# Experimental constraints on the behaviour of sulphur in the 2021 Cumbre Vieja (La Palma) basanite

Diletta Frascerra, Bruno Scaillet, Joan Andújar, Clive Oppenheimer,
Stéphane Scaillet, Joan Martí, Ramón Casillas, Carmen López

<figure><img src="image_1.png" /></figure>

## To cite this version:

Diletta Frascerra, Bruno Scaillet, Joan Andújar, Clive Oppenheimer, Stéphane Scaillet, et al.. Ex-
perimental constraints on the behaviour of sulphur in the 2021 Cumbre Vieja (La Palma) basanite.
Journal of Volcanology and Geothermal Research, 2024, 456, 10.1016/j.jvolgeores.2024.108219 . insu-
04796214

HAL Id: insu-04796214

https://insu.hal.science/insu-04796214v1

Submitted on 5 Dec 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

# Experimental constraints on the behaviour of sulphur in the 2021 Cumbre Vieja (La Palma) basanite

Diletta Frascerra<fnref n="1" />*, Bruno Scaillet<fnref n="1" />, Joan Andújar<fnref n="1" />, Clive Oppenheimer<fnref n="2" />, Stéphane Scaillet<fnref n="1" />, Joan Martí<fnref n="3" />, Ramón Casillas<fnref n="4" />, Carmen López<fnref n="5" />.

**Abstract.** We performed experiments to constrain the effects of sulphur and oxygen fugacities on magma chamber and outgassing conditions of the La Palma 2021 eruption. Based on a series of controlled experiments on basanitic products carried out at 1040°C and 200 MPa, we show that sulphur addition affects the stabilities of amphibole and olivine, in particular at high fO₂ and elevated S contents which together inhibit amphibole crystallization. We also show that the overriding control on S systematics is oxygen fugacity, with melts capable of dissolving from 1000 up to 8000 ppm S, depending on fO₂. Increasing the bulk S content increases the S content of the silicate melt up to ~ 2000 ppm for fO₂<NNO+2, and 7000–8000 ppm at higher fO₂. Further increase in dissolved S is prevented by the buffering effects of either sulphide at low fO₂ or anhydrite at high fO₂. Modelling shows that the observed CO₂/SO₂ and H₂O/SO₂ ratios of volcanic gas emissions during the eruption imply a pre-existing > 5 wt% exsolved fluid in the reservoir, with fS₂ at ~ 0.1 MPa at fO₂ above NNO. Our work confirms that basaltic magmas may coexist with a significant amount of excess fluid which in turn holds an important part of the sulfur budget emitted to the atmosphere.

**Keywords:** La Palma, sulphur solubility, basanite, sulphur degassing

## 1. Introduction

The 2021 Cumbre Vieja eruption on La Palma produced ~ 0.2 km<fnref n="3" /> of alkali basalt over a three month period, with devastating impacts on the built environment and agricultural land (Bonadonna et al., 2022; Del Fresno et al., 2023a; González et al., 2019; Ubide et al., 2023; Dayton et al., 2024). La Palma is made up of two volcanic centres. The oldest is the Taburiente centre in the north and the presently active Cumbre Vieja centre in the south of the island (Carracedo et al., 2001 and references therein). The volcanic activity of Cumbre Vieja area began about 123,000 years ago, and its complex extends from N to S being mainly composed of single eruptive centers spread along fissures. The eruptive products belong to the alkaline series, with emission of alkaline basalts, basanites, trachybasalts, tephrites and phonolites (e.g., Carracedo et al., 2001). Prior to the 2021 eruption, several eruptions have been recorded over the last 500 years (about 8), all associated with explosive events on the summit, and effusive lava flows along the flanks (Carracedo et al., 2001). La Palma is part of the oceanic island basalt system of the Canary Islands, which is fed by a hotspot of presumed mantle origin probably influenced by the rotation of the African plate (e.g., Day et al. 2022 and references therein).

<footnote n="1">¹Institut des Sciences de la Terre d'Orléans, UMR 7327, CNRS-Université d'Orléans-BRGM (France).</footnote>

<footnote n="2">²Department of Geography, University of Cambridge (UK).</footnote>

<footnote n="3">³Dep. of Geosciences, IDAEA-CSIC, Barcelona, Spain.</footnote>

<footnote n="4">⁴ Department of Earth Sciences, Universidad de la Laguna, Tenerife, Spain</footnote>

<footnote n="5">⁵ IGN, Madrid, Spain.</footnote>

<footnote>*Corresponding author: diletta.frascerra@univ-orleans.fr</footnote>
The 2021 eruption was accompanied by vigorous degassing of CO₂ and S gas species, which were measured intermittently using a variety of sensors (e.g., Burton et al., 2023). Estimates of the quantity of the total SO₂ emitted range from 1 to over 4 Tg (Albertos et al., 2023; Burton et al., 2023; Dayton et al., 2024; Hayer et al., 2022). Melt inclusion analyses reveal an average pre-eruptive S content of ~ 3000 ppm (Castro and Feisel, 2022; Burton et al., 2023; Dayton et al., 2024). Complete syneruptive degassing of this sulphur would yield over 3 Tg of SO₂, i.e., an amount within the range of estimated emissions. However, estimates of initial CO₂ contents lie in the range 3–5 wt% (Burton et al., 2023), which is more than sufficient to saturate a basanite magma (e.g. Jiménez-Mejías et al., 2021; Lo Forte et al., 2024) at crustal pressures (<1 GPa). Given the likelihood of a pre-eruptive gas phase in the reservoir (Sandoval-Velasquez et al., 2023; Zanon et al., 2024; Dayton et al., 2024) raises the question of how much sulphur was partitioned into it? In silicic magmas, S is inferred to reside dominantly in the gas phase (e.g. Scaillet et al., 1998; Keppler, 1999).

Critical to understanding the behaviour of S in magmatic systems is to constrain their redox state or oxygen fugacity ($fO_2$), which exerts a major control on S solubility and partitioning (e.g., (Carroll and Rutherford, 1988; Luhr, 1990; Scaillet et al., 1998; Jugo, 2004; Moretti and Ottonello, 2005; O'Neill, 2021; Boulliung and Wood, 2023; Hughes et al., 2023). Knowing whether S goes into the fluid/gas or not is crucial for interpreting the composition of volcanic gases at the surface, which are routinely measured for the purposes of hazard assessment.

Our overall aim here is to develop understanding of S solubility and partitioning in mafic magmas with hotspot and ocean-island basalt (OIB) affinities through a set of experiments on La Palma 2021 basanite in which $fO_2$ and the amount of S were varied. To this end, we reconstructed eruptive conditions at La Palma. In particular, we focused on the amount of sulphur and its fugacity at pre-eruptive conditions in the reservoir and in the fluid phase during eruptive outgassing.

## 2. Experimental technique

### 2.1 Starting material and apparatus

Basanite lapilli (1 Top/27-9-2021) from the 2021 eruption of La Palma were selected as the starting material. The lapilli were finely ground using an agate mortar and then melted in a Pt crucible at 1400°C for 4 h at atmospheric pressure. These steps were repeated to obtain an homogeneous and anhydrous glass. Homogeneity was verified using the Electron Micro Probe analyzer (EMPA). The composition of the glass is reported in Table 1.

The experiments were performed with Internally Heated Pressure Vessels (IHPV) at the Institut des Sciences de la Terre d'Orléans (ISTO), using as pressure media either Ar or a H₂-Ar mixture gas (Scaillet et al., 1992). Up to eight gold capsules were placed in a ceramic sample holder, which was suspended between two type-S thermocouples with a Pt or Rh wire, depending on the redox conditions. During the experiments, we maintained a thermal gradient of less than 10 °C between the top and the bottom thermocouples. All experiments concluded with a rapid drop quench with cooling rates of order 100°C/s (Di Carlo et al., 2006).

<table><caption>Table 1 Composition starting material</caption><thead><tr><th>SiO<sub>2</sub></th><th>TiO<sub>2</sub></th><th>Al<sub>2</sub>O<sub>3</sub></th><th>FeO</th><th>MnO</th><th>MgO</th><th>CaO</th><th>Na<sub>2</sub>O</th><th>K<sub>2</sub>O</th><th>P<sub>2</sub>O<sub>5</sub></th><th>Cl</th><th>S</th><th>Total</th></tr></thead><tbody><tr><td>44.11<br>(0.26)</td><td>3.83<br>(0.10)</td><td>14.42<br>(0.13)</td><td>12.22<br>(0.26)</td><td>0.18<br>(0.05)</td><td>7.49<br>(0.05)</td><td>10.92<br>(0.11)</td><td>4.05<br>(0.08)</td><td>1.73<br>(0.10)</td><td>0.97<br>(0.07)</td><td>0.01<br>(0.01)</td><td>0.01<br>(0.01)</td><td>97.75</td></tr></tbody></table>
## 2.2 Capsule preparation and experimental conditions

The finely ground starting material was divided into three batches. Two S-bearing batches were prepared either by adding 2 wt.% native sulphur or 3 wt.% pyrrhotite (corresponding to 1.1 wt.% sulphur) and the third batch was left S-free. These bulk sulphur contents are above the sulphur solubility of basaltic melts under our experimental conditions (e.g. Moune et al. 2009; Luhr, 1990). Hence, when using the S-bearing batches directly (i.e. without mixing them with the S-free batch) as a starting material, the bulk content of sulphur should promote saturation in either sulphide or sulphate unless the coexisting fluid scavenges sulphur (see results).

For each experiment, six to seven Au capsules were prepared (inner and outer diameter of 2.5–2.9 mm, height of 1.5 cm). Gold was used to minimize the loss of sulphur and iron. Capsules were loaded first with 3 mg of deionized water to ensure fluid saturation of the system (corresponding to about 5 wt% dissolved H₂O at 200 MPa at H₂O saturation, e.g. Jiménez-Mejías et al. (2021)), then with 30 mg of silicate powder prepared by mixing S- or FeS-doped powder with S-free glass in various proportions to obtain different concentrations of sulphur (Table 2). In the following, we refer to these two series as S-doped or FeS-doped charges. The weight of the capsules was measured after welding, then after a test in an oven at 125 °C for at least 1 h, and finally after the experiment to check for volatile leaks. Only charges with a difference of less than 0.0003 g were considered successful. Considering the context of La Palma 2021 eruption as summarised above, it would have been interesting to add CO₂ as a fluid component. This however would have needed to raise the temperature of the experiments which would have in turn prohibited the use of Au containers: Containers made of either Pt or of AuPd alloys are prone to significant alteration by sulphur, which severely complicates the interpretation of results.

All the experiments were run at 1040 °C and 200 MPa but with variable fO₂ (between NNO-0.48 and NNO+4.1), controlled by sensors of NiPd for experiments above NNO and CoPd for experiments below NNO (Taylor et al., 1992; Table 2). The fS₂ of pyrrhotite-bearing charges was calculated following Froese and Gunter (1976).

On-going experiments aimed at determining pre-eruptive conditions of La Palma basalts (Andújar et al., submitted) suggest storage conditions of early erupted magmas at somewhat higher P and T (i.e., 300 MPa, 1060–1080°C). A number of petrological studies have shown that latter erupted magmas record higher pressures, >500 MPa, and temperatures above 1100°C (e.g., Castro and Feisel, 2022; Day et al., 2022; Ubide et al., 2023; Dayton et al., 2024). The reason of choice of our P-T conditions is essentially practical. As stressed above, the lower temperature allows us to use Au capsules, which considerably limits S loss from the melt+fluid towards the caspule (and also that of Fe loss), compared to either AuPd or Pt capsules, maintaining the physical integrity of containers. Such a low temperature is achieved by working with elevated melt water contents, which depress liquidus temperatures significantly in basaltic systems while maintaining the composition of near liquidus residual melts broadly basaltic (e.g., Sisson and Grove, 1993). Performing experiments at 300 MPa would have been possible, but the higher water content of the basaltic melts (>7 wt%) at this pressure renders those liquid poorly quenchable, even with drop
quench technique. Therefore, given the H₂O-reach conditions of our experiments, we decided to perform the experiments at 200 MPa, with the objective of favouring the solubility of the sulphur and facilitating the quench of the glass. Nevertheless, we recognise the potential for this approach to result in differences with the natural system, in particular a higher proportion of amphibole relative to what is observed in the rocks. Higher temperatures will also affect the solubility of sulphur: for instance an increase of 50°C in the fO₂ range NNO - NNO+1.5 increases the S solubility by 10-30%, if fS₂ is kept constant (e.g., Boulliung and Wood, 2023).

126

## 3. Analytical methods

### 3.1 Analytical techniques

Half of the recovered run products were embedded in epoxy and polished for optical inspection and, then carbon-coating, for scanning electron microscopy (SEM) using the Zeiss FEG of ISTO to identify phases, including those of quench origin.

Glass and minerals were analysed using a Cameca SX FIVE EMPA (CNRS-Université d'Orléans-BRGM). The analytical conditions were 15 kV, 10 nA and a peak count time of 10 s. Glasses were analysed with a defocused beam of 5, 10 or 20 µm, depending on the size of the available glass pools. Sulphur was determined using an LPET crystal and a 20 s counting time. A focused beam was used for the minerals. Sulphides were analysed during separate sessions with the following analytical conditions: 20 kV and 50 nA, using PET and LPETcrystals for S, an acquisition time of 30 s, while Fe was analyzed with LIF and LLIF crystals. The Ni and Cu had acquisition times of 10s. In addition, Si was used to detect possible glass contamination. At the beginning and end of the analytical session, two synthetic pyrrhotites of known compositions (as determined by X-ray analyses, (Clemente et al., 2004), Po5 and Po7, were analysed to check the stability of the calibration.

Three glasses with different sulphur concentrations were synthesised at 1200°C using the same experimental apparatus and starting glass. The sulphur concentrations measured by the microprobe were found to differ by less than 100 ppm relative to the added amount, validating our analytical procedure for measuring S.

The H₂O concentration in the run products was estimated following Devine et al. (1995), analyzing at the beginning and end of each analytical session standard basanitic glasses of known water contents (F1c, F05, F3c2 and F2b, in Jiménez-Mejías et al. (2021)).

### 3.2 *Mass balance and ImageJ software calculations*

The proportion of each phase was calculated by mass balance using a constrained least-squares model with the propagation of analytical errors of the experimental phases (Albarède, 1996; Scaillet and Evans, 1999). The proportion of glass was also calculated by processing SEM images at 100 µm magnification using ImageJ software, on a vesicle-free basis.

119

120

121

122

123

124

125

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

151

152

153

154
The amount of sulphur in the coexisting fluid phase was estimated by mass balance, i.e. by
155
156 subtracting the masses of S in sulphur-bearing phases (glass, sulphide, sulphate) from the initial
157 mass of sulphur, taking into account the phase percentages as calculated above. The S wt% was
158 then calculated by determining the amount of H₂O in the fluid using the same method (Table 2).

159
<table><caption>Table 2 Experimental conditions, water and sulphur contents of quenched glass. H₂O is calculated with the method of Devine et al (1996). The fS₂ is calculated using the method of Froese and Gunter (1976). Amph? = quench phase</caption><thead><tr><th>Run</th><th>P (MPa)</th><th>T (°C)</th><th>Time (min)</th><th>ΔNNO</th><th>log fO2</th><th>log fS2 (bar)</th><th>H2O&</th><th>S% and type loaded</th><th>S wt% Glass</th><th>S wt% Fluid</th><th>Mineral assemblage</th></tr></thead><tbody><tr><td>lpm 1</td><td>200</td><td>1040</td><td>960</td><td>1.34</td><td>8.40</td><td>0.28</td><td>4.1</td><td>2%-native</td><td>0.22 (0.02)</td><td>9.2</td><td>Ol-Amph-Px-FeS</td></tr><tr><td>lpm 2</td><td></td><td></td><td></td><td></td><td></td><td>-0.24</td><td>1.8</td><td>1%-native</td><td>0.11 (0.01)</td><td>5.2</td><td>Ol-Amph-Px - Mt-FeS</td></tr><tr><td>lpm 33</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4.0</td><td>0.5%-native</td><td>0.18 (0.01)</td><td>5.4</td><td>Ol-Amph - Px - Mt</td></tr><tr><td>lpm 4</td><td></td><td></td><td></td><td></td><td></td><td>-0.24</td><td>3.1</td><td>1.12%-FeS</td><td>0.23 (0.01)</td><td>5.1</td><td>Ol-Amph-Px-Mt-FeS</td></tr><tr><td>lpm 5</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4.1</td><td>0.56%-FeS</td><td>0.21 (0.03)</td><td>6.3</td><td>Ol-Amph-Px-Mt</td></tr><tr><td>lpm 6</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5.9</td><td>0.28%-FeS</td><td>0.10 (0.02)</td><td>3.5</td><td>Ol-Amph-Px-Mt</td></tr><tr><td>lpm 34</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4.5</td><td>0%S</td><td></td><td></td><td>Ol-Amph-Px-Mt</td></tr><tr><td>lpm 7</td><td>200</td><td>1040</td><td>960</td><td>2.38</td><td>7.37</td><td></td><td>3.8</td><td>2%-native</td><td>0.73 (0.04)</td><td>16.6</td><td>Ol-Mt-Ilm</td></tr><tr><td>lpm 8</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4.7</td><td>1%-native</td><td>0.86 (0.06)</td><td>3.6</td><td>Ol-Px-Mt</td></tr><tr><td>lpm 9</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3.9</td><td>0.5%-native</td><td>0.57 (0.03)</td><td>2.5</td><td>Ol-Amph-Px-Mt</td></tr><tr><td>lpm 13</td><td>200</td><td>1040</td><td>360</td><td>3.30</td><td>6.44</td><td></td><td>5.4</td><td>2%-native</td><td>0.75 (0.04)</td><td>21.1</td><td>Ol-Mt-Ilm</td></tr><tr><td>lpm 14</td><td></td><td></td><td></td><td></td><td></td><td></td><td>6.3</td><td>1%-native</td><td>0.75 (0.04)</td><td>13.3</td><td>Ol-Px-Mt</td></tr><tr><td>lpm 15</td><td></td><td></td><td></td><td></td><td></td><td></td><td>6.8</td><td>0.5%-native</td><td>0.65 (0.09)</td><td></td><td>Px-Mt</td></tr><tr><td>lpm 16</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.0</td><td>1.12%-FeS</td><td>0.79 (0.03)</td><td>6.9</td><td>Px-Mt-Ilm</td></tr><tr><td>lpm 17</td><td></td><td></td><td></td><td></td><td></td><td></td><td>6.1</td><td>0.56%-FeS</td><td>0.65 (0.09)</td><td>0.3</td><td>Ol-Px-Mt</td></tr><tr><td>lpm 18</td><td></td><td></td><td></td><td></td><td></td><td></td><td>6.5</td><td>0.28%-FeS</td><td>0.33 (0.03)</td><td>1.7</td><td>Amph-Px-Mt</td></tr><tr><td>lpm 19</td><td>200</td><td>1040</td><td>360</td><td>4.10</td><td>5.65</td><td></td><td>4.8</td><td>2%-native</td><td>0.68 (0.05)</td><td></td><td>Ol-Px-Mt-Ilm-Anhy</td></tr><tr><td>lpm 20</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5.6</td><td>1%-native</td><td>0.64 (0.01)</td><td>9.3</td><td>Ol-Amph-Px-Mt-Ilm</td></tr><tr><td>lpm 21</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4.5</td><td>0.5%-native</td><td>0.58 (0.05)</td><td>3.1</td><td>Amph-Px-Mt</td></tr><tr><td>lpm 22</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5.2</td><td>1.12%-FeS</td><td>0.71 (0.04)</td><td>9.0</td><td>Ol-Px-Mt</td></tr><tr><td>lpm 23</td><td></td><td></td><td></td><td></td><td></td><td></td><td>5.8</td><td>0.56%-FeS</td><td>0.65 (0.03)</td><td>3.1</td><td>Amph-Px-Mt</td></tr><tr><td>lpm 24</td><td></td><td></td><td></td><td></td><td></td><td></td><td>6.4</td><td>0.28%-FeS</td><td>0.38 (0.03)</td><td>1.4</td><td>Amph-Px-Mt-Ap</td></tr><tr><td>lpm 25</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4.6</td><td>0%S</td><td></td><td></td><td>Amph-Px-Mt</td></tr><tr><td>lpm 26</td><td>200</td><td>1040</td><td>360</td><td>-0.48</td><td>1023</td><td>-0.63</td><td>3.5</td><td>2%-native</td><td>0.12 (0.01)</td><td>3.7</td><td>Ol-Amph-Px-FeS</td></tr><tr><td>lpm 27</td><td></td><td></td><td></td><td></td><td></td><td>-1.59</td><td>2.4</td><td>1%-native</td><td>0.10 (0.01)</td><td>1.2</td><td>Ol-Amph-Px-FeS</td></tr><tr><td>lpm 28</td><td></td><td></td><td></td><td></td><td></td><td></td><td>3.1</td><td>0.5%-native</td><td>0.13 (0.01)</td><td>5.5</td><td>Ol-Amph-Px-Mt</td></tr><tr><td>lpm 29</td><td></td><td></td><td></td><td></td><td></td><td>-1.02</td><td>3.6</td><td>1.12%-FeS</td><td>0.19 (0.03)</td><td>6.7</td><td>Ol-FeS-Mt</td></tr><tr><td>lpm 30</td><td></td><td></td><td></td><td></td><td></td><td>-0.75</td><td>3.1</td><td>0.56%-FeS</td><td>0.19 (0.03)</td><td>3.7</td><td>Ol-Px-FeS</td></tr><tr><td>lpm 32</td><td></td><td></td><td></td><td></td><td></td><td></td><td>4.7</td><td>0%S</td><td></td><td></td><td>Ol-Amph?-Px-Mt</td></tr></tbody></table>
165 **4. Results**

166 The experiments generated different mineral assemblages, depending on fO₂ and the amount of S
167 added, as shown in Fig. 1.

<figure><img src="image_3.png" /><figcaption>Fig. 1 Equilibrium phase diagram at 1040°C and 200 MPa for both S-doped (a) and FeS-doped (b) charges. Phases lie inside their stability field. Ol=olivine; Cpx= clinopyroxene; Amph = amphibole; Anhy = anhydrite; mt=magnetite.</figcaption></figure>

168 In the S-doped series, anhydrite crystallizes at high fO₂ while pyrrhotite is present at low fO₂. In
169 detail, anhydrite is found only in the charge with 2 wt.% added S at NNO+4.1, while pyrrhotite is
170 present with 1 wt.% and 2 wt.% S added at NNO+1.34 and NNO-0.48. Olivine occurs in almost
171 every charge, except for those poorer in sulphur at high fO₂. Apart from three charges with 2 wt.%
172 S added at NNO+2.38, 3.3 and 4.1, pyroxene is present in all experimental charges. Amphibole
173 distribution is more complex. It did not crystallise in charges with 2 wt.% and 1 wt.% S at
174 NNO+2.38, in any experiments at NNO+3.3, in the charge at 2 wt.% S under the most oxidising
175 conditions and in the S-free charge at NNO-0.48 (Fig.1a).

176 The phase diagram of the FeS-doped series is broadly similar. The stability range of olivine is
177 almost identical, except that Ol was also found in the 0.56 wt.% S charge at NNO+4.10. In the
178 sulphur-rich experiment at NNO+3.3, Ol was not found but owing to its low abundance in other
179 charges, it may have been overlooked. In the charge lpm 1-top+S17, olivine is present as inclusions
180 in the pyroxene. Pyroxene is present in all charges, except for that with 1.12 wt.% S at NNO-0.48.
181 FeS has a similar stability field to that identified by the S-doped series, however it is absent at 0.56
182 wt.% S and NNO+1.34. The amphibole field is also similar in S-doped case, except that it is not
183 found at NNO-0.48 (Fig.1b).

184

185

186

187
188 4.1 Major element glass and mineral composition

<figure><img src="image_4.png" /><figcaption>Fig. 2 Variation of oxides with SiO₂ of experimental glasses in S doped (coloured symbols) and FeS doped (open symbols) charges. When not shown, the error bars are smaller than the symbol size.</figcaption></figure>

189 The major elements of glasses of both the S and FeS doped series (Table 3), show similar trends
190 (Fig. 2). SiO₂ increases regularly with fO₂, from about 44 wt.% up to a of 56 wt.%, as does Al₂O₃,
191 which reaches up to 20 wt.%, reflecting the absence of plagioclase crystallisation under the
192 investigated conditions. Reflecting clinopyroxene crystallization, CaO shows the opposite
behaviour, decreasing with increasing SiO₂ and fO₂. The same trend is observed for TiO₂ and FeO.

The alkalies show no clear trends, with the possible exception of Na₂O which increased slightly with SiO₂. These fractionation trends reflect the effect of the main crystallising phases, but above all the increasing abundance of magnetite as fO₂ increases (Fig. 1).

The concentration of sulphur in the glasses does not differ between the S- or FeS-doped experiments (Fig. 3). The charges produced at low fO₂ are significantly poorer in sulphur than those at high fO₂, the former having S concentration in the range 1000–2300 ppm, while the later have S

<figure><img src="image_5.png" /><figcaption>Fig. 3. Variation of S content of the glass with fO₂ as a function of wt.% of sulphur added to the capsules. When not shown, the error bars are smaller than the symbol size.</figcaption></figure>

contents ranging between 3300–8800 ppm. Note however that the charge doped with 0.28 wt.% S using FeS yielded 0.8 wt.% dissolved S, which we attribute to an error in loading S to the charge.

This individual run is not further considered.

From inspection of the Mg# of the glass and of Fe-Mg minerals, the amount of sulphur added does not appreciably affect their composition at fixed fO₂, though under reduced conditions
($<$NNO+1.5), charges with higher bulk S contents tend to have phases with higher Mg# (in particular for charges with 2 wt.% added S). At high fO₂ the reverse is observed. Similarly, an increase in fO₂ increases slightly the Mg# of the glass and olivine, as shown in figure in Supplementary information (SIa). No clear trends with S appears for either amphibole or pyroxene compositions (SIa).

The measured S contents in glasses saturated in pyrrhotite can be compared to those calculated using the S-solubility model of Lesne et al. (2015), which was developed for hydrous alkali-rich basalts, using the fS₂ determined by pyrrhotite (Table 2). We also calculated S contents using the model of Boulliung and Wood (2023). The results are shown in Fig. 4, illustrating a general good correspondence between calculated S contents with both models and those measured, though the Boulliung and Wood (2023) model tends to underestimate S contents. Discrepancies likely reflect analytical uncertainties in pyrrhotite composition as determined by EPMA, which translates into an uncertainty in calculated fS₂ of order ±1 log unit (e.g., Whitney, 1984). For instance, increasing log fS₂ of charge lpm 29 from -1.02 to -0.5 (Table 2) would increase the calculated S content from

<figure><img src="image_6.png" /></figure>

Fig. 4 Comparison between the measured S content of experimental glasses saturated in pyrrhotite with that calculated using the models of Lesne et al. (2015, blue symbols) and Boulliung and Wood (2023, orange symbols). The arrow shows the effect of increasing fS₂ by 0.5 log unit on the calculated S content of melt with the model of Lesne et al. (2015).

0.14 wt% to 0.19 wt%, the same as the measured amount (Fig. 4).
<table><caption>Table 3 Major elements compositions, normalized to 100% anhydrous, and S contents of quenched glasses; *Original total.</caption><thead><tr><th></th><th>ΔNNO</th><th>SiO<sub>2</sub></th><th>TiO<sub>2</sub></th><th>Al<sub>2</sub>O<sub>3</sub></th><th>FeO</th><th>MnO</th><th>MgO</th><th>CaO</th><th>Na<sub>2</sub>O</th><th>K<sub>2</sub>O</th><th>P<sub>2</sub>O<sub>5</sub></th><th>S</th><th>Total*</th></tr></thead><tbody><tr><td>lpm 1</td><td>1.34</td><td>46.19<br>(0.25)</td><td>3.75<br>(0.10)</td><td>15.68<br>(0.14)</td><td>9.93<br>(0.36)</td><td>0.20<br>(0.08)</td><td>6.39<br>(0.10)</td><td>10.14<br>(0.25)</td><td>4.07<br>(0.05)</td><td>2.00<br>(0.20)</td><td>1.17<br>(0.06)</td><td>0.22<br>(0.02)</td><td>93.75</td></tr><tr><td>lpm 2</td><td></td><td>47.93<br>(0.98)</td><td>3.10<br>(0.15)</td><td>17.22<br>(0.39)</td><td>10.06<br>(0.19)</td><td>0.31<br>(0.07)</td><td>3.72<br>(0.15)</td><td>8.46<br>(0.62)</td><td>4.81<br>(0.62)</td><td>2.34<br>(0.700)</td><td>1.82<br>(0.66)</td><td>0.11<br>(0.01)</td><td>96.23</td></tr><tr><td>lpm 33</td><td></td><td>46.81<br>(0.45)</td><td>3.60<br>(0.21)</td><td>16.17<br>(0.07)</td><td>10.27<br>(0.34)</td><td>0.20<br>(0.07)</td><td>4.52<br>(0.25)</td><td>10.62<br>(0.37)</td><td>4.61<br>(0.25)</td><td>1.61<br>(0.25)</td><td>1.19<br>(0.06)</td><td>0.18<br>(0.01)</td><td>92.59</td></tr><tr><td>lpm 4</td><td></td><td>44.88<br>(0.22)</td><td>3.56<br>(0.14)</td><td>15.79<br>(0.11)</td><td>11.79<br>(0.12)</td><td>0.25<br>(0.05)</td><td>5.14<br>(0.10)</td><td>10.52<br>(0.15)</td><td>4.60<br>(0.15)</td><td>1.84<br>(0.06)</td><td>1.13<br>(0.06)</td><td>0.23<br>(0.01)</td><td>94.81</td></tr><tr><td>lpm 5</td><td></td><td>45.43<br>(0.40)</td><td>3.40<br>(0.16)</td><td>15.25<br>(0.21)</td><td>11.58<br>(0.28)</td><td>0.20<br>(0.09)</td><td>5.76<br>(0.57)</td><td>11.24<br>(0.72)</td><td>4.42<br>(0.16)</td><td>1.17<br>(0.34)</td><td>1.07<br>(0.06)</td><td>0.21<br>(0.03)</td><td>93.74</td></tr><tr><td>lpm 6</td><td></td><td>46.52<br>(0.15)</td><td>3.46<br>(0.16)</td><td>16.00<br>(0.09)</td><td>10.73<br>(0.34)</td><td>0.22<br>(0.08)</td><td>5.19<br>(0.27)</td><td>11.58<br>(0.16)</td><td>4.03<br>(0.08)</td><td>0.96<br>(0.14)</td><td>1.07<br>(0.09)</td><td>0.10<br>(0.02)</td><td>91.88</td></tr><tr><td>lpm 34</td><td></td><td>48.42<br>(0.27)</td><td>2.98<br>(0.11)</td><td>17.42<br>(0.21)</td><td>9.17<br>(0.30)</td><td>0.19<br>(0.05)</td><td>3.58<br>(0.09)</td><td>9.08<br>(0.22)</td><td>5.54<br>(0.25)</td><td>2.40<br>(0.10)</td><td>1.18<br>(0.02)</td><td>0.00<br>(0.01)</td><td>92.60</td></tr><tr><td>lpm 7</td><td>2.38</td><td>48.93<br>(0.23)</td><td>3.24<br>(0.06)</td><td>15.92<br>(0.12)</td><td>7.92<br>(0.09)</td><td>0.15<br>(0.03)</td><td>5.85<br>(0.06)</td><td>9.73<br>(0.13)</td><td>3.81<br>(0.06)</td><td>1.66<br>(0.09)</td><td>0.95<br>(0.08)</td><td>0.73<br>(0.04)</td><td>93.55</td></tr><tr><td>lpm 8</td><td></td><td>46.13<br>(0.28)</td><td>3.52<br>(0.14)</td><td>15.36<br>(0.10)</td><td>7.95<br>(0.26)</td><td>0.21<br>(0.02)</td><td>6.24<br>(0.17)</td><td>10.93<br>(0.23)</td><td>4.44<br>(0.09)</td><td>1.94<br>(0.17)</td><td>1.05<br>(0.09)</td><td>0.86<br>(0.06)</td><td>93.00</td></tr><tr><td>lpm 9</td><td></td><td>48.78<br>(0.15)</td><td>2.97<br>(0.10)</td><td>17.36<br>(0.21)</td><td>6.71<br>(0.21)</td><td>0.20<br>(0.07)</td><td>4.61<br>(0.18)</td><td>8.66<br>(0.22)</td><td>5.50<br>(0.07)</td><td>2.38<br>(0.14)</td><td>1.38<br>(0.13)</td><td>0.57<br>(0.03)</td><td>94.81</td></tr><tr><td>lpm 13</td><td>3.30</td><td>50.68<br>(0.35)</td><td>2.45<br>(0.11)</td><td>16.17<br>(0.22)</td><td>6.10<br>(0.30)</td><td>0.20<br>(0.08)</td><td>6.42<br>(0.09)</td><td>9.62<br>(0.14)</td><td>3.75<br>(0.42)</td><td>1.72<br>(0.06)</td><td>0.99<br>(0.05)</td><td>0.75<br>(0.04)</td><td>92.63</td></tr><tr><td>lpm 14</td><td></td><td>49.60<br>(0.21)</td><td>2.47<br>(0.16)</td><td>17.28<br>(0.22)</td><td>5.29<br>(0.19)</td><td>0.24<br>(0.09)</td><td>5.53<br>(0.32)</td><td>10.32<br>(0.42)</td><td>4.65<br>(0.12)</td><td>1.48<br>(0.13)</td><td>1.20<br>(0.12)</td><td>0.75<br>(0.04)</td><td>91.99</td></tr><tr><td>lpm 15</td><td></td><td>48.12<br>(0.33)</td><td>2.87<br>(0.16)</td><td>16.15<br>(0.10)</td><td>5.89<br>(0.20)</td><td>0.19<br>(0.07)</td><td>6.44<br>(0.26)</td><td>10.76<br>(0.14)</td><td>4.68<br>(0.07)</td><td>1.93<br>(0.18)</td><td>1.19<br>(0.06)</td><td>0.69<br>(0.05)</td><td>92.01</td></tr><tr><td>lpm- 16</td><td></td><td>49.77<br>(0.23)</td><td>2.27<br>(0.04)</td><td>16.37<br>(0.21)</td><td>6.07<br>(0.23)</td><td>0.12<br>(0.04)</td><td>6.25<br>(0.05)</td><td>10.48<br>(0.08)</td><td>4.17<br>(0.06)</td><td>1.72<br>(0.11)</td><td>1.16<br>(0.00)</td><td>0.79<br>(0.03)</td><td>91.16</td></tr><tr><td>lpm 17</td><td></td><td>49.79<br>(0.169)</td><td>2.49<br>(0.12)</td><td>16.62<br>(0.37)</td><td>5.83<br>(0.23)</td><td>0.20<br>(0.11)</td><td>5.17<br>(0.58)</td><td>11.54<br>(0.75)</td><td>4.03<br>(0.33)</td><td>1.14<br>(0.29)</td><td>1.27<br>(0.09)</td><td>0.65<br>(0.09)</td><td>89.92</td></tr><tr><td>lpm 18</td><td></td><td>51.87<br>(0.31)</td><td>2.29<br>(0.30)</td><td>18.26<br>(1.05)</td><td>5.17<br>(0.52)</td><td>0.26<br>(0.07)</td><td>4.07<br>(0.90)</td><td>9.96<br>(0.46)</td><td>4.39<br>(0.45)</td><td>1.58<br>(0.23)</td><td>1.46<br>(0.10)</td><td>0.33<br>(0.03)</td><td>89.41</td></tr><tr><td>lpm 19</td><td>4.10</td><td>52.79<br>(0.15)</td><td>1.73<br>(0.08)</td><td>17.04<br>(0.23)</td><td>5.24<br>(0.09)</td><td>0.17<br>(0.07)</td><td>5.83<br>(0.06)</td><td>9.19<br>(0.52)</td><td>3.97<br>(0.03)</td><td>1.80<br>(0.24)</td><td>0.85<br>(0.04)</td><td>0.68<br>(0.05)</td><td>91.44</td></tr><tr><td>lpm 20</td><td></td><td>51.66<br>(0.09)</td><td>1.89<br>(0.07)</td><td>17.67<br>(0.10)</td><td>4.74<br>(0.07)</td><td>0.22<br>(0.04)</td><td>5.52<br>(0.34)</td><td>10.07<br>(0.42)</td><td>4.32<br>(0.05)</td><td>1.37<br>(0.12)</td><td>1.21<br>(0.10)</td><td>0.64<br>(0.01)</td><td>90.53</td></tr><tr><td>lpm 21</td><td></td><td>55.88<br>(0.19)</td><td>1.42<br>(0.13)</td><td>19.71<br>(0.58)</td><td>3.35<br>(0.44)</td><td>0.23<br>(0.05)</td><td>1.33<br>(0.11)</td><td>7.77<br>(0.38)</td><td>5.52<br>(0.10)</td><td>2.01<br>(0.17)</td><td>1.51<br>(0.14)</td><td>0.58<br>(0.05)</td><td>91.59</td></tr><tr><td>lpm 22</td><td></td><td>51.50<br>(0.19)</td><td>1.69<br>(0.08)</td><td>17.57<br>(0.39)</td><td>5.13<br>(0.19)</td><td>0.25<br>(0.07)</td><td>3.71<br>(0.53)</td><td>12.64<br>(0.63)</td><td>4.20<br>(0.11)</td><td>0.65<br>(0.08)</td><td>1.22<br>(0.04)</td><td>0.71<br>(0.04)</td><td>90.99</td></tr><tr><td>lpmS 23</td><td></td><td>55.01<br>(0.17)</td><td>1.35<br>(0.11)</td><td>19.49<br>(0.71)</td><td>3.51<br>(0.52)</td><td>0.26<br>(0.10)</td><td>1.71<br>(0.95)</td><td>8.59<br>(0.81)</td><td>5.17<br>(0.14)</td><td>1.89<br>(0.24)</td><td>1.64<br>(0.22)</td><td>0.65<br>(0.03)</td><td>90.14</td></tr><tr><td>lpm S 24</td><td></td><td>56.03<br>(0.45)</td><td>1.52<br>(0.13)</td><td>20.19<br>(1.25)</td><td>3.74<br>(0.47)</td><td>0.20<br>(0.09)</td><td>1.68<br>(0.64)</td><td>6.69<br>(0.70)</td><td>4.98<br>(0.29)</td><td>2.76<br>(0.13)</td><td>1.38<br>(0.13)</td><td>0.38<br>(0.03)</td><td>89.50</td></tr><tr><td>lpmS 25</td><td></td><td>53.38<br>(0.12)</td><td>2.00<br>(0.11)</td><td>18.85<br>(0.21)</td><td>4.62<br>(0.22)</td><td>0.27<br>(0.11)</td><td>4.28<br>(0.05)</td><td>7.89<br>(0.07)</td><td>5.28<br>(0.11)</td><td>2.33<br>(0.10)</td><td>1.05<br>(0.08)</td><td>0.01<br>(0.01)</td><td>91.49</td></tr><tr><td>lpm 26</td><td>-0.48</td><td>46.28<br>(0.12)</td><td>3.88<br>(0.06)</td><td>16.78<br>(0.22)</td><td>8.89<br>(0.11)</td><td>0.22<br>(0.09)</td><td>5.88<br>(0.06)</td><td>10.28<br>(0.06)</td><td>4.45<br>(0.05)</td><td>1.77<br>(0.10)</td><td>1.24<br>(0.12)</td><td>0.12<br>(0.01)</td><td>92.87</td></tr><tr><td>lpm 27</td><td></td><td>47.16<br>(0.38)</td><td>3.50<br>(0.20)</td><td>17.35<br>(0.52)</td><td>10.19<br>(0.36)</td><td>0.24<br>(0.14)</td><td>4.53<br>(0.37)</td><td>9.66<br>(0.49)</td><td>4.00<br>(0.77)</td><td>1.99<br>(0.06)</td><td>1.18<br>(0.07)</td><td>0.10<br>(0.01)</td><td>94.19</td></tr><tr><td>lpm 28</td><td></td><td>45.26<br>(0.07)</td><td>3.86<br>(0.15)</td><td>15.22<br>(0.32)</td><td>11.65<br>(0.26)</td><td>0.21<br>(0.05)</td><td>5.77<br>(0.07)</td><td>11.31<br>(0.17)</td><td>3.72<br>(0.19)</td><td>1.57<br>(0.06)</td><td>1.13<br>(0.10)</td><td>0.13<br>(0.01)</td><td>93.35</td></tr><tr><td>lpm 29</td><td></td><td>44.24<br>(0.10)</td><td>3.77<br>(0.06)</td><td>15.16<br>(0.06)</td><td>12.64<br>(0.18)</td><td>0.21<br>(0.04)</td><td>5.75<br>(0.23)</td><td>11.40<br>(0.27)</td><td>3.89<br>(0.09)</td><td>1.55<br>(0.25)</td><td>0.94<br>(0.06)</td><td>0.19<br>(0.03)</td><td>92.82</td></tr><tr><td>lpm 30</td><td></td><td>44.59<br>(0.14)</td><td>3.93<br>(0.12)</td><td>15.02<br>(0.23)</td><td>12.36<br>(0.26)</td><td>0.20<br>(0.05)</td><td>5.34<br>(0.14)</td><td>11.83<br>(0.23)</td><td>3.89<br>(0.09)</td><td>1.42<br>(0.11)</td><td>0.95<br>(0.08)</td><td>0.19<br>(0.03)</td><td>93.35</td></tr><tr><td>lpm 32</td><td></td><td>46.09<br>(0.64)</td><td>4.34<br>(0.15)</td><td>15.85<br>(0.14)</td><td>9.92<br>(0.75)</td><td>0.14<br>(0.05)</td><td>5.38<br>(0.81)</td><td>13.09<br>(1.24)</td><td>3.29<br>(0.17)</td><td>0.79<br>(0.18)</td><td>1.01<br>(0.06)</td><td>0.01<br>(0.01)</td><td>92.35</td></tr></tbody></table>
225 4.2 *Mass balance and ImageJ*

226 For most experiments, the volumetric percentage of glass obtained by mass balance is similar to
227 that calculated using ImageJ (Table 4). The mass balance estimates indicate that amphibole content
228 peaks at 40 wt.%, while clinopyroxene abundance is generally below 10 wt% and not higher than
229 19 wt% (Table 4). Similarly, olivine proportion does not exceed 10 wt.%. The fact that amphibole
230 proportion is higher than that in the rocks (<5 wt%, e.g. Ubide et al., 2023) reflects the lower
231 temperature of our experiments.

232 The calculated wt.% of glass correlates well with P₂O₅ abundance, as P is incorporated only by
233 apatite (SIb). The dashed line in SIb is calculated assuming perfectly incompatible behaviour of
234 P₂O₅. Deviations from it signify apatite formation, which occurs after 20–30 wt.% crystallisation.

235

236
<table><caption>Table 4. Phase proportions calculated by mass balance and image analyses (glass, using ImageJ software).</caption><thead><tr><th rowspan="2"></th><th colspan="9">Mass balance</th><th colspan="3">ImageJ estimation</th></tr><tr><th>Gl<br>wt%</th><th>Ol<br>wt%</th><th>Amph<br>wt%</th><th>Cpx<br>wt%</th><th>Fes<br>wt%</th><th>Anhy<br>wt%</th><th>Mt<br>wt%</th><th>Ilm<br>wt%</th><th>Ap<br>wt%</th><th>Gl<br>vol%</th><th>Sr</th><th>Gl %</th></tr></thead><tbody><tr><td>lpm 1</td><td>75.6<br>(0.02)</td><td>&lt;1<br>(0.01)</td><td>18.5<br>(0.03)</td><td>4.6<br>(0.01)</td><td>2.8<br>(0.002)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>79.4</td><td>0.22</td><td>86.5</td></tr><tr><td>lpm 2</td><td>56.0<br>(0.01)</td><td>&lt;1<br>(0.03)</td><td>33.4<br>(0.03)</td><td>8.2<br>(0.01)</td><td>1.1<br>(0.01)</td><td>-</td><td>1.7<br>(0.01)</td><td>-</td><td>-</td><td>61.0</td><td>0.18</td><td>55.1</td></tr><tr><td>lpm 33</td><td>75.1<br>(0.03)</td><td>3.6<br>(0.01)</td><td>15.9<br>(0.04)</td><td>3.0<br>(0.01)</td><td>-</td><td>-</td><td>2.4<br>(0.003)</td><td>-</td><td>-</td><td>79.1</td><td>0.41</td><td>72.2</td></tr><tr><td>lpm 4</td><td>78.6<br>(0.03)</td><td>3.6<br>(0.01)</td><td>10.0<br>(0.04)</td><td>4.4<br>(0.02)</td><td>1.3<br>(0.005)</td><td>-</td><td>1.9<br>(0.01)</td><td>-</td><td>-</td><td>82.6</td><td>0.02</td><td>84.3</td></tr><tr><td>lpm 5</td><td>86.6<br>(0.03)</td><td>2.5<br>(0.01)</td><td>7.8<br>(0.03)</td><td>0.2<br>(0.03)</td><td>-</td><td>-</td><td>2.9<br>(0.003)</td><td>-</td><td>-</td><td>89.5</td><td>0.53</td><td>72.2</td></tr><tr><td>lpm 6</td><td>77.7<br>(0.02)</td><td>4.8<br>(0.01)</td><td>15.8<br>(0.03)</td><td>&lt;1<br>(0.01)</td><td>-</td><td>-</td><td>2.5<br>(0.003)</td><td>-</td><td>-</td><td>81.4</td><td>1.22</td><td>77.4</td></tr><tr><td>lpm 34</td><td>62.3<br>(0.02)</td><td>2.5<br>(0.004)</td><td>17.0<br>(0.03)</td><td>14.0<br>(0.01)</td><td>-</td><td>-</td><td>4.3<br>(0.003)</td><td>-</td><td>-</td><td>68.0</td><td>0.16</td><td>57.0</td></tr><tr><td>lpm 7</td><td>90.1<br>(0.01)</td><td>3.3<br>(0.002)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>5.5<br>(0.003)</td><td>1.1<br>(0.002)</td><td>-</td><td>93.7</td><td>7.22</td><td>95.2</td></tr><tr><td>lpm 8</td><td>87.4<br>(0.01)</td><td>1.5<br>(0.003)</td><td>-</td><td>5.1<br>(0.009)</td><td>-</td><td>-</td><td>6.0<br>(0.002)</td><td>-</td><td>-</td><td>92.4</td><td>1.20</td><td>99.3</td></tr><tr><td>lpm 9</td><td>54.7<br>(0.03)</td><td>&lt;1<br>(0.01)</td><td>26.1<br>(0.05)</td><td>11.8<br>(0.02)</td><td>-</td><td>-</td><td>8.5<br>(0.003)</td><td>-</td><td>-</td><td>77.9</td><td>0.08</td><td>68.2</td></tr><tr><td>lpm 13</td><td>89.9<br>(0.01)</td><td>1.8<br>(0.003)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>12.2<br>(0.004)</td><td>&lt;1<br>(0.003)</td><td>-</td><td>95.3</td><td>9.99</td><td>91.8</td></tr><tr><td>lpm 14</td><td>76.7<br>(0.01)</td><td>2.1<br>(0.003)</td><td>-</td><td>12.7<br>(0.01)</td><td>-</td><td>-</td><td>8.5<br>(0.002)</td><td>-</td><td>-</td><td>84.6</td><td>6.15</td><td>78.7</td></tr><tr><td>lpm 15</td><td>80.0<br>(0.01)</td><td>-</td><td>-</td><td>11.6<br>(0.01)</td><td>-</td><td>-</td><td>8.3<br>(0.002)</td><td>-</td><td>-</td><td>85.8</td><td>1.59</td><td>70.6</td></tr><tr><td>lpm 16</td><td>77.2<br>(0.01)</td><td>-</td><td>-</td><td>9.8<br>(0.01)</td><td>-</td><td>-</td><td>13.4<br>(0.003)</td><td>&lt;1<br>(0.003)</td><td>-</td><td>84.5</td><td>0.80</td><td>84.5</td></tr><tr><td>lpm 17</td><td>79.9<br>(0.01)</td><td>2.1<br>(0.003)</td><td>-</td><td>4.3<br>(0.01)</td><td>-</td><td>-</td><td>7.0<br>(0.003)</td><td>-</td><td>-</td><td>86.8</td><td>1.54</td><td>84.6</td></tr><tr><td>lpm 18</td><td>51.5<br>(0.01)</td><td>-</td><td>37.1<br>(0.03)</td><td>1.6<br>(0.02)</td><td>-</td><td>-</td><td>9.8<br>(0.003)</td><td>-</td><td>-</td><td>60.8</td><td>3.10</td><td>72.3</td></tr><tr><td>lpm 19</td><td>89.5<br>(0.01)</td><td>7.4<br>(0.01)</td><td>-</td><td>&lt;1<br>(0.02)</td><td>-</td><td>5.7<br>(0.004)</td><td>11.4<br>(0.003)</td><td>0.4<br>(0.003)</td><td>-</td><td>94.0</td><td>0.40</td><td>93.4</td></tr><tr><td>lpm 20</td><td>56.8<br>(0.02)</td><td>&lt;1<br>(0.01)</td><td>33.3<br>(0.04)</td><td>3.6<br>(0.01)</td><td>-</td><td>-</td><td>12.1<br>(0.004)</td><td>&lt;1<br>(0.003)</td><td>-</td><td>63.4</td><td>1.07</td><td>68.5</td></tr><tr><td>lpm 21</td><td>43.0<br>(0.01)</td><td>-</td><td>39.7<br>(0.02)</td><td>9.0<br>(0.01)</td><td>-</td><td>-</td><td>8.4<br>(0.002)</td><td>-</td><td>-</td><td>48.57</td><td>0.96</td><td>59.8</td></tr><tr><td>lpm 22</td><td>77.8<br>(0.01)</td><td>6.1<br>(0.003)</td><td>-</td><td>2.5<br>(0.01)</td><td>-</td><td>-</td><td>13.6<br>(0.002)</td><td>-</td><td>-</td><td>86.6</td><td>4.48</td><td>84.7</td></tr><tr><td>lpm 23</td><td>47.6<br>(0.01)</td><td>-</td><td>27.9<br>(0.01)</td><td>13.8<br>(0.01)</td><td>-</td><td>-</td><td>10.7<br>(0.002)</td><td>-</td><td>-</td><td>57.5</td><td>2.51</td><td>62.8</td></tr><tr><td>lpm 24</td><td>45.1<br>(0.01)</td><td>-</td><td>31.1<br>(0.03)</td><td>12.0<br>(0.04)</td><td>-</td><td>-</td><td>10.3<br>(0.002)</td><td>-</td><td>1.6<br>(0.004)</td><td>51.7</td><td>0.97</td><td>55.6</td></tr><tr><td>lpm 25</td><td>57.3<br>(0.01)</td><td>-</td><td>14.4<br>(0.01)</td><td>18.8<br>(0.01)</td><td>-</td><td>-</td><td>9.5<br>(0.002)</td><td>-</td><td>-</td><td>67.2</td><td>1.27</td><td>66.4</td></tr><tr><td>lpm 26</td><td>77.1<br>(0.01)</td><td>0.8<br>(0.01)</td><td>8.4<br>(0.04)</td><td>9.6<br>(0.01)</td><td>4.1<br>(0.002)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>81.5</td><td>0.26</td><td>72.3</td></tr><tr><td>lpm 27</td><td>67.0<br>(0.02)</td><td>3.2<br>(0.004)</td><td>18.8*<br>(0.04)</td><td>&lt;1<br>(0.02)</td><td>2.1<br>(0.002)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>71.7</td><td>1.22</td><td>82.5</td></tr><tr><td>lpm 28</td><td>99.0<br>(0.13)</td><td>&lt;1<br>(0.01)</td><td>&lt;1<br>(0.14)</td><td>-</td><td>-</td><td>-</td><td>&lt;1<br>(0.003)</td><td>-</td><td>-</td><td>99.0</td><td>1.19</td><td>94.8</td></tr><tr><td>lpm 29</td><td>93.1<br>(0.01)</td><td>4.8<br>(0.003)</td><td>-</td><td>&lt;1<br>(0.01)</td><td>1<br>(0.003)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>95.0</td><td>0.20</td><td>89.5</td></tr><tr><td>lpm 30</td><td>96.6<br>(0.03)</td><td>6.6<br>(0.003)</td><td>-</td><td>&lt;1<br>(0.01)</td><td>0.2<br>(0.003)</td><td>-</td><td>0.5<br>(0.01)</td><td>-</td><td>-</td><td>97.5</td><td>0.53</td><td>86.5</td></tr><tr><td>lpm 32</td><td>80.0<br>(0.12)</td><td>9.3<br>(0.005)</td><td>17.5*<br>(0.13)</td><td>&lt;1<br>(0.01)</td><td>-</td><td>-</td><td>1.7<br>(0.01)</td><td>-</td><td>-</td><td>83.1</td><td>2.96</td><td>97.8</td></tr></tbody></table>

*Amphibole partly of inferred quench origin.
241 **5. Discussion**

Our experiments emphasise the control of fO₂ on the S-carrying capacity of silicate melts, as shown in many previous studies (e.g., Carroll and Rutherford, 1985; Luhr, 1990; Scaillet et al., 1998; Jugo et al., 2005). The effects of sulphur on phase relations are subtle and complex, depending on the fO₂ of the experiments. In particular, amphibole is unstable at intermediate fO₂, between NNO+2.38 and NNO+4.10, and S-rich conditions, while sulphide precipitates only below NNO+1.5. The minor differences noted between the S- and FeS-doped series may be explained by the presence of higher iron abundance in the latter case. Sulphur does not appear to affect significantly the composition of individual phases, except for a tendency of FeMg silicate phases to become more Mg-rich with S addition. In contrast, oxygen fugacity does affect phase compositions, in particular olivine and glass, whose Mg# increases markedly under more oxidising conditions in both the S-doped and FeS-doped experiments.
242
243
244
245
246
247
248
249
250
251
252

The mass balance data also show no systematic effect of sulphur on phase proportions in the different experiments, aside from the obvious cases of sulphide or anhydrite. Here again, oxygen fugacity appears to exert the stronger influence. As expected, the amounts of oxides, both titanomagnetite and ilmenite, increase from reducing to oxidising conditions (Table 4). In detail,
253
254
255
256

<figure><img src="image_7.png" /><figcaption>Fig. 5 Concentration of major element versus SiO2 wt.%. The experiments are compared to the water-saturated, 1050°C and 200-300 MPa experiments of Moune et al. (2009) and the composition A (trachyandesite) performed at 1000°C, 200 MPa from Luhr (1990).</figcaption></figure>
amphibole abundance increases slightly in more oxidised runs than in reduced ones, but with no clear difference between sulphur-rich and sulphur-poor charges. This confirms that oxygen fugacity, not the amount of sulphur in the system, exerts the stronger control on phase proportions.

From the perspective of sulfur content in the residual glass, both sets of experiments show a consistent pattern of increasing sulfur content with elevated fO₂. The changes in melt composition resulting from fO₂ variation are perhaps best illustrated by changes in Ti and Fe contents: from NNO-0.48 to NNO+4.10, both the TiO₂ and FeO abundances in the glass decrease by 75 wt%, reflecting substantial crystallisation of Fe-Ti oxides. This increase in crystallisation is accompanied by an increase in abundances of Al₂O₃ and SiO₂ in the glass, owing to the lack of plagioclase crystallisation. These significant changes in melt composition do not, however, seem to affect the overall positive effect that fO₂ has on S concentrations.

Our results can be compared with sulphur solubility experiments performed at comparable P-T-H₂O conditions on hydrous basaltic-andesitic magmas erupted in contrasting geodynamic contexts: i) at Hekla volcano in 2000, which is taken to here represent mid-ocean ridge volcanism, though interaction with plume material is possible (Moune et al., 2009); ii) the trachyandesite magma erupted at El Chichón volcano in 1982, which belongs to an arc setting (Luhr, 1990) though some rift related processes are likely (Arce et al., 2014). The water-saturated, 1050°C and 200-300 MPa experiments of Moune et al., (2009), and the composition A (trachyandesite) performed at 1000°C, 200 MPa from Luhr (1990), are compared with our data in Fig. 5. At any given SiO₂, differences in some oxide contents (e.g., CaO, Al₂O₃) are evident. These can be attributed to bulk compositional effects (Fig. 5) and to slightly different experimental conditions which impart different degrees of crystallization. The broad correspondences remain when oxygen fugacity is considered (Figure SIc). The TiO₂ content of the andesitic charges of Moune et al (2009) and Luhr (1990) are lower than ours, reflecting the lower Ti content of the corresponding starting materials. This is particularly evident in the Luhr (1990) experiments, in which the concentration of TiO₂ in the starting composition is so low that no difference exists between reduced and oxidised conditions. Based on these data, it appears that the presence of sulphur does not significantly affect the concentrations of the major elements of residual melts. Irrespective of geodynamic context, the factor that most influences melt composition is oxygen fugacity.

As in many previous studies(e.g., Carroll and Rutherford, 1985; Liu et al., 2007; Moune et al., 2009), our experiments reveal a significant difference in the amount of sulphur in the glasses between low and high fO₂ experiments (Fig. 6). At low fO₂, the sulphur concentrations in the glasses measured by Moune et al (2009) and Luhr (1990) are comparable to those found in our experiments, most falling in the interval 1000-2500 ppm. Furthermore, as noted by Moune et al. (2009), at fO₂ between NNO-0.48 and NNO1.34, sulphur abundance in the glass increases in proportion to the increase of added sulphur, until bulk S exceeds 0.5 wt.% (Fig 6). Thereafter, the S content in the glass levels off at 2000±100 ppm. At fO₂ above NNO+2.38, a similar pattern is observed with a positive trend up to about 1 wt.% sulphur added, at which point the dissolved S levels off at 0.7 wt%.
<figure><img src="image_8.png" /><figcaption>Fig.6 Sulphur concentration in the melt versus the amount of sulphur added in the runs. The experiments are compared to the water-saturated, 1050°C and 200-300 MPa experiments of Moune et al. (2009) and the composition A (trachyandesite) performed at 1000°C, 200 MPa from Luhr (1990). The dashed trendlines are calculated assuming an incompatible behaviour of S at 50%, 25% and 0% of crystallization.</figcaption></figure>

The experiments of Luhr (1990) carried out under oxidised conditions resulted in lower S concentrations in the glass than we obtained for the same amount of sulphur added. Anhydrite crystallization in the Luhr (1990) runs, which did not occur in our experiments under the same conditions, likely explains this. The levelling off of both trends at high bulk S contents likely results from the buffering effect of other S-bearing phases. In addition to fluid, under reducing conditions this would be sulphide, while under oxidising conditions this would be anhydrite. Oxidised charges with less than 0.5 wt.% added S fall on, or close to, the 1-to-1 correlation line, which shows that under these conditions a significant proportion of S resides in the melt phase (those data that fall above the 1/1 line reflect the amount of crystallisation of charges).
308 5.1 Significance for understanding the La Palma 2021 eruption

309 The pre-eruptive fO₂ of Cumbre Vieja 2021 basanite has been broadly constrained from V
310 systematics in olivine to fall between NNO+0.6 and NNO+1.3 (Day et al., 2022). We note however
311 that a recent reassessment of V behaviour has concluded that current formulations of this
312 oxybarometer tend to overestimate fO₂ by up to 0.7 log unit in hydrous basalts (Erdmann et al.,
313 2024), which would bring the La Palma magma redox state into the NNO-NNO+1 range.

<figure><img src="image_9.png" /></figure>

Fig. 7 Sulphur concentration in the melt versus logfO2. The experiments are compared to the water-saturated, 1050°C and 200-300 MPa experiments of Moune et al., 2009 and the composition A (Trachyandesite) performed at 1000°C, 200 MPa from Luhr, 1990; MI-La Palma (2021) = S wt% in melt inclusions (Castro and Feisel, 2022; Burton et al., 2023; Dayton et al., 2024).

314 Considering a NNO-NNO+1.3 range, our data indicate that under these conditions the bulk magma
315 S content was ~2500–5000 ppm, a significant part of which was dissolved in the melt, broadly
316 consistent with melt inclusion analyses (Fig.7) (e.g., Castro and Feisel, 2022; Burton et al., 2023;
317 Dayton et al., 2024). Note that the highest S content so far measured in melt inclusions (4800 ppm,
318 Burton et al., 2023) points to fO2 at the upper end of the range inferred from V in olivine (Fig. 10),
319 or higher temperatures. The occasional occurrence of sulphides (as inclusions in phenocrysts) in
320 erupted products (Andujar et al., submitted) is consistent with our experiments at NNO+1.34,
321 although the absence of sulphide in the matrix glass suggests that the erupting magma was not
322 saturated in sulphide.
323

323 Our experiments show that to achieve the observed S content analysed in melt inclusions of La
324 Palma 2021 basanite (around 3000 ppm S) at the inferred pre-eruptive fO2 between NNO+0.6 and
325 NNO+1.6 (Day et al., 2022), the fS2 should be around 0.1–1 MPa, as recorded by the composition
326 of pyrrhotite in our run products (Table 2).
Using these constraints, in what follows we have have carried out calculations aimed at modelling
the fluid phase composition for three different scenarios: (1) we have first calculated the fluid
composition at equilibrium with the basanite magma lying in the crustal reservoir, which is inferred
to lie at ~ 300 MPa, based on seismic source locations and petrological arguments (e.g., D'Auria
et al., 2022; Del Fresno et al., 2023b; Ubide et al., 2023; Dayton et al., 2024; Andujar et al.,
submitted). (2) We next perform calculations of magma degassing during uprise, starting at 300
MPa with variable amount of exsolved fluid. (3) Finally, we simulate degassing from higher
pressures (i.e. deeper levels) and higher temperature (about 1125°C), in keeping with the elevated
CO2 dissolved contents (up to 1.2 wt%) retrieved from olivine inclusions (e.g., Zanon et al., 2023;
Dayton et al., 2024) and seismic data (e.g., D'Auria et al., 2022; Del Fresno et al., 2023) which
point to a mantle source at 400-800 MPa.

(1) For the first step, we use the following constraints: a pre-eruptive dissolved CO2 content ranging from 3000-5000 ppm, and a dissolved H2O<sub>melt</sub> of 1-3 wt%, drawing on melt inclusion analyses (e.g., Burton et al., 2023; Dayton et al., 2023). We perform calculations at 1080°C, which corresponds to the inferred temperature for the basaltic magma at equilibrium with amphibole ((González-García et al., 2023) González-García et al., 2023; Sandoval-Velasquez et al., 2023; Andujar et al., submitted), using an MRK equation of state for fluid coupled to the S solubility model of Lesne et al. (2015), calibrated for alkali-rich
<figure><img src="image_10.png" /><figcaption>Fig. 8 (a) Evolution of the S content of the excess fluid in the reservoir at 300 MPa with fO₂. (b) Evolution of the ratio XCO₂/XSO₂ of the fluid with ΔNNO. The calculations have been made at three different fS₂; The thick green line shows the XCO₂/XSO₂ ratio of volcanic gases measured at la Palma during explosive emissions (Burton et al., 2023). See text for details.</figcaption></figure>

basalt melts, and to the CO₂-H₂O solubility model of Jímenez-Mejías et al. (2021), calibrated for a basanite from the Canary islands. The calculation then yields the saturation pressure in H₂O, CO₂, SO₂ and H₂S fluid species. The key assumption is that of equilibrium between the fugacities of volatiles in the fluid with those in the melt (e.g., Lesne et al., 2015). Given uncertainty in the magma redox state, and in its possible variation during decompression (e.g., Burgisser and Scaillet, 2007; Moussallam et al., 2016), we performed the calculations for a range of fO₂ between NNO-2 and NNO+2. Fig 8a shows the variation of S content of the fluid in the reservoir at 300 MPa with fO₂, calculated for three different fS₂. This calculation gives the composition of fluids at the surface if they could leave the crustal reservoir on their own, i.e. without being accompagnied by melts, and traversing the crustal section unmodified. Although this scenario is possibly not directly applicable to the La Palma 2021 eruption, it provides context for the interpretation of gas monitoring during repose periods. In the range of fO₂ inferred by Day et al. (2022), the S content of the fluid falls between 1 and 10 wt%, depending on fS₂, comparable with S contents calculated for more silicic compositions (e.g., Scaillet et al., 2003) and to that calculated by mass balance
for most of our experiments (Table 2). The calculations further show that XCO₂/XSO₂ progressively decreases as fO₂ increases (Fig. 8b). In the fO₂ interval NNO+0.7 to NNO+1.3, XCO₂/XSO₂ ranges from ~2 up to ~100, within the range of measurements of volcanic gas emissions during the 2021 La Palma eruption (Burton et al., 2023). Measured ratios range from 35 for explosive activity down to less than 10 for effusive emissions (Burton et al., 2023), and the higher end is to be favoured as a characteristic of gas-rich magma, presumably of deeper provenance.

(2) We next consider degassing during magma ascent, especially of S and H₂O, which can exsolve and separate from the melt extensively near the surface (Oppenheimer et al., 2014). The full calculation should also take into account the possible role of an excess fluid in the crustal reservoir. For instance, the bulk CO₂ content of La Palma magma has been estimated to be at 4±1.5 wt% based on the measured S emissions and the average XCO₂/XSO₂ ratio (Burton et al., 2023). Taking a conservative value of 3 wt% fluid (with 3 wt% H₂O and

<figure><img src="image_11.png" /></figure>

Fig. 9 (a) Evolution of total amount of SO₂ degassed by 0.2 km³ of basanite magma with fO₂ expressed as ΔNNO. (b) Evolution of the XCO₂/XSO₂ ratio of the gas emitted at the vent with ΔNNO. The calculations have been performed at 1080°C.

3000 ppm CO₂ dissolved in melt, which correspond to the volatile contents of a fluid saturated basanite at 300 MPa), we calculate as a function of oxygen fugacity both the total
amount of S released by the 0.2 km³ of erupted magma, and the XCO₂/XSO₂ ratio of the gas at the vent (i.e. melt+fluid), accounting for the 400–600 ppm of S that remains in matrix glass (Fig. 12). With these constraints and assuming an fO₂ of ~ NNO+1, 2-4 Mt SO₂, we find that the pre-eruptive magma must have had an fS₂ in the range 0.1-1 MPa (Fig. 9a). A fS₂ significantly lower than 0.1 MPa will fall short in reproducing this figure. With respect to the final XCO₂/XSO₂ ratio (i.e. the one measured at the vent), the same set of calculations shows that such a ratio displays a bell-shaped pattern, with a maximum in between NNO and NNO+0.5 (fig.9b). For fS₂ values in the range 0.1-1 MPa, the maximum possible XCO₂/XSO₂ ratio is about 30, lying slightly above NNO, i.e. at an fO₂ more reduced than that retrieved from V systematic.
It is also interesting to consider the XH₂O/XSO₂ ratio, which was also measured during La Palma 385 386 2021 eruption (Burton et al., 2023). The variation of this ratio with fO₂ (as for XCO₂/XSO₂) with 387 the amount of excess fluid in the reservoir is shown in Fig. 10b. Here the calculations are made for 388 a magma at 300 MPa with 4000 ppm CO₂, 2 wt% H₂O and for fS₂=0.2 MPa, at 1080°C, also 389 consistent with available melt inclusion and phase equilibrium constraints for the top portion of the 390 plumbing system (González-García et al., 2023; Sandoval-Velasquez et al., 2023; Andujar et al., 391 submitted). As with the previous calculations, both ratios exhibit a similar bell shaped trend with 392 fO₂. They are both sensitive to the amount of free fluid: as it increases, so the XH₂O/XSO₂ ratio 393 drops, while the XCO₂/XSO₂ increases, due to the contrasting H₂O and CO₂ contents in melt and 394 fluid phases. Gas emissions during the most explosive phase of La Palma eruption had an

<figure><img src="image_12.png" /><figcaption>Fig. 10. Evolution of the XH₂O/XSO₂ (a) and XCO₂/XSO₂ (b) ratios of gases vented at 0.1 MPa with fO₂, for different amounts of exsolved fluid in the reservoir at 300 MPa. (c) Evolution of the mass of SO₂ produced for the three different amounts of fluid. In all panels the thick horizontal green dashed line indicates the measured value of the corresponding parameter.</figcaption></figure>
XCO₂/XSO₂ of ~ 35 and an XH₂O/XSO₂ ratio of ~ 22 (Burton et al., 2023). For the conditions shown in Fig. 10, these ratios are reproduced at around NNO+0.5 to NNO+1 for 6 wt% excess fluid, broadly consistent with previous inferences. Clearly, the amount of SO₂ released increases with the amount of pre-eruptive fluid in the crustal reservoir (Fig. 13c). For this set of conditions, fO₂ in the range NNO+1 to NNO+1.5 are required to yield 4 Tg SO₂. These calculations point therefore to the presence of a significant amount of free fluid in the plumbing system, as indicated by previous work (e.g., Burton et al., 2023; Sandoval-Velasquez et al., 2023; Zanon et al., 2024)).

(3) The last set of calculations explores the deeper part of the plumbing system. As noted earlier, melt inclusions hosted by olivine record a range of dissolved CO₂, up to 5000 ppm (e.g., Dayton et al., 2024). If account is made for the occurrence of exsolved fluid in the

<figure><img src="image_13.png" /></figure>

Fig. 11(a) Evolution of total amount of SO₂ degassed by 0.2 km³ of basanite magma with fO₂ expressed as ΔNNO with increasing CO₂ from 5000 ppm to 10000ppm. (b) Evolution of the XCO₂/XSO₂ ratio of the gas emitted at the vent with ΔNNO with increasing CO₂ from 5000 ppm to 10000ppm. The calculations have been performed at 1125°C. In all panels the measured values of the corresponding parameter are in green dashed line (burton et al., 2023).
melt inclusions, the CO₂ content rises up to 1.2 wt% (Dayton et al., 2024), underscoring the deep mantle provenance of some of the magma erupted during the eruption. We have therefore also carried out calculations using higher dissolved CO₂, from 5000 to 10000 ppm (corresponding to pressures in the range 400-800 MPa). We keep the excess fluid at 3 wt% as in most calculations above and the amount of H₂O dissolved at 3 wt% (hence the total amount of volatiles sums up to over 6 wt%). Results are shown on figure 11. In terms of XCO₂/XSO₂, increasing pressure makes high fS₂ (1 MPa) less likely than a moderate one (0.1 MPa), since the family of curves corresponding to fS₂=1MPa does not allow to reproduce the observed XCO₂/XSO₂ ratio of vented gases. Note that for an fS₂=0.1 MPa, the intersection happens at around NNO+1, which is an fO₂ slightly lower than the one inferred by Day et al. (2022).

For what regards the amount of SO₂ released, a magma with an fS₂ of 1 MPa would require an fO₂ slightly over NNO, while that with an fS₂ of 0.1 MPa would require slightly more oxidizing conditions, both fS₂ being compatible with the inferred range of redox state of La Palma magma (Day et al., 2022).

The above sets of calculations show that reproducing the observations reported for La Palma eruption, in particular the S content of melt inclusions, the gas composition, and the amount of S released, requires a subtle combination of fO₂, fS₂ and amount of fluid of the magma (in addition to T and P). Elevated S contents in the melt point to fO₂ conditions above NNO (Fig.6). The fS₂ should be in the vicinity of 0.1 MPa in order to reproduce the amount of SO₂ released (Fig 8a, 10c). An fS₂ too high will not be compatible with the observed XCO₂/XSO₂ ratio, in particular if the majority of outgassed sulphur is sourced from magma of deep mantle provenance (Fig 11). The amount of fluid in the reservoir is also critical if the final fluid released is to have an XH₂O/XSO₂ lower than XCO₂/XSO₂, as observed. According to our calculations, amounts of fluid significantly below 5 wt% (at 300 MPa) cannot satisfy this constraint (Fig. 10). An XH₂O/XSO₂ ratio of 22 and an XCO₂/XSO₂ ratio of 35 requires fO₂ to be ~ NNO+0.6, which is lower than inferred, and which would not sustain elevated S content in the melt (Fig. 6). This illustrates the challenge of delineating conditions that satisfy all observations. Beyond model uncertainties, such discrepancies may also reflect fractionation of gases during magma ascent, either near the surface (Burton et al., 2023), or deeper in the plumbing system. Uncertainties in magma's fO₂ remain large also and more work is needed to refine La Palma redox state, given the importance of this parameter on S behaviour. An additional caveat is that observed gases at La Palma likely represent the mixture of volatiles sourced from magma already stagnating in the reservoir, possibly years before the eruption (e.g., Day et al., 2022; Andujar et al., submitted), as well as mantle-derived volatile-rich magmas (Zanon et al., 2024; Dayton et al., 2024), injected shortly before or during eruption. Such processes, likely in play, are not captured by our treatment.

442

## 6. Conclusions
We have shown that the composition of the residual glass as well as the phase relationships and their proportions are primarily influenced by oxygen fugacity, but also by the amount of sulphur in the system, though to a lesser extent. Similarly, our experiments emphasise the considerable influence of fO₂ on the solubility of S in silicate melts (Figs. 5,6). Between NNO-0.48 and NNO1.34, the maximum S concentration in the residual glass is 0.2±0.01 wt%, while at oxygen fugacity above NNO+2.38, the maximum value is 0.7–0.8 wt%. These limits are imposed by the buffering effect of sulphide/sulphate phases in addition to the fluid.

Modelling of the fluid phase composition using an MRK equation of state for fluid and the models of Lesne et al. (2015) and Jiménez-Mejías et al. (2021) for volatile solubilities, shows that the S content of the fluid lies between 1 and 10 wt%, depending on fS₂. Overall, the calculations show that in order to expel 2-4 Mt of SO₂, the pre-eruptive magma must have had a fS₂ at the 0.1 MPa level (Fig. 11a) with an fO₂ above NNO, in general agreement with the oxidised character inferred for hot spot basalts (Moussallam et al., 2019), and coexisted with a significant amount of exsolved fluid in the crustal reservoir.

Acknowledgement

Acknowledge support from both LabEx VOLTAIRE (ANR-10-LABX-100-01) and EquipEx PLANEX (ANR-11-EQPX-0036) projects. We thank Mike Burton and an anonymous reviewer for their constructive comments which helped to improve significantly the manuscript, as well as the editorial handling of Sonia Calvari.
466 References

467 Albarède, F., 1996. Introduction to geochemical modeling, 1. paperback ed. (with corr.). ed. Cambridge
468 Univ. Press, Cambridge.

469 Albertos, V.T., Hernández, P.A., Melián, G.V., Álvarez Díaz, A.J., Martín-Lorenzo, A., Padrón, E., Pérez, N.M., 2023. Diffuse CO2 and H2S degassing from Tajogaite volcanic cone, La Palma, Canary Islands (other). oral. https://doi.org/10.5194/egusphere-egu23-9916

472 Andújar, et al., 2024. Evolution of the crustal reservoir feeding La Palma 2021 eruption. Insights from phase equilibrium experiments and petrologically derived time scales. J. Volcanol. Geotherm. Res. submitted

475 Arce, J.L., Walker, J., Keppie, J.D., 2014. Petrology of two contrasting Mexican volcanoes, the Chiapanecan (El Chichón) and Central American (Tacaná) volcanic belts: the result of rift- versus subduction-related volcanism. Int. Geol. Rev. 56, 501–524.
https://doi.org/10.1080/00206814.2013.879375

479 Bonadonna, C., Pistolesi, M., Biass, S., Voloschina, M., Romero, J., Coppola, D., Folch, A., D'Auria, L., Martin-Lorenzo, A., Dominguez, L., Pastore, C., Reyes Hardy, M., Rodríguez, F., 2022. Physical Characterization of Long-Lasting Hybrid Eruptions: The 2021 Tajogaite Eruption of Cumbre Vieja (La Palma, Canary Islands). J. Geophys. Res. Solid Earth 127, e2022JB025302.
https://doi.org/10.1029/2022JB025302

484 Boulliung, J., Wood, B.J., 2023. Sulfur oxidation state and solubility in silicate melts. Contrib. Mineral. Petrol. 178, 56. https://doi.org/10.1007/s00410-023-02033-9

486 Burgisser, A., Scaillet, B., 2007. Redox evolution of a degassing magma rising to the surface. Nature 445, 194–197. https://doi.org/10.1038/nature05509

488 Burton, M., Aiuppa, A., Allard, P., Asensio-Ramos, M., Cofrades, A.P., La Spina, A., Nicholson, E.J., Zanon, V., Barrancos, J., Bitetto, M., Hartley, M., Romero, J.E., Waters, E., Stewart, A., Hernández, P.A., Lages, J.P., Padrón, E., Wood, K., Esse, B., Hayer, C., Cyrzan, K., Rose-Koga, E.F., Schiavi, F., D'Auria, L., Pérez, N.M., 2023. Exceptional eruptive CO2 emissions from intra-plate alkaline magmatism in the Canary volcanic archipelago. Commun. Earth Environ. 4, 467. https://doi.org/10.1038/s43247-023-01103-x

494 Carracedo, J.C., Badiola, E.R., Guillou, H., de La Nuez, J., Perez Torrado, F.J., 2001. Geology and volcanology of la Palma and El Hierro, Western Canaries. Estud. Geol.-Madr. 57, 175–273.

496 Carroll, M.R., Rutherford, M.J., 1988. Sulfur speciation in hydrous experimental glasses of varying oxidation state; results from measured wavelength shifts of sulfur X-rays. Am. Mineral. 73, 845–849.

499 Carroll, M.R., Rutherford, M.J., 1985. Sulfide and sulfate saturation in hydrous silicate melts. J. Geophys. Res. Solid Earth 90. https://doi.org/10.1029/JB090iS02p0C601

501 Castro, J.M., Feisel, Y., 2022. Author Correction: Eruption of ultralow-viscosity basanite magma at Cumbre Vieja, La Palma, Canary Islands. Nat. Commun. 13, 3929.
https://doi.org/10.1038/s41467-022-31649-x

504 Clemente, B., Scaillet, B., Pichevant, M., 2004. The Solubility of Sulphur in Hydrous Rhyolitic Melts. J. Petrol. 45, 2171–2196. https://doi.org/10.1093/petrology/egh052

506 D'Auria, L., Koulakov, I., Prudencio, J., Cabrera-Pérez, I., Ibáñez, J.M., Barrancos, J., García-Hernández, R., Martínez Van Dorth, D., Padilla, G.D., Przeor, M., Ortega, V., Hernández, P., Peréz, N.M., 2022. Rapid magma ascent beneath La Palma revealed by seismic tomography. Sci. Rep. 12, 17654. https://doi.org/10.1038/s41598-022-21818-9

510 Day, J.M.D., Troll, V.R., Aulinas, M., Deegan, F.M., Geiger, H., Carracedo, J.C., Pinto, G.G., Perez-Torrado, F.J., 2022. Mantle source characteristics and magmatic processes during the 2021 La Palma eruption. Earth Planet. Sci. Lett. 597, 117793. https://doi.org/10.1016/j.epsl.2022.117793

513 Dayton, K., Gazel, E., Wieser, P., Troll, V.R., Carracedo, J.C., La Madrid, H., Roman, D.C., Ward, J., Aulinas, M., Geiger, H., Deegan, F.M., Gisbert, G., Perez-Torrado, F.J., 2023. Deep magma
515 storage during the 2021 La Palma eruption. Sci. Adv. 9, eade7641.

516 https://doi.org/10.1126/sciadv.ade7641

517 Dayton, K., Gazel, E., Wieser, P.E., Troll, V.R., Carracedo, J.C., Aulinas, M., Perez-Torrado, F.J., 2024.

518 Magmatic Storage and Volatile Fluxes of the 2021 La Palma Eruption. Geochem. Geophys.

519 Geosystems 25, e2024GC011491. https://doi.org/10.1029/2024GC011491

520 Del Fresno, C., Cesca, S., Klügel, A., Domínguez Cerdeña, I., Díaz-Suárez, E.A., Dahm, T., García-

521 Cañada, L., Meletlidis, S., Milkereit, C., Valenzuela-Malebrán, C., López-Díaz, R., López, C.,

522 2023a. Magmatic plumbing and dynamic evolution of the 2021 La Palma eruption. Nat. Commun.

523 14, 358. https://doi.org/10.1038/s41467-023-35953-y

524 Del Fresno, C., Cesca, S., Klügel, A., Domínguez Cerdeña, I., Díaz-Suárez, E.A., Dahm, T., García-

525 Cañada, L., Meletlidis, S., Milkereit, C., Valenzuela-Malebrán, C., López-Díaz, R., López, C.,

526 2023b. Magmatic plumbing and dynamic evolution of the 2021 La Palma eruption. Nat. Commun.

527 14, 358. https://doi.org/10.1038/s41467-023-35953-y

528 Devine, J.D., Gardner, J.E., Brack, H.P., Layne, G.D., Rutherford, M.J., 1995. Comparison of

529 microanalytical methods for estimating H₂O contents of silicic volcanic glasses. Am. Mineral.

530 80, 319–328. https://doi.org/10.2138/am-1995-3-413

531 Di Carlo, I., Pichavant, M., Rotolo, S.G., Scaillet, B., 2006. Experimental Crystallization of a High-K Arc

532 Basalt: the Golden Pumice, Stromboli Volcano (Italy). J. Petrol. 47, 1317–1343.

533 https://doi.org/10.1093/petrology/egl011

534 Erdmann, S., Pichavant, M., Gaillard, F., 2024. Mineral-melt vanadium oxybarometry for primitive arc

535 magmas: effect of hydrous melt composition on fO₂ estimates. Contrib. Mineral. Petrol. 179, 39.

536 https://doi.org/10.1007/s00410-024-02113-4

537 Froese, E., Gunter, A.E., 1976. A note on the pyrrhotite-sulfur vapor equilibrium. Econ. Geol. 71, 1589–

538 1594. https://doi.org/10.2113/gsecongeo.71.8.1589

539 González, F., Seas, C., Barrientos, Z., Quesada-Acuña, S.G., Mora Amador, R.A., 2019. Poás Volcano

540 Biodiversity, in: Tassi, F., Vaselli, O., Mora Amador, Raul Alberto (Eds.), Poás Volcano: The

541 Pulsing Heart of Central America Volcanic Zone, Active Volcanoes of the World. Springer

542 International Publishing, Cham, pp. 309–317. https://doi.org/10.1007/978-3-319-02156-0_13

543 González-García, D., Boulesteix, T., Klügel, A., Holtz, F., 2023. Bubble-enhanced basanite–tephrite

544 mixing in the early stages of the Cumbre Vieja 2021 eruption, La Palma, Canary Islands. Sci. Rep.

545 13, 14839. https://doi.org/10.1038/s41598-023-41595-3

546 Hayer, C., Barrancos, J., Burton, M., Rodríguez, F., Esse, B., Hernández, P., Melián, G., Padrón, E.,

547 Asensio-Ramos, M., Pérez, N., 2022. From up above to down below: Comparison of satellite- and

548 ground-based observations of SO₂ emissions from the 2021 eruption of Cumbre Vieja, La Palma

549 (other). display. https://doi.org/10.5194/egusphere-egu22-12201

550 Hughes, E.C., Saper, L.M., Liggins, P., O'Neill, H.S.C., Stolper, E.M., 2023. The sulfur solubility

551 minimum and maximum in silicate melt. J. Geol. Soc. 180, jgs2021-125.

552 Jiménez-Mejías, M., Andújar, J., Scaillet, B., Casillas, R., 2021. Experimental determination of H₂O and

553 CO₂ solubilities of mafic alkaline magmas from Canary Islands. Comptes Rendus Géoscience

554 353, 289–314. https://doi.org/10.5802/crgeos.84

555 Jugo, P.J., 2004. An Experimental Study of the Sulfur Content in Basaltic Melts Saturated with

556 Immiscible Sulfide or Sulfate Liquids at 1300 C and 1{middle dot}0 GPa. J. Petrol. 46, 783–798.

557 https://doi.org/10.1093/petrology/egh097

558 Jugo, P.J., Luth, R.W., Richards, J.P., 2005. Experimental data on the speciation of sulfur as a function of

559 oxygen fugacity in basaltic melts. Geochim. Cosmochim. Acta 69, 497–503.

560 https://doi.org/10.1016/j.gca.2004.07.011

561 Keppler, H., 1999. Experimental Evidence for the Source of Excess Sulfur in Explosive Volcanic

562 Eruptions. Science 284, 1652–1654. https://doi.org/10.1126/science.284.5420.1652

563 Lesne, P., Scaillet, B., Pichavant, M., 2015. The solubility of sulfur in hydrous basaltic melts. Chem. Geol.

564 418, 104–116. https://doi.org/10.1016/j.chemgeo.2015.03.025
565 Liu, Y., Samaha, N.-T., Baker, D.R., 2007. Sulfur concentration at sulfide saturation (SCSS) in magmatic silicate melts. Geochim. Cosmochim. Acta 71, 1783-1799.

567 https://doi.org/10.1016/j.gca.2007.01.004

568 Lo Forte, F.M., Schiavi, F., Rose-Koga, E.F., Rotolo, S.G., Verdier-Paoletti, M., Aiuppa, A., Zanon, V., 2024. High CO2 in the mantle source of ocean island basanites. Geochim. Cosmochim. Acta 368, 93-111. https://doi.org/10.1016/j.gca.2024.01.016

571 Luhr, J.F., 1990. Experimental Phase Relations of Water- and Sulfur-Saturated Arc Magmas and the 1982 Eruptions of El Chich n Volcano. J. Petrol. 31, 1071-1114.

573 https://doi.org/10.1093/petrology/31.5.1071

574 Moretti, R., Ottonello, G., 2005. Solubility and speciation of sulfur in silicate melts: The Conjugated Toop-Samis-Flood-Grjotheim (CTSFG) model. Geochim. Cosmochim. Acta 69, 801-823.

576 https://doi.org/10.1016/j.gca.2004.09.006

577 Moune, S., Holtz, F., Botcharnikov, R.E., 2009. Sulphur solubility in andesitic to basaltic melts: implications for Hekla volcano. Contrib. Mineral. Petrol. 157, 691-707.

579 https://doi.org/10.1007/s00410-008-0359-0

580 Moussallam, Y., Edmonds, M., Scaillet, B., Peters, N., Gennaro, E., Sides, I., Oppenheimer, C., 2016. The impact of degassing on the oxidation state of basaltic magmas: A case study of Kīlauea volcano.

582 Earth Planet. Sci. Lett. 450, 317-325. https://doi.org/10.1016/j.epsl.2016.06.031

583 O'Neill, H.St.C., 2021. The Thermodynamic Controls on Sulfide Saturation in Silicate Melts with Application to Ocean Floor Basalts, in: Moretti, R., Neuville, D.R. (Eds.), Geophysical Monograph Series. Wiley, pp. 177-213. https://doi.org/10.1002/9781119473206.ch10

585 Monograph Series. Wiley, pp. 177-213. https://doi.org/10.1002/9781119473206.ch10

586 Oppenheimer, C., Fischer, T.P., Scaillet, B., 2014. Volcanic Degassing: Process and Impact, in: Treatise on Geochemistry. Elsevier, pp. 111-179. https://doi.org/10.1016/B978-0-08-095975-7.00304-1

588 Pérez, I.C., 2022. Relative velocity variations curves. https://doi.org/10.5281/ZENODO.6678861

589 Sandoval-Velasquez, A., Rizzo, A.L., Casetta, F., Ntaflos, T., Aiuppa, A., Alonso, M., Padrón, E., Pankhurst, M.J., Mundl-Petermeier, A., Zanon, V., Pérez, N.M., 2023. The noble gas signature of the 2021 Tajogaite eruption (La Palma, Canary Islands). J. Volcanol. Geotherm. Res. 443, 107928. https://doi.org/10.1016/j.jvolgeores.2023.107928

593 Scaillet, B., Clemente, B., Evans, B.W., Pichavant, M., 1998. Redox control of sulfur degassing in silicic magmas. J. Geophys. Res. Solid Earth 103, 23937-23949. https://doi.org/10.1029/98JB02301

595 Scaillet, B., Evans, B.W., 1999. The 15 June 1991 Eruption of Mount Pinatubo. I. Phase Equilibria and Pre-eruption P-T-fO2-fH2O Conditions of the Dacite Magma. J. Petrol. 40, 381-411.

597 https://doi.org/10.1093/petroj/40.3.381

598 Scaillet, B., Luhr, J., Carroll, M.R., 2003. Petrological and volcanological constraints on volcanic sulfur emissions to the atmosphere. Geophys. Monogr.-Am. Geophys. Union 139, 11-40.

600 Scaillet, B., Pichavant, M., Roux, J., Humbert, G., Lefevre, A., 1992. Improvements of the Shaw membrane technique for measurement and control of fH2 at high temperatures and pressures. Am.

602 Mineral. 77, 647-655.

603 Sisson, T.W., Grove, T.L., 1993. Experimental investigations of the role of H2O in calc-alkaline differentiation and subduction zone magmatism. Contrib. Mineral. Petrol. 113, 143-166.

605 https://doi.org/10.1007/BF00283225

606 Taylor, J.R., Wall, V.J., Pownceby, M.I., 1992. The calibration and application of accurate redox sensors. Am. Mineral. 77, 284-295.

608 Ubide, T., Márquez, Á., Ancochea, E., Huertas, M.J., Herrera, R., Coello-Bravo, J.J., Sanz-Mangas, D., Mulder, J., MacDonald, A., Galindo, I., 2023. Discrete magma injections drive the 2021 La Palma eruption. Sci. Adv. 9, eadg4813. https://doi.org/10.1126/sciadv.adg4813

611 Whitney, J.A., 1984. Fugacities of sulfurous gases in pyrrhotite-bearing silicic magmas. Am. Mineral. 69, 68-78.

613 Zanon, V., D'Auria, L., Schiavi, F., Cyrzan, K., Pankhurst, M.J., 2024. Toward a near real-time magma ascent monitoring by combined fluid inclusion barometry and ongoing seismicity. Sci. Adv. 10,

615 eadi4300. https://doi.org/10.1126/sciadv.adi4300