Nolwenn Le Gall

Michel Pichavant

Experimental simulation of bubble nucleation and magma ascent in basaltic systems: Implications for Stromboli volcano

Keywords: Basalt, Stromboli, volatiles, magma degassing, magma ascent, bubble nucleation, fragmentation

The ascent of H 2 O-and H 2 O-CO 2 -bearing basaltic melts from the deeper to the shallower part of the Stromboli magmatic system and their vesiculation were simulated from decompression experiments. A well-studied "golden" pumice produced during an intermediate-to a large-scale paroxysm was used as starting material. Volatile-bearing glasses were synthesized at an oxygen fugacity (f O 2 ) ranging from NNO-1.4 to +0.9, 1200 °C and 200 MPa. The resulting crystal-and bubble-free glasses were then isothermally (1200 °C) decompressed to final pressures P f ranging between 200 and 25 MPa, at a linear ascent rate of 1.5 m/s (or 39 kPa/s) prior to be rapidly quenched. Textures of postdecompression glasses that were characterized by X-ray computed tomography result from different mechanisms of degassing that include bubble nucleation, growth, coalescence, and outgassing, as well as fragmentation. Homogeneous bubble nucleation occurs for supersaturation pressures (difference between saturation pressure and pressure at which bubbles start to form homogeneously, DP HoN ) ≤ 50 MPa. In the CO 2 -free melts, homogeneous nucleation occurs as two distinct events, the first at high P f (200-150 MPa) and the second at low P f (50-25 MPa) near the fragmentation level. In contrast, in the CO 2 -bearing melts, multiple events of homogeneous bubble nucleation occur over a substantial P f interval along the decompression path. Bubble coalescence occurs in both H 2 O-and H 2 O-CO 2 -bearing melts and is the more strongly marked between 100 and 50 MPa P f . The CO 2 -free melts follow equilibrium degassing until 100 MPa P f and are slightly supersaturated at 60 and 50 MPa P f , thus providing the driving force for the second bubble nucleation event. In comparison, disequilibrium degassing occurs systematically in the CO 2 -bearing melts that retain high CO 2 concentrations. Fragmentation was observed in some CO 2 -free charges decompressed to 25 MPa P f and is intimately associated with the occurrence of the second bubble nucleation event. Textures of H 2 O-CO 2 -bearing glasses reproduce certain critical aspects of the Stromboli natural textures (bubble number densities, shapes, sizes, and distributions) and chemistries (residual volatile concentrations). Average bubble sizes, bubble size distribution (BSD), and bubble number density (BND) data are used together to estimate that the "golden" pumice magmas ascend from their source region in 43 to 128 min.

iNtroductioN

Water and carbon dioxide, which are the two main volatile components dissolved in basalt magmas, control the physical processes involved in volcanic eruptions (e.g., [START_REF] Cashman | How volcanoes work: A 25 year perspective[END_REF]. As magma ascends to the Earth's surface, pressure decreases and this causes exsolution of the dissolved volatiles from the supersaturated melt. Accordingly, gas bubbles nucleate, grow, and coalesce as magma continues to ascend. The evolution of the gas phase within the volcanic conduit is thought to govern the eruptive behavior. The gas phase can either remain as bubbles within the melt ("closed-system" degassing) or escape from the magma ("open-system" degassing). The former case would lead to explosive behavior and the latter to effusive behavior (e.g., [START_REF] Gonnermann | Nonequilibrium magma degassing: Results from modeling of the ca. 1340 A.D. eruption of Mono Craters, California[END_REF]Manga 2005, 2007). As an illustration, Stromboli volcano (Aeolian Islands, Italy) is, among other basaltic volcanoes, characterized by various eruptive styles ranging from lava flows to mild Strombolian explosions to more violent explosions. Such a variety is thought to be controlled by the kinetics of magma vesiculation (bubble nucleation, growth, and coalescence) and fragmentation, as well as by changes in magma ascent rate [START_REF] Woods | Transitions between explosive and effusive eruptions of silicic magmas[END_REF][START_REF] Sparks | Dynamics of magma degassing[END_REF][START_REF] Edmonds | New geochemical insights into volcanic degassing[END_REF].

Studies of when and how gas bubbles form and separate from magma are needed to better understand whether a volcanic eruption is effusive or explosive [START_REF] Edmonds | New geochemical insights into volcanic degassing[END_REF]. Volcanic magma degassing, corresponding to the loss of dissolved volatiles, can be studied from different approaches. The first, including petrological studies and phase equilibria experiments, aims at determining the volatile compositions and concentrations in magma prior to significant degassing [START_REF] Edmonds | New geochemical insights into volcanic degassing[END_REF]) (e.g., Bertagnini et al. 2003;[START_REF] Métrich | Triggering mechanism at the origin of paroxysms at Stromboli (Aeolian Archipelago, Italy): the 5 April 2003 eruption[END_REF][START_REF] Métrich | Conditions of magma storage, degassing and ascent at Stromboli: new insights into the volcano plumbing system with inferences on the eruptive dynamics[END_REF][START_REF] Di Carlo | Experimental crystallization of a high-K arc basalt: The Golden Pumice, Stromboli Volcano (Italy)[END_REF][START_REF] Pichavant | Experimental constraints on the deep magma feeding system at Stromboli volcano, Italy[END_REF][START_REF] Pichavant | Petrography, mineralogy and geochemistry of a primitive pumice from Stromboli: implications for the deep feeding system[END_REF]. Volatile solubility models (e.g., [START_REF] Newman | VolatileCalc: a silicate melt-H 2 O-CO 2 solution model written in Visual Basic for Excel[END_REF][START_REF] Papale | The compositional dependence of the saturation surface of H 2 O+CO 2 fluids in silicate melts[END_REF][START_REF] Iacono-Marziano | New experimental data and semi-empirical parameterization of H 2 O-CO 2 solubility in mafic melts[END_REF] play an important role. The second, including textural and geochemical studies, deals with the exsolved, integrated products of degassing [START_REF] Edmonds | New geochemical insights into volcanic degassing[END_REF]) (e.g., [START_REF] Mangan | The structure of basaltic scoria and reticulite and inferences for vesiculation, foam formation, and fragmentation in lava fountains[END_REF][START_REF] Gaonac'h | Scaling effects on vesicle shape, size and heterogeneity of lavas from Mount Etna[END_REF][START_REF] Lautze | Linking variable explosion style and magma textures during 2002 at Stromboli volcano, Italy[END_REF][START_REF] Polacci | Threedimensional investigation of volcanic textures by X-ray microtomography and implications for conduit processes[END_REF][START_REF] Polacci | Large vesicles record pathways of degassing at basaltic volcanoes[END_REF][START_REF] Polacci | Vesiculation in magmas from Stromboli and implications for normal Strombolian activity and paroxysmal explosions in basaltic systems[END_REF]Burton et al. 2007;Allard 2010;Aiuppa et al. 2010aAiuppa et al. , 2011). In addition, numerical models are becoming available to simulate the physical (textures) and chemical (volcanic gases, volatile solubilities) evolution of gas bubbles and melt during degassing (e.g., Blower et al. 2001Blower et al. , 2002;;Toramaru 2006;Burgisser et al. 2015). However, none of these two main approaches are completely satisfactory. Volatile solubility models as well as the interpretation of volcanic gas data assume gas-melt equilibrium degassing of basaltic magmas, while recent experiments [START_REF] Pichavant | Generation of CO 2 -rich melts during basalt magma ascent and degassing[END_REF][START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF] have reported the possibility of disequilibrium degassing during ascent and decompression of CO 2 -bearing basaltic melts. There are also problems and disagreements associated with the interpretation of textural and chemical data in natural eruption products [START_REF] Gaonac'h | Scaling effects on vesicle shape, size and heterogeneity of lavas from Mount Etna[END_REF]Blower et al. 2001Blower et al. , 2002;;[START_REF] Edmonds | New geochemical insights into volcanic degassing[END_REF].

In complement to these two main approaches, high-pressure and temperature-decompression experiments (e.g., [START_REF] Hurwitz | Bubble nucleation in rhyolitic melts: Experiments at high pressure, temperature, and water content[END_REF][START_REF] Gardner | Experimental constraints on degassing of magma: isothermal bubble growth during continuous decompression from high pressure[END_REF][START_REF] Mourtada-Bonnefoi | Experimental study of homogeneous bubble nucleation in rhyolitic magmas[END_REF]Mangan andSisson 2000, 2005;[START_REF] Mourtada-Bonnefoi | Experimental study of homogeneous bubble nucleation in rhyolitic magmas[END_REF]Laporte 2002, 2004;[START_REF] Iacono-Marziano | Equilibrium and disequilibrium degassing of a phonolitic melt (Vesuvius AD 79 "white pumice") simulated by decompression experiments[END_REF][START_REF] Cluzel | Kinetics of heterogeneous bubble nucleation in rhyolitic melts: implications for the number density of bubbles in volcanic conduits and for pumice textures[END_REF][START_REF] Gardner | Bubble nucleation in rhyolite and dacite melts: temperature dependence of surface tension[END_REF] have the advantage to simulate the vesiculation process during magma ascent. Therefore, in an attempt to assist in the interpretation of textural and chemical data collected on basaltic eruptive products, we performed experimental simulations of the ascent and degassing of H 2 O-and H 2 O-CO 2 -bearing Stromboli melts. The run products were texturally and chemically characterized to model the behavior of the major volatiles (H 2 O, CO 2 ) during decompression and, in particular, to assess the effect of ascent rate on the degassing kinetics. Our results bring direct constraints on degassing processes at Stromboli, which is one representative example of explosive basaltic volcanoes [START_REF] Rosi | Stromboli volcano, Aeolian Islands (Italy): present eruptive activity and hazards[END_REF]. It is also a very well-studied system and melt inclusion data (e.g., Bertagnini et al. 2003;[START_REF] Métrich | Triggering mechanism at the origin of paroxysms at Stromboli (Aeolian Archipelago, Italy): the 5 April 2003 eruption[END_REF][START_REF] Métrich | Conditions of magma storage, degassing and ascent at Stromboli: new insights into the volcano plumbing system with inferences on the eruptive dynamics[END_REF] and gas measurements (e.g., Burton et al. 2007;Aiuppa et al. 2010aAiuppa et al. , 2010bAiuppa et al. , 2011;;[START_REF] Spina | New insights into volcanic processes at Stromboli from Cerberus, a remote-controlled open-path FTIR scanner system[END_REF]) are available. In addition, H 2 O and CO 2 solubility data (both models and experiments, [START_REF] Newman | VolatileCalc: a silicate melt-H 2 O-CO 2 solution model written in Visual Basic for Excel[END_REF][START_REF] Shishkina | Solubility of H 2 O-and CO 2 -bearing fluids in tholeiitic basalts at pressures up to 500MPa[END_REF]Lesne et al. 2011aLesne et al. , 2011b) ) allow detailed interpretation of natural products.

volcaNoloGical backGrouNd

Stromboli is a basaltic volcano located in the Aeolian Islands, Italy. It is well known for its persistent explosive activity established 1300-1700 yr ago [START_REF] Rosi | Onset of the persistent activity at Stromboli volcano (Italy)[END_REF]. This normal activity, which consists of rhythmic, mild to moderate explosions lasting a few seconds (e.g., [START_REF] Rosi | Stromboli volcano, Aeolian Islands (Italy): present eruptive activity and hazards[END_REF]) is associated with a continuous degassing dominated by H 2 O, CO 2 , and SO 2 (Aiuppa et al. 2010a). Every 10-20 min, scoriaceous lapilli and bombs, ash, and lithic blocks are ejected to heights of a few tens to hundreds of meters above the summit craters [START_REF] Rosi | Onset of the persistent activity at Stromboli volcano (Italy)[END_REF]Bertagnini et al. 2003;[START_REF] Francalanci | The volcanic activity of Stromboli in the 1906-1998 AD period: mineralogical, geochemical and isotope data relevant to the understanding of the plumbing system[END_REF]). According to Burton et al. (2007), such explosions result from the buoyant rise of deep-sourced (<3 km) gas slugs. This normal Strombolian activity can be suddenly interrupted by lava flows, and by violent explosions of variable scale defined as Strombolian paroxysms [START_REF] Mercalli | Vulcani attivi della Terra[END_REF][START_REF] Rosi | Stromboli volcano, Aeolian Islands (Italy): present eruptive activity and hazards[END_REF]. Paroxysms range from small-scale [START_REF] Métrich | Triggering mechanism at the origin of paroxysms at Stromboli (Aeolian Archipelago, Italy): the 5 April 2003 eruption[END_REF]Bertagnini et al. 2008;[START_REF] Rosi | Stromboli volcano, Aeolian Islands (Italy): present eruptive activity and hazards[END_REF], also designated as "major explosions" (Barberi et al. 1993), to large-scale, the latter often called paroxysms for simplicity (Bertagnini et al. 2011;[START_REF] Rosi | Stromboli volcano, Aeolian Islands (Italy): present eruptive activity and hazards[END_REF]). These more violent explosions occur at a rate from 1.7 episodes per year [START_REF] Rosi | Stromboli volcano, Aeolian Islands (Italy): present eruptive activity and hazards[END_REF]) to 1-10 episodes per century [START_REF] Pichavant | Experimental constraints on the deep magma feeding system at Stromboli volcano, Italy[END_REF]. During these highly energetic events, fallouts of meter-sized bombs and blocks, gas and ash, are produced and ejected up to a few kilometers from the vents.

These three types of eruptive activity at Stromboli are fed by two distinct magmas: a volatile-poor black scoria and a volatilerich yellowish pumice (designated as "golden" pumice; [START_REF] Métrich | Crystallization driven by decompression and water loss at Stromboli volcano (Aeolian Islands, Italy)[END_REF]Bertagnini et al. 2003Bertagnini et al. , 2008)). The former, which supplies normal Strombolian activity and lava flows, is highly porphyritic (~50 vol% crystals of plagioclase, clinopyroxene, and olivine; [START_REF] Landi | Dynamics of magma mixing and degassing recorded in plagioclase at Stromboli (Aeolian Archipelago, Italy)[END_REF][START_REF] Pichavant | Petrography, mineralogy and geochemistry of a primitive pumice from Stromboli: implications for the deep feeding system[END_REF]. In contrast, the latter, commonly produced during the paroxysms, has low porphyricity (~10 vol% crystals of clinopyroxene, olivine, and plagioclase; e.g., [START_REF] Francalanci | The volcanic activity of Stromboli in the 1906-1998 AD period: mineralogical, geochemical and isotope data relevant to the understanding of the plumbing system[END_REF][START_REF] Pichavant | Petrography, mineralogy and geochemistry of a primitive pumice from Stromboli: implications for the deep feeding system[END_REF]). The present-day feeding system is thought to comprise a shallow reservoir hosting the black scoria magmas, recharged with the periodic arrival of "golden" pumice magmas from a deeper crustal reservoir [START_REF] Pichavant | Experimental constraints on the deep magma feeding system at Stromboli volcano, Italy[END_REF][START_REF] Pichavant | Petrography, mineralogy and geochemistry of a primitive pumice from Stromboli: implications for the deep feeding system[END_REF][START_REF] Métrich | Conditions of magma storage, degassing and ascent at Stromboli: new insights into the volcano plumbing system with inferences on the eruptive dynamics[END_REF]. Both magmas are often intermingled, and crystals in the "golden" pumices mainly come from the black scoria because of syn-eruptive mingling between the two magma types (e.g., Di [START_REF] Di Carlo | Experimental crystallization of a high-K arc basalt: The Golden Pumice, Stromboli Volcano (Italy)[END_REF].

Strombolian paroxysms constitute a serious hazard for inhabitants and visitors, due to their high intensity and potential to strike inhabited areas [START_REF] Rosi | Stromboli volcano, Aeolian Islands (Italy): present eruptive activity and hazards[END_REF]. Development of the monitoring system because the 2002-2003 crisis now allows to daily collect a large body of geochemical and geophysical data (e.g., [START_REF] Ripepe | Dynamics of the 5 April 2003 explosive paroxysm observed at Stromboli by a near-vent thermal, seismic and infrasonic array[END_REF][START_REF] Rosi | Stromboli volcano, Aeolian Islands (Italy): present eruptive activity and hazards[END_REF]. Continuous measurements of CO 2 and SO 2 emissions have evidenced significant changes in the chemical composition of the gases between quiescent, passive degassing and eruptions (Burton et al. 2007;Aiuppa et al. 2009Aiuppa et al. , 2010aAiuppa et al. , 2010bAiuppa et al. , 2011;;[START_REF] Spina | New insights into volcanic processes at Stromboli from Cerberus, a remote-controlled open-path FTIR scanner system[END_REF]. Concerning Strombolian paroxysms, these appear systematically preceded by medium-term (days to weeks) increases of CO 2 fluxes (Aiuppa et al. 2010a(Aiuppa et al. , 2010b(Aiuppa et al. , 2011)). Two main models have been proposed to explain these observations. According to Bertagnini et al. (2003) and [START_REF] Métrich | Crystallization driven by decompression and water loss at Stromboli volcano (Aeolian Islands, Italy)[END_REF][START_REF] Métrich | Triggering mechanism at the origin of paroxysms at Stromboli (Aeolian Archipelago, Italy): the 5 April 2003 eruption[END_REF][START_REF] Métrich | Conditions of magma storage, degassing and ascent at Stromboli: new insights into the volcano plumbing system with inferences on the eruptive dynamics[END_REF], the more violent explosions would be generated by the rapid ascent, decompression, and fragmentation of a volatile-rich, low-porphyritic magma ("golden" pumice) batch. Alternatively, Allard (2010) suggests that such events would result from the bursting of CO 2 -rich gas slugs generated at 8-10 km depth. In addition, [START_REF] Pichavant | Generation of CO 2 -rich melts during basalt magma ascent and degassing[END_REF] have proposed that Strombolian paroxysms would be driven by explosive degassing and fragmentation of CO 2 -oversaturated melts produced as a result of disequilibrium degassing during ascent.

exPeriMeNtal Methods

Two types of experiments were performed: synthesis and decompression. The synthesis experiments were conducted to generate the bubble-free H 2 O-and H 2 O-CO 2 -bearing basaltic melts to be used in the decompression experiments, to simulate their ascent.

Scaling of the decompression experiments

Experimental conditions (P, T, basaltic composition, dissolved H 2 O/CO 2 , ascent rate, and f O2 ) were scaled against Stromboli. In this way, the initial pressure (P in = 200 MPa) chosen in the decompression experiments is consistent with the depth of the storage region of "golden" pumice melts (around 7.5 km, Di Carlo et al. 2006;[START_REF] Pichavant | Experimental constraints on the deep magma feeding system at Stromboli volcano, Italy[END_REF][START_REF] Métrich | Conditions of magma storage, degassing and ascent at Stromboli: new insights into the volcano plumbing system with inferences on the eruptive dynamics[END_REF]. Final pressures (P f = 200-25 MPa) correspond to different heights in the volcanic conduit. The temperature (T = 1200 °C and kept constant) was chosen to be above the liquidus of "golden" pumice melts, on the basis of previous phase-equilibrium experiments [START_REF] Di Carlo | Experimental crystallization of a high-K arc basalt: The Golden Pumice, Stromboli Volcano (Italy)[END_REF][START_REF] Pichavant | Experimental constraints on the deep magma feeding system at Stromboli volcano, Italy[END_REF]. All experiments were performed with the same basaltic composition representative of "golden" pumice melts involved in the present-day activity at Stromboli [START_REF] Francalanci | Volcanological and magmatological evolution of Stromboli volcano (Aeolian Islands): the roles of fractional crystallization, magma mixing, crustal contamination and source heterogeneity[END_REF][START_REF] Francalanci | Geochemical and isotopic variations in the calc-alkaline rocks of Aeolian arc, southern Tyrrhenian Sea, Italy: constraints on magma genesis[END_REF][START_REF] Francalanci | The volcanic activity of Stromboli in the 1906-1998 AD period: mineralogical, geochemical and isotope data relevant to the understanding of the plumbing system[END_REF][START_REF] Di Carlo | Experimental crystallization of a high-K arc basalt: The Golden Pumice, Stromboli Volcano (Italy)[END_REF]. The pre-decompression ranges of volatile concentrations (0.71-4.94 wt% H 2 O, 818-1094 ppm CO 2 ) investigated overlap with the H 2 O and CO 2 concentrations in Stromboli melt inclusions (e.g., [START_REF] Métrich | Conditions of magma storage, degassing and ascent at Stromboli: new insights into the volcano plumbing system with inferences on the eruptive dynamics[END_REF]. Concerning the ascent rate, there is a large uncertainty on Stromboli. On the one hand, an ascent rate of 3 mm/s [START_REF] Calvari | Lava effusion-A slow fuse for paroxysms at Stromboli volcano?[END_REF] implies that "golden" magmas would ascend from 7-8 km depth in about 1 month. This seems much too slow because "golden" pumices lack microlites, which implies ascent durations of a maximum of 10 h [START_REF] Di Carlo | Experimental crystallization of a high-K arc basalt: The Golden Pumice, Stromboli Volcano (Italy)[END_REF][START_REF] Pichavant | Petrography, mineralogy and geochemistry of a primitive pumice from Stromboli: implications for the deep feeding system[END_REF]. On the other hand, an ascent velocity of 32 m/s has been proposed from Stromboli melt viscosity data [START_REF] Misiti | Viscosity of high-K basalt from the 5th April 2003 Stromboli paroxysmal explosion[END_REF], implying an ascent time of only a few minutes from 7-8 km depth. In this study an average ascent rate value of 1.5 m/s was investigated more in line with the petrological constraints (<10 h). This value is in the average of ascent rates determined for Vulcanello shoshonite magmas (0.27-3.2 m/s; [START_REF] Vetere | The viscosity of shoshonitic melts (Vulcanello Peninsula, Aeolian Islands, Italy): insight on the magma ascent in dikes[END_REF], a system closely similar to that of Stromboli [START_REF] Pichavant | Generation of CO 2 -rich melts during basalt magma ascent and degassing[END_REF]. Concerning the redox state, oxidizing redox conditions around DNNO = +0.5 (where NNO is the nickel-nickel oxide buffer) were determined for the near-liquidus evolution of "golden" pumice melts [START_REF] Di Carlo | Experimental crystallization of a high-K arc basalt: The Golden Pumice, Stromboli Volcano (Italy)[END_REF][START_REF] Pichavant | Experimental constraints on the deep magma feeding system at Stromboli volcano, Italy[END_REF]) and this f O2 range was imposed in our decompression experiments.

Starting material

The starting material used for the experiments is a high-K basalt from a paroxysmal explosion (PST-9 "golden" pumice, Di [START_REF] Di Carlo | Experimental crystallization of a high-K arc basalt: The Golden Pumice, Stromboli Volcano (Italy)[END_REF][START_REF] Pichavant | Experimental constraints on the deep magma feeding system at Stromboli volcano, Italy[END_REF][START_REF] Pichavant | Petrography, mineralogy and geochemistry of a primitive pumice from Stromboli: implications for the deep feeding system[END_REF]. The whole-rock composition of this pumice sample is shown in Table 1. PST-9 is highly vesicular (~60 vol% vesicles) and slightly porphyritic (~11 vol%; [START_REF] Pichavant | Petrography, mineralogy and geochemistry of a primitive pumice from Stromboli: implications for the deep feeding system[END_REF], within the range of other pumices. A homogeneous starting glass was obtained by crushing the PST-9 pumice and melting the fine powder at 1400 °C, 1 atm, during 3 h, in a Pt crucible (Table 1). The resulting crystal-and bubble-free glass was then cored to cylinders with a diameter of 2.5 and, less frequently, 5 mm and typical lengths around 10 and 6 mm, respectively. The 5 mm diameter was tested to explore the influence of sample size on bubble nucleation.

For the synthesis experiments (Table 2), the glass cylinders were loaded into capsules (1.5-3 cm length, 2.5 or 5 mm internal diameter, 0.2 wall thickness) made of Au 80 Pd 20 . Such a metal composition was used to minimize iron loss during the experiments [START_REF] Di Carlo | Experimental crystallization of a high-K arc basalt: The Golden Pumice, Stromboli Volcano (Italy)[END_REF][START_REF] Pichavant | Experimental constraints on the deep magma feeding system at Stromboli volcano, Italy[END_REF]. Distilled water and carbon dioxide as silver oxalate (Ag 2 C 2 O 4 ) were used as volatile sources. Three different proportions of H 2 O and CO 2 were introduced in the capsules, corresponding to X H2Oin [molar H 2 O/(H 2 O+CO 2 )] = 1 (series #1: only H 2 O dissolved in glass, no CO 2 present), 0.25-0.56 (series #2: H 2 O and CO 2 both dissolved in glass, high dissolved H 2 O/CO 2 ), and 0 (series #3: H 2 O and CO 2 both dissolved in glass, low dissolved H 2 O/CO 2 , see below for the origin of H 2 O). For the 5 mm diameter cores, only X H2Oin = 1 conditions were investigated, because homogenization of melt CO 2 concentrations would have required a prohibitively long experimental duration [START_REF] Zhang | Diffusion of H, C, and O components in silicate melts[END_REF]. In one of the synthesis experiments (S5, Table 2), a separate Ni-NiPd sensor capsule was included for the determination of the experimental f H2 . It consisted of two pellets of NiPd metal mixtures (with different Ni/Pd ratio) plus NiO, placed in a Pt capsule in the presence of excess H 2 O [START_REF] Taylor | The calibration and application of accurate redox sensors[END_REF].

For the decompression experiments (Table 3), the synthesized volatilebearing glass cores (2.5 or 5 mm in diameter and about 4 mm long) were fitted into Au 80 Pd 20 capsules without further addition of volatiles. Capsules of identical internal diameter (2.5 and 5 mm) but variable lengths (from 1 to 5 cm for the capsules decompressed to the lowest pressures) were used to accommodate gas expansion during decompression.

Capsules were weighed before and after welding to ensure that no leaks occurred.

Equipment

All experiments were carried out in an internally heated pressure vessel (IHPV), working vertically and equipped with a rapid-quench device. The vessel was pressurized with Ar-H 2 mixtures obtained by sequential loading of H 2 and Ar at room temperature [START_REF] Scaillet | Improvements of the Shaw membrane technique for measurement and control of f H2 at high temperatures and pressures[END_REF]. The synthesis and decompression experiments were performed with an initial H 2 pressure of 1 bar and experimental f H2 measured in one run with a redox sensor (see above). Then, Ar was pumped into the IHPV up to the pressure needed to attain the final target conditions [START_REF] Pichavant | Generation of CO 2 -rich melts during basalt magma ascent and degassing[END_REF]. Total pressure was recorded continuously by a transducer calibrated against a Heise gauge with an accuracy of ±20 bars. The capsules were placed together in a sample holder made of an alumina tube and suspended by a thin Pt wire in a molybdenum furnace having a 2-3 cm long hotspot. Temperature was measured using two S-type thermocouples placed along the length of the capsules and recorded continuously (uncertainty ±5 °C) with a Eurotherm controller. Near-isothermal conditions (gradient <2-3 °C/cm) were maintained in the sample holder. At the end of the synthesis and decompression experiments, the Pt suspension wire was fused electrically, allowing the sample holder to fall into the cold part of the vessel, leading to a cooling rate of about 100 °C/s [START_REF] Di Carlo | Experimental crystallization of a high-K arc basalt: The Golden Pumice, Stromboli Volcano (Italy)[END_REF].

Run procedure

All synthesis and decompression experiments were performed independently from each other.

The synthesis experiments were performed at 200 MPa and 1200 °C (Table 2), [START_REF] Gall | Basaltic magma ascent and degassing-Experimental approach[END_REF]. X H2Oin = initial molar H 2 O/(H 2 O+CO 2 ) in the charge. T = run temperature; P = run pressure; t = duration of the synthesis experiment. a ~2.50 wt% H 2 O (see text for explanation).

which are conditions known to be above the PST-9 liquidus on the basis of previous phase-equilibrium experiments [START_REF] Di Carlo | Experimental crystallization of a high-K arc basalt: The Golden Pumice, Stromboli Volcano (Italy)[END_REF][START_REF] Pichavant | Experimental constraints on the deep magma feeding system at Stromboli volcano, Italy[END_REF]. Up to four capsules (one for each series plus the sensor capsule) were placed together in the IHPV for duration of about 40 h. According to H 2 O and CO 2 melt diffusion calculations [START_REF] Zhang | Diffusion of H, C, and O components in silicate melts[END_REF], initial experiments have shown that such a duration is sufficient to attain an equilibrium distribution of dissolved H 2 O and CO 2 in the 2.5 mm diameter melt cores (Le Gall and Pichavant 2016). For the 5 mm diameter melt core, a run duration of 24 h was long enough to dissolve water and attain an equilibrium distribution. The synthesized crystal-and bubble-free glasses were used as starting materials in the decompression experiments (Table 3).

Each decompression run included up to three capsules (one for each series, Table 3). The experiments were conducted at a constant temperature of 1200 °C, from an initial pressure (P in ) of 200 MPa to final pressures (P f ) ranging between 200 (no decompression) and 25 MPa. The 5 mm diameter glass cylinder was decompressed to 60 MPa P f . All runs began with a step of approximately 1 h at 200 MPa and 1200 °C, to re-equilibrate the starting volatile-bearing glasses. Pressure was then released manually to P f at a decompression rate of 39 kPa/s (or 1.5 m/s taking a rock density of 2650 kg/m 3 ), which leads to decompression durations of 20-75 min depending on P f . Immediately after attainment of P f , decompression charges were rapid-quenched (within ~1-2 s) to freeze the glass textures and chemistries.

After the quench, capsules were weighted to check for leaks and then opened.

aNalytical Methods

Sample preparation

After each synthesis experiment, a part of the glass cylinder (one for each series) was analyzed by IR spectroscopy to check for the homogeneity of H 2 O and CO 2 concentrations and distributions. To do so, sections were cut perpendicularly (initial pressure) = pressure at the beginning of decompression ramp; P f (final pressure) = pressure at which the experiment was quenched; t ramp = duration of the ramp; |dP/dt| = decompression/ascent rate [= 10 6 (P in -P f )/(gdt ramp )], with g = 9.81 m/s 2 and d = 2650 kg/m 3 (d = average density of crustal rocks); nd = not determined. X-ray microtomographic data acquired on entire charges (except V d ). n = number of bubbles counted in the analyzed volume. peak size = main peak diameter in bubble size distribution histograms. Range = total range of bubble diameters. D = average bubble diameter. V Equi.H2O and V Equi.CO2 = equilibrium vesicularities computed for the PST-9 composition considering the degassing of pure H 2 O and pure CO 2 , respectively (see text for details). a BND = bubble number density expressed in number of bubbles per mm 3 of the total sample (glass + bubbles). b BND melt = bubble number density per melt volume (without bubbles, following [START_REF] Proussevitch | Statistical analysis of bubble and crystal size distributions: Formulations and procedures[END_REF]). S = average spacing between bubbles calculated from BND melt [S = (3/4pBND melt ) 1/3 ; [START_REF] Lyakhovsky | Bubble growth in rhyolitic melts: experimental and numerical investigation[END_REF][START_REF] Polacci | Threedimensional investigation of volcanic textures by X-ray microtomography and implications for conduit processes[END_REF]]. c V = vesicularity (volume fraction of bubbles, vol%) measured from the total sample. d V = vesicularity measured from representative sub-volumes. e Textural data on the first bubble population of D24#1 charge. f Textural data on the second bubble population of D24#1 charge. g Standard deviation.

to the long axis of the glass cylinders, double-polished, and analyzed.

After the decompression experiments, the glass cylinders were carefully removed from their capsules. Their texture was studied by X-ray microtomography (the analysis is performed on the entire charge). Then, the glasses were subdivided into several sections, again cut perpendicularly to the cylinder long axis. One of these sections (or several sections when numerous analyses were needed) was double-polished for the determination of volatile concentrations dissolved in the glass, by IR spectroscopy. Another section was embedded into epoxy resin and polished for scanning electron microscope (SEM) observations.

The metallic pellets in the sensor capsule were also recovered, mounted in epoxy resin, and then analyzed by electron microprobe.

Textural analyses

We used the Phoenix Nanotom 180 at ISTO, Orléans, to perform X-ray computed tomography (X-ray CT) analyses of each post-decompression charge. Between 1000 and 1100 projection images were collected from the 360° rotation of the samples, using a tungsten filament and either a molybdenum (most of the time) or a tungsten (more rarely) target. During the acquisition of the X-ray CT scans, the glass cylinders were mounted on carbon fiber rods with thermoplastic adhesive. Operating voltages ranged from 90 to 110 kV, with filament currents of 58-170 mA. Voxel edge lengths ranged between 2.78 and 6.77 mm, and they represent the minimum bubble sizes that can be detected. Reconstruction of the projections into a stack of grayscale images was performed with a Phoenix program (datos|x reconstruction). Then, a complete three-dimensional reconstruction of the sample was produced using the ImageJ software package (Abràmoff et al. 2004). This allows the determination of the textural parameters [individual bubble volume, individual bubble size (D) calculated from volume assuming a spherical shape, bubble number density (BND) defined as the number of bubbles per unit volume of melt, average spacing between bubbles (S) and vesicularity (V), see Table 3], following the procedure described in Le [START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF]. Image analysis was performed either on entire X-ray CT data set (V c determination, Table 3) or on four representative sub-volumes of each sample (V d determination, Table 3). For charge D24#1 (Fig. 1c), the population of very large interconnected voids opened toward the exterior of the charge were counted as bubbles. Their sizes and number densities were estimated from two-dimensional tomographic slices.

For comparison with the vesicularities measured in our run products, theoretical vesicularities generated from equilibrium degassing were computed for the PST-9 melt composition, as detailed in Le [START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF]. Two end-member cases were considered corresponding to the equilibrium degassing of pure H 2 O and pure CO 2 gas, respectively.

A limited number of samples was examined by scanning electron microscopy (SEM), to check for the presence of bubbles that cannot be detected by X-ray CT because of their size (<4 mm). SEM images were collected using the MIRA3 TESCAN FEG instrument at ISTO, Orléans. An accelerating voltage of 15-25 kV was applied.

Glass volatile concentrations

H 2 O and CO 2 contents in the samples were determined by Fourier transform infrared spectroscopy (FTIR). We used a Nicolet 6700 spectrometer and a Continumm FTIR microscope, together with an IR source, a KBr beamsplitter, and a MCT/A detector (mercury, cadmium, tellurium). Punctual analyses and concentration profiles, to control the homogeneity of the starting glass cores and the distribution of the volatiles, were performed with a 50 mm diameter spot. FTIR spectra were acquired between 650 and 7000 cm -1 on doubly polished samples (18-207 mm) from 128 scans collected at a resolution of 4 cm -1 . H 2 O and CO 2 concentrations (C, wt%) were calculated from the Beer-Lambert law, as (e.g., [START_REF] Métrich | 2001 flank eruption of the alkali-and volatile-rich primitive basalt responsible for Mount Etna's evolution in the last three decades[END_REF]):

C = 100 ⋅ A⋅ M ε ⋅ρ ⋅ e (1)
where A is the absorbance (measured at 3530 cm -1 for H 2 O and at 1515 cm -1 for CO 2 ), M the molar mass of the species (g/mol), ɛ the molar absorptivity [L/(mol•cm)], r the glass density (g/cm 3 ), and e the sample thickness (cm) measured with an optical microscope.

Absorbance of the 3530 cm -1 total H 2 O band was measured with a straight base line, and that of the 1515 cm -1 carbonate ions band was determined by subtracting a spectrum obtained on a glass with no dissolved volatiles. For H 2 O we considered a ɛ of 64 L/(mol•cm) (Dixon et al. 1995) and for CO 2 , we calculated a ɛ of 363 L/(mol•cm) from the equation of [START_REF] Dixon | Determination of the molar absorptivity of dissolved carbonate in basanitic glass[END_REF], as ɛ 1525 = 451-342 [Na/ (Ca+Na)]. Densities of the experimental glasses were calculated using the method of [START_REF] Richet | Water and the density of silicate glasses[END_REF], using the measured density of the anhydrous starting glass (r = 2.747 ± 0.001). With this method we consider only the amount of water dissolved in the glass and assume that the quantity of CO 2 dissolved does not significantly affect densities [START_REF] Lange | The effect of H 2 O, CO 2 , and F on the density and viscosity of silicate melts[END_REF]Bourgue and Richet 2001;Lesne et al. 2011a). Analytical uncertainties on volatile concentrations in glasses are ±0.1 wt% (H 2 O) and ±100 ppm (CO 2 ).

Equilibrium gas-melt computations (volatile solubilities as a function of P-T conditions, isobaric solubility curves, and closed-system degassing paths) were calculated with the VolatileCalc model of [START_REF] Newman | VolatileCalc: a silicate melt-H 2 O-CO 2 solution model written in Visual Basic for Excel[END_REF], for a basalt with 49 wt% SiO 2 . H 2 O and CO 2 contents in glasses from the synthesis experiments and from the series #1 decompression experiments were also compared with the recent experimental solubilities of Lesne et al. (2011aLesne et al. ( , 2011b) ) and [START_REF] Shishkina | Solubility of H 2 O-and CO 2 -bearing fluids in tholeiitic basalts at pressures up to 500MPa[END_REF], determined for a pressure of 200 MPa and temperatures of 1200-1250 °C.

Electron microprobe analyses of metallic sensor phases were performed with the Cameca SX-50 at Orléans. Analyses were carried out under an acceleration voltage of 20 kV, counting times of 10 s, and a sample current of 20 nA.

exPeriMeNtal results

Redox conditions

The mole fraction of Ni in the alloy phase of the sensor capsule (X Ni ) indicated a f H 2 of 9 bar. This translates to f O 2 conditions in the synthesis experiments ranging from NNO-1.4 (series #3) to NNO+0.1 (series #2) to NNO+0.9 (series #1) depending on the H 2 O concentrations (and thus the f H 2 O ) in the three experimental series (NNO is the f O 2 of the Ni-NiO equilibrium at the P-T of interest). The f O 2 conditions determined for series #1 and #2 melts are close to the f O 2 around NNO+0.5 determined for the near-liquidus evolution of "golden" pumice melts [START_REF] Di Carlo | Experimental crystallization of a high-K arc basalt: The Golden Pumice, Stromboli Volcano (Italy)[END_REF]. It is worth noting that the f O 2 determined for series #3 melts is more reduced, because of the lower melt H 2 O concentrations (and so lower f H 2 O ) measured in this series (see below).

H 2 O and CO 2 concentrations in starting glasses

The volatile contents of the crystal-and bubble-free glasses from the synthesis experiments (hereafter designated as predecompression glasses) are presented in Table 2. No concentration gradients of either H 2 O or CO 2 were observed on FTIR profiles from capsule walls toward glass cores. If the standard deviations and analytical errors for the volatile concentration measurements are considered, the pre-decompression glasses have homogeneous H 2 O and CO 2 concentrations.

Starting glasses divide into three compositional groups according to the synthesis conditions (Table 2). Series #1 glasses contain about 4.92 ± 0.02 wt% dissolved H 2 O and no CO 2 . 3 for details about the experimental conditions and textural results.

Water-saturated conditions were confirmed in series #1 charges by the presence of water bubbles hissing out from the capsules during their opening (Lesne et al. 2011b). The H 2 O concentration measured in sample S8#1 is clearly lower (2.53 ± 0.05 wt%, Table 2) and thus appears anomalous, being excluded from the average. Actually, H 2 O loss occurred in this charge during the experiment. Series #2 glasses have between 1.95 and 2.37 wt% H 2 O and from 818 to 1011 ppm CO 2 (Table 2). One synthesis charge has a clearly lower H 2 O content (0.58 wt%, S4#2) than the others. This deviation is related to an analytical problem (in spite of multiple checks, the analytical problem persisted). The glass decompressed from S4#2 to P f = P in = 200 MPa (D3#2 charge) was found to contain a reasonable H 2 O concentration (2.45 wt%, Tables 3 and5 1 ). Therefore, the H 2 O content of charge S4#2 is estimated to be around 2.5 wt%. Apart from S4#2, the series #2 volatile concentrations are within the range of melt inclusions in Stromboli "golden" pumices (H 2 O = 1.8-3.4 wt%, CO 2 = 894-1689 ppm; [START_REF] Métrich | Crystallization driven by decompression and water loss at Stromboli volcano (Aeolian Islands, Italy)[END_REF][START_REF] Métrich | Conditions of magma storage, degassing and ascent at Stromboli: new insights into the volcano plumbing system with inferences on the eruptive dynamics[END_REF]Bertagnini et al. 2003). Although water was not initially added in series #3 capsules (X H 2 O in = 0, Table 2), this volatile component was found dissolved in all series #3 pre-decompression glasses (concentration range: 0.71-1.12 wt%, Table 2). Glass CO 2 concentrations are of the order of 850-1100 ppm. H 2 O is generated through the reduction of the Fe 3+ of the melt during synthesis, because of the pressurization of the vessel with H 2 . The reduction reaction can be written (e.g., Lesne et al. 2011a):

Fe 2 O 3(melt) + H 2(vap/melt) = 2FeO (melt) + H 2 O (melt) .
(2)

Part of the water may also come from the silver oxalate used as the CO 2 source, as mentioned by Lesne et al. (2011a), reaction (Eq. 2) being insufficient to account for the measured H 2 O contents of series #3 glasses.

The dissolved H 2 O and CO 2 concentrations in all compositional series are in agreement with the experimental solubilities found in basaltic melts equilibrated at 200 MPa, 1200-1250 °C [START_REF] Shishkina | Solubility of H 2 O-and CO 2 -bearing fluids in tholeiitic basalts at pressures up to 500MPa[END_REF]Lesne et al. 2011aLesne et al. , 2011b)).

Textures of post-decompression glasses: Qualitative observations

Charges from the decompression experiments (hereafter designated as post-decompression glasses) were generally recovered as glassy blocks. Exceptions are provided by the series #1 charges decompressed to 25 MPa, which yielded a range of textures totally different from all the other charges from this paper. Bubbly glass fragments, foams (Fig. 1c), and in one case a glass powder were observed in the five series #1 charges decompressed to 25 MPa P f (Table 4). All post-decompression glasses were crystal free. The absence of crystals was checked by optical microscopy on the doubly polished sections prepared for FTIR and also by SEM. Tiny oxide crystals (Ti-bearing magnetite, Di [START_REF] Di Carlo | Experimental crystallization of a high-K arc basalt: The Golden Pumice, Stromboli Volcano (Italy)[END_REF][START_REF] Pichavant | Experimental constraints on the deep magma feeding system at Stromboli volcano, Italy[END_REF][START_REF] Pichavant | Generation of CO 2 -rich melts during basalt magma ascent and degassing[END_REF] occur in some charges but always in very small amounts. Some charges show evidence for bubble nucleation on those Fe-Ti oxides (Le Gall 2015). However, this was observed only for a negligible proportion of nucleated bubbles (i.e., for less than 1.5% of total bubbles in most charges and up to 6% in charge D5#2).

Two main types of post-decompression glasses were distinguished on the basis of textures observed in the core of the samples. The first type corresponds to bubble-free glasses (Fig. 1a). It concerns the D3#1 and D3#3 samples (Table 3). Although the interior of these glasses is completely devoid of bubbles, D3#1 charge exhibits a thin (<50 mm, Fig. 1a) bubbly rim resulting from heterogeneous nucleation on the inner wall of the capsule (e.g., Mourtada-Bonnefoi and Laporte 2002). The second type of post-decompression glasses is characterized by a nucleated core with a nearly homogeneous texture (Fig. 1b). Three distinct zones can be identified in these glasses: (1) a bubbly rim (generally up to ~300 mm, e.g., in the order of 150-200 mm in D24#3 sample, Fig. 1b) at the glass-capsule interface, followed by (2) a bubbly free zone (depleted in volatiles), and (3) a core with uniformly spaced bubbles having variable sizes, from a few micrometers up to 266 mm (range of bubble diameters, Table 3). Given the almost uniform spatial distribution of bubbles and the absence of crystals (hence of possible nucleation sites), we interpret the textures of type 2 post-decompression glasses to result from homogeneous bubble nucleation. Charge D1#2 is characterized by a somewhat heterogeneous distribution of relatively large bubbles (6-60 mm, Table 3). However, SEM imaging revealed the presence of a large population of smaller (<5 mm) bubbles, homogeneously distributed within the charge. This seems to be the case for charges D1#3 and D2#3, although no check for the presence of small bubbles could be performed by SEM because no samples were left for analysis.

Bubbles are absent in series #1 and #3 experiments quenched at P f = P in = P synthesis = 200 MPa. In series #2, by contrast, the sample quenched at P f = 200 MPa (D3#2) contains a few large bubbles (10 bubbles with an average size of 40 mm, Table 3). The presence of these bubbles may reflect an excess of the fluid phase (early excess fluid-phase bubbles), as observed by [START_REF] Lensky | Bubble nucleation as a trigger for xenolith entrapment in mantle melts[END_REF], or may correspond to trapped air bubbles. Consequently, these bubbles are not considered below as products of homogeneous nucleation.

Textures of post-decompression glasses: Quantitative observations

Textural information about the decompression experiments are given in Tables 3 and4 and depicted in Figures 234.

Vesicularities range from 0 to 71.2 vol% (series #1), 0.01 to 13.8 vol% (series #2), and 0 to 9.25 vol% (series #3). It is worth noting that the series #1 charge (D24#1) with a 71.2 vol% vesicularity is part of the texturally specific 25 MPa P f charges (Table 4). This charge yielded a highly vesicular foam that was found extruded out of the capsule (Fig. 1c). However, this unusual texture is not the result of capsule failure as detailed below, and is considered to be representative of the degassing process between 50 to 25 MPa P f in series #1 charges. Consequently, the data from charge D24#1 will be given below full consideration. Another series #1 charge (D8#1) is also worth being detailed because it was performed with a pre-decompression melt having a H 2 O concentration ~50% lower than all the other series #1 charges. D8#1 was decompressed to 25 MPa P f and yielded a vesicularity of 1.45 vol% that cannot be directly compared with the data for the other series #1 charges. For this reason, D8#1 is plotted with a different symbol on Figure 2.

In general, vesicularity increases with decreasing P f from 200 to 25 MPa (Fig. 2a, Tables 3 and4), especially between P f = 50 and 25 MPa. Besides the dependence on P f , vesicularities are a function of the volatile series since the highest vesicularities are for the H 2 O-rich glasses (series #1). For example, when decreasing the melt H 2 O content at constant P f (25 MPa, Fig. 2a), V decreases from 71.2 (series #1) to 13.8 (series #2) to 9.7 (series #3) vol%. Vesicularities for series #1 are lower than theoretical vesicularities calculated from equilibrium degassing, except the point at 25 MPa P f that plots on the theoretical curve. The series #2 data plot intermediate between the two theoretical vesicularity curves, whereas the series #3 glasses plot close to the theoretical curve for CO 2 degassing (Fig. 2a).

Average bubble diameters in series #1 range from 8 to 741 mm. Charge D24#1 (P f = 25 MPa, Fig. 1c) is characterized by two distinct bubble populations with sizes ranging from 9 mm to 1.8 mm. The first population has an average bubble size of 741 mm and the second of 17 mm (Fig. 2b). The series #1 D24#1 charge is the only one hosting a bubble population (the first one) with shapes that deviate significantly from spherical. In comparison with the other series #1 glasses, sample D8#1 (P f = 25 MPa) deviates from the general behavior since bubble sizes are lower on average (28 mm) as a result of its lower pre-decompression melt H 2 O concentration. For the series #2 samples, D ranges from 13-74 and 6-18 mm for the series #3. For the three series, bubble diameter generally increases with decreasing P f from 200 to 25 MPa (Fig. 2b, Table 3). The average bubble diameter is also dependent on 3. The three glass series are distinguished, series #1 = black circles; series #2 = gray circles; series #3 = white circles. The series #1 charge D8#1 is plotted with a different symbol (black diamond) since it started from a pre-decompression melt with a H 2 O concentration ~50% lower than all the other series #1 charges. In a, equilibrium vesicularities (thick black and gray lines) calculated for pure H 2 O and CO 2 degassing, respectively (see text), are shown for comparison with the experimental data. Both the first and the second bubble populations of sample D24#1 (Table 3) are plotted in b and c. In a and b, error bars (standard deviations, Table 3) are indicated on the data points. The V, D, and BND melt values for Strombolian pumices (data from [START_REF] Polacci | Threedimensional investigation of volcanic textures by X-ray microtomography and implications for conduit processes[END_REF][START_REF] Polacci | Vesiculation in magmas from Stromboli and implications for normal Strombolian activity and paroxysmal explosions in basaltic systems[END_REF] are shown for comparison with the experimental data points. the concentration of dissolved volatiles. The larger bubble sizes are for the H 2 O-rich series #1 post-decompression glasses (741 mm at 25 MPa P f ), decreasing with lowering the melt H 2 O content (69-74 mm for series #2 and 16-18 mm for series #3).

Bubble number densities (BND melt , Table 3 and Fig. 2c) range from about 10 0 to 10 2 mm -3 (series #2), 10 3 mm -3 (series #1), and 10 4 mm -3 (series #3). Upon decreasing P f , BNDs of series #1 glasses generally decrease, from 10 3 mm -3 (150 MPa, D30#1) to 10 0 mm -3 (50 MPa, D5#1). Nevertheless, two BND increases are observed along the decompression path, the first and largest between 200 (0 mm -3 , D3#1) and 150 MPa and the second from 50 to 25 MPa (10 0 -10 1 mm -3 , D24#1) . In contrast, the series #2 and #3 glasses have BNDs generally increasing from 200 (10 0 and 0 mm -3 , D3#2 and D3#3) to 25 MPa (10 2 and 10 4 mm -3 , D8#2 and D24#3) . Nevertheless, in both glass series there are a few exceptions characterized by BND decreases, for example between P f = 150 and 100 MPa for one series #3 charge and between P f = 100 and 50 MPa for one series #2 and also one series #3 charge (Fig. 2c).

Bubble size distributions (BSDs) are analyzed from histograms based on the diameter of the bubbles (Fig. 3) and from cumulative distributions of volumetric classes (Fig. 4), constructed for each series. Two main types of distributions were distinguished in Figure 4, exponential and power law, although the two are mixed in most samples. Regressions were performed with Excel software. Very good fits were generally obtained, yielding R 2 > 0.99 for more than 50% charges. Series #1 glasses are initially (at P f = 150 MPa) characterized by bubbles sizes ranging between 4 and 46 mm (D30#1, Fig. 3a, Table 3), leading to a power law bubble size distribution with an exponent of 1.91 (Fig. 4a). Then, from P f = 100 to 50 MPa bubbles become larger (40-200 mm, D5#1) and multiple peaks occur in the histogram (Fig. 3a), corresponding to exponential distributions (Fig. 4a). It is worth mentioning that the bubble size distribution in D5#1 is uncertain because of its low number of bubbles. At P f = 25 MPa, the two bubble populations in D24#1 charge have sizes of 400-1800 and 9-56 mm, respectively (Fig. 3a). The former exhibits a power law and the latter a mixed power law-exponential distribution with exponents of 0.50 and 0.63, respectively (Fig. 4a). Series #2 glasses have bubble sizes from 6-60 mm at 150 MPa P f (D1#2, Fig. 3b, Table 3) to 15-48 mm at 100 MPa (D2#2, Table 3), both fitted by power law distributions with exponents of 0.49 and 2.22, respectively (Fig. 4b). Upon decreasing P f , bubble sizes become larger (24-175 mm, D8#2, P f = 25 MPa, Fig. 3b and Table 3), yielding mixed power law-exponential distributions (Fig. 4b). In fact, two types of distributions can be recognized in the charges decompressed to P f = 50 and 25 MPa: the small-to medium-sized bubbles can be fitted by an exponential function, whereas the larger bubbles are best described by a power law with an exponent of 0.78-1.96. Series #3 post-decompression glasses have numerous small bubbles (<10 mm, Fig. 3c) at 150 MPa P f (range: 7-57 mm, D1#3, Table 3). Upon lowering P f to 25 MPa, the bubbles become a little larger (8-135 mm, D24#3, Table 3), and the maximum is shifted to 10-20 mm (Fig. 3c). The BSDs are characterized by both power law and exponential shapes (Fig. 4c). For example, glasses decompressed to P f = 150 and 50 MPa (D1#3 and D5#3, Fig. 4c) are best described by exponential functions, while the three duplicated glasses decompressed to 100 MPa P f can be described by either power law functions (D2#3 and D18#3, Fig. 4c) or a combination of both (D16#3, Fig. 4c) as the two samples decompressed to 25 MPa P f (D8#3 and D24#3, Fig. 4c). It is worth noting that two charges with exponential distributions yielded relatively poor fits (Fig. 4c): D1#3 (P f = 150 MPa, R 2 = 0.88) and D24#3 (P f = 25 MPa, R 2 = 0.94 for the small-to-medium bubble sizes).

H 2 O and CO 2 concentrations in post-decompression glasses

H 2 O and CO 2 concentrations in post-decompression glasses are presented in Table 5 1 and shown in Figure 5. Series #1 glasses 3. The number of bubbles within each population is specified (n, Table 3). Details about experimental conditions and other textural data in Table 3. FiGure 4. Bubble size distributions (BSD) expressed as log-log plots of bubble number density (BND melt , in mm -3 ) vs. bubble volume for all postdecompression glasses from this study. For each glass sample, the bubble population is characterized by a range of bubble size (expressed as diameters in Table 3) and a bubble number density value (Table 3). Each point along the distribution curve corresponds to the number of bubbles with a volume strictly larger than indicated. have H 2 O contents ranging from 4.91 wt% (D3#1, P f = 200 MPa) to 1.52 wt% (D8#1, P f = 25 MPa). Thus, a general decrease of the concentration of dissolved H 2 O is observed when decreasing P f (Fig. 5a). Considering the analytical uncertainties (Fig. 5a, Table 5 1 ), the H 2 O contents of series #1 glasses are in good agreement with H 2 O solubilities determined by Lesne et al. (2011b), with the exception of two glasses decompressed to P f = 60 (D22#1) and 50 (D5#1) MPa that have H 2 O concentrations slightly exceeding solubilities (H 2 O supersaturations of 0.2-0.35 and 0.3 wt% absolute for D22#1 and D5#1, respectively, Fig. 6). In addition, in these two series #1 charges, H 2 O concentrations are close to solubilities near the glass-capsule interface and become higher in the core of the glass cylinder (Fig. 6). The fact that the increase of the H 2 O concentration toward the core is more progressive in the charge with the larger diameter (D22#1, 5 mm) is consistent with a mechanism of diffusive motion of H 2 O inside the melt toward the gas phase.

Series #2 post-decompression glasses have H 2 O concentrations ranging between 2.45 and 0.82 wt% and CO 2 concentrations ranging from 850 to 550 ppm (Table 5 1 ). Both their H 2 O and CO 2 contents progressively decrease with P f (Fig. 5b). However, the drop in H 2 O and CO 2 concentrations is nonlinear with P f . For example, the glass decompressed to 50 MPa has a much lower H 2 O content (0.82 wt%, D5#2) than the glasses decompressed to 25 MPa (1.60 wt%, D6#2 and D8#2), and a higher CO 2 content (775 ppm) than the two glasses decompressed to 150 (754 ppm, D1#2) and 100 MPa (732 ppm, D2#2). Degassing trajectories in our experiments are different from closed-system equilibrium decompression trends, in that there is a marked drop of H 2 O content for a comparatively slight CO 2 decrease. All post-decompression glasses retain elevated CO 2 concentrations, since the data points plot well above their respective gas-melt saturation isobars. For example, measured CO 2 contents in the glasses decompressed to 25 MPa (550-558 ± 62-76 ppm, D6#2 and D8#2) largely exceed the calculated value (<50 ppm).

Series #3 glasses have H 2 O contents ranging between 0.69 and 0.95 wt% and CO 2 contents ranging from 873 to 461 ppm (Table 5 1 ). Post-decompression glass CO 2 concentrations progressively decrease from 873 (D1#3, P f = 150 MPa), 699-540 (D2#3, D16#3, and D18#3, P f = 100 MPa), 626 (D5#3, P f = 50 MPa) to 513-461 ppm (D8#3 and D24#3, P f = 25 MPa), at approximately constant melt H 2 O contents (Table 5 1 and Fig. 5c). Taken globally, the data points follow degassing trajectories that are nearly vertical, as are the theoretical equilibrium closedsystem decompression paths. However, the decompressed glasses retain CO 2 contents that are well above equilibrium values. For example, at P f = 25 MPa the equilibrium CO 2 concentration is <100 ppm while our samples contain 461 ± 80 (D8#3) and 513 ± 94 ppm CO 2 (D24#3, Table 5 1 ).

iNterPretatioN aNd discussioN oF exPeriMeNtal observatioNs

Supersaturation pressures required for homogeneous bubble nucleation

The homogeneous nature of bubble nucleation in our experiments is supported by the lack of crystals to serve as nucleation sites in the melts, and by the near textural homogeneity of our post-decompression glasses, as shown by the quite homogeneous distribution of bubbles in the total volume of the samples. Additional supporting arguments include the little spatial variation of the bubble number density inside the glass and the small dispersion of bubble sizes in a given sample.

From our decompression experiments, we can determine the supersaturation pressure required to trigger homogeneous bubble nucleation DP HoN , which is defined as the difference between the saturation pressure (P sat = P in , except in charge D8#1 considered apart) and the final pressure (P f ) at which bubbles begin to form homogeneously. In each post-decompression glass series, we observed a transition from a bubble-free glass core (except for series #2, where we noted the presence of heterogeneously nucleated bubbles at P f = 200 MPa) at a high P f to a nucleated glass core at a lower P f . As previously mentioned, in series #1 post-decompression glasses, bubbles are absent at P f = 200 MPa (D3#1, Table 3 and Fig. 1a). They appear uniformly distributed in the melts from P f = 150 MPa (D30#1, Table 3), suggesting that homogeneous bubble nucleation takes place between 200 and 150 MPa P f , hence a DP HoN ≤ 50 MPa. The series #1 D8#1 sample made from a pre-decompression melt with a low H 2 O concentration yields a DP HoN of 40-45 MPa by taking a P sat of 65-70 MPa (Lesne et al. 2011b). Overall a critical supersaturation pressure of 45 MPa maximum is determined for the series #1 melts. This DP HoN value is consistent with that found by Le Gall and Pichavant (DP HoN << 50 MPa 2016) in their faster decompression rate experiments. This range of DP HoN value is less than recorded for more evolved melts (60-150 MPa; Mangan andSisson 2000, 2005;Mourtada-Bonnefoi and Laporte 2004;[START_REF] Iacono-Marziano | Equilibrium and disequilibrium degassing of a phonolitic melt (Vesuvius AD 79 "white pumice") simulated by decompression experiments[END_REF][START_REF] Gardner | Bubble nucleation in rhyolite and dacite melts: temperature dependence of surface tension[END_REF], reinforcing the idea that bubble nucleation takes place at low supersaturations in hydrous basaltic melts (Le Gall and Pichavant 2016).

The series #2 melts contain a few heterogeneously nucleated bubbles at P f = 200 MPa (D3#2, Table 3). At P f = 150 MPa, the D1#2 glass contain small (main peak diameter of 6-7 mm) bubbles. Only 15 bubbles were detected by X-ray CT because their size is hardly higher than the instrumental spatial resolution. Yet, SEM imaging revealed the presence of a population of small (<6 mm) uniformly distributed bubbles, suggesting that an event of homogenous nucleation takes place between 200 and 150 MPa P f . Therefore, a DP HoN of 50 MPa maximum is inferred for the series #2 melts. This value is less than found for similar compositions in the study of Le Gall and Pichavant (2016, DP HoN < 100 MPa) performed at a faster decompression rate. [START_REF] Pichavant | Generation of CO 2 -rich melts during basalt magma ascent and degassing[END_REF] found a supersaturation pressure of 150 MPa maximum in their experiments performed on compositions similar to our series #2 melts. However, no data were given for P f > 50 MPa, and so it cannot be excluded that, in their decompression experiments, homogeneous bubble nucleation would start at pressures > 50 MPa, leading to DP HoN << 150 MPa.

Series #3 post-decompression glasses are bubble-free at P f = 200 MPa (D3#3, Table 3). We observed small (main peak diameter of 8 mm) bubbles in the glass core decompressed to P f = 150 MPa (D1#3, Table 3). The number of bubbles analyzed by X-ray CT is very small (8 bubbles) presumably because of their small size. However, they indicate an event of homogenous bubble nucleation between 200 and 150 MPa P f . From this observation, a DP HoN of 50 MPa maximum is also inferred for the series #3 melts. This DP HoN value is the same as found for similar compositions in the study of Le [START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF] performed at a faster decompression rate. For comparison, a critical supersaturation pressure of 200 ± 100 MPa was found by [START_REF] Lensky | Bubble nucleation as a trigger for xenolith entrapment in mantle melts[END_REF] for CO 2 bubbles in a synthetic mafic melt decompressed from 1.5 GPa, larger than determined here for series #2 and #3 melts. However, it is worth specifying that [START_REF] Lensky | Bubble nucleation as a trigger for xenolith entrapment in mantle melts[END_REF] worked on nominally H 2 O-free melts. The range of supersaturations (DP HoN ≤ 50 MPa) found in our series #2 and #3 melts is less than recorded for the nucleation of H 2 O-CO 2 bubbles in more evolved melts (160-350 MPa, Mourtada-Bonnefoi and Laporte 2002).

Because the range of supersaturation pressures required for homogeneous nucleation is essentially the same (DP HoN ≤ 50 MPa) for each glass series, it is difficult from our data to quantify the effects of H 2 O and CO 2 on DP HoN , as proposed for melts more evolved than basalts (Mourtada-Bonnefoi and Laporte 2002; Gardner and Webster 2016). In addition, our experimental results confirm previous observations and conclusions on the fact that DP HoN values ≤50 MPa are specific to basaltic compositions, and that bubble nucleation takes place at low supersaturations in H 2 O-and H 2 O-CO 2 -bearing basaltic melts (Le [START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF]. Surface tensions (s) have been calculated (Appendix) by taking the supersaturation pressures determined for each series and our measured experimental nucleation rates. The supersaturation pressures are given as maxima, hence the calculated surface tensions are upper limits. Computations give maximum s values ranging from 0.054 (series #1) to 0.059 N/m (series #2 and #3). For comparison, Le [START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF] obtained maximum surfaces tensions of 0.058 (series #1), 0.059 (series #3) and 0.091 (series #2) N/m for the same melt compositions and volatile concentrations. The differences observed (mostly for series #2 melts) are related to differences in supersaturation c, respectively. Circles = pre-decompression glasses synthesized at 200 MPa P in (initial pressure); crosses = glasses decompressed to 200 MPa P f (final pressure); rectangles = glasses decompressed to 150 MPa P f ; triangles = glasses decompressed to 100 MPa P f ; squares = glasses decompressed to 50 MPa P f ; diamonds = glasses decompressed to 25 MPa P f . In b, the symbol color refers to the synthesis experiments, either S3 (black), S6 (gray), or S4 (white, Table 2). Error bars (standard deviations, Table 5) are indicated on the data points. The thin continuous lines are fluid-melt equilibrium saturation isobars (25-250 MPa) and the dashed curves are equilibrium decompression paths calculated for some series #2 and #3 glasses assuming closedsystem behavior. Equilibrium fluid-melt calculations were performed with VolatileCalc [START_REF] Newman | VolatileCalc: a silicate melt-H 2 O-CO 2 solution model written in Visual Basic for Excel[END_REF].

Le Gall and Pichavant. 5. H 2 O solubilities (at pressures of 150-25 MPa, dashed horizontal lines) come from Lesne et al. (2011b).

pressures between the two studies since the decompression rate is not expected to have a significant influence on the bubble nucleation pressure (Mourtada-Bonnefoi and Laporte 2004). Note that the apparently large difference between supersaturation pressures in the two studies (series #2) is probably in part due to the large intervals between our experimental P f . Le [START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF] observed bubbles homogeneously nucleated from 100 MPa (from 150 MPa in this study), but these could have started to form at pressures below than but close to 150 MPa. In the same way, [START_REF] Pichavant | Generation of CO 2 -rich melts during basalt magma ascent and degassing[END_REF] found a s of 0.18 N/m maximum for compositions as our series #2 melts. This maximum is higher than determined here, but again consistent with their higher supersaturation pressures (DP HoN < 150 MPa). Surface tensions from this study are lower than the values found by [START_REF] Khitarov | Effect of temperature, pressure and volatiles on the surface tension of molten basalt[END_REF]: 0.1 to 0.4 N/m for basaltic melts at 1200 °C and 100-500 MPa, the lowest end of the range corresponding to hydrous compositions.

Physical mechanisms of degassing and textures

In this section, we discuss the physical mechanisms of degassing occurring in our decompression experiments, from nucleation, growth, and coalescence of gas bubbles, up to fragmentation. Emphasis is placed on textural differences between the three glass series.

Vesicularities. The three series of post-decompression glasses have vesicularities that generally increase upon decompression (i.e., upon decreasing P f ). The general increase in vesicularity observed upon decreasing P f is consistent with a mechanism of progressive melt vesiculation associated with decompression. It is worth remembering that, for all glass series, the increase in vesicularity is the most strongly marked between P f = 50 and 25 MPa (Fig. 2a). Nevertheless, the series #2 measured vesicularities are lower than expected for a closed-system degassing. It is also the case of the series #1 glasses decompressed up to 50 MPa P f whose measured vesicularities remain very low (<3%), well below equilibrium values. It is recalled that the series #1, 25 MPa P f D24#1 charge has a very high vesicularity (71.2%), slightly above the range of vesicularities for Strombolian pumices (47 and 67%, [START_REF] Polacci | Threedimensional investigation of volcanic textures by X-ray microtomography and implications for conduit processes[END_REF]. Apart from that charge, our experimental vesicularities are systematically lower than equilibrium values. This is interpreted to result from the combination of two processes: (1) diffusive volatile loss from the melts and (2) bubble outgassing. On the one hand, diffusive volatile loss is demonstrated by the H 2 O concentration profiles in the series #1, 60 and 50 MPa P f samples (Fig. 6). Calculations of diffusion distances for H 2 O and CO 2 using the diffusion coefficients from [START_REF] Zhang | Diffusion of H, C, and O components in silicate melts[END_REF] show that H 2 O can migrate out of the sample over lengths <2 mm (for a duration of 4500 s that corresponds to the longest experiments), whereas the mobility of CO 2 is much lower. On the other hand, bubble outgassing would account for the reduction in BNDs observed in particular between 100 and 50 MPa (Fig. 2c). However, textures such as bubble accumulation on top of the charges, systematically elongated bubble shapes, and charges totally devoid of bubbles have generally not been observed. Calculations of the gravity-driven upward movement of the water bubbles have been performed using the Hadamard-Rybcynski bubble velocity equation (Bottinga and Javoy 1990). In detail, results depend sensitively on the bubble diameter, the gas density, and the viscosity of the melt. For series #1 melts, calculated distances are ~2-3 mm for bubbles of 60 mm diameter (and ~9-14 mm for bubbles of 120 mm) and ascent durations of 21 min (corresponding to the 100-50 MPa P f interval), suggesting that outgassing possibly takes place in our experiments and can contribute to the loss of the larger bubbles and the reduction in vesicularity.

Nucleation events. The melt vesiculation mechanism observed in our experiments results from different sub-processes that include bubble nucleation, growth, coalescence, and outgassing, as well as fragmentation. Textural evidence (bubble size distributions and bubble number densities) can be used to distinguish between single vs. multiple bubble nucleation events (or pulses) in our experiments. In series #1 post-decompression glasses, a large increase of BND is first observed from P f = 200 (BND melt = 0 mm -3 ) to 150 (BND melt = 1325 mm -3 , Table 3, Fig. 2c) MPa, implying that an event of homogeneous bubble nucleation takes place. Then, there is a general decrease of BND with decreasing P f from 150 to 50 (BND melt = 1.33 mm -3 ) MPa. This trend reflects a mechanism of bubble coalescence combined with bubble outgassing. This interpretation is supported by the small number (5) of bubbles in the charge decompressed to 50 MPa (D5#1) and the very low (<3%) vesicularities measured up to 50 MPa P f . In addition, textural differences exist between the two charges of different diameter decompressed to P f = 60 (D22#1) and 50 (D5#1) MPa. The 5 mm diameter charge (D22#1) contains many more bubbles (149), and accordingly has a higher vesicularity (2.1%) than the 2.5 mm diameter charge (5 bubbles and 0.3% vesicularity). This suggests that, with a higher diameter charge, diffusive H 2 O loss and bubble outgassing from the melt are both limited. Although we do not observe BND stabilization (which would be marked by a horizontal line in Fig. 2c and would reflect the end of a nucleation event), the absence of small (<10 mm) newly formed bubbles from 100 to 50 MPa P f testifies to the end of the first nucleation event. This is also suggested by the exponential distributions of bubble sizes from P f = 100 to 50 MPa (Fig. 4a) that are indicative of an absence of small bubbles. Below 50 MPa, an additional increase of BND is observed, suggesting that a second nucleation event takes place between 50 and 25 MPa P f . This is supported by the small newly formed bubbles in D24#1 as revealed both by X-ray CT and microscopic textural observations (second population with main peak diameter 10 mm, Fig. 1c). It is also worth emphasizing that the 4 other charges decompressed to 25 MPa P f contain a population of small bubbles (Table 4). The mechanism of bubble nucleation observed in series #1 melts is thus discontinuous and restricted to two narrow P f intervals .

In series #2 glasses, a general increase of the BND is observed from P f = 200 (BND melt = 1.15 mm -3 ) to 100 (BND melt = 104 mm -3 , Table 3, Fig. 2c) MPa that corresponds to the beginning of a homogeneous bubble nucleation mechanism. It is worth noting that the early event of heterogeneous bubble nucleation observed in charge D3#2 (P f = 200 MPa) leads to a small number (10) of bubbles and, accordingly, to a low but nonzero BND. Below 100 MPa, we observe a decrease of BND (BND melt = 19.2 mm -3 , D5#2, P f = 50 MPa) that is interpreted to reflect a mechanism of bubble coalescence, and possibly bubble outgassing. As a result, the number of bubbles is reduced from 665 (D2#2, P f = 100 MPa) to 114 (D5#2, P f = 50 MPa). At the same time, bubble sizes give evidence for the appearance of small (<10 mm) newly formed bubbles, indicating the occurrence of secondary nucleation events. The evolution below 50 MPa and down to 25 MPa P f is marked by an increase of the BND that is interpreted as the continuation of the same nucleation process.

In series #3 melts, an increase of BND is observed from P f = 200 (BND melt = 0 mm -3 ) to 150 MPa (BND melt = 4.38 mm -3 , Table 3, Fig. 2c) that corresponds to the beginning of a homogeneous bubble nucleation mechanism. Below 150 MPa, three cases were observed, either a continuous increase of the BND (D18#3), a decrease of the BND (D2#3) or a near-steady evolution of the BND (D16#3). The first case suggests the continuation of the same nucleation process below 150 MPa. This interpretation is supported by an increase in the number of bubbles from 8 (P f = 150 MPa, D1#3) to 2042 (P f = 100 MPa, D18#3), by the appearance of small (main peak size of 6 mm, Table 3) newly formed bubbles and by the power law distribution of the bubble sizes (Fig. 4c) that suggests that small bubbles are continuously appearing. The second case is interpreted to reflect a mechanism of bubble coalescence. However, numerous small (<5 mm) bubbles could not be measured in D2#3, and so its BND is underestimated. The third case corresponds to a BND stabilization that reflects the end of a nucleation event and the beginning of bubble growth and coalescence. In this sense, the BSD of charge D16#3 evolves to a mixed power law-exponential relation that indicates a decrease in the number of small newly formed bubbles and an increase in the number of larger bubbles (Fig. 4c). Below 100 MPa and down to 50 MPa P f , two new situations are possible, either an increase of the BND (continuous bubble nucleation) or a decrease of the BND (bubble coalescence). In any case, the evolution below 50 MPa and down to 25 MPa P f is marked by an increase of BNDs, which is interpreted as the continuation of the same nucleation process and the occurrence of secondary nucleation events.

We conclude to a major difference in the mechanism of bubble nucleation between series #1, on the one hand, and series #2 and #3, on the other hand, as observed in the experiments of Le [START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF]. In H 2 O-rich melts, two distinct events of bubble nucleation occur in narrow P f intervals (the first at high pressure and the second at low pressure). In contrast, in CO 2 -bearing melts, a single mechanism of continuous bubble nucleation takes place over a substantial P f interval along the decompression path, leading to multiple bubble nucleation events.

Bubble coalescence. Textural evidence (decrease of the BND and common coalescence structures) can be used as indicators of bubble coalescence process in our experiments. Common coalescence structures were generally not observed in the three glass series. Therefore, evidence for coalescence mainly comes from decrease of BNDs and bubble numbers and possibly from the increase in bubble sizes. It is worth mentioning that a decrease of BND can also be due to bubble outgassing (see above). The series #1 post-decompression glasses are characterized by a general decrease of the BND from P f = 150 to 50 MPa (Fig. 2c). This decrease is associated with a reduction in the number of bubbles from 8350 (D30#1, P f = 150 MPa) to 5 (D5#1, P f = 50 MPa) and with a large increase of the average bubble size (Fig. 2b), suggesting that both bubble growth and coalescence take place in series #1 melts. In fact, a few coalescence structures (dimpling, [START_REF] Castro | Mechanisms of bubble coalescence in silicic magmas[END_REF] were observed in the charge decompressed to P f = 60 MPa (D22#1). In addition, the evolution of the bubble size distribution from power law to exponential indicates the presence of larger bubbles interpreted to result from coalescence (Figs. 3a and4a). Therefore, as observed in the experiments of Le [START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF], bubble coalescence starts very early along the decompression path in series #1 glasses. It is worth mentioning that the charge decompressed to 25 MPa P f (D24#1) present numerous coalescence structures (dimpling, bending, and stretching; [START_REF] Castro | Mechanisms of bubble coalescence in silicic magmas[END_REF][START_REF] Martel | Timescales of bubble coalescence, outgassing, and foam collapse in decompressed rhyolitic melts[END_REF][START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF] involving particularly large (up to 1.8 mm) bubbles (Fig. 1c) whose shape deviates from spherical. This suggests that the mechanism of bubble coalescence continues below 50 MPa and until 25 MPa P f .

In series #2 glasses, the decrease of BND observed between 100 and 50 MPa P f (Fig. 2c) provides evidence for the occurrence of a bubble coalescence mechanism. In this way, the number of bubbles decreases from 665 (D2#2, P f = 100 MPa) to 114 (D5#2, P f = 50 MPa). Increases in the average and the main bubble sizes are, however, hidden by the superimposition of a bubble nucleation process that continuously generates small (<10 mm) bubbles and contributes to reduce bubble sizes.

In series #3 glasses, two decreases of BND are observed, the first between 150 and 100 MPa P f and the second between 100 and 50 MPa P f , both interpreted as evidence for coalescence. However, it is worth mentioning that the observed BND evolutions for the different charges at 100 and 50 MPa P f indicate that coalescence is not systematic. We interpret these differences from one charge to the other at a given P f to reflect variations in distances between bubbles. For example, the average distance between bubbles in charges D2#3 (734 mm) and D16#3 (385 mm) is larger than in charge D18#3 (101 mm), all at P f = 100 MPa. This would make bubble interactions upon further decompression progressively more difficult in charges such as D2#3 and D16#3 than in D18#3.

We conclude that, in series #2 and #3 glasses, coalescence occurs as bubbles continue to nucleate and the space between neighboring bubbles is sufficiently small. For the three glass series, bubble coalescence is the more strongly marked in the same pressure range (between 100 and 50 MPa P f ), as observed in faster decompression rate experiments (Le [START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF].

Bubble size distributions. Each of the three glass series shows a different evolution of the bubble size distribution (Figs. 3 and4). With decreasing P f , the BSD of series #1 glasses evolve from a power law (D30#1, P f = 150 MPa, Figs. 3a and4a), exponential (D2#1, D22#1, and D5#1, P f = 100-50 MPa, Fig. 4a) and then to a mixed power law-exponential distribution that is specific of the 25 MPa P f D24#1 charge. The power law BSD (which was not found in the faster decompression rate experiments, Le Gall and Pichavant 2016) is interpreted to reflect ongoing bubble nucleation and bubble growth. The fact that the small (volumes < 200 mm 3 ) bubbles are not fitted by the power law suggests that the nucleation process is close to its end. The exponential distributions are interpreted to indicate a mechanism of bubble coalescence that goes along without further bubble nucleation. The mixed power law-exponential BSD observed at 25 MPa is due to the occurrence of the second bubble nucleation event. The increase in the number of bubbles and sizes when compared to the 50 MPa charge requires either fast bubble growth or a combination of bubble growth and coalescence, possibly promoted by rapid gas expansion between 50 and 25 MPa.

Series #2 glasses are characterized by a continuous evolution from a power law (D1#2 and D2#2, P f = 150 and 100 MPa, Figs. 3b and4b) to mixed power law-exponential distributions (D5#2, D6#2, and D8#2, P f = 50 and 25 MPa, Fig. 4b) upon decreasing P f . This transition is consistent with a mechanism of bubble growth dominated by coalescence, taking place between P f = 100 and 50 MPa, as well as by a lowering in the bubble nucleation rate.

Series #3 glasses are characterized by power law, exponential, and mixed power law-exponential bubble size distributions (Figs. 3c and4c). Exponential distributions first were not found in series #2 and second appear at different P f in series #3 samples. We interpret this type of BSD to reflect the pre-dominant influence of bubble growth, bubble nucleation playing a relatively minor role. Bubble coalescence would become more important in the case of mixed power law-exponential distributions.

We conclude that power law, exponential and mixed power law-exponential bubble size distributions are observed in all glass series, with the exception of the series #2 glasses that lack exponential BSDs.

Fragmentation. A process of magma fragmentation was observed in a total of three series #1 charges decompressed to 25 MPa P f (Table 4). D19#1 was recovered entirely as a fine (<500 mm) glass powder and S+D40#1 partially so. D12#1 yielded coarse (<1.5 mm) glass fragments. Two other 25 MPa P f series #1 charges were unfragmented but yielded strongly unusual textures (extruded foam for D24#1 and extruded dense block for D27#1). Capsule failure was observed systematically in the series #1 charges decompressed to 25 MPa, occurring in four out of the five charges performed under these conditions, despite capsules having lengths up to 5 cm to accommodate gas expansion during decompression. However, capsule failure and fragmentation are not always associated since the capsule of the fragmented D19#1 charge did not fail. When capsules failed, failures were systematically found around the melt cylinders and never in void spaces. Both fragmented and unfragmented charges contain a population of small bubbles (Table 4). Therefore, melt fragmentation in our experiments is intimately associated with the occurrence of the second event of bubble nucleation characterized for charge D24#1. Our experimental observations thus strengthen the proposal [START_REF] Massol | The effect of magma flow on nucleation of gas bubbles in a volcanic conduit[END_REF] that late nucleation of gas bubbles in the conduit triggers fragmentation. Although detailed discussion of the fragmentation mechanism is outside the scope of this paper, our observations (presence of small bubbles, capsule failures) are consistent with fragmentation being driven by high internal pressures inside the newly formed bubbles [START_REF] Zhang | A criterion for the fragmentation of bubbly magma based on brittle failure theory[END_REF][START_REF] Massol | The effect of magma flow on nucleation of gas bubbles in a volcanic conduit[END_REF].

Equilibrium vs. disequilibrium degassing

Chemical equilibrium is reached or approached in the H 2 Oonly melts (series #1). On the one hand, glasses decompressed to P f = 200, 150, 100, and 25 MPa have H 2 O concentrations in agreement with their respective solubilities, and thus follow an equilibrium degassing trend (Fig. 5a). On the other hand, deviation from equilibrium is encountered in glasses decompressed to P f = 60 and 50 MPa (D22#1 and D5#1), which have H 2 O concentrations in excess compared to their respective equilibrium solubilities (Fig. 6). H 2 O supersaturations of the order of 0.2-0.35 wt% absolute were found in these two glasses. This indicates the possibility of near-or slight non-equilibrium degassing in the H 2 O-only melts, which would provide the driving force for the nucleation of the second bubble population observed at 25 MPa. However, and despite chemical equilibrium being approached, textural equilibrium (defined here as the texture that corresponds to an equilibrium vesicularity, the latter theoretically generated by assuming degassing along the equilibrium vesicularity curves, see Fig. 2a and Le Gall and Pichavant 2016) is not attained in the series #1 melts that have vesicularities lower than expected from equilibrium degassing (Fig. 2a). This demonstrates that, to achieve chemical equilibrium, H 2 O can be lost diffusively from the melts during decompression, either toward the gas-melt capsule interface, as suggested by the H 2 O distribution profiles measured in D22#1 and D5#1 charges (Fig. 6), or toward the gas bubbles present inside the glass cylinder.

In contrast, disequilibrium degassing occurs systematically in the CO 2 -bearing melts (series #2 and #3). CO 2 is retained within these melts at elevated concentration levels (Figs. 5b and5c). In parallel, H 2 O is lost in significant amounts, especially in series #2 glasses. The combination of high melt CO 2 concentrations and significant H 2 O losses generates a disequilibrium degassing trend. Such a deviation from a closed-system equilibrium decompression trend was previously observed in the experiments of [START_REF] Pichavant | Generation of CO 2 -rich melts during basalt magma ascent and degassing[END_REF] and Le [START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF] and modeled using a diffusive fractionation mechanism by [START_REF] Yoshimura | Diffusive fractionation of H 2 O and CO 2 during magma degassing[END_REF]. For series #2, glass CO 2 concentrations are weakly negatively correlated with vesicularities and positively correlated with BNDs. As discussed by [START_REF] Pichavant | Generation of CO 2 -rich melts during basalt magma ascent and degassing[END_REF] and Le [START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF], equilibrium degassing in CO 2 -bearing melts need both numerous and large bubbles, i.e., high vesicularities, which is the case neither in our series #2 nor in our series #3 post-decompression glasses.

Effect of decompression rate on degassing mechanisms

Previous experiments on hydrated rhyolites and phonolites [START_REF] Mangan | Delayed, disequilibrium degassing in rhyolite magma: decompression experiments and implications for explosive volcanism[END_REF]Mourtada-Bonnefoi and Laporte 2004;[START_REF] Iacono-Marziano | Equilibrium and disequilibrium degassing of a phonolitic melt (Vesuvius AD 79 "white pumice") simulated by decompression experiments[END_REF][START_REF] Cluzel | Kinetics of heterogeneous bubble nucleation in rhyolitic melts: implications for the number density of bubbles in volcanic conduits and for pumice textures[END_REF]) have demonstrated strong variations in bubble number density, bubble size and vesicularity with decompression rates, as anticipated on the basis of numerical simulations [START_REF] Toramaru | Numerical study of nucleation and growth of bubbles in viscous magmas[END_REF](Toramaru , 2006)). In line with these observations, below we compare our experimental products with those from the experiments of Le [START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF] performed at a higher decompression rate of 78 kPa/s (or 3 m/s), under the same conditions and on compositions similar to those in this study. The comparison is focused on the series #2 glasses and it is extended to the experimental products from the experiments of [START_REF] Pichavant | Generation of CO 2 -rich melts during basalt magma ascent and degassing[END_REF] performed at lower decompression rates (17 and 27 kPa/s, or 0.64 and 1.03 m/s) under similar conditions and compositions.

First, a positive correlation between bubble number density and decompression rate (dP/dt) is generally observed. For a given P f , the experiments decompressed the most rapidly have the highest BNDs (Fig. 7a). Note that the data points for the two slowest decompression rates (17 and 27 kPa/s) are for 1150 °C experiments, whereas experiments for the two fastest decompression rates (39 and 78 kPa/s) are performed at 1200 °C. The positive correlation between decompression rate and BND results from timescales for bubble growth and coalescence becoming shorter and volatile supersaturations larger when dP/dt is increased. Both effects would promote the nucleation of new bubbles, and so increase the BNDs. The general positive correlation found in this study is consistent with previous results on rhyolitic systems (e.g., Mourtada-Bonnefoi and Laporte 2004;[START_REF] Cluzel | Kinetics of heterogeneous bubble nucleation in rhyolitic melts: implications for the number density of bubbles in volcanic conduits and for pumice textures[END_REF]). However, our experimental results show more variability. For a given decompression rate, no stationary BND value is reached and BND depends in a complex way on P f (Fig. 2c; Le [START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF] and on the combination between nucleation (marked by two events for the CO 2 -free melts and continuous for the CO 2 -bearing melts), growth (coalescence) processes, and outgassing. Therefore, application of BNDs to infer magma ascent rates (Toramaru 2006) needs caution in the case of basaltic melts.

Average bubble diameters for the series #2 glasses show little variations with dP/dt > 25 kPa/s (Fig. 7b). The 25 MPa P f data points have D slightly negatively correlated with dP/dt, whereas the trends for the 50 MPa P f range from negative to slightly positive. Below 25 kPa/s, significant variations in bubble diameters observed at 1150 °C (Fig. 7b). This is interpreted to reflect the predominant role of bubble growth since bubble growth and maybe coalescence would be favored by lowering dP/dt (e.g., [START_REF] Mangan | Delayed, disequilibrium degassing in rhyolite magma: decompression experiments and implications for explosive volcanism[END_REF]. Vesicularities are constant or generally slightly decrease with decreasing dP/dt (Fig. 7c). These variations reflect the combined influences of the bubble diameter (whose increase below 25 kPa/s contributes to a vesicularity increase) and of the BND (whose decrease with decreasing dP/dt contributes to lowering the number of bubbles).

Previous works in rhyolitic systems have suggested a very small effect of decompression rate on nucleation pressure (Mourtada-Bonnefoi and Laporte 2004;[START_REF] Cluzel | Kinetics of heterogeneous bubble nucleation in rhyolitic melts: implications for the number density of bubbles in volcanic conduits and for pumice textures[END_REF]). In our experiments on basaltic compositions, a significant difference in nucleation pressure is found in the case of our series #2 glasses, DP HoN being lower (≤50 MPa, this study) at 39 than at 78 kPa/s (<100 MPa, Le [START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF]. This difference in nucleation pressure cannot be attributed to heterogeneous bubble nucleation since D1#2 (Table 3), one of the charges examined by SEM, showed a large population of homogeneously distributed bubbles. It is possible that the higher DP HoN measured at 78 kPa/s results from a higher glass CO 2 concentration (901 ± 104 ppm, Le Gall and Pichavant 2016) than in D1#2 (818 ± 111 ppm, Table 3). However, as mentioned above, bubbles in the 39 kPa/s charge could have started to nucleate at pressures below than but close to 150 MPa, which would lead to similar supersaturation pressures in the two studies (DP HoN ≈ 50 MPa).

volcaNoloGical iMPlicatioNs

Comparison between experimental and Strombolian textural parameters

Despite the fact that our experimental products do not simulate the last stages of degassing near the surface and post-fragmentation processes, the comparison of bubble textures in our H 2 O-CO 2 -bearing melts decompressed at 39 kPa/s (or 1.5 m/s, series #2 from this study) and in Strombolian explosive samples can provide insights on degassing processes occurring in the Stromboli volcanic conduit. The comparison focuses on pumices from paroxysmal explosive activity, as well as on scoriae from normal explosive activity [START_REF] Polacci | Threedimensional investigation of volcanic textures by X-ray microtomography and implications for conduit processes[END_REF][START_REF] Polacci | Vesiculation in magmas from Stromboli and implications for normal Strombolian activity and paroxysmal explosions in basaltic systems[END_REF] although it is clear that the two systems correspond to two contrasted degassing regimes. At P f = 25 MPa (i.e., at the pressure corresponding to the shallower depth in our experiments), the series #2 charges show a narrow range of bubble sizes ranging from 21-24 to 175-179 mm (Table 3). For comparison, the pumice samples have a similar minimum bubble size (21-23 mm) but a larger maximum bubble size around 1 mm [START_REF] Polacci | Vesiculation in magmas from Stromboli and implications for normal Strombolian activity and paroxysmal explosions in basaltic systems[END_REF]). From our results, the smaller bubbles would result from a mechanism of continuous nucleation. The absence of bubbles <10 mm in pumices suggests that nucleation ended before magma fragmentation. The large bubble sizes in pumices would result from a combination of growth and coalescence processes in the conduit. These large bubbles have spherical to subspherical shapes. Coalescence is limited during paroxysmal activity as shown by the lack of connected bubbles in both our series #2 melts and in pumice samples. In contrast, connected bubbles occur in scoriae in the form of large coalescing bubbles from 0.5 up to 1.2 mm [START_REF] Polacci | Vesiculation in magmas from Stromboli and implications for normal Strombolian activity and paroxysmal explosions in basaltic systems[END_REF].

The series #2 glasses have vesicularities that extend up to 13.8%, i.e., well below the vesicularities measured in Strombolian eruptive products. For comparison, vesicularities of pumices range from 47 to 67% [START_REF] Polacci | Threedimensional investigation of volcanic textures by X-ray microtomography and implications for conduit processes[END_REF]Fig. 2a) and those of scoriae range between 24 and 78% [START_REF] Polacci | Threedimensional investigation of volcanic textures by X-ray microtomography and implications for conduit processes[END_REF][START_REF] Polacci | Large vesicles record pathways of degassing at basaltic volcanoes[END_REF][START_REF] Polacci | Vesiculation in magmas from Stromboli and implications for normal Strombolian activity and paroxysmal explosions in basaltic systems[END_REF]. Nevertheless, because a rapid vesicularity increase is observed between 50 and 25 MPa P f , it is reasonable to expect that vesicularities typical of Strombolian explosive products can be attained by extrapolating the data to P f << 25 MPa, i.e., by postulating a fragmentation level shallower than ~1 km.

Strombolian pumices have bubble number densities (6-9 × 10 2 mm -3 , [START_REF] Polacci | Vesiculation in magmas from Stromboli and implications for normal Strombolian activity and paroxysmal explosions in basaltic systems[END_REF]Fig. 2c) higher by 0.5 order of magnitude than the series #2 melts at 25 MPa P f (up to 2 × 10 2 mm -3 , Fig. 2c). Nevertheless, the BNDs measured in series #2 are in the same range as the BNDs measured in scoriae (1-4.6 × 10 2 mm -3 , [START_REF] Polacci | Vesiculation in magmas from Stromboli and implications for normal Strombolian activity and paroxysmal explosions in basaltic systems[END_REF]. It is reminded here that the bubble nucleation process is continuous in our series #2 melts and that CO 2 -supersaturated melt compositions are obtained at 25 MPa P f . This suggests the possibility that additional bubble nucleation can take place below 25 MPa, which would result in experimental BND becoming closer to the range found in pumices.

BSDs in both our series #2 melts and pumice samples (Fig. 4b) can be fitted by mixed power law-exponential distribution, with power law exponents of 1.51 and 1.96 (this study) and up to 1.4 [START_REF] Polacci | Vesiculation in magmas from Stromboli and implications for normal Strombolian activity and paroxysmal explosions in basaltic systems[END_REF]. In contrast, the BSDs of scoriae follow power law trends with exponents of 1 ± 0.2 [START_REF] Polacci | Large vesicles record pathways of degassing at basaltic volcanoes[END_REF][START_REF] Polacci | Vesiculation in magmas from Stromboli and implications for normal Strombolian activity and paroxysmal explosions in basaltic systems[END_REF]). From our results, the mixed power law-exponential distributions found in Strombolian pumices would be indicative of a system where growth and coalescence are superimposed on a continuous bubble nucleation mechanism, as the system evolves toward equilibrium (compare with [START_REF] Polacci | Vesiculation in magmas from Stromboli and implications for normal Strombolian activity and paroxysmal explosions in basaltic systems[END_REF]). The power law distributions found in scoriae would also result from a combination of continuous bubble nucleation and coalescence, in agreement with previous interpretation [START_REF] Polacci | Vesiculation in magmas from Stromboli and implications for normal Strombolian activity and paroxysmal explosions in basaltic systems[END_REF]. The decrease in the power law exponent between pumices and scoriae reflects the pre-dominant influence of coalescence in the latter.

Series #2 melts decompressed between 200 and 25 MPa have CO 2 and H 2 O concentrations both in the range of Stromboli embayments and melt inclusions data (Fig. 8). Series #2 melts from this study and decompressed at a faster rate (Le Gall and Pichavant 2016) overlap. The agreement between the experimental and analytical data strongly suggests that the natural Stromboli degassing trend is simulated [START_REF] Pichavant | Generation of CO 2 -rich melts during basalt magma ascent and degassing[END_REF].

We conclude that our decompression experiments on series #2 melts either reproduce or approach certain critical aspects of the natural textures (BNDs, bubble sizes, shapes, and distributions) and chemistries (residual volatile concentrations) of Stromboli explosive basaltic eruptions. The main differences between experimental and natural products concern the maximum bubble sizes and the vesicularities (both lower in the experiments), but the range of natural characteristics is expected to be approached in experiments at P f below 25 MPa.

Implications for the dynamics of magma ascent at Stromboli volcano

Timescales of magma ascent at Stromboli are poorly constrained yet this is critical information for volcanic risk mitigation. On the one hand, slow geophysically derived ascent rates (3 mm/s, [START_REF] Calvari | Lava effusion-A slow fuse for paroxysms at Stromboli volcano?[END_REF] have been proposed, leading to unrealistically large timescales of magma transport to the surface (~30 days). On the other hand, the petrologic constraints lead to timescales for ascent of volatile-rich magmas at the origin of paroxysms (Bertagnini et al. 2003;[START_REF] Métrich | Triggering mechanism at the origin of paroxysms at Stromboli (Aeolian Archipelago, Italy): the 5 April 2003 eruption[END_REF]) that are much shorter, of the order of minutes to hours (<10 h, equivalent to ascent rates >0.21 m/s). In this context, [START_REF] Polacci | Vesiculation in magmas from Stromboli and implications for normal Strombolian activity and paroxysmal explosions in basaltic systems[END_REF] used the experimental data of [START_REF] Polacci | Threedimensional investigation of volcanic textures by X-ray microtomography and implications for conduit processes[END_REF][START_REF] Polacci | Large vesicles record pathways of degassing at basaltic volcanoes[END_REF] to suggest timescales from "minutes to hours" for bubble size distributions to evolve from power law to mixed power law-exponential. In our experiments, such a transition was observed to take place at a minimum pressure of 50 MPa both for a decompression rate of 1.5 (this study) and 3 m/s (Le [START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF]. This implies that timescales of 32 (3 m/s) to 64 (1.5 m/s) minutes maximum would be needed to start producing mixed power law-exponential BSDs. These texturally based constraints are in the lower range of timescales estimated from petrological studies.

Additional constraints are provided by the D and BND data [START_REF] Métrich | Conditions of magma storage, degassing and ascent at Stromboli: new insights into the volcano plumbing system with inferences on the eruptive dynamics[END_REF]) and comparison with experimental series #2 glasses from this study (39 kPa/s, Table 5) and from Le Gall and Pichavant (2016, 78 kPa/s). Stromboli glasses plotted include melt inclusions (MI) and embayments (Emb.) from pumices and scoriae. Experimental glasses include pre-(circles) and post-decompression glasses (squares). The closed system equilibrium degassing trend (dashed curve) is calculated using VolatileCalc [START_REF] Newman | VolatileCalc: a silicate melt-H 2 O-CO 2 solution model written in Visual Basic for Excel[END_REF].

(Fig. 9). The range of natural average bubble sizes and BNDs in Strombolian pumices is bracketed by experiments from this study, Le [START_REF] Gall | Homogeneous bubble nucleation in H 2 O-and H 2 O-CO 2 -bearing basaltic melts: results of high temperature decompression experiments[END_REF] and [START_REF] Pichavant | Generation of CO 2 -rich melts during basalt magma ascent and degassing[END_REF]. In detail, the 3 m/s experiments on series #2 melts produce BNDs that exceed the natural values. Note, however, that the associated bubble sizes are far too small compared to the natural pumices. Taking 3 m/s as an upper range of ascent rates, timescales of 43 min for "golden" pumice magma to ascend from their source region at 7-8 km depth to the surface are obtained. The 1.5 m/s experiments do not yield BNDs as high as the natural values, although higher experimental BNDs would be expected for P f below 25 MPa. Therefore, an ascent rate of 1.5 m/s, corresponding to a timescale of 86 min for "golden" pumice magma ascent, also seems plausible. The 1 m/s experiments produce BNDs very close to the natural range both at 25 and 50 MPa P f . For this decompression rate and below, we observe a decrease of BND with decreasing P f , interpreted to reflect the pre-dominant influences of bubble growth and coalescence. Below 1 m/s (0.64 m/s), experimental BNDs are lower than natural values.

Both the 1 and 0.64 m/s 25 MPa P f samples are characterized by equilibrium degassing, implying that the driving force for increasing BNDs has been lost. We therefore propose 1 m/s as the lower end of the range of ascent rates at Stromboli, corresponding to ascent timescales of 128 min. In conclusion, use of our experimental D-BND systematics enable the ascent rate of the "golden" pumice magma emitted during paroxysms to be constrained between 1 and 3 m/s.

FiGure 1 .

 1 FiGure 1. Representative types of textures of post-decompression glass samples. (a) Tomographic slice of sample D3#1 quenched at P f = P in = 200 MPa, showing a bubble-free core and a thin (<50 mm) bubbly rim indicated by black arrows. (b) Tomographic slice of sample D24#3 decompressed to 25 MPa P f , showing three distinct zones: (1) a thick (150-200 mm) bubbly rim indicated by a black arrow, (2) a bubble-free zone depleted in volatiles delimited by a double black arrow, and (3) a core with numerous nearly homogeneously distributed bubbles. (c) Tomographic slice of sample D24#1 decompressed to 25 MPa P f , characterized by two distinct bubble populations. The inset gives a close-up view of the small bubbles that correspond to the second bubble population. See Table3for details about the experimental conditions and textural results.

FiGure 2 .

 2 FiGure 2. (a) Vesicularity V, (b) average bubble diameter D, and (c) bubble number density per unit volume of melt BND melt plotted as a function of final pressure P f for the post-decompression glasses of this study. Experimental data in Table3. The three glass series are distinguished, series #1 = black circles; series #2 = gray circles; series #3 = white circles. The series #1 charge D8#1 is plotted with a different symbol (black diamond) since it started from a pre-decompression melt with a H 2 O concentration ~50% lower than all the other series #1 charges. In a, equilibrium vesicularities (thick black and gray lines) calculated for pure H 2 O and CO 2 degassing, respectively (see text), are shown for comparison with the experimental data. Both the first and the second bubble populations of sample D24#1 (Table3) are plotted in b and c. In a and b, error bars (standard deviations, Table3) are indicated on the data points. The V, D, and BND melt values for Strombolian pumices (data from[START_REF] Polacci | Threedimensional investigation of volcanic textures by X-ray microtomography and implications for conduit processes[END_REF][START_REF] Polacci | Vesiculation in magmas from Stromboli and implications for normal Strombolian activity and paroxysmal explosions in basaltic systems[END_REF] are shown for comparison with the experimental data points.

FiGure 3 .

 3 FiGure 3. Evolution of the bubble size distribution (BSD) during decompression within each glass series. (a) Series #1, (b) series #2, (c) series #3 post-decompression glasses. For each glass series, two postdecompression glass samples are detailed, one representative of the early and the other of the late stage of the nucleation process. Note that for series #1 glasses, the D24#1 charge is also detailed. For each postdecompression glass sample, histograms show frequencies (normalized to 100%) of diameters of individual bubbles in the population (or the two populations for charge D24#1) using size classes of 10 mm each. The range of bubble diameters of each population is given in Table3. The number of bubbles within each population is specified (n, Table3). Details about experimental conditions and other textural data in Table3.

  FiGure 4. Bubble size distributions (BSD) expressed as log-log plots of bubble number density (BND melt , in mm -3 ) vs. bubble volume for all postdecompression glasses from this study. For each glass sample, the bubble population is characterized by a range of bubble size (expressed as diameters in Table3) and a bubble number density value (Table3). Each point along the distribution curve corresponds to the number of bubbles with a volume strictly larger than indicated. (a) Series #1 glasses, (b) series #2 glasses, and (c) series #3 glasses. Rectangles = glasses decompressed to 150 MPa P f (final pressure); triangles = glasses decompressed to 100 MPa P f ; crosses = glass decompressed to 60 MPa P f ; squares = glasses decompressed to 50 MPa P f ; diamonds = glasses decompressed to 25 MPa P f . The inset in a shows the bubble size distributions of the two bubble populations in charge D24#1. The blue continuous lines are power law fits and the red continuous curves are exponential fits, both regressed with Excel software. a is the power law exponent. The bubble volume distribution (black continuous line and curve) of a pumice sample from Polacci et al. (2009, Str50403 from a paroxysmal explosion at Stromboli) is given in b for comparison with the experimental BSDs. (Color online.)

FiGure 5 .

 5 FiGure 5. H 2 O and CO 2 concentrations in pre-and post-decompression glasses. (a) Plot of series #1 H 2 O concentrations as a function of final pressure P f . H 2 O solubilities are computed using the Lesne et al. (2011b) regression equation. They define the closed-system equilibrium decompression path (black continuous line). H 2 O vs. CO 2 concentrations in series #2 and #3 glasses are shown in b andc, respectively. Circles = pre-decompression glasses synthesized at 200 MPa P in (initial pressure); crosses = glasses decompressed to 200 MPa P f (final pressure); rectangles = glasses decompressed to 150 MPa P f ; triangles = glasses decompressed to 100 MPa P f ; squares = glasses decompressed to 50 MPa P f ; diamonds = glasses decompressed to 25 MPa P f . In b, the symbol color refers to the synthesis experiments, either S3 (black), S6 (gray), or S4 (white, Table2). Error bars (standard deviations, Table5) are indicated on the data points. The thin continuous lines are fluid-melt equilibrium saturation isobars (25-250 MPa) and the dashed curves are equilibrium decompression paths calculated for some series #2 and #3 glasses assuming closedsystem behavior. Equilibrium fluid-melt calculations were performed with VolatileCalc[START_REF] Newman | VolatileCalc: a silicate melt-H 2 O-CO 2 solution model written in Visual Basic for Excel[END_REF].

FiGure 6 .

 6 FiGure 6. FTIR profiles of H 2 O concentrations across the cylinder starting from the sample edge toward the core for series #1 glasses decompressed to different P f from 150 to 25 MPa (note that the 25 MPa data points are for the D8#1 charge performed with a low H 2 O concentration pre-decompression melt). The 150, 100, 50, and 25 MPa P f cylinders have diameters ~2.5 mm; the 60 MPa P f cylinder has a diameter of ~5 mm. Average H 2 O concentration data are given in Table5. H 2 O solubilities (at pressures of 150-25 MPa, dashed horizontal lines) come fromLesne et al. (2011b).

FiGure 7 .

 7 FiGure 7. (a) Bubble number density per unit volume of melt BND melt , (b) average bubble diameter D, and (c) vesicularity V plotted as a function of decompression rate for the series #2 glasses. Textural data from this study (dP/dt = 39 kPa/s, Table3) are compared with data from Le Gall and Pichavant (2016, dP/dt = 78 kPa/s) and fromPichavant et al. (2013, dP/dt = 17 and 27 kPa/s). The BND, D, and V values for Strombolian pumices (data come from[START_REF] Polacci | Threedimensional investigation of volcanic textures by X-ray microtomography and implications for conduit processes[END_REF][START_REF] Polacci | Vesiculation in magmas from Stromboli and implications for normal Strombolian activity and paroxysmal explosions in basaltic systems[END_REF] are shown for comparison. The gray continuous lines are P f isobars drawn for P f = 100, 50, and 25 MPa.

Table 1 .

 1 Composition of PST-9 golden pumice and starting glass

	Label	PST-9 a	Glass b (n = 54)
	SiO 2	49.4	50.9(3) c
	TiO 2	0.79	0.81(8)
	Al 2 O 3	15.75	15.99(28)
	Fe 2 O 3	1.3	nd
	FeO	6.5	7.7(6) d
	MnO	0.15	0.16(8)
	MgO	7.96	7.21(41)
	CaO	12.73	12.34(24)
	Na 2 O	2.27	2.39(9)
	K 2 O	1.85	1.90(12)
	P 2 O 5	0.43	0.55(17)
	Cr 2 O 3	-	0.03(4)
	NiO	-	0.05(6)
	Total	99.1	97.4(10)
	Notes: Oxides are in wt%. nd = not determined.
	a Whole-rock analysis performed at CRPG, Nancy, France (from Di Carlo et al.
	2006).
	b Electron microprobe analysis (normalized to 100%) of PST-9 glass (from Le Gall
	and Pichavant 2016), n = number of analyses.
	c One standard deviation in terms of last digit.

d Total Fe as FeO.

Table 2 .

 2 Synthesis experiments

	Run	X H2Oin T (°C) P (MPa) t (min) H 2 O glass (wt%) CO 2 glass (ppm)
			Volatile: H 2 O (no. 1)
	S3#1	1	1200 202.2	2793	4.91(3)	0(0)
	S4#1	1	1200 203.1	2509	4.93(5)	0(0)
	S5#1	1	1200 202.8	2985	4.94(4)	0(0)
	S6#1	1	1200 202.2	2760	4.90(1)	0(0)
	S8#1	1	1200 203.8	4198	2.53(5)	0(0)
	S11#1	1	1200 202.1	2900	4.90(3)	0(0)
	S14#1	1	1200 201.9	1465	4.91(1)	0(0)
	S16#1	1	1200 201.8	2873	4.90(2)	0(0)
			Volatile: H 2 O+CO 2 (no. 2)
	S3#2	0.25	1200 202.2	2793	1.95(1)	818(111)
	S4#2	0.55	1200 203.1	2509	a 0.58(1)	864(17)
	S6#2	0.56	1200 202.2	2760	2.37(1)	1011(106)
			Volatile: H 2 O+CO 2 (no. 3)
	S3#3	0	1200 202.2	2793	1.12(1)	840(92)
	S4#3	0	1200 203.1	2509	0.71(1)	860(78)
	S5#3	0	1200 202.8	2985	0.84(4)	1063(109)
	S6#3	0	1200 202.2	2760	0.80(3)	852(57)
	S8#3	0	1200 203.8	4198	0.79(1)	1094(56)
	S13#3	0	1200 201.5	2878	1.09(3)	923(132)
	Notes: S11 synthesis from Le

Table 3 .

 3 Decompression experiments: Run conditions and textural information

	Sample Starting P in (MPa) P f (MPa) t ramp (s) |dP/dt|					Bubble 3D characteristics
		glass				(kPa/s)	n	peak size range	D	BND a BND melt b	S	V c	V d	V Equi.H2O	V Equi.CO2
								(µm)	(µm)	(µm)	(mm -3 ) (mm -3 ) (µm) (vol%) (vol%) (vol%)	(vol%)
								Volatile: H 2 O (no. 1)
	D3#1	S5#1	200	200	0	39	0	-	-	0(0) g	0.00	0.00	-	0.00	0.00(0) 0.00
	D30#1 S16#1	200	150	1284	39	8350	6	4-46	8(3)	1324	1325	56	0.06	0.05(0) 9.22
	D2#1	S3#1	200	99.8	2568	39	42	29	9-120 58(28)	7.97	7.98	310	0.14 0.28(0.1) 24.1
	D22#1 S14#1	200	60	3649	39	149	-	15-266 121(67)	2.51	2.52	456	0.45 2.10(1.5) 44.3
	D5#1	S4#1	200	50	3840	39	5	-	40-200 113(58)	1.33	1.33	564	0.17 0.31(0.3) 51.0
	D8#1	S8#1	200	25	4488	39	567	27	7-73	28(11)	397	400	84	0.64 1.45(0.2) 72.5
	D19#1	S6#1	200	25	4488	39	nd	nd	nd	nd	nd	nd	nd	nd	nd	72.5
	D24#1 e S11#1	200	25	4488	39	> 28	nd 400-1800 741	0.65	0.76	680	0.00 71.2(1.8) 72.5
	D24#1 f S11#1	200	25	4488	39	58	10	9-56	17(10)	6.89	6.89	326	0.00 71.2(1.8) 72.5
								Volatile: H 2 O+CO 2 (no. 2)
	D3#2	S4#2	200	200	0	39	10	19	6-141 40(43)	1.15	1.15	592	0.02	0.05(0) 0.00	0.00
	D1#2	S3#2	200	149.9	1284	39	15	6-7	6-60	13(14)	1.95	1.95	497	0.00	0.01(0) 9.22	0.17
	D2#2	S3#2	200	99.8	2568	39	665	15	15-48	19(4)	104	105	132	0.04	0.10(0) 24.1	0.47
	D5#2	S4#2	200	50	3840	39	114	15	6-73	17(11)	19.2	19.2	232	0.01	0.04(0) 51.0	1.48
	D6#2	S6#2	200	25	4488	39	179	53	21-179 69(33)	152	159	115	4.70 12.6(2.7) 72.5	3.47
	D8#2	S6#2	200	25	4488	39	171	61, 97 24-175 74(28)	186	198	107	5.82	13.8(2) 72.5	3.47
								Volatile: H 2 O+CO 2 (no. 3)
	D3#3	S4#3	200	200	0	39	0	-	-	0(0)	0.00	0.00	-	0.00	0.00(0) 0.00	0.00
	D1#3	S3#3	200	149.9	1284	39	8	8	7-57	15(17)	4.38	4.38	379	0.01	0.00(0) 9.22	0.17
	D2#3	S3#3	200	99.8	2568	39	5	5	5-8	6(4)	0.60	0.60	734	0.00	0.04(0) 24.1	0.47
	D16#3	S6#3	200	100	2568	39	27	13	8-39	17(7)	4.18	4.18	385	0.00	0.02(0) 24.1	0.47
	D18#3 S13#3	200	100	2568	39	2042	6	6-28	7(2)	231	231	101	0.01	0.01(0) 24.1	0.47
	D5#3	S5#3	200	50	3840	39	270	13	7-31	16(6)	25.1	25.1	212	0.01	0.01(0) 51.0	1.48
	D8#3	S8#3	200	25	4488	39	4029	9	7-59	16(7)	3183	3220	42	1.15 3.87(1.1) 72.5	3.47
	D24#3 S13#3	200	25	4488	39	91765	12	8-135	18(9)	9016	9549	29	5.59 9.65(0.3) 72.5	3.47
	Notes: P in

Table 4 .

 4 Experimental details and textural data for the 25 MPa series #1 charges

	Charge	PST-9	Capsule	Capsule	Glass	Bubble	Interpretation	Interpretation	Bubbles
		starting	length	after	after	texture	capsule	charge	(vol%)
		material	(cm)	experiment	experiment
	D12#1	Cylinder	3.5	Swollen around sample,	Large blocks inside	Bubbles	Sample causes	Coarsely	nd
				weight gain, perforated	and outside the	(<2 to >100 µm)	capsule failure	fragmented
				around sample	capsule
	D19#1	Cylinder	4	Unswollen, no weight	Glass powder inside	Bubbles	No capsule failure	Finely	nd
				change, unperforated	the capsule	(<4 to >200 µm)		fragmented
	D24#1	Cylinder	4	Entirely swollen, weight	Foam leaked	Highly vesicular	Sample causes	Unfragmented	71.2
				gain, perforated	outside the capsule		capsule failure
				around sample	(3-4 mm diameter)
	D27#1	Cylinder	5	Unswollen, weight?,	Dense block flown	Bubbles	Sample causes	Unfragmented	0.00
				perforated around	outside the capsule	(<11 to 46 µm)	capsule failure
				sample
	S+D40#1 Powder	4.5	Swollen around	Foam and powder	Highly vesicular,	Sample causes	Partially	High
				sample, weight gain	inside the capsule	slug	capsule failure	fragmented

Note: Experimental conditions: T = 1200 °C; P in = 200 MPa; P f = 25 MPa; t ramp = 4488 s; |dP/dt| = 39 kPa/s; nd = not determined.

Deposit item AM-16-95639, Table5. Deposit items are free to all readers and found on the MSA web site, via the specific issue's Table of Contents (go to http:// www.minsocam.org/MSA/AmMin/TOC/).

ackNowledGMeNts

This project has been financially supported by the VUELCO (EC FP7) and DEGAZMAG (ANR 2011 Blanc SIMI 5-6 003-02) projects. Ida Di Carlo is acknowledged for SEM analyses. Discussions with Don R. Baker, Didier Laporte, Bruno Scaillet, Massimo Pompilio, Alain Burgisser, and Caroline Martel have been helpful. We thank Renat Almeev for the editorial work, as well as Michael R. Carroll and Didier Laporte for their comments and suggestions on the manuscript.

reFereNces cited

Abràmoff, M.D., Magalhães, P.J., and Ram, S.J. ( 2004) Image processing with ImageJ. Biophotonics International, 11, 36-43. Aiuppa, A., Federico, C., Giudice, G., Giuffrida, G., Guida, R., Gurrieri, S., Liuzzo, M., Moretti, R., and Papale, P. (2009) 533-547 (DOI:10.1016533-547 (DOI:10. /j.epsl.2007.11.063.11.063). Baker, D.R., Lang, P., Robert, G., Bergevin, J.-F., Allard, E., and Bai, L. (2006) Bubble growth in slightly supersaturated albite melt at constant pressure. Geochimica et Cosmochimica Acta, 70, 1821-1838. Barberi, F., Rosi, M., and Sodi, A. (1993) Volcanic hazard assessment at Stromboli based on review of historical data. Acta Vulcanologica, 3, 173-187. Bertagnini, A., Métrich, N., Landi, P., and Rosi, M. (2003) FiGure 9. Comparison between textural parameters for natural (Stromboli basaltic pumices) and experimental samples decompressed at various ascent rates. Source of data: natural samples, [START_REF] Polacci | Threedimensional investigation of volcanic textures by X-ray microtomography and implications for conduit processes[END_REF][START_REF] Polacci | Vesiculation in magmas from Stromboli and implications for normal Strombolian activity and paroxysmal explosions in basaltic systems[END_REF]; experimental samples, this study (series #2 glasses, 1.5 m/s, circles, Table 3), Le Gall and Pichavant (2016, 3 m/s, crosses), [START_REF] Pichavant | Generation of CO 2 -rich melts during basalt magma ascent and degassing[END_REF]0.64 and 1 m/s, squares and triangles, respectively). Average bubble diameters D are plotted as a function of bubble number densities BNDs. The arrows indicate the direction of evolution of the textural parameters from 50 (gray symbols) to 25 MPa P f (black symbols). Notice that for ascent rates of 1.5 and 3 m/s, the evolution is positive (D increases along with BND from 50 to 25 MPa), whereas for ascent rates <1.5 m/s the evolution is negative. The arrow with a question mark extending the 1.5 m/s trend illustrates the possible evolution of textural parameters at P f below 25 MPa. The respective influences of the different possible degassing mechanisms (bubble nucleation, growth, coalescence, and outgassing) on textural parameters are indicated. Ascent rates of 1, 1.5, and 3 m/s yield experimental samples with bubble sizes lower than in Strombolian pumices. However, for the 1.5 and 3 m/s data points further evolution (either bubble nucleation, growth, and coalescence, or their combination) below 25 MPa P f would make it possible to approach the textural characteristics of the pumices. In contrast, volatile supersaturation is absent in both the 1 and 0.64 m/s 25 MPa P f samples, and so there is no longer a driving force for further nucleation and BND to reach the natural values. In addition, the 0.64 m/s 25 MPa P f charges have bubble sizes higher than in Strombolian pumices. Consequently, ascent rates >1 m/s are necessary to approach the characteristics of the Strombolian pumices. aPPeNdix Surface tensions (s) have been calculated from our experimentally determined supersaturation pressures (DP HoN ) and nucleation rates (J) computed from our measured bubble number densities and decompression timescales. Strictly speaking our calculations consider only water as the sole dissolved volatile, and so are applicable only to series #1 melts. The expression of the critical degree of supersaturation DP HoN is given by (e.g., [START_REF] Hurwitz | Bubble nucleation in rhyolitic melts: Experiments at high pressure, temperature, and water content[END_REF]Mourtada-Bonnefoi and Laporte 2002):

where k is the Boltzmann constant (1.38 × 10 -23 J/K), T is the temperature (in K) and J 0 is the preexponential nucleation rate (in m -3 /s). The parameter J 0 that is given by (e.g., Mourtada-Bonnefoi and Laporte 2004):

where W L is the volume of water molecules in the liquid (W L = 3 × 10 -29 m 3 ), n 0 is the number of water molecules per unit volume of liquid, a 0 is the mean distance between water molecules (a 0 ≈ n 0 -1/3 ) and D is the water diffusivity in the liquid, has been estimated. D is taken from the equation of [START_REF] Zhang | Diffusion of H, C, and O components in silicate melts[END_REF] that takes into consideration the effects of H 2 O content and temperature. n 0 is defined as 6.02 × 10 23 × X m × r liq /M, where 6.02 × 10 23 is the Avogadro number, X m is the mass fraction of molecular water in the liquid, r liq is the liquid density (2650 kg/m 3 ), and M is the molar mass of water (0.018 kg/mol). W L and X m parameters are poorly constrained in basalt melts and we have used the values given by Mourtada-Bonnefoi and Laporte (2004), determined for rhyolitic liquids. Checks were performed to evaluate their influence on the calculated results and found to be small (<0.001 N/m). In the same way, the choice of the D equation leads to very small (<0.001 N/m) differences in s.