PhD Jacob G Martin

BLA Charles E Davis

PhD Maximilian Riesenhuber

PhD Simon J Thorpe

Microsaccades

Microsaccades during high speed continuous visual search

Keywords: microsaccades, continuous visual search, eye tracking, oculomotor, fixations, saccades

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Introduction

During active visual search, humans often make high velocity eye-movements called saccades to target various regions of interest in a scene with their gaze. When saccades are involuntary and smaller than around 1 degree of visual angle, these ballistic eye movements are typically called "microsaccades." A recent review used scientific evidence collected over a period of more than 60 years to argue that microsaccades "are necessary to achieve continual perception during fixation" and "contribute unique-ly to visual processing by creating strong transients in the visual input stream. [START_REF] Rolfs | Microsaccades: Small steps on a long way[END_REF]." Thus, microsaccades can play an important role in human visual perception.

One source of recent controversy was that studies investigating microsaccades generally use prolonged periods of fixation, leaving open the question of whether microsaccades occur during active visual search. That is, "microsaccades are known to occur during prolonged visual fixation, but it has been a matter of controversy whether they are also produced during free-viewing [START_REF] Otero-Millan | Saccades and microsaccades during visual fixation, exploration, and search: Foundations for a common saccadic generator[END_REF]." In their study, Otero-Millan and colleagues found that microsaccades not only occurred during prolonged visual search of static natural visual scenes, but also shared similar spatiotemporal properties with saccades. The authors concluded that saccades and microsaccades likely share a common neural generator [START_REF] Otero-Millan | Saccades and microsaccades during visual fixation, exploration, and search: Foundations for a common saccadic generator[END_REF]. Additionally, their study found that microsaccades increased in frequency after a saccade landed on an area of interest in a visual scene, such as a human face.

In 1935, Buswell published a book entitled 'How people look at pictures.' In it, Buswell found patterns of eye fixations that were related to various patterns of elements in the pictures [START_REF] Buswell | How people look at pictures: a study of the psychology and perception in art[END_REF][START_REF] Land | Eye movements and the control of actions in everyday life[END_REF]. In 1967, Yarbus noticed that instructions influenced these patterns of eye fixations [START_REF] Yarbus | Eye Movements and Vision[END_REF]. A few years later, Noton and Stark postulated a theory that humans recognize objects using small "scanpaths" in eye movements which form stereotypical patterns [START_REF] Noton | Scanpaths in Eye Movements during Pattern Perception[END_REF]. This hypothesis was based on the fact that when humans look at pictures, they typically fixate in stereotypical sequences of locations that vary according to the category of the picture that was displayed. The scanpath theory was a prototypical motor theory and inspired a lot of subsequent work on perception.

How does the scanpath theory from Noton and Stark relate to the results from Otero-Milan et al.? In particular, are such scan-paths made with microsaccades before the first saccade after trial onset? If we interrupted the stimulus with a new stimulus so that a new target appeared immediately after each correct saccade entered the previous target, would the participant still attempt to explore the previous face with microsaccades? Are there any perceptual functions of microsaccades that occur after the first saccade after trial onset? If so, how long do these perceptual microsaccades take to make after the saccade landed?

To answer these questions, we analyzed a large cohort of results from a new visual search paradigm called "continuous visual search zapping" [START_REF] Martin | Zapping 500 faces in less than 100 seconds: Evidence for extremely fast and sustained continuous visual search[END_REF](Martin et al., , 2018a[START_REF] Martin | High Resolution Human Eye Tracking During Continuous Visual Search[END_REF]. The "zapping" refers to the fact that as soon as the subject found the target with their gaze, that target was erased ("zapped") and a new target was painted. Furthermore, instead of visual search on a static screen containing perhaps multiple regions of interest, this "zapping" paradigm changed the location and background scene of subsequent face targets around 18ms after the subject's gaze reached each face. Subjects achieved up to 6.5 faces targeted each second in this paradigm (including all time for blinks and eye movements). There was not much time for fixation on any particular face because it took only an average of 18ms to paint the new target and background image.

In this paper, we explore the properties of microsaccades in this novel environment: the continuous visual search task. Based on other tasks, we formed some hypotheses of how microsaccades may behave in this task. Therefore, our work is a description of microsaccades in a new task paradigm and care should be taken when comparing our results with other papers. The purpose of the current study was to investigate whether or not microsaccades occurred during continuous visual search zapping for faces. The main hypothesis was that microsaccades would not often occur before the first saccade after trial onset. We reasoned that under a feedforward model of human visual processing, a single wave of feedforward neural activity should suffice to allow a saccade to accomplish the search task. We also hypothesized that, if we found microsaccades, that they would most often serve to perceptually correct their preceding saccades.

Nevertheless, we left open the possibility that microsaccades may occur as part of the search process, but we predicted that they would occur mainly only after saccades. Because the study from Otero-Millan et al. found a large number of microsaccades on areas of interest during visual search, we hypothesized that even though microsaccades would be rare, when they did occur, they would have a task-related perceptual function during successful targeting of the searched object (overshoot/undershoot correction, face exploration). However, we hypothesized that before the first saccade after trial onset, the microsaccade rates would drop to zero like found in previous studies [START_REF] Gao | Modulation of microsaccade rate by task difficulty revealed through between-and within-trial comparisons[END_REF]. Validating these hypotheses would be evidence that microsaccades are not critical for successful continuous visual search but do sometimes occur after saccades to more-finely hone in on the target of interest.

Methods

Participants

We conducted three separate experiments designed to explore the speed of continuous face detection (N1=24 subjects, N2 =24 subjects, N3=24 subjects). We did three separate experiments, but we only present the results from Experiments 1 and 3. We have numbered the experiments the same way as described in our other papers (Martin et al., 2018a[START_REF] Martin | Zapping 500 faces in less than 100 seconds: Evidence for extremely fast and sustained continuous visual search[END_REF]. A total of 44 subjects with normal or corrected-to-normal vision participated in a total of 72 separate sessions divided into 3 experiments: Experiment 1 (N1=24, two left-handed, 14 females, ages 21-39), Experiment 2 (N2=24, two left-handed, 10 females, ages 22-53), and Experiment 3 (N3=24, two lefthanded, 13 females, ages 21-40). Some subjects participated in more than one of the three experiments: 6 took part in all three experiments, 9 in only Experiments 1 and 2, 6 in only Experiments 1 and 3, 1 in only Experiments 2 and 3, 3 in only Experiment 1, 8 in only Experiment 2, and 11 in only Experiment 3. We recruited participants via a common laboratory mailing list for participants. Participants were compensated 15 euros for each experiment. One participant quit the task prematurely in Experiment 3, and we excluded their data and ran another participant to complete the cohort of 24 subjects in Experiment 3.

Design

Each experiment consisted of 4 different conditions (No Scene, Upright; No Scene, Inverted; Scene, Upright; Scene, Inverted) that were separated into separate blocks. That is, in each block, participants continuously localized 500 inverted or upright faces that were either directly pasted into one of 500 different cluttered background scenes, or pasted only a gray screen as the background. Experiment 1 had a large range of eccentricities and polar angles, so that each face could appear anywhere on the screen (see Figure 1). To minimize the time required for large magnitude eye movements, every subsequent face in Experiment 3 appeared only 4° in eccentricity away from the previous face. Also, the polar angles in Experiment 3 were set such that subsequent targets appeared at polar angles of 0°-45°, 135°-235°, 315°-360° from the previous target. In Experiment 1, we pasted faces directly on the gray backgrounds or cluttered background scenes, whereas in the Experiment 3, we also locally blended the faces into the background scene by matching their grayscale histogram distribution to that of the local histogram at the pasted location [START_REF] Martin | Zapping 500 faces in less than 100 seconds: Evidence for extremely fast and sustained continuous visual search[END_REF].

Materials

We created the face stimuli from a set of 2316 images of segmented faces from the Humanae project (with written permission from the artist Angélica Dass, http://humanae.tumblr.com/ ) [START_REF] Dass | The Beauty of Human Skin in Every Color[END_REF]. Background image stimuli for all experiments were selected from a large database of 861 images, some of which have been used in previous psychophysical studies [START_REF] Thorpe | Speed of processing in the human visual system[END_REF]. We converted the faces and backgrounds to grayscale. We resized faces to have a height of 3° of visual angle. We resized image backgrounds to cover the entire screen resolution of 2560×1440 pixels.

Stimuli were presented on an ASUS ROG Swift PG278Q GSYNC monitor with 1ms response time and 120 Hz refresh rate, driven by two SLI linked NVIDIA GeForce 980GT GPUs, at a screen resolution of 2560×1440 pixels [START_REF] Zhang | A consumer-grade LCD monitor for precise visual stimulation[END_REF]. The display subtended approximately 31° horizontal and 22° vertical of visual angle. We controlled the display with a custombuilt workstation running Gentoo Linux with a 64-bit kernel that we tuned for real-time processing. The paradigm was programmed in Matlab R2008a (The Mathworks, MA) using Psychtoolbox version 3 [START_REF] Brainard | The Psychophysics Toolbox[END_REF][START_REF] Pelli | The VideoToolbox software for visual psychophysics: Transforming numbers into movies[END_REF]. We recorded target onset presentation times with a photodiode that was time-synchronized with the eyetracker.

We recorded eye movements using the SMI iViewX High Speed system with a 1250 Hz sampling rate. Before the first session, we determined each subject's dominant eye and subsequently recorded and calibrated that eye. The eye-tracker sent gaze position samples at a delay of approximately 5ms to the presentation hardware. We compared the time of the entrance of the eye within the target face area and the subsequent photodiode onset for the next trial to determine that the median screen update time was 18.03ms. These values did not differ by more than 1ms when examined by condition (e.g. for Experiment 1: 17.67s, 17.95ms, 18.09ms, and 18.42ms).

To detect saccades after the experiment, we used the "microsacc plugin" for saccade detection with a smoothing level of 2 ("the raw data is smoothed over a 5-sample window to suppress noise" (R. [START_REF] Engbert | Microsaccades are triggered by low retinal image slip[END_REF][START_REF] Engbert | Microsaccades uncover the orientation of covert attention[END_REF] ), a velocity factor of λ=5 to determine the velocity threshold for saccade detection ("thresholds were relative to the noise level, calculated as λ = 5 multiples of a median-based SD estimator" (R. [START_REF] Engbert | Microsaccades are triggered by low retinal image slip[END_REF]), and a minimum saccade duration of 10 samples (corresponding to 8 milliseconds) (Ralf [START_REF] Engbert | Microsaccades uncover the orientation of covert attention[END_REF] . The velocity threshold of 5 determined the velocity threshold required for saccade detection. Detection thresholds were relative to the noise level, calculated as λ = 5 multiples of a median-based Standard Deviation estimator. We considered an eye movement a saccade if and only if it went over this noise-relative threshold and had a duration of at least 10 samples, equaling 8 milliseconds (R. [START_REF] Engbert | Microsaccades are triggered by low retinal image slip[END_REF]. Furthermore, we considered all detected saccades with amplitude less than 1 degree as microsaccades.

The parameters we chose for microsaccade detection were the same as those recommended in the detection toolbox by Engbert and used by many previous studies (R. [START_REF] Engbert | Microsaccades are triggered by low retinal image slip[END_REF][START_REF] Engbert | Microsaccades uncover the orientation of covert attention[END_REF]. However, note that microsaccade detection is an inexact science and recent work has seen many algorithms and toolboxes released [START_REF] Nyström | An adaptive algorithm for fixation, saccade, and glissade detection in eyetracking data[END_REF][START_REF] Otero-Millan | Unsupervised clustering method to detect microsaccades[END_REF]. For example, decreasing the lambda parameter, which usually is set to 5 or 6, as in our study, will allow many more events to be classified as saccades [START_REF] Engbert | Spatial statistics and attentional dynamics in scene viewing[END_REF].

To allow an exploration of the effect of different parameter choices by the community, we have described and made available the data from our study in a recent article, that researchers can freely download and explore [START_REF] Martin | High Resolution Human Eye Tracking During Continuous Visual Search[END_REF](Martin et al., , 2018a)). For example, the effects of the lambda parameter and the minimum microsaccade duration on subsequent microsaccade detection may prove a fruitful area of future research for the data in our task.

Procedure

Each block contained 500 trials of a single condition (No Scene, Upright; No Scene, Inverted; Scene, Upright; Scene, Inverted). The orders of the blocks were counterbalanced across subjects so that each of the subjects did one of the possible 24 possible block orderings of the 4 conditions. This same order of 4 blocks was then repeated in another section of 4 blocks, so that subjects did a total of 8 blocks. After each block of 500 trials, there was a small pause of about 2 minutes while we recalibrated the eye tracker to ensure that the calibration remained accurate throughout the experiment.

Within each block, participants performed a continuous detection task in which we pasted the 3° tall face stimuli into large scenes that filled the entire 2560×1440 pixel screen of the monitor (see Figure 1A). Participants were told to find the faces with their eyes as fast as they possibly could. During the experiments, we only used the gaze position data to advance to the next trial. To make the paradigm go as fast as possible, but to also retain some robustness to noise, subjects had to maintain gaze within the 3°x3° region centered on the face for at least 2 samples (1.6 milliseconds) in order proceed to the next target. Each subsequent trial started immediately after the subject's eye landed within the 3x3 degree window surrounding the center of the previous face (with a median screen-update error of 18ms after the subject found the previous face).

We randomly pasted the faces either based upon the position of the face in the previous trial (Experiment 3) or completely randomly within the 2560×1440 pixel scene (Experiment 1). All faces and background images within any given block were unique. We paired and combined the faces and background images before the block and counterbalanced them across subjects so that each face and background image combination appeared equally in every condition.

During the experiments, we did not place the faces based on the gaze position (which may have been better but would have slowed the experiment down considerably given the computational complexity required to blend and paste a face into a large 2560x1440 image at runtime). As subjects could have had their gaze anywhere in the 3x3 degree face detection window, the next trial's facewhich, for example, appeared at 4° eccentricity from the center of the previous face in Experiment 3could have been presented further or closer to the actual eye position at trial onset. Nevertheless, after the experiment, we were able to determine the actual eccentricity of the target according to the recorded gaze location at trial onset. All analyses of eccentricity used the gaze position at the time of trial onset. Even though we pasted images based on the previous target's location, the average actual eccentricity indeed had a mean value of 4.12° during Experiment 2, and 4.09° during Experiment 3. We also checked that the average actual eccentricity did not differ by condition within each experiment (p>0.11, Wilcoxon rank sum, df=25).

Results

Figure 1A shows the experimental paradigm, during which subjects continuously targeted small 3-degree faces. In our previous work, we did not find significant differences between the conditions in Experiments 2 and 3. Thus, the results in the current paper correspond to the data in Experiments 1 and 3 from the original datasets [START_REF] Martin | High Resolution Human Eye Tracking During Continuous Visual Search[END_REF](Martin et al., , 2018a)). Furthermore, microsaccade rates did not differ between conditions (see Figure 1C). Thus, to calculate continuous saccade and microsaccade rates and properties in Figures 234, we collapsed the data from all conditions. There were 24 subjects and 96,000 trials in Experiment 1 and 24 subjects and 96,000 trials in Experiment 3. Microsaccades and saccades followed the main sequence (Figure 1B). We defined microsaccades as ballistic movements with magnitude less than 1 degree (see Materials for the parameters and algorithm that we used). Saccade rates during the one second surrounding each trial were higher, but similar to targeting rates, indicating a small degree in error in targeting (Figure 1C).

Microsaccade rates during the one second surrounding each trial averaged around 1Hz in each condition (Figure 1C). We next investigated the temporal dynamics of saccade rates by aligning trials based on trial onset. During the -100ms -0ms period before trial onset, a single microsaccade occurred in only ~20% of the trials. On the other hand, during the first 100ms after trial onset, ~99% of the time, there were no microsaccades at all (Figure 2A).

During only 12ms after trial onset, the microsaccade rate dropped to near zero levels (Figure 2AB). We did an additional analysis that shows that the saccade-following microsaccades were not strictly always in the same direction as the preceding saccade. From the experimental data where faces were pasted using the entire screen (Experiment 1), we found that in 27% of the trials, a single microsaccade occurred directly after a saccade. Of these 27%, 84% had a polar angle target that was more than 45 degrees away from the saccadic polar angle, whereas 16% had a polar angle target that was less than 45 degrees. Thus, there were cases where the microsaccade was in the same direction of the saccade, but the subsequent microsaccade was launched more often in a different direction from the preceding saccade.

Next, we aligned the eye movement data to the onset or offset of the first saccade after trial onset (Figure 3AB). Microsaccades occurred ~20% of the time directly after a saccade offset, but not before (Figure 3A). When we aligned trials on the saccade offset, saccades or microsaccades occurred within 25ms after the saccade offset (Figure 3B). The time before the saccade onset was almost completely without saccades or microsaccades (Figure 3C,left). Thus, the vast majority of the microsaccades we found in our study followed the offsets of the first saccade after trial onset (Figure 3D right). Figure 5A shows an example trial where there were 3 microsaccades after an initially correct saccade. It is important to note that the appearance of 3 microsaccades, like in this figure, was extremely rare. We analyzed the landing locations of each saccade and microsaccade by first recording various facial landmarks in every trial (hair top middle, forehead top middle, left eye, right eye, nose tip, mouth center, chin bottom center, Figure 5A). Next, we calculated the frequency of occurrences of saccade and microsaccade landing locations relative to the facial landmarks of a template face. We only analyzed the saccades that landed within the 3x3 degree face target area. We only counted microsaccades that started and ended within the 3x3-face target area. Concretely, for each of the aforementioned saccades and microsaccades, we linearly transformed its end point to a template face using the Procrustes algorithm [START_REF] Stegmann | A Brief Introduction to Statistical Shape Analysis[END_REF]. Note that this algorithm does not produce an exact match to the template, because the relative facial landmarks differed from face to face. Finally, we counted the number of times a microsaccade landed at each particular location on the mapped template face and smoothed the result with a 5x5-pixel disk spatial averaging filter that subtended 0.077x0.077 degrees of visual angle. The landing locations of saccades and microsaccades had similar facial location preferences depending on whether the face was upright (Figure 5B) or inverted (Figure 5C). These results match with what has been found in previous studies of eye movements on face stimuli [START_REF] Xu | Does face inversion qualitatively change face processing: An eye movement study using a face change detection task[END_REF]. Saccades with following microsaccades were less accurate than saccades without following microsaccades (see Figure 5CD). However, the microsaccades that occurred after saccades shared the same landing endpoint distributions as saccades without microsaccades (see Figure 5CD). Figure 5B shows that the velocity profiles were different between saccades with a following microsaccade saccade and those without a following microsaccade before the saccade offset at 0ms. We ran a temporal RUSBoost classifier at the single trial level by training on the pre-microsaccade eye velocities and trying to predict whether each saccade had a subsequent microsaccade. We found a ROC area of 0.70 (10-fold cross validation, default RUSBoost parameters, correct-trials, upright, background trials only).

The results from Experiment 3 (wherein faces were only presented 4 degrees from their previous target) were similar to those in the other experiments. However, Experiment 1's design also allowed us to confirm whether or not there was a relation between the target eccentricity and the microsaccade rate (because in that experiment, targets could appear at any location on the screen). Figure 4 shows there was no difference between the likelihood of a saccade onset or microsaccade onset across eccentricities from 4 degrees to 20 degrees. These results indicate that the microsaccade onset rate or timing did not change according to the target eccentricity .

Figure 4: Saccade start (blue), saccade end (green), and microsaccade occurrence probabilities per time bin according to the target eccentricity of the face target that appeared at 0ms. Time 0 corresponds to the new trial onset, which was immediately after the participant's gaze had reached the previous trial's face. Eccentricities are listed on the y-axis. The color and height of each data point represent the percent occurrence over all 96000 trials for saccade start times (left), saccade end times (center), and microsaccade start times (right). The percent occurrence over 96000 trials is color coded according to the respective colorbars to the right of each plot. Note that microsaccades almost never occurred before the initial saccade after trial onset at any eccentricity Figure 5: (A) An example with 2 microsaccades directly after a correct saccade in Experiment 3. (B) Median velocity on correct upright background trials at each timepoint. Trials were aligned on the offset time of the first saccade after trial onset. Note the microsaccades that occurred almost immediately after the preceding saccade (green line after 0ms). (C,D) Saccades without microsaccades and saccades with microsaccades

shared the same facial landmark target frequencies within correct background trials for both upright and inverted face conditions. Saccades with following microsaccades were qualitatively less accurate than saccades without following microsaccades. However, the microsaccades that occurred after saccades shared the same landing endpoint distributions as saccades without microsaccades. The heatmaps for the inverted faces were flipped vertically for ease of presentation. To make the heatmaps, the 7 face landmark locations for each trial were mapped to the 7 face landmark locations of the template face using the Procrustes algorithm. We then mapped the first saccade after trial onset or the subsequent microsaccades into the template face's space. Finally, we fit a normalized 2D gaussian to the raw saccade/microsaccade endpoint data using the heatmap function in PyGaze. Source images in Figures 1ACD are from one of the authors of this paper.

We also calculated the number of consecutive correct trials of each possible length, ignoring sub-sequences (e.g. a run of 3 correct trials did not change the totals for runs of length 1 or 2, Figure 6A). An incorrect trial was defined as one where the first saccade after trial onset did not land on the face. A correct trial was defined as one where the first saccade after trial onset did land in the 3x3 degree square around the face. We did a similar analysis to compute the number of consecutive trials without a microsaccade (Figure 6B). The longest consecutive sequence of correct trials by any subject was 219 consecutive correct trials in the no scene, upright face condition. The longest consecutive sequence of trials without any microsaccades within the -200ms to 800ms intervals surrounding the trials by any subject was 118 consecutive trials in the scene, upright face condition.

Figure 6: (A) Number of occurrences of consecutive sequences of correct trials without a mistake (x-axis) during two blocks of 500 trials in each condition (see legend). Note that sub-runs of consecutive trials were not counted (e.g. a run of 3 correct trials did not change the totals for runs of length 1 or 2) (B)

Number of occurrences of consecutive sequences of trials without a microsaccade. Note that sub-runs of trials without microsaccades were not counted (e.g. a run of 3 trials did not change the totals for runs of length 1 or 2).

An exploration of the time required for a microsaccadic search strategy also proved illuminating. Gao et al. recently showed that microsaccade rates on non-continuous tasks (i.e., tasks that have pauses in between trials) drop dramatically (e.g., to less than .01 microsaccades/second) during the first 200ms after trial onset and are modulated according to task difficulty [START_REF] Gao | Modulation of microsaccade rate by task difficulty revealed through between-and within-trial comparisons[END_REF]. Average overall rates found in such non-continuous tasks are typically between 1-2 microsaccades each second. On the other hand, we found that subjects could target up to 5-6 faces each second -rates that are 3-6 times faster than the microsaccade rates published in the literature. Therefore, it does not seem likely that the subjects could have used a microsaccadic strategy during our study and yet achieved such high rates of search. To be certain, we counted the number of microsaccades that occurred during the first 200ms after trial onset. In Experiment 3, 97.96% of trials did not contain a microsaccade in the first 200ms after trial onset, 1.98% of the trials had one microsaccade, 0.05% of the trials had two microsaccades, and 0.01% of the trials had three or more microsaccades. In addition, the average saccade amplitude after trial onset was 4.0031°. There were only 0.01% (i.e. 89/96000) of trials in which there were microsaccades away from the target during the first 200 ms after trial onset in Experiment 3. Of the subsequent saccades after these microsaccades, 84.27% landed on the target. However, of all saccades detected, 84.37% of them landed on target. Thus, subjects rarely used a microsaccadic search strategy during the paradigm, and if they did, the strategy did not yield any improvement in accuracy over a single directed saccade.

Discussion

We were interested in finding out whether microsaccades occurred during continuous visual search. If they do exist, do the serve any perceptual function? In addition, are microsaccades critical to the success of a continuous search process? If they occur, is there any perceptual function to them or not? To answer these questions, we analyzed the properties of microsaccades that occurred during a continuous visual search task for small faces. We called this paradigm "continuous visual search zapping" to reflect the fact that as soon as the gaze reached the target, the current target was "zapped" (erased) and an entirely new scene and target was painted [START_REF] Martin | Zapping 500 faces in less than 100 seconds: Evidence for extremely fast and sustained continuous visual search[END_REF].

Due to the high speeds of saccadic targeting during this task [START_REF] Martin | High Resolution Human Eye Tracking During Continuous Visual Search (Dataset)[END_REF]) and the published low microsaccade rates in the literature [START_REF] Gao | Modulation of microsaccade rate by task difficulty revealed through between-and within-trial comparisons[END_REF], it seemed that there would not be enough time for a local microsaccadic search strategy before each saccade. Indeed, microsaccades mainly occurred only after the targeting of the face and before the next target's trial onset (Figure 2A, 3A, 3B). During the period before saccade onset, there were almost never any microsaccades. As soon as the next target appeared, the microsaccade rate dropped to near zero levels within only 12ms. Our paradigm is different from "visual search" and "visual exploration" because the stimulus changed as soon as the eyes reach the face. We call this paradigm "continuous visual search." It is true that subjects may have done some "visual exploration" and "visual search" until the target was found, but this was not indicated by any saccadic or microsaccadic eye movements before the first saccade after trial onset in our task. Indeed, subjects made a saccade towards the target with almost zero microsaccades intervening between the trial onset and the first saccade. Thus, there was no evidence of "visual search," in either the saccadic or the microsaccadic sense after trial onset until the first saccade after trial onset was launched. Furthermore, microsaccades mainly occurred at the end of a saccade. Microsaccades only rarely occurred before the start of a saccade. As proof that search could successfully continue without any microsaccades at all, one participant successfully targeted up to 119 faces consecutively without the presence of any microsaccades. Therefore, it does not appear that microsaccades were a necessary component of continuous visual search and targeting.

While there were microsaccades that occurred during our task, when they did occur, they most often directly followed a saccade. These saccade-following microsaccades were task oriented. That is, such microsaccades were either corrections for an overshoot or undershoot, or local explorations within the face area. Indeed, when microsaccades occurred inside a target area after a saccade reached the target, they most often landed closer to the eyes/forehead when the face was upright and closer to the nose/chin for inverted faces (see Figure 5BC). These results are similar to those seen while recording gaze preference in previous free-viewing face inversion studies [START_REF] Xu | Does face inversion qualitatively change face processing: An eye movement study using a face change detection task[END_REF]. Moreover, the endpoints for microsaccades and saccades both shifted their preferred locations equivalently depending on whether or not the face was inverted. Thus, the microsaccades that occurred directly after a saccade offset shared clear behavioral properties with the saccades. This means that the microsaccades and saccades both served the same perceptual function for completing the task. Interestingly, these corrective microsaccades occurred only ~1-25ms after a saccade offset (see Figures 2A, 3AB, and5B). This suggests that these perceptual saccade-following microsaccades were involved in some kind online mechanism that quickly corrected previous saccadic targeting attempts. These microsaccades saccades happened so fast, that they likely were planned. A very interesting question for further research is whether these microsaccades were planned: before the first saccade, during it, or immediately after checking some "hypothetical motor execution program." Our hunch is that these microsaccades were all planned beforehand, so that the humans in our study had likely planned 12 eye movements a second, not only 6.

A previous study found that microsaccades occur during self-paced visual search and free viewing tasks [START_REF] Otero-Millan | Saccades and microsaccades during visual fixation, exploration, and search: Foundations for a common saccadic generator[END_REF]. That study concluded that microsaccades have similar statistics to those of saccades and therefore likely share a common generator. This landmark study used self-paced paradigms in which the subject freely made saccades on a static screen. In contrast, our study erased the stimulus very quickly, on average only 18ms after the eye crossed into the target zone. Like the Otero-Millan et al. study, the microsaccades that occurred in our study mostly occurred immediately after a saccade. These microsaccades were goal oriented insofar as they landed on the same unique parts of the faces within both upright and inverted conditions as saccades (see Figure 5). Thus, the small inspection or correction microsaccades in our study were behavioral and were not distinguishable from saccades in any sense other than their magnitude or their frequency of occurrence and speed of onset. Our data therefore support the hypothesis that other studies have made that microsaccades and saccades may share a common generator [START_REF] Martinez-Conde | The impact of microsaccades on vision: Towards a unified theory of saccadic function[END_REF].

Another study concluded that microsaccades and small "inspection saccades" have fundamental differences in intersaccade intervals and generating processes [START_REF] Mergenthaler | Microsaccades are different from saccades in scene perception[END_REF]. Their study compared microsaccades in a 10-second free viewing tasks to those that occurred during a fixation task. In our study, we found almost no microsaccades during the only times in which subjects made fixations (i.e. when the previously targeted face disappeared and the next targeted face appeared). The differences between our study and the former is likely due to the continuous nature of our task, which forced the processing of an entirely new scene and target almost immediately after each saccade. Furthermore, because subjects had no way to predict the exact location of the next face target, the parallel processing "carwash" model of visual search was not likely a major factor for the saccades in our study [START_REF] Wolfe | Moving towards solutions to some enduring controversies in visual search[END_REF](Wolfe, , 2012a[START_REF] Wolfe | The rules of guidance in visual search[END_REF]. However, microsaccades may have indeed sometimes played a role in such a pipelined "carwash" scenario, as indicated by the task-oriented microsaccades that sometimes occurred immediately after saccade offset. Such a carwash model could have played a larger role in previous studies on microsaccades (e.g (Otero-Millan et al., 2008)), because in those studies, the stimulus was not erased when the saccade landed on the target.

Noton and Stark's scanpath theory was a prototypical motor theory and inspired a lot of subsequent work on perception [START_REF] Noton | Scanpaths in Eye Movements during Pattern Perception[END_REF]. Our data speak to this long-standing idea in the literature that the sequence of eye movements is a major part of the process of perception. Clearly, at least in our study of continuous visual search, the participants did not use local or remote scan paths to locate the targets before they launched each saccade. This fact does not preclude the possibility that scan paths may happen after the saccade landed on the face, but by then, the brain had already computed where the face was located.

On the other hand, after the first saccade after trial onset had already landed, about 25% of the time, there was a subsequent microsaccade (see Figure 2A). This following microsaccade was also task-oriented because it served to target the same face locations as the saccades (see Figure 5BC). In addition, in only about 20% (Experiment 1) and 27% (Experiment 2) of trials, the microsaccade was in the same direction as the preceding saccade. Thus, the post-saccadic microsaccades we found in our study were not random and did not appear to play any role for reducing retinal slip or fading. Rather, these microsaccades served a perceptual and task-oriented function. Interestingly, these perceptual microsaccades occurred very quickly after a saccade (0-25ms). Thus, they appeared to be an online redirection of saccades, perhaps indicating that the microsaccades in our study had a different generator than the saccades.

Our data fit with a whole range of "feedforward" computational neuroscience models of visual processing that use variants of convolutional neural networks [START_REF] He | Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification[END_REF][START_REF] Krizhevsky | ImageNet Classification with Deep Convolutional Neural Networks[END_REF][START_REF] Riesenhuber | Hierarchical models of object recognition in cortex[END_REF][START_REF] Taigman | DeepFace: Closing the gap to human-level performance in face verification[END_REF]. These experiments imply that humans should not need a lot of eye movements to recognize and localize stimuli. Indeed, once training has taken place in a deep learning system, only a single feedforward pass is necessary to recognize just about anything [START_REF] Krizhevsky | ImageNet Classification with Deep Convolutional Neural Networks[END_REF]. Consider that each saccadic movement provokes a new wave of spikes that traverse the visual hierarchy [START_REF] Delorme | Face identifcation using one spike per neuron: resistance to image degradations[END_REF][START_REF] Vanrullen | Surfing a spike wave down the ventral stream[END_REF]. If participants can get the answer and the localization of the target on the first feedforward pass through the visual system, then there is really no need for them to keep processing with microsaccades. That is, if subjects could compute the answer using only a single feedforward pass, then there would be no need to make a microsaccade to provoke another "wave" of feedforward activity. In effect, once they had the answer in one feedforward pass through the visual hierarchy, participants could simply make a saccade towards the target face. In our experiment, participants used microsaccades to continue to process the images when they made an error, but microsaccades did not occur during the fixation period before the saccade. Thus, the zapping task and our analyses are proof that microsaccades are not required for that first feedforward pass through the visual system. The Deep Learning and Convolutional Neural Network community, who can do just about anything on the first pass through the system, should be happy with this result.

While we did not find evidence for traditional fixation based microsaccades before the first saccade after trial onset during our task, we cannot generally invalidate the need for microsaccades during other visual tasks. Indeed, as Ditchburn (1980) wrote: "Some acrobats walk on their hands with amazing agility and most young people can learn to do this tolerably well. Certain tasks, such as following a line marked on the floor can be performed with reasonable accuracy. Yet no one suggests, from these facts, that it is mysterious that feet have evolved. Similarly, the fact that many subjects can perform certain kinds of visual tasks in the absence of frequent [micro]saccades does not conflict with the view that [micro]saccades play an important and, indeed, essential part in normal vision." Nevertheless, it is quite impressive that the humans in our study could continuously target up to 119 consecutive faces in only around 20 seconds without the occurrence of a single microsaccade. It is important to note that our results do not invalidate any particular study of microsaccades. Microsaccades will almost certainly be very important when one needs to keep attending to a particular location (e.g. when awaiting a subtle change in some feature, for example). Our results show how humans can "walk on either their hands or feet," with or without microsaccades, while targeting small faces in large scenes at high rates. In conclusion, microsaccades during continuous visual search did not appear to be a critical or necessary component for success in the type of continuous visual search and targeting that we used in our study. However, sometimes after a saccade, a post-saccadic microsaccade did serve a perceptual function that was task-related. Thus, microsaccades sometimes served a perceptual function after saccades, but hardly ever occurred directly before the first saccade after trial onset.

(NeCiOL Project) as part of the National Science Foundation (NSF, USA), the National Institute of Health (NIH, USA) and the Agence Nationale de la Recherche (ANR, France) NSF/NIH/ANR Collaborative Research in Computational Neuroscience. NEI R01EY024161, ANR-13-NEUC-0004, and ERC Advanced Grant No323711 (M4). Copyright © 2020, the authors.

Figure 1 :Figure 2 :

 12 Figure 1: Task, presentation, and saccade analyses. (A) Task (reproduced from[START_REF] Martin | High Resolution Human Eye Tracking During Continuous Visual Search (Dataset)[END_REF]. Red dot represents a hypothetical gaze location. The face shown is only for illustration, as we actually used 500 different faces in each block of 500 trials. (B) Main sequence of peak velocity versus magnitude for microsaccades (red dots) and saccades (blue dots). (C) Average subjectspecific saccade, targeting, and microsaccade rates calculated within the -200ms to 800ms interval of each trial. Error bars correspond to the 95% confidence intervals around the mean. Figure1Ais an unmodified reproduction from the source's Fig 1A[START_REF] Martin | Zapping 500 faces in less than 100 seconds: Evidence for extremely fast and sustained continuous visual search[END_REF]

Figure 3 :

 3 Figure 3: Eye dynamics around the saccade onsets (left column) and saccade offsets (right column). (A, B) Saccade starting times (blue) and ending times (green) plotted against microsaccade starting times (red) when onsets were aligned on saccade onset times (A) and when onsets were aligned on saccade offset times (B). (C, D) The percentage of trials (y-axis) which had 0, 1, or greater than or equal to 2 microsaccades during the first 100ms before saccade onset (left) or during the first 100ms after saccade onset (right) when aligned on the onset time (C) or offset time (D) of the first saccade after trial onset.

Acknowledgements

Funding was provided by NEI R01EY024161, ANR-13-NEUC-0004, and ERC Advanced Grant No323711 (M4). Work supported by grant ANR-13-NEUC-0004-01

Ethics and Conflict of Interest

The author(s) declare(s) that the contents of the article are in agreement with the ethics described in http://biblio.unibe.ch/portale/elibrary/BOP/jemr/ethics.ht ml and that there is no conflict of interest regarding the publication of this paper. The Committee for the Evaluation of Ethics of INSERM (CEEI Institutional Review Board) approved the experimental procedures and protocol, and we obtained written informed consent from all participants prior to each experiment. The experiments were performed in accordance with all relevant guidelines and regulations.


Methodology

To study the insertion of O atoms in the TiAl system, DFT calculations were performed using the Vienna ab initio Simulation Package (VASP) [START_REF] Kresse | Ab initio molecular dynamics for liquid metals[END_REF]. The self-consistent Kohn-Sham equations were solved using the projector augmented wave (PAW) pseudo-potentials method [START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmented-wave method[END_REF] and with the Perdew-Burke-Ernzerhof generalized gradient approximation of the exchange and correlation functional (PBE) [START_REF] Perdew | Generalized gradient approximation made simple[END_REF]. The investigations showed that TiAl is non-magnetic, wether with or without O insertion. Calculations were thus performed without magnetism. A kinetic energy cut-off of 600 eV was used for the plane-wave basis set. Γ-centered 20 × 20 × 20 Monkhorst-Pack k-meshes [START_REF] Monkhorst | Special points for brillouinzone integrations[END_REF] were used to sample the first Brillouin zone of the primitive cell. For large super-cells, the band-folding method was used to reduce the k-points meshes. The forces and the stress tensor were relaxed and calculations were performed at zero pressure.

The investigation of migration processes at the atomic scale was conducted through NEB calculations on 3 × 3 × 3 super-cells [START_REF] Henkelman | A climbing image nudged elastic band method for finding saddle points and minimum energy paths[END_REF]. Five intermediate positions were used for each 'trajectory'. The energy of the transition states was then calculated using the same criteria of convergence as for insertion sites. In the Eyring transition state theory [START_REF] Eyring | The activated complex in chemical reactions[END_REF], the key quantity at the atomic scale is the probability of leaving a site a to a site b. This probability is given by the jump rate, Γ ab , computed by:

Γ ab [T] = k B T h Z TS Z a exp - ∆E ab m k B T (1)
where ∆E ab m is to the migration energy to go from a to b, Z TS the (vibration) partition function for the transition state and Z a the (vibration) partition function for the initial state, i.e. a. Z is linked to the Helmholtz free energies, F v , by

F v = -k B T ln Z (2)
where F v is given by:

F v = k B T 3N ν=1 n ν (q) ln 2 sinh ω ν,q 2k B T dq (3)
ω ν,q are the frequencies in the wave vector q and the mode ν . Vibrational properties were performed on 3 × 3 × 3 supercells, i.e. 54 atoms, for each configuration (insertion sites and transition states). Phonon free energies were therefore calculated to analyze configuration stability and to compute Z. The summation was done on fine q-mesh grids (i.e. 20 × 20 × 20). This was done by using the phonopy package [START_REF] Togo | First-principles calculations of the ferroelastic transition between rutile-type and cacl 2 -type SiO 2 at high pressures[END_REF].

Insertion of oxygen in the TiAl system

The γ-TiAl L1 0 structure belongs to space group 123 (P4/ mmm, tP2). It is a tetragonal structure, where Ti and Al atoms occupy 1a and 1d positions, respectively. The L1 0 structure can be depicted as an ordered centered-tetragonal structure where the two types of atoms alternate in the (0 0 2) atomic planes. In this representation, the lattice parameters a o and c o are equal to 3.999 and 4.076 Å respectively. To simplify, a bct representation was used Ti atoms occupying the corners of the tetragonal lattice and Al atom the center. The lattice parameters are thus equal to 2.822 and 4.074 Å, see figure 1. As shown by Connétable [START_REF] Connétable | Theoretical study on hydrogen solubility and diffusivity in the γ-tial L1 0 structure[END_REF], interstitial species can then occupy various sites in the L1 0 system, as represented in figure 1. Eleven Wyckoff positions were tested: 1b, 1c, 2e, 2f, 2h, 4i, 4k, 4m, 4n, 4o and 8r positions. Atomic positions are given in table 1.

In the TiAl-L1 0 structure, there are four non-equivalent octahedral sites: 1c, 2e, 1b and 2f sites. 1c and 2e sites (resp. 1b and 2f sites) correspond to two non-equivalent octa hedral sites where interstitial atoms are surrounded by four Ti (resp. Al) atoms and two Al (resp. Ti) atoms. Each octahedral configuration differs from the others in the distance between first-nearest neighboring atoms, Al-Al, Ti-Al and Ti-Ti. In addition, the 4i, 4n and 4m positions correspond to three non-equivalent tetrahedral sites. As for the bcc structures, the volume defined by the tetrahedral site is inside the octahedral volume.

Simulations were conducted on three different sizes of super-cell: 2 × 2 × 2 (16 atoms), 3 × 3 × 3 (54 atoms) and 4 × 4 × 4 (128 atoms) super-cells. Larger super-cells were considered large enough to accurately compute the insertion energy in the limit of infinite dilution. However, for numerical reasons, using intermediate size super-cells, 3 × 3 × 3, is a good compromise. They were hence used to compute phonon properties and study migration processes. The insertion energy of an O atom in an interstitial site, E i , is expressed by:

E i = E o [TiAl + O] -E o [TiAl] - 1 2 E o [O 2 ] (4)
where E o energies correspond to the DFT energies. The reference state for oxygen is the O 2 molecule. E o [O 2 ] was computed with the spin effects. E i values are listed in table 2 for stable configurations only. After relaxation, eight configurations remain stable: 1b, 1c, 2e, 2f, 2h, 4i, 4k and 4m. Two of them, 2h and 1c, have almost the same lowest energy, about -3.48 eV. From a geometrical point-of-view, both configurations are very similar. The analysis of phonons nevertheless shows that the 1c site is not a local minimum, as shown in figure 2. When the O atom moves slightly away from the 1c site, it always falls into one of the two neighboring 2h sites. It is a 'stable' configuration for symmetry reasons only (by symmetry, forces along the c axis are equal to zero). Therefore, the only stable position, 2h, is located near the top face of the unit-cell, about 0.4 Å up/down of the [0 0 1] face, as displayed in figure 1. The Al-O distance is then equal to 1.85 Å, and to 2.08 Å for Ti-O. The other configurations are found almost 900 meV higher in energy than 2h, see table 2. Moreover, 4i and 2e (resp. 4k and 4m) configurations almost have the same energy, about -2.6 eV (resp. -2.4 eV). Regarding these sites, positions are also rather near, d(4i -2e) 0.7 Å, see figure 1. Phonon calculations show that they are all stable, as discussed below. This result is unusual because, there are three stable near-neighboring sites in the x (resp. z) direction. Finally, as regards 1b (∆H = 0.940 eV) and 2f (∆H = 2.955 eV) sites, their insertion energy is high in comparison with 2h sites.

Configuration stability was analyzed by studying interatomic force constants (IFC). Results (phonon density-ofstates only) are displayed in figures 2 and 3, for unstable and stable configurations, respectively. Three configurations, 1b, 1c and 2f, show imaginary (negative here) frequencies associated with the O atom, see figure 2. These positions are thus unstable. The analysis of vibrations shows that there are two imaginary frequencies in the case of 1b and 2f but only one in Table 1. Wyckoff positions and site symmetry extracted from [START_REF] Aroyo | Bilbao crystallographic server: I. databases and crystallographic computing programs[END_REF]. the case of 1c. When the O atom is located in the 1c site, it is located in the transition state between two first nearest-neighboring 2h positions, as explained above. For the 1b and 2f configurations, many 'equivalent' stable positions are located around these positions. In such sites, the O atom could move into one of the four neighboring stable sites. This explains the two imaginary frequencies. These are second-order transition states, as mentioned in [START_REF] Connétable | Diffusion of interstitial species (h and o atoms) in fcc systems (Al, Cu, Co, Ni and pd): Contribution of first and second order transition states[END_REF]. Concerning stable sites, in the 4k case, there is a peak around 1THz mainly associated with the O atom (in addition to the high frequencies associated with O atoms, too). This result suggests that this site must be located in the vicinity of a transition state. It can also be noticed that the pDOS of the 4m and 4k sites are strongly similar, except that the low-energy peak in the 4k pDOS is split into two small peaks and that O frequencies are shifted at higher energies. For the other stable sites, the vibrations of the O atom are decoupled from the rest of the network. It is in the 2h sites that the O atom least modifies the phonon of the bulk. Finally, there are five stable positions for the O atom in the TiAl system: 2e, 2h, 4i, 4k and 4m, as displayed in figure 3.

1b 1c 2e 2f (0, 0, 1/2) (1/2, 1/2, 0) (0, 1/2, 1/2) (0, 1/2, 0) (1/2, 0, 1/2) (1/2, 0, 0) 2h 4i 4m 4n (1/2, 1/2, -z h ) (0, 1/2, z i ) (x m , 0, 1/2) (x n , 1/2, 0) (1/2, 1/2, z h ) (1/2, 0, z i ) (-x m , 0, 1/2) (-x n , 1/2, 0) (0, 1/2, -z i ) (0, x m , 1/2) (1/2, x n , 0) (1/2, 0, -z i ) (0, -x m , 1/2) (1/2, -x n , 0) 4k 4o 8r (x k , x k , 1/2) (x o , 1/2, 1/2) (x r , x r , z r ) (-x r , -x r , z r ) (-x k , -x k , 1/2) (-x o , 1/2, 1/2) (-x r , x r , z r ) (x r , -x r , z r ) (-x k , x k , 1/2) (1/2, x o , 1/2) (-x r , x r , -z r ) (x r , -x r , -z r ) (x k , -x k , 1/2) (1/2, -x o , 1/2) (x r , x r , -z r ) (-x r , -x r , -z r )
The zero-point energies (ZPE), H v , were afterwards computed with the following expression:

H v = F v [TiAl + O] -F v [TiAl] - 1 2 F v [O 2 ], (5)
where F v is the Helmholtz free energy given by the equation (3). Values are reported in table 2. The zero-point energy is found low, <20 meV, as compared to hydrogen [START_REF] Connétable | Theoretical study on hydrogen solubility and diffusivity in the γ-tial L1 0 structure[END_REF]. The 2h and 4i configurations have the same enthalpy energy. These results can now be compared with literature values. Bakulin et al [START_REF] Bakulin | Theoretical study of oxygen sorption and diffusion in the volume and on the surface of a γ-tial alloy[END_REF] also studied oxygen solubility in the TiAl system using first-principles calculations. However, they only considered five sites in their paper, labeled O1, O2, O3, O4 and T. Here is the site notation equivalence: O1 = 1c, O2 = 1b, O3 = 2e, O4 = 2f and T = 4i. The 2h site was not taken into account, nor were the 4m and 4n sites. By analyzing their NEB calculations (see figure 1, [START_REF] Bakulin | Theoretical study of oxygen sorption and diffusion in the volume and on the surface of a γ-tial alloy[END_REF]), a minimum can be identified in the path along O1-T, which should be the 2h site. Bakulin et al explain that the O atom should occupy the O1 ( 1c) site and that the 1b and 2f sites are stable. This is in contradiction with the

Oxygen diffusivity

The question of interest now is to determine how the O atom diffuses in the TiAl system. As seen before, O atoms can occupy many stable insertion sites, which induces many possible jumps.

To simplify, 4k sites were omitted, because 4k and 4m sites are very close (d < 0.35 Å) and have almost the same energy. The barrier energy between both sites is therefore necessarily very low, <10 meV. Therefore, 4k sites do not influence the diffusion coefficient. By omitting the 4k sites, the number of jumps between 2h, 2e, 4m and 4i sites is reduced. The first jump consists of a jump between two first-nearest neighboring 2h sites. Then, we considered two jumps to escape from a 2h site directly to a 4i site or to a 4m site. Once it escaped, the O atom can then move between 2e, 4m and 4i sites. The jumps between 2e-2e sites via 1b, and between 1c-1c (or 4i-4i) via 2f were omitted. As explained in the previous section, oxygen shows two-imaginary frequencies in the 2f and 1b sites. These configurations are second-order transition states, their jump rates are smaller (see appendix A), short-cuts are preferred. Figure 5 summarizes the energy landscapes of the jumps computed using NEB calculations. Six paths were finally considered as acceptable jumps, as depicted in figure 1. Their migration energies are summarized in table 4.

As explained above, to move from a 2h to another 2h site, the O atom passes through a 1c site. The barrier is low, about 80 meV. The direct jump between 2h and 4m is found impossible (not represented here). Indeed, the O atom prefers to go through a 4i site first. Most of the energy barriers are low, in the range of 0.10-0.30 eV. The limiting step is consequently the jump from a 2h site to a 4i site, with an energy of 1.26 eV. This significant value is the consequence of the high stability of 2h configuration as compared to the other configurations, therefore the energy cost to leave the site is important. This site is a local 'trap' for the O atoms. These results suggest that diffusion along the z axis should be slower than in the xy directions, because it requires going through a 2h site.

The macroscopic diffusion can now be computed. Due to the symmetry of the system, oxygen has two distinct diffusion coefficients, D z and D x,y . In first-approximation, as the residence time in the 4i, 4m and 4k sites is small (low energy barriers), only the jumps between 2e and 2h sites were considered. The diffusion coefficients can then be expressed simply in terms of Γ he , Γ eh , Γ hh , Γ ee , the jump rates of 2h-2e, 2e-2h, 2h-2h and 2e-2e jumps, respectively, and a o and c o , the lattice parameters. Γ were plotted in appendix A. By applying Landman's method [START_REF] Landman | Stochastic theory of multistate diffusion in perfect and defective systems. II. Case studies[END_REF], we found:

D x,y = a 2 o 2 • (Γ ee + 2Γ eh )Γ he Γ eh + Γ he (6) D z = c 2 o • Γ eh Γ he Γ hh (Γ eh + Γ he )(2Γ he + Γ hh ) (7)
where a o = 2.822 Å and c o = 4.076 Å. By combining equations (6) and ( 7), the degree of anisotropy of the diffusion coefficient, A D , is given by:

A D = D z D x = c o a o 2 • 2 Γ eh Γ hh (Γ ee + 2Γ eh )(2Γ he + Γ hh ) . (8)
A second set of equations (B.3) and (B.4), which includes 4i sites, was also deduced, see appendix B. It will help to evaluate the accuracy of the approximations. The diffusion coefficients, D x and D z , were calculated using DFT results and are depicted in figure 6. An Arrhenius fit was applied to the oxygen diffusion coefficients, D[T] = D o exp(-E a /k B T), to obtain D o and activation energies, E a . Parameters are summarized in table 5. As is the case for hydrogen [START_REF] Connétable | Theoretical study on hydrogen solubility and diffusivity in the γ-tial L1 0 structure[END_REF], the oxygen diffusion is anisotropic in the TiAl system. It is almost two orders of magnitude faster in the x-y plans than along the z direction. The slopes are quantitatively the same, only the value of D o changes. A D can be approximated by A D ∝ Γ eh /Γ ee (Γ hh Γ he and Γ ee Γ eh ). The difference between both jumps is small, thus explaining the anisotropy.

Again, there is no experimental data to compare with the theoretical diffusion coefficients found here. Our results can be seen as the upper limit of the diffusion coefficient in the bulk. In our numerical experiments, oxygen is located in interstitial sites, i.e. the O atom is not supposed to form clusters in the metal. The oxygen therefore diffuses from one interstitial site to another, as described above, so the result presented above should be accurate. However, if O atoms form clusters with vacancies for instance, it is reasonable to assume that oxygen diffusion would be slower in the bulk. The diffusivity of O atoms should depend on the concentration of these clusters, which can therefore be considered as traps [START_REF] Hodille | Study of hydrogen isotopes behavior in tungsten by a multi trapping macroscopic rate equation model[END_REF]. Oriani's model [START_REF] Oriani | The diffusion and trapping of hydrogen in steel[END_REF] is thus accurate enough to describe the diffusion coefficient in first approximation. However, this model still requires using ideal diffusion coefficients.

To highlight these results, the diffusion of oxygen in the TiAl-L1 0 system is compared with its diffusion in the Ti-hcp [START_REF] David | A study of the diffusion of oxygen in α-titanium oxidized in the temperature range 460 °C-700[END_REF][START_REF] Wu | Direct diffusion through interpenetrating networks: oxygen in titanium[END_REF], fcc-Al [START_REF] David | Diffusion of interstitials in metallic systems, illustration of a complex study case: aluminum[END_REF] and Ti 3 Al-D0 19 [START_REF] Bakulin | Absorption and diffusion of oxygen in the Ti3Al alloy[END_REF][START_REF] Koizumi | Effect of impurity atoms on alpha-2/gamma lamellar interfacial misfit in Ti-Al alloy: a systematic first principles study Phil[END_REF] systems, as reported in figure 6. It is obvious that oxygen diffuses faster in TiAl than in the other titanium compounds, between 3 and 6 orders of magnitude faster. By contrast, the diffusion is slightly slower than in fcc-Al [START_REF] David | Diffusion of interstitials in metallic systems, illustration of a complex study case: aluminum[END_REF]. Two antagonistic effects can be highlighted: the solubility is lower in TiAl than in Ti 3 Al or Ti, but diffusion is much faster. In the Ti 3 Al system, the stable configuration-oxygen surrounded by Ti atoms only [START_REF] Bakulin | Absorption and diffusion of oxygen in the Ti3Al alloy[END_REF]-is much more stable than the other sites that are composed of Al atoms. However, to diffuse, the O atom must necessarily pass through less stable sites, surrounded by Al atoms, so it diffuses slowly. In the case of the γ-TiAl system, results show that the most stable site is in the vicinity of an Al atom. This explains why oxygen is less stable in γ than in α 2 -Ti 3 Al, and consequently its lower solubility in TiAl than in Ti 3 Al. However, on the other hand, the energy difference between stable sites in TiAl-L1 0 is smaller than in Ti 3 Al-D0 19 . The O diffusivity in L1 0 is thus faster than in D0 [START_REF] Togo | First-principles calculations of the ferroelastic transition between rutile-type and cacl 2 -type SiO 2 at high pressures[END_REF] .

From these results, it can be assumed that modifying the Al/Ti ratio should have an impact on the solubility and diffusion of O in the TiAl-L1 0 system. The chemical homogeneity of insertion sites in the TiAl system induces in smaller migration energies than in other Ti-Al alloys.

Conclusion

This manuscript presents a complete study of the insertion and diffusion of oxygen in TiAl-L1 0 system. Different stable sites were found, but one site, the 2h site, is significantly more stable than the others. The interactions with Al atoms are stronger than with Ti atoms, and the 2h site minimizes them. Results indicate that the preferred site ( 2h) minimizes elastic effects, but most importantly reduces the number of O-Al interactions.

Figure 1 .

 1 Figure 1. Schematic representations of the TiAl-L1 0 structure (bold-centered tetragonal representation) indicating the interstitial positions tested (left), and the stable positions (right).

Figure 2 .

 2 Figure 2. Projected density-of-states (pDOS) of O in 1b, 1c and 2f sites (from top to bottom). The amplitude of the pDOS onto Ti and Al atoms was divided by 10. Frequencies are expressed in THz.

Figure 6 .

 6 Figure 6. Diffusion coefficients of oxygen as a function of 1/T. Al: (a) = [29]; Ti-hcp: (b) = [30], (c) = [31],; (d) = [32], (e) = [33], (f) = [34], (g) = [35]; Ti 3 Al: (h) = [36]; (i) = [25].

Figure A1 .

 A1 Figure A1. Attempt frequencies of all jumps as a function of T.

Table 2 .

 2 Insertion energies (E i , in eV), zero-point energies (ZPE, in meV) and enthalpy energies (H f , in eV) of an oxygen atom in different configurations. The zero point energy of the O 2 molecule is equal to 45 meV. ∆H is the energy difference (in eV) between the 2h site and the other sites.

		nb
		atom	1b	1c	2e	2f	2h	4i	4k	4m
			Unstable	Unstable	-	Unstable	z h = 0.109	z i = 0.330	x k 0.044	x m = 0.234
	E i	16	-2.369	-3.366	-2.921	-0.421	-3.368	-2.555	-2.365	-2.369
		54	-2.310	-3.393	-2.522	-0.341	-3.460	-2.571	-2.317	-2.319
		128	-2.344	-3.443	-2.589	-0.529	-3.484	-2.601	-2.349	-2.347
	ZPE		-	-	-5	-	13	7	-20	-10
	H f		-	-	-2.594	-	-3.471	-2.594	-2.369	-2.357
	∆H		-	-	0.88	-	0	0.88	1.10	1.11

Table 5 .

 5 Activation energies (E a , in eV) and D o (in 10 -6 m 2 s -1 ) obtained from an Arrhenius fit. The label † and ‡ refer to the model 1 and 2 respectively.

	Direction	E a			D o
	x, y	1.197	† /1.246	‡	22.43	† /30.78	‡
	z	1.189	† /1.189	‡	0.92	† /0.91	‡


Vito Mennella
email: vito.mennella@inaf.it

M Ciarniello

A Raponi

F Capaccioni

G Filacchione

T Suhasaria

C Popa

D Kappel

L Moroz

V Vinogradoff

A Pommerol

B Rousseau

I Istiqomah

P Beck

D Bockelee-Morvan

R W Carlson

C Pilorget

Typeset using

Keywords: astrochemistry -comets, general -methods, laboratory, atomic processestechniques, spectroscopic

The VIRTIS imaging spectrometer aboard Rosetta has shown that the nucleus surface of comet 67P/Churyumov-Gerasimenko (67P/CG) is characterized by a broad absorption band at around 3.2 µm. The feature is ubiquitous across the surface and its attribution to (a) specific material(s) has been challenging. In the present paper, we report an experimental investigation showing that the interaction of hydrogen atoms with Mg-rich amorphous silicates determines the formation of hydroxyl groups. The resulting IR spectrum exhibits a broad feature around 3.2 µm similar to that of comet 67P/CG. Hapke's radiative transfer model was employed to estimate an upper limit contribution of 65% of hydroxylated silicates to the observed cometary band intensity. The presence of a hydroxylated fraction in silicates on the cometary surface would represent an evolutionary link between primitive objects of the solar system and dust in the interstellar medium (ISM), where silicate grains can be hydroxylated after having interacted with hydrogen atoms. This link is consistent with the detection of the aliphatic organics in 67P/CG that also originate in the ISM.

INTRODUCTION

The payload instruments on-board ESA's Rosetta mission have observed the evolution of the Jupiterfamily comet 67P/Churymov-Gerasimenko (67P/CG) in a period from August 2014 to September 2016 and encompassing the perihelion passage occurring in August 2015 at a heliocentric distance of 1.24 AU. The data collected have provided unprecedented spatial, spectral and temporal coverage of the changes occurring on a cometary surface and surrounding inner coma before, during and after perihelion passage (Taylor et al. 2017). Determining the nucleus surface composition was one of the primary scientific objectives of the Visible, Infrared and Thermal Imaging Spectrometer (VIRTIS) (Coradini et al. 2007).

When observed at global scale, the 67P/CG surface appears dominated by a dust layer, remarkably uniform in composition. The overall spectral reflectance is characterized by a low albedo (0.06) and red slope at visible wavelengths while a wide absorption band centered at 3.2 µm is a distinctive feature in the infrared range (Capaccioni et al. 2015;Ciarniello et al. 2015). Temporal and spatial spectral variability at global scale has been observed on the 67P/CG surface (Ciarniello et al. 2016) in addition to spatial variations on meter-sized scales where color changes have been correlated with surface composition inhomogeneities and active sources (Filacchione et al. 2019). In particular, local water ice enrichments show higher albedo and flatter-to-blue spectral response in contrast to the more dark and red reflectance typical of the rest of the surface. The lack of the 1.5 and 2.0 µm water ice absorption bands in the ubiquitous lowalbedo material on 67P/CG indicates a very dehydrated surface with the water ice abundance <2% on average (Raponi et al. 2020). Crystalline water ice has been identified only on specific areas of the nucleus during the pre-perihelion phase (De Sanctis et al. 2015;Filacchione et al. 2016a;Barucci et al. 2016;Raponi et al. 2016). Also CO 2 ice has been detected for the first time on a cometary nucleus surface by VIRTIS in a small area located in the meridional Anhur region (Filacchione et al. 2016b). Note that the surface composition of 67 P/CG is pristine since a continuous rejuvenation of its surface occurs during the perihelion passages. For each orbit, cometary activity erodes on an average at least a layer of 1.0±0.5 m surface thickness (Bertaux 2015) whereas Fulle et al. (2019) estimate an erosion of about 4 m at perihelion for the southern hemisphere.

The most striking spectral feature is the broad band between 2.8 and 3.6 µm centered at 3.2 µm, whose attribution is challenging. The band falls in a spectral region where the contribution to the absorption of X-H stretching vibrations in different functional groups is expected. C-H vibrations in aliphatic and aromatic C bonding have recently been established as sub-structures of the observed absorption band in newly calibrated VIRTIS spectra (Raponi et al. 2020). O-H vibrational modes in water ice, structural water or chemisorbed hydroxyl groups absorb from 2.7 to 3.1 µm but cannot explain the entire feature. Quirico et al. (2016) suggested several possibilities, OH groups in carboxylic acids inserted in a macromolecular organic solid and NH 4 + (ammonium) ions were proposed as plausible candidates to encompass the broad width of the cometary feature. More recently on the basis of laboratory experiments, the 3.2 µm band and some of its sub-features have been interpreted to be ammonium (NH 4 + ) salts (such as ammonium formate, sulfate, citrate) mixed with dark cometary surface material (Poch et al. 2020).

Silicates, together with powders of coal and iron sulphides, have been used to model the red visible and near infrared slope and low albedo of 67P/CG (Rousseau et al. 2018). Detection in the coma of a mineral phase, predominantly composed of silicates and carbonaceous components, was carried out by the COSIMA experiment aboard Rosetta (Bardyn et al. 2017). The presence of silicates in comets was first reported by Bregman et al. (1987) and later confirmed by Campins & Ryan (1989) in comet 1/Halley and by Crovisier et al. (1997) in Hale-Bopp (C/1995 O1). During their journey from the birth sites around evolved stars through interstellar medium to comets, silicates interact with ions (mainly protons), which induce many effects such as amorphization, sputtering and implantation with the formation of OH groups (Demyk et al. 2001(Demyk et al. , 2004;;Carrez et al. 2002;Jäger et al. 2003a;Brucato et al. 2004;Djouadi et al. 2005). The abundance of amorphous silicates in ISM is 98 % with respect to the crystalline counterpart, whereas the abundance varies between 70-98 % for Jupiter family comets (Sugita et al. 2005). Furthermore, the silicates are primarily Mg-rich e.g. Kelley et al. (2017). Direct evidence of silicate processing by ions has come from analysis of Interplanetary Dust Particles (IDPs) (Bradley 1994;Bradley et al. 1999Bradley et al. , 2005)). During their journey, silicates can also interact with hydrogen atoms both in diffuse and dense regions of the ISM.

In this paper, we experimentally investigate the consequence of the interaction of H atoms with analogues of interstellar silicate grains. Hydrogen atoms, with an energy of a few tens of meV, form hydroxyl groups in Mg-rich amorphous silicates with different Mg/Si ratios. The resulting IR spectrum is characterized by a broad absorption band centered at 3.2 µm similar to the one observed in 67P/CG spectrum.

EXPERIMENTS AND RESULTS

Interstellar amorphous silicate analogues were prepared by the pulsed laser ablation of targets and subsequent condensation of vapor on a polished substrate in a quenching gas atmosphere. Nd-YAG solid state laser at 1024 nm wavelength equipped with II and IV harmonics at 532 and 266 nm, respectively, was adopted. By using a focusing lens, the power density on the target was measured by LaserMate-P power meter (Coherent) to be 1×10 8 W cm -2 . The target to be ablated was mounted inside a chamber, filled with a 10 mbar Ar atmosphere, on a rotating sample holder placed in front of the laser beam. Silicate grains were collected at a distance of 5 cm from the target on ZnSe windows and carbon stubs, respectively, for IR spectroscopy and electron microscopy. We have used pellets made out of oxide mixtures in two different proportions (MgO:SiO 2 in a 1:1 and 2:1 mix- SUPRA 25). The FESEM images show that mainly a fluffy structure of amorphous grain aggregates characterizes the morphology of the silicate samples. For a detailed characterization of texture, grain dimension and size distribution of the samples see Rotundi et al. (2000). The atomic ratio of the samples obtained by EDX is also reported in Table 1. Taking into account the variations due to non-homogeneity of the samples, the Mg/Si ratio is in agreement with the corresponding value of the starting oxide mixtures for SIL1, while it is slightly lower in the case of SIL2. The values, Fe/Mg = 0.11 and (Mg+Fe)/Si = 1.9, indicate that the composition of the sample obtained from natural olivine (SIL3) is Mg-rich.

Figure 1 shows the optical depth of the silicates acquired with a Fourier Transform Infrared (FTIR) spectrometer (Bruker Equinox 55). Transmittance spectra were acquired in air at room temperature, in the range 2-16 µm at a spectral resolution of 2 cm -1 . The spectra are characterized by a strong band around 10 µm due to the Si-O stretching mode, whose profile slightly varies with the sample composition. The band is centered at 9.8 µm for SIL1 and it shifts to 10.2 µm as the Mg/Si ratio increases (for SIL2 and SIL3 samples). In the latter cases, an additional band at around 10.8 µm is also evident. Jäger et al. (2003b) also reported a similar redshift in the band position with increasing MgO/SiO 2 ratio in their amorphous magnesium silicate samples, prepared by the sol-gel method. The absorption increase for wavelengths longer than 13 µm is due to the low energy wing of the Si-O bending feature at around 20 µm while the increase at high-energy (<7µm) is attributed to the scattering by micron sized particles present in the sample. The small double band at 6.5 and 7 µm, more intense in the case of SIL2, is caused by traces of magnesium carbonate, formed during sample preparation (Jäger et al. 2003b). Figure 2 shows the silicate infrared spectra in the 3 µm spectral range after continuum removal. A broad band centered at 2.88 µm, produced by adsorbed water and chemisorbed hydroxyl groups, due to ambient contamination during the sample handling at the time of pellet preparation and also at the time of laser ablation, characterizes this region. Two narrow bands at 2.67 µm and 2.69 µm are respectively attributed to isolated Si-OH and Mg-OH groups [START_REF] Iler | The chemistry of silica (John Wiley and Sons Inc) Jäger[END_REF]Shinoda et al. 2002). Their relative intensity varies according to the Mg/Si ratio. In the case of SIL3, produced from natural olivine, only a weak band, resulting from the blend of the two features, is observed. Similar bands have been detected in silicates produced by the sol-gel method (Jäger et al. 2003b), suggesting that laser ablation and sol-gel techniques provide materials that are good analogues for cosmic silicates. In fact, the formation of silicates in space with a small content of isolated Si-OH and Mg-OH bonds can be considered highly probable, since H 2 O, the most abundant oxygenbearing molecule, participates in the formation of olivine and pyroxene-type silicates around evolved stars [START_REF] Gail | Dust formation in M stars[END_REF]Jäger et al. 2003b).

To study the interaction of hydrogen with silicates, our samples were placed inside a vacuum chamber, with a base pressure of 2×10 -8 mbar, on a rotating sample holder at the right angle intersection between an atomic hydrogen beam and the IR beam of an FTIR spectrophotometer (Bruker Vertex 80). H atoms were produced by microwave dissociation of molecular hydrogen; they have a Maxwellian velocity distribution at 300 K (Mennella 2006). After H atom exposure, the sample was rotated by 90 • to face the IR beam, and we measured the IR spectrum with a resolution of 2 cm -1 in the range 2-5 µm (5000-2000 cm -1 ). The background was acquired before any spectral measurement of the samples as produced and after each exposure dose, removing the sample holder from the IR beam with a micromanipulator. Figure 3 shows the spectral changes, obtained by subtracting the pre-exposed spectrum from the exposed one, induced by H atom exposure in amorphous silicates. The activation of a broad band centered at about 3.2 µm takes place in all the silicates. At shorter wavelengths, an absorbance decrease in the exposed sample (resulting in a negative optical depth difference in Figure 3) centered at 2.76 µm (broad band) and bands at 2.67 and 2.69 µm (sharp doublet) are observed. This behavior indicates that the H atoms induced a depletion of the O-H bonds already present in the starting silicate samples.

In addition, a weak feature at 3.36 µm with a shoulder at 3.39 µm is possibly due to asymmetric C-H stretching modes of aliphatic CH 3 and CH 2 groups. They could have originated from processing of carbonate and other atmospheric contaminant present in the sample. The faint feature at around 4.25 µm is associated to uncompensated ambient CO 2 . Exposure of a blank ZnSe substrate to hydrogen (see Figure 3) does not induce any variation in the spectrum, demonstrating that the observed spectral changes are due to the interaction of hydrogen with silicate grains.

To investigate whether the presence of OH groups in the pristine silicates affects their interaction with hydrogen, we tried to eliminate/reduce them by annealing one of the samples (SIL3) at 300 • C for 1 hour before exposure to H atoms. In the case of the annealed SIL3, only a small absorbance decrease centered at 2.76 µm is present after exposure to hydrogen atom (see Figure 3), testifying that the starting sample was almost fully depleted of the chemisorbed hydroxyl groups. Despite that, the activation of the 3.2 µm band does not vary. Hydroxylation of Mg-rich amorphous silicates by H atoms is therefore independent of the OH groups already present in silicates and of the specific composition of the samples.

DISCUSSION AND CONCLUSIONS

The spectral variations induced in Mg-rich silicates by atomic hydrogen are clear evidence for chemical reactions producing hydroxyl groups on silicates. According to density functional quantum mechanical calculations, the formation of OH groups in Mg-rich silicate nanoclusters by impinging H atoms takes place without any significant energy barrier (Kerkeni et al. 2017). The observed spectral evolution with H atom exposure suggests that hydroxyl groups are formed by hydrogen atom interaction on surface of amorphous silicates, which have a wide range of binding sites enhancing both physisorption and chemisorption of hydrogen. The nature (distribution of sites and chemical state) of our samples determine the observed broad band. The spectral changes indicate that exchange reactions (addition and abstraction of H atoms in OH) are active during H atom ex- posure of our samples. Once an H atom form an OH group on an available site (addition reaction), a second impinging H atom can abstract it, forming H 2 (abstraction reaction). This leaves a site available to form again a hydroxyl group when a third atom arrives. The equilibrium value for the number of OH groups after H atom exposure depends on the cross section of the abstraction and addition process1 . The observed absorbance decrease at 2.76 µm (broad band) and at 2.67, 2.69 µm (sharp doublet) indicates a reduction in the number of OH bonds (already present in the samples) since their initial value was higher than the equilibrium value. On the other hand, the absorbance increase at longer wavelengths corresponds to an increase of the number of OH groups, initially absent in the sample.

Formation of OH bonds with a peak at around 2.8 µm has been reported after implantation of keV to MeV en- ergy range protons in silicates with different composition and structure (e.g. Zeller et al. (1966); Djouadi et al. (2011); Schaible & Baragiola (2014)). Exchange of H/D in hydroxyl groups has also been observed after 1.1 keV D + implantation of Apollo lunar soils [START_REF] Ichimura | [END_REF]. Hydroxylated silicates produced by proton implantation have also been considered as a potential reservoir of water during the formation of terrestrial planets (Djouadi et al. 2011). So far, it has been believed that hydroxylation of silicates occurred by high-energy proton implantation on the surface of airless solar system bodies such as the Moon. Our experiments show that the process can also take place when low energy (a few tens of meV) H atoms interact with amorphous silicate grains. This can happen in the ISM where both atomic hydrogen and amorphous silicate grains are present (see next section).

There is a clear difference in the width and peak position of the OH IR band in the two interactions. As shown in the present experiments, the band is centered at longer wavelengths and it is much wider than that obtained by proton implantation. The origin of the observed differences is the distribution of sites and chemical state of the samples studied in the two cases. To get a further insight, besides IR spectroscopy, other analytical techniques such as X-ray photoelectron spectroscopy (XPS) would be useful to understand the difference in the chemical state of the oxygen atoms present in the sample. In addition, high energy proton implantation on our amorphous silicate grains will also be essential to compare the effects induced by the two processes.

The profile of the band formed by H atoms in the considered silicates (see Figure 3) is reminiscent of the 3.2 µm absorption band in the reflectance spectrum of 67P/CG observed by VIRTIS onboard Rosetta (Raponi et al. 2020). Figure 4 shows the comparison of the cometary profile with that of annealed SIL3. The similarity in profile suggests that OH groups of hydroxylated amorphous silicates can be a constituent of the 67P/CG nucleus surface, together with aliphatic carbons, ammonium salts, water ice and possibly PAHs. (Quirico et al. 2016;Poch et al. 2020;Raponi et al. 2020).

To quantitatively evaluate the spectral contribution of hydroxylated amorphous silicate to the 3.2 µm band, we have modeled the average reflectance (I/F) spectrum of the comet 67P/CG surface with a similar approach already used to estimate the spectral contribution of water ice (Raponi et al. 2020). The Hapke radiative transfer model [START_REF] Hapke | Theory of reflectance and emittance spectroscopy[END_REF]) was adopted to calculate the reflectance of an intimate mixture of hydroxylated amorphous silicate with a synthetic continuum representing a dark-red terrain. Model fits to the average 67P/CG reflectance spectrum indicate that hydroxylated silicate can reproduce on average 65% of the 3.2 µm cometary band intensity with an abundance of hydroxylated amorphous silicate of 15%. An example of the resulting mod-eling is shown in Figure 5. For more detail see Table 2 and Figure 9 in the Appendix. The estimated contribution should be considered as an upper limit due to the involved assumptions (see Appendix). It is worth stressing that for an accurate quantitative estimation, one should also consider the contributions of the other proposed carriers of the 3.2 µm band as mentioned above.

The presence of a hydroxylated fraction in silicates on the surface of a comet can represent an evolutionary link between a primitive object of the solar system and dust in the ISM. The spectral homogeneity of the nucleus surface observed by VIRTIS indicates that the composition of the refractory surface materials does not change despite the rejuvenating processes active during the perihelion passages of 67P/CG (Ciarniello et al. 2016). The refractory material seen at the surface must be then representative of the bulk pristine material of the nucleus. As for all cosmic dust, silicates participate in the life cycle of matter that brings dust from their circumstellar birth sites to the diffuse interstellar medium and dense clouds where stars form. The formation of planetary systems, like our solar system, can also take place during this cycle. Since silicates are involved in the evolution of the interstellar matter, from diffuse medium to comets, they interact with hydrogen atoms in the ISM. The laboratory H atom fluence of 1×10 18 atoms cm -2 used in the present experiments as reported in Figure 3 corresponds to an H atom exposure time of 4×10 3 and 4×10 5 years, respectively, in interstellar diffuse and dense regions (considering the respective H atom flux of 8×10 6 and 9×10 4 atoms s -1 cm -2 for these regions, Mennella (2010)). In addition, we observed the formation of the 3.2 µm band already at a lower fluence of ca. 10 16 atoms cm -2 . Therefore, hydroxylation can take place on a much shorter time scale compared to the residence time of 3×10 7 years of dust grains in both dense and diffuse regions of the ISM. However, for a complete understanding of the degree of hydroxylation of the silicates in different regions of the ISM, we also need to know the effects of the dehydrogenation processes induced by energetic processing such as by UV photons and cosmic rays.

The evolutionary link suggested by the present results is consistent with the detection of the aliphatic matter in 67P/CG (Raponi et al. 2020). We thus can trace for both aliphatic carbon and hydroxylated amorphous silicates a common origin in the ISM during the journey of the dust from its birth-sites around evolved stars to our solar system.

We apply the Hapke model (Hapke 2012) to derive an upper limit of the amount of hydroxylated Mg-rich amorphous silicates contributing to the 3.2 µm band intensity of 67P/CG (Raponi et al. 2020). To this aim, 67P/CG's surface is modeled as an intimate mixture of a featureless dark-red synthetic component, representing predominantly the optically opaque phases in the comet regolith, and a hydroxylated Mg-rich amorphous silicate. The spectral output of the featureless end-member is modeled as a continuum by means of a 2nd degree polynomial, while for the hydroxylated Mg-rich amorphous silicate material, synthetic optical constants have been computed. Upon exposure to H atom, the optical properties of the amorphous silicates are modified by formation of the absorption feature centered at 3.2 µm. This effect can be interpreted as an increase of the value of the imaginary part of the refractive index k, ∆k, in correspondence to the 3.2 µm absorption feature. To estimate ∆k, we represent the contribution of OH groups formed on the fluffy and amorphous grain aggregates in consideration by assuming a homogenous film of hydroxylated amorphous silicate of equivalent thickness d. Then the measured optical depth difference (exposedpristine) can be expressed as:

∆τ (λ) = 4π λ d ∆k. (A1)
The equivalent thickness d can be derived from the integrated optical depth through the following relation:

band ∆τ (ν) dν = N A = ρ d N A m A, ( A2
)
where N is the column density, A is the integrated band strength and N A is Avogadro's number. ρ and m are the density and the molecular weight of the film, respectively. We evaluated the integral in the left hand term of Eq. A2 from the annealed SIL3 reported in Figure 6 and adopt A = 2×10 -17 cm molecule -1 , as in the case of the OH groups in natural olivine (Schaible & Baragiola 2014). Moreover, we assumed ρ = 1 g cm -3 and m = 101 g mol -1 for hydroxylated silicate film with a starting silicate stoichiometry as [MgO.SiO 2 ]. We obtain a starting value of d = 0.35 µm. It is then possible to derive the corresponding increase of the imaginary part of the refractive index from Eq. A1 as seen in Figure 7. To see how the final results are affected by our assumptions, we also varied d by a factor of 10 higher and lower, reflecting possible uncertainties in the assumptions on A, ρ and m. . Optical depth difference (after continuum removal) for annealed SIL3. As mentioned in the text, the H atom interaction results in abstraction of H atoms in OH groups already present in the sample, introducing a spurious negative signature in the ∆τ spectrum between 2.65 and 2.85 µm. To eliminate this spurious signature, we discard the measurement in this range and replace it by a polynomial (blue segment) that connects the part of the optical depth difference spectrum shortward of 2.65 µm with the region longward of 2.85 µm.

Since the H atom processing of Mg-rich amorphous silicates does not lead to variations of the absorption spectrum outside the 3.2 µm band, it is reasonable to assume the imaginary part of the refractive index k b of the unprocessed silicate as a baseline. However, optical constant values of the unprocessed silicates analyzed in the present work are missing. Therefore, we adopted the optical constants of similar silicates. The choice is further justified by the fact that H atom interaction modifies different Mg-rich amorphous silicates in a similar way, as also evidenced by the reported measurements. We considered real and imaginary parts of optical constants of Mg-rich glass from Dorschner et al. (1995). Further, to incorporate the effects of H atom processing on the optical constants, a synthetic imaginary part of the refractive index k s = k b +∆k is derived as shown in Figure 8, for the Mg-rich glass for different values of d. For each synthetic refractive index values, a fit to the 67P/CG spectrum is performed in a similar way as Raponi et al. (2020) did for water ice. We forced the fit to match the continuum level of the cometary spectrum in the range between 2.7-2.9 µm and 3.5-3.6 µm to ensure that the modeled absorption is not more intense than the one shown by 67P/CG. The best fits to the 67P/CG spectrum are reported in Figure 9 while the best fit parameters i.e. the amount of hydroxylated silicates with respect to dark-red terrain, R, and the corresponding grain size, S, are listed in Table 2. Note that R values reported in Table 2 represent the corresponding fractional cross section seen by the light propagating within the medium. These quantities can be interpreted as volumetric abundances under the assumption that the featureless dark-red terrain has the same grain size as the hydroxylated silicate. The derived R values are constant at 0.15, and F is very similar for the three cases with an average value of around 0.65. Conversely, the obtained S values increase with d. This can be explained by the fact that ∆k as obtained from Eq. A1 is lower for larger d, thus producing a smaller absorption for a given grain size. Given this, in order to reproduce the observed spectral contrast, a larger value of S is required in the modeling. One should note that a rigorous application of the Hapke's model would limit it's application to the geometric optics regime, where particles are larger than wavelength. This is the case for the derived value of S = 0.5 µm which implies that small particle sizes (likely sub-µm) are required to match the observed spectrum with the adopted set of optical constants. The estimated abundance of 15 % of hydroxylated silicates with respect to the dark component (see R in Ta-ble2) is in good agreement with the previous results obtained by Rousseau et al. (2018). They reproduced the reflectance spectra of the cometary nucleus of 67P/CG using mixtures of silicate and dark materials (coal and sulphide) where the silicate fraction was estimated to be <30% (weight%) with respect to the total mixture. Assuming the density of the silicates as 3 g cm -3 , and the average density of the dark components as 2 g cm -3 , results in a volumetric silicate abundance as 20%. In addition, our result leaves enough room for other darkening agents that can justify the observed low albedo. . From top to bottom: best fits (blue dashed lines) to average 67P/CG reflectance spectrum (black lines) obtained with synthetic optical constants computed using Mgrich glass (Dorschner et al. 1995) as baseline for different values of d.

Figure 1 .

 1 Figure1. Infrared spectra of the silicates reported in Table1. The spectra of SIL2 and SIL3 are offset in ordinate by 0.3 and 0.5, respectively.

Figure 3 .

 3 Figure3. Spectral changes of silicates under exposure (shown after subtraction of the initial spectrum) of 1×10 18 H atoms cm -2 . The spectrum of a ZnSe window (blank) after the same exposure is also reported for comparison. The feature at around 4.25 µm is associated to uncompensated ambient CO2.

Figure 4 .

 4 Figure 4. Qualitative comparison of 3.2 µm absorption band in SIL3 (blue line) first annealed at 300 • C and then exposed with 1×10 18 H atoms cm -2 to the observed absorption band in the 67P/CG reflectance spectrum (black line).The left vertical axis is for the SIL3 spectrum whereas the right vertical axis refers to that of the cometary band.

Figure 5 .

 5 Figure 5. Fit to the average 67P/CG reflectance spectrum (black line, Raponi et al. (2020)) by the modeled hydroxylated amorphous silicate mixed with the dark-red endmember (blue dashed line) using Hapke's model for 5 µm grain size and 15% of hydroxylated amorphous silicate abundance. See the Appendix for the meaning of d and other parameters.

  Figure6. Optical depth difference (after continuum removal) for annealed SIL3. As mentioned in the text, the H atom interaction results in abstraction of H atoms in OH groups already present in the sample, introducing a spurious negative signature in the ∆τ spectrum between 2.65 and 2.85 µm. To eliminate this spurious signature, we discard the measurement in this range and replace it by a polynomial (blue segment) that connects the part of the optical depth difference spectrum shortward of 2.65 µm with the region longward of 2.85 µm.

Figure 7 .

 7 Figure 7. ∆k as a function of wavelength for d = 0.35 µm.

Figure 8 .

 8 Figure 8. Imaginary part of the synthetic refractive index derived by using Mg-rich glass as baseline. The three curves represent the different values of ks obtained for d values of 0.035, 0.35 and 3.5 µm from top to bottom, respectively.

Table 2 .

 2 Best fit parameters (R, S) of the model to the average reflectance spectrum of 67P/CG. Equivalent film Hydroxylated silicate Grain size Fraction of the 3.2 µm band

Figure 9

 9 Figure9. From top to bottom: best fits (blue dashed lines) to average 67P/CG reflectance spectrum (black lines) obtained with synthetic optical constants computed using Mgrich glass(Dorschner et al. 1995) as baseline for different values of d.

Table 1 .

 1 Atomic ratios of silicates produced by laser ablation period

	Sample name Starting material Measured ratios
			Mg/Si	Fe/Si
	SIL1	MgO:SiO2 (1:1)	1.1	-
	SIL2	MgO:SiO2 (2:1)	1.7	-
	SIL3	Natural Olivine	1.7	0.2
	ture) and a natural forsterite olivine (dunite, Webster-
	Addie, N. Carolina, acquired from Wards Science) as
	targets. The oxide mixtures were prepared by weighing
	the exact amounts of MgO (99.99 %, Sigma-Aldrich) and
	SiO 2 (99.8 %, Sigma-Aldrich) in order to have the start-
	ing stoichiometric composition of enstatite (MgSiO 3 ) for
	the first sample (SIL1) and forsterite (Mg 2 SiO 4 ) for the
	second sample (SIL2). The mixtures were produced in
	the form of pellets (13 mm in diameter and a few mil-
	limeters in thickness) by pressing finely ground oxides
	at 10 tons. The third sample (SIL3) was prepared from
	a piece of olivine mineral as target. The three silicates
	(SIL1, SIL2 and SIL3) prepared in the present work are
	listed in Table 1. The chemical composition resulting
	from the process of vaporization and condensation was
	analysed with an Electron Dispersive X-ray (EDX) sys-

tem (Oxford Inca Energy 350) linked to a Field Emission Scanning Electron Microscope (FESEM) (ZEISS

Table 1 .

 1 The spectra of SIL2 and SIL3 are offset in ordinate by 0.3 and 0.5, respectively.

	Figure 2. Infrared spectra, after continuum removal, of the
	silicates reported in Table 1 in the 2.5 -3.3 µm range. The
	spectra of SIL2 and SIL1 are offset in ordinate by 0.006 and
	0.012, respectively.

Assuming a first-order kinetics, the asymptotic solution of the equation governing the evolution of the number of X-H bonds (i. e. the equilibrium value) under two competitive processes depends on the formation and destruction cross sections. With processing, the number of X-H bonds can either increase or decrease depending on whether their initial value is lower or higher than the equilibrium value. As an example, see

Figure2in(Mennella et al. 2002) for the case of C-H bond evolution in hydrogenated carbon grains.

ACKNOWLEDGMENTS

This work is supported by the international space science institute (ISSI) through the collaboration of the ISSI international team "Comet 67P/Churyumov-Gerasimenko Surface Composition as a Playground for Radiative Transfer Modelling and Laboratory Measurements", number 397.

APPENDIX

A. MODELING OF THE SPECTRAL CONTRIBUTION OF HYDROXYLATED SILICATES TO THE 3.2 µm FEATURE OF 67P/CG