A M Collin

D James

J Claudet

Modelling the connectivity of the coastal social-ecological networks subject to oceanic hazards

Earth observation of complex scenes, such as coastal fringes, is based on a plethora of optical sensors constrained by trade-offs between spatial, spectral, temporal and radiometric resolution. The spaceborne hyperspectral EO-1 Hyperion sensor (decommissioned in 2017) was able to acquire imagery with 10 nm spectral (220 bands) at 30 m spatial resolutions over 1424.5 km 2 scenes. Conversely, the widespread unmanned airborne vehicle (UAV) hyperspatial DJI Mavic Pro camera can collect only naturalcoloured imagery of 100 nm spectral (3 bands) but at 0.1 m spatial resolution over ~10 km 2 scenes (with a single battery and calm meteo-marine conditions). The spaceborne WorldView-3 (WV3), featured by 60 nm spectral (16 bands) at 0.3 m spatial resolution (when pansharpened) over 1489.6 km 2 scenes, has the capacity to bridge both sensors. This study aims at testing the spectral and spatial performances of the WV3 to discriminate 10 complex coastal classes, ranging from ocean, reefs and terrestrial vegetation in Moorea Island (French Polynesia). Our findings show that geometrically-and radiometrically-corrected 0.3-m 16-band WV3 bands competed with (30-m) 167-band Hyperion performance for classifying 10 coastal classes with 2-neuron artificial neural network modelling, while being able to segment objects seized by 0.1-m (3-band) UAV. Unifying superspectral and hyperspatial specificities, the WV3 also leverages hypertemporal resolution, that is to say 1-day temporal resolution, rivalling UAV's one.

INTRODUCTION 1.1 Space-Spectrum-Time prism

Coastal fringes host complex social-ecological systems facing global changes (sea-level rise and cyclone/storm intensification) and local pressures (unprecedented urbanization and ecosystem services degradation), thus requiring specific imagery sensors to be used. Ad hoc sensors are expected to capture coastal processes at the scale at which they act, that is to say over regional extents (> 1000 km 2 ) but with high spatial resolution (1 m). Furthermore, sensors need to monitor a sufficient number of wavebands (> 10 bands) in order to disentangle spectrally-close coastal features, both within marine and terrestrial realms [START_REF] Collin | Bridging ridgeto-reef patches: Seamless classification of the coast using very high resolution satellite[END_REF]. In addition, the revisit or tasking time should be short enough to match the temporal frame in which coastal mechanisms occur, from days to months. However, a sensor delivering daily-tomonthly, hyperspectral images over regional extents at hyperspatial resolution does not exist, because of the hardware-based limitations. Judicious trade-offs between temporal, spectral and spatial resolutions have to be considered.

Airborne and spaceborne hyperspectral platforms

Even if handborne hyperspectral sensors provide very satisfactory results to retrieve inherent optical properties of the * Corresponding author waters [START_REF] Keller | Hyperspectral Data and Machine Learning for Estimating CDOM, Chlorophyll a, Diatoms, Green Algae and Turbidity[END_REF], the spatial coverage of coastal regional extents cannot be reached in a cost-effective manner, hindering monthly iterative acquisition.

Leveraging higher footprints, airborne hyperspectral sensors revealed great performance to classify coastal areas [START_REF] Zhou | Classification of coastal areas by airborne hyperspectral image[END_REF], discriminate seagrasses [START_REF] Peneva | Seagrass mapping in the northern Gulf of Mexico using airborne hyperspectral imagery: a comparison of classification methods[END_REF], or macroalgae [START_REF] Dierssen | Hyperspectral discrimination of floating mats of seagrass wrack and the macroalgae Sargassum in coastal waters of Greater Florida Bay using airborne remote sensing[END_REF]. The integration of LiDAR data was also strongly validated for species distribution [START_REF] Jones | Assessing the utility of airborne hyperspectral and LiDAR data for species distribution mapping in the coastal Pacific Northwest, Canada[END_REF], agricultural and urban features (Tuia et al., 2016). Hyperspectral sensors mounted on unmanned airborne vehicle (UAV) recently showed suitable results for monitoring trees [START_REF] Honkavaara | Band registration of tuneable frame format hyperspectral UAV imagers in complex scenes[END_REF]. Covering regional extents at high spatial resolution, those surveys are good candidates for coastal issues, but the time-consuming mission planning and the costly aircraft pricing [START_REF] Collin | Mapping VHR water depth, seabed and land cover using Google Earth data[END_REF] make the temporal resolution too coarse to capture coastal processes.

Benefiting from a greater agility, concomitant with affordability, thus temporal resolution, spaceborne sensors have demonstrated their efficiency in estimating water quality [START_REF] Brando | Satellite hyperspectral remote sensing for estimating estuarine and coastal water quality[END_REF][START_REF] Van Mol | The Compact High Resolution Imaging Spectrometer (CHRIS): the future of hyperspectral satellite sensors. Imagery of Oostende coastal and inland waters[END_REF][START_REF] Lucke | Hyperspectral Imager for the Coastal Ocean: instrument description and first images[END_REF], mapping coastal wetlands [START_REF] Pengra | Mapping an invasive plant, Phragmites australis, in coastal wetlands using the EO-1 Hyperion hyperspectral sensor[END_REF], coral reefs [START_REF] Kutser | Mapping coral reef benthic substrates using hyperspectral space-borne images and spectral libraries[END_REF], soil parameters [START_REF] Anne | Modeling soil parameters using hyperspectral image reflectance in subtropical coastal wetlands[END_REF], and land cover/land use when fused with Sentinel-2 [START_REF] Weinmann | Investigations on the potential of hyperspectral and Sentinel-2 data for land cover/land use classification[END_REF]. Conciliating high spectral and temporal resolution with regional extents, the downside of those sensors (CHRIS, 19 bands at 17 m or 63 bands at 34 m; Hyperion, 220 bands at 30 m; HJ-1, 128 bands at 30 m; HICO installed in the international space station, 128 bands at 90 m) lies in their spatial resolution, mismatching coastal processes. Even PRISMA (220 bands), launched this year, or EnMAP (228 bands, [START_REF] Müller | The processing chain and Cal/Val operations of the future hyperspectral satellite mission EnMAP[END_REF], will provide coastal images, relatively too coarse (30 m).

Spaceborne superspectral and hyperspatial sensor

In parallel with the newly launched Venμs micro-satellite (12 bands at 5 m), the WorldView-3 (WV3) sensor can capture, at the daily rate, 1 panchromatic band at 0.31 m (hyperspatial), 8 multispectral (5 visible, VIS, and 3 near-infrared, NIR) bands at 1.24 m, surpassing its predecessor, WorldView-2, provided with 0.46 and 1.84 m, respectively [START_REF] Collin | What is the value added of 4 bands within the submetric remote sensing of tropical coastscape? Quickbird-2 vs WorldView-2[END_REF]. In addition, WV3 has the capabilities for collecting 8 short-wave infrared (SWIR) at 3.7 m. The increase in spatial resolution improved the bathymetry extraction [START_REF] Collin | VHR coastal bathymetry using WorldView-3: colour versus learner[END_REF], and the addition of spectral bands meliorated the classification of minerals [START_REF] Kruse | Mineral mapping using simulated Worldview-3 short-wave-infrared imagery[END_REF] and salt marshes (Collin et al., 2018a). WV3 VIS, NIR and SWIR showed the potential to be Gram-Schmidt pansharpened [START_REF] Belfiore | Application of different Pan-sharpening methods on WorldView-3 images[END_REF], resulting in 16 spectral bands at 0.3 m.

We hypothesize that the superspectral (16 bands), hyperspatial (0.3 m) WV3 can both compete with satellite hyperspectral performance and UAV spatial segmentation, for detecting complex coastal features. Classification of Moorea generic coral reefscape (Figure 1) will be examined to confront WV3 and Hyperion (30 m with 220 bands) spectral data, using artificial neural network (ANN) modelling. A spatial analysis will be tackled to compare WV3 and UAV (0.1 m with 3 bands) fine-scale patterns.

MATERIALS AND METHODS

Study site

The study area is located on Moorea Island (17°32′S, 149°50′W) in South Pacific French Polynesia (Figure 1). Tahiti's sister island, 1.6-million-year-old Moorea tops at 1 207 m and extends over 187 km 2 , composed of 134-km 2 terrestrial and 53-km 2 lagoon realms (Collin et al., 2018b). Rich of its ecological land and marine diversity, as well as exposed to growing urbanization, Moorea embodies a scientific hub addressing global changes in the Anthropocene era, through a nexus of French and USA researchers (Davies et al., 2015). The area of interest stretches over 3.5 km 2 , and encompasses typical features of tropical reefscapes, such as outer, barrier and fringing coral reefs, lagoon with channel, and forests.

Air truth using Unmanned Aerial Vehicle

The variety of studied habitats has been examined using a consumer-grade UAV, DJI Mavic Pro, provided with 3 naturalcoloured bands (red-green-blue, RGB), and 0.1 m pixel size. Fixed at 35 m altitude, the automatic flight covered a 0.08-km 2 transect (Figure 2). A series of 86 geolocated and overlapped photographs were processed using a photogrammetric approach, resulting in a RGB orthomosaic. Given the centimetre scale, this by-product was fine enough to be considered as air-truth (Collin et al. 2018a) and discriminate 7 classes: deep outer reef, shallow outer reef, barrier reef, pavement with reef, shallow lagoon, deep lagoon and fringing reef (green disks in Figure 2). Deep ocean, wet forest and dry forest were selected directly based on the satellite imageries (red disks in Figure 2).

Spaceborne hyperspectral Hyperion

Launched in 2000, Hyperion imager, borne on Earth Observing-1, was the first civilian spaceborne sensor, offering 220 calibrated bands. Characterized by a low temporal resolution (200 days), Hyperion acquired imagery fitted a 30 m pixel size, what could be deemed as moderate spatial resolution (Table 1). Hyperion imagery was collected on May 5, 2003 at 19 h 52 min 14 s UTC. The study area (Figure 2A), composed of 65 × 66 pixels, was orthorectified using ground control points and bilinear resampling (datum WGS84, UTM 6 South). The radiometric correction included three steps: the factor calibration of the digital number to the top-of-atmosphere (TOA) radiance, the TOA radiance to the down-of-atmosphere (DOA) radiance considering atmosphere absorption, and the DOA radiance to the DOA reflectance, accounting for solar irradiance. Out of 220 initial bands, 167 bands were further investigated taking into account both water vapour transmission windows and overlap regions of both spectrometers.

Table 1. Hyperion and WorldView-3 specificities

Spaceborne superspectral / hyperspatial WorldView-3

The WV3 instrument was orbited in 2014 and is still the finest civilian VIS, NIR and SWIR sensor. The spatial enhancement of 5 VIS, 3 NIR and 8 SWIR wavebands thanks to the 0.3 m panchromatic resolution makes the WV3 very attractive to the scientific community tasked with submeter-, day-scale processes (Table 1). WV3 imagery, obtained on July 12, 2018 at 20 h 35 min 39 s UTC, was subset to the study area in the form of 6243 × 6379 pixels (Figure 2B). Like Hyperion, WV3 imagery was processed to be geometrically corrected, then radiometrically standardized to DOA reflectance.

Spectral-based classification

The first assumption of this work pointed out upfront that superspectral WV3 could classify as satisfactorily as hyperspectral Hyperion. This hypothesis has been tested across 10 coral reefscape classes, chosen for their structural, thus spectral, complexity but also their representativeness of tropical coasts. A great challenge to be overcome lay in the highly contrasted spatial resolutions of 30-m Hyperion and 0.3-m WV3, but also 0.1-m UAV data.

Classes investigated:

Based on UAV air truth and natural-coloured inspection, 10 spectrally-homogeneous areas were selected over Hyperion imagery (1 pixel per class), corresponding to 10 000 pixels per class over WV3 imagery (Table 2). Benefiting from the correction up to the DOA reflectance level, natural-coloured patterns between Hyperion and WV3 were conspicuously recognizable across the 10 classes, irrespective of their marine or terrestrial nature (see ad hoc columns in Table 2). Dry Forest

Hyperion WV-3 UAV h( X ) k w n ( X ) (1)
i i i
Beyond overall accuracies derived from confusion matrices, a generalization of the R 2 was adopted to compare fitting performances (1000-fold validation, keeping the best model) of Hyperion/WV3 spectral combinations to categorize the 10 classes of interest. The statistic uses the 2/n root of the likelihood. It ranges from the value 0, for a model as good as a constant model, to the value 1 for a perfect model.

Spatial-based segmentation

In addition to its superspectral specificities, WV3 has the potential to provide information at 0.3 m, leading the civilian spaceborne optical imagery. The second assumption of this research relied on WV3 hyperspatial capacity to discriminate complex spatial patterns as suitable as centimetre-scale UAV. This conjecture has been evaluated by segmenting both imageries using the edge algorithm (objects with sharp edges), and the full lambda schedule for merging small objects within larger, textured ones. The selected texture kernel size has been fixed at 3 pixels.

RESULTS AND DISCUSSION

Our results, firstly, focused on the bridge between spaceborne hyperspectral Hyperion and superspectral WV3, and secondly dealt with the linkage between hyperspatial WV3 and UAV.

Hyperion and WV3 spectral classification

Prior to show ANN results of the classification, DOA reflectances of the 8 marine and 2 land classes were plotted for Hyperion and WV3 (Figures 3 and4). 2), overreflecting water classes within absorbing NIR and SWIR, due to sun glint integration in the coarse pixel.

Results of the ANN modelling, classifying the 10 classes based on combinations of Hyperion and WV3 spectral wavebands, were significant (Figure 5). RGB (3 bands), RGBNIR (4 bands), RGB-Coastal-yellow (5 bands) and RGBNIRs (8 bands) classifications showed greater performances for Hyperion than WV3 (0.06 difference in R 2 ). The combination, including 16 WV3 bands, and corresponding 16 Hyperion bands, was still better for Hyperion, but with a reduction in deviation (0.04 difference in R 2 ), due to the rise trend of WV3 and a slight decrease of Hyperion. The latter sensor's score further declined when all 167 bands were integrated into ANN modelling, making the 16-band WV3 combination a better predictor than Hyperion. Hyperion counter-performance might be justified by the spectro-statistical noise conveyed by too many bands, thus the need for dimensionality reduction [START_REF] Keller | Investigation of the impact of dimensionality reduction and feature selection on the classification of hyperspectral EnMAP data[END_REF].

on UAV, and barely detected on WV3. The segmentation could be enhanced using the intensity algorithm, leveraging 16 WV3 information, compared to 3 UAV one. Beyond the physical limitations of pixel size, WV3 pansharpening procedure, producing halo-like artefacts, might be improved using a dedicated hypersharpening technique [START_REF] Kwan | Blind quality assessment of fused worldview-3 images by using the combinations of pansharpening and hypersharpening paradigms[END_REF].

CONCLUSIONS

Complex scenes, such as coastal tropical systems, require sensors provided with high spectral, spatial and temporal resolution.

We propose here to bridge hyperspectral 30-m spaceborne instruments, such as Hyperion, and hyperspatial 3-band UAV, such as DJI Mavic Pro. The 0.3-m WV3 sensor has Figure 5. Hyperion and WorldView-3 comparison of the classification performances using one-layered artificial neural networks for the 10 classes investigated

WV3 and UAV spatial segmentation

Comparisons of segmentation applied to WV3 and UAV subsets were informative (Figure 6). relying on edge algorithm and full lambda schedule fusion, produced similar outcomes in a qualitative perspective: pavement/sand patches over WV3 imagery were as successfully delineated as UAV one within the fringing reef matrix. The main difference resided in the refined delimitation of small pavement/sand patches, visible demonstrated that its 16-band combination rivalled 167-band Hyperion for classifying 10 classes using ANN modelling, while competing with 0.1-m UAV for segmenting fringing coral reefs. Conciliating spectral and spatial requirements needed for coasts, the WV3 benefits from an hypertemporal resolution, namely a daily revisit, as good as UAV's one.

Figure 1 .

 1 Figure 1. Natural-coloured WorldView-3 imagery of Moorea Island (French Polynesia)

Figure 2 .

 2 Figure 2. Natural-coloured (A) Hyperion (30 m × 30 m) and (B) WorldView-3 (0.3 m × 0.3 m) imageries of the study site in Moorea Island (French Polynesia), over which is draped the unmanned aerial vehicle natural-coloured Mavic Pro imagery (0.1 m × 0.1 m). Green and red points represent geolocations of the classes investigated, provided with and deprived of UAV

  Table2. Hyperion, WorldView-3 and unmanned aerial vehicle Mavic Pro images of the 10 classes investigated2.5.2 Artificial neural network modelling:The ANN, a machine learner, builds non-linear models, h, by minimizing least squares using a one-layer perceptron feed-forward technique, approximating the i (here, i=2) training responses with a constant, k, and Hyperion/WV3 combinations of spectral predictors, X, through weighted functions, wi, adjusting neurons, ni, that are based on the hyperbolic tangent activation function[START_REF] Heermann | Classification of multispectral remote sensing data using a back-propagation neural network[END_REF]):

Figure 3 .

 3 Figure 3. Hyperion spectral signatures of the 10 classes (A: 8 marine, B: 2 terrestrial). 167 bands out of 220 were operable

Figure 4 .

 4 Figure 4. WorldView-3 spectral signatures of the 10 classes (A: 8 marine, B: 2 terrestrial). 16 bands were operable

Figure 6 .

 6 Figure 6. Comparison of a fringing reef subset of naturalcoloured (A) WorldView-3 (0.3 m pixel size) and (B) UAV (0.1 m pixel size), as well as segmented (C) WorldView-3 and (D) UAV imageries Despite a 3-fold factor separating WV3 and UAV spatial resolution, the segmentation processing, relying on edge algorithm and full lambda schedule fusion, produced similar outcomes in a qualitative perspective: pavement/sand patches over WV3 imagery were as successfully delineated as UAV one within the fringing reef matrix. The main difference resided in the refined delimitation of small pavement/sand patches, visible

ACKNOWLEDGEMENTS

Fieldwork and UAV survey was carried out into the "Reef I Were" project supported by the CNRS PEPS TOHMIS, and spaceborne imagery was delivered by DigitalGlobe Foundation.


Denis Gapais

Jonathan Poh

Philippe Yamato

Thibault Duretz

Florence Cagnard

Shortening of Archaean and Paleoproterozoic continental lithospheres: large strains, but no orogeny

come

In many ancient deformation belts of Archaean and Paleoproterozoic age (e.g. Terre Adélie in East Antarctica, Finnish Svecofennides in Southern Finland, Murchison Belt in South Africa, Thompson Nickel Belt in Manitoba, Dharwar Craton in western India, Abitibi sub-Province in Québec, Trans-Hudson belt of Canada, Trans-Amazonian belt of Suriname), latest recorded deformations are compressive or transpressive. In these belts that involved hot and weak continental crusts, deformations are distributed with basically vertical tectonics and important crustal thickening. On the other hand, there is no evidence of syn-orogenic extension or late-orogenic collapse, as classically observed in modern orogens where extensional detachments are widespread. Analogue and numerical models emphasize that shortening of weak and hot lithospheres basically favour downward motions, which result in limited topographies. Field evidence further point to metamorphic isogrades rather parallel to the Earth surface at belt scale. Hence, metamorphic conditions are rather monotonous at the scale of individual belts, with limited metamorphic jumps and typical P-T paths with no significant adiabatic retrograde segments. Consistently, localized deep detrital sedimentary basins like foreland or intra-mountain basins, are not documented. Sedimentary records rather suggest distributed sedimentation processes. In addition, several lines of evidence tend to point out that cooling of ancient hot deformation belts was rather slow, which is consistent with distributed topographies and long-lasting erosion-driven exhumation processes. On these bases, we propose that gravity-driven collapse had no reason to occur in ancient hot deformation belts because important topographic gradients and orogeny could not develop as observed in modern mountain chains.


Apurva V Oza

Francois Leblanc

Robert E Johnson

Carl Schmidt

Ludivine Leclercq

Timothy A Cassidy

Jean-Yves Chaufray

Dusk Over Dawn O 2 Asymmetry in Europa's Near-Surface Atmosphere

Keywords: Exospheres, O 2, Atmospheres, Aurorae

The evolution of Europa's water-product exosphere over its 85-hour day, based on current models, has not been shown to exhibit any diurnal asymmetries. Here we simulate Europa's exosphere using a 3-D Monte Carlo routine including, for the first time, the role of Europa's rotation on the evolution of exospheric molecules tracked throughout the orbit. In this work we focus on understanding the behavior of a single atmospheric constituent, O 2 , sputtered by a trailing hemisphere source with a temperature-dependence under isotropic plasma conditions as also modeled by previous works. Under rotation, the O 2 is also subject to the centrifugal and Coriolis forces in addition to the standard gravitational forces by Jupiter and Europa in our model. We find that the O 2 component, while global, is not homogeneous in Europa local time. Rather, the O 2 consistently accumulates along the direction of Europa's rotation at the dusk hemisphere. When rotation is explicitly excluded in our simulations, no diurnal asymmetries exist, and any accumulation is due to the prescribed geometry of the sputtering source. We find that the assumed thermal-dependence on the O 2 source is critical for a diurnal asymmetry: the diurnal surface temperature profile is imprinted on to the near-surface O 2 atmosphere, due to small hop times for the non-adsorbing O 2 , which then effectively rotates with Europa. Simulation tests demonstrate that the diurnal asymmetry is not driven by the thermal inertia of the ice, found to have only a weak dependence (< 7 %). Altogether, the various test cases presented in this work conclude that the dusk-over-dawn asymmetry is driven by Europa's day-night O 2 cycle synchronized with Europa's orbital period based on our model assumptions on O 2 production and loss. This conclusion is in agreement with the recent understanding that a non-adsorbing, rotating O 2 source peaking at noon will naturally accumulate from dawn-to-dusk, should the O 2 lifetime be sufficiently long compared to the orbital period. Lastly we compare hemispherically-averaged dusk-over-dawn ratios to the recently observed oxygen emission data by the Hubble Space Telescope. We find that while the simulations are globally consistent with brighter oxygen emission at dusk than at dawn, the orbital evolution of the asymmetries in our simulations can be improved by ameliorating the O 2 source & loss rates, and possibly adsorption onto the regolith.

Introduction

Europa's molecular oxygen is of keen interest as it has been suggested to be a possible source of ∼ 0.1-100 kg/s of O 2 [START_REF] Johnson | The Production of Oxidants in Europa's Surface[END_REF][START_REF] Hand | Energy, Chemical Disequilibrium, and Geological Constraints on Europa[END_REF][START_REF] Greenberg | Transport Rates of Radiolytic Substances into Europa's Ocean: Implications for the Potential Origin and Maintenance of Life[END_REF] to Europa's putative saltwater ocean, thought to have a chemistry analogous to Earth's oceans [START_REF] Vance | Geophysical controls of chemical disequilibria in Europa[END_REF]. This range of oceanic source rates can in principle be connected to the production and dynamics of the tenuous oxygen atmosphere, or exosphere, which we simulate in this work.

The origin of Europa's water-product exosphere is ultimately linked to its neighboring satellite Io. Since the Voyager spacecraft first confirmed the presence of energetic ions trapped in the Jovian magnetosphere, the exosphere has been modeled to 1 * apurva.oza@space.unibe.ch be predominantly generated by the bombardment of oxygen and sulfur ions ultimately sourced by Io's extreme volcanism [START_REF] Peale | Melting of Io by tidal dissipation[END_REF]. These energetic ions both electronically excite and impart significant momentum to the water molecules in Europa's surface triggering dissociation and chemistry [START_REF] Johnson | Sputtering of Ices[END_REF]. The energy released by these processes leads to the ejection, or sputtering, of water-products: primarily H 2 O, H 2 , O 2 , and trace amounts of OH, H, O, and H 2 O 2 , which then populate the exosphere. We focus here on a single component: the molecular oxygen, to isolate our discussion to the orbital evolution of the neutral exosphere. In particular, we focus on the observed near-surface component [START_REF] Hall | The Far-Ultraviolet Oxygen Airglow of Europa and Ganymede[END_REF]) derived to have a variable column density between 2 -14 × 10 14 O 2 cm -2 at an altitude below 400 km. The origin and fate of this O2 [START_REF] Oza | Dusk/dawn atmospheric asymmetries on tidally-locked satellites: O 2 at Europa[END_REF], as well as a comprehensive overview of Europa's global exosphere [START_REF] Plainaki | Towards a Global Unified Model of Europa's Tenuous Atmosphere[END_REF]) has been recently reviewed.

In order to focus primarily on the influence of rotation on Europa's near-surface atmosphere, we employ a ballistic, 3-D Monte Carlo Exosphere Global Model (EGM: §2 ). The EGM simulates Europa's neutral exosphere as it orbits Jupiter in Europa's rotating frame (EphiO). The neutral O 2 exosphere is governed by various physical processes illustrated in Fig. 1. The simulations demonstrate how Europa's near-surface O 2 exosphere behaves in the absence of detailed knowledge of influences such as the putative H 2 O plumes (Roth et al. (2014b); Roth et al. (2014a); [START_REF] Sparks | Probing for Evidence of Plumes on Europa with HST/STIS[END_REF]; [START_REF] Teolis | Dione and Rhea seasonal exospheres revealed by Cassini CAPS and INMS[END_REF] ; [START_REF] Sparks | Active Cryovolcanism on Europa? Astrophysical[END_REF]) and the near-surface plasma conditions. Although such uncertain effects could be adjusted to fit the observations, here we focus on the neutral dynamics, the effect of the source distribution, and the rotation. Our work includes the influence of Europa's rotation on the near-surface O 2 exosphere for the first time. The simulations are carried out in Europa's rotating reference frame, where the Coriolis and centripetal forces act on the exospheric molecules under a gravitational potential dictated by both Europa and Jupiter's gravitational fields.

Europa Exosphere Global Model

Europa's water product exosphere is simulated here by tracking representative particles (H 2 O, H 2 , O 2 , OH, H, and O) in a rotating, non-inertial reference frame, in spherical coordinates (r, θ, φ), centered on Europa and extending up to ∼ 15R Eu . We employ a parallelized Monte Carlo routine which is the core of the Exosphere Global Model (EGM). The numerical routines are similar to those described in detail in [START_REF] Turc | Modelling Ganymede's neutral environment: A 3D test-particle simulation[END_REF], as well as in a companion paper on Ganymede's orbital evolution [START_REF] Leblanc | On the orbital variability of Ganymede's atmosphere[END_REF], where the collisionless Boltzmann equation is solved for an imposed function distribution at the surface f i , for a species i, a velocity v, and the acceleration due to gravity g = GM Eu r 3 r, where r is the radial distance from Europa's center . For a more detailed description of the EGM we refer the readers to [START_REF] Turc | Modelling Ganymede's neutral environment: A 3D test-particle simulation[END_REF] and Section 2.2 of [START_REF] Leclercq | From exosphere to magnetosphere of planetary objects : optimization of parallelized modelisations for an application to Ganymede[END_REF]. In the EGM we eject ∼ 10 7 test particles from Europa's surface following known energy and angle distributions, f (E, θ) as described later ( §2.1). These test particles are on ballistic (collisionless) trajectories, and can escape, stick, and be re-emitted from the surface depending on their properties as indicated in Fig. 1. The fate of ions is not considered in this work. In the case of O 2 , we track its interaction with the surface and account for electron and photon induced dissociation as well as ionization. Following dissociation, we also track the O formed. This procedure is carried out until a steady state O 2 exosphere is achieved. Steady state in our simulations is achieved when the computed thermodynamic quantities change by less than 10 % from one orbit to the next for any orbital position. These thermodynamic quantities are calculated based on the statistical weights of each test particle: W i = Φ i A cell N i dt . Here Φ i is the flux of ejected test particles, A cell the area of the grid-cell, N i is the number of time steps between each test particle ejection, and dt is the time step between two successive positions of the test-particles, chosen so that these two positions are within one cell or two nearby cells. After a sufficient number of time-steps to achieve approximate steady state, the average number density n , temperature T , and velocity v are calculated in each cell on a spherical grid, and at seven orbital positions, φ obs the sub-observer longitude of the satellite defined as φ obs = 0 • when Europa is in eclipse behind Jupiter. In our analysis, we display the calculated densities at seven subobserver longitudes: ling), and φ obs = 340 • . To improve statistics, these quantities are reconstructed on intervals spanning six degrees in orbital longitude, around each orbital position, corresponding to a total of 1.4 hours.

φ obs = 0 • , φ obs = 20 • , φ obs = 90 • (sunlit leading), φ obs = 150 • , φ obs = 210 • , φ obs = 270 • (sunlit trai-

Sputtering.

The O 2 exosphere is thought to be produced primarily by ions originating in the Io-plasma torus. The torus, composed predominantly of sulfur and oxygen ions trapped in Jupiter's magnetic field rotates, on average, seven times as fast as Europa, with the plasma primarily impacting Europa's trailing hemisphere in the corotation direction (+x). Evidence for preferential bombardment of the trailing hemisphere by heavy ions has been observed by the Galileo Near-Infrared Mapping Spectrometer (NIMS) [START_REF] Carlson | Sulfuric acid on Europa and the radiolytic sulfur cycle[END_REF]. Following [START_REF] Leblanc | Europa's Sodium Atmosphere: An Ocean Source?[END_REF], we model the effective ion flux Φ e f f , onto Europa's trailing hemisphere as diminishing with the corotation longitude φ :

Φ e f f (φ ) = Φ i 4π cos( 1 2 (φ -π)) (1)
Where the planetary longitude is 90 • out of phase with the corotation: φ = φ +π/2. Molecules are ejected from the trailing surface by the energy and momentum deposited by the incident ion flux Φ i in the water ice regolith. Here we use sputtering rates summarized in [START_REF] Cassidy | Magnetospheric ion sputtering and water ice grain size at Europa[END_REF] to discuss the fate of the oxygen component. We note that plasma diversion can affect the incoming flux of all ions and electrons, and thus the exact sputtering rates are still uncertain at present [START_REF] Cassidy | Widespread confusion in the modeling of Europa's magnetospheric interaction: what the potential modeler should consider before getting started[END_REF]. In [START_REF] Cassidy | Magnetospheric ion sputtering and water ice grain size at Europa[END_REF] both the hot and thermal components of the incident plasma are accounted for as well as the regolith porosity, assuming the surface is primarily pure water ice. [START_REF] Cassidy | Magnetospheric ion sputtering and water ice grain size at Europa[END_REF] construct a temperature-dependent yield as the number of molecules ejected per incident ion based on [START_REF] Fama | Sputtering of ice by lowenergy ions[END_REF] and [START_REF] Johnson | Sputtering of ice grains and icy satellites in Saturn's inner magnetosphere[END_REF]:

Y(T 0 ) i = Y 0 (1 + q i e -0,06eV kT 0 ) (2)
In Equation 2, T 0 is the local surface temperature, Y 0 the yield at low temperature, and q i scales the temperature dependence of the yield for a species i. For the total yield given, in terms of equivalent water molecules, q H2O = 200. The globally averaged O 2 ejection rate also depends on the surface temperature of the ice, with q O2 = 1000, empirically derived from extensive laboratory data described in [START_REF] Teolis | Cassini Finds an Oxygen-Carbon Dioxide Atmosphere at Saturn's Icy Moon Rhea[END_REF]; [START_REF] Teolis | Water Ice Radiolytic O 2 , H 2 , and H 2 O 2 Yields for Any Projectile Species, Energy, or Temperature: A Model for Icy Astrophysical Bodies[END_REF]), is 10 26 O 2 s -1 , with an H 2 yield that is twice this rate. [START_REF] Cassidy | Magnetospheric ion sputtering and water ice grain size at Europa[END_REF]

f (E) S putt ∼ EU x (E + U) 2+x
(3) where x = 0.7, and the effective surface binding energy U = 0.052 eV. The highly volatile molecular species O 2 and H 2 are produced by radiolysis. As the energetic ions penetrate the ice, they break bonds leading to chemistry and the temperature dependent formation of H 2 and O 2 . The initial ejection energy of O 2 (and H 2 ) can also be described by Equation 3 using x = 0 and U = 0.015 eV [START_REF] Johnson | Energetic Charged-Particle Interactions with Atmospheres and Surfaces[END_REF]. We refer to this distribution as f (E) U2 in this work. After the first ejection, those molecules returning to the surface can either react or are subsequently thermally desorbed so that their ejection speeds are roughly determined by a Maxwell Boltzmann (MB) distribution at the surface. The Maxwell Boltzmann speed distribution, accurate for a localized point is given by:

f MB (v)dv = 4π m 2πk b T 0 3/2 v 2 exp -mv 2 2k b T 0 dv (4)
This distribution applies since the desorbed molecules undergo multiple interactions with the surface, which we model to be fast relative to the production of a new O 2 , and are thus in local thermodynamic equilibrium with the surface ice, with an average energy, 3 2 k b T 0 .

Surface Temperature

The effective temperature of the surface ice, T 0 is defined by radiative equilibrium. In our model, we consider a slab of ice with conductivity κ T = 2.52 × 10 2 erg cm -1 K -1 s -1 [START_REF] Abramov | Numerical modeling of endogenic thermal anomalies on Europa[END_REF], and calculate the equilibrium temperature across the surface, over latitude θ and planetary longitude φ:

F ,1AU (1 -A) R 2 cosθcosφ = εσT 4 0 -κ T ∂T ∂r (5)
F ,1AU is the total solar irradiance in erg s -1 cm -2 at 1 AU, R the orbital distance in AU, and σ the Stefan-Boltzmann constant. The albedo, A, is assumed to vary linearly with φ between 0.65 on the leading hemisphere and 0.45 on the trailing, approximating the most recent interpretation of Galileo PPR results [START_REF] Rathbun | Galileo PPR Observations of Europa: Correlations of Thermophysical Properties with Exogenic and Endogenic Processes[END_REF]. The emissivity of the ice, ε, is set at 0.96. A small correction for the latent heat of sublimation is included [START_REF] Abramov | Numerical modeling of endogenic thermal anomalies on Europa[END_REF]. Endogenic heatflow, as estimated by [START_REF] Spencer | Nighttime Thermal Anomalies on Europa[END_REF] with an upper limit of 5 × 10 8 erg s -1 cm -2 , is neglected in this work.

The temperature gradient at the surface, ∂T ∂r in the last term of Eqn. 5 is given by the one dimensional equation for heat conduction along a direction r that is normal to the surface:

ρC P ∂T ∂t = ∂ ∂r κ T ∂T ∂r ( 6
)
where ρ is the mass density, taken as 0.92 g cm -3 , and the specific heat at constant pressure, C p , is 1.96 × 10 7 erg g -1 K -1 [START_REF] Vance | Oceanography of an Ice-Covered Moon[END_REF]. Eq. 6 is solved with the aid of a thermal routine using the slab boundary method [START_REF] Spencer | Systematic biases in radiometric diameter determinations[END_REF]; [START_REF] Young | Volatile transport on inhomogeneous surfaces: II. Numerical calculations (VT3D)[END_REF]). Forcing of solar insolation over a synodic day in late Feb. 2015 is determined in 2 • increments of θ and φ using the 309.bsp kernel provided by JPL. While this approach simplifies the variation of thermophysical parameters over the surface [START_REF] Rathbun | Galileo PPR observations of Europa: Hotspot detection limits and surface thermal properties[END_REF], it provides a basis for longitudinal asymmetries about the subsolar axis that result from the thermal inertia of the ice.

In Figure 2(a) we show the evolution of Europa's equatorial surface ice temperature along its orbit in panel A, where we include the effect of Jupiter's shadow. The Figure 2(a) inlet is a zoom of the eclipse region where Europa's temperature drops by ∼ 30 K before rising to ∼ 110K at the brighter, leading hemisphere. Figure 2(b) is the corresponding temperature map of the darker, trailing hemisphere mapped in west longitude. As is true for most planetary bodies, on average, the largest thermal gradient is between noon and midnight, or day and night, as indicated in Fig. 2(b) with a slight increase in surface temperature, ∆T ∼ 10 K , at dusk over dawn due to the thermal inertia of the ice. The surface temperature inhomogeneities due to thermal inertia, as we will explore below, contribute only ∼ 10 % to the observed dusk-over-dawn asymmetry.

Results

Here we present two results of our 3-D simulations of Europa's water product exosphere. One in which Europa was held static, and one where Europa was able to rotate about Jupiter's axis. In this work we focus on understanding the behavior of the primary atmospheric constituent: the near surface O 2 .

Atmospheric Bulges

No Rotation: Atmospheric O 2 Bulge at Noon

A trailing hemisphere O 2 source at Europa may be expected to have a large 'atmospheric bulge' at plasma ram, where the near-surface column density is larger than the background exosphere. As O 2 is thought to weakly interact with the water ice, the O 2 migrates stochastically due to the day-night temperature gradient. The gray vectors in our simulation depicted in Figure 3, demonstrate this migration. If migration were rapid, a night-side bulge would be expected like the Helium bulges on the Moon and Mercury [START_REF] Leblanc | Mercury and Moon He exospheres: Analysis and modeling[END_REF]. However, migration is slow compared to the O 2 lifetime (c.f. Table 1) such that no asymmetry other than sputtering remains.

In a collisionless exosphere, ejected molecules return to the surface where they stick or are re-emitted with an energy determined by the local, surface ice temperature. On interacting with the surface, the fate of a molecule is sensitive to the surface residence time: τ res = τ 0 exp( E ads k b T 0 ) where E ads is the effective heat of adsorption. Initially for molecular oxygen, we assume the heat of adsorption is negligible and the surface residence time is extremely short, on the order of the vibration time for a Van der Waals potential (τ 0 ∼ 10 -13 s) so that O 2 has a negligible sticking coefficient. The effect of O 2 sticking due to a longer residence time will be examined in section 4. Thus one can treat O 2 motion as a series of random walks. [START_REF] Hunten | The Mercury atmosphere[END_REF] for example, defines λ 0 = U 0 k b T 0 , the ratio of gravitational binding energy, U 0 = GM p m i r p

to the thermal energy k b T 0 at the surface, approximately equal to the ratio of planetary radius r p to the scale height, H(T 0 ), so that λ 0 ∼ r p H . λ 0 , is roughly equivalent to the number of ballistic hops a molecule experiences in traveling an average distance r p yielding a diffusion timescale: t d ∼ r 2 p /D, where D is the effective diffusion coefficient. As approximated in [START_REF] Hunten | The Mercury atmosphere[END_REF], D ∼ H 2 t hop , so that the migration time for traveling a distance r p at the surface is:

t d ∼ λ 2 t hop (7)
In Table 1, we estimate several timescales scaled to Europa's orbital period τ orb , critical to the evolution of the nearsurface O 2 in the static and rotating cases (3.1.2). Under a uniform gravitational potential, the ballistic hop time for an O 2 molecule is on the order of a few minutes, far shorter than the O 2 lifetime. Table 1 also indicates that the O 2 lifetime, τ O2 , limited by the O 2 production and loss rates is comparable to the orbital period, yielding an average exospheric column of N O 2 ∼ 10 14 O 2 cm -2 . Thus the exosphere, based on our assumptions, should be actively built and destroyed within one orbital timescale. Lastly, it is seen that the timescale for the day-to-night flow t d , is not only about four times longer than the O 2 lifetime in the static case, but also four times as long as the orbital period, in the rotating case. In this way, the net spreading of the O 2 source is on average slower than Europa's orbital speed so we can, to first order, consider the O 2 as coupled to the rotating surface. We will demonstrate that this coupling is the principal mechanism for the time-dependent atmospheric O 2 bulge.

Rotating Case

: Atmospheric O 2 Bulge at Dusk.
Once rotation is activated and the O 2 column density is tracked throughout the orbit, we simulate an atmospheric bulge persisting throughout Europa's orbit. What is fascinating about this bulge, representing more than 10 % of the bulk O 2 column density, is it exhibits a diurnal dependence peaking consistently Figura 2: a: Equatorial subsolar surface temperature (K) as a function of sub-observer longitude, or Europa's orbital longitude, demonstrating the leading-trailing temperature profile asymmetry due to albedo. The darker, trailing hemisphere (A b = 0.45) is seen to be ∼ 18 K warmer than the brighter, leading hemisphere (A b = 0.65). b: Surface temperature map of Europa's sunlit trailing hemisphere at φ obs = 270 • . The surface temperature rapidly increases from dawn, φ obs = 90 until the subsolar point at φ obs = 0. The surface then begins to cool slightly more slowly, passing through dusk at 18h Europa local time. The largest thermal gradients driving migration are therefore between 6h -12h, and 12h-18h. Due to the thermal inertia of the ice, the dusk hemisphere is warmer than the dawn hemisphere. at dusk. A diurnal dependence is of course linked to the solar cycle, which in our model only influences the surface ice temperature (Sec. 2.1). As described in Sec. 2.2, the O 2 production is strongly dependent on the ice temperature. In this way, one can gain an intuitive understanding of an atmospheric bulge at dusk, by reexamining the timescales in Table 1 alone. Given that t hop τ orb the O 2 is effectively coupled to the rotating surface and the near-surface O 2 can be expected to follow the diurnal temperature variations in Fig. 2(b), and one can simply consider the atmospheric lifetime of an O 2 bulge over one Europa day. For instance, the nominal atmospheric bulge at the sunlit trailing hemisphere noon (Fig. 3), will be able to survive for at least τ orb /4 in the direction of rotation towards the dusk hemisphere. This 90 • shift from noon was derived analytically for a tidally-locked satellite atmosphere in [START_REF] Oza | Dusk/dawn atmospheric asymmetries on tidally-locked satellites: O 2 at Europa[END_REF]. It was shown that the balance between the satellite's atmospheric lifetime and orbital period over the orbit can be expressed as a parameter β = 2π τ O2 τ orb . The rotational shift of an atmospheric column peaking at noon for a thermally-desorbed collisionless exosphere then, can be estimated as: ∆φ ∼ tan -1 (β). Based on the modeled production and loss timescales, for Europa and for Ganymede [START_REF] Leblanc | On the orbital variability of Ganymede's atmosphere[END_REF], the O 2 lifetime approaches one orbital period, so that β ∼ 2π, yielding ∆φ ∼ π 2 . The 90 • longitudinal shift is responsible for a maximum column at dusk and minimum column at dawn, yielding the dusk-over-dawn atmospheric asymmetry. A dusk-over-dawn asymmetry is not expected if β 1 due to far slower O 2 loss for example, at Rhea and Dione [START_REF] Teolis | Dione and Rhea seasonal exospheres revealed by Cassini CAPS and INMS[END_REF]. On the other hand, if β 1, the O 2 bulge would be lost too quickly, before it has time to accumulate towards dusk. , where κ = 4,4 • 10 -8 cm 3 s -1 is the orbit-integrated reaction rate coefficient including e-impact as well as ionization, and n e = 70 cm -3 the electron number density.

We illustrate this apparent surface-exosphere synergy occurring throughout the orbit by using two sets of simulated 2-D spatial morphology maps in Figure 4. The center image indicates the orbital longitudes of the seven simulated orbital positions. The inner and outer maps represent the orbital synergy between the O 2 surface and O 2 exosphere varying with rotation. The inner circle, maps the O 2 source flux at the surface: radiolytically sputtered ejecta in cm -2 s -1 , and the outer circle maps the O 2 exosphere: vertical column density in cm 2 . On the outer maps, consistent with the inner maps, we have indicated dusk, dawn, and the subsolar position (X), along with the plasma leading (L) and trailing (T) hemispheres. The outer maps indicate O 2 bulges consistently accumulating near the dusk terminator. The inner maps illustrate that the O 2 source is also concentrated as bulges, suggesting that the atmospheric morphology is shaped by the surface ejecta.

Orbital Evolution of Europa's O 2 Europa's Diurnal Cycle

Ultimately, since our modeled trailing hemisphere O 2 source exhibits a thermal dependence, the surface-exosphere synergies can be examined qualitatively based on Europa's day & night phases illustrated in Figure 5(a) (red vector: trailing hemisphere). Our Monte Carlo simulations in Figure 5(b) show that the day & night phases for the trailing hemisphere correspond to two different orbital phases: a globally increasing O 2 exosphere during the "Trailing Day"(between 180 and 360 • longitude, shaded in red) and a globally diminishing O 2 exosphere during the "Trailing Night"(shaded in gray). Altogether, Figures 5(a) & 5(b) illustrate Europa's diurnal O 2 cycle, for a thermally-dependent, trailing hemisphere O 2 source. Unlike the static, non-rotating case simulated in Section 3.1.1 and previous works, this diurnal cycle is found to peak at dusk due to atmospheric O 2 accumulation over time.

Second order effects, such as O 2 migration or thermal effects during eclipse, treated in our simulations, may contribute to angular deviations from a 90 • longitudinal offset derived analytically for a highly thermal-dependent O 2 source. In our simulations, the O 2 bulges are vastly more apparent post-eclipse, near the sunlit leading hemisphere phases (i.e. 90 • & 150 • ) during which the bulk O 2 is being lost as described in figures 5(b) & 5(a).

Overall, the 2-D maps of Fig. 4 reveal that the local O 2 column densities vary substantially, by more than an order of magnitude ∼ 90 %, due to the thermally-dependent O 2 source fluxes also responsible for the shape of the atmospheric dusk bulges. These simulated maps provide a first attempt at a detailed picture of how Europa's rotating O 2 exosphere could be evolving throughout its orbit in latitude and longitude, due to the diurnal O 2 production likely responsible for the observed dusk-over-dawn oxygen asymmetries.

Discussion

Observations of Europa's O 2 exosphere over the decades have been limited, in that the only evidence of gas phase O 2 has been based on ratios of the far-ultraviolet atomic oxygen emission lines first observed by the Hubble Space Telescope (HST) as aurorae [START_REF] Hall | Detection of an oxygen atmosphere on Jupiter's moon Europa[END_REF][START_REF] Hall | The Far-Ultraviolet Oxygen Airglow of Europa and Ganymede[END_REF]. The ratio of the auroral line intensities

I 1356 I 1304 ∼ 2 is suggestive of e - impact dissociation of O 2 : O 2 + e -→ O * + O + e -+ ∆E.
The line-of-sight O 2 column density then can be derived based on the electron density n e [cm -3 ]and electron-impact dissociation reaction rates κ [cm 3 /s] (e.g. Table 2 Turc et al. ( 2014)) from:

I λ = n e κ O 2 +e-N O 2 + (n e κ O+e-) N O .
Remarkably, the first set of HST observations confirmed the predicted O 2 column density within a factor of two, based on sputtering experiments and atmospheric escape estimates [START_REF] Brown | Fast Ion Bombardment of Ices and its Astrophysical Implications[END_REF][START_REF] Johnson | Planetary applications of ion induced erosion of condensed-gas frosts[END_REF]. Based on a re-analysis of Voyager, Galileo, and Cassini data [START_REF] Bagenal | Plasma conditions at Europa's orbit[END_REF] demonstrated that one can expect the O 2 to vary by at least a factor of two. Nevertheless, our knowledge on the near-surface plasma conditions influencing the derived column densities is still severely limited-a point recently reviewed in detail by [START_REF] Plainaki | Towards a Global Unified Model of Europa's Tenuous Atmosphere[END_REF] along with previous models of Europa's asymmetric O 2 exosphere [START_REF] Cassidy | The spatial morphology of Europa's near-surface O 2 atmosphere[END_REF][START_REF] Plainaki | Exospheric O 2 densities at Europa during different orbital phases[END_REF]. Indeed, [START_REF] Plainaki | Exospheric O 2 densities at Europa during different orbital phases[END_REF] did reproduce asymmetries in the exosphere by modeling the uncertain temperature-dependence of O 2 , however without rotation the model did not reproduce consistent dusk-over-dawn asymmetries.

Despite the uncertainties [START_REF] Roth | Europa's far ultraviolet oxygen aurora from a comprehensive set of HST observations[END_REF] (hereafter R16), equipped with the upgraded Space Telescope Imaging Spectrograph (STIS) with a spatial resolution of 71-95 km, altered the nominal paradigm of a globally-uniform exosphere. The STIS observations were able to distinguish a two-component atmosphere in altitude z and oxygen mixing ratios: (1) near-surface O 2 exosphere (z 400km; ≈ 95 %-99 % O 2 ) and ( 2) corona (z 400 km; 85 % O 2 ). Previous observations did however provide evidence of asymmetric oxygen emission at various longitudes, φ = 200 -250 • (McGrath et al. (2004, 2009)) and φ ∼ 90 • [START_REF] Saur | Hubble Space Telescope/Advanced Camera for Surveys Observations of Europa's Atmospheric Ultraviolet Emission at Eastern Elongation[END_REF] influenced by various external mechanisms such as the plasma. R16 assessed the influence of Jupiter's plasma torus on the oxygen aurorae, and found that the polar aurorae are periodically more intense depending on the magnetic tilt. Monitoring Europa's oxygen aurorae at such high spatial resolutions throughout the orbit additionally discerned a longitudinal, diurnal asymmetry of unknown origin. The dusk hemisphere was observed to be consistently brighter on average than the dawn hemisphere by a factor of ∼ two.

In order to better understand the bulk physical processes regulating the dusk-over-dawn asymmetry we compare hemispherically averaged, dusk-over-dawn ratios for HST observations (black circles) with several EGM simulations assuming isotropic plasma conditions for a range of O 2 adsorption conditions (squares, triangles, Xs) in Figure 6. The HST data is confined to the near-surface O 2 region, and independent of photo-excitation as we uniquely evaluate the forbidden line ratios at 1356 Å.

All simulated data in the shaded region, correspond to a duskover-dawn asymmetry, whereas points in the unshaded region represent a dawn enhancement. In our simulated O 2 case with the least assumptions (no surface interactions; black squares) the dusk hemisphere is brighter than the dawn hemisphere throughout the entire orbit, in the same manner as the HST oxygen observations. Upon varying the initial conditions for our EGM simulations, our results appear to imply that the duskover-dawn asymmetry is thermal. That is, the surface temperature regulates the O 2 production and the adsorption probability which when varied, strongly influence the diurnal asymmetry. The open squares are identical to the former, nominal case, except that a low temperature-dependence is applied to the O 2 yield (q O2 ' = q O2 10 in Eqn. 2). The reduced thermal dependence is seen to considerably reduce the dusk-over-dawn asymmetry. Conversely, increasing the O 2 thermal dependence was found to increase the dusk-over-dawn asymmetry in the 1-D atmospheric evolution model by [START_REF] Oza | Dusk/dawn atmospheric asymmetries on tidally-locked satellites: O 2 at Europa[END_REF]. Including the thermal inertia of Europa's ice on the other hand only increased the asymmetry by < 7 %. Furthermore, simply turning on the non-inertial forces in our model (i.e. Coriolis, centripetal) without accounting for Europa's rotation about Jupiter resulted in no dusk-over-dawn asymmetry. The result is shown in Figure 7(b).

Next, we evaluate how the dusk-over-dawn asymmetry varies with a variable heat of adsorption for O 2 .

O 2 Adsorption on Grains in the Water Ice Regolith

As discussed in Section 3.1.1, O 2 on Europa's ∼ 100K surface is thought to undergo a series of unimpeded ballistic hops due to its low sublimation temperature of ∼ 54K. Recently, on the far colder Rhea and Dione, evidence of atmospheric evolution due to O 2 adsorption was discussed by [START_REF] Teolis | Dione and Rhea seasonal exospheres revealed by Cassini CAPS and INMS[END_REF]. In this regard, we simulate two additional cases where we alter the surface heat of adsorption for the returning O 2 : E ads = 0,26eV (Xs) and E ads (L) E ads (T ) (triangles).

The large heat of adsorption case (X) results in stronger interactions with the regolith (i.e. H 2 O molecules freezing), and in effect longer residence and migration times, which is seen to significantly reduce the dusk-over-dawn asymmetry. The atmospheric bulges described in section 3 then, will not have time to rotate to dusk as the longer timescales will permit destruction near the production region. Lastly, we consider a case where the heat of adsorption is non-uniform between the leading and trailing hemispheres (triangles). To test this effect globally we model the heat of adsorption with a simple cos 2 function with latitude (θ) and planetary longitude (φ ):

E ads (φ , θ) = E 1 cos 2 (φ -φ 0 ) 2 cos 2 (θ -π/2) + E 0 (8)
Equation 8 is a simple surface adsorption relation modeled in the EphiO frame where φ 0 = 0 treats E ads as preferential adsorption on the leading hemisphere and φ 0 = π as preferential adsorption on the trailing hemisphere. In Fig. 6 the triangles present a simulation where E 1 = 0,04eV , E 0 = 0,2eV, and φ 0 = 0. It can be seen that the non-uniform heats of adsorption also reduce the dusk-over-dawn asymmetry, and additionally mitigate the orbital asymmetries near the leading hemisphere phases. This could imply that the simulated region between 90 • < φ obs < 150 • possesses stronger O 2 interactions with the regolith. Conversely, the trailing hemisphere could also adsorb more efficiently since the column of O 2 driven towards leading hemisphere phases is due to the ejection roughly half of a rotation earlier. Thus we are currently unable to deduce whether the O 2 adsorbs more efficiently at the leading or trailing surfaces.

The transient O 2 adsorption simulated here may describe the trapped O 2 observed at 5771 Åas a condensed frost [START_REF] Spencer | Condensed O 2 on Europa and Callisto[END_REF] ; Spencer & Grundy 2017). That is, the O 2 could be trapped in bubbles before it is radiolytically ejected, should the temperature be sufficiently high to allow for va-cancies produced by diffusion of the incoming ion [START_REF] Johnson | O 2 /O 3 Microatmospheres in the Surface of Ganymede[END_REF]. Recently, Johnson et al. 2018 (submitted) reviewed the origin and fate of the trapped O 2 in ice. It was suggested that the observed O 2 was trapped at dangling hydrogen bonds, from where it is thermally released.

Conclusion/Summary

Allowing Europa to rotate about Jupiter in our 3-D Monte Carlo simulations of Europa's water product exosphere, results in a dusk-over-dawn O 2 asymmetry at all orbital phases. The hemispherically-averaged asymmetry is roughly consistent with the near-surface dusk-over-dawn oxygen emission recently observed by HST. We suggest that the near-surface, dusk-overdawn O 2 asymmetry is more generally part of Europa's diurnal cycle of O 2 , built and destroyed over one orbit. This O 2 cycle appears to depend strongly on the (1) O 2 production (therefore also the surface temperature), (2) O 2 loss, and (3) Europa's rotation rate, all of which lead to a peak in column density at dusk.

The diurnal cycle described in this work, can be summarized as follows :

1. Trailing Day: The trailing hemisphere source is illuminated and rapidly builds an O 2 column rotating with Europa's surface, ejecting between ∼ 2,5 -3,5 • 10 8 O 2 cm -2 s -1 throughout the day.

After half of an orbit, the rotating O 2 column has accumulated an atmospheric bulge of average density N O 2 8 • 10 13 O 2 cm -2 spread across a quarter of a hemisphere from dusk, local time.

Trailing Night:

The trailing hemisphere source enters night, at which point the e --impact dissociation begins to slowly overwhelm the O 2 production and acts to isotropically diminish the bulk O 2 exosphere.

A similar dusk-over-dawn asymmetry is predicted at all subobserver longitudes in Ganymede's near-surface O 2 atmosphere [START_REF] Leblanc | On the orbital variability of Ganymede's atmosphere[END_REF]. We note that these O 2 bulges maintained near dusk, hinge on the timescales of tidally-locked atmospheres as described by [START_REF] Oza | Dusk/dawn atmospheric asymmetries on tidally-locked satellites: O 2 at Europa[END_REF]. The orbital timescale is comparable to the average atmospheric lifetime of the radiolytic O 2 , so that τ orb ∼ τ O2 . In other words, the O 2 exosphere survives long enough so that the O 2 can accumulate towards dusk during the day, given its simulated thermal dependence. If the O 2 exosphere survived for too long, for instance τ orb τ O2 , the continued production would average out any asymmetries as the O 2 loss would be negligible over the orbit. If the O 2 exosphere was destroyed too quickly on the other hand, τ orb τ O2 , the diurnal asymmetries would not have time to build an O 2 bulge. Overall, the comparable size of the satellite's rotation rate and the rate at which the near-surface O 2 is being lost results in a shift towards dusk. The relative sizes of the rotation rate and the estimated loss rate at Europa and Ganymede, result in a periodic O 2 asymmetry, which can be probed in satellite local time.

While we have provided evidence for a dusk-over-dawn asymmetry at Europa, a global understanding of Europa's exosphere is far from fulfilled. The O 2 cycle depends on the O 2 production and loss: source rates may require a largely thermal source (e.g. [START_REF] Oza | Dusk/dawn atmospheric asymmetries on tidally-locked satellites: O 2 at Europa[END_REF], [START_REF] Oza | Dusk/dawn atmospheric asymmetries on tidally-locked satellites: O 2 at Europa[END_REF]), and loss rates may need to include plasma interactions (e.g. [START_REF] Dols | Europa's atmospheric neutral escape: Importance of symmetrical O 2 charge exchange[END_REF]; [START_REF] Lucchetti | Loss rates of Europa's tenuous atmosphere[END_REF]). A self-consistent exosphere model including the plasma interaction is therefore sorely needed. A stronger understanding of the spatial morphologies of O 2 exospheres will be of particular interest for the spacecraft trajectories at the icy Galilean satellites (i.e. NASA's Europa Clipper; ESA's JUICE).

Acknowledgments: The authors express their gratitude to Lorenz Roth for insight on better comparing the HST observations and the EGM exosphere simulations, and to Ben Teolis for constructive discussions on O 2 -water ice interactions. AVO and FL acknowledge the support of LabEx/ ESEP . This work was also supported by CNES "Systéme Solaire"program. REJ acknowledges support from NASA's Planetary Data Systems Program. This work is also part of HELIOSARES Project supported by the ANR (ANR-09-BLAN-0223) and ANR MARMITE-CNRS (ANR-13-BS05-0012-02). Authors also acknowledge the support of the computational platform CICLAD hosted by the Institut Pierre Simon Laplace.

Figura 1 :

 1 Figura 1: Top-down geometry of the simulation domain and associated physical processes at a sub-observer longitude of φ obs = 90 deg, corresponding to the sunlit leading hemisphere. The O 2 ejection flux due to sputtering, highlighted by the red vector Φ 0 , dominates ejection at the sub-plasma point against the ram direction of the plasma, following Equation 1. The ejected O 2 is assumed to be thermalized to the local surface temperature and is subject to dissociation and ionization. Adsorption, or sticking, is indicated in violet.

Figura 3 :

 3 Figura 3: Europa's static, O 2 exosphere for a simulation fixed at the sunlit trailing hemisphere with no rotation. Vectors are shown to demonstrate the day-night migration in the absence of rotation. An artificial day-side O 2 asymmetry is highlighted, due to preferential ion bombardment at the sunlit trailing hemisphere in the absence of rotation. The low albedo, sunlit trailing hemisphere has an equilibrium temperature of T d ∼ 135K, further exaggerating the effect of O 2 production on the exosphere due to the strong thermal dependence of the O 2 sputtering yield.

  Figura 5: a: Illustration of Europa's diurnal O 2 cycle for our modeled thermally-dependent trailing hemisphere source. Day-night phases are superimposed in the frame of an observer at the trailing hemisphere. During 'Trailing Day', the exosphere grows on average ( N O 2 production phase). During 'Trailing Night', the O 2 exosphere slowly diminishes on average ( N O 2 loss phase). The production and loss phases corresponding to the diurnal asymmetry therefore results in the orbital evolution of Europa's O 2 throughout its 85-hour day. b: Monte Carlo simulation results for Europa's trailing hemisphere while rotation about Jupiter is active.Orbital evolution of the surface-averaged O 2 column density (black) along with the surface-averaged O 2 production flux ( f e j : blue) as well as the average O 2 loss flux ( f loss : magenta) versus the sub-observer longitude. f loss estimates the loss of the average O 2 content, throughout the exospheric lifetime of the O 2 , at each sub-observer longitude: N O 2 ∼ f loss t exo . X indicates the day-night terminator separating the average production and loss phases.

Figura 6 :

 6 Figura 6: Orbital evolution of the dusk-over-dawn ratio, < R >. Black circles with error bars: HST near-surface 1356 Å auroral emission data. The average oxygen emission from the dusk hemisphere is divided by the average dawn hemisphere emission. EGM simulations of < R > for an exosphere subject to isotropic plasma conditions, n e = 70 cm -3 and T e = 20 eV, are shown for non-adsorbing O 2 (black squares), non-adsorbing with a small thermal dependence (open squares), highly adsorbing O 2 "sticking"to the surface (Xs), and a non-uniform adsorption (triangles).

  Figura 7: Simulated line of sight column densities of Europa's O 2 without (a) and with (b) rotation at the sunlit leading hemisphere φ obs = 90 • . Both simulations include the non-inertial Coriolis and centripetal forces. The hemispherically averaged dusk-over-dawn column density ratio is indicated in the caption as < R >.

  Exospheric timescales for Europa. Given τ orb = 3 • 10 5 sec. The average hop time for an O 2 molecule is computed using an average surface temperature . The ballistic hop ,t hop , assumes no interaction with the surface. The day-night migration time is estimated as a random-walk process across one Europa radius assuming no O 2 trapping or reactions with the surface ice. The O 2 lifetime,τ O2 , is limited by dissociation and ionization, computed by the product of the net reaction rate coefficient and the electron number density: (κ × n e ) -1

					Timescale (τ orb )
				Orbital Period	τ orb	1.0
				Ballistic O 2 hop	t hop	8 • 10 -4
				Day-night migration	t d	4.2
				O 2 lifetime *	τ O2	1.08
	Tabla 1: of T ∼ 110K, as	√	2	v 0

g