Daniel J Sligte
email: d.j.sligte@uva.nl.

Carsten K W De Dreu

Bernard A Nijstad

ÔØ Å ÒÙ× Ö ÔØ Power, Stability of Power, and Creativity

Keywords: creativity, power, global/local processing, avoidance, motivation

Power hierarchies are an essential aspect of social organization, create stability and social order, and provide individuals with incentives to climb the hierarchical ladder. Extending previous work on power and creativity, we put forward that this relationship critically depends on both the stability of the power hierarchy and the relevance of creative efforts to power. Across three experiments, we show that when power positions are unstable, low power individuals are more flexible thinkers, are less avoidant and process information more globally. Consequently, they achieve more creative insights, especially when being creative is relevant to power. As such, when the power hierarchy is unstable, those lacking power hold the power to creativity.

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Power and Creativity

Power, Stability of Power, and Creativity

Power hierarchies are so pervasive across both animal species and humans, that it appears a fundamental feature of social organization. Apart from behavioral manifestations ranging from abuse to benevolence and generosity (e.g., [START_REF] Handgraaf | Less power or powerless? Egocentric empathy gaps and the irony of having little versus no power in social decision making[END_REF], possessing power in and by itself fundamentally influences individuals' information-processing and behavioral tendencies [START_REF] Fiske | Social cognition and social perception[END_REF][START_REF] Keltner | Power, approach, and inhibition[END_REF]. However, mixed findings emerge for creative performance, with some studies demonstrating that power leads to higher creativity [START_REF] Galinsky | Power reduces the press of the situation: Implications for creativity, conformity, and dissonance[END_REF]Smith & Trope, 2006) while others point to an opposite pattern [START_REF] Kuhl | Motivation, Affect, and Hemispheric Asymmetry: Power Versus Affiliation[END_REF]. In this article we show that the relationship between power and creativity critically depends on both the stability of the power hierarchy and the relevance of creative efforts to power. When the power hierarchy is unstable, individuals with low power employ a global and flexible processing style and become more creative especially when being creative is functional to climbing the ladder.

Power leads to higher creativity

Power refers to the ability to influence others [START_REF] Bacharach | Bargaining: Power, tactics, and outcomes[END_REF][START_REF] Kelley | Interpersonal relations: A theory of interdependence[END_REF], and derives from a variety of power bases, such as someone's position in the hierarchy within a group or organization, or the possession of valuable resources, such as knowledge and expertise (French & Raven, 1958;Lee & Tiedens, 2001;Podsakoff & Schriescheim, 1985;[START_REF] Yukl | Influence tactics and objectives in upward, downward, and lateral influence attempts[END_REF]. Power hierarchies create social order and stability, and because having power yields control over one's environment and resources to survive and prosper, individuals are motivated to climb the hierarchical ladder.

Recent work in psychological science revealed that power has metamorphic effects on power holders [START_REF] Fiske | Social cognition and social perception[END_REF][START_REF] Keltner | Power, approach, and inhibition[END_REF]. Powerful individuals process information more abstractly and flexibly [START_REF] Power | Power affects basic cognition: Increased attentional inhibition and flexibility[END_REF]Smith & Trope, 2006;

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT Power and Creativity Förster, 2009), use less diagnostic and more confirmatory strategies [START_REF] De Dreu | The influence of power on the information search, impression formation, and demands in negotiation[END_REF][START_REF] Leyens | Why and under what circumstances is a hypothesis-consistent testing strategy preferred in interviews[END_REF], and are less influenced by situational cues [START_REF] Galinsky | Power reduces the press of the situation: Implications for creativity, conformity, and dissonance[END_REF] and emotional expressions of others [START_REF] Van Kleef | Power and emotion in negotiation: Power moderates the interpersonal effects of anger and happiness on concession making[END_REF]. Behaviorally, the powerful take more risks in their decisions (Anderson & Galinsky, 2006), they act more swiftly when facing an annoying obstacle [START_REF] Galinsky | From power to action[END_REF] and behave more in a goal-consistent manner [START_REF] Power | Power affects basic cognition: Increased attentional inhibition and flexibility[END_REF].

The key explanation for these effects proceeds on the basis of the assumption that powerful individuals think and act so as to maintain and increase power [START_REF] Bruins | Cognitions and behaviour in a hierarchy: Mulder's power theory revisited[END_REF]Maner, Gaillot, Butz & Peruche, 2003;[START_REF] Maslow | Dominance-feeling, behavior, and status[END_REF]; powerless individuals, in contrast, think and act to protect against possible threat (in part coming from powerful others).

As a result, having power leads to approach motivation with its concomitant global attentional focus [START_REF] Förster | Enactment of approach and avoidance behavior influences the scope of perceptual and conceptual attention[END_REF]. Having power frees one from influence from others, and leads to feelings of safety and security [START_REF] Friedman | Implicit affective cues and attentional tuning: An integrative review[END_REF]. Lacking power, in contrast, triggers avoidance motivation, a focus on potential losses, and a narrow attentional focus [START_REF] Keltner | Power, approach, and inhibition[END_REF][START_REF] Förster | Enactment of approach and avoidance behavior influences the scope of perceptual and conceptual attention[END_REF]. Because both approach motivation (Baas, De Dreu, & Nijstad, 2008;[START_REF] Friedman | The effects of promotion and prevention cues on creativity[END_REF][START_REF] West | Sparkling fountains or stagnant ponds: An integrative model of creativity and innovation implementation in work groups[END_REF], 2005) and global attentional focus [START_REF] De Dreu | Behavioral activation links to creativity because it promotes cognitive flexibility[END_REF][START_REF] Förster | How global versus local perception fits regulatory focus[END_REF]Förster, Liberman & Friedman, 2005) promote cognitive flexibility, set-breaking and abstract thinking, it follows that powerful individuals also are more creative than their powerless counterparts (Forster, 2009;Galinksy et al., 2008;Smith & Trope, 2006; but see [START_REF] Kuhl | Motivation, Affect, and Hemispheric Asymmetry: Power Versus Affiliation[END_REF]).

An interesting implication of this socio-functional perspective on power and cognition is that cognitive processes operate in the service of the underlying motivation to maintain and increase power. Put differently, the tendency among powerful individuals to think globally and display cognitive flexibility should be particularly pronounced when doing so serves the

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Power and Creativity goal of maintaining or expanding power. When creative performance is functionally relevant to one's power position, we would thus expect more creativity than when creative performance is functionally irrelevant. An example of such functionally relevant creativity is when a middle-manager of a company is facing decreasing revenues, and new and creative ideas are needed to turn the situation around. By solving the company's problems in creative ways (e.g., through introducing new products or services, or by increasing market share through creative marketing) a manager can show high competence and may as a consequence be promoted to a higher position.

Psychological science provides some support for the idea that creative performance can be boosted when it is functionally relevant. Recent work shows that in addition to costs and risk, being original and creative accrues desirable benefits. For example, being creative increases individuals' attractiveness as a potential mate [START_REF] Griskevicius | Peacocks, Picasso, and parental investment: The effects of romantic motives on creativity[END_REF]Miller, 2000), and helps individuals winning a conflict (De Dreu & Nijstad, 2008).

Unstable power and creativity

A socio-functional perspective on power further implies that individual power is not a given and that power is not necessarily a stable feature of the situation within which the individual operates. Rather, power positions may change: powerful individuals may become powerless, and powerless people may become powerful (Tajfel, 1984). In an unstable power hierarchy, the powerful can be expected to be motivated to maintain their privileged position (Tetlock, 1981), especially when their position is directly disputed. They may become threatoriented (Scheepers & Ellemers, 2008), leading the powerful to become risk averse and more focused on preventing that someone takes over (some of their) privileges [START_REF] Lammers | Illegitimacy moderates the effects of power on approach[END_REF]Maner et al., 2003). Moreover, subtle cues signaling a potentially dangerous environment may lead to attentional focusing and less creativity [START_REF] Friedman | Implicit affective cues and attentional tuning: An integrative review[END_REF]. When power becomes unstable, the intricate link between being

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Power and Creativity powerful, approach motivation and global attentional focus may thus break down. Those having and valuing high power may become afraid of losing power, and powerless individuals face the prospect of moving up the hierarchy, thus realizing greater safety [START_REF] Higgins | Beyond pleasure and pain[END_REF].

Those with low power may therefore become approach motivated and beget a broad attentional focus [START_REF] Friedman | Implicit affective cues and attentional tuning: An integrative review[END_REF]; see also [START_REF] Kuhl | Motivation, Affect, and Hemispheric Asymmetry: Power Versus Affiliation[END_REF].

Indirect evidence for our thesis that the stability of the power hierarchy matters comes from work manipulating the legitimacy of the individual's power position. When the power position is legitimate, powerful individuals are more action-oriented, use more flexible strategies to attain their goals and are more persistent in the face of obstacles than powerless individuals. When the power position is illegitimate, however, the pattern reverses and powerless individuals display greater action-orientation and cognitive flexibility than powerful individuals [START_REF] Willis | Illegitimacy improves goal pursuit in powerless individuals[END_REF]. Illegitimacy may undermine the perceived stability of the power hierarchy, and increases the likelihood of losing power (among powerful individuals) and gaining power (among powerless individuals).

Accordingly, we expected that when the power hierarchy is stable, powerful individuals have stronger approach motivation, engage in more global rather than local processing, and therefore are more creative than powerless individuals. We furthermore hypothesized that when the power hierarchy is unstable, these general tendencies reverse:

powerful individuals facing the possibility of power loss become avoidance oriented, engage in more local rather than global processing and become relatively more rigid and less creative in their thinking than powerless individuals facing the possibility of power gains. We finally hypothesized that the latter tendency for powerless individuals to be more creative than powerful individuals under unstable conditions is particularly pronounced when creative performance is functionally relevant, rather than irrelevant, to the goal of gaining power.

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Power and Creativity

We tested these predictions in three experiments in which power roles were assigned and stability of power and functionality of creativity were manipulated. Experiment 1 was a first test of our predictions using a creativity test of conceptual insight. Experiment 2, a brainstorm study, focused on unstable power positions and was designed to test if low power individuals would be cognitively more flexible and consequently more creative especially when creativity was functionally relevant. Experiment 3 was designed to uncover the mediating process: it assessed whether it is approach (vs. avoidance) motivation, global (vs.

local) attentional focus, or some combination of the two that explains why powerless individuals in unstable hierarchies are more creative than powerful individuals.

Experiment 1

Experiment 1 was designed to test if under stable power high power individuals would be more creative than low power individuals especially when creativity was functionally relevant to power. Moreover, we tested if these effects would reverse under unstable power, making low power individual more creative than high power individuals. Our measure of creativity was the Remote Associates Test (RAT; [START_REF] Mednick | The associative basis of the creative process[END_REF], a test in which people have to break set to find one word that relates to three other words. The RAT benefits from flat associative hierarchies and seeing interrelationships between concepts, which is generally beneficial to creativity.

Method

Design and participants

One hundred thirty nine students (age M = 21.3, SD = 4.2; 51 male) participated for €7 (approximately U.S. $9.50) or partial course credit. Participants were randomly assigned to the conditions of a 2 (power position: high vs. low) x 2 (stability of power position: stable vs.

unstable) x 2 (functionality: relevant vs. not relevant) between-participants factorial design, with creative insight performance as the dependent variable.

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Power and Creativity

Procedures and manipulations

Upon arrival at the laboratory, participants were seated in front of a computer with keyboard. Instructions and measures were given on the computer. Participants were told that they would engage in a task in which they had to work with another participant. Power position was manipulated by assigning participants randomly to the position of high or low power. Participants were told that the high power individual would be in charge of the division of labour, monitor progress and assess performance of the low power individual after completion of the joint task (see e.g., De Dreu & [START_REF] De Dreu | The influence of power on the information search, impression formation, and demands in negotiation[END_REF]. The rewards of the low power individual would be contingent on this assessment. Stability of power position was manipulated by telling participants that power positions were assigned randomly and that power positions would remain unchanged during the experiment (stable power condition), or that power positions might be switched later on in the experiment (unstable power condition).

Before participants did the joint task, they were asked to do a task that putatively measured verbal intelligence, the Remote Associates Test (RAT; see under "Dependent measures").

Relevance was manipulated by telling participants (or not) that research had shown that verbal intelligence was relevant to effective functioning in high power positions. We did not directly state, however, that performance on the RAT could change the power hierarchy. After completing the RAT, participants were informed that the experiment was over, were debriefed, paid and dismissed.

Dependent measures. The RAT consisted of 10 moderately difficult items (see De [START_REF] De Dreu | Behavioral activation links to creativity because it promotes cognitive flexibility[END_REF]Harkins, 2006;Isen, Daubman, & Nowicki, 1987) in which participants have to find the correct word that connects three other words (e.g. black-beans-break -> coffee). We coded the number of correctly solved RAT-items (ranging from 0 to 10). We also included manipulation checks for power, stability and functionality. For the power manipulation, participants were asked to tick the correct box for the question: "In the joint

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Power and Creativity task, I will have:". The options were: 1 = low power; 2 = high power; 3 = don't know. For the stability manipulation, participants were asked to tick the correct box for the question "The power differences in the joint task:". The options were: 1 = can change; 2 = cannot change; 3 = don't know). Finally, to check our manipulation of relevance, participants answered on a 5-point Likert scale (1= not at all, 5 = very): "How relevant is verbal intelligence to effective functioning in high power positions?".

Results and Discussion

Manipulation checks. All participants correctly answered the manipulation check on More importantly, this effect was qualified by a significant three-way interaction among power, stability and relevance, F (1, 138) = 3.95, p < .05, partial η 2 = .03. Analyses showed that when creative performance was functionally irrelevant to power, no significant effect occurred, F (1, 138) < 1, p = .64, and creative performance was generally low (see

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Power and Creativity

Figure 1). When creative performance was functionally relevant to power, there was a significant two-way interaction among power position and power stability, F (1, 138) = 10.47, p < .01. As predicted, when creative performance was relevant and positions were stable, individuals with high power outperformed individuals with low power, F (1, 138) = 6.19, p < .05. The opposite pattern occurred when positions were unstable, F (1, 138) = 4.28, p < .

05, thus supporting our predictions.

Taken together, results support the prediction that under stable power, high power individuals are more creative than low power individuals. Under unstable power, however, low power individuals are more creative, but only when creativity was relevant to power. This adds to the important role the relevance of creative endeavors seems to play. Experiment 2 was designed to replicate these findings with a different creativity task.

Experiment 2

In Experiment 2 we used an idea generation task to test our hypothesis that under unstable power, people low in power are more creative than those high in power, especially when creative efforts are relevant to one's power position. Because the most interesting results occurred in the unstable power position, where -unlike in previous work -the low power individuals were more creative than the high power individuals, we focused on unstable power conditions in this experiment. More than creative insight tasks, an idea generation task allows one to examine an important predictor of creativity, namely cognitive flexibility. This was achieved by coding ideas into semantic categories, the idea being that cognitive flexibility shows up in the use of many rather than few different categories of ideas (e.g., [START_REF] Guilford | Creativity[END_REF]Torrance, 1966;also see De Dreu et al., 2008;[START_REF] Nijstad | Towards a dualpathway to creativity model: Creative ideation as a function of flexibility and persistence[END_REF].

In addition to cognitive flexibility, we also assessed the number of ideas generated (fluency) and the average originality of ideas. Using these different indices of performance

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Power and Creativity allows one to gain some insight into the cognitive processes that underlie our effects. The number of ideas (fluency) is generally highly dependent on effort, but this is less true for average originality (although fluency and originality may be positively correlated; see e.g., De Dreu et al., 2008;[START_REF] Diehl | Productivity loss in brainstorming groups: Toward the solution of a riddle[END_REF][START_REF] Nijstad | Towards a dualpathway to creativity model: Creative ideation as a function of flexibility and persistence[END_REF][START_REF] Osborn | Applied imagination[END_REF] and flexibility.

We expect that power position and the relevance of creativity not only affects effort, but also one's motivational orientation (approach vs. avoidance) and attentional focus (broad vs.

narrow). Therefore, we predict that -given unstable power-cognitive flexibility would be higher for people low in power than for people high in power, especially when creativity is relevant to power. Furthermore, analogous effects on fluency and originality are expected.

Method

Design and participants

Participants were 55 undergraduate students (age M = 21.8, SD = 5.0; 17 male) at the University of Amsterdam and they received either €7 (approximately U.S. $9.50) or partial course credit. The design was a 2 (power position: high vs. low) x 2 (brainstorming relevant vs. not relevant) factorial design. All power positions were unstable. Dependent measures were flexibility, creative fluency and originality of generated ideas.

Procedures and manipulations

These were largely the same as in Experiment 1. Power and relevance were manipulated as before. Participants then proceeded with a four-minute brainstorming task about ways to protect and improve the environment. They were told that they had to come up with as many ideas as possible, refraining from self-criticism and evaluation. Additionally, we told them that they did not have to elaborate on the ideas but to describe them in catchwords. Thereafter participants filled out manipulation checks and were debriefed, paid and dismissed.

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Power and Creativity

Dependent measures. To get at cognitive flexibility, we counted the number of cognitive categories participants drew their ideas from. These 10 categories were imposed on the data and used to guide the coding. The 10 categories relate to the goal of intervention to protect and improve the environment (e.g. reducing pollution, improving use of energy sources), adapted from Nijstad, Stroebe, and Lodewijkx (2003). A second rater coded a random subset of the ideas (N = 340, 30 %) into one of the ten categories with good agreement (Cohen's κ = .79). The number of non-redundant ideas was counted per participant to come to a measure of creative fluency. Finally, originality was coded by two independent raters on a 5-point scale (1= not original, 5= highly original; see Rietzschel, [START_REF] Nijstad | How the group affects the mind: A cognitive model of idea generation in groups[END_REF]. Interrater agreement was satisfactory following criteria of Cicchetti and Sparrow (1981; intraclass correlation, ICC (2) = .71) and we used the aggregation across raters as an indicator of originality.

Results and Discussion

Manipulation checks

All but two participants correctly answered the manipulation checks on power and stability. Excluding these participants did not change the results. Participants in the functionally relevant condition (M = 4.75, SD = .52) indicated verbal intelligence was more important to effective functioning in high power positions than in the functionally irrelevant condition (M = 4.07, SD = .86), F(1, 54) = 14.13, p < .01, partial η 2 = .21.

Flexibility, originality and fluency

We tested the effects of power and relevance on flexibility by submitting flexibility to a 2 (Power position) x 2 (Functionality of Creativity) ANOVA. Recall that all power positions were unstable. Results showed a significant two-way interaction, F (1, 54) = 7.32, p < .01, partial η 2 = .13. As shown in Figure 2, analyses of simple effects showed that low power individuals were more flexible (M = 3.79, SD = 1.25) than high power individuals (M =

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Power and Creativity 2.36, SD = 1.55) but only when the brainstorming task was relevant to power, F (1, 54) = 6.25, p < .05. This is in line with our predictions. We also tested the effects of power and relevance on originality and fluency with a 2 x 2 ANOVA. The two-way interaction among power and relevance on originality was not significant, F (1, 54) < 1, p = .34. The two-way interaction on fluency was also not significant, F (1, 54) < 1, p = .49.

Taken together, results provide a conceptual replication of our earlier finding.

Specifically, under unstable power, low power individuals displayed higher cognitive flexibility (but not greater originality). That we did find predicted effects on cognitive flexibility, but not on originality may be due greater measurement error in the ratings of originality and to the fact that average ratings of originality were rather low overall (i.e., a floor effect; M = 1.80, SD = 0.50). Future research is needed to clarify this.

Experiment 3

Experiment 3 was designed to further insight into the underlying processes responsible for the effects of power position and functionality of creativity on creative insight performance (see Experiment 1) and cognitive flexibility (see Experiment 2). At the outset, we identified two such mechanisms. One possibility is that under unstable power conditions, those with low power adopt an approach motivation. In fact, when power is illegitimate, low power individuals become more approach and less avoidant motivated, have greater risk preferences [START_REF] Lammers | Illegitimacy moderates the effects of power on approach[END_REF], are more action-oriented, persistent and more flexible in attaining their goals [START_REF] Willis | Illegitimacy improves goal pursuit in powerless individuals[END_REF]. It is thus conceivable that -when power differences are unstable-low power individuals become more approach and less avoidant motivated than high power individuals and that this leads them to become more creative. A second possibility is that under unstable power, low power individuals beget more of a global attentional focus, think more abstractly and therefore are more creative than those high in power. Following Construal Level Theory (Trope & Liberman, 2003), high power people -

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Power and Creativity more than those low in power-tend to adopt a global helicopter view of their environment and focus on the gist of a situation rather than losing themselves in details (Smith & Trope, 2006).

However, when power differences are unstable, this pattern may reverse causing low power individuals to focus on the big picture to be able to seize power. Abstract thinking and a global focus generally benefit creativity [START_REF] Förster | Temporal construal effects on abstract and concrete thinking: Consequences for insight and creative cognition[END_REF].

We designed Experiment 3 to disentangle the two possible mediating mechanisms.

We included a word completion task (Roskes, De Dreu & Nijstad, 2010) to measure approach vs. avoidance motivation and the Navon task [START_REF] Navon | Forest before trees: The precedence of global features in visual perception[END_REF] to assess global vs. local attentional focus. To measure creativity, we used the Snowy Pictures Test (SPT; [START_REF] Ekstrom | Manual for kit of factor referenced cognitive tests[END_REF]. The SPT consists of 24 pictures hidden in a complex pattern of visual noise and measures perceptual insight. To get at the correct solution, people typically have to restructure information to discover the solution (Schooler & Melcher, 1995), and such restructuring also benefits creativity.

Method

Design and participants

Fifty four undergraduate students (21 males) at the University of Amsterdam participated for either €7 (approximately U.S. $9.50) or partial course credit. The design was a 2 x 2 factorial design, with power position (high vs. low power) and relevance (yes vs. no) as between-subjects factors. All power positions, again, were unstable. Participants were randomly assigned to experimental conditions.

Procedures and manipulations

Procedures and manipulations were largely the same as in Experiment 2. We manipulated relevance of creativity by making the SPT relevant to power or not. When the SPT was relevant, participants were informed that to function effectively in power positions, it is important to have well-developed spatial abilities. When starting the SPT, participants

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Power and Creativity were informed that they were about to do a test that measured spatial ability and reminded of the importance of this quality for functioning well in power positions. After instructions and assignment to experimental conditions, participants were asked to do two supposedly unrelated tasks: the Navon task [START_REF] Navon | Forest before trees: The precedence of global features in visual perception[END_REF] and a Word Completion Task (Roskes et al., 2010). Participants were then asked to do the SPT. The items in this task followed in random order. Once participants had finished the SPT, they were informed that the experiment was over and the joint task would not take place. They filled out manipulation checks and were debriefed, paid and dismissed.

Dependent measures. We coded the number of correct solutions to the SPT-items (range between 0 and 24). To measure global vs. local processing, we used the Navon task (Navon, 1978). In this task, participants are asked to respond as quickly as possible to letters shown on screen. These letters are large letters composed of small letters that always differed from the large letters, for example an A made up of small T's. Participants did one hundred trials. The task was to press a key as fast as possible when they saw a specific letter. In half of the trials these were small letters composing a large letter, in the other half of the trials this was a large letter composed of small letters. Only correct trials were included in the analyses.

After an outlier analysis, the average reaction time (in seconds) on the large and small letters was computed. We subsequently computed a composite measure by subtracting the reaction time on the large letters from the small letters. A positive score on this measure thus evidenced a global processing style (seeing the large letters faster than the small letters), a negative score a local processing style.

To measure approach vs. avoidance motivation, we used a Word Completion Task.

Participants were presented with words from which one or two letters were missing. They were asked to complete these words. Seven of these words could be completed relating to avoidance (e.g. VERM...DEN -> VERMIJDEN; to avoid) or neutral (VERMOEDEN; to

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Power and Creativity suspect), seven could be completed relating to approach (BEREI.EN -> BEREIKEN; to achieve) or neutral (BEREIDEN; to prepare). We coded the number of words completed as approach or avoidance.

Results and discussion

Manipulation checks

All participants answered the manipulation check on power correctly. Participants in the functionally relevant condition (M = 4.37, SD = 1.01) indicated verbal intelligence was more important to effective functioning in high power positions than in the functionally irrelevant condition (M = 2.81, SD = 1.49), F(1, 53) = 19.55, p < .01, partial η 2 = .26.

Creative insight

We submitted the scores on the SPT to a 2 (Power position) X 2 (functionality of creativity) ANOVA. We found an interaction effect among position and functionality, F (1, 53) = 4.03, p < .05, partial η 2 = .08. As shown in Figure 3 and Table 1, analyses of simple effects showed that low power individuals had higher performance on the SPT than high power individuals when the SPT was functional to position (M = 10.79, SD = 3.02 vs. M = 7.85, SD = 2.91, F (1, 53) = 6.86, p < .05) while there were no differences when the SPT was nonfunctional (M = 9.00, SD = 3.21 vs. M = 9.29, SD = 2.64; F (1, 53) = .06, p > .05), lending additional support to our predictions.

Processing style and approach/ avoidance

There was a significant two-way interaction among position and functionality on performance on the Navon task, F (1, 53) = 5.87, p < .05, partial η 2 = .12. Simple effects analyses showed that low power individuals were more globally focused than high power individuals when the SPT was functional to their position (M = .027, SD = .064 vs. M = -.017, SD = .054; F (1, 53) = 4.99, p < .05) while no differences were found when the SPT was

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Power and Creativity nonfunctional (M = -.009, SD = .034 vs. M = .015, SD = .050; F (1, 53) = 1.50, p > .10), see Table 1.

No significant interactions were found on the approach measure. We did, however, find a significant interaction among position and functionality on the avoidance measure, F

(1, 53) = 6.69, p < .05, partial η 2 = .12. Inspection of simple effects showed that low power individuals were less avoidant than high power individuals when the SPT was functional (M = 1.86, SD = .77 vs. M = 2.85, SD = 1.21; F (1, 53) = 5.64, p < .05) while no differences were found when the SPT was nonfunctional (M = 2.77, SD = 1.24 vs. M = 2.21, SD = 1.12; F (1, 53) = 1.72, p > .10), see Table 1. Moreover, processing style and the avoidance measure correlated negatively (r = -.34, p < .05).

Mediation of processing style on creative insight

We conducted a hierarchical regression analysis to test if the effects of position and functionality on performance on the SPT were mediated by either processing style (Navon) or avoidance (Word Completion). We first entered the main effects of dummy coded independent variables position and functionality, then the interaction effect of position x functionality, and finally scores on the Navon or Word Completion Task. The Word Completion Task did not mediate the effects on the SPT. Scores on the Navon significantly predicted SPT-performance, B = 2.40, t = 3.35, p < .01. And, when controlled for the effect of the scores on the Navon task, the interaction effect among position and functionality on the SPT disappeared, B = 1.84, t = 1.15, p = .26. A Sobel test (see Sobel, 1986) showed that the mediation of processing style was significant, Z = 1.99, p < .05 (see Figure 4).

In short, low power individuals outperformed high power individuals on creative insight when doing was functional to position because they had a global processing style. The reason for the fact that processing style and not avoidance motivation mediated the effects of unstable power on creativity may be twofold. First, processing style is a more proximate

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Power and Creativity predictor of behavior, as it relates to the scope of perceptual and conceptual attention. In fact, approach motivation may lead to global processing [START_REF] Förster | Enactment of approach and avoidance behavior influences the scope of perceptual and conceptual attention[END_REF]. Second, small differences in the reliability of measurement may have consequences for the ability to show mediation. Our measure of processing style was very accurate, using a measure of reaction times accurate at the level of milliseconds. Our measure of avoidance motivation may have been less reliable, and this may explain the weaker effects for this variable.

General discussion

The current research tested the hypothesis that under stable power, high power individuals would be more creative than low power individuals especially when creativity was functionally relevant to power. Moreover, we hypothesized that under unstable power this pattern would reverse, making low power individuals more creative than high power individuals when creativity was functionally relevant to power. These predictions were confirmed in Experiment 1. We further showed that under unstable power, low power individuals were more flexible thinkers than high power individuals, especially when creativity was relevant to power (Experiment 2). Finally, we found that under unstable power, low power individuals were less avoidant and had a global attentional focus compared to high power individuals, again, when creativity was relevant to power. A global attentional focus (but not reduced avoidance orientation or increased approach orientation) in turn led to higher creativity (Experiment 3). This research underscores the importance of the relevance of creativity to the goals and motives people have in a certain situation. In this research, people could show competence in exerting power by being creative. When the possibility existed to gain power -instead of the possibility of losing power-by being creative, this boosted creative performance, but only on those tasks that were functional to gaining power.

New research on power should take into account the importance of the stability of power positions. Most research on power assumes power positions are stable and secure, and

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT
Power and Creativity no possibilities exist to loose the privileged position. Often, however, power positions are all but stable: managers leading international companies, dictators ruling a country, or leaders of a soccer team all face the possibility of losing their position. Once company results dramatically decline, support from the people collapses, or the game is lost once too often, leaders can be -and often are-replaced. Interestingly, one could presume that for low power individuals, power instability in itself is empowering, leading them to act and behave as high power individuals. Subjectively, they may feel as if they have high power in this situation.

This is an interesting question future research could address.

Moreover, a more distal mediating mechanism for our findings may be that having unstable low power leads to feelings of confidence and self-efficacy, especially when low power individuals can gain power by being creative. They may be more confident about their abilities and also perceive that they have the 'power' to change their situation. Conversely, when high power individuals have the idea their power basis is disputed, they may perceive their actual level of power to be lower. Additionally, for high power people, instability of power creates unsafety and insecurity, which may narrow attentional focusing and lower creativity [START_REF] Easterbrook | The effect of emotion on cue utilization and the organization of behavior[END_REF]. For low power people, instability of power and thus the possibility to gain power, may lead a broad attentional focus as a gain in power can concurrently lead to more safety and less dependency on others [START_REF] Friedman | Implicit affective cues and attentional tuning: An integrative review[END_REF].

In the paper by [START_REF] Kuhl | Motivation, Affect, and Hemispheric Asymmetry: Power Versus Affiliation[END_REF], power was operationalized as a chronic personality motive. People with such a motive may be more afraid of losing power. This may explain why it was found that power leads to lower creativity. In Smith andTrope (2006) and[START_REF] Förster | Relations between perceptual and conceptual scope: How global versus local processing fits a focus on similarity versus dissimilarity[END_REF], power was operationalized as "having power over others", which may have reminded people of situations in which they had relatively stable power over others.

A different but compatible mechanism may also explain the pattern of results that emerged. Recently, it has been suggested that the global information processing system is

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT
Power and Creativity activated when people are confronted with novel information, but only when novelty is not potentially dangerous [START_REF] Förster | GLOMO sys: A systems account of global versus local processing[END_REF]. Under instability of power, low power people see a beneficial potential for change, and this opens up a broader conceptual and perceptual scope. For high power people, however, novelty in this situation signals the possibility of losing their privileged position, is perceived as a threat, and leads to the activation of the local processing system -lo-sys [START_REF] Easterbrook | The effect of emotion on cue utilization and the organization of behavior[END_REF].

Whereas in the current experiments a change in the power hierarchy was not directly contingent on creative performance, new research could examine what happens when people lacking power can actually seize power by being creative. One possibility is that powerful individuals facing the risk of losing their position, are more prone to subversive and (c)overt aggression to secure their position, while low power individuals find creative ways of tackling problems, thereby coming into the picture and forwarding their interests. Moreover, under unstable power, powerful individuals may engage in deceit and plagiarize ideas of others they are competing with to forward their interests.

Perverse manifestations of power hierarchies come to mind quickly, such as domination and corruption, but hierarchy can create social order and coordination, and individual incentives to climb the ladder (Magee & Galinsky, 2008). One interesting feature of power hierarchies is that they appear self-reinforcing; powerful individuals are more likely to act [START_REF] Keltner | Power, approach, and inhibition[END_REF][START_REF] Galinsky | From power to action[END_REF] use ideology, such as stereotyping [START_REF] Jost | The role of stereotyping in system-justification and the production of false consciousness[END_REF] and legitimizing myths [START_REF] Chen | Cloaking power: Legitimizing myths and the psychology of the advantaged[END_REF], choose those jobs that forward their interests (Pratto, Stallworth, Sidanius, & Sears, 1997), and consequently, accumulate more resources and influence. Taken to its extreme, power hierarchies should result in a monopolistic 'winner takes all' power constellation (Magee & Galinsky, 2008). We know that this is rarely the case; external changes, fairness and legitimacy and fierce competition over standing in the hierarchy can attenuate the self-

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT

Power and Creativity reinforcing powers of hierarchies. Among those lacking power being creative may be another way to change the power hierarchy. When power positions are unstable, low power individuals are more flexible thinkers, are less avoidant and process information more globally. Consequently, they achieve more creative insights and generate more original thoughts, especially when being creative is relevant to (gain) power. As such, when the power hierarchy is unstable, those lacking power hold the power to creativity.

  power. All but nine participants correctly answered the manipulation check on stability of power. Excluding these participants from analyses did not change the results. Participants in the functionally relevant condition (M = 4.74, SD = .75) indicated verbal intelligence was more important to effective functioning in high power positions than in the functionally irrelevant condition (M = 3.09, SD = 1.36), F(1, 144) = 50.78, p < .01, partial η 2 = .26. Creative performance. We submitted the number of correctly solved RAT-items to a 2 (Power Stability) x 2 (Power Position) x 2 (Functionality of Creativity) Analysis of Variance (ANOVA). Results showed a significant two-way interaction among power position and power stability, F (1, 138) = 7.05, p < .05, partial η 2 = .05. Simple effects analyses showed that when power positions were stable, individuals with high power tended to outperform individuals with low power (M = 4.74, SD = 1.94 vs. M = 3.92, SD = 1.86, F (1, 138) = 3.18, p < .10) while the opposite trend emerged when positions were unstable (M = 3.79, SD = 2.05 vs. M = 4.85, SD = 1.87; F (1, 138) = 3.53, p < .10).

Figure 1 .(Figure 2 .

 12 Figure 1. Creative insight as a function of power, stability and functional relevance (Experiment 1). Bars indicate +one standard error

Table 1

 1 Processing style, avoidance motivation and creative insight as a function of unstable power and functional relevance (Experiment 3). Note. Means (SD) with different superscripts in one row differ at p < .05

		Relevant	Not relevant
		High power	Low power	High power	Low power
	Creative insight	7.85 a (2.91)	10.79 b (3.02)	9.29 ab (2.64)	9.00 ab (3.21)
	Processing style	-.017 a (.054)	.027 b (.064)	.015 ab (.050)	-.009 ab (.034)
	Avoidance	2.85 a (1.21)	1.86 b (0.77)	2.21 ab (1.12)	2.77 ab (1.24)

This research was supported by Grant NWO-400-06-098 from the Netherlands Organization for Scientific Research (NWO) awarded to Carsten de Dreu and Bernard Nijstad, and the FMG-UvA Research Priority Grant on Affect Regulation. The authors thank Hillie H. Aaldering for coding data in Experiment 2.


E Hébrard
email: hebrard@crpg.cnrs-nancy.fr

B Marty

Coupled noble gas-hydrocarbon evolution of the early Earth atmosphere upon solar UV irradiation

Keywords: early Earth, young Sun, noble gases, photochemistry

.

Introduction

The Earth atmosphere evolved through time via extraterrestrial contributions, interactions with the solar and galactic cosmic ray irradiations and complex exchanges with the lithosphere, hydrosphere and, once arisen, biosphere. Understanding the state and evolution of the atmosphere during the Hadean and the Archean eons is of prime importance, most notably because Life evolved and flourished during this first half of Earth's history. Information about the atmosphere at such remote time is elusive owing to the lack of direct records, and the state and evolution of the atmosphere over Earth's history have been constrained for years from the geological record, no matter how blurred by metamorphism and rock alteration. There have been remarkable advances in the recent years and available information suggests nowadays that the ancient atmosphere was indeed very different from today. For instance, mass-independent isotopic fractionation of sulfur have been found in Archean sedimentary rocks, and is believed to be related to the occurrence of enhanced photochemical reactions induced by UV solar light at significant atmospheric depths [START_REF] Farquhar | Amospheric influence of Earth's earliest sulfur cycle[END_REF]. Likewise, the persistence of liquid water during the Archean eon, despite a faint young Sun, required certainly the presence of elevated concentrations of greenhouse gases in the early Earth's atmosphere [START_REF] Sagan | The early Faint Sun paradox: Organic shielding of ultraviolet-labile greenhouse gases[END_REF][START_REF] Feulner | The faint young Sun problem[END_REF]. Despite these studies, there is still considerable uncertainty concerning the origin and the evolution of the atmospheric volatiles themselves.

Noble gases are exceptional tracers of the sources and sinks of atmospheric volatiles, due to their chemical inertness and to contributions from nuclear reactions (e.g., [START_REF] Ozima | Noble gas geochemistry[END_REF]. Studies based on compositional differences between the present-day atmosphere and potential cosmochemical end-members (the meteorites, the solar nebula, the solar wind), and/or mantle-derived rocks (e.g., [START_REF] Ozima | Noble gas geochemistry[END_REF][START_REF] Pepin | On the origin and early evolution of terrestrial planet atmospheres and meteoritic volatiles[END_REF][START_REF] Pepin | Xenon isotope systematics, giant impacts, and mantle degassing on the early Earth[END_REF] have provided important geochemical constraints. Firstly, the atmosphere contains noble gas isotopes produced by extant and extinct radioactive isotopes produced in the solid Earth, which permits investigation of mantle/crust degassing chronology. These tracers indicate that the atmosphere is a geologically old reservoir which formed early during accretion and differentiation of the Earth [START_REF] Allègre | Constraints on evolution of Earth's mantle from rare gas systematics[END_REF][START_REF] Zartman | Helium, argon, and carbon in some natural gases[END_REF]. Xenon presents an interesting discrepancy, known as the "xenon paradox". Firstly, this element is depleted by one order of magnitude relative to other nobles gases and other volatile elements (e.g. H( 2 O), C) when normalized to the chondritic composition (Marty, 2012, and references therein). Secondly, atmospheric xenon is largely enriched in its heavy isotopes relatively to potential extraterrestrial end-member compositions (3-4% u -1 ), whereas other noble gas isotopic ratios resemble to those of potential cosmochemical ancestors (although atmospheric krypton is slightly fractionated too, by < 1% u -1 , relatively to its chondritic composition). Thirdly, atmospheric xenon corrected for 3-4% u -1 isotope fractionation still differs from known chondritic or solar compositions suggesting that it originated from an extraterrestrial component having a specific composition. In order to circumvent the last point, [START_REF] Pepin | On the origin and early evolution of terrestrial planet atmospheres and meteoritic volatiles[END_REF] postulated the existence of an adequate xenon ancestor that was subsequently isotopically fractionated to yield the composition of modern atmospheric xenon. However, mass-dependent fractionation from either an extraterrestrial reservoir during loss of noble gases from the atmosphere cannot account alone for both the elemental and isotopic of atmospheric xenon. Attemps to resolve this "xenon paradox", has led to sophisticated models of early atmospheric evolution coupled with mantle geodynamics [START_REF] Pepin | On the origin and early evolution of terrestrial planet atmospheres and meteoritic volatiles[END_REF][START_REF] Tolstikhin | The evolution of terrestrial volatiles: a view from helium, neon, argon and nitrogen isotope modelling[END_REF] and cometary contributions [START_REF] Dauphas | The dual origin of the terrestrial atmosphere[END_REF][START_REF] Owen | Possible cometary origin of heavy noble gases in the atmospheres of Venus, Earth and Mars[END_REF] that could explain terrestrial noble gas patterns under ad hoc conditions during the building stages of the Earth. Alternatively, it has been proposed that the xenon underabundance in the atmosphere could be due to its early sequestration in minerals at high pressures deep in the Earth [START_REF] Sanloup | Retention of xenon in quartz and earth's missing xenon[END_REF][START_REF] Shcheka | The origin of the terrestrial noblegas signature[END_REF][START_REF] Zhu | Stability of xenon oxides at high pressures[END_REF][START_REF] Sanloup | Reactivity of xenon with ice at planetary conditions[END_REF], but this possibility alone cannot account for the specific xenon isotope composition of the Earth's atmosphere.

Constraints from Archean noble gas isotopic composition

Recently, the analysis of Archean samples (3.5 Ga-old barite, [START_REF] Pujol | Xenon in Archean barite: Weak decay of 130 Ba, mass-dependent isotopic fractionation and implication for barite formation[END_REF]andhydrothermal quartz, Pujol et al. (2011, 2013)) permitted insight into the composition of noble gases in the Archean atmosphere. These samples have trapped several ancient fluids mixed up with a surface water component having dissolved noble gases, presumably from the Archean atmosphere. The isotopic 2011)). Chondritic/solar value is the mean value of the solar and chondritic compositions (from [START_REF] Wieler | Krypton and xenon from the solar wind and solar energetic particles in two lunar ilmenites of different antiquity[END_REF]).

Barite and quartz samples are both from the Dresser formation at the North Pole area in Pilbara craton, Western Australia [START_REF] Srinivasan | Barites: Anomalous xenon from spalation and neutron-induced reactions[END_REF][START_REF] Pujol | Xenon in Archean barite: Weak decay of 130 Ba, mass-dependent isotopic fractionation and implication for barite formation[END_REF][START_REF] Pujol | Chondritic-like xenon trapped in Archean rocks: A possible signature of the ancient atmosphere[END_REF][START_REF] Pujol | Argon isotopic composition of Archaean atmosphere probes early Earth geodynamics[END_REF]. Quartz samples are in fact fluid inclusions trapped in Archean hydrothermal quartz. The 1.65 Gaold shungite sample is from the Shun'ga area in the Karelia region, Russia [START_REF] Lokhov | Volatile components in Karelian shungites as indicators of composition of Protherozoic atmosphere[END_REF]. 2.0-3.0 Ga-old deep fracture fluid sample is from the Timmins mine in Ontario [START_REF] Holland | Deep fracture fluids isolated in the crust since the Precambrian era[END_REF]. The younger, 170 Ma-old, barite sample is from the Belorechenskoe deposit, Northern Caucasus, Russia [START_REF] Meshik | Weak decay of 130 Ba and 132 Ba: Geochemical measurements[END_REF]. The modern atmospheric ratio is from [START_REF] Basford | Krypton and xenon in lunar fines[END_REF]. The data fit an exponential decay curve, suggesting that the xenon isotopic fractionation was progressive with time.

composition of xenon in these samples is intermediate between that of the modern atmosphere and that of potential cosmochemical ancestors. Furthermore, available data for xenon isotopes trapped in ancient rocks seem to define a temporal evolution (Fig. 1) suggesting that the xenon isotope composition of the atmosphere changed with time from a chondritic (or solar) one to the present-day one.

The isotopic composition of atmospheric xenon differs from that of the chondritic, or solar, compositions by a 3.5% u -1 on average enrichment in its heavy isotopes relative to the light ones. Atmospheric xenon is elementally depleted relative to krypton by a factor of 23 on average, compared to carbonaceous chondrites (e.g., [START_REF] Pepin | On the origin and early evolution of terrestrial planet atmospheres and meteoritic volatiles[END_REF]. We assume that these atmospheric depletion and isotope fractionation had a common cause and followed a Rayleigh distillation :

i+1 Xe i Xe t / i+1 Xe i Xe t=0 = f α-1 (1)
where α is the fractionation factor during loss, i the mass number of any stable xenon isotope and f (= 1 ⁄23) is the depletion factor of atmospheric xenon. Thus :

i+1 Xe i Xe t=4.56 Ga, today / i+1 Xe i Xe t=0 = f α-1 ∼ 1.035
(2) The instantaneous fractionation factor α required for explaining the current enrichment in heavy isotopes for xenon remaining in the atmosphere is thus equal to 1.1% u -1 . Processes able to fractionate the isotopes of xenon at such percent level require ionization of xenon [START_REF] Frick | Noble gas trapping and fractionation during synthesis of carbonaceous matter[END_REF][START_REF] Bernatowicz | Xe isotopic fractionation in a cathodeless glow discharge[END_REF][START_REF] Bernatowicz | Isotopic fractionation of Kr and Xe implanted in solids at very low energies[END_REF][START_REF] Ponganis | Isotopic fractionation in lowenergy ion implantation[END_REF][START_REF] Hohenberg | Active capture and anomalous adsorption: new mechanisms for the incorporation of heavy noble gases[END_REF][START_REF] Marrocchi | Adsorption of xenon ions onto defects in organic surfaces: Implications for the origin and the nature of organics in primitive meteorites[END_REF]. In experiments aimed at fractionating xenon isotopes upon ionization, ionized xenon is implanted into solids where it is enriched in heavy isotopes, whereas neutral xenon is much less efficiently trapped and is not isotopically fractionated.

Xenon depletion and isotope fractionation could have taken place progressively in the Archean atmosphere, through interaction with UV light from the young Sun. Compared to today, the irradiation flux was probably 5 times higher at 3.5 Ga and 3 times higher at 2.5 Ga, based on observations of nearby solar type stars [START_REF] Ribas | Evolution of the solar activity over time and effects on planetary atmospheres. I. High-energy irradiances (1-1700 Å)[END_REF]. We suggest that most of the ionized xenon would have escaped while only a small fraction, implanted into atmospheric aerosols and enriched in heavy isotopes, would have been preserved. Such processing should have affected mostly xenon and not the other noble gases (although there is room for fractionating krypton to a much lesser extent), as developed in the present work. Over time, this combination of atmospheric escape and preservation of a tiny fraction of isotopically-fractionated xenon would have resulted in a Rayleigh-type distillation. Elemental and isotopic compositions of noble gases in general, and xenon in particular, may therefore reflect the chemical conditions of the early Earth's atmosphere.

It has been hypothesized that the Earth's atmosphere contained an organic haze similar to that of Titan well before widespread oxygenation about 2.45 Gyr ago [START_REF] Kasting | Photochemistry of methane in the Earth's early atmosphere[END_REF][START_REF] Zahnle | Photochemistry of methane and the formation of hydrocyanic acid (HCN) in the Earth's early atmosphere[END_REF][START_REF] Sagan | The early Faint Sun paradox: Organic shielding of ultraviolet-labile greenhouse gases[END_REF]. This prediction arose from the fact that, because the Sun was fainter by 20-30% than today, and because there is no evidence in the geological record for a very high P CO 2 in the Archean, another greenhouse gas had to be present in the ancient atmosphere to counter-balance the lower solar energy and prevent global glaciation (e.g., Kasting, 2010, and references therein). This prediction has been substantiated by geological evidence only recently. Pavlov et al. (2001b) have first argued that the occurence of kerogens with extremely low-13 C in late Archean sediments constitutes a indirect evidence for the occurence of an organic haze at the time. [START_REF] Farquhar | Multiple sulfur isotopes and the evolution of the atmosphere[END_REF] have used the sulfur isotope record to conclude that early to mid-Archean conditions were anoxic. The lifetime of methane in the early Earth's atmosphere was therefore of the order of 10 3 to 10 4 years in contrast to about 10 years in our modern atmosphere [START_REF] Zahnle | Photochemistry of methane and the formation of hydrocyanic acid (HCN) in the Earth's early atmosphere[END_REF]. [START_REF] Domagal-Goldman | Organic haze, glaciations and multiple sulfur isotopes in the Mid-Archean Era[END_REF] have gone further by suggesting that the sulfur isotopic variability was modulated by the thickness of an organic haze. [START_REF] Zerkle | A bistable organic-rich atmosphere on the Neoarchaean Earth[END_REF] multiproxy geochemical analyses of sediments from the 2.65-2.5-billion-years-old Ghaap Group in South Africa, have indicated the presence at that time of a reduced atmosphere that was periodically rich in methane, consistent with the prediction of a hydrocarbon haze. Overall, as limited as they are, ground-truth evidences from 3.5 to 2.5-Ga-old geological records suggest that methane was indeed an important component of the atmosphere throughout the Archean, which might have driven the formation of a hydrocarbon haze.

Numerical simulations of the responses of organic haze formation and noble gases photoionization to the early Earth's atmosphere conditions and solar EUV variations are therefore worth performing. To evaluate these, we have developed a one-dimensional photochemical model of the primitive Earth's atmosphere in appropriate conditions for an organic haze to be formed and at different times along the course of the Sun's evolution. We explore conjointly the possible temporal evolution of the noble gas elemental and isotopic compositions of the atmosphere, due to the interaction with extreme UV light from the Sun.

Model description

Our photochemical model is derived from a recent model of the atmosphere of Titan [START_REF] Hébrard | Neutral production of hydrogen isocyanide (HNC) and hydrogen cyanide (HCN) in Titan's upper atmosphere[END_REF] , which has been updated on the basis of the latest model for the early Earth [START_REF] Tian | Revisiting HCN formation in Earth's early atmosphere[END_REF]. The model now includes 83 species, for which transport is considered, linked by 351 chemical reactions. Instead of using a classical Crank-Nicholson method, we use the ODEPACK library, which implements Hindmarsh's solvers for ordinary differential equations [START_REF] Hindmarsh | ODEPACK, a systematized collection of ODE solvers[END_REF].

Our one-dimensional photochemical model uses a constant background atmosphere. Atmospheric parameter inputs (P , T , n) were taken from [START_REF] Tian | Revisiting HCN formation in Earth's early atmosphere[END_REF]. The corresponding temperature profile, without stratospheric heating and with a surface temperature of 273 K, is at the lower limit of what is expected for the Archean, as evidenced by the presence of liquid water on the early Earth (see [START_REF] Feulner | The faint young Sun problem[END_REF], for a complete review). The density profile is quite consistent with a recent study of fossil raindrop imprints that limits total air density at 2.7 Ga to less than twice today's level, with the most likely value similar to the present-day density [START_REF] Som | Air density 2.7 billion years ago limited to less than twice modern levels by fossil raindrop imprints[END_REF].

Previous theoretical studies have indicated that the rate of organic haze formation was a function of the atmospheric CH 4 /CO 2 ratio (Pavlov et al., 2001a;[START_REF] Trainer | Haze aerosols in the atmosphere of early Earth: Manna from Heaven[END_REF][START_REF] Kharecha | A coupled atmosphereecosystem model of the early Archean Earth[END_REF]. A high concentration of methane and a relatively low concentration of carbon dioxide tends to favor the production of an hydrocarbon haze both in theoretical models (Pavlov et al., 2001a) and in laboratory experiments [START_REF] Trainer | Organic haze on Titan and the early Earth[END_REF]. Formation of hydrocarbon aerosols is calculated using methods similar to those used in previous works (Pavlov et al., 2001a; Hydrocarbon aerosols formation in our model relies therefore on the following reactions :

C 2 H + C 2 H 2 → C 4 H 2 + H (3) C 2 H + CH 2 CCH 2 → H + C 5 H 4 (4)
Truncating the polymerization scheme in this over-simplified way should maximize the formation of aerosol particles since no backward reactions for the resulting high molecular weight products are introduced. Following Pavlov et al.

(2001a), we are here less interested in deriving the aerosols genuine composition than in finding a way to quantify simply the efficiency of the haze formation. To rely on an efficient haze formation in Earth's early atmosphere, we focus our calculations on the 1000 ppmv CH 4 and 3000 ppmv CO 2 case of [START_REF] Tian | Revisiting HCN formation in Earth's early atmosphere[END_REF] model, which is applicable to the Archean postbiotic Earth [START_REF] Rye | Atmospheric carbon dioxide concentrations before 2.2 billion years ago[END_REF][START_REF] Kharecha | A coupled atmosphereecosystem model of the early Archean Earth[END_REF][START_REF] Rosing | No climate paradox under the faint early Sun[END_REF]. Volcanic outgassing of sulfur dioxide SO 2 and molecular hydrogen H 2 is included. Their surface fluxes are set equal to 3.5 × 10 9 and 2.5 × 10 10 molecules cm -2 s -1 , respectively [START_REF] Pavlov | Mass-independent fractionation of sulfur isotopes in Archean sediments: Strong evidence for an anoxic Archean atmosphere[END_REF]. A zero flux is assumed as an upper boundary condition for most of the species, except for atomic hydrogen H and molecular hydrogen H 2 , which are allowed to escape with velocities based on the diffusionlimited escape formula [START_REF] Walker | Evolution of the atmosphere[END_REF]. This provides an upper limit on the escape rate, and hence a lower limit for their atmospheric abundances. The possibility of nonthermal escape of xenon will be discussed later on. The water vapor content in the troposphere is controlled by the temperature profile. Above the tropopause, the water vapor concentration is calculated by solving the combined equations of photochemistry and transport. The eddy diffusivity profile is taken from [START_REF] Massie | Stratospheric eddy diffusion coefficients from tracer data[END_REF].

Calculations are performed with a solar zenith angle of 50°t o account for diurnally averaged conditions at the equator. We use a non-uniform grid of altitude with 125 levels from the ground to 150 km. Two consecutive levels are separated by a distance smaller than H(z)/5, where H(z) is the atmospheric scale height at the altitude z.

Helium is lost continuously to space through thermal and non thermal processes, and is considered here only for the sake of illustration. The abundances of noble gas isotopes not produced by nuclear reactions and nor lost from the atmosphere, 20 Ne and 84 Kr, are considered to be invariant through time. [START_REF] Pujol | Argon isotopic composition of Archaean atmosphere probes early Earth geodynamics[END_REF] recently reported the analysis of argon in 3.5-Ga-old hydrothermal quartz which revealed a 40 Ar/ 36 Ar ratio of 143 ± 24, lower than the present-day atmospheric value of 298.56 ± 0.31 [START_REF] Lee | A redetermination of the isotopic abundances of atmospheric Ar[END_REF]. The evolution of atmospheric argon abundance through time was calculated by assuming that 36 Ar was primordial and by using the Archaean atmospheric 40 Ar/ 36 Ar ratios yielded by [START_REF] Pujol | Argon isotopic composition of Archaean atmosphere probes early Earth geodynamics[END_REF]. The evolution of atmospheric xenon abundance through time was calculated by assuming that it follows a Rayleigh type isotope evolution. The xenon isotopic fractionation δXe data displayed in Fig. 1 are fitted with an exponential decay curve : δXe = 35.124e -0.740t -1 (5)

We consider that the instantaneous fractionation factor α did not vary through time. We calculate the depletion factor of atmospheric xenon f through time as :

1 + 35.124e -0.740t -1 1000 1.035

1 α-1 (6)
The corresponding atmospheric abundances we derived are listed in Table 1.

The Sun was significantly more active in its past. This early activity for Sun-like stars has been shown in the Xray/EUV range [START_REF] Ribas | Evolution of the solar activity over time and effects on planetary atmospheres. I. High-energy irradiances (1-1700 Å)[END_REF] and in the UV range [START_REF] Ribas | Evolution of the solar activity over time and effects on planetary atmospheres. II. κ 1 Ceti as an analog of the Sun when Life arose on Earth[END_REF]. These emissions might have had an impact on the early evolution of Earth's atmosphere. It has been proposed, for instance, that UV radiation might help the synthesis of complex ribonucleotides in plausible early Earth conditions [START_REF] Powner | Synthesis of activated pyrimidine ribonucleotides in prebiotically plausible conditions[END_REF]. Through the use of a photochemical model, [START_REF] Ribas | Evolution of the solar activity over time and effects on planetary atmospheres. II. κ 1 Ceti as an analog of the Sun when Life arose on Earth[END_REF] indicate that such enhanced UV light emission leads indeed to a significant increase in photodissociation rates compared with those commonly assumed for the early Earth. These results emphasize the fact that reliable calculations of the physical state and the chemical composition of early planetary atmospheres need to account for the stronger solar photodissociating EUV-UV irradiation. As the solar emission in this wavelength range drives the photochemistry and thus the atomic and molecular compositions of planetary atmospheres, it might have impacted the formation of an organic haze as well as the photoionization of noble gases during the Archean. The high-resolution dipole (e,e) method has proven to be suitable for the measurement of absolute photoabsorption oscillator strengths (e.g. cross sections) for electronic excitation of free atoms and molecules and has been used therefore to derive the photoabsorption and photoionization cross sections for the different noble gases in the energy range 16-250 eV [START_REF] Chan | Absolute optical oscillator strengths for the electronic excitation of atoms at high resolution: Experimental methods and measurements for helium[END_REF](Chan et al., , 1992a,b),b). The specific electronic structure of xenon which makes it the most reactive element among noble gases is due to both its lowest ionization potential (12.13 eV or 102.23 nm (Lide, 2009)) and to its extended photoabsorption cross section covering part of the VUV spectrum (up to about 150 nm).

We have run our one-dimensional photochemical model for the reducing Archean atmosphere using the modernday solar flux and fluxes for the Sun at 2.5 Ga, 3.0 Ga and 3.5 Ga. [START_REF] Claire | The evolution of solar flux from 0.1 nm to 160 µm: Quantitative estimates for planetary studies[END_REF] provided quantitative estimates of the wavelength dependence of the solar flux for periods of time relevant to the early evolution of planetary atmospheres in the Solar System or around other G-type stars. Fig. 3 displays solar actinic fluxes at 2.5, 3.0, and 3.5 Ga along with the modern-day flux [START_REF] Claire | The evolution of solar flux from 0.1 nm to 160 µm: Quantitative estimates for planetary studies[END_REF] and focuses on the specific emission-line behavior in the UV with inset showing the overall behavior with time of the whole solar spectrum. 3: Predicted incoming solar flux at Earth vs. wavelength, at 3.5 Ga (dark red), 3.0 Ga (red) and 2.5 Ga (red), compared to the present solar flux (bold blue). Each panel displays the solar flux for the given paleodate, each binned at 1 nm resolution for comparison.

In the main panel, the solar fluxes vs. wavelength are displayed on a logarithmic vertical scale in units of photons cm -2 s -1 nm -1 in the UV region of the spectrum driving the photochemistry, up to 250 nm. The subpanel zooms out on the solar fluxes vs. wavelength, linearly displayed on most of the solar spectrum (adapted from Claire et al. ( 2012)).

Results and discussion

The fact to use a constant vertical temperature profile in this work is obviously not consistent with the evolution of insolation conditions through time. It would require to compute a vertical temperature profile at radiative equilibrium with a one-dimensional radiative-convective model. This is clearly beyond the scope of the present paper. This approximation has however little impact on the calculation of photolysis rates. Indeed, the purpose here is not to run a fully consistent radiative-convective-photochemical model, but to illustrate how the photoionization rates, the photodissociation rates and the subsequent photochemistry are sensitive to an enhanced UV irradiance in constant atmospheric conditions, all other things being kept equal.

Temporal evolution of atmospheric chemistry

We find that the atmospheric composition is very sensitive to the incoming solar flux that relates to the age of the Sun. The concentrations of important atmospheric species with corresponding rates for chemical production and loss reactions relevant to noble gases and haze photochemistry are displayed in Fig. 4 under the present Sun and in Figs. 5 under the Sun at 3.5 Ga. The most apparent differences in atmospheric gas concentrations are that: 1) methane CH 4 and its photolysis derivatives (acetylene C 2 H 2 , ethylene C 2 H 4 , ethane C 2 H 6 and propane C 3 H 8 ) are less abundant with the Sun at 3.5 Ga than with the present Sun (Figs. 4(a) and 5(a)); and 2) ionized noble gases are more abundant with the Sun at 3.5 Ga than with the present Sun (Figs. 4(b) and 5(b)). The decrease of the abundances of methane and more complex hydrocarbons with the Sun at 3.5 Ga is consistent with the fact that their photolysis are their major loss processes in our modeled atmosphere, no matter what the age of the Sun is. As expected from previous studies [START_REF] Ribas | Evolution of the solar activity over time and effects on planetary atmospheres. II. κ 1 Ceti as an analog of the Sun when Life arose on Earth[END_REF][START_REF] Claire | The evolution of solar flux from 0.1 nm to 160 µm: Quantitative estimates for planetary studies[END_REF], the enhanced UV emission for the Sun at 3.5 Ga leads indeed to a significant increase in photodissociation rates compared with those of the modern Sun. As illustrated in Figs. 4(c) and 5(c), the photodissociation rates are increased by 220% for methane, 150% for acetylene and ethylene and 90% for carbon dioxide. Such enhanced photodissociation rates likely triggered a peculiar atmospheric chemistry in the early Earth's atmosphere, linked to the methane and more complex hydrocarbons increased photodissociation rates, which lead in turn to a more efficient formation of hydrocarbon aerosols. In our model, this formation relies exclusively on two reactions involving primary and secondary products of hydrocarbon photochemistry: ethynyl radical C 2 H, acetylene C 2 H 2 and allene CH 2 CCH 2 . These two reactions, the overall rate of which being displayed as double-dashed curves entitled "AER" in Figs. 4(c) and 5(c), are found to be more efficient in the Archean. In our model, the strong UV emission of the Sun at 3.5 Ga enhances the organic haze formation rate by about 150%.

The enhancement of the EUV emission of the Sun at 3.5 Ga contributes even more importantly to the evolution of noble gases photoionization. As illustrated in Fig. 4(d) and 5(d), helium, neon, argon and krypton photoionization rates are increased by about 1000% whereas xenon photoionization rate increases by about 4000%. Such increase is due to the enhanced EUV part of the spectrum (< 100 nm) where the young Sun exhibits the most enhanced fluxes compared to the modern Sun (cf. Fig. 3). Moreover, in our model, the abundance of xenon in the ancient atmosphere is larger than in the modern one (Table 1) thus contributing to the particular increase of the xenon photodissociation rate in the Archean. Ionized nobles gases abundances -and particularly ionized xenon abundanceare therefore more important in the Archean.

CO 2 CH 4 H 2 C 2 H 2 C 3 H 8 C 2 H 6
The column-integrated photoionization rates are normalized to the respective abundances of noble gases in Fig. 6, to get rid of the variability of the different noble gases atmospheric abundances. The evolution of these rates as a function of time confirms that (i) noble gases were more efficiently photoionized under the ancient Sun than under the present Sun, and that (ii) xenon was more subject to photoionization than krypton and argon, but less than neon and helium.

Vertical distribution of reaction rates

The maximum production rate of organics by photochemistry takes place in an altitude range of approximately 60-100 km (Figs. 4 and5). In this range, only xenon among noble gases is quantitatively photoionized as its photoionization rate takes place mainly in the 80-120 km range. Photoionization of neon, krypton and argon tends to occur at higher altitudes (> 100 km). This general behavior can be explained in terms of their competiting opacity, each peaking at different altitudes. Therefore, if photoionized noble gases are prone to be trapped into growing organics, this photoionization rate distribution will tend to favour the interaction of ionized xenon with the organic haze relatively to the other ionized noble gases. This effect is illustrated in Fig. 7 which represents the integrated effect of cross correlating the organic haze formation rate and noble gas photoionization rate over the whole atmosphere. Such cross-correlation takes into account the different altitudes at which the reactions considered here take place. The evolution of these crosscorrelations as a function of time emphasizes the facts that (i) the photochemical production of organics and the photoionization of xenon peak at about the same altitude in our modelled atmosphere, that (ii) xenon was therefore more subject to interaction with an organic haze than all the other noble gases, and that (iii) such interaction was enhanced under the ancient Sun compared to the present Sun.

Trapping of ionized noble gases into organic haze

There is experimental evidence that ionized noble gases are efficiently trapped into growing organics [START_REF] Marrocchi | Adsorption of xenon ions onto defects in organic surfaces: Implications for the origin and the nature of organics in primitive meteorites[END_REF]. Furthermore, several works have shown that (i) the yield of noble gas trapping into solids increases by orders of magnitude when noble gases are ionized compared to their neutral state, and (ii) trapped noble gases, when ionized, are mass-dependent isotopically fractionated, i.e., enriched in their heavy isotopes at the percent level. Two experiments are particularly relevant to this process. [START_REF] Frick | Noble gas trapping and fractionation during synthesis of carbonaceous matter[END_REF] reported the results of an exhaustive investigation relative to different noble gases entrapment during Miller-Urey-like synthesis of carbonaceous, macromolecular, and kerogen-like substances. In particular, kerogen-like materials produced when applying an electric discharge to an artificial gas mixture contained high concentrations of noble gases trapped in the formed carbon-rich films that displayed strong elemental fractionation from their reservoirs. As pointed out in others subsequent investigations, noble gases photoionization is indeed responsible for establishing the observed noble gas patterns in the synthetic products but the underlying physicochemical mechanisms remain still to be unveiled [START_REF] Bernatowicz | Xe isotopic fractionation in a cathodeless glow discharge[END_REF][START_REF] Bernatowicz | Isotopic fractionation of Kr and Xe implanted in solids at very low energies[END_REF][START_REF] Ponganis | Isotopic fractionation in lowenergy ion implantation[END_REF][START_REF] Hohenberg | Active capture and anomalous adsorption: new mechanisms for the incorporation of heavy noble gases[END_REF][START_REF] Marrocchi | Adsorption of xenon ions onto defects in organic surfaces: Implications for the origin and the nature of organics in primitive meteorites[END_REF]. In a recent experiment, [START_REF] Marrocchi | Adsorption of xenon ions onto defects in organic surfaces: Implications for the origin and the nature of organics in primitive meteorites[END_REF] evaporated kerogen and condensed it under ionizing conditions in a dilute xenon atmosphere, and observed a xenon isotopes enrichment of 1.3% u -1 in the carbon condensate, which is comparable to the fractionation factor of 1.1% u -1 expected here (Eqn. 1 and 2). In contrast, [START_REF] Marrocchi | Experimental determination of the xenon isotopic fractionation during adsorption[END_REF] have recently shown that isotopic fractionation of neutral xenon during adsorption onto solids was indeed negiligbly small (< 0.02 % u -1 ).

As observed in laboratory experiments, the trapping properties of noble gases increases dramatically with their increasing mass (Table 2). Again, in presence of organic materials such as the photochemical haze, this process will favour the trapping of xenon over the other noble gases as, for instance its trapping efficiency is two orders of magnitude higher than that of argon, and marginally higher than that of krypton. However, we have shown previously that the different noble gases were not equally interacting with the organic haze over the whole atmosphere. Fig. 8 represents the overall efficiency of noble gas trapping into organic haze, that takes into account all processes involved, that is, the electronic properties of noble gases, the photochemical formation of organic haze, the vertical composition of our modelled atmosphere and the trapping properties of noble gases. The enhancement of the trapping efficiency of xenon over the other noble gases is clearly demonstrated. The second best-trapped noble gas is krypton, which is about a factor of 3 less efficiently trapped than xenon. It is therefore possible that the same process of isotopic fractionation and trapping could have affected as well atmospheric krypton which is also notably isotopically fractionated relative to chondritic krypton (by 0.5% u -1 ), to a less extent than xenon however. The evolution of these trapping efficiencies as a function of time emphasizes once again the fact that such interactions were enhanced under the ancient Sun compared to the present Sun.

Based on the coincidence of peaks for photochemical production of organics and the enhanced photoionization of xenon in our modelled atmosphere, we propose that the formation of an organic haze in the Archean atmosphere provided an efficient trap for the atmospheric xenon ionized by the enhanced flux of EUV from the younger Sun. This mechanism provides a way to isolate in a solid phase a xenon component enriched in its heavy isotopes, as is the present-day atmospheric xenon (with respect to cosmochemical xenon). As a consequence, to be able to explain the xenon paradox, atmospheric xenon (not trapped in the organic haze) had to be lost into space, the haze acting only as a temporary trap of isotopically "heavy" xenon that tends to concentrate heavy xenon isotopes in the lower part (< 120 km) of the atmosphere. We therefore envision a distillation process during which xenon is continuously lost from the atmosphere into space by a nonthermal escape process, with only a tiny fraction, enriched in heavy isotopes, being temporarily stored in organics. The cumulative effect of such process will result into progressive depletion of atmospheric xenon together with its enrichment in its heavy isotopes, as observed in the modern atmosphere.

Our model does not resolve entirely the xenon paradox since one needs to find a suitable non-thermal process to loose atmospheric xenon preferentially to other noble gases. One possibility is that photoionized xenon indeed escaped as an ion, probably in polar winds of hydrogen atoms H and hydrogen ions H + channelled by open planetary magnetic field lines. Since xenon, alone among the noble gases, is more easily ionized than hydrogen, it will tend to stay so in this hydrodynamic H-H + wind and be dragged by the strong resulting Coulomb interactions, whilst the other noble gases would get quickly neutralized and unable to follow. Under these circumstances, hydrodynamic escape could apply uniquely to xenon among the noble gases over a wide range of hydrogen escape fluxes [START_REF] Zahnle | Xenon the Magnificent[END_REF]. And since both hydrodynamic escape and photoionizations are fueled by solar EUV radiation, this mechanism would have been all the more efficient as the Sun was younger. In such a scheme the combination of atmospheric escape (∼ 500 km) and temporal trapping into the organic haze at a lower altitude (< 120 km) could have resulted in the overall concentration of heavy xenon isotopes. It may also be that xenon escape could have further fractionated its isotopes in the same way, that is, preferential retention of heavy xenon isotopes in the atmosphere over time. Investigating properly the combined effects of these two processes on the xenon elemental and isotopic compositions will require to develop a quantitative model for xenon trapping into organics and its escape from the atmosphere.

If our approach is correct, however, it leads to several important planetary implications. Firstly, our model implies that the isotopic composition of xenon of the ancient atmosphere may provide independent evidence for the existence of an organic haze in the Archean atmosphere. Secondly, since the atmosphere of Mars also presents a xenon paradox comparable (but not exactly similar in term of isotopic fractionation) to the terrestrial one, our model suggests that the ancient atmosphere of Mars might have also hosted an organic haze, therefore rising the question of a source of methane on Mars. Thirdly, our model predicts that xenon in the atmosphere of Titan, which is effectively highly depleted as are the other noble gases [START_REF] Niemann | The abundances of constituents of Titan's atmosphere from the GCMS instrument on the Huygens probe[END_REF], should also be isotopically fractionated to an extent exceeding probably the case of terrestrial xenon. This inference is subject to be tested when a sufficiently sensitive dedicated analytical system will be launched to Titan.

Conclusion

The evolution of the isotopic composition of xenon in the atmosphere over time has been re-evaluated in the light of the enhanced UV emission of the young Sun and of the peculiar atmospheric chemistry that such enhancement presumably triggered. We interpret the "xenon paradox" as resulting from its efficient photoionization by hard UV light incoming into the early atmosphere, which triggers an efficient trapping of its heavier isotopes within a primitive organic haze as well as its preferential escape compared to other atmospheric volatiles. Most of the ionized xenon remaining in the atmosphere would have then escaped into space by hydrodynamic escape, even if it still requires us to figure out how to keep the xenon ionized long enough.

Figure 1 :

 1 Figure 1: Proposed evolution of the xenon isotopic fractionation relative to the modern atmospheric composition, expressed in per mil per atomic mass unit ( u -1 ), as a function of time (adapted from Pujol et al. (2011)). Chondritic/solar value is the mean value of the solar and chondritic compositions (from[START_REF] Wieler | Krypton and xenon from the solar wind and solar energetic particles in two lunar ilmenites of different antiquity[END_REF]).Barite and quartz samples are both from the Dresser formation at the North Pole area in Pilbara craton, Western Australia[START_REF] Srinivasan | Barites: Anomalous xenon from spalation and neutron-induced reactions[END_REF][START_REF] Pujol | Xenon in Archean barite: Weak decay of 130 Ba, mass-dependent isotopic fractionation and implication for barite formation[END_REF][START_REF] Pujol | Chondritic-like xenon trapped in Archean rocks: A possible signature of the ancient atmosphere[END_REF][START_REF] Pujol | Argon isotopic composition of Archaean atmosphere probes early Earth geodynamics[END_REF]. Quartz samples are in fact fluid inclusions trapped in Archean hydrothermal quartz. The 1.65 Gaold shungite sample is from the Shun'ga area in the Karelia region, Russia[START_REF] Lokhov | Volatile components in Karelian shungites as indicators of composition of Protherozoic atmosphere[END_REF]. 2.0-3.0 Ga-old deep fracture fluid sample is from the Timmins mine in Ontario[START_REF] Holland | Deep fracture fluids isolated in the crust since the Precambrian era[END_REF]. The younger, 170 Ma-old, barite sample is from the Belorechenskoe deposit, Northern Caucasus, Russia[START_REF] Meshik | Weak decay of 130 Ba and 132 Ba: Geochemical measurements[END_REF]. The modern atmospheric ratio is from[START_REF] Basford | Krypton and xenon in lunar fines[END_REF]. The data fit an exponential decay curve, suggesting that the xenon isotopic fractionation was progressive with time.

Figure 2 :

 2 Figure2: Absolute photoabsorption (plain lines) and photoionization (thick lines) cross sections of helium He, neon Ne, argon Ar, krypton Kr and xenon Xe binned at 1 nm resolution (adapted from[START_REF] Chan | Absolute optical oscillator strengths for the electronic excitation of atoms at high resolution: Experimental methods and measurements for helium[END_REF]Chan et al. ( , 1992a,b),b)) along with their first ionization potentials (dashed lines)(Lide, 2009). Xenon has the lowest first ionization potential and the most extended photoabsorption range among noble gases.

Figure 4 :

 4 Figure 4: Results of the photochemical model with an incoming solar flux representative of the present Sun. Panel A displays the abundance profiles of molecular hydrogen H 2 , carbon dioxide CO 2 and some key hydrocarbons. Panel B displays the abundance profiles of the neutral and photoionized noble gases. Panel C displays the photodissociation rates of carbon dioxide CO 2 and some key hydrocarbons. The reaction AER mentioned in panel C is a combination of the following reactions: C 2 H + C 2 H 2 → C 4 H 2 + H and C 2 H + CH 2 CCH 2 → H + C 5 H 4 . Panel D displays the photoionization rates of the noble gases. Please note the concordance between the altitude at which xenon photoionization peaks and the organic haze formation region.

Figure 5 :

 5 Figure 5: Results of the photochemical model with an incoming solar flux representative of the Sun at 3.5 Ga.

Figure 6 :

 6 Figure 6: Noble gas photoionization rates, integrated over the whole atmospheric column, relative to the initial abundances of neutral nobles gases and normalized to the xenon photoionization rate under the present Sun.

Figure 7 :

 7 Figure 7: Cross-correlations between the haze formation rate and the noble gas photoionization rates, integrated over the whole atmospheric column and normalized to the xenon photoionization rate coefficient under the present Sun.

Figure 8 :

 8 Figure 8: Noble gases trapping properties, integrated over the whole atmospheric column and normalized to the xenon trapping properties under the present Sun.

Table 1

 1

	: Noble gases atmospheric abundances through time (in
	ppmv).
		Today	2.5 Ga	3.0 Ga	3.5 Ga
	He	5.24	(5.24)	(5.24)	(5.24)
	Ne		18.18
	Ar	9340	6889	5953	4488
	Kr		1.14
	Xe	0.09	0.17	0.23	0.37

Table 2 :

 2 Noble gases trapping properties for electron discharge kerogen (calculated from[START_REF] Frick | Noble gas trapping and fractionation during synthesis of carbonaceous matter[END_REF], Table1) 10 -4 5.65 × 10 -4 1.20 × 10 -4 1.61 × 10 -2 1.84 × 10 -2 (in ccSTP g -1 atm -1 )

	He	Ne	Ar	Kr	Xe
	2.26 ×

Acknowledgement

This project was funded by the European Research Council under the European Community's Seventh Framework Program (FP7/20072013 grant agreement no. 267255 to BM). We appreciated discussions with Kevin Zahnle and James Lyons. CRPG contribution #XXX (to be added later on if the paper accepted)