Océane Barraud

Sébastien Besse

Alain Doressoundiram

Thomas Cornet

Claudio Munoz

Spectral investigation of Mercury's pits' surroundings: Constraints on the planet's explosive activity

The understanding of volcanic explosive episodes on the surface of Mercury has important implications for the origin, history and inventory of Mercury's volatiles and for the thermal evolution of the planet. The hermean explosive features are pits, interpreted as endogenic pyroclastic vents often surrounded by bright and diffuse deposits, named faculae, and interpreted as pyroclastic material. We present a global spectroscopic survey of the surroundings of the listed endogenous pits, derived from spectra obtained by the Mercury Atmospheric and Surface Composition Spectrometer (MASCS/MESSENGER). The spectral properties of 26 faculae around endogenous pits were characterized. The diameter of 80% of them has been reassessed upwards by 17 km on average, implying volatile contents needed to emplace these deposits consequently higher than estimated in previous studies. These observations suggest a higher bulk volatile content or subsurface volatile enhancement. Spectral similarities between faculae located in the same crater indicate either a similar magmatic source or a large fraction of country rocks. The size, volatile content, location, and spectral properties of Nathair Facula seem to indicate an anomaly with respect to the other faculae that may be explained by a phreatomagmatic-like event by interaction between hot-magma and local carbon-rich layer.

Introduction

The remains of the hermean explosive activity were first observed by the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft on the edge of the Caloris basin [START_REF] Head | Volcanism on Mercury: Evidence from the first MESSENGER flyby[END_REF]. Subsequently, additional potential features were identified on impact crater floors and on smooth plains elsewhere [START_REF] Kerber | Explosive volcanic eruptions on Mercury: Eruption conditions, magma volatile content, and implications for interior volatile abundances[END_REF][START_REF] Kerber | The global distribution of pyroclastic deposits on Mercury: The view from MESSENGER flybys 1-3[END_REF]. The explosive features are represented on Mercury by pits and faculae. Pits are interpreted to be endogenic pyroclastic vents on the basis of their irregular and often elongated morphology and their lack of associated raised rim [START_REF] Pegg | Explosive vent sites on mercury: Commonplace multiple eruptions and their implications[END_REF]. Referred first as red-spots, faculae are high-albedo (compared to Mercury's average), spectrally red (increasing reflectance with increasing wavelength), and surficial deposits that have diffuse margins. Faculae with central pits are interpreted as pyroclastic deposits formed by the fragmentation and ejection of magma particles driven by volatile species released from rising magma [START_REF] Wilson | Ascent and eruption of basaltic magma on the Earth and Moon[END_REF]. Therefore, such faculae represent important sources of information about planetary physical and geochemical properties, including thermal history, interior structure and volatile budgets.

Since the first flyby of MESSENGER, several global mappings of explosive volcanic features, based on images from the Mercury Dual Imaging System (MDIS) have been done [START_REF] Kerber | Explosive volcanic eruptions on Mercury: Eruption conditions, magma volatile content, and implications for interior volatile abundances[END_REF][START_REF] Kerber | The global distribution of pyroclastic deposits on Mercury: The view from MESSENGER flybys 1-3[END_REF][START_REF] Goudge | Global inventory and characterization of pyroclastic deposits on Mercury: New insights into pyroclastic activity from MESSENGER orbital data[END_REF][START_REF] Jozwiak | Explosive volcanism on Mercury: Analysis of vent and deposit morphology and modes of eruption[END_REF]. The first catalogues were based on the concomitance between pits and the surrounding faculae. Thomas et al., (2014b) used a different approach by inventorying hermean endogenous pits even if they were not surrounded by faculae. They listed, first, 327 pits regrouped in 174 candidate endogenic pit sites, 150 of which possess a red spectral anomaly and high albedo in their surroundings. This number was reassessed to 353 pits in 184 pit sites by [START_REF] Thomas | Planet Mercury: volatile release on a contracting world[END_REF]. Around 79 % of pits surrounded by facula occur within an impact crater (Thomas et al., 2014b). This correlation may be the result of the easier ascent of the magma because of impact-induced fracturation and crustal weaknesses beneath the largest impact features (e.g., [START_REF] Klimczak | Open Questions on the Global Contraction of Mercury[END_REF]. Stratigraphic relationships, degradation state of the host impact craters and the datation of certain faculae suggest that the explosive volcanic activity on Mercury likely occurred over a substantial fraction of Mercury's geologic history, with the emplacement of some pyroclastic deposits from at least 3.9 Ga until less than a billion years ago [START_REF] Goudge | Global inventory and characterization of pyroclastic deposits on Mercury: New insights into pyroclastic activity from MESSENGER orbital data[END_REF]Thomas et al., 2014a).

Compositional information, derived from visible to near-infrared spectroscopic observations, as well as X-ray, neutron, and gamma-ray spectrometry, can be used to characterize the explosive activity of the planet as well as to make inferences about the nature and origin of the pyroclasts constituting the faculae. Spectral investigations of the faculae with the Mercury Atmospheric and Surface Composition spectrometer (MASCS) revealed, in addition to a red slope in the visible and high reflectance at 750 nm, a strong downturn of the reflectance in the ultraviolet [START_REF] Goudge | Global inventory and characterization of pyroclastic deposits on Mercury: New insights into pyroclastic activity from MESSENGER orbital data[END_REF]. [START_REF] Besse | Spectroscopic properties of explosive volcanism within the Caloris basin with MESSENGER observations[END_REF] investigated spectral properties of the faculae and demonstrated that, as on the Moon [START_REF] Jawin | Examining spectral variations in localized lunar dark mantle deposits[END_REF], they change as a function of distance to the central vent. [START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF] used these spectral variations to define the extent of 14 faculae at the surface of Mercury by using for each deposit the 3 best orbits of MASCS. They reassessed the radius of 65 % of the faculae analyzed upwards, and demonstrated the implications of these results on the volatile contents needed to drive explosive eruptions on Mercury.

Here we investigate the spectral properties of the surroundings of the endogenous pits listed by Thomas et al (2014b) and [START_REF] Thomas | Planet Mercury: volatile release on a contracting world[END_REF] with MASCS in order to extend the analysis done by [START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF]. All the MASCS available observations are used with the aim to better constrain the size and shape of the faculae. The spectral properties of the faculae are then analyzed and discussed to understand their composition and origin.

Search for spectral anomaly in the Mercury's pits' surroundings

The Visible and Infrared Spectrograph (VIRS) of the Mercury Atmospheric and Surface Composition Spectrometer (MASCS) instrument is a non-imaging point spectrometer operating between 300 and 1450 nm [START_REF] Mcclintock | The Mercury Atmospheric and Surface Composition Spectrometer for the MESSENGER mission[END_REF] with a spectral resolution of 5 nm. A visible (VIS) detector is sensitive to wavelengths that extend from 300 to 900 nm, and a near-infrared (NIR) detector to wavelengths between 900 to 1450 nm [START_REF] Mcclintock | The Mercury Atmospheric and Surface Composition Spectrometer for the MESSENGER mission[END_REF]. In this study, we used the VIRS Derived Data Record (DDR) data products available on the Planetary Data System (PDS). These data have been radiometrically and photometrically calibrated by the MESSENGER team. Additional processing, using the method developed by [START_REF] Besse | Spectroscopic properties of explosive volcanism within the Caloris basin with MESSENGER observations[END_REF], is applied to the data to combine the VIS and NIR data in a continuous spectrum from 300 to 1450 nm. A first step consists in removing the outliers deviating by more than 2 sigma. Only the most distant outliers are removed using this method, which represents less than 1% of the measurements by the VIS detector and less than 4% in the NIR [START_REF] Barraud | Near-ultraviolet to near-infrared spectral properties of hollows on Mercury: Implications for origin and formation process[END_REF]. In a second step, a moving average window of 3 points is applied to the entire VIS and NIR, reducing the scatter of the channel-to-channel reflectance. Finally, an offset is applied to the NIR to combine the two parts of the spectrum [START_REF] Besse | Spectroscopic properties of explosive volcanism within the Caloris basin with MESSENGER observations[END_REF]. The approach tested on lunar spectra by [START_REF] Besse | Spectroscopic properties of explosive volcanism within the Caloris basin with MESSENGER observations[END_REF] has been validated for observations of Mercury's surface.

Data selection and significance level

The average diameter of the faculae measured by [START_REF] Kerber | The global distribution of pyroclastic deposits on Mercury: The view from MESSENGER flybys 1-3[END_REF] is 46 km and by Besse et al., (2020) is 64 km. Thus, the MASCS/VIRS spectra are selected in a 100x100 km area around each pit (Thomas et al., 2014b[START_REF] Jozwiak | Explosive volcanism on Mercury: Analysis of vent and deposit morphology and modes of eruption[END_REF]. The dimension of the area is then adjusted if necessary. For example, the area around the pit centered (35.8°N, 63.8°E) in Nathair Facula [START_REF] Rothery | On the asymmetry of Nathair Facula[END_REF] is enlarged to a 400 km square to include the entire facula which is interpreted as the largest pyroclastic deposit on Mercury. The selection box is conversely reduced if the deposit radius is known to be smaller to optimise the computing time.

The selected observations are then filtered by instrument temperature and incidence angle. The NIR detector is more susceptible to increased background and noise from high temperatures [START_REF] Izenberg | The low-iron, reduced surface of Mercury as seen in spectral reflectance by MESSENGER[END_REF]. However, the effect of high temperature on MASCS/VIRS spectra is not fully characterized at this stage. Therefore, the data recorded in the highest temperature regime of the instrument (temperature exceeding 40°C) are discarded. High phase angles affect the detected spectral reflectance, which is more sensitive to local topography. In order to secure the comparison between faculae at different geographical locations, observations made at incidence angles greater than 75° have also been removed.

In each of the selected areas around the pits, a significance level (Table 1) for the analysis of spectral anomalies is established based on:

-The number of observations. First quality index Q 1 is the ratio between the number of footprints in the region and the number of footprints with the median spatial resolution of MASCS at the planet scale needed to cover the selected region. The median spatial resolution of the MASCS footprints is calculated from 3,677,857 filtered (temperature and incidence angle) observations and corresponds to 6 km². As an example, for a Q 1 equal to 100 % in an area of 10 000 km², the ideal number of evenly spaced footprints should be 1667. -The spatial coverage of MASCS footprints. A second quality index Q 2 corresponds to the ratio between the total coverage of the footprints in the region to the area of the region. -The spatial distribution of observations around the pit. The third and fourth quality index Q 3 and Q 4 evaluate the distribution of footprints respectively by concentric 10 km-wide rings and by 90° azimuth intervals around the vent (Figure 1). 1).

The black squares at the corners indicate the region used to define the local spectral properties of the background.

Depending on the values of the previously defined quality indexes (Table 1), the significance level (SL) is represented by a score between 1 and 5. Since its individual score can reach 2 (see Table 1), Q1 has more importance than the other quality indexes. If the SL is between 0 and 2, spectral analysis cannot be done with MASCS observations. If the SL is 3, spectral analysis can be done but the result must be treated with caution and validated visually. If the SL is equal to 4 or 5, the total number and spatial distribution of the observations ensure the proper analysis of a spectral anomaly. Given its spatial coverage and its average spatial resolution, a spectral anomaly in an area below 500 km² (10-12 km radius area) is difficult to properly analyze with MASCS (value arbitrarily defined). is the number of observations in the selected area. is the sum of the area 𝑁 𝐴 𝐴 𝑓𝑜𝑜𝑡𝑝𝑟𝑖𝑛𝑡𝑠 covered by the footprints. is the number of observations in the region i of the selected area 𝑁 𝑖 (Figure 1).

Quality index Mathematical formula Values

Equivalence in significance level

Q 1 𝑄 1 = 𝑁 𝐴 𝐴/6 Q 1 < 0.15 0.15 ≤ Q 1 < 0.45 0.45 ≤ Q 1 Q 2 𝑄 2 = 𝐴 𝑓𝑜𝑜𝑡𝑝𝑟𝑖𝑛𝑡𝑠 𝐴 Q 2 < 0.25 Q 2 ≥ 0.25 Q 3 (Fig. 1a) 𝑄 3 = 1 -𝑚𝑒𝑑𝑖𝑎𝑛 ⎡ ⎢ ⎣ ⎤ ⎥ ⎦ Q 4 < 0.5 Q 4 ≥ 0.5
Significance level 5/5

Spectral analysis

Based on previous studies [START_REF] Goudge | Global inventory and characterization of pyroclastic deposits on Mercury: New insights into pyroclastic activity from MESSENGER orbital data[END_REF], Besse et al., 2015, Besse et al., 2020), the slope in the visible (VIS), the downturn of reflectance in the ultraviolet (UV) and the absolute reflectance in the visible seem the best indicators for the presence of faculae. The spectral parameters used are summarized in Table 2. The absolute reflectance at 750 nm (R750) and at 575 nm (R575) are average values of 3 points due to the smoothing of the data [START_REF] Besse | Spectroscopic properties of explosive volcanism within the Caloris basin with MESSENGER observations[END_REF]. The slope parameters are normalized to the reference spectrum provided by [START_REF] Izenberg | The low-iron, reduced surface of Mercury as seen in spectral reflectance by MESSENGER[END_REF], who computed it from the average of 850,000 spectra of Mercury's surface. By definition, slopes are equal to 1 for the average surface of Mercury.

The spectral properties of pyroclastic deposits are known to change as a function of distance from their source on Mercury [START_REF] Besse | Spectroscopic properties of explosive volcanism within the Caloris basin with MESSENGER observations[END_REF], Besse et al., 2020). Therefore, to identify possible faculae around the pit, the spectral parameters are investigated in the selected area as a function of distance to the central pit. Some pits are located in terrains presenting spectral properties that differ from Mercury's mean surface. This is the case for pits located in the Caloris basin, which is spectrally different from Mercury's background [START_REF] Head | Volcanism on Mercury: Evidence from the first MESSENGER flyby for extrusive and explosive activity and the volcanic origin of plains[END_REF]. In order to eliminate the possible contribution of the background terrain, which could hinder the characterisation of the faculae, the spectral parameters are normalized by a local average. Observations located in 10 by 10 km squares at each corner of the selected area are used to define the local average (Fig. 1).

On the generic assumption that the faculae are mostly circular and centered on the pits, these regions are considered to be representative of the background material and free of pyroclastic material. If a corner area falls in a closed pit/faculae (as for the SW corner in Fig. 1), the observations are removed in this area. A faculae is recognized when at least the spectral parameters UV-downturn, VIS-slope and R750 are greater than the local mean close to the pit and decrease from the pit to a certain distance, interpreted as the limit of the facula, where they reach the local average.

𝑅 λ = 𝑆 𝑣𝑖𝑠 × λ + 𝑏

Global investigation

Global investigations of Mercury's pit surroundings reveal that 73 pit sites (with a total of 146 individual pits) were not sufficiently observed with MASCS to be analyzed in this study. This result is mainly due to the spatial coverage of the spectrometer. 88 pits lack data within a 10 km distance from the pit and the 58 other pits have a significance level lower or equal 2. 38 % (56) of the pits insufficiently observed with MASCS are located in the southern hemisphere compared to 61 % ( 215) for all pits (Figure 2). This result therefore confirms that the main factor limiting the study of pit surroundings is the spatial coverage which is lower in the northern hemisphere because of MESSENGER's highly eccentric orbit [START_REF] Solomon | MESSENGER mission overview[END_REF]. In addition, 77 pit sites (118 individual pits) do not display a spectral anomaly despite their good significance level (greater or equal to 3).

The 34 remaining pit sites (89 individual pits) display a spectral anomaly in near-ultraviolet to visible domains (Figure 2). We focused our analysis on these pits, in order to better understand the pyroclastic activity of Mercury. Among these pits, 61 (69 %) are in the southern hemisphere.

Figure 2:

Distribution of pits at the surface of Mercury. The pits' geographic locations are from Thomas et al. (2014b) and [START_REF] Jozwiak | Explosive volcanism on Mercury: Analysis of vent and deposit morphology and modes of eruption[END_REF]. The background map is the Basemap Reduced Data Record (BDR) from Mercury Dual Imaging System (32 pixels/degree, [START_REF] Denevi | Calibration, projection, and final image products of MESSENGER's Mercury Dual Imaging System[END_REF].

Analysis of faculae

The analysis of the faculae around the pits is done under the assumption that on an airless body, such as Mercury, the final shape of pyroclastic deposits is mostly circular and centred on the volcanic vent. In the case where the volcanic vent is considered as a single pit, it is relatively simple to determine the radius of the facula using the method developed by [START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF].

However, the proximity of some pits, involving an overlap of circular deposits, complicates their individual spectral analysis. Several assumptions are therefore taken into account depending on the proximity and arrangement of the pits within a pit site:

-When a pit site contains multiple pits close to each other, the pits were counted as a multiple/compound volcanic vent. The centre was defined to be in the centre of the pit site and the radius of the volcanic vent to encompass all the pits (Fig. S1a). -When the pits in a single pit site were sufficiently far apart from each other, they were considered as separate volcanic vents. This is for example the case for the pit site numbered 1047 by Thomas et al. (2020) in Praxiteles impact crater. The 3 pits identified are considered as 2 volcanic vents (1 simple vent and 1 compound vent) separated by 60 km (Fig. S1a). The pits from these two first categories are listed in Table 3. -When the pits of a pit site were not close enough to be considered as a unique volcanic vent but too close to be considered as separate vents, and when the pits could not be approximated by circles (Fig. S1b), the dimensions of the faculae could not be estimated. These pits are listed in Table S1 and need further individual study. They will not be mentioned in the rest of this study.

Extent of faculae 3.1.1. Nathair and Orm Faculae

Nathair Facula, which is the largest known facula on Mercury, and possibly in the inner Solar System, has been analyzed in detail by Thomas et al. (2014b), [START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF] and Rothery et al., (2021). Its radius is well constrained to about 140 km. In their study, [START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF] used 3 MASCS orbits which represent 604 footprints in this region, to characterize the extent of this facula. Here, Nathair Facula is investigated with 9917 footprints (44 orbits). While the parameters are normalized by Mercury's mean spectrum in the analysis of [START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF], here they are normalized by the local mean. As in [START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF], the linear decay of the spectral parameters from the volcanic vent to the edge of the deposit is used to define the radius of the deposit. A linear fit is adjusted to the normalized parameters VIS-slope, UV-downturn, R575 and R750. The radius is defined as the distance to the vent where the linear fit reaches the value of the local average (1 for the normalized parameters). Given the spatial resolution of MASCS and the diffuse character of faculae borders, the radius is estimated with an uncertainty of ± 5 km. In line with previous studies, the radius of Nathair Facula is estimated at 140 ± 5 km validating this mathematical approach (Fig. 3). Also, the radius of Orm Faculae (SW vent) in Praxiteles impact crater defined by [START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF] to 28 km is confirmed as 30 ± 5 km (Fig. 4). Using this method, 26 faculae have been measured around the volcanic pits listed in Table 3. Interestingly, [START_REF] Rothery | On the asymmetry of Nathair Facula[END_REF] demonstrated that the Nathair facula's midpoint is offset by 10-30 km northwards or northeastwards from the volcanic vent. This asymmetry is confirmed with the larger amount of data used here. Observations with an azimuth around 180°(south of the facula) lie below the linear regression line comprising all azimuths while observations with an azimuth around 0 or 360°(north of the facula) lie above this line (see Fig. 3). Therefore, the radius will be smaller in the south than in the north. Nathair Facula is the only one for which we were able to measure an asymmetry. 3) in Orm Faculae located within Praxiteles impact crater, presented in the same way as Fig. 3. The significance level is 4.

3.1.2.

Spectral measurement of facula size

The measured faculae are located over a latitudinal range between 60°S and 50°N and a longitudinal range between -165°E and 160°E. About three quarters of the measured faculae are located in impact craters. The analysis done here made it possible to refine, by including all data available, the radius calculated by previous analyses [START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF], [START_REF] Kerber | The global distribution of pyroclastic deposits on Mercury: The view from MESSENGER flybys 1-3[END_REF]. Slang Facula in the eastern part of the Caloris basin, which has a significance level of 2, was excluded from this analysis for reasons of global consistency in the spectral treatment between faculae (number and distribution of the data). Suge Facula was also excluded since it is categorized as a Red Pitted Ground by Thomas et al. (2014b). This texture is believed to arise from the sublimation of a volatile species within a young volcanic unit, rather than a primary volcanic explosion (Thomas et al., 2014b;[START_REF] Jozwiak | Explosive volcanism on Mercury: Analysis of vent and deposit morphology and modes of eruption[END_REF]. Of the 12 remaining faculae radii estimated by [START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF], 7 were confirmed within a ± 5 km range and 5 were reassessed upwards (by up to 12.5 km). Direct comparison of the extent measured in this study and area measured with multispectral data (MDIS) is complicated since the methodology is different. [START_REF] Kerber | The global distribution of pyroclastic deposits on Mercury: The view from MESSENGER flybys 1-3[END_REF] assumed that the facula was circular and centred on the volcanic vent and defined a radius, which is not the case in Thomas et al. (2014b) where they defined the area of the facula. Among the deposits analyzed by [START_REF] Kerber | The global distribution of pyroclastic deposits on Mercury: The view from MESSENGER flybys 1-3[END_REF], 80% have a radius that was reassessed upwards in this study by more than 5 km. The average faculae radius increase is about 17 km (78 % of the initial radius). The maximum reassessment is 24 km excluding Nathair Facula for which the radius is doubled. Assuming that the MASCS uncertainty is around 500 km² (10-12 km radius), 93% of the deposits measured here cover a larger area than estimated by [START_REF] Kerber | The global distribution of pyroclastic deposits on Mercury: The view from MESSENGER flybys 1-3[END_REF] and 55% compared to the areas estimated by Thomas et al. (2014b). However, direct comparison should be treated with caution as the areas determined by Thomas et al. (2014b) are not circular and sometimes contain several deposits in a single measurement. Seven faculae detected in Thomas et al. (2014b) have their radii determined for the first time in this study (Table . 3). A facula around the pit within the Neruda impact crater has been identified in this study (Fig. 5). The radius of the facula is estimated at 40 km. However, this facula was not mapped in multispectral analyses [START_REF] Kerber | The global distribution of pyroclastic deposits on Mercury: The view from MESSENGER flybys 1-3[END_REF] and Thomas et al. (2014b). The geographical locations of the faculae and their dimensions are not related. There is no correlation between radius of the faculae and crater host properties (diameter and degradation class) or vent size.

Table 3: Pits interpreted as volcanic vents with measurable faculae interpreted as pyroclastic deposit.

ID [START_REF] Kerber | The global distribution of pyroclastic deposits on Mercury: The view from MESSENGER flybys 1-3[END_REF][START_REF] Jozwiak | Explosive volcanism on Mercury: Analysis of vent and deposit morphology and modes of eruption[END_REF][START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF]Thomas et al., 2014b) Host

Implication of faculae's size reassessment on volatiles contents

The presence of volatiles within the interior of Mercury sufficient to drive explosive eruptions has crucial implications for the planet's formation scenario and its geochemical, physical and thermal evolution. The dominant volatiles expected to drive volcanic eruptions would depend on the initial composition of the planet, the reduction state of the mantle and the temperature and pressure conditions encountered during the rise of the erupting magma [START_REF] Kerber | The global distribution of pyroclastic deposits on Mercury: The view from MESSENGER flybys 1-3[END_REF]. Volatile species commonly encountered on Earth's magmas are H 2 O, CO 2 , SO 2 , H 2 S and HCl. In the chemical conditions of the mantle of Mercury, a combination of more reduced species is expected. Chemical equilibrium models suggest that CO, N 2 , S 2 , CS 2 , S 2 Cl, Cl, Cl 2 and COS may be among the most abundant volcanic gases on the planet [START_REF] Zolotov | On the chemistry of mantle and magmatic volatiles on Mercury[END_REF]). MESSENGER's XRS (X-ray spectrometer) and neutron spectrometer observations show that Nathair Facula is depleted in S and C compared with the rest of the surface [START_REF] Weider | Evidence from MESSENGER for sulfur-and carbon-driven explosive volcanism on Mercury[END_REF]. The authors interpreted this observation as the result of pyroclastic eruptions driven by volatiles originating from oxidation of graphite and/or sulfides in the subsurface magma [START_REF] Weider | Evidence from MESSENGER for sulfur-and carbon-driven explosive volcanism on Mercury[END_REF]. [START_REF] Kerber | The global distribution of pyroclastic deposits on Mercury: The view from MESSENGER flybys 1-3[END_REF] estimated abundances of CO, H 2 O, CO 2 SO 2 and H 2 S needed to create the pyroclastic deposits that they measured on the surface of Mercury. The horizontal distance reached by any ballistic particle is directly proportional to the released magma gas fraction [START_REF] Wilson | Relationships between pressure, volatile content and ejecta velocity in three types of volcanic explosion[END_REF][START_REF] Kerber | The global distribution of pyroclastic deposits on Mercury: The view from MESSENGER flybys 1-3[END_REF]. [START_REF] Wilson | Ascent and eruption of basaltic magma on the Earth and Moon[END_REF] determined that approximately 500 ppm of CO (eruption speed of 90 m/s) would be needed to emplace pyroclasts to a distance of 5 km on the Moon. It would take 2.3 times the amount of a particular volatile species to emplace to the same distance on Mercury due to the difference in gravitational acceleration at the surface [START_REF] Kerber | The global distribution of pyroclastic deposits on Mercury: The view from MESSENGER flybys 1-3[END_REF]. Following the same approach, we converted the equivalent proportion of volatiles needed to eject a pyroclast particle to the distance given by our faculae radii on Mercury. The volatile content obtained with this approach is based on the assumption that the measured facula was emplaced by a single event. However, if the vent is compound, as is likely on Mercury [START_REF] Rothery | Prolonged eruptive history of a compound volcano on Mercury: Volcanic and tectonic implications[END_REF], Pegg et al., 2021), the ballistic range from each eruption can be somewhat smaller than implied by the radius of the facula as a whole. On the other hand, if a facula is the result of one large event creating a deposit with the extent of the facula and several other small events creating multiple small faculae superimposed on the largest, the volatile content calculated here will be a minimum value. Results and comparison with the previously determined abundances of CO and H 2 S [START_REF] Kerber | The global distribution of pyroclastic deposits on Mercury: The view from MESSENGER flybys 1-3[END_REF] are displayed in Fig. 6.

Because the volatile content is proportional to the size of the faculae, the volatile content is, like the radii, increased on average by 78% compared to [START_REF] Kerber | The global distribution of pyroclastic deposits on Mercury: The view from MESSENGER flybys 1-3[END_REF]. The faculae reassessed here, if correctly interpreted as pyroclastic in origin, imply average volatile contents of 0.9 wt% CO, 1.4 wt% CO 2 , 0.6 wt% H 2 O, 1.1 wt% H 2 S or 2.1 w% SO 2 (Table S2). The spatial resolution of MASCS does not allow the study faculae smaller than 500 km 2 , so the average volatile content expressed here could be revised with future BepiColombo observations. Volatile contents of some arc and back-arc basaltic magmas on Earth, measured in melt inclusions, vary from 0.1 to 8 wt% H 2 O, 0 to 2100 ppm CO 2 and 300-6000 ppm S [START_REF] Wallace | Volatiles in subduction zone magmas: Concentrations and fluxes based on melt inclusion and volatile gas data[END_REF]. Melt inclusions from explosive deposits of the Bishop Tuff [START_REF] Wallace | Gradients in H2O, CO2, and exsolved gas in a large-volume silicic magma system: Interpreting the record preserved in melt inclusions from the Bishop Tuff[END_REF], the Tuff of Pine Grove [START_REF] Lowenstern | Major-element, trace-element, and volatile concentrations in silicate melt inclusions from the tuff of Pine Grove[END_REF], Mount Pinatubo (Wallace and Gerlach 1994) and Altiplano-Puna volcanic complex [START_REF] Schmitt | Gas-saturated crystallization and degassing in large-volume, crystal-rich dacitic magmas from the Altiplano-Puna, northern Chile[END_REF] reveal CO 2 contents that range from 10 to 1085 ppm and water contents between 2.8 wt% and 7 wt%. H 2 O contents measured on Earth are comparable (basaltic magma) or higher (rhyolitic magma) than those measured on Mercury. However, the highest values are from subduction settings where partial melting of the mantle is generated by the addition of water from the subducted oceanic crust into the mantle; such a process is unlikely to be comparable with those on Mercury. The actual gas driving the pyroclastic eruptions on Mercury will most likely be a combination of several volatiles, including S and C [START_REF] Weider | Evidence from MESSENGER for sulfur-and carbon-driven explosive volcanism on Mercury[END_REF]. CO 2 contents on Earth are lower than those necessary for the formation of faculae on Mercury. In particular for the extreme case of Nathair Facula where the CO 2 content, assuming that it is the only gas at the origin of the eruption, is up to an order of magnitude higher than those measured on Earth. The size of the faculae and the resulting volatile contents in magmas support the point that Mercury's interior is far more enriched in volatile species than had been thought. Such a result may favor a formation history that allows for the accretion of volatile-rich planetesimals [START_REF] Kerber | Explosive volcanic eruptions on Mercury: Eruption conditions, magma volatile content, and implications for interior volatile abundances[END_REF] or perhaps the consequence of magma storage in the shallow subsurface (Thomas et al., 2014b). [START_REF] Goudge | Global inventory and characterization of pyroclastic deposits on Mercury: New insights into pyroclastic activity from MESSENGER orbital data[END_REF] emphasized the spectral variability between faculae in the near-ultraviolet to visible. In order to better investigate this variability, the spectral properties of the 26 measured faculae are compared together. However, this work should be done carefully since the spectral parameters change as a function of distance to the vent. A way to minimize the issue due to this intrinsic variability is to take the spectral properties of the faculae at a similar location from their vents [START_REF] Besse | Spectroscopic properties of explosive volcanism within the Caloris basin with MESSENGER observations[END_REF]. As in [START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF], the spectral properties of the faculae are taken at the midpoint between the limit of the vent and edges of the facula. In order to compare the spectral properties of the faculae at global scale, the values of the spectral parameters are no longer normalized by the local mean.

Spectral variability of the faculae

The fact of not reducing the analysis to 3 MASCS orbits and thus increasing considerably the number of observations for the faculae has slightly modified the values of the spectral parameters in the near-UV to visible already calculated by [START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF] (Fig. 7). However, the range of UV-downturn and VIS-slope of these faculae remains globally the same (see black rectangle in Fig. 7). By increasing the sample studied (12 to 26), the spectral variability of the faculae also increased. Previously, [START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF] mentioned that the faculae were easily distinguishable from the mean surface of Mercury thanks to their VIS-slope and UV-downturn always respectively higher than 1 or 3.1. This characteristic is no longer valid since the faculae located in Neruda, Unnamed crater 5c and Enheduanna impact craters and the faculae named "No name 4" have a VIS-slope lower than 1. The UV-downturn remains higher than 3.1 for the faculae except for the facula in Neruda impact crater which has a UV-downturn egal to 3.1. [START_REF] Izenberg | The low-iron, reduced surface of Mercury as seen in spectral reflectance by MESSENGER[END_REF] and an averaged floor spectra of the Hesiod region [START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF]. The black rectangle shows the range of values in figure 6 of [START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF].

The faculae are not systematically brighter (at the midpoint of the deposit) than the average surface of Mercury. The parameters R750 (Fig. 8a) and R575 are in several cases lower than the value of the reference spectrum of Mercury. Finally, what differentiates the pyroclastic deposits are their spectral properties in relation to the local spectral properties, i.e. the surrounding terrain.

For most of the faculae, the UV-downturn ranges, at the midpoint, between 3.15 and 3.35 (Fig. 8), the VIS-slope between 0.8 to 1.2 and the R750 between 0.04 and 0.06. Nathair Facula with a R750 and VIS-slope parameters, at the midpoint of the facula, of respectively 0.072 and 1.65 appears as an end member in the visible. The facula in the Neruda impact crater is also an endmember, with the minimum value of VIS-slope, R750 and UV-downturn. These low values compared to the other faculae could explain why the facula was not mapped with the MDIS data.

The spectral properties of the faculae are not correlated with other parameters such as geographic location, size of the facula, diameter of the crater host and size of the vent. In particular, the spectral parameters are not related to the degradation class of the host craters, which fixes an upper limit on the age of the faculae. Space-weathering affects spectral properties of lunar soils by darkening and reddening the spectrum at visible to near-infrared wavelengths [START_REF] Mccord | Progress in remote optical analysis of lunar surface composition[END_REF][START_REF] Fischer | Remote determination of exposure degree and iron concentration of lunar soils using VIS-NIR spectroscopic methods[END_REF]. However, recents study [START_REF] Jozwiak | Investigating the Unexpected Youth of Mercury's Pyroclastic Deposits[END_REF] of vent morphologies reveals that the most degraded vents on Mercury are not constrained to the most degraded host craters. A comparison between vents degradation class and spectral properties of faculae seems therefore more appropriate to determine the contribution of space-weathering to the spectral properties of faculae.

The faculae that are located within the same impact crater present very close values of spectral parameters (Fig. 8). The vents in the Lermontov impact crater are separated by about 60 km. However the radii of the faculae around each of these vents are 55 and 45 km (Table 3). Thus, the faculae could be superimposed in some places, contributing mutually to the spectral properties of the other. However, this hypothesis is refuted for the faculae within the Caloris basin and Praxiteles impact crater. The vents of RS-03 SW and Agwo Facula are located about 40 km from each other. Since the faculae have radii of 35 and 45 km, mixing between the two may well have occurred. But in the case of RS-04b, the facula cannot be superimposed on the other two because the pits are separated by about 500 km. The close spectral properties of Agwo, RS-03 SW, and RS-04b are therefore not due to a mixing between the faculae.

Discussion

Fraction of juvenile magma in faculae

The similarity in spectral properties between faculae in the same impact crater (Fig. 8) could be explained by (1) the composition of the magma or (2) by large contribution of the country rocks in spectral properties.

The closed spectral properties of the faculae in the same host crater could be the result of a similar magmatic source producing faculae with the same composition. For example, lunar pyroclastic deposits in Lavoisier (70 km in diameter) and Lavoisier F impact craters share similar spectral features, indicating similar mineralogical compositions and possibly the same volcanic origin [START_REF] Souchon | Local spectrophotometric properties of pyroclastic deposits at the Lavoisier lunar crater[END_REF]. Here, we propose, for Caloris basin, Praxiteles and Lermontov impact craters that a dike propagates to a shallow subsurface, forms a sill/laccolith leading to several other dikes propagating to the surface and generating pyroclastic features. In the case of the Caloris basin, where the faculae are separated by 500 km, the laccolith does not need to extend over similar dimensions. Globally the lithosphere of Mercury has been under a contractional tectonic regime for most of its history [START_REF] Byrne | Mercury's global contraction much greater than earlier estimates[END_REF]. Under contractional tectonic regimes, magma preferentially migrates horizontally to form sills and laccolith rather than vertically [START_REF] Sibson | Brittle-failure controls on maximum sustainable overpressure in different tectonic regimes[END_REF]. If the magma ascends along pre-existing weaknesses in the lithosphere, such as thrust fault and fractures associated with impact structures (Caloris basin), magma propagation is not necessarily vertical.

The three deposits analyzed in the Caloris Basin (RS-03b, Agwo and RS-04b) have different volatile content, ranging from 5800 to 10400 ppm CO (Fig 6). On Earth, it is observed that different content in volatiles can be achieved by fractional crystallization during magma storage at shallow levels [START_REF] Fowler | Phase equilibria trigger for explosive volcanic eruptions[END_REF]. The three Caloris deposits could therefore have been emplaced at different times (different degrees of fractional crystallization), explaining why they have different volatile contents. However, fractional crystallization implies different mineralogical compositions between the lava forming the three faculae. In this case, a spectral difference could be observed. Moreover, on the Moon, formation of sill/laccolith produces an uplifted/domed floor and concentric and/or radial floor fractures. This is the formation mechanism of lunar floor fractured craters and Lavoisier impact crater is one of them [START_REF] Schultz | Floor-fractured lunar craters[END_REF][START_REF] Jozwiak | Lunar floor-fractured craters: Classification, distribution, origin and implications for magmatism and shallow crustal structure[END_REF]. On Mercury, there is no evidence for such craters that host pyroclastic vents. The Caloris basin hosts an extensional system composed of a radial fracture network, Pantheon fossae, which may be formed in response to upwelling beneath the basin [START_REF] Head | Volcanism on Mercury: Evidence from the first MESSENGER flyby for extrusive and explosive activity and the volcanic origin of plains[END_REF]. However, [START_REF] Klimczak | Evaluation of the origin hypotheses of Pantheon Fossae, central Caloris basin[END_REF] demonstrated that the graben are not consistent with intrusive magmatic formation. Based on these arguments and morphological analyzes, [START_REF] Jozwiak | Explosive volcanism on Mercury: Analysis of vent and deposit morphology and modes of eruption[END_REF] suggested a dike-venting model as formation geometry for the majority of hermean pyroclastic vents.

The spectral similarities between faculae in the same impact crater may also be due to a low fractions of juvenile (magmatic) material in the faculae. If the magmatic sources and/or the magmatic differentiation (fractional crystallization during magma storage) are different for faculae in the same impact crater, their similarities in spectral properties could be due to the fraction of country rocks. The mixing between juvenile and country rock materials could occur in several ways: during magma ascent, during emplacement of ballistic particles, and/or after pyroclastic emplacement by impact cratering and gardening. The proportion of non juvenile material in the faculae could vary a lot. The juvenile magma may be mainly composed of gas and a very small amount of melt. In this case, the faculae will be mostly composed of country rocks fragmented during the eruption of high-velocity rising gas. The spectral contrast with the surroundings will therefore be due to the physical properties of the material such as grain size rather than compositional differences. Phase-ratio images of Agwo faculae reveal that the pyroclastic deposit is characterized by smoother sub-resolution texture or smaller particles than adjacent background terrain [START_REF] Blewett | Phase-ratio images of the surface of Mercury: Evidence for differences in sub-resolution texture[END_REF]. Topographic data (Thomas et al., 2014b) and modelling (Bröz et al., 2018) suggested that faculae are composed of a very gentle blanket of pyroclasts. Thus, the high volatile content and the possible limited eruption volume support the hypothesis of a low fraction of juvenile magma compared to country rocks in faculae. In addition, the facula in the Neruda impact crater (Fig 5 ) with the lowest values of VIS-slope, UV-downturn and R750 (Fig. 8) is in a representative area of LRM [START_REF] Klima | Global distribution and spectral properties of low-reflectance material on Mercury[END_REF]. LRM is known to have values of R750, UV-downturn and VIS-slope parameters generally lower than Mercury's mean surface (Barraud et al., 2020). This also reinforces the hypothesis of a low proportion of juvenile magma in the facula compared to the proportion of country rocks contributing predominantly to its spectral properties.

Eruptive style

Mercury's pits are incised into bedrock and are surrounded by low-relief deposits. Based on these morphological characteristics, Thomas et al. (2014b) suggested that hermean pits and deposits are similar to maars on Earth resulting from phreatomagmatic eruption (interaction between rising magma and non magmatic volatiles). The XRS and GNRS measurements revealed that the surface of Mercury is volatiles-rich, in particular with relatively high abundances of S and C [START_REF] Nittler | The major-element composition of Mercury's surface from MESSENGER X-ray spectrometry[END_REF]. Thus, the hypothesis that Mercury's explosive features are formed by a process comparable to phreatomagmatism seems compatible. Hermean phreatomagmatic eruption may be involved by interaction between rising magma and S or C-rich layer.

Phreatomagmatic events are characterized by high degree of explosivity, wide dispersal of deposits, and high degree of fragmentation of the lava [START_REF] Walker | Explosive volcanic eruptions -a new classification scheme[END_REF]. Nathair Facula is the most widely dispersed faculae on the surface of Mercury (Table 3). In addition to its dimensions, Nathair Facula appears as an end-member in terms of spectral parameters (Fig. 8). Its high reflectance value at 750 nm could be explained by a difference of physical properties. Indeed, when the grain size decreases the reflectance increases [START_REF] Crown | Spectral properties of plagioclase and pyroxene mixtures and the interpretation of lunar soil spectra[END_REF]. On Earth, the proportion of pyroclasts with a size lower than 1 mm in phreatomagmatic products can reach 100%. Thus, we propose that Nathair Facula is the result of phreatomagmatic-like events having caused wider dispersion and higher degree fragmentation of the material than for the other faculae. In many terrestrial maar formations, the country rock is the predominant constituent of the erupted mass where the juvenil material makes up a small portion [START_REF] White | Maar-diatreme volcanoes: A review[END_REF]. Therefore, the Nathair Facula formation hypothesis is consistent with our earlier hypothesis that the faculae on Mercury's surface could consist of a large portion of country rocks.

A difference in elemental composition is observed between the Nathair Facula and its surrounding terrain; the facula is depleted in S and C [START_REF] Weider | Evidence from MESSENGER for sulfur-and carbon-driven explosive volcanism on Mercury[END_REF]. However, this difference may be, as originally reported by Thomas et al. (2014b), induced by the loss of volatile elements rather than by a compositional difference with the country rocks. If the formation of the explosive features (vent and facula) occurs by interaction between hot-magma and initially sulfur-and/or carbon-rich country rock, sulfur or carbon may have been changed to gaseous compounds during the eruption.

LRM regions measured by neutron spectroscopy [START_REF] Peplowski | Remote sensing evidence for an ancient carbon-bearing crust on Mercury[END_REF] are carbon-rich compared to Mercury's mean surface. Mercury's extreme mantle composition may have led to primary graphite flotation crust production that was subsequently covered by secondary magmas [START_REF] Vander Kaaden | Exotic crust formation on Mercury: Consequences of a shallow, FeO-poor mantle[END_REF]. This graphite layer would then be excavated on the surface by impact events forming the visible LRM. [START_REF] Klima | Global distribution and spectral properties of low-reflectance material on Mercury[END_REF] reported a relationship between a 600-nm band depth observed in multispectral MDIS data and carbon content as derived from neutron spectroscopy measurements, which can be used to estimate carbon enrichment of LRM. Typical LRM exposures contain an excess of 2-2.5 wt% carbon but LRM related to Basho and Rachmaninoff craters have higher excess carbon (>4 wt%, perhaps up to 4.5 wt%) [START_REF] Klima | Global distribution and spectral properties of low-reflectance material on Mercury[END_REF]. Nathair Facula lies about 200 km beyond the northeast rim of the Rachmaninoff crater. Therefore, the ascent of a magma at this location where the subsurface seems unusually rich in carbon may have generated a phreatomagmatic eruption. This result explains why Nathair Facula is an end-member in terms of spectral properties, dimensions and volatile content. The magmas at the origin of the other pyroclastic deposits on the surface of Mercury would not have crossed a layer as rich as the one present at the Rachmaninoff crater, leading to such a high energetic eruption.

Conclusions

The results of the spectral investigation of Mercury's pit's surroundings with MASCS/MESSENGER are:

-At least 25 % of the pits are related to faculae. Using the linear decrease of three spectral parameters: the UV-downturn, the slope in the visible and the reflectance at 750 nm, we estimated the radius of 26 faculae. 80 % of the radii were reassessed upwards in this study by more than 5 km (on average 17 km). As the radius, estimates of the volatile contents needed to emplace faculae were on average reassessed upwards by 78 % from previous analysis. The volatile mass fractions are in many cases comparable or greater than those found in explosive products on Earth. Although it is admitted today that Mercury is not depleted in volatiles as thought before MESSENGER, the explosive activity of the planet seems to have been underestimated.

-The spectral properties of faculae located in the same host crater are relatively similar suggesting that these faculae are dominated by country rocks. Magmas at the origin of the Hermean explosive eruptions may be mainly composed of gas with a small fraction of melt. Faculae are not always brighter and redder than Mercury's mean surface but rather than their local surroundings. The difference in spectral properties between faculae and country rocks could be related to variations of grain size between fragmented and not fragmented country rocks, or as in the case of Nathair Facula by volatilization of sulfur-rich and/or carbon-rich substrates.

-The extreme spectral properties of Nathair Facula, especially in the visible, could be induced by a high degree of fragmentation of the pyroclasts, characteristic of a phreatomagmatic-like process. Moreover, the widely dispersed deposit and the extreme volatile content of Nathair Facula are consistent with phreatomagmatic events, produced by interaction between hot magma and a possible subsurface layer locally enriched in carbon. This hypothesis is in agreement with our proposition that country rocks are predominant in faculae on Mercury, since the phreatomagmatic products on Earth are composed of a small portion of juvenil material.

Our analysis also revealed that the low spatial coverage of MASCS is an important shortcoming for the study of explosive volcanism from a spectral point of view as 60% of the pits' surroundings are not covered or not covered enough to be studied consistently with MASCS. Future observations with BepiColombo should certainly solve some of these issues. The global coverage at 480 m/pixel by the hyperspectral imager VIHI (Visual and Infrared Hyperspectral Imager) from the instrumental suite SIMBIO-SYS (Spectrometer and Imaging for MPO BepiColombo Integrated Observatory SYStem; [START_REF] Cremonese | SIMBIO-SYS: Scientific Cameras and Spectrometer for the BepiColombo Mission[END_REF] will allow a detailed spectral analysis of a larger sample of faculae. It would be useful, with future observations of SIMBIO-SYS at different phase angles and of the MERTIS (Mercury Radiometer and Thermal Infrared Spectrometer, [START_REF] Hiesinger | The Mercury radiometer and thermal infrared spectrometer (MERTIS) for the BepiColombo mission[END_REF] spectrometer, to define the degree of fragmentation of the material constituting the faculae, in order to better constrain the eruptive style. Moreover, determination of composition, volume and volcanic glass content of the faculae using a combination of measurements from VIHI, MERTIS, the BepiColombo Laser Altimeter (BELA), the Gamma-Ray and Neutron Spectrometer (MGNS) and the Mercury Imaging X-Ray spectrometer (MIXS) should provide important constraints on Hermean's explosive activity [START_REF] Rothery | Rationale for BepiColombo studies of Mercury's surface and composition[END_REF].

Figure 1 :

 1 Figure 1: Area (100 km square) selected around a pit in Praxiteles impact crater (26.85°N; 59.18°W). The pit is surrounded by a white circle. a) Distribution of the 10 km intervals around the pit. The number of intervals depends on the size of the selected area. b) Distribution of the 90°azimuth intervals around the pit. N i is the number of observations in the colored region (Table1).The black squares at the corners indicate the region used to define the local spectral properties of the background.

Figure 3 :

 3 Figure 3: Variability of the spectral parameters in Nathair Facula. The selected area is a 200 km square and the significance level is 5. The top three panels represent plan views with footprints color-coded based on the strength of normalized spectral parameters. North is up, corresponding to azimuth 0°or 360°. The background map is the Basemap Reduced Data Record (BDR) from Mercury Dual Imaging System (166 m/pixel,[START_REF] Denevi | Calibration, projection, and final image products of MESSENGER's Mercury Dual Imaging System[END_REF]. The black squares at the corners indicate the region used to define the local spectral properties and normalize the parameters. The lower three panels display the evolution of each spectral criterion with respect to distance from the vent centre, color-coded based on the geographical azimuth from the vent centre. The white and grey circles in the top panels, and the corresponding vertical lines in the lower panels, indicate respectively the limit of the vent and the limit of the facula calculated in this work.The black line in each of the bottom plots is a linear regression line. Points within the circle encompassing the vent were excluded from the regression analysis.

Figure 4 :

 4 Figure 4: Variability of the spectral parameters around the pit n°5 (Table3) in Orm Faculae located within Praxiteles impact crater, presented in the same way as Fig.3. The significance level is 4.

Figure 5 :

 5 Figure 5: Comparison between MASCS and MDIS data. a) Variability of the spectral parameters around the pit n°13 (Table 3) within Neruda impact crater, presented in the same way as Fig. 3. b) MDIS monochrome mosaic (left, 166 m/pixel), 3-color mosaïc (center, R:1000 nm, G:750 nm and B:430 nm, 665 m/pixel) and enhanced color mosaïc (right, R:second principal component, G:first principal component, and B:430/1000 nm ratio, 665 m/pixel) of the Neruda impact crater. The mosaics are from[START_REF] Denevi | Calibration, projection, and final image products of MESSENGER's Mercury Dual Imaging System[END_REF].

Figure 6 :

 6 Figure 6: Magmatic content of CO (top) or H 2 S (bottom) needed to form the measured faculae on Mercury, under the assumption that CO or H 2 S was the only driving volatile. The error bars, related to the uncertainty to the radius (± 5 km), correspond to 1150 ppm CO and 1400 ppm H 2 S.

Figure 7 :

 7 Figure 7: UV-downturn versus VIS-slope at the midpoint of the 26 measured faculae. The spectral parameters are absolute values and are not normalized by the local mean. The bars represent the standard deviation of all the MASCS observations in each facula. Histograms show the distribution of the data within the diagram. The black dashed lines at 3.0 and 3.1 respectively represent the Mercury mean spectrum[START_REF] Izenberg | The low-iron, reduced surface of Mercury as seen in spectral reflectance by MESSENGER[END_REF] and an averaged floor spectra of the Hesiod region[START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF]. The black rectangle shows the range of values in figure6of[START_REF] Besse | Spectral properties and physical extent of pyroclastic deposits on Mercury: Variability within selected deposits and implications for explosive volcanism[END_REF].

Figure 8 :

 8 Figure 8: Parameter spaces for the 26 measured faculae in the visible and ultraviolet domains. The values of the spectral parameters are absolute and are not normalized by the local mean. The black dashed lines represent the Mercury mean spectrum (Izenberg et al., 2014). The bars represent the standard deviation of the MASCS observations in each facula. The color code represents the host crater diameter (km). Histograms show the distribution of the data within the diagrams. The three yellow dots correspond to deposits located in Caloris basin, the two orange and the two pink/red are the deposits located respectively in Praxiteles and Lermontov impact craters. a) UV-downturn versus R750 at the midpoint of the facula. b) UV-Downturn versus VIS-slope at the midpoint of the facula. The R750 and the VIS-slope are linearly correlated (Pearson coefficient correlation of 0.98, at 99.9%) but it may be related to the mathematical definition and the overlapping wavelength range between the parameters.

Table 1 :

 1 Definition of quality indexes and significance level.

	𝐴	corresponds to the area of the

Table 2 :

 2 Mathematical formulas of spectral parameters used to detect and analyze the spectral anomalies linked to faculae. is the absolute reflectance at the wavelength λ.

		𝑅	λ
	Parameter	Spectral range (nm) Mathematical definition
	UV-downturn			𝐷𝑒𝑝𝑡ℎ	303 + 𝐷𝑒𝑝𝑡ℎ	324 + 𝐷𝑒𝑝𝑡ℎ	350
	(Goudge et al., 2014)		300-400	where, 𝐷𝑒𝑝𝑡ℎ λ = 𝑅 ⎡ ⎢ ⎢ ⎣	401 -(401 -λ)	𝑅 750 -𝑅 445 750-445	⎤ ⎥ ⎥ ⎦	/𝑅 λ
	R575		570-580			𝑅	575
	R750		745-755			𝑅	750
	VIS-slope ( ) 𝑆 𝑣𝑖𝑠		445-750

Table S2 :

 S2 Magmatic abundances (ppm) of most probable volatile species required to emplace the measured faculae. The uncertainties related to the uncertainty of the radius (± 5 km) correspond to 1150 ppm CO, 1800 ppm CO 2 , 2700 ppm SO 2 , 700 ppm H 2 O and 1400 ppm H 2 S.

		CO		CO 2	SO 2	H 2 O	H S
		Kerber		Kerber		Kerber		Kerber		Kerber
		et al.,	This	et al.,	This	et al.,	This	et al.,	This	et al.,	This
	Crater/Facula Name	(2011)	study	(2011)	study	(2011)	study	(2011)	study	(2011)	study
	Mistral SE	4300	6900 6800	11000	9900	16600	2800	4800	5600
	Mistral NW	2600	5800 4100	9200	6000	13800	1700	4000	3300
	Lermontov NE	7600 10000 12000	16600	17000	24800	4900	7200	9800
	Lermontov SW	7200 12700 11000	20200	17000	30400	4700	8900	9300
	Praxiteles SW/Orm	4100	6900 6500	11000	9400	16600	2700	4800	5300
	Praxiteles NE/Orm	600	6900 9400	11000	14000	16600	3800	4800	7700

Acknowledgements

The authors thank the two anonymous referees for helpful comments at the review stage. The authors acknowledge the Centre National des Etudes Spatiales (CNES) for continuous and long term support. O. Barraud acknowledges the support of the European Space Astronomy Centre (ESAC) faculty council for funding a visit to ESAC as part of this work.

Data availability

The data used in this work are available at the PDS Geosciences Node of Washington University, St. Louis, MO, USA. The dataset used contains the latest calibration provided by the MESSENGER science team. (https://pds-geosciences.wustl.edu/messenger/mess-e_v_h-mascs -3-virs-cdr-calda-ta-v1/messmas_2101/data/ddr/)

SUPPLEMENTARY MATERIALS

Spectral investigation of Mercury's pits surroundings: Constraints on the planet's explosive activity

Authors: Océane Barraud 1 (corresponding author), Sébastien Besse 2 , Alain Doressoundiram 1 , Thomas Cornet 2 and Claudio Munoz 2 .


J K Mohanta

S Mohan

P Wenger

C Chevallereau
email: christine.chevallereau@ls2n.fr

A New Sitting-type Lower-Limb Rehabilitation Robot based on a Spatial Parallel Kinematic Machine

Keywords: Lower limb rehabilitation robot, Orthoglide, foot-plate based, parallel manipulator, passive orthosis

This paper proposes a lying/sittingtype lower-limb rehabilitation robot based on a three degrees of freedom spatial parallel kinematic manipulator namely "The Orthoglide" along with an actuated rotational degree of freedom at the endeffector for the purpose of lower-limb rehabilitation treatments. This rehabilitation robot is an end-effector/foot-plate based mechanism which controls the ankle-joint movements to assist physiotherapists in performing therapeutic treatments along with a passive orthosis (supporting system). The conceptual and detail design of the rehabilitation device is presented along with its kinematics. Further, the functional validation of the proposed robot in terms of the kinematic motion capabilities to provide physiological motions like knee flexion-extension, hip adduction-abduction and hip flexion-extension are also investigated. The required safety features for the proposed rehabilitation robot in terms of mechanical constraints and non-actuated joints are also discussed.

Introduction

Lower limb treatments using mechanized systems has improved the speed of recovery of patients from the bedridden state [START_REF] Diaz | Lower-limb robotic rehabilitation: Literature review and challenges[END_REF]. The lower limb impairments are caused by motor nerves dysfunction, which are generally caused by spinal cord injury (SCI), stroke and accidental disability. Continuous physical motion of the impaired limb, known as motor rehabilitation, required for this process [START_REF] Johnson | Robot assisted neurological rehabilitation at home: motivational aspects and concepts for tele-rehabilitation[END_REF]. These are done in numerous ways for example with a body weight support (BWS), using supportive orthosis, using foot-pate motion and limb motion in sitting/lying posture. The sitting/lying treatments are appropriate for the bedridden patients. Example of sitting/lying type systems are the ANKUR-LL2 [START_REF] Mohanta | Development and control of a new sitting-type lower limb rehabilitation robot[END_REF], an improved Lambda [START_REF] Akdoğan | The design and control of a therapeutic exercise robot for lower limb rehabilitation: Physiotherabot[END_REF], the Supine [START_REF] Mohanta | Kinematic analysis of a passive sitting/lying type lower limb rehabilitation robot[END_REF], Physiotherabot [START_REF] Mohan | Design, development and control of a 2PRP-2PPR planar parallel manipulator for lower limb rehabilitation therapies[END_REF], the Lambda [START_REF] Lim | A supine gait training device for stroke rehabilitation[END_REF] and the ANKUR-LL1 [START_REF] Bouri | A new concept of parallel robot for rehabilitation and fitness: The Lambda[END_REF].

Lower limb mechanisms with high mechanical advantage joints, outfits the system with a self-locking capability, which helps in case of emergency stop [START_REF] Wang | A novel leg orthosis for lower limb rehabilitation robots of the sitting/lying type[END_REF]. Structures of the mechanisms consist of bulky actuators and system appears dynamically heavy. To avoid such difficulty a passive light-weight orthosis, with no actuators, is used along with joint feedback sensors [START_REF] Akdoğan | The design and control of a therapeutic exercise robot for lower limb rehabilitation: Physiotherabot[END_REF]. Here the orthosis is indirectly controlled.

Rehabilitation devices are generally having motion in sagittal plane [START_REF] Diaz | Lower-limb robotic rehabilitation: Literature review and challenges[END_REF]. Although many therapies need off-planar movements but complexity of the arrangement and safety of the patient is major concern. In this direction a device namely Hipbot [START_REF] Guzmán-Valdivia | HipBot -The design, development and control of a therapeutic robot for hip rehabilitation[END_REF] is designed to give off-planar motions to the lower limbs, when the patient is in lying posture. Still Hipbot is having limitation that it can give adduction-abduction away from the body not towards the body because of physical limitations. To address this issue a new manipulator configuration is proposed. The major difficulty in off-planar movement is movement of the actuator assembly as they are mounted in single plane. So, here we have used a parallel manipulator based mechanism with passive orthosis which can render four degrees of freedom to the lower limb.

The rest of the paper is organized as follows:Section 2 discusses the architecture of the proposed rehabilitation robot and its geometrical aspects. Section3 describes thesystemkinematics, Section 4 demonstrates the physiological motion validation of the proposed manipulator and section 5 concludes the paper with safety aspects and scope of future works.

Proposed Manipulator's Architecture

The proposed rehabilitation robot shown in Figure 1 consists of a driving mechanism and a passive orthosis. The driving mechanism is made using the concept of a parallel manipulator namely "The Orthoglide" [START_REF] Chablat | Architecture optimization of a 3-DOF translationalparallel mechanism for machiningapplications, the Orthoglide[END_REF]. Instead of an overhead structure a modified version with actuators on ground is taken for usage in rehabilitation purpose.

Here three linear joints are placed orthogonally and three links with each leg having configuration PUU is connecting to the end-effector. The orthosis consists of three links corresponding to the thigh, crus and foot of the limb with a vertical hip joint. These three links are joined in series at the hip, knee and ankle positions, with rotary joint. The solid model of the proposed orthosis is shown in Figure 2. The passive orthosis can be seen in Figure 1. Forward kinematics for the passive orthosis is as follows:

          1 1 2 3 1 1 2 3 1 1 2 cos cos cos cos cos sin sin sin thigh crus thigh crus thigh crus x L L y L L z L L                     (1)

  

, shows orientation of the crus link at the ankle jointHere, the ankle rotation is controlled by an independent actuator which is placed at the ankle joint. the angle requirement for the foot link at the end effector is.

Manipulator Kinematics

For the Orthoglide kinematic solution can be determined by the following relations

      2 2 2 2 1 2 2 2 2 2 2 2 2 2 3 x x y z l x y y z l x y z z l             (2)
Here,

               (3)
Where the

By substituting eq. ( 4) and eq.( 1) in eq. ( 3) we can obtain complete inverse kinematics relation for the assembly. The parameters t y and t z are shown in Figure 4. The point ( , , )

x y z is with respect to (w.r.t.) frame {2}, while ( , , ) o o o

x y z is w.r.t. frame {1}. To bring all the points to one coordinates system linear transformation is applied to the frames the distances

Physiological Motions

Physiological motions are decided by the therapist according to rehabilitation status of the patient. Here in this section basic physiological motions are shown to validate the kinematics of the proposed system. Each individual joint are given motion according to the angular limits used in therapeutic treatments [START_REF] Stansfield | Regression analysis of gait parameters with speed in normal children walking at self-selected speeds[END_REF].

Hip flexion-extension

Hip flexion-extension motion refers to motion of hip joint about the sagittal plane. To visualize this motion the values input is shown in Table 1. The joint-space movement shown in Figure 7. shows that the motion is possible and mechanism is not encountering any singularities while performing the task.

Parallel singularity can be avoided by regulation the parameter l , higher values are more stable, which is the length of the connecting link from the actuator to end endeffector with universal joints. Furthermore, optimization can be done as this parameter. The stroke length of the linear actuator is taken as 1.2 m. Hence, during the motion system is not overruling the limits.

Hip adduction-abduction

The trajectory taken for hip adduction-abduction is shown in Table 2. Here we have given motion to 3  as, This joint-space in Figure 8 clearly shows that mechanism is able to providebidirectional adduction and abduction which was not possible in case of Hipbot. Only one condition is to be verified that the lower limb under treatment is should not hit the other limb which is not being treated.

Knee flexion-extension

For knee flexion-extension the 2  angle is to be varied, this angle cannot be less than zero as it is constrained by human body constraints, also a safety feature in the knee joint is also required which stops the orthosis to go less than zero physically, for this simulation the task-space is shown in Table 3 and the joint-space output is shown in All the joint must be protected by physical restriction and numerical restriction through integrated software. Other than this two emergency switches must be installed. One near patient's hand and another with the physiotherapist. These treatments must be provided in presence of a therapist. This devices are supportive devices which increases the efficiency of the therapist to give long duration treatments without making the therapist tired.

Figure 1 :

 1 Figure 1: Proposed Lower limb rehabilitation robot

Figure 2 :Figure 3 :Figure 4

 234 Figure 2: Passive orthosis

Figure 4 :

 4 Figure 4: End-Effector orientation arrangement

z

  are the Orthoglide end-effector point.

Figure 5 :

 5 Figure 5: Kinematic parameters of Orthoglide

  is having independent actuator whose actuation is represented by ankle  which is a function of hip and knee adduction-abduction angle,

Figure 6 :

 6 Figure 6: Passive orthosis

Figure 7 :

 7 Figure 7: Hip flexion-extension joint space movement

  function with a time period of 30 seconds. The trajectory would be a circle transverse plane as the patient is in lying posture.

Figure 8 :

 8 Figure 8: Hip adduction-abduction joint space movement

Figure 9 .Table 3 :

 93 Figure 9. Here we have taken

Table 1 :

 1 Task-space for validation of hip flexion-extension motion

	Joint	1 				2 	3 	ankle 
	Value	   2 60(168.75 15 ) t  	o	10 o	0 o	0 o
			225  
	To validate the motion possibility each joint is simulated for a 30 second motion
	trajectory. Here in this case the hip flexion-extension,	1 oo 15 45    	is simulated
	the geometric parameters are taken as:	thigh L	 0.42 m,	crus L  0.4 m, l  1.4 m, 1 d 
	0.28m, 2 d  0.4 m, 3 d  1.6 m,	x p  1.2 m,	y p  0.14 m,	z p  0.917 m,	t y  0.05
	m and	z  0.1 m.
		t

Table 2 :

 2 Task-space for validation of hip adduction-abduction motion

	Joint	1 	2 	3 	ankle 
	Value	30 o	20 o	15sin(12 ) o t	0 o

Conclusions

Lower limb rehabilitation techniques are designed in order to provide continuous therapy for a longer period of time at a stretch. For such purpose the mechanisms should perform continuous operation without facing any kind of singularity and joint space limitations. Also, it should be safe for the patient and the therapist. The proposed system is designed to provide and addition dimension to the therapists that is hip adduction-abduction which is not present with proper features in other devices. The design and kinematics is explained in order to realize the system. The basic physiological motions are kinematically simulated to verify the manipulator behavior towards the joint input. This architecture has potential to provide wide range of rehabilitation treatments. In future we would like to find dynamic based control schemes and real-time validation on human subject.