altitude to >60 km [START_REF] Fedorova | Water vapor in the middle atmosphere of Mars during the 2007 global dust storm[END_REF][START_REF] Heavens | Hydrogen escape from Mars enhanced by deep convection in dust storms[END_REF]. Sensitive solar occultation measurements by NOMAD and ACS NIR instruments onboard the ExoMars Trace Gas Orbiter (TGO) showed water reaching 80-100 km [START_REF] Aoki | Water Vapor Vertical Profiles on Mars in Dust Storms Observed by TGO/NOMAD[END_REF]Fedorova et al., 2020) during two storms in 2018-2019 (the global one at L S 190°-220° and the regional one at L S 330° in MY34; [START_REF] Montabone | Martian Year 34 column dust climatology from Mars Climate Sounder observations: Reconstructed maps and model simulations[END_REF]. Fedorova et al. (2020) revealed the water supersaturation at 70-90 km even in the presence of H 2 O ice clouds not only during the GDS but also near the Southern summer solstice (L S ~270 o ) when water reached 90-100 km as well. Altogether, these studies promote a new mechanism for controlling H 2 O escape through direct delivery to above 80 km and further photodissociation [START_REF] Chaffin | Elevated atmospheric escape of atomic hydrogen from Mars induced by high-altitude water[END_REF][START_REF] Krasnopolsky | Photochemistry of water in the martian thermosphere and its effect on hydrogen escape[END_REF]. The only general circulation model describes an upward water flux into the thermosphere (>120 km) for the GDS scenario [START_REF] Shaposhnikov | Seasonal water "pump" in the atmosphere of mars: Vertical transport to the thermosphere[END_REF]. They predict high water volume mixing ratio (VMR) values: ~100 ppm at 100 km and ~200 ppm at 150 km for the southern middle latitudes.

The discussion regarding a relative contribution of perihelion or GDS to the mesospheric water enrichment was recently fed by SPICAM/MEx long-term observations covering Martian Years 28 through 35. Here, [START_REF] Fedorova | Multi-annual monitoring of the water vapor vertical distribution on Mars by SPICAM on Mars Express[END_REF] claimed a regular rise of water abundance up to 80-90 km in perihelion, which is compatible with GDS quantities. The new ACS/TGO dataset confirms those conclusions for altitudes below 100 km in MY34-MY35 (Fedorova et al. 2020, Alday et al., 2021). In parallel, during the perihelion season, the D/H ratio in water decreases with altitude from 4-6 times SMOW (Standard Mean Ocean Water) in the lower atmosphere to 2-3 times in the middle one (50-70 km) as measured by ACS MIR (Alday et al., 2021) and NOMAD [START_REF] Villanueva | Water heavily fractionated as it ascends on Mars as revealed by ExoMars/NOMAD[END_REF] spectrometers. Alday et al. (2021) show that ultraviolet H 2 O photolysis dominates the production of H relative to D atoms in the upper atmosphere.

From above, ion chemistry in the thermosphere has been characterized by the NGIMS mass-spectrometer on MAVEN [START_REF] Benna | First measurements of composition and dynamics of the Martian ionosphere by MAVEN's Neutral Gas and Ion Mass Spectrometer[END_REF] and interpreted by the ionospheric model of [START_REF] Fox | Water and water ions in the Martian thermosphere/ionosphere[END_REF]. Using NGIMS data, [START_REF] Stone | Hydrogen escape from Mars is driven by seasonal and dust storm transport of water[END_REF] measured H 2 O ion concentrations around ~150 km for the 2014-2018 period (MY32-MY34). With the help of the model by Fox et al., the relative abundance of water at this altitude on the dayside was found to vary seasonally from 2 to 5 ppm. Several enhanced dusty episodes disrupt this seasonal signal: 7-9 ppm during the regional storm of MY32, 10-20 ppm in the southern summer of MY33, and up to 60 ppm in the GDS of MY34. [START_REF] Stone | Hydrogen escape from Mars is driven by seasonal and dust storm transport of water[END_REF] concluded that water transport into the ionosphere and its destruction are the main mechanisms in the overall hydrogen escape from Mars. We used the data of the middle infrared spectrometer of the Atmospheric Chemistry Suite (ACS MIR) onboard the ExoMars TGO, which measures water vapor VMR and atmospheric density in a wide range of altitudes, from the troposphere to the lower thermosphere, using the strong absorption bands of H 2 O and CO 2 around 2.66-2.70 μm. A high spectral resolution and a good signal-to-noise ratio of ACS MIR allows the measurements of water profiles up to 120 km, the altitude unreachable for the ACS NIR, and SPICAM spectrometers, sensing the 1.38 μm manuscript submitted to Geophysical Research Letters absorption band (Fedorova et al., 2020;2021). The strong H 2 O absorption around 2.6 μm is also used by NOMAD, yielding water profiles up to ~90 km [START_REF] Aoki | Water Vapor Vertical Profiles on Mars in Dust Storms Observed by TGO/NOMAD[END_REF][START_REF] Villanueva | Water heavily fractionated as it ascends on Mars as revealed by ExoMars/NOMAD[END_REF].

Here we report the first water vapor abundance measurements in the upper mesosphere (up to 120 km) of Mars. The goal of our paper is to compare the mesospheric water behavior between the second halves of MY34 and MY35 when the high H 2 O content is observed. We aim to clarify the dominant role of H 2 O delivery to the upper mesosphere: either it belongs to sporadic dust events (GDS or a strong regional storm) or it also occurs regularly, every martian year, around Southern summer solstice. For that, we analyze seasonal and latitudinal variations of H 2 O VMR vertical profiles retrieved from the ACS MIR solar occultation experiment.

Measurements and dataset overview

2.1 ACS MIR spectroscopy and retrievals ACS MIR, a solar occultation cross-dispersion echelle spectrometer, records spectra from a set of adjacent diffraction orders (from 10 to 20 per occultation) projected onto a 2D detector array [START_REF] Korablev | The Atmospheric Chemistry Suite (ACS) of Three Spectrometers for the ExoMars 2016 Trace Gas Orbiter[END_REF]. To retrieve high altitude water vapor abundances together with the atmospheric temperature and pressure, we use MIR spectra from the diffraction order #223. They cover a narrow wavelength interval of 2.66-2.68 μm (3733-3753 cm -1 ), including a part of the 2.7-μm CO 2 absorption band and a few strong H 2 O lines near 2.66 μm (Fig. 1a, 1b, Fig. S1). The instrument's spectral resolution is ~0.15 cm -1 , while the signal-to-noise ratio ranges from 2,000 to 4,000, which provides high sensitivity for detections in the upper atmosphere where atmospheric constituents are low. Temperature (Fig. 1c) is retrieved by fitting a synthetic model to the CO 2 rotational band taking advantage of its temperature dependence under the assumption of hydrostatic equilibrium. This procedure was applied iteratively, with feedback of the retrieved temperature to the model. The temperature measurements were then validated against those made by MIR near the 2.6 μm CO 2 band [START_REF] Alday | Oxygen isotopic ratios in Martian water vapour observed by ACS MIR on board the ExoMars Trace Gas Orbiter[END_REF] and by ACS NIR around the 1.58 μm band (Fedorova et al., 2020). As a result, one occultation session allows us to simultaneously retrieve profiles of pressure and temperature (from CO 2 absorption bands) and the H 2 O number density (Fig. 2c). The water abundance can then be expressed relative to the total atmospheric density, that is, in VMR (in ppmv). Specific details of the algorithms pertaining to this work can be found in the Supporting Information.

The dataset analyzed here consists of a series of transmission spectra obtained during a solar occultation while the line of sight of the instrument progressively penetrates from the upper into deeper layers of the atmosphere, or vice versa (see examples in Fig. 1a,1b). The transmission is determined as the solar spectrum ratio measured through the atmosphere to the reference one, taken from the data above a tangential height of 200 km. This altitude level is negligibly attenuated by the atmosphere even within the very strong CO 2 band system at 2.7 μm.

The typical integration time is 2 seconds that provides an altitude resolution ranging from 0.5 to 2.5 km, depending on the occultation duration. It gives sufficiently fine vertical sampling for an atmosphere whose scale height ranges from 5 to 10 km depending on temperature. The ACS MIR field of view projected at the limb is estimated to be around 1-3 km in altitude equivalent. manuscript submitted to Geophysical Research Letters Northern Hemisphere and 156 sessions in the Southern Hemisphere, encompassing seasonal periods from L S 180° to 355° in MY34 and from L S 185° to 356° in MY35 (Fig. 2a). Figure 2a shows the latitude coverage with the corresponding aerosol activity, which was defined for each occultation as an altitude level where the slant opacity equals 0.3 (~0.75 of the atmospheric transmittance in the continuum). Measurements in the Northern Hemisphere occurred mostly in the mid-latitude range, which is between 40°N and 70°N. In the South, occultations before, during the GDS (L S <230°), and around the regional storm of MY34 (L S 320°-330°) were performed close to the polar region (60°S-90°S), while perihelion observations (L S 270°) were made in mid-latitudes. Only a few sessions occurred in the equatorial region at L S ~240° and L S ~300° of MY34 and at L S ~210° and L S ~280° of MY35. These observations are accompanied by a higher aerosol loading than those, which are close to the Poles (Fig. 2a). The overall map of the MY34 dust climatology can be found in [START_REF] Montabone | Martian Year 34 column dust climatology from Mars Climate Sounder observations: Reconstructed maps and model simulations[END_REF].

Seasonal variation of altitude profiles

Observations in the second half of MY34 and MY35 uncover events, which drastically perturbed the temperature and water vapor vertical distributions. The peculiar pattern to compare with is the MY34 GDS and perihelion periods in MY34 versus MY35, which had no GDS but a regular dust activity in its second half. The seasonal variation of the processed altitude profiles is presented in Figure 2(b,c). We binned the profiles into intervals of 2° in solar longitude (L S ) and 2 km in altitude. Depending on the L S and altitude sampling, the value in each bin is calculated as the weighted mean of one to five individual points. We excluded all points with uncertainties exceeding 20 K in temperature and 1-sigma in the H 2 O mixing ratio. The second rejection criterion corresponds to the detection limit (~10 7 cm -3 ) of water number density (see in Fig. 1c) that defines the seasonal variations of the uppermost detectable points in Figure 2c.

We observe temperature (Fig. 2b) and H 2 O (Fig. 2c) peaking in the middle atmosphere (40-80 km) during the GDS of MY34, L S 190°-220°, and an additional smaller peak at L S 320°-330°, corresponding to a regional storm. Moreover, the rise of water vapor to higher altitudes, up to the mesopause at 110-130 km where temperature encounters a minimum, is observed during two perihelion intervals (L S 250°-290°) of MY34 and MY35. Here, the Southern summer (Fig. 2c, right panel) is accompanied by a more humid mesosphere (40-60 ppm of H 2 O) than the Northern Winter (Fig. 2c, left panel) where the mean mesospheric water reaches 20-30 ppmv on average between 80 and 120 km. On the contrary, out of the perihelion peak or dust events, i.e.

for the selected data at the beginning of the MY34 GDS and at the very end of MY 34, 35, water content above 80 km never exceeds 2-3 ppmv.

H 2 O variations around perihelion

To quantify seasonal trends of water content in the mesosphere, we selected three altitude layers corresponding to 80 km, 100 km, and 110-120 km. The first layer, which corresponds to the lower mesosphere, is accessible in all profiles (Fig. 2c) when the vapor concentration exceeds the detection limit of ~10 7 cm -3 , even in low water loading periods. A value of H 2 O VMR at 80 km could be derived in every individual altitude profile when interpolating between adjacent points below and above this level. The water content at 100 km was found similarly, though based on a smaller number of profiles. Water at 110-120 km, in the upper mesosphere, shows up only in stormy periods and around perihelion (Fig. 2c).

Observed variations during perihelion for the three selected levels are presented in Figure 3 for both Martian Years. The number of MIR observations at Position #4 is low during the stormy events of MY34. Nevertheless, a comparison with MY35 reveals a significant excess of H 2 O mixing ratio during the GDS: by a factor of 6-8 at 80 km (Fig. 3c) and by a factor of 3-5 at 100-120 km from L S 190° to 220° (Fig. 3a,3b). A surge at L S 320°-330° reveals the effect of the regional dust storm of MY34, which delivers far less water into the mesosphere than the GDS.

Around the perihelion, L S =240°-300° water behaves almost identical between MY34 and MY35. manuscript submitted to Geophysical Research Letters levels, 80 through 120 km. We compare our results at 80 km with the corresponding ACS NIR dataset derived from the MY34 profiles of Fedorova et al. (2020). The NIR dataset is five times denser than used in the present work, and it observed the H 2 O variations in greater detail, especially during the dust events of MY34. (Fedorova et al., 2020).

Discussion and Conclusions

For the first time, we report observations of H 2 O relative abundances in a previously unexplored altitude range (from 100 to 120 km). There we find 10-30 ppm of water vapor during the MY34 GDS and 20-50 ppm around the perihelion point (L S =250°-290°) of MY34 and MY35 in both hemispheres. Our stormy retrievals at 100-120 km are of the same order of magnitude as MAVEN NGIMS results reported by [START_REF] Stone | Hydrogen escape from Mars is driven by seasonal and dust storm transport of water[END_REF] low water, corresponding to 2 ppm prescribed at 80 km in a non-GDS case; and high water, of 40 ppm in a GDS case [START_REF] Stone | Hydrogen escape from Mars is driven by seasonal and dust storm transport of water[END_REF]as corrected in March 2021). Notably, all the solar occultation observations performed by TGO and MEX to date [START_REF] Fedorova | Water vapor in the middle atmosphere of Mars during the 2007 global dust storm[END_REF](Fedorova et al., , 2020[START_REF] Fedorova | Multi-annual monitoring of the water vapor vertical distribution on Mars by SPICAM on Mars Express[END_REF][START_REF] Aoki | Water Vapor Vertical Profiles on Mars in Dust Storms Observed by TGO/NOMAD[END_REF][START_REF] Villanueva | Water heavily fractionated as it ascends on Mars as revealed by ExoMars/NOMAD[END_REF], including the present dataset (Fig. 3a), report It is important to consider how ACS's high altitude water vapor abundances combine with photolysis since this process has been hypothesized to be essential, if not the dominant, source for the H atoms observed in the exosphere [START_REF] Chaffin | Elevated atmospheric escape of atomic hydrogen from Mars induced by high-altitude water[END_REF]. The conclusion of [START_REF] Stone | Hydrogen escape from Mars is driven by seasonal and dust storm transport of water[END_REF] insists on the GDS's predominance and related ion chemistry in the H atoms' production. Our observations suggest that while the GDS period corresponds to the maximum of water abundance at 80 km, H 2 O at 120 km peaks only later, at the Southern summer solstice, when it is twice as large as during the GDS. This enhanced solstice maximum suggests that relative water abundance declines more rapidly above 80 km during the GDS than after, during perihelion (Fig. 4). The GDS curves are also indicated for MY35 to facilitate comparison.

In Figure 4, we combined altitude profiles from GDS-only (L S 195°-220°) and perihelion (L S 250°-295°) intervals to compare averaged vertical trends between them and to estimate an integral escape flux of the atomic hydrogen in each case. For that, we applied the model of [START_REF] Chaffin | Elevated atmospheric escape of atomic hydrogen from Mars induced by high-altitude water[END_REF], which predicts the atmospheric escape rate depending on the water injection into different altitudes (see Figure 3 of their paper). Our rough calculations show that the H escape flux is about 5.7×10 9 cm -1 s -1 during GDS for both hemispheres, while around perihelion point it is 4.0×10 9 cm -1 s -1 for the Northern Hemisphere and 6.0×10 9 cm -1 s -1 for the manuscript submitted to Geophysical Research Letters Southern one in both Martian Years. These values were derived when integrating the flux over altitudes from 20 to 120 km and in time intervals of 25 sols for GDS (L S 195°-220°) and 45 sols for perihelion (L S 250°-295°). Thus, we claim nearly equivalent contributions from a single GDS and the perihelion period into the hydrogen escape by the high water enrichment in the middle/upper atmosphere. [START_REF] Fedorova | Multi-annual monitoring of the water vapor vertical distribution on Mars by SPICAM on Mars Express[END_REF] come to a similar conclusion based on SPICAM/MEx water profiles up to 80 km. A GDS occurs every 3-4 martian years on average [START_REF] Zurek | Interannual variability of planet-encircling dust storms on Mars[END_REF][START_REF] Wang | The origin, evolution, and trajectory of large dust storms on Mars during Mars years 24-30[END_REF], and the yearly perihelion contribution to the hydrogen escape should prevail by a factor of ≥3.5. Moreover, the enhanced circulation and heating of the atmosphere in perihelion driven by the hemispheric dichotomy of Mars [START_REF] Richardson | Investigation of the nature and stability of the Martian seasonal water cycle with a general circulation model[END_REF] might be, in the long term, a more robust climate phenomenon rather than GDS, likely affected by changing obliquity of the planet [START_REF] Laskar | Long term evolution and chaotic diffusion of the insolation quantities of Mars[END_REF].

Overall, our results cannot be easily reconciled with water values inferred from NGIMS ion measurements, suggesting the thermosphere hosts much more water during the GDS than during the rest of the year. However, we note that the only time when [START_REF] Stone | Hydrogen escape from Mars is driven by seasonal and dust storm transport of water[END_REF] reported measurements around perihelion concerned the L S interval between 240° and 265° of MY33 (Figure 4 of [START_REF] Stone | Hydrogen escape from Mars is driven by seasonal and dust storm transport of water[END_REF]. It showed the same brutal trend as during the onset of the MY34 GDS, with values far exceeding those reported for the regional dust storm of MY32, still a factor of 3 smaller than during the GDS.

Our results remain in line with Fedorova et al. (2020[START_REF] Fedorova | Multi-annual monitoring of the water vapor vertical distribution on Mars by SPICAM on Mars Express[END_REF] conclusion about the perihelion season being the main conveyor of water to high altitudes on a long-term basis. A bridge between the ACS measurements presented here and NGIMS measurements leaves room for an additional or refined photochemical process that could link H 2 O relative abundances at 120 km with those inferred from NGIMS at 150 km. Both measurements bring unique constraints in our attempt to understand how the water in the lower atmosphere connects with the escaping hydrogen in the exosphere, an essential step before extrapolating the water escape back in time safely.

  ESSOAr | https://doi.org/10.1002/essoar.10506560.1 | CC_BY_NC_4.0 | First posted online: Mon, 5 Apr 2021 03:06:03 | This content has not been peer reviewed.

  ESSOAr | https://doi.org/10.1002/essoar.10506560.1 | CC_BY_NC_4.0 | First posted online: Mon, 5 Apr 2021 03:06:03 | This content has not been peer reviewed.

Figure 1 .

 1 Figure 1. Example ACS MIR spectra and profiles of the retrieved quantities. Measured transmission spectra (red) at tangent altitudes of 115.1 km (a) and 39.5 km (b) are compared with the best-fit models, including both CO 2 and H 2 O absorptions (black), and only CO 2 absorption (green). Blue arrows indicate water absorption lines. Zoom in (a) shows a part with the strongest H 2 O absorption detected at 115 km. (c) Retrieved vertical profiles of temperature (left), number densities (center), and H 2 O volume mixing ratio (VMR) (right). Black triangles mark H 2 O upper limits (see Supporting Information for the description of uncertainties).2.2 Data selectionTo reveal the upper mesospheric water we focused on the second halves of MY34 and MY35, which correspond to ACS MIR observations from May 2018 to March 2019 and from April 2020 to January 2021. The selected dataset comprises 187 occultation sessions in the

Figure 2 .

 2 Figure 2. Seasonal map of atmospheric temperature and H 2 O mixing ratio during the second half of MY34 and MY35. The data are plotted in function of L S and altitude for the Northern (left) and the Southern (right) hemispheres. (a) Latitudinal distribution of the ACS-MIR solar occultations, depending on an altitude level where the aerosol slant opacity (τ) equals 0.3. (b) Temperature. (c) Volume mixing ratio (VMR) of water vapor. Grey frames outline time intervals of the global dust storm (GDS) in MY34 and the two perihelions in MY34 (Per34) and MY35 (Per35).

  For both Martian Years, the maximum H 2 O mixing ratio was observed near the Southern summer solstice (L S ~270°), reaching values of 40-80 ppm at 80 km, 30-60 ppm at 100 km, and 20-50 ppm at 110-120 km. In the Northern winter solstice, it varied from 20 to 40 ppm at all ESSOAr | https://doi.org/10.1002/essoar.10506560.1 | CC_BY_NC_4.0 | First posted online: Mon, 5 Apr 2021 03:06:03 | This content has not been peer reviewed.

Figure 3 .

 3 Figure 3. Seasonal trends of H 2 O volume mixing ratio (VMR) at three altitude levels, 80, 100, 120 km. The season is the second half of MY34 (in blue) and of MY35 (in red). Each point corresponds to an individual vertical profile: weighted mean value obtained in between 110-120 km (a), and interpolated value for the levels of 100 km (b) and 80 km (c). Data at 80 km in grey (c) are taken from the ACS NIR profiles(Fedorova et al., 2020).

  at ~150 km. Surprisingly, NGIMS water relative abundances reveal a mission-wise maximum of H 2 O at 150 km during the MY34 GDS, whereas we repeatedly observe the annual maximum around the Southern summer solstice both in MY34 and MY35. NGIMS measures ions from which neutral H 2 O VMRs at 150 km were derived and injected into a 1D photochemical model. The model was adjusted to reproduce the H 2 O abundance at 150 km inferred from the [H 2 O + ] ions measured by NGIMS under two scenarios:

  ESSOAr | https://doi.org/10.1002/essoar.10506560.1 | CC_BY_NC_4.0 | First posted online: Mon, 5 Apr 2021 03:06:03 | This content has not been peer reviewed. manuscript submitted to Geophysical Research Letters even higher water vapor VMRs, of 50-80 ppm during the GDS. Stone et al. (2020) indicate a systematic uncertainty of 69% on their neutral H 2 O inference, which brings MAVEN, TGO, and MEX values to an agreement within error bars.

Figure 4 .

 4 Figure 4. Altitude profiles of average H 2 O volume mixing ratio (VMR) during the GDS (MY 34) and the perihelion season (MY 34, 35). The dataset used includes all ACS MIR observations highlighted in Fig. 2: GDS of MY34 (L S =195°-220°), brown average curve, and individual MIR detections; the bin around the perihelion point (L S =250°-295°) (blue). Upper panels: MY34 (a); lower panels: MY35 (b). The left and right panels are for the Northern and Southern hemispheres. Averaged profiles are presented with 1-sigma dispersion over 2-km altitude bins.

  ESSOAr | https://doi.org/10.1002/essoar.10506560.1 | CC_BY_NC_4.0 | First posted online: Mon, 5 Apr 2021 03:06:03 | This content has not been peer reviewed.

Acknowledgments, Samples, and Data

ExoMars is a joint space mission of the European Space Agency (ESA) and Roscosmos.

The ACS experiment is led by the Space Research Institute (IKI) in Moscow, assisted by LATMOS in France. Retrievals and analysis of temperature and water distributions in IKI are funded by grant #20-42-09035 of the Russian Science Foundation. The ACS MIR data are available from ESA's Planetary Science Archive at https://archives.esac.esa.int/psa/#!Table%20View/ACS=instrument. The retrieved data with altitude profiles of H 2 O VMR for the GDS and perihelion intervals are available at https://data.mendeley.com/datasets/995y7ymdgm/draft?a=daa72362-898d-4c86-8a13-023b4b59134c.