Hugo Dutilleul

Anthony Partaloglu

Patrick Da Costa

Maria Elena Galvez

Shock-induced cavitation as a way of accelerating phenol oxidation in aqueous media

Keywords: Sonochemistry, cavitation, phenol oxidation, AOPs, water treatment

Highlights

 Cavitation induced by the impact of a solid piston on liquid surface  Shock-waves of several bars amplitude exciting a wide frequency range  Phenol degradation initiated at ambient temperature and absence of oxidants  High phenol mineralization extents measured upon H2O2 addition  Accelerated active radical formation in the presence of shock-induced cavitation Abstract Shock-induced cavitation phenomena, resulting from the propagation of the trail of shockwaves generated upon the impact of a solid piston on a liquid surface, was used as an innovative way of intensifying the oxidation of phenol in aqueous media. The amount of energy communicated by the impact was found to be proportional to the impact height, and was directly related to the maximal pressure attained, i.e. in the order of several tens of bars. This peak was followed by a rarefaction period that results in the origination of several cavitation phenomena, which continued upon piston rebound and further shock-wave generation and propagation. The multi-frequency nature of shock-induced cavitation, capable of exciting a wide range of frequencies between 1 kHz and 100 kHz, was confirmed by means of wavelet analysis. Under shock-induced cavitation conditions, phenol degradation was found to be possible even in the absence of any oxidizing agent. High extents of mineralization, i.e. 45.3 and 56.2% TOC elimination, 50 mg/L solution, neutral pH, were obtained in the presence of H2O2 (aprox. 10% vol.), pointing to an acceleration of the oxidation reaction based in a faster and more efficient creation of radical species.

Introduction

Water pollution, as a consequence of our industrial/agricultural development, jeopardizes one of our most precious and scarce resources. Worldwide actions promote a rational use of water and introduce new regulations that force the scientific and technological communities to seek for each time more efficient technologies for water treatment. Such water treatment technologies, i.e. the oxidation of recalcitrant organic pollutants in wastewaters, are a clear example of highly-energy demanding processes, due to their inherent problems of mass transfer and their sluggish reaction kinetics.

The technologies known as Advanced Oxidation Processes (AOPs) consider different approaches for the intensification of the oxidation of organic pollutants [START_REF] Comninellis | Advanced oxidation processes for water treatment: advances and trends for R&D[END_REF][START_REF] Andreozzi | Advanced oxidation processes (AOP) for water purification and recovery[END_REF]. They are based on the intensive generation of reactive radicals, such as hydroxyls, able to oxidize the organic pollutants contained in wastewaters. Ultrasounds are frequently used in the intensification of chemical processes, among them the oxidation of organic pollutants in wastewaters in which ultrasonic sonochemistry plays an important role for several decades [START_REF] Adewuyi | Sonochemistry in environmental remediation. 1. Combinative and hybrid sonophotochemical oxidation processes for the treatment of pollutants in water[END_REF][START_REF] Gogate | Treatment of wastewater streams containing phenolic compounds using hybrid techniques based on cavitation: a review of the current status and the way forward[END_REF][START_REF] Navarro | Effect of ultrasonic frequency on the mechanism of formic acid sonolysis[END_REF][START_REF] Chave | Sonocatalytic degradation of oxalic acid in the presence of oxygen and Pt/TiO2[END_REF][START_REF] Gogate | Cavitational reactors for process intensification of chemical processing applications: a critical review[END_REF][START_REF] Bagal | Wastewater treatment using hybrid treatment schemes based on cavitation and Fenton chemistry: A review[END_REF][START_REF] Golash | Degradation of dichlorvos containing wastewaters using sonochemical reactors[END_REF][START_REF] Gogate | A sonochemical reactor for the removal of formic acid from wastewater[END_REF]. Typically induced by piezoelectric transducers [START_REF] Leighton | The Acoustic Bubble[END_REF], ultrasonic sonochemistry is based in the phenomena of cavitation, i.e. the formation of vapor nuclei when pressure falls below its vapor pressure at a constant temperature [START_REF] Brennen | Cavitation and bubble dynamics[END_REF]. In fact, the physical and chemical effects of sonochemistry occur upon the cavitation of the bubbles generated during the rarefactionnegative pressureperiod of the ultrasound wave. During rarefaction the liquid continuity is broken at nucleation sites, microbubbles are formed and grow through a mechanism of rectified diffusion (unequal mass transfer of gas and vapors across the liquid-vapor interface), until they collapse upon pressure recuperation through both stable (non-inertial cavitation, cavity oscillation for several acoustic cycles) and transient (inertial, violent implosion) cavitation phenomena [START_REF] Shah | Cavitation reaction engineering[END_REF][START_REF] Nikitenko | Green Process Engineering: From concepts to industrial applications[END_REF][START_REF] Suslick | Sonochemical hot spot[END_REF].

In the presence of a reactive media, such cavitation events contribute to the formation of radical species (active in free radical reaction mechanism, e.g. oxidation of organic pollutants in aqueous media), to the generation of local hot spots of extremely high temperatures (enhancing the pyrolytic or temperature-activated route of chemical reactions) and to accelerate mass transfer phenomena (i.e. by means of turbulence).

In an ultrasound type of excitation both the original amplitude and frequency of the ultrasound wave are unique. Frequency determines the scale (size and volume) of the system that will be excited, i.e. affected, by cavitation. Fewer but larger bubbles are preferably formed at low frequencies whereas more dense bubble clouds of smaller size are generated when working at higher frequencies. In consequence, the influence of the ultrasound frequency on the cavitation phenomena is clearly evidenced in the existing literature, though there is not a general agreement on the frequency ranges and their particular effects (enhancement of cavitation, mass transfer, sonication, formation of radical species, etc.) [START_REF] Navarro | Effect of ultrasonic frequency on the mechanism of formic acid sonolysis[END_REF][START_REF] Cum | Role of frequency in the ultrasonic activation of chemical reactions[END_REF][START_REF] Entezari | Effect of frequency on sonochemical reactions. I: Oxidation of iodide[END_REF][START_REF] Mason | New evidence for the inverse dependence of mechanical and chemical effects on the frequency of ultrasound[END_REF][START_REF] Rooze | Effect of resonance frequency, power input, and saturation gas type on the oxidation efficiency of an ultrasound horn[END_REF]. The intensity of ultrasonic cavitation is moreover a function of the acoustic pressure in the liquid and of the attenuation of the longitudinal wave within it, as it propagates far away from the excitation source (transducer). Attenuation strongly depends on the frequency of the ultrasound wave, i.e. higher frequencies are attenuated more rapidly than low frequencies, or, in other words, the higher the frequency of the ultrasound, the greater must be the initial intensityamplitudeto provide an equivalent intensity at an equivalent depth [START_REF] Thompson | Sonochemistry: science and engineering[END_REF].

The difficulty of tailoring both frequency and amplitude at a time, together with the directional sensitive effect of ultrasound and its non-uniform volumetric energy density, are the main drawbacks of ultrasound cavitation that may complicate its scale-up [START_REF] Gogate | Sonochemical reactors: important design and scale up considerations with a special emphasis on heterogeneous systems[END_REF][START_REF] Sutkar | Design aspects of sonochemical reactors: techniques for understanding cavitational activity distribution and effect of operating parameters[END_REF][START_REF] Gogate | Sonophotocatalytic reactors for wastewater treatment: a critical reviewAIChE[END_REF][START_REF] Mahamuni | Advanced oxidation processes (AOPs) involving ultrasound for waste water treatment: a review with emphasis on cost estimation[END_REF]. A highintensity, bulk and multi-frequency type of excitation would be the ideal acoustic wave. The violent rupture of liquid continuity, i.e. caused through cavitation phenomena, can be as well induced by shock-waves, as seen for example in under water explosions [START_REF] Wang | Underwater explosion bubble dynamics in a compressible liquid[END_REF]. Moreover, Randolph and co-workers [START_REF] Randolph | Do not drop: mechanical shock in vials causes cavitation, protein aggregation, and particle formation[END_REF] have recently reported that the mechanical shock in vials, i.e. caused by their accidental drop, induced several cavitation phenomena that promoted protein aggregation within the liquid media contained in such recipients. They further claimed that this was due to the formation of hydroxyl radicals formed as a consequence of cavitation.

Analogously, the strong impact of a piston on a liquid surface can induce a series of acoustic waves that propagates inside the bulk of the liquid media. The objective of the present work is to evaluate the possibility of using this particular type of excitation for the intensification of oxidation reactions occurring in a liquid media. With this aim, the oxidation of phenol in water was chosen as model reaction. The influence of the impact intensity was also considered.

Experimental

Shock waves were induced by the impact of a piston on the surface of the liquid contained in a stainless cylindrical reactor (75 mm diameter, 13 mm thickness, 125 mm height). A piston of 75 mm diameter and 485 mg weight is hold at a certain distance from the liquid surface with an electro magnet attached to an electric linear actuator. Once the piston is released it falls and reaches the liquid surface generating the impact. The evolution of static pressure in the liquid media upon this impact can be followed with two piezoelectric sensors (Kistler 601A, connected to a 5018A amplifier), respectively placed under the piston and at the bottom of the cylindrical reactor. The cylindrical reactor is moreover equipped with two glass windows, allowing the visualization of the cavitation phenomena. A CDD camera (Phantom V711) was used for recording videos during piston impact. The bottom of the cylinder is equipped with a mobile bottom, which can be displaced by the impact, acting as a secondary source of shock waves. Compressed air can be injected below the bottom of the reactor, reaching pressures between 1 and 6 bar. Before each experiment, the piston was captured by the electromagnet and lifted with the aid of the linear actuator. The air contained in the space in between the piston and the water surface was evacuated using a rotary vane pump (Alcaltel), until a vacuum pressure corresponding to the saturation pressure of the liquid contained in the reactor (water, in this case) was reached. A liquid volume of 500 mL was used in all the experiments. Figure 1 depicts the set-up used and the piston and moving bottom evolution upon impact.

The raw pressure signals were visualized and recorded in an oscilloscope (Keysight-Agilent MSO7054A). In order to remove a great part of the acoustic noise and to get betterresolved signals a smoothing Gaussian filter was applied. The position of the piston during the shots was measured by the post-treatment of the video acquired with the Phantom camera.

The image was focused on a sight placed on the upper external surface of the piston. The frames were treated using a Matlab code that, based on pixel brightness distinction, was able to determine the sight's position at each instant. The derivate of position in time finally yielded the piston's velocity and thus the energy transmitted during the impact. Experiments were performed for relative heights piston-liquid surface of 8, 12, 16 and 20 mm. The influence of using a moving bottom was also tested: the bottom was either fixed, or released, using in this last case a flow of compressed air at 2 and 4 bar, respectively. Phenol oxidation in aqueous media was chosen as a model reaction in order to evaluate the possible chemical effects of the cavitation phenomena induced by the piston impact. Phenol solutions containing either 10 mg/L or 50 mg/L were prepared. H2O2 (30% VWR) was used in some experiments as oxidizing agent. Phenol concentration as a function of the number of impacts (reaction time) was followed with the aid of a gas chromatograph (Shimatzu GC2025, equipped with a Phenomenex Zebron ZB-WAX capillary column and a FID detector). The total organic carbon (TOC) content in the treated phenol solutions was as well analyzed (Multi N/C 2100S Analytic Jena).

Results and discussion

Observation and characterization of piston impact and shock-induced cavitation

Figure 2 shows the pressure signals recorded during a typical piston impact (4 mm height, moving bottom 4 bar, in this case). Very similar pressure signals were obtained using the two piezoelectric captors placed either under the piston (top) or at the bottom of the reactor. Both show a first rapid increase of the pressure, due to the impact and reaching several tens of bar, followed by a rarefaction negative pressure period, see points 2 and 3 in the piston velocity vs. time curve in Figure 2. The harmonics found upon this depression period are due to bubbles cavitating in the nearby of the pressure sensor. A second peak appears 4-5 ms after the impact that can be assigned to the rebound of the piston, finally impacting the liquid surface. This rebound peak reaches only few bars, and does not have the intensity of the previous main impact peak, but its consequences cannot be neglected. As stated before, the noise in the pressure signals and the presence of harmonics points to the occurrence of cavitation phenomena upon the piston rebound and impact. Figure 2 also presents the time evolution of piston's velocity upon its release and during its impact. A first initial period of acceleration can be observed (1), right after piston's release. It is followed by a deceleration pressure (2) due to the formation of a thin layer at the interface between the piston and the liquid surface, probably containing a mixture of air and water vapor. Then, the piston finally impacts the surface, its velocity becoming almost zero, and rebounds (3) corresponding to a subsequent increase in velocity (4), until it reached for a second time the liquid's surface [START_REF] Navarro | Effect of ultrasonic frequency on the mechanism of formic acid sonolysis[END_REF] and further continues to rebound [START_REF] Chave | Sonocatalytic degradation of oxalic acid in the presence of oxygen and Pt/TiO2[END_REF], generating the trail of shock-waves that cause the secondand even thirdpressure peaks observed in the pressure signals. The maximal impact peak pressure, the minimal pressures attained in the rarefaction period, the number of rebounds and their intensity, depend on the energy transmitted by the fall and impact of the piston. This will ultimately depend on the impact height, the mass of the piston and its surface, as well as on pressure condition, since, applying the fundamental laws of dynamics to the piston, its maximal velocity, 𝑣 𝑚𝑎𝑥 in [m/s], can be expressed as:

𝑣 𝑚𝑎𝑥 = √ 2 𝑃 𝑎𝑡𝑚 𝑆 ℎ 𝑚 𝑝 (eq. 1)
Where 𝑃 𝑎𝑡𝑚 represents the atmospheric pressure, 𝑆 the surface of the piston, 𝑚 𝑝 its mass, and ℎ the impact height, all in SI units. The analysis of the velocity curves acquired clearly evidence a direct influence of impact height on the maximal velocity reached by the piston, which can be therefore directly extracted from these curves (Figure 3 a). Since this parameter, vmax, can be considered as representative of the energy transmitted during the impact, it can be further correlated to the maximal pressure reached, Pmax (Figure 3 b).

The Joukowsky equation, derived from the water hammer theory [START_REF] Joukowsky | Über den hydraulischen Stoss in Wasserleitungsrohren[END_REF], i.e. the hydrodynamic description of the flow of a fluid in a pipe being stopped at a time t, can be used to establish the correlation between vmax and Pmax:

∆𝑃 = 𝜌 𝑐 ∆𝑣 (eq. 2)
Where ∆𝑃 stands for the pressure difference (Pmax -Patm), 𝜌 represents the density of the liquid media, 𝑐 the speed of sound, and ∆𝑣 the difference between vmax and the piston speed at t = 0, i.e. v0 = 0 m/s. Taking into account that initially the piston is held by the electromagnet, thus its velocity at that instant equals zero, and that the pressure inside the reactor is fixed at around 20 mbar just before the release of the piston, according to eq. 2 a linear trend should define the variation of Pmax as a function of vmax. Therefore, the slope of this line should be equal to the product of liquid density and the speed of sound in the liquid, i.e. water1000 kg/m 3 and 1500 m/s, respectively. There are, however, other important parameters that vary depending not only on the impact height, but also on the configuration of the set-up, i.e. the use of a mobile bottom and different bottom pressures. Figure 4 a shows Pmax as well as Pmin, the minimal pressure measured during the rarefaction period taking place right after the impact, as a function of impact height and for three experimental configurations: fixed bottom, moving bottom at a pressure of 2 bar, and moving bottom at a pressure of 4 bar.

The fact of liberating the bottom of the reactor and, moreover, adding an external pressure, makes the whole liquid column behave as a kind of a spring that, upon the impact will move from the bottom to the top and back, forcing as well the rebound of the upper main piston. In fact, Pmax increases as expected as a function of the impact height, however, the differences are softened when using the moving bottom configuration, especially when the upper piston rebound appears some milliseconds earlier as the impact height is decreased, as depicted in Figure 5. At the highest impact height the amplitude of the shock wave generated is too big and it propagates more slowly than a shock wave of smaller amplitude generated by a softer impact.

All the parameters mentioned before determine the type of cavitation phenomena, the distribution of bubble diameters and its evolution as a function of time, i.e. upon impact, rarefaction, rebound, etc. The use of the CDD camera allowed the direct visualization of the cavitation phenomena occurring in the bulk of the liquid. Several videos were acquired using a frame rate of 25000 fps (frames per second). Figure 6 presents different snapshots of one of the videos recorded during a typical piston impact. Just before the release of the piston (t = -1.928 ms) the liquid contains already several small bubbles that are formed upon its degasification while pulling vacuum between the piston and the water surface. The presence of these bubbles is crucial, since they may act as cavitation nuclei. The piston is then released and finally impacts the liquid surface. The bubbles first disappear upon the impact, i.e. water is fully degased as due to pressure increase, and then grow, as a consequence of the rarefaction period that follows the impact (negative pressures period).

A cluster of bubbles appears as a consequence of this negative pressure period, that instigates cavitation. These bubbles change rapidly their diameter in the scale of only a few microseconds, until they finally violently collapse. Several softer cavitation events are continuously observed, moreover after the rebound of the piston, see for example the snapshots at t = 8.272 and 8.522 ms. Figure 7 shows the evolution of bubble size during these cavitation phenomena. Formed initially in the bulk of a bubble cloud, the cavitation bubble grows and then shrinks periodically as the shock-waves created upon the impact and/or rebound of the piston propagate. The analysis of bubble size distribution during an impact remains difficult, since resonant bubbles of different sizes are simultaneously excited, due to the multi-frequency nature of the trail of shock-waves.

Figure 8 presents the results of a Daubechies-type wavelet analysis performed on the pressure signal acquired during an experiment performed at 20 mm height, using the moving bottom configuration at 4 bar. The Daubechies wavelet method (coded in C language) allows the determination of the frequency distribution corresponding to the pressure variations induced in the liquid media as a consequence of the propagation of the shock-waves generated by the piston impact. This kind of analysis is preferred to traditional Fast Fourier Transform (FFT) analysis when frequencies are multiple and distributed along a time scale, since it allow the complete characterization and reconstruction of a given signal in time and frequency [START_REF] Brani | Wavelets for kids[END_REF].

The color scale in Figure 8 represents the normalized amplitudes, whereas the frequencies are plotted versus time. Two peaks can be clearly distinguished in this plot, appearing at the same time intervals than the main pressure peaks, respectively corresponding to piston impact and rebound. High frequencies thus appear when pressure increases in the liquid media, reaching maximal values around 100 kHz. Note there that the resonant frequency of the pressure sensors is 125 kHz, thus, the frequencies higher than this limit identified in the wavelet analysis are not quite reliable due to this fact, moreover taking into account that the raw pressure signal (non-filtered) was employed. High frequencies nevertheless correspond all the time to low amplitudes whereas the highest amplitudeshighest populationcorrespond to low frequencies, i.e. < 1 kHz, and occur in the time interval between impact and rebound, further corresponding to the continuous cavitation phenomena observed in the videos captured during the experiment, and depicted in Figure 7. The same wavelet analysis was performed for different impact heights and set-up configurations. The frequency distribution visibly changes when using either the fixed or the mobile bottom configuration at different pressures. However, differences are quite minimal, this allowing us to conclude that in the bulk of the liquid media, the trail of sock-waves created and its propagation are able to excite cavitation bubbles/nuclei in a wide range of frequencies between 0.1 and 100 kHz, thus confirming the multi-frequency character of this kind of impact-induced cavitation.

Phenol oxidation in water media under shock-induced cavitation

The first consequence of this multi-frequency type of cavitation will be thus the possibility of exciting the whole bulk of the liquid comprising bubbles of very different sizes.

The collapse of bubbles will thus result in the formation of ultra high local temperatures and pressures, similar to the ones in the presence of classical ultrasounds. These phenomena are thought to contribute to the formation of free radicals in a water media, which can be finally consumed in oxidation of organic pollutants in wastewaters.

In order to explore the intensification of the oxidation of organic pollutants under shock-induced sonochemical conditions, the impact experiments were performed introducing an aqueous solution containing either 10 or 50 mg/L of phenol in the cylindrical reactor. The piston was thus held at either 8, 15 or 20 mm over the surface of the liquid and released several times, up to 1000 successive impacts. The content of phenol in the treated solution was periodically analyzed by gas chromatography and total organic carbon (TOC). Let us note here that the free radical reaction was quenched through the addition of MnO2 and the resulting samples were filtered prior to their analysis. A chemical oxidant, H2O2 (30 wt.% solution) was then added to the reaction media, in order to boost the generation of free radicals. Figure 10 shows the results obtained in terms of phenol degradation, when adding either 5 or 65 mL of the H2O2 solution. In fact, the differences observed between the reaction extents measured upon the impact at different piston initial positions are directly related to the particular features of the cavitation induced in each case, such as the maximal cavitation bubble diameter, limited by the rebound of the piston, and the co-existence of different cavitation regimes of different intensity. Further studies are needed in order to quantify the amount of active radicals created under different cavitation conditions and thus to determine their influence in the acceleration of the oxidation of organic pollutants in aqueous solutions. Therefore it seems that the amount of total energy provided to the system, controlled by the impact height, or the maximal pressure attained are not the key influencers. The control of bubble size growth and collapse through the propagation of the shock-waves is preponderant, this can be observed through the faster oxidation rate measured at 8 mm rather than at 20 mm. Moreover, the duration of the treatment needs to be optimized, i.e. in terms of number of impacts. This implies a thoughtful study of the degradation mechanisms involved, which is been currently overtaken by means of the quantification of the amount of radicals formed in the reaction media. Reducing the number of impacts while achieving the same mineralization extent may result in important energy savings.

Conclusions

The cavitation phenomena induced by means of the impact of a solid piston on a liquid surface was considered and applied for the acceleration of phenol oxidation in aqueous media.

The impact intensity, as well as the energy communicated in the impact, were directly related to the impact height. This proportionality was verified using a simple water hammer model.

Reactor configuration, i.e. fixed or moving bottom, moreover conditioned the type of phenomena observed upon the piston impact. In this way, setting the bottom of the reactor free resulted in a spring-like behavior of the liquid column that enhanced the propagation of the induced shock-waves.

The rarefaction period observed upon the piston impact was the origin of several violent cavitation phenomena occurring in a cloud of bubbles having very different diameters.

The collapse of these bubbles finally resulted in a complete rupture of the liquid, as visualized with the CDD camera. After the main impact and rarefaction period, several cavitation effects, less violent, were continuously observed, specially as a consequence of piston rebound, which was further favored when using the moving bottom configuration. The wavelet analysis of the pressure signals recorded in the liquid media confirmed the multi-frequency nature of this shock-induced cavitation and evidenced the possibility of exciting a wide range of frequencies between 1 kHz and 100 kHz in a very short time interval.

Phenol degradation was found to be possible in the presence of impact-induced cavitation, even in the absence of any oxidizing agent. However, no mineralization was measured in this case. In order to achieve acceptable mineralization extents, H2O2 was added to the reaction mixture. A considerable acceleration of the oxidation reaction was then observed, with TOC reductions reaching 45.3-56.2% upon less than 2 hours total reaction time. This fact was linked to the enhancement of H2O2 hydrolysis leading to the formation of a high concentration of active radical species in the liquid media, and to the acceleration of their subsequent reaction with phenol molecules, under shock-induced cavitation conditions.

Captions to Figures Pressure (bar) t"="$1.928"ms"" t"="0.000"ms"" t"="0.432"ms"" t"="0.272"ms"" t"="2.832"ms"" t"="8.272"ms"" t"="8.522"ms"" t"="9.912"ms"" t"="3.392"ms""

Figure 3 b

 3 Figure 3 b plots the values of Pmax vs. vmax measured during different experiments

working at 4

 4 bars. At 20 mm impact height, the three configurations converge into the same value of Pmax. For such a strong impact, no further energy can be recuperated from the moving bottom and the spring-like behavior of the liquid column. Minimalrarefaction -pressures, Pmin, also vary with impact height. Moreover, Pmin are always smaller when using the moving bottom at 4 bar, reaching values close to -35 bar at 20 mm impact height. The spring-like movement of the liquid column results in bigger depressions adding more tension to the liquid that would be thus more prompt to spall. The values of deltaP, i.e. maximal pressure difference Pmax -Pmin, measured during the experiments and shown in Figure 4 b are just a consequence of these facts and are all the time higher when using the moving bottom at 4 bar. Note here that Pmin is most of the time negative (rarefaction period), thus resulting in deltaP values well above Pmax. The maximal velocity attained by the piston in its fall is also depicted in Figure 4 b, as a function of impact height and experiment configuration. Higher values of vmax are always measured for the most intensive configuration, i.e. moving bottom at 4 bar. Using the fixed bottom configuration results in a deceleration of the piston by the air/vapor boundary layer on the surface of water, that cannot be further compressed/displaced by pushing the base of the cylindrical reactor. The use of a moving bottom has moreover important consequences in terms of the rebound of the upper piston, since the shockwave departing from the bottom of the reactor is further pushed up, lifting the upper piston and causing a different rebound phenomena, in terms of time and intensity. When using the moving bottom configuration at 4 bar pressure,

Figure 9

 9 Figure 9 contains the results obtained in the first set of experiments, performed using

Figures 10 a and 10 b

 10 show as well the results of phenol degradation in the absence of the shock-induced cavitation phenomena, i.e. using the same reactor volume, the same amount of H2O2, under conventional stirring at ambient temperature. Phenol degradation reaches 15% after 1000 impacts, i.e. 120 minutes of reaction, when adding only 5 mL of the H2O2 solution. When adding 65 mL of H2O2 30 wt.%, degradation upon 1000 impacts reaches 61%, whereas 14% degradation was measured in the absence of shock-induced cavitation, i.e. under conventional stirring. These results further support the fact of increased free radical formation as a consequence of piston impact, either due to the enhanced hydrolysis of H2O2 to generate these active species[START_REF] Chand | Phenol degradation using 20, 300 and 520 kHz ultrasonic reactors with hydrogen peroxide, ozone and zero valent metals[END_REF], or to the favoring of the phenol oxidation reaction in their presence, or maybe to the simultaneous intensification of both processes. The percentages of mineralization determined from the TOC analysis were all the time around 25-35% lower than the phenol degradation values determined by means of gas chromatography. The peaks at low retention times were all the time observed, confirming the formation of oxidation intermediates.Moreover, the phenol solutions treated with 1000 impacts were left inside the reactor and analyzed 80 minutes after the treatment. Final phenol degradation extentsupon 200 min reaction timeof 84.2 and 92.3% were measured for the reactions impacted with an initial position of the piston of 20 and 8 mm, respectively, corresponding to TOC elimination of 45.3 and 56.2%. Such high degradation extents clearly evidence a substantial acceleration of the oxidation of phenol in aqueous solution, assisted by the presence of the shock-induced cavitation phenomena. The comparison of the results obtained in presence and in absence of H2O2 point to phenol oxidation preferably occurring through a radical-formation route involving the generation of hydroxyl radicals, rather than through simple air induced oxidation, i.e. pyrolysis route. In this sense, we believe that the mechanisms behind phenol oxidation under shock-induced cavitation conditions may be very similar to typical ultrasound sonochemistry, with two different types of acoustical phenomena taking place, i.e. the propagation of a shock wave and an ultrasonic wave in each case.

Figure 1 .

 1 Figure 1. Shock-induced cavitation set-up, schematic representation of piston impact.

Figure 2 .

 2 Figure 2. Time evolution of pressure signals (top and bottom), as well as piston velocity, upon

Figure 3 .

 3 Figure 3. a) Velocity as a function of time registered during a piston impact, fixed bottom;

Figure 4 .

 4 Figure 4. a) Pmax and Pmin, and b) delta P and vmax, as a function of impact height and

Figure 5 .

 5 Figure 5. Pressure vs. time profiles for the experiments performed at 20, 16, 12 and 8 mm,

Figure 6 .

 6 Figure 6. Different snapshots of the video recorded with the aid of the CDD camera during a

Figure 7 .

 7 Figure 7. Detail of the cavitation phenomena induced upon piston rebound, evolution of the

Figure 8 .

 8 Figure 8. Wavelet analysis of frequency distribution during a 20 mm impact, moving bottom

Figure 9 .

 9 Figure 9. Evolution of phenol concentration with the number of impacts and time, during the

Figure 10 .

 10 Figure 10. Phenol degradation experiments in the presence of a) 5 mL H2O2 30 wt.% solution

Figure 1 .Figure 2 .Figure 3

 123 Figure 1. Shock-induced cavitation set-up, schematic representation of piston impact.

Figure 4

 4 Figure 4. a) Pma x and Pmin, and b) delta P and vmax, as a function of impact height and

Figure 5 .

 5 Figure 5. Pressure vs. time profiles for the experiments performed at 20, 16, 12 and 8 mm,

Figure 6 .

 6 Figure 6. Different snapshots of the video recorded with the aid of the CDD camera during a

Figure 7 .Figure 8 .Figure 9 .

 789 Figure 7. Detail of the cavitation phenomena induced upon piston rebound, evolution of the


Keywords: Pluto, Atmosphere, Haze, Modeling, GCM, 70

The New Horizons spacecraft, which flew by Pluto on July 14, 2015, revealed 39 the presence of haze in Pluto's atmosphere that were formed by CH 4 /N 2 pho-40 tochemistry at high altitudes in Pluto's atmosphere, as on Titan and Triton.

41

In order to help the analysis of the observations and further investigate the 42 formation of organic haze and its evolution at global scales, we have imple-43 mented a simple parametrization of the formation of organic haze in our Pluto 44 General Circulation Model. The production of haze in our model is based on 45 the different steps of aerosol formation as understood on Titan and Triton: 46 photolysis of CH 4 in the upper atmosphere by Lyman-α UV radiation, pro-47 duction of various gaseous species, and conversion into solid particles through 48 accumulation and aggregation processes. The simulations use properties of 49 aerosols similar to those observed in the detached haze layer on Titan. We 50 compared two reference simulations ran with a particle radius of 50 nm: with, 51 and without South Pole N 2 condensation. We discuss the impact of the par-52 ticle radius and the lifetime of the precursors on the haze distribution. We 53 simulate CH 4 photolysis and the haze formation up to 600 km above the sur-54 face. Results show that CH 4 photolysis in Pluto's atmosphere in 2015 occured 55 mostly in the sunlit summer hemisphere with a peak at an altitude of 250 km, 56 though the interplanetary source of Lyman-α flux can induce some photolysis 57 even in the Winter hemisphere. We obtained an extensive haze up to altitudes 58 comparable with the observations, and with non-negligible densities up to 500 59 km altitude. In both reference simulations, the haze density is not strongly 60 impacted by the meridional circulation. With no South Pole N 2 condensa-61 tion, the maximum nadir opacity and haze extent is obtained at the North 62 Pole. With South Pole N 2 condensation, the descending parcel of air above 63

http://icarus.cornell.edu/information/keywords.html Pluto, Titan and Triton all have a nitrogen-based atmosphere containing a significant fraction of methane, an efficient recipe known to lead to the formation of organic haze in the atmosphere, as confirmed by observations [START_REF] Tomasko | Rain, winds and haze during the Huygens probe's descent to Titan's surface[END_REF][START_REF] Rages | Voyager imaging of Triton's clouds and hazes[END_REF][START_REF] Herbert | CH4 and haze in Triton's lower atmosphere[END_REF][START_REF] Gladstone | Ly α @Pluto[END_REF] and laboratory experiments [START_REF] Trainer | Inaugural Article: Organic haze on Titan and the early Earth[END_REF][START_REF] Rannou | Titan haze distribution and optical properties retrieved from recent observations[END_REF]Lavvas et al., 2008). Here, we use the Global Climate Model of Pluto (herein referred to as GCM), developed at the Laboratoire de Météorologie Dynamique (LMD) and designed to simulate the atmospheric circulation and the methane cycle on Pluto and to investigate several aspects of the presence of haze at a global scale on Pluto [START_REF] Forget | A post-New Horizons Global climate model of the Pluto system including the N2, CH4 and CO cycle -submitted to Icarus[END_REF][START_REF] Bertrand | Observed glacier and volatile distribution on Pluto from atmospheretopography processes[END_REF]. What controls haze formation on Pluto? At which altitudes and latitudes does it form and where does sedimentation occur? What amount of particles forms the haze, and what is its opacity? To address those key questions we have developed a simple parametrization of haze in the GCM. The parametrization is based on a function of aerosols production, which directly depends on the amount of the Lyman-α UV flux. The photolysis reaction of CH 4 is photonlimited. That is, all incident photons are absorbed by the CH 4 molecules present in Pluto's atmosphere.

During the flyby of the Pluto system on July 14, 2015, the New Horizons spacecraft recorded data about the structure, composition and variability of Pluto's atmosphere. In particular, Alice, the UV spectrometer on-board, observed solar occultations of Pluto's atmosphere which help to determine the vertical profiles of the densities of the present atmospheric constituents and provide key information about the haze. Within this context, our work aims

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to help the analysis of the New Horizons observations with model predictions of the possible evolution, spatial distribution and opacity of haze in Pluto's atmosphere and on its surface.

We begin in Section 2 with a background on haze formation processes as understood on Titan, Triton and Pluto. In Section 3 we describe the GCM. The parametrization of organic haze, as well as its implementation in the model are described step by step in Section 4. Finally, results are shown in Section 5 for two climate scenarios: with and without South Pole N 2 condensation.

Background on planetary haze formation

One of Titan's most fascinating features is the dense and widespread organic haze shrouding its surface and containing a large variety of molecules which strongly impact the global climate. This makes Titan a perfect place to study organic chemistry and the mechanisms involved in a planetary haze formation. Since 2004, the exploration of Titan's haze by the Cassini/Huygens mission has provided a large amount of observational data, revealing complex chemistry, particularly at high altitudes. This has stimulated more interest in understanding this phenomenon. The haze on Titan is vertically divided into two regions: a main haze up to 300 km altitude, and a thinner, overlying detached haze typically between 400-520 km (Lavvas et al., 2009), whose origin is thought to be dynamic [START_REF] Rannou | A wind origin for Titan's haze structure[END_REF], although other scenarios were suggested (Larson et al., 2015). Both layers contain solid organic material resulting from photochemistry and microphysical mechanisms, some of which remain unknown (Lebonnois et al., 2002;Wilson and Atreya, 2003;Lavvas et al., 2008).

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First, methane and nitrogen molecules are dissociated and ionized in the upper atmosphere (up to 1000 km above the surface) by solar UV radiation, cosmic rays and energetic electrons from Saturn's magnetosphere [START_REF] Sittler | Saturn's magnetospheric interaction with Titan as defined by Cassini encounters T9 and T18: New results[END_REF].

It is commonly thought that the molecules resulting from photolysis chemically react with each other, which leads to the formation of larger and heavier molecules and ions such as hydrocarbons, nitriles and oxygen-containing species [START_REF] Niemann | Composition of Titan's lower atmosphere and simple surface volatiles as measured by the Cassini-Huygens probe gas chromatograph mass spectrometer experiment[END_REF][START_REF] Cravens | Composition of Titan's ionosphere[END_REF][START_REF] Coates | Discovery of heavy negative ions in Titan's ionosphere[END_REF][START_REF] Waite | The Process of Tholin Formation in Titan's Upper Atmosphere[END_REF]Crary et al., 2009, e.g.). While CH 4 is easily destroyed by photolysis and provides most of the organic materials, N 2 is dissociated as well by extreme UV radiation which explains the rich composition of Titan's upper atmosphere. In particular, observations from Cassini and Huygens spacecrafts show the presence of hydrocarbons and nitriles, such as C 2 H 2 , C 2 H 4 , C 2 H 6 , C 4 H 2 , C 6 H 6 , and HCN, as well as other more complex organics [START_REF] Shemansky | The Cassini UVIS Stellar Probe of the Titan Atmosphere[END_REF]. These species, formed after photolysis in the upper atmosphere, are the precursors of the haze. Then, through multiple processes of sedimentation, accumulation and aggregation, the precursors are thought to turn into solid organic aerosols which become heavy enough to form the orange haze surrounding the moon as seen in visible wavelengths (West and Smith, 1991;[START_REF] Rannou | Titan's geometric albedo: Role of the fractal structure of the aerosols[END_REF][START_REF] Cravens | Composition of Titan's ionosphere[END_REF]Lavvas et al., 2009). These aerosols are thought to be aggregates (modeled as fractal-like particles) composed of many spherical particles (monomers) that bond to each other. On Titan, the aerosols start to become large enough to be visible in the detached haze layer around 500 km altitude. Typically, they grow spherical up to radius 40-50 nm and then form fractal particles with monomer sizes of around 50 nm (Lavvas et al., 2009).

What are the haze's dominant pathways? What are the chemical natures of

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A N U S C R I P T complex haze particles? Several microphysical models [START_REF] Toon | A physical model of Titan's aerosols[END_REF]Rannou et al., 1997;Lavvas et al., 2009) and photochemical models (Wilson and Atreya, 2004;Lavvas et al., 2008;[START_REF] Hébrard | Photochemistry of C 3 H p hydrocarbons in Titan's stratosphere revisited[END_REF] have been developed, combining both transport and chemistry effects. The formation mechanisms of aerosol particles in Titan's atmosphere have also been investigated using laboratory experiments.

By performing UV irradiation of CH 4 in a simulated Titan atmosphere, several experiments have been successful in producing solid particles and have found that they contain mostly high-molecular-weight organic species (e.g., [START_REF] Khare | The organic aerosols of Titan[END_REF][START_REF] Khare | Analysis of the Time-Dependent Chemical Evolution of Titan Haze Tholin[END_REF][START_REF] Coll | Experimental laboratory simulation of Titan's atmosphere: aerosols and gas phase[END_REF][START_REF] Imanaka | Laboratory experiments of Titan tholin formed in cold plasma at various pressures: implications for nitrogen-containing polycyclic aromatic compounds in Titan haze[END_REF][START_REF] Szopa | PAM-PRE: A dusty plasma experiment for Titan's tholins production and study[END_REF][START_REF] Gautier | Mid-and far-infrared absorption spectroscopy of Titan's aerosols analogues[END_REF]. Experimental results from [START_REF] Trainer | Inaugural Article: Organic haze on Titan and the early Earth[END_REF] also show a linear relationship between the rate of aerosol production and the rate of CH 4 photolysis. In addition, they found that an increased CH 4 concentration could lead to a decrease in aerosol production in photon-limited reactions (this could be due to reactions between CH 4 and precursors forming non-aerosol products).

Titan's atmosphere is not the unique place where organic haze can form.

First, similar processes of haze formation are also thought to occur on Triton but yield less haze. During the Voyager 2 flyby in 1989, evidence of a thin haze was detected in Triton's atmosphere from limb images taken near closest approach [START_REF] Smith | Voyager 2 at Neptune -Imaging science results[END_REF][START_REF] Pollack | Scatterers in Triton's atmosphere -Implications for the seasonal volatile cycle[END_REF][START_REF] Rages | Voyager imaging of Triton's clouds and hazes[END_REF] and from Voyager 2 UVS solar occultation measurements [START_REF] Herbert | CH4 and haze in Triton's lower atmosphere[END_REF][START_REF] Krasnopolsky | Properties of haze in the atmosphere of Triton[END_REF][START_REF] Krasnopolsky | On the haze model for Triton[END_REF]. These data enabled the mapping of the horizontal and vertical distribution of CH 4 and haze as well as estimation of radiative and microphysical properties of the haze material.

Analyses showed that the haze is present nearly everywhere on Triton, from

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the surface up to 30 km at least [START_REF] Pollack | Scatterers in Triton's atmosphere -Implications for the seasonal volatile cycle[END_REF], where it reached the limit of detectability. Vertical optical depth derived from observations were found to be in the range 0.01-0.03 at UV wavelength 0.15 µm, and 0.001-0.01 at visible wavelength 0.47 µm. Haze particle sizes were estimated to be spherical and small, around 0.1-0.2 µm [START_REF] Krasnopolsky | Properties of haze in the atmosphere of Triton[END_REF][START_REF] Rages | Voyager imaging of Triton's clouds and hazes[END_REF][START_REF] Pollack | Scatterers in Triton's atmosphere -Implications for the seasonal volatile cycle[END_REF]. As on Titan, complex series of photochemical reactions may be involved in the formation of this haze, starting with CH 4 photolysis by the solar and the interstellar background Lyman-α radiation in the atmosphere of Triton at altitudes between 50-100 km, producing hydrocarbons such as [START_REF] Strobel | The photochemistry of methane in the atmosphere of Triton[END_REF]Krasnopolsky and Cruikshank, 1995b). Dissociation of N 2 molecules is also suggested in the upper atmosphere around 200-500 km. Transitions between haze precursors to solid organic particles are still incompletely known, but it is commonly thought that it involves similar mechanisms to those on Titan. Secondly, organic chemistry has also been studied in the Early Earth climate context, where a scenario of a N 2 /CH 4 atmosphere is plausible to form a hydrocarbon haze [START_REF] Trainer | Inaugural Article: Organic haze on Titan and the early Earth[END_REF].

C 2 H 2 , C 2 H 4 , C 2 H 6
Finally, the presence of a haze on Pluto was suspected [START_REF] Elliot | Pluto's atmosphere[END_REF][START_REF] Stansberry | Upper limits on possible photochemical hazes on Pluto[END_REF][START_REF] Forget | What will Pluto's atmosphere look like ? Predictions from a Global Climate Model including the methane cycle[END_REF] and confirmed in 2015 by New Horizons.

At high phase angles, Pluto's atmosphere revealed an extensive haze reaching up to 200 km above the surface, composed of several layers [START_REF] Gladstone | Ly α @Pluto[END_REF].

Observations show that the haze is not brightest to the sub solar latitude, where the incoming solar flux is stronger, but to Pluto North Pole. The haze is strongly forward scattering in the visible with a blue color, while at the same time there is haze extinction optical depth exceeding unity in the UV. The blue color and UV extinction are consistent with a small size of about 10 nm for P lit (kg m -2 s -1 ) 0.5 -3 × 10 -13 d 6.0 × 10 -14 e 9.8 × 10 -14 f properties may also be consistent with fractal aggregate particles composed

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202 A C C E P T E D M A N U S C R I P T
of 10 nm monomers [START_REF] Cheng | Haze Layers in Pluto's Atmosphere[END_REF][START_REF] Cheng | Haze Layers in Pluto's Atmosphere[END_REF].

Although the specific mechanisms of haze formation are not fully understood, it seems that the main parameters controlling the formation of haze in a N 2 /CH 4 atmosphere are the fractional amount of CH 4 (enough CH 4 is required to avoid CH 4 -limited reactions, that is when the CH 4 concentration in the atmosphere is not sufficient to absorb all incoming photons) and the UV flux available to photolyze it.

One can compare the UV flux and the fraction of methane for Titan, Triton and Pluto to estimate the haze formation rate to first order. Here we assume that the impact of cosmic rays and energetic electrons from Saturn's magnetosphere is negligible for this first order comparison. As shown on Table 1 and observed on Triton, although it also depends on the scattering properties of haze particles. On Titan, the pressure corresponding to the location of the detached haze layer at about 400 km altitude is about 1 Pa, which is similar to the surface pressure on Pluto in 2015. While [START_REF] Rannou | A model of Titan's haze of fractal aerosols constrained by multiple observations[END_REF] predicted the peak of production of haze in Titan's GCMs at a pressure around 1.5 Pa, Cassini observations [START_REF] Waite | Ion Neutral Mass Spectrometer Results from the First Flyby of Titan[END_REF][START_REF] Teanby | Active upper-atmosphere chemistry and dynamics from polar circulation reversal on Titan[END_REF] pointed

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to active chemistry and haze formation at lower pressures. In addition, the amounts of methane at these altitudes on Titan and in Pluto's atmosphere are of the same order of magnitude. Thus, Pluto has sufficient pressure and material in its atmosphere so that complex and opaque organic aerosols form, in a manner similar to the detached haze layer on Titan. Consequently, in this paper, we use the microphysical and single scattering optical properties of Titan detached haze around 400 km altitude as a reference to define the haze properties on Pluto while the mass of aerosols is calculated by the model without any empirical assumption.

Model description

The LMD Pluto General Circulation Model (GCM) contains a 3D Hydrodynamical core inherited and adapted from the LMD Mars GCM [START_REF] Forget | Improved general circulation models of the Martian atmosphere from the surface to above 80 km[END_REF]. It is described in more details in [START_REF] Forget | A post-New Horizons Global climate model of the Pluto system including the N2, CH4 and CO cycle -submitted to Icarus[END_REF] not at the same wavelengths. N 2 is the primary absorber at wavelength between 10 and 100 nm, while CH 4 absorbs mainly between 100 and 145 nm.

Thus the interaction between CH 4 and Lyman-α emission dominates the other interactions between the UV flux and the N 2 -CH 4 atmosphere by a factor of 100. On Pluto, CO may also contribute to the formation of haze. It absorbs in the far UV spectrum at similar rates that N 2 . However, at 121.6 nm, it absorbs 10 times less than CH 4 . Here we chose to neglect the effect of N 2 and CO absorption. This first assumption enables us to write Beer's law as the following:

I(λ, P ) = I 0 e - P 0 σ CH4 Na q CH4 M CH4 g dP cos(θ) (1)
where I 0 is the incident intensity (in ph m -2 s -1 ) and I(λ, P ) the intensity after absorption for a given wavelength λ and pressure P , σ CH4 is the absorption cross section of CH 4 at wavelength λ (here in m 2 molec -1 but usually given in cm 2 molec -1 ), q CH4 is the mass mixing ratio of CH 4 at pressure P (kg kg -1 air ), M CH4 is the methane molecular mass (kg mol -1 ), N a is the Avogadro constant, θ is the flux incident angle and g the surface gravity. We use σ CH4 = 1.85 × 10 -17 cm 2 at Lyman-α wavelength [START_REF] Krasnopolsky | Detection of methane in the martian atmosphere: evidence for life?[END_REF] and q CH4 as calculated by the GCM for each vertical layer. The calculation of the Lymanα flux radiative transfer is performed independently for the solar and the interplanetary medium fluxes in order to take into account different values for the incident flux I 0 and the incident angle θ (see Section 4.2).

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4.2 Sources of Lyman-α

The sources of Lyman-α flux at Pluto are adopted from [START_REF] Gladstone | Ly α @Pluto[END_REF], which takes into account the solar as well as the interplanetary medium (IPM)

Lyman-α fluxes. The IPM emission corresponds to interplanetary hydrogen atoms passing through the solar system which resonantly scatter solar Lymanα photons and thus diffuse Lyman-α emission. Therefore the total Lyman-α flux at any pressure level P in Pluto's atmosphere is:

I tot (P ) = I sol (P ) + I IP M (P ) (2)
The solar Lyman-α flux at Pluto is inversely proportional to the square of the 2, the precursors production rate (in kg kg -1 air s -1 ) is calculated as:

347 P prec (P ) = M CH4 g N a dI tot dP (3) 348
In the model, all possible precursors which can form during this reaction are 349 represented by a unique gas. The equation of the reactions is:

350 CH 4 + hν → precursors → haze aerosols (4) A C C E P T E D M A N U S C R I P T
This mechanisms correlates linearly the rate of haze precursors production with the rate of CH 4 photolysis. It has also been used by [START_REF] Trainer | Inaugural Article: Organic haze on Titan and the early Earth[END_REF] to estimate aerosols production on Titan and Early Earth. In reality, the reactions are more complex and could lead to the irreversible production of HCN, or to the production of molecules such as C 2 H 2 or C 2 H 6 which can later be photolyzed themselves as well. In addition, CH 4 molecules may be chemically dissociated by reacting directly with the precursors. Consequently, these reactions could lead either to an increase in the amount of carbon atoms available as haze material, increasing the haze production, or to non-aerosol products, slowing down the haze production [START_REF] Trainer | Inaugural Article: Organic haze on Titan and the early Earth[END_REF].

In the parametrization, the haze production is regulated by a factor K CH4 , that corresponds to the ratio between the total number of carbon atoms in the tholins and the number of carbon atoms coming from CH 4 photolysis. K CH4 would range from 1 to 2 (respectively all or half of the carbon in the tholins are formed by direct CH 4 photolysis) if direct reactions between precursors and CH 4 occur and contribute to provide tholins with carbon atoms. However, the ratio could be lower than 1 considering the formation of other non-aerosol products (see Section 5.3.3).

Additionally, nitrogen may contribute to the chemical reactions and provide material for aerosol formation. In order to take into account this process, the haze production is also boosted by a factor K N =1+N/C, N/C representing the mass ratio between nitrogen and carbon atoms contribution observed in the tholins (since molar masses of nitrogen and carbon are quite similar, the mass ratio is close to the number ratio). Different values of this ratio have been observed in laboratory experiments, ranging from 0.25 to 1 depending on the pressure (the higher the pressure, the lower the ratio), the temperature and

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the amount of methane in the simulated atmosphere (e.g. [START_REF] Coll | Experimental laboratory simulation of Titan's atmosphere: aerosols and gas phase[END_REF][START_REF] Tran | Titan's atmospheric chemistry: Photolysis of gas mixtures containing hydrogen cyanide and carbon monoxide at 185 and 254 nm[END_REF][START_REF] Nna-Mvondo | Thermal characterization of Titan's tholins by simultaneous TG-MS, DTA, DSC analysis[END_REF]). In the model, we adopt N/C = 0.5, in line with the values obtained in Nna-Mvondo et al. ( 2013) at low pressure, and K CH4 = 1, so that the total production of tholins remains in the range of estimated values on Titan and Pluto (see Section 4.5).

Conversion of haze precursors to aerosols

As the mechanisms at the origins of formation of organic haze are not well known, another assumption is made in the parametrization: we consider that the precursors become solid organic particles (by a set of processes of aggregation and polymerization that are not represented) after a given time. In practice, the amount of precursors is subject to exponential decay and is converted into aerosols with characteristic decay time τ (or characteristic time for aerosol growth). In other words, τ is the mean lifetime of the precursors before they become solid aerosols. This time is difficult to estimate as it depends on atmospheric conditions (concentration, pressure...). However, Titan's atmospheric models show that the time needed for precursors to evolve from the photolysis area to the detached layer is typically around 10 6 -10 8 s (Lavvas et al., 2011;[START_REF] Rannou | Growth of aerosols in Titan's atmosphere and related time scales -A stochastic approach[END_REF]. Consequently, we used in our reference GCM simulations a value of 10 7 s for Pluto aerosols and we examine the sensitivity of the results to this parameter in Section 5.3.1.

Once produced, the aerosols are transported by the atmospheric circulation, mixed by turbulence, and subject to gravitational sedimentation (see Section 4.6).

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A N U S C R I P T 4.5 Discussion on total aerosol production Equation 4 enables us to estimate the total haze production rate P (kg m -2 s -1 ) in a N 2 /CH 4 atmosphere:

P = (F SOL + F IP M ) M CH4 N a K CH4 K N with F SOL = I Earth 4 d P 2 E H (5)
where F SOL and F IP M are the solar and IPM Lyman-α flux respectively (in ph m -2 s -1 ), M CH4 is the molar mass of methane (M CH4 = 16×10 -3 kg mol -1 ),

N a is the Avogadro constant, I Earth is the initial Lyman-α flux at Earth (we set I Earth =4 × 10 15 ph m -2 s -1 ), d P is the distance in astronomical units of the considered planet P to the Sun and E H is a constant extinction factor due to interaction with interplanetary hydrogen between the planet P and the Sun.

Here E H is set to 0.875 for the case of Pluto [START_REF] Gladstone | Ly α @Pluto[END_REF] and to 1

for the other cases. The solar flux F SOL is equal to the incident solar flux I sol 0 divided by a factor of 4 to take into account the distribution on the planetary sphere.

It is important to note that the haze production rate is independent of the CH 4 concentration, even for CH 4 concentrations several orders of magnitude lower than on Pluto (see Section 5.3). The reactions are photon-limited, i.e. that enough CH 4 is present in Pluto's atmosphere for all photons to be absorbed by CH 4 .

In order to validate the approach described by equation 4, we apply equation 5 to Titan, Triton and Pluto and compare the haze production rates obtained with the literature. The values, obtained with K CH4 =1 and K N =1.5, are summarized in Table 1. For Titan's case, we consider that the IPM flux is negligible

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compared to the solar flux. Using an average Sun-Titan distance d T itan =9.5 UA, we find for Titan's atmosphere a Lyman-α flux of 1.11 × 10 13 ph m -2 s -1

(dissipated on the planetary sphere) and a production rate of 2.94 × 10 -13 kg m -2 s -1 . This is comparable to values found by Wilson and Atreya (2003) and [START_REF] Mckay | Physical properties of the organic aerosols and clouds on Titan[END_REF], as shown on Table 1. For Triton's case, we consider an averaged IPM flux of 340 R [START_REF] Broadfoot | Ultraviolet spectrometer observations of Neptune and Triton[END_REF]Krasnopolsky and Cruikshank, 1995a), which correspond to an IPM flux of 170 × 10 10 ph m -2 s -1 distributed on the planetary sphere. Using an average Sun-Triton distance d T itan =30 UA, we find for Triton's atmosphere a total Lyman-α flux (solar and IPM) of 2.81×10 12 ph m -2 s -1 and a photolysis rate of 7.47×10 -14 kg m -2 s -1 , which is also in line with the literature references. Since this approach provides good estimation of Titan's and Triton's total aerosol production, we used it to estimate the aerosol production rate for Pluto's atmosphere. Equation 5gives a production rate of 5.98 × 10 -14 kg m -2 s -1 using the solar and IPM flux as calculated in Section 4.2. This value is one order of magnitude lower than the one on Titan (due to the UV flux one order of magnitude lower) and comparable to the value found on Triton. It is of the same order of magnitude as the value estimated on Pluto from photochemical models [START_REF] Cheng | Haze Layers in Pluto's Atmosphere[END_REF] shown in Table 1.

Properties of haze particles for sedimentation and opacity estimations

Haze precursors and particles are transported in the model by atmospheric circulation and are not radiatively active. In addition, the haze is considered too thin to affect the surface energy balance and does not change its ground albedo (in line with haze and surface observations on Triton as discussed in [START_REF] Hillier | Photometric properties of Triton hazes[END_REF]).

A C C E P T E D M A N U S C R I P T
The density of the aerosol material in the model is set to 800 kg m -3 , which is in the range of values typically used on Titan [START_REF] A C C E P T E D M A N U S C R I P T C. Sotin | Observations of Titan's Northern lakes at 5 µm: Implications for the organic cycle and geology[END_REF]Lavvas et al., 2013;[START_REF] Trainer | Inaugural Article: Organic haze on Titan and the early Earth[END_REF]. The size of the haze particles affects their sedimentation velocity and thus the haze distribution in Pluto's atmosphere. In the GCM, we prescribe a uniform size distribution of particles. For the reference simulations (with and without South Pole N 2 condensation), we assumed spherical particles with a radius of 50 nm, consistent with the properties of the detached haze layer on Titan (see Section 2). We also examine the sensitivity of the results to different sizes of particles in Section 5.3.2, in order to bracket the different possible scenarios for Pluto's haze. We consider two lower radii of 30 nm and 10 nm, which is in the range of recent estimations [START_REF] Cheng | Haze Layers in Pluto's Atmosphere[END_REF], and one larger radius of 100 nm.

The particles fall with their Stokes velocity ω, corrected for low pressures [START_REF] Rossow | Cloud microphysics -Analysis of the clouds of Earth, Venus, Mars, and Jupiter[END_REF]:

ω = 2 9 r 2 ρ g v (1 + α Knud) with Knud = k B T √ 2 π d 2 p r (6)
with r the particle radius, ρ the particle density, g the Pluto's gravitational constant, v the viscosity of the atmosphere, Knud the Knudsen number, p the considered pressure, T the atmospheric temperature, d the molecular diameter, k B the Boltzmann's constant and α a correction factor.

On Pluto, the Knudsen number is significant and thus the sedimentation velocity is proportional to the particle radius. Consequently, in an ideal atmosphere without atmospheric circulation, a 100 nm particle will fall twice faster than a 50 nm particle, leading to a twice lower column mass of haze. Assuming

A C C E P T E D M A N U S C R I P T
an atmospheric temperature of 100 K and a surface pressure of 1 Pa, the 472 sedimentation velocities above Pluto's surface are about 4.6×10 -4 , 1.4×10 -3 , 473 2.3×10 -3 and 4.6×10 -3 m s -1 for an aerosol radius of 10, 30 50 and 100 nm 474 respectively.

475

One can note that the Stokes velocity is proportional to the inverse of the 476 pressure. Theoretically, the lower the pressure, the higher the sedimentation 477 velocity of the aerosol and thus the lower the mass of haze in the atmosphere.

478

The choice of the size and the shape of aerosol particles is also critical to those settings can be found in [START_REF] Forget | A post-New Horizons Global climate model of the Pluto system including the N2, CH4 and CO cycle -submitted to Icarus[END_REF].

501
The model is run with the haze parametrization using a precursor charac- 3 summarizes the surface conditions and haze parameters used in 506 the reference simulations [START_REF] Forget | A post-New Horizons Global climate model of the Pluto system including the N2, CH4 and CO cycle -submitted to Icarus[END_REF]. Characteristic time for aerosol growth τ (s)

10 7 K CH4 1 K N 1.5
Effective radiusof haze particles (nm) 50

Density of haze particles (kg.m -3 ) 800

Table 3 Surface conditions and settings for haze parametrization set for the GCM reference non-negligible with values up to 4×10 -19 g cm -3 at 500 km altitude. In this case, the meridional circulation is quite weak: the diurnal condensation and sublimation of N 2 ice in Sputnik region only impacts the circulation in the first km above the surface, and at higher altitudes, the circulation is forced by the radiative heating (the northern CH 4 warms the atmosphere, leading to a transport of this warm air from the summer to the winter hemisphere)

inducing low meridional winds. Consequently, the general circulation does not impact the haze distribution, which is dominated by the incoming flux and the sedimentation velocity. In other words, the vertical and meridional atmospheric motions are not strong enough to signicantly push and impact the latitudinal distribution of the haze composed of 50 nm particles: the haze density in the atmosphere is always higher at the summer pole, where a stronger CH 4 photolysis occurs.

In the summer hemisphere, the haze density is typically 2-4×10 -15 g cm -3 at 100 km altitude while it reaches 1-2×10 -13 g cm -3 above the surface.

Figure 5 shows the evolution of the mean column atmospheric mass of haze aerosols since 1988. Assuming a constant initial flux of Lyman-α (at Earth) and a particle radius of 50 nm, the column mass of haze reaches a peak of 1.8×10 -7 g cm -2 in 2015. Because the transport of haze is dominated by its sedimentation, the column mass of haze directly depends on the sedimentation velocity of the haze particles. As shown by equation 6, the sedimentation velocity decreases when pressure increases, hence the increase of column mass of haze, in line with the threefold increase of surface pressure since 1988.

Note that this trend still applies when considering the real and variable initial Lyman-α flux at Earth between 1988 and 2015, as shown by Figure 5. The sublimation of N 2 in mid northern latitudes (Sputnik region and the latitudinal band) and its condensation in the winter hemisphere induce an atmospheric flow from the northern to the southern hemisphere, and thus a stronger meridional circulation than in the reference simulation without South

Pole N 2 condensation, although the latitudinal winds remain relatively weak [START_REF] Forget | A post-New Horizons Global climate model of the Pluto system including the N2, CH4 and CO cycle -submitted to Icarus[END_REF]. Although the atmospheric methane is more mixed in the atmosphere in this case, the state of the atmosphere remains similar to the reference simulation without South Pole N 2 condensation. The surface pressure is increasing before 2015 and reaches 1 Pa in 2015.

Because of the condensation flow from the northern to the southern hemisphere, the air in the upper atmosphere is transported along with the haze precursors from the summer atmosphere to the winter atmosphere. As shown on Figure 3, the characteristic decay time of haze precursors (18 sols) is sufficient for some of the precursors to be transported from the summer to the winter hemisphere where the descending branch bring them at lower altitudes down to the surface.

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

As a consequence of that, more haze is formed in the winter hemisphere than in the reference simulation without N 2 condensation flow, which compensates the haze production in the summer hemisphere due to the higher CH 4 photolysis rate. It leads to a similar haze density at all latitudes, as shown by Figure 4.

The haze density is typically 4×10 -15 g cm -3 at an altitude of 100 km, which is similar to the reference simulation without the condensation flow. The haze remains latitudinally well dispersed down to 3 km, where the meridional circulation driven by the N 2 condensation flow affects the haze distribution: the haze is pushed towards southern latitudes by the N 2 ice sublimation above the N 2 frost latitudinal band and Sputnik Planum, avoiding an accumulation of haze at the mid and high northern latitudes. Between -70˚S and -90˚S, haze particles in the first layers are suctioned towards the surface of the N 2 polar cap. The haze reaches a density of about 5-20×10 -12 g cm -3 below 1 km in the winter hemisphere, and 3-6×10 -14 g cm -3 in the summer hemisphere, which is twice less compared to the reference simulation without the condensation flow.

In line with the previous results, the column mass of haze in the simulation with condensation flow shown on Figure 6 (right figure) is well dispersed on Pluto, with small variations: in the summer atmosphere, the mass is about 2×10 -7 g cm -2 , but it is slightly less at low and mid latitudes because the haze above the surface is transported towards the south polar cap, and slightly more at the North Pole because the haze is not impacted by the N 2 ice sublimation and transport which occur at lower latitudes.

As in the previous simulation without South Pole N 2 condensation, the mean column mass of haze increases with surface pressure. In 2015, a similar averaged column mass of haze is obtained. Slight discrepancies are found due to

A C C E P T E D M A N U S C R I P T
slightly different surface pressures to first order [START_REF] Forget | A post-New Horizons Global climate model of the Pluto system including the N2, CH4 and CO cycle -submitted to Icarus[END_REF], and to the different circulation to second order.

Haze opacity

In order to better quantify the amount of haze formed on Pluto and compare with the observations as well as with the Titan and Triton cases, one can compute the total column opacity and the line of sight opacity of the haze (as a diagnostic of the results). Here we focus on the opacity at UV (λ = 150 nm) and visible (λ = 550 nm) wavelengths for sake of comparison with the data recorded by the UV spectrometer Alice and the Ralph and LORRI instruments on board New Horizons. Assuming a homogeneous size and extinction efficiency for the aerosols in Pluto's atmosphere, the opacity τ λ for a given wavelength λ is directly proportional to the atmospheric column mass of aerosols:

τ λ = α.M with α = 3 4 Q ext,λ ρ aer r ef f (7)
where Q ext is the aerosol extinction efficiency, r eff the aerosol particle effective radius, ρ aer the aerosol density and M is the atmospheric column mass of aerosol in kg m -2 .

Spherical particles

Assuming that the haze on Pluto is composed of spherical particles and be-

684

Here we compare the opacities obtained in the reference simulations when 685 considering spherical or fractal particles. We consider fractal particles com-686 posed of 50 nm monomers, with a fractal dimension equal to 2 and with a 687 bulk radius of 100 nm and 232 nm (N=8 and N=100 monomers respectively).

688

The model gives an extinction efficiency Q ext of 4.1 in the UV and 0.49 in the 689 visible wavelengths for the 100 nm fractal particle and 7.2 in the UV and 1.93 690 in the visible wavelengths for the 232 nm fractal particle. The resulting nadir 691 opacities are summarized in Table 4 and limb opacities are shown on Figure 7.

692

The opacities obtained for fractal particles are higher than for spherical par-693 ticles in the visible, with a factor of 1.3 for the 100 nm and 2.2 for the 232 nm

694 A C C E P T E D M A N U S C R I P T
particle but lower in the UV with a factor of 0.9 and 0.7 respectively for the 100 nm and the 232 nm particle. This is shown by Figure 7.

As shown in Table 4, the visible nadir opacity obtained in the summer hemisphere are in the range of what is estimated from New Horizons observations (0.004-0.012, [START_REF] Gladstone | Ly α @Pluto[END_REF]; [START_REF] Cheng | Haze Layers in Pluto's Atmosphere[END_REF]) in both the spherical and the 100 nm fractal cases, and in both reference simulations. Values of the 232 nm fractal case are outside the observational range. The case of fractal particles composed of 10 nm particles is discussed in Section 5.3.2.

Line of sight opacity profiles

Figure 7 shows the line of sight opacity profiles in the UV and in the visible wavelengths obtained for both reference simulations at the ingress and the egress points of Pluto's solar occulation by New Horizons. The profiles are computed using an onion peeling method and considering that the line of sight only crosses one GCM atmospheric column.

Generally speaking, few differences are obtained between both reference simulations. The difference of opacity between the egress point (which is above the equator at the latitude 15˚N) and the ingress point (which is below the equator at the latitude 17˚S) are larger for the simulation without South Pole N 2 condensation, because of the higher haze density in the summer hemisphere shown in Figure 4. to the fractal cases with R s =100 nm / N=8 and R s =232 nm / N=100 respectively.

Sensitivity studies 715

The poor constraint on haze properties on Pluto gives us a flexibility to explore 716 further other scenarios for Pluto's haze. In this section, the haze parametriza-717 tion is tested with different precursor lifetimes and sedimentation radius. We formed from photolysis reactions), 10 6 s (1.81 Pluto sols), 10 7 s (18.12 sols, 748 reference simulations), 10 8 s (181.20 sols, that is about 3 terrestrials years).

749

The rest of the settings remain similar to both reference simulations. Haze column (g cm we compare eight simulations: the reference simulations (50 nm particles, with and without condensation flow) and simulations performed with particle sizes of 10, 30 and 100 nm (with and without condensation flow). We compare the column atmospheric mass obtained (Figure 10), the limb opacities (Figure 11)

¡2 ) ¿ = 1 s ¿ = 1e6 s ¿ = 1e7 s ¿ = 1e8 s
and the nadir opacities (Table 4). These simulations correspond to the four first lines of Table 4. The six last lines of Table 4 show the nadir opacities obtained from the simulations with 10 nm and 50 nm particles, but considering fractal particles (four cases with 10 nm monomers and two cases with 50 nm monomers). Haze aerosol density is also shown for the simulation with condensation flow and with a particle radius of 10 nm (Figure 12).

Aerosol particles with radii of 10, 30, 50 and 100 nm typically fall from 200 km down to the surface in 1110, 370, 220 and 111 Earth days respectively. Basically, this corresponds to the time needed to reach an equilibrated mass of haze in the atmosphere. As shown by Figure 10, the latitudinal mass distribution is not impacted by the considered size of the particle. The column mass of haze is driven by the sedimentation velocity and the mass ratios correspond to the particle size ratios. This is also shown by Figure 5.

As shown by Table 4 and Figure 11, the nadir and limb opacities remain in the same order of magnitude for the simulations performed with different particle radii. Lower opacities are obtained with a particle radius of 30 nm. We also investigated nadir opacities for fractal particles with a bulk radius of 22, 46, 100 and 200 nm, respectively composed of 10, 100, 1000 and 8000 monomers of 10 nm radius. As discussed in Section 2, the 200 nm fractal particle is the best hypothesis for the particle shape and size in order to fit the observations.

Here we find that the nadir visible opacities obtained in this case are higher than the upper observational limit (see Table 4). Realistic values are obtained particle radii. Generally speaking, the profiles have similar shapes because 799 changing the particle radius does not affect the haze distribution but only the 800 mass of haze in the atmosphere, due to the change of sedimentation velocity.

801

However, for 10 nm particles, the opacities at ingress are significantly higher 802 than at egress below 50 km, which is not the case for higher radii. This is Haze aerosol opacities obtained at nadir in the summer hemisphere in the GCM, for four particle radii and for both climate scenarios with and without South Pole N 2 condensation. The time for aerosol growth used is 10 7 s. The particles with a number of monomers N m equal to 1 are spherical particles, otherwise they are fractal particles (R s is the bulk radius, r is the monomer radius). The first four fractal particles are composed of 10 nm monomers, and the last two are composed of 50 nm monomers.

Sensitivity to the mass of aerosols 812

The haze production rate used in the reference simulations corresponds to an 813 optimal scenario where the photolysis of one molecule of CH 4 gives one carbon 814 atom available for the production of haze (K CH4 =1). However, the carbon First, it is depending on the photolysis rate and the complex recombinations of carbon and nitrogen atoms. The parametrization uses K CH4 and K N equal to 1 and 1.5 to take these mechanisms into account. However, the production could be overestimated. In fact, New Horizons detected the presence of on Pluto, that is 0.003-0.012 [START_REF] Cheng | Haze Layers in Pluto's Atmosphere[END_REF][START_REF] Gladstone | Ly α @Pluto[END_REF], and thus suggest an acceptable order of magnitude for the mass of haze obtained. allows precursors to be transported towards southern latitudes by radiative heating and meridional circulation. Finally, another way to distinguish both cases is to compare the haze distribution in the first kilometers above the surface. Figure 12 shows that the condensation flow induced by the presence of N 2 ice in the winter hemisphere leads to a lack of haze above the surface in the summer hemisphere, and an accumulation of haze between 3 and 20 kilometers in the winter hemisphere, which is more pronounced for small particle radii. Although the simulations were done with uniform particle sizes, in reality the haze particle size may be locally distributed and vary in space and time, especially in the vertical. Thus it may be more realistic to consider a distribution of haze particle sizes, in order to take into account the gravitational segregation. Compared to the uniform size case, if 10 nm spherical particles in the upper atmosphere become fractal particles in the lower atmosphere, with same monomer radius, then there will be a change in opacity but not in haze vertical distribution (because the sedimentation velocity remains the same).

If 10 nm spherical particles grow up to 100 nm during their fall down towards the surface, then the sedimentation velocity of the particle would change. The increase of the particle size during the fall would compensate the increase of atmospheric pressure and lead to a more homogeneous haze density with altitude. In addition, at the altitudes where transitions of particle size occur, layers of haze could form.

A C C E P T E D M

A N U S C R I P T

a

  above the tropopause, Niemann et al. (2010) b Lellouch et al. (2010) c Lellouch et al. (2011) d Wilson and Atreya (2003); McKay et al. (2001) e Strobel and Summers (1995) f Gladstone et al. (2016)

Fig. 1 .

 1 photons entering Pluto's atmosphere at a given location, we integrated the all-sky IPM brightness estimated in 2015 from[START_REF] Gladstone | Ly α @Pluto[END_REF] over the half celestial sphere as seen at the considered location. The flux I IP M 0 obtained varies with the local time but does not strongly depend on the Sun-

479

  estimate their optical properties and thus their detectability. In Section 5.3.2, 480 we compare the opacities obtained with different particle radii. In Section 5.2, 481 we examine the case of fractal particles by considering that they fall at the 482 velocity of their monomers, due to their aggregate structure, which is only true 483 for a fractal dimension equal to 2(Lavvas et al., 2011;[START_REF] Larson | Simulating Titan's aerosols in a three dimensional general circulation model[END_REF].

4844. 7

 7 Description of the reference simulations 485 In this paper, we compare two reference simulations which correpond to the 486 two climate scenarios detailed in Forget et al. (2016): One is the case of Sputnik 487 Planum as the only reservoir of N 2 ice without N 2 condensation elsewhere 488 (referred as No South Pole N 2 condensation), and the other is the case with a 489 latitudinal band of N 2 ice at northern mid latitudes, as an additional reservoir 490 of N 2 ice with Sputnik Planum, and an initially colder South Pole, allowing 491 the N 2 ice to condense (with South Pole N 2 condensation). 492 The reference simulations study are defined as follows. A seasonal volatile 493 model of Pluto is used to simulate the ice cycles over thousands of years 494 A C C E P T E D M A N U S C R I P T and obtain consistent ices distribution, surface and subsurface temperatures 495 as initial conditions for the GCM (see Bertrand and Forget (2016) for more 496 details). Then, GCM runs are performed from 1988 to 2015 included so that 497 the atmosphere has time to reach equilibrium before 2015 (the spin up time of 498 the model is typically 10-20 Earth years). The initial conditions, the settings 499 of the model, as well as discussions about the sensitivity of the predictions to 500

502

  teristic time for aerosol growth of 10 7 s (about 18 sols on Pluto), a fraction 503 K CH4 =1 and K N =1.5. The density and sedimentation effective radius of haze 504 particles are set uniformly to 800 kg m -3 and 50 nm respectively (see Section 505 4.4). Table

Fig. 2 .Fig. 4 .

 24 Fig. 2. Photolysis rate of CH 4 (g cm -3 s -1 ) obtained with the reference simulation without South Pole N 2 condensation for July 2015 (color bar in log scale)

Figure 4 A

 4 Figure4shows the zonal mean latitudinal section of haze density predicted in 545

Fig. 5 .

 5 Fig.5. Evolution of the mean column atmospheric mass of haze aerosols (g cm -2 ) from 1988 to 2016 obtained with different particle radius in the reference simulation without South Pole N 2 condensation: 10 nm (blue), 30 nm (green), 50 nm (red) and 100 nm (black). The dashed lines correspond to similar simulations started with a higher initial amount of haze. With 50 nm particles (red curve), the mass of haze reaches an equilibrium within less than one year. The dash-dotted line corresponds to the 10 nm case with the real variable initial Lyman-α flux (at Earth).

Figure 6

 6 Figure6shows the column atmospheric mass of haze aerosols. In line with 575

Fig. 6 .

 6 Fig. 6. Column atmospheric mass map of haze aerosols (g cm -2 ) obtained with the reference simulation without (left) and with (right) South Pole N 2 condensation

  haves like the detached haze layer on Titan, we used a Mie code to generate single scattering extinction properties for different spherical particle sizes. The code takes into account a modified gamma size distribution of particles with the considered effective radius and an effective variance ν ef f = 0.3, as well as A C C E P T E D M A N U S C R I P T ticles. As shown by the figure 10 in Larson et al. (2014), the optical depth 669 of a 1 µm fractal particle is strongly dependent on the considered wavelength 670 and decreases from the UV to the near infrared, while the optical depth of 671 a similar sized spherical particle remains quite constant with the wavelength. 672 One can use equation 7 to calculate the opacity of fractal particles with Q ext 673 the aerosol extinction efficiency (referred to the equivalent mass sphere), r eff 674 the equivalent mass sphere radius of the particle and ρ aer the density of the 675 material (or density of the monomers). Here we used a mean field model of 676 scattering by fractal aggregates of identical spheres (Botet et al., 1997; Ran-677 nou et al., 1997) to estimate the extinction efficiency of fractal particles. From 678 the number of monomers N and the monomers radius r m , on can calculate 679 the equivalent mass sphere radius of the corresponding fractal particle, given 680 by R s = N 1 3 × r m . Using these parameters and the fractal dimension of the 681 particle, the model computes Q ext by dividing the extinction cross section of 682 the particle by the geometrical cross section of the equivalent mass sphere 683 (π R 2 s ).

Fig. 7 .

 7 Fig. 7. Line of sight opacity profiles obtained with the GCM for the spherical and fractal cases, at the ingress (-163˚E, 17˚S, solid lines) and egress point (16˚E, 15˚N, dashed lines) of Pluto's solar occultation, for the reference simulation without (top) and with (bottom) South Pole N 2 condensation. Left and right are the results in UV and VIS wavelength respectively. The red curve is the reference simulation with 50 nm spherical particles. The blue and green curves correspond

718

  also discuss the possible values for K CH4 in the parametrization. One objective 719 A C C E P T E D M A N U S C R I P T years simulated and will allow precursors to be more mixed in the entire 745 atmosphere. Here we compare simulation results obtained with different char-746 acteristic times for aerosol growth (Figure 8 and Figure 9): 1 s (haze directly 747

Fig. 8 .

 8 Fig. 8. Zonal mean of column atmospheric mass of haze aerosols (kg m -2 ) obtained for July 2015 with different times for aerosol growth τ (s), for the simulations without (solid lines) and with (dashed lines) South Pole N 2 condensation.

Fig. 9 .A

 9 Fig. 9. Line of sight opacity profiles in VIS wavelength obtained with the GCM with different times for aerosol growth, at the ingress (-163˚E, 17˚S, solid lines) and egress point (16˚E, 15˚N, dashed lines) of Pluto's solar occultation, for the simulations without (left) and with (right) South Pole N 2 condensation

AFig. 12 .

 12 Fig. 10. Zonal mean of column atmospheric mass of haze aerosols (kg m -2 , log scale) obtained with different particle radii, for the simulations without (solid lines) and with (dashed lines) South Pole N 2 condensation.

803

  Figure 12 which shows the 10 nm haze particles density in the simulation with 808

  CH 4 photolysis may form different gaseous species and slow down tholins production. As an example,[START_REF] Mckay | Physical properties of the organic aerosols and clouds on Titan[END_REF] suggest that the tholins production is about 25 less than the photolysis rate of methane. Therefore, lower values of K CH4 remain possible and would lead to a decrease of aerosol mass and thus of opacity.6 SummaryThe parametrization of haze aerosols in the Pluto GCM consists of several steps: the photolysis of methane by the solar and IPM flux, the creation of haze precursors and their transport in the atmosphere, the conversion of precursors to haze aerosols and the sedimentation of the aerosols. The haze parametrization has been tested with 50 nm particles, a time for aerosol growth of 10 7 s, and for the two climate scenarios described in[START_REF] Forget | A post-New Horizons Global climate model of the Pluto system including the N2, CH4 and CO cycle -submitted to Icarus[END_REF]: with and without South Pole N 2 condensation (reference simulations). The sensitivity of the model to other particle sizes and times for aerosol growth has been explored. Results show that the CH 4 photolysis occurs at all latitudes, with a maximum rate at high northern latitudes and around 250 km in altitude. In all simulations, the haze extends to high altitudes, comparable to what has been observed by New Horizons. From 200 km altitude upwards, the density decreases with the altitude by one order of magnitude every 100 km, leading to a density scale height of typically 40 km above 60 km altitude. This is comparable to the typical haze brightness scale height of 50 km observed by New Horizons[START_REF] Cheng | Haze Layers in Pluto's Atmosphere[END_REF]. Without South Pole N 2 condensation, the meridional atmospheric circulation is dominated by the radiative heating but remains weak, even in the first kilometers above the surface. The haze precur-A C C E P T E D M A N U S C R I P Tsors remains at high altitudes and in larger amount at high northern latitudes. This leads to a higher density of haze in the summer hemisphere, decreasing with the latitudes. With South Pole N 2 condensation, the circulation is also weak in the upper atmosphere, except above the South Pole where a descending branch of air driven by the condensation of N 2 transports the precursors to lower altitudes. This leads to a distribution of haze latitudinally more homogeneous with a slight peak of haze density above the South Pole. This peak is reiforced by the circulation in the first kilometers above the surface, which is more intense and able to move light aerosols from the northern hemisphere towards the South Pole. In both climate scenarios, because of the generally weak meridional circulation, the computed mean atmospheric column mass of haze remains similar, and primarily depends on the sedimentation velocity and thus on the pressure and the considered monomer radius. In our simulations, the initial flux of Lyman-α at Earth remains constant between 1990 and 2015, but even if we consider the variable initial flux of Lyman-α, the flux of Lymanα at Pluto remains relatively constant. Consequently, the mean column mass of haze follows the trend in surface pressure, that is an increase by a factor of 3 between 1990 and 2015. Haze particles with a small radius remain longer in the atmosphere before reaching the surface. In our simulations, the sedimentation fall of 10 nm particles lasts about 3 terrestrial years, which could be enough time to form fractal aggregates. The mean column atmospheric mass of haze on Pluto is difficult to assess because it depends on many parameters.

C

  2 H 2 , C 2 H 4 and maybe other carbon-based gas in Pluto atmosphere, which A C C E P T E D M A N U S C R I P Tsuggests another pathway for carbon atoms formed by CH 4 photolysis. In addition, HCN has been detected, and the irreversible nature of its formation may lead to less nitrogen atoms available for the haze formation. The column mass of haze also strongly depends on the sedimentation radius of the haze particle, and to a lesser extent on the lifetime of the haze precursors. However, we computed the UV and VIS opacities of the haze as a diagnostic of our simulation results and in all simulation cases, the column visible opacities have similar values (same order of magnitude) around 0.001-0.01, and slightly higher values when considering large fractal particles. This is because the extinction factor of smaller particles is lower but is compensated by a larger mass of haze. These opacities are in the range of what has been estimated

  Comparing the haze distribution (obtained with and without South Pole N 2 condensation) with the observations (made by imaging with the instruments Ralph/MVIC and LORRI and by UV occultation with the Alice spectrometer) can help to reveal the presence or the absence of N 2 ice at the South Pole. A latitudinally homogeneous haze density with a slight peak above the North and particularly above the South Pole is typical of our simulation with South Pole N 2 condensation. Conversely, simulations without South Pole N 2 condensation show a more extensive haze in the summer hemisphere. Comparing the line of sight opacity profiles at the egress and the ingress points can also help to distinguish both cases. The opacity at the egress point is at least twice the opacity at the ingress point in the case without South Pole N 2 condensation, and no significant difference is obtained in the case without. However, a latitudinally homogeneous haze density can also be the results of a long characteristic time for precursors growth (several terrestrial years), that A C C E P T E D M A N U S C R I P T

Table 1 Comparison

 1

		Titan (at 400km)	Triton	Pluto
	Gravity (m 2 s -2 )	1.01	0.779	0.62
	Pressure (Pa)	1.5	1.4-1.9	1-1.1 a
	Visible normal opacity	0.07 b	0.003-0.008 c	0.004 a

of the incident UV flux and fraction of methane for a first order estimation of aerosol production rates on Titan, Triton and Pluto. The estimated rate P est is compared to the observed rate P lit , as detailed in the literature. a Stern et al. (2015) b Cours et al. (2011)

c

[START_REF] Rages | Voyager imaging of Triton's clouds and hazes[END_REF]

;

[START_REF] Krasnopolsky | Properties of haze in the atmosphere of Triton[END_REF]

Table 2

 2 Gravity,surface pressure and visible aerosol opacity on Pluto and Triton, compared to the the values encountered in the detached haze layer on Titan monomers, whereas the high forward scatter to back scatter ratio in the visible

	199
	200	suggests a much larger overall size of at least 200 nm. Although the haze may
	201	contain particles of diverse sizes and shapes depending on the altitude, these

Table 2

 2

	, Pluto's atmosphere contains 10 times less CH 4 and receives 10
	times less solar UV flux than Titan (relative to the atmospheric mass). Con-
	sequently, it is likely that CH 4 photolysis on Pluto leads to the formation of
	haze aerosols (and precursors) in lower quantities than on Titan. Compared
	to Triton, Pluto has similar surface pressure and gravity and its atmosphere
	contains 10 times more CH 4 , for a comparable UV flux. Thus, similar amounts
	of haze are expected on Pluto and Triton, depending on the accelerating or
	decelerating role of larger CH 4 amount. Stern et al. (2015) reported a visible
	normal opacity of 0.004 on Pluto, which is in the range of what has been

Table 4

 4

Acknowledgements

We wish to thank P. Rannou and E. Lellouch for helpful conversations and suggestions. We are grateful to P. Rannou for supplying a mean model of

A C C E P T E D M

A N U S C R I P T the optical indices of [START_REF] Rannou | Titan haze distribution and optical properties retrieved from recent observations[END_REF]. These indices have been updated 645 from [START_REF] Khare | The organic aerosols of Titan[END_REF] thanks to new sets of Cassini observations. For 50 646 nm particles, we obtain an extinction efficiency Q ext of 2.29 in UV and 0.19 647 in visible wavelengths. Using equation 7 with a density of aerosol material of 648 800 kg m -3 , we find that the haze column opacity in July 2015 reaches 0.077-649 0.17 (UV) and 0.0064-0.014 (VIS) in the summer hemisphere, in the reference

Fractal particles

654

The case of fractal particles can also be discussed. On Titan, an upper limit 655 of the maximum equivalent mass sphere radius (or bulk radius) of fractal 656 particles in the detached haze layer has been estimated to 300 nm, containing 657 up to 300 monomers [START_REF] Larson | Simulating Titan's aerosols in a three dimensional general circulation model[END_REF], while larger particles containing a 658 higher number of monomers are mostly found in the main haze atmosphere 659 of Titan, at lower altitudes. In fact, some aerosols of the detached haze layer 660 on Titan are large aggregates that grow within the main haze layer at lower 661 altitudes and that are lift up back to the detached layer by ascending currents 662 occurring in the summer hemisphere [START_REF] Rannou | A wind origin for Titan's haze structure[END_REF]Lebonnois et al., 663 2009). On Pluto, such mechanisms are not likely to occur because of the thin 664 atmosphere, and the size of fractal particles, if formed, should be limited.

665

Consequently, we consider only a small fractal particle with a limited amount 666 of monomers.

667

Fractal particles have a different optical behavior compared to spherical par-

is to investigate if another set of haze parameters can cause a more realistic aerosol distribution and concentration in the sunlit equatorial and summer atmosphere, compared to the observations. In addition, the sensitivity study aims to bracket the reality of Pluto's haze by analyzing extreme cases and compare them to both reference simulations. First, it has been checked that the haze production is insensitive to the amount of CH4 present in the upper atmosphere. Although the amount of CH4 molecules decreases in the upper atmosphere due to the absorption of incident photons and photolysis reactions, this loss remains negligible compared to the total amount of CH4 in Pluto's atmosphere. In addition, the production of haze precursors still occurs at high altitudes above 100 km even for low values of CH 4 mixing ratio. The ratio between the production rate of precursors at 100 km and the rate at 220 km (top of the model) becomes higher than 1% for a mean CH 4 mixing ratio of 0.04%, which is one order of magnitude less than the typical values found on Pluto. This confirms that the reaction is photon-limited and that different (and realistic) CH4 mixing ratio will not impact haze production and distribution.

Sensitivity to characteristic time for aerosol growth

The characteristic time for aerosol growth, defined in Section 4.4, is challenging to estimate. Here we consider two possible extreme values in the model.