Absorption spectra measurements at ~1 cm^–1 spectral resolution of ³²S, ³³S, ³⁴S, and ³⁶S sulfur dioxide for the 206–220 nm region and applications to modeling of the isotopic self-shielding

Abstract

The sulfur isotope fractionation that occurs during SO₂ photolysis is key to explaining the isotope signatures stored in ancient sedimentary rocks and understanding the atmospheric compositions of the early Earth and early Mars. Here, we report the photoabsorption cross-sections of ³²SO₂, ³³SO₂, ³⁴SO₂, and ³⁶SO₂ measured from 206 to 220 nm at 296 K. The wavelength resolution was set to 1 cm^–1, 25 times higher than that of previous SO₂ isotopologue absorption spectra measurements. The precision of ~10% is in agreement with previously reported SO₂ absorption spectra. In comparison with previously reported high-resolution spectra of natural abundance, SO₂ measurements demonstrate smaller cross-sectional magnitudes at absorption peaks and an offset wavelength by ~0.016 nm. Using the newly recorded isotopologue spectra, we calculated the sulfur isotope fractionation for self-shielding during SO₂ photolysis. The calculated ³⁴S fractionation (³⁴ε) roughly reproduces the observed relationship between ³⁴ε and the SO₂ column density in previous photolysis experiments. Thus, the cross-section is useful for predicting ³⁴S/³²S isotope fractionation in an optically thick SO₂ atmosphere. In contrast, for mass-independent fractionation (MIF-S, i.e., non-zero Δ³³S), the measured spectra predicted a weakly negative Δ³³S/δ³⁴S slope of about –0.1. The small Δ³³S/δ³⁴S slope is consistent with the slopes of SO₂ photolysis experiments under high-pressure atmospheres (i.e., the pressure broadened absorption line width will be comparable to the spectral resolution). Therefore, MIF-S during photolysis experiments was linked to spectroscopic measurements for the first time. We conclude that reasonable precision and high-resolution spectroscopic measurements are key to explaining the origin of MIF-S at column densities below 10¹⁸ cm^–2. However, MIF-S production in chamber experiments or atmospheric conditions may require understanding pressure or temperature effects, such as linewidth broadening on the UV-absorption spectra, and how these effects manifest themselves on isotopologues.

Introduction

Sulfur dioxide (SO₂) plays an important role in planetary atmospheres, including that of the Earth. This gas has been released into the atmosphere by volcanic activity throughout Earth’s history (Holland, 2002; Gaillard et al., 2011; Olson et al., 2019; Ohmoto, 2020), is a candidate greenhouse gas in early Mars (Halevy et al., 2007; Johnson et al., 2008), and has also been observed in Venus and Io’s atmospheres (e.g., Vandaele et al., 2017; Feaga et al., 2009).

SO₂ has two strong structured absorption bands in the UV region; therefore, UV radiation triggers complex photochemical processes in this molecule (e.g., Heicklen et al., 1980). The 165–230 nm absorption band occurs where SO₂ is photolyzed by wavelengths below 218.7 nm (Katagiri et al., 1997) by its excitation to the C¹B₂ state. The second absorption band occurs in the 250–340 nm region, where SO₂ is excited to the B(¹B₁ + ¹A₂) state. In the oxygen-free and ozone-free atmosphere of the early Earth, photons above approximately 190 nm penetrated the troposphere (Ueno et al., 2009), making complex light-induced chemistry possible for this molecule.

SO₂ photolysis originates large mass-independent fractionation of sulfur isotopes (MIF-S), which is notably distinct from the more commonly observed mass-dependent fractionation (e.g., Farquhar et al., 2001; Whitehill and Ono, 2012; Franz et al., 2013; Ono, 2017). Specifically, MIF-S has been found in Archean sedimentary rocks (e.g., Farquhar et al., 2000a), Martian meteorites (e.g., Farquhar et al., 2000b), sulfate aerosols in polar ice (e.g., Savarino et al., 2003), and in the present atmosphere (e.g., Romero and Thiemens, 2003). The Archean MIF-S may provide insights into the atmospheric chemical composition at that time (e.g., Ono, 2017). Previous laboratory experiments and numerical modeling suggest that MIF-S reflects various atmospheric parameters: very low partial pressure (<2 ppm) of O₂ is required to preserve the MIF-S signatures (Δ³³S≠0) in both sulfide and sulfate minerals (Pavlov and Kasting, 2002; Zahnle et al., 2006); SO₂ column density (or partial pressure of SO₂) changes Δ³³S and Δ³⁶S magnitudes (Ono et al., 2013); atmospheric pressure changes Δ³⁶S/Δ³³S slope (Lyons et al., 2018; Endo et al., 2019); reducing gases such as hydrocarbons and carbon monoxide (CO) changes the Δ³⁶S/Δ³³S slope by MIF-S in SO₂-photoexcitation chemistry (Whitehill et al., 2013; Endo et al., 2016; Kroll et al., 2018); and strong UV absorption, such as by organic haze, changes the branching ratios of SO₂ photolysis/photoexcitation and MIF-S (Zerkle et al., 2012). In addition, the polymerization of elemental sulfur, excluding SO₂ photochemistry, has also been proposed as an MIF-S mechanism (Babikov, 2017; Harman et al., 2018; Lin and Thiemens, 2020).

The most common feature of the Archean geologic MIF-S is a Δ³⁶S/Δ³³S-slope of ~–0.9 (Farquhar et al., 2000a). Recently, Endo et al. (2016) and Mishima et al. (2017) argued that this can be explained by mixing MIF-S during SO₂ photolysis (Δ³⁶S/Δ³³S ~ –2.4) with MIF-S induced during SO₂ photoexcitation (Δ³⁶S/Δ³³S ~ +0.8). A highly reducing atmosphere, such as Earth’s ancient atmosphere containing a significant percentage of carbon monoxide or methane, is required to propagate MIF-S induced by SO₂ photoexcitation. Independently, a highly reducing atmosphere is also speculated based on xenon isotopes (Avice et al., 2018; Zahnle et al., 2019). However, the second most basic trend, Δ³³S/δ³⁴S (~+0.9; Ono et al., 2009), cannot be explained. The mechanisms underlying MIF-S still require further exploration.

In the present study, we focused on MIF-S during SO₂ photolysis, although SO₂ photoexcitation also causes a large MIF-S (Whitehill et al., 2013). The underlying mechanisms of MIF-S in the photoexcitation are likely isotopologue-specific perturbations (Whitehill et al., 2013), and the mechanisms may also occur in isotope fractionation during N₂ and CO photolysis (Chakraborty et al., 2008, 2014). The MIF-S during SO₂ photolysis is dependent on the SO₂ column density and total pressure. This relationship can be explained by decreasing ³²SO₂ (and possibly ³³SO₂ at high pressure, i.e., significant pressure broadening in SO₂ absorption lines) photolysis rates due to SO₂ own absorption. This process is known as self-shielding or isotopic self-shielding (Ono et al., 2013; Lyons et al., 2018; Endo et al., 2019). The nature of self-shielding was recently summarized and reviewed by Lyons (2020) and Thiemens and Lin (2021). Isotope fractionation in photolysis is predicted by the absorption cross-sections of isotopologues (Miller and Yung, 2000). A small MIF-S was predicted for optically thin SO₂ (i.e., without self-shielding) based on high-precision and low-wavelength resolution ³²SO₂, ³³SO₂, ³⁴SO₂, and ³⁶SO₂ (hereafter ^32,33,34,36SO₂) absorption spectra (Endo et al., 2015; Izon et al., 2017); this was consistent with the results of SO₂-photolysis experiments (Endo et al., 2016). In principle, a large MIF-S at optically thick SO₂ (i.e., with self-shielding) can also be predicted; however, predictions by absorption measurements for cross-sections of SO₂ isotopologues did not match the MIF-S observed using SO₂-photolysis experiments (Ono et al., 2013). This discrepancy is likely caused by the complex ro-vibrational structures of SO₂-absorption spectra and the insufficient wavelength resolutions of spectroscopic measurements.

In this study, we report reasonable precision and high-resolution measurements of UV-absorption spectra of ^32,33,34,36SO₂ isotopologues using isotope enrichment samples. The experimental device used in this report was a full-vacuum fast Fourier transform (FFT) spectrometer with a wavelength resolution of 1 cm^–1. This was ~25 times higher than that in previous reports of SO₂ isotopologues (Danielache et al., 2008; Endo et al., 2015), and ~8 times lower than that reported by a previous study that used the highest resolution to measure the natural abundance of SO₂ (Stark et al., 1999). Due to the trade-off between resolution and precision, the precision used was ~10 times lower than that of previous studies using a dual-beam monochromator to attain high-precision measurements (Endo et al., 2015). Absorption spectra were measured from 206 to 220 nm with sufficient precision, although most of the SO₂ was photolyzed by photons from 190 to 220 nm in the Archean atmosphere. Although uncertainty remains as a result of this, the fractionation factors predicted by this study are comparable with isotope compositions of products used in previous SO₂-photolysis experiments at optically thick SO₂ conditions in which self-shielding occurs. In addition, we compared the results with a simple analytical self-shielding model for the Archean MIF-S. This simple model allowed us to predict the large enrichment or depletion of clumped isotope signatures caused by self-shielding. In sum, we attempted to link sulfur isotope fractionations during photolysis experiments to spectroscopic measurements and discuss the Archean MIF-S trend produced by self-shielding.

Methods

Experimental samples

The samples measured in this report were previously presented and described in detail by Danielache et al. (2012). To ensure the isotopic purity of the samples, CuO and elemental ³²S, ³³S, ³⁴S, and ³⁶S sealed in a quartz tube under vacuum were heated at 950°C for 15 min. The resultant ^32,33,34,36SO₂ gas and unreacted O₂ were separated using freeze-pump-thaw cycling and further purified using gas chromatography. The stability of the samples during long storage periods was maintained using sealed preheated Pyrex tubes, and the tubes were stored in a dark environment. During the experiments, when samples were used on a daily basis, containers consisting of stainless steel (SUS316) tubing welded to a bellows-sealed valve (SS-4H-TH3, Swagelok Company, U.S.A.) were used.

Spectrometry and measurements

The absorption cross-sections were determined using an FFT spectrometer (VERTEX80v, Bruker Inc., U.S.A.) equipped with a deuterium lamp (L6301-50, Hamamatsu Photonics K.K., Japan), a 10.0-cm long cell with UV-grade LiF windows, and a VUV-diode detector and calcium fluoride beam splitter. The inside of the spectrometer was constantly evacuated by a dry pump, and the interferometer was operated under a constant nitrogen gas flow. The wavelength scale of this study was calibrated using a He–Ne laser (15,798 cm^–1) and water absorption lines (1554.353 and 7306.74 cm^–1). Under these experimental conditions, a spectral resolution of 1 cm^–1 yielded signal-to-noise ratios (SNRs) of ~20 and ~100 at 206 and 220 nm, respectively.

The SO₂ cross-section is known to vary more than one order of magnitude within the measured wavelength range. To maximize the SNR conditions for all wavelengths, the sample gas pressures were set between 15 and 300 Pa by diffusion in a vacuum line. Pressures were measured using two capacitance manometers (CMR362, 0.01–110 Pa range and CMR364, 1–1.1 × 10⁴ Pa range; Pfeiffer Vacuum GmbH, Germany). The resolution and accuracy of both manometers were 0.003 and 0.2% at full scale and reading, respectively. Inaccuracies in pressure measurements induce an uncertainty of approximately ≤0.5% of the estimated cross-section. The measurements took approximately 15 min, and during this process, the sample gas pressure gradually decreased (maximum 0.3 Pa), potentially due to adsorption to the gas cell and the stainless steel vacuum line. The sample pressure utilized was the average of the pressures before and after the measurement. We assigned a conservative maximum uncertainty of 1% from the pressure.

The absorption spectrum was obtained from photon intensity spectra of the empty cell and sample. The photon intensity spectra were calculated from 100 interferograms at a resolution of 1 cm^–1. A Blackman–Harris three-term apodization function, a Fourier transform window from 0 to 60,000 cm^–1, and a zero-filling factor of 2 were used to produce a spectrum with an energy range of 54,000 to 35,000 cm^–1 with a data point spacing of 0.241085 cm^–1. Background intensity spectra (I_vacuum) and gas sample spectra (I_sample) were measured in an alternating fashion.

The amplitude drift of the signal can be assessed by comparing the two background spectra. The average signal drift between 206 and 220 nm was calculated to be ~15%. A moving average of 41 points was introduced to reduce noise in the background spectra. In contrast, no such smoothing procedure was implemented for the sample spectra (I_sample).

In our previous reports (Danielache et al., 2008, 2012), the background spectra at the time of the measurement were taken as the average spectra of the empty cell before (I_{vacuum-before}) and after (I_vacuum-after) recording the sample spectra. This approach partially corrects the drift effects on the background spectrum. In this study, a more realistic approach was used to reduce uncertainties induced by drift effects. Since SO₂ spectra in the energy range of 235 to 245 nm have very weak absorption cross-sections that are more than one order of magnitude smaller (6 × 10^–20 cm²; Rufus et al., 2003, at transmittance above 0.96) than the spectra involved in the photolysis process, which is far beyond the photolysis threshold (219.2 nm; Okabe, 1971), the background spectrum was calculated by minimizing x for the following relationship:

  

$$\sum \left[\left.x\right|\left.I_{\text{vaccum-before}}(\lambda )-I_{\text{sample}}(\lambda )\right|\left.+\left(1-x\right)\right|\left.I_{\text{vaccum-after}}(\lambda )-I_{\text{sample}}(\lambda )\right|\right]$$(1)

where the summation expands over the 235–245-nm energy range. x was selected from 0.0, 0.1, ..., 1.0. Once x was obtained, the corrected background spectrum (I_vacuum’(λ)) was calculated as:

  

$$I_{\text{vacuum}}’(\lambda )=x{I}_{\text{vaccum-before}}(\lambda )+\left(1-x\right)I_{\text{vaccum-after}}(\lambda )$$(1’)

This correction to the spectral drift from the UV source produces a difference ranging from 1% to 4.5%. Additionally, even when the deuterium lamp was turned off, the recorded intensities were not zero (I_dark), indicating that the intensities include a signal that arises from the UV (such as electronics or stray light). To correct for this error, the averaged intensities from 200 to 220 nm were subtracted from I_vacuum’(λ) and I_sample and defined as:

  

$$\begin{array}{l}{I}_{\text{vacuum}}”=I_{\text{vacuum}}’-I_{\text{dark-average}}\\ I_{\text{sample}}’=I_{\text{sample}}-I_{\text{dark-average}}\end{array}$$

The plots describing these calibrations are summarized in Fig. S1. I_dark-average and I_dark-stdev were calculated using the averaged intensities between 200 and 220 nm under no-light conditions, and resulting data that satisfied the following conditions were excluded:

  

$$\begin{array}{l}1)I_{\text{sample}}<2I_{\text{dark-average}}+2I_{\text{dark-stdev}}\\ 2)I_{\text{vacuum}}’-I_{\text{sample}}<2I_{\text{dark-stdev}}.\end{array}$$

By imposing these strict filters, instances with low SN ratios were not included in the final spectra.

Absorption cross-sections were calculated by the Beer’s law:

  

$$\sigma =A/\rho$$(2)

where σ is the absorption cross-section (cm²), ρ is the column density of the sample gas (calculated by the ideal gas law in cm^–2), and A is the absorbance, defined as

  

$$A=\ln \left(I_{\text{vacuum}}”/I_{\text{sample}}’\right)$$(3)

Because the wavelength resolution is not sufficient to resolve absorption lines, σ likely depends on ρ; the ρ dependence is suggested in a report by Endo et al. (2015). However, the results did not demonstrate a clear ρ dependence, likely because the random errors of σ were much larger than those reported by Endo et al. (2015). Pure sulfur isotopologue ^32,33,34,36SO₂ cross-sections were calculated from the isotopic purity as reported by the manufacturer (99.99%, 99.80%, 98.80%, and 99.24% for ³²S, ³³S, ³⁴S, and ³⁶S, respectively).

Calculating fractionation factors for isotopic self-shielding

Once ^32,33,34,36SO₂ cross-sections are determined, the fractionation factors during SO₂ photolysis can be calculated as follows (Miller and Yung, 2000):

  

$${}^{3x}J=\; \int {}^{3x}\sigma (\lambda )\Phi (\lambda )I_0(\lambda ){\text{e}}^{-\rho L\sigma (\lambda )}\text{d}\lambda$$(4)

  

$${}^{3y}\epsilon =\ln \left({}^{3y}J/{}^{32}J\right)\times 1000‰$$(5)

  

$${}^{33}\text{E}={}^{33}\epsilon -0.515\times {}^{34}\epsilon ‰$$(6.1)

  

$${}^{36}\text{E}={}^{36}\epsilon -1.90\times {}^{34}\epsilon ‰$$(6.2)

where 3x represents each sulfur isotope (32, 33, 34, or 36), 3y represents each sulfur isotope excluding ³²S (33, 34, or 36), ^3xσ represents the ^3xSO₂-absorption cross-section [cm²], ^3xJ is the ^3xSO₂-photolysis rate constant [s^–1], L is the path length [cm], λ is the wavelength [nm], and σ is the natural abundance SO₂-absorption cross-section [cm²] (³²S/³³S/³⁴S/³⁶S = 95.018/0.75/4.215/0.017, Farquhar, 2018). I₀ is the incident photon flux [cm^–2s^–1nm^–1], Φ is the quantum yield of SO₂ photolysis from Okazaki et al. (1997), and ρ is the SO₂ number density [cm^–3]. Here, the quantum yield is assumed to be the same for all isotopologues since the isotopic effect on the quantum yield is negligible during SO₂ photolysis (Ono, 2017). Fractionation factors (³³ε, ³⁴ε, ³⁶ε, ³³E, and ³⁶E) were used, where ^33,34,36ε represents the magnitudes of fractionation to ³²S and ^33,36E represents the magnitudes of mass-independent fractionation.

Assumptions of a simple analytical self-shielding model

Very high spectral resolution and high precision are required to compare fractionation factors predicted by absorption spectra with photolysis experiments. Because such experimental quality is technically difficult to achieve, we modeled self-shielding analytically to capture its trends. Recently, Lyons (2020) reported this phenomenon. In the present paper, we have added this discussion to the present paper.

The difference in absorption wavelength between isotopologues is caused by a difference in vibration frequency. The shifted absorption spectra of ³²SO₂ were used as the absorption spectra of ^33,34,36SO₂ (Lyons, 2007). This shift model is valid for approximating reproducible photolysis experiments. Specifically, the shifted spectra were compared with the isotope fractionations observed in SO₂ photolysis experiments at room temperature (Ono et al., 2013; Endo et al., 2019). The natural abundance SO₂ absorption spectra reported by Freeman et al. (1984) (~0.5 cm^–1 of spectral resolution, 213 K; Table 1) and Stark et al. (1999) (~0.12 or 0.18 cm^–1 of spectral resolution, 295 K; Table 1) were used as the ³²SO₂ absorption spectra in Ono et al. (2013) and Endo et al. (2019), respectively. When the SO₂ column density increased, δ³⁴S and Δ³³S of the products increased in both experiments, and the shift models explained the overall trends. However, this shift did not quantitatively explain the magnitudes of δ³⁴S and Δ³³S. In the report by Ono et al. (2013), the model overestimated the δ³⁴S of the products and predicted a ~1.9 times larger δ³⁴S/(SO₂ column density). They speculated that this discrepancy could be attributable to the difference in temperature. In the study by Endo et al. (2019), the model predicted a ~1.15 times larger δ³⁴S/(SO₂ column density) and a ~2 times larger Δ³³S/δ³⁴S. They speculated that this discrepancy was due to errors in the cross-section.

Absorption line widths are nearly the sum of Doppler and pressure widths at the troposphere and stratosphere, because a natural width is much smaller than others. The overlap of absorption spectra may be reduced when photolysis is conducted at low temperature and low total atmospheric pressure or using molecules that have more discrete absorption spectra. The simplest case of self-shielding occurs when the absorption line is narrow (sub-Doppler width) and ^32,33,34,36SO₂ absorbs only one wavelength, which depends on isotopologues. In other words, the cross-section is σ at wavelengths of absorption lines and 0 at wavelengths excluding the absorption lines; the absorption line width is Δλ (Fig. 1A).

Fig. 1.

The simplest case of modeled (A) ^32,33,34,36SO₂ absorption spectra and (B) ¹A¹B, ²A¹B, ¹A²B, and ²A²B, each of which absorbs different wavelength. The line width is Δλ. Cross-sections are σ at wavelength of absorption lines and 0 at wavelength excluding the absorption lines.

Furthermore, as for multiply-substituted isotopologues (called as “clumped isotope”; e.g., ¹³C¹⁸O¹⁶O in case of CO₂; Eiler, 2007), the simplest self-shielding model is useful to capture the nature of the isotope signature. Self-shielding may produce clumped isotope enrichment and depletion, although it has not been found that self-shielded clumped isotope signature is preserved in natural samples in research to date. We modeled the simplest case of molecule AB’s excitation (AB→AB*). Isotopologues of AB are assumed to be ¹A¹B, ¹A²B, ²A¹B, and ²A²B, with major isotopes of ¹A and ¹B and minor isotopes of ²A and ²B. A unique clumped isotope of the AB molecule was ²A²B. It was assumed that each isotopologue absorbs a different wavelength (Fig. 1B). The analytical calculations and results of the models are described in Section “Calculations of self-shielding using synthesized absorption spectra”.

Results

Absorption spectra measurements

The measured absorption cross-sections are shown in Figs. 2 and S2. The absorption spectra of ^33,34,36SO₂ appeared red-shifted with respect to the ³²SO₂ spectrum. Random errors (standard error of 1 s. d.) were approximately 10% following the data treatment as presented in Section “Spectrometry and measurements”. Even at high resolution, such as in this study, ^32,33,34,36SO₂ absorption spectra overlap with each other (Fig. S2). The errors in this report are consistent with those of the previous spectra (Table 1).

Fig. 2.

Comparison of measured ^32,33,34,36SO₂ absorption cross-sections from 206 to 220 nm. As previously reported (Danielache et al., 2008; Endo et al., 2015; Tokue and Nanbu, 2010), the main absorption band, wherein the bound-bound C¹B₂-X¹A₁ is the main cause of the observed red-shifting.

Table 1. Summary and comparison of reported SO₂ absorption spectra. Photolysis rate constants (J value) are presented for measurements at room temperature. The J values are those of ³²SO₂ for the present study, Danielache et al. (2008), and Endo et al. (2015) or natural abundance SO₂ for Stark et al. (1999) and Wu et al. (2000). They were calculated from Eq. (4), where I₀(λ) is 1, L is 0, and Φ is from Okazaki et al. (1997).

Reference	Isotope	Spectral range (nm)	Resolution (cm–1)	Precision (%)	J (206–220 nm, 10–17 s–1)	Temp (K)
The present study	32S, 33S, 34S, 36S	206–220	1	~10	4.18	295
Stark et al. (1999)	natural abundance	198–220	0.18, 0.12	~10–50	4.29	295
Wu et al. (2000)	natural abundance	175–295	12.5	<10	4.22	200–400
Danielache et al. (2008)	32S, 33S, 34S	183–350	25	~1.2	4.95	293
Endo et al. (2015)	32S, 33S, 34S, 36S	190–225	25	~1	5.28	293
Freeman et al. (1984)	natural abundance	170–240	0.5	~4		213
Vandaele et al. (1994)	natural abundance	250–333	2	~2.5		296
Koplow et al. (1998)	natural abundance	215.21–215.23	0.0003	N/A		295
Rufus et al. (2003)	natural abundance	220–325	0.12	~5		295
Rufus et al. (2009)	natural abundance	199–220	0.18, 0.12	~12–50		160
Hermans et al. (2009)	natural abundance	227–345	2	~1.5		298–358
Vandaele et al. (2009)	natural abundance	345–416	2	~4–6		298–358
Blackie et al. (2011)	natural abundance	212–325	0.12	~4.5		198
Danielache et al. (2012)	32S, 33S, 34S, 36S	250–320	8	~2.5		293

The ³²SO₂ absorption spectrum of the present study is compared with four previous measurements of ³²SO₂ or natural abundance SO₂ absorption spectra (Stark et al., 1999; Wu et al., 2000; Danielache et al., 2008; Endo et al., 2015) in Fig. 3. The close comparison of the five measurements ranging from low-resolution and high precision (~25 cm^–1, 1%; Endo et al., 2015) to high resolution and low precision (~0.12 and ~0.18 cm^–1, 10%–50%; Stark et al., 1999) shows a clear change in the spectrum waveform. A measurement of the high-resolution and precision of isotopically enriched spectra is ideal, yet not realistically achievable. An in-depth analysis of the ideal trade-off between resolution and precision is beyond the scope of this study. Here, we discuss the limits of the required spectral resolution required to account for the waveform features of the spectra. As presented in Fig. 3, spectral resolution at 12.5 cm^–1 (Wu et al., 2000) and 25 cm^–1 (Danielache et al., 2008; Endo et al., 2015) were not capable of capturing the fine features of a high-resolution spectrum as reported by Stark et al. 1999 (~0.12 and ~0.18 cm^–1). The spectral resolution of 1 cm^–1 in this report shows sharp features; however, the fine structure, most likely produced by either a single or a combination of multiple ro-vibrational electronic transitions, is not fully resolved. A key question to address is whether these spikes in the spectra, regardless of how visually large they appear, significantly contribute to the photolysis rate constant, and its associated isotopic effect.

Fig. 3.

Comparison of five measurements including the present study at different spectral resolution (See Table 1 for spectral details). All of the displayed spectra were measured at room temperature. The differences in the waveform can be attributed to the spectral resolution of the measurement.

To aid understanding of the trade-off between spectral resolution and precision, a comparison between these measurements and the data reported by Stark et al. (1999) is presented in Fig. S3. Narrow-band, tunable, frequency-quadrupled diode laser measurements carried out by Koplow et al. (1998) estimated that a spectral resolution of below ~0.1 cm^–1 is required to resolve the highly structured spectra of the SO₂ molecule. The data reported by Stark et al. (1999) is the closest to the required spectral resolution to achieve a fully resolved spectrum (~0.12 and ~0.18 cm^–1). When these spectra are used to calculate the photolysis rate constants for rare isotopologues, there is a need for high precision. Stark et al. (1999) reported minimum and maximum cross-section errors ranging from 10% to 50%. We converted these values to actual cross-sections and compared them against the data presented in this report. The spectral range presented in Fig. S3 was selected from the study by Koplow et al. (1998). This spectral region shows an absorption peak with a maximum SN ratio, which is a 10% error for Stark et al. (1999). In comparison, the data in this report for the same spectral range contain an error rate between 3% and 4%. Although inferences from synthetic isotopologue spectra derived from this spectrum may be appealing due to their high spectral resolution and importance to self-shielding phenomena, errors that will be propagated to fractionation factors must be considered when applying such spectra to geochemical processes.

The spectral resolution in this report was 25 times higher than that of the previously reported SO₂ isotopologues spectra. To confirm the wavelength accuracy, natural SO₂ absorption spectra of our results were compared with the spectra reported by Stark et al. (1999) and the spectra convolved with a 1-cm^–1 (FWHM) Gaussian function (Fig. S4). We noticed that a wavelength shift of ~0.016 nm exists between the convoluted and the spectra presented in this report (Fig. S4). The wavelength calibration of the VERTEX80v is based on the wavelength of the He–Ne laser fixed at 15.798 cm^–1, and is therefore, in principle, exact. The cause of the observed ~0.016 nm difference is not clear. Further calibration of wavelengths in the UV region can be performed by using the absorption band of a well-known molecule such as O₂ or NO₂. We opted to use the literature spectra to calibrate the wavelength of our measurements. The wavelength scale by Stark et al. (1999) reproduces that reported by Freeman et al. (1984) and Koplow et al. (1998), although spectrometers and wavelength calibration methods vary among the three reports. The calibration procedure consisted of shifting the spectrum by 17 wavenumber steps or 4.0984 cm^–1 (~0.0164 nm). Following wavelength calibration, the ³²SO₂ spectrum replicated the literature data reasonably well (Figs. S4 and S5).

Next, the magnitudes of the cross-sections were evaluated against data in the literature (Fig. S5). The magnitudes of the measured cross-sections at some wavelengths were smaller than that of the literature data. Of note, these discrepancies are larger at absorption peaks due to insufficient spectral resolution. For highly structured spectra such as SO₂, measurements under insufficient spectral resolution may yield significantly smaller cross-sections than those measured at high resolution.

Isotopic self-shielding estimation using measured cross-sections

We calculated the fractionation factors using our spectroscopic measurements (Eqs. 4–6) (Figs. 4 and 5). Fig. 4 shows the values of SO₂ photolysis rate constants (³²J) (A) and fractionation factors (B) vs. SO₂ column density (from 2 × 10¹⁵ to 7 × 10¹⁸ cm^–2), and a three- or four-isotope plot (C and D) in which the incident photon flux is constant against wavelength (I₀(λ) = 1). The C band absorption, where SO₂ is photolyzed, is located from 165 to 219.2 nm. In assumed Archean atmospheres, carbon dioxide (CO₂) scatters most of the <190-nm UV photons. The SO₂ photolysis rate constant (the J value in Eq. 4) between 206 and 220 nm is approximately 2/3rd of that between 190 and 220 nm (Endo et al., 2015). The calculation assumes that the fractionations, including self-shielding, do not vary based on the wavelength. Therefore, the calculation may be more accurate when absorption spectra below 206 nm are reported.

Fig. 4.

Using measured absorption spectra, estimation of (A) ^32,33,34,36SO₂ photolysis rate constants (^3xJ values) vs. SO₂ column density, (B) ^33,34,36ε and ^33,36E values vs. SO₂ column density, and (C) a three-isotope plot of ³⁴ε and ³³E, and (D) four-isotope plot of ³³E and ³⁶E. Error bars are smaller than symbols.

Fig. 5.

Calculated fractionation factors by SO₂ isotopologues absorption cross-sections. Plots of ((A) ³⁴ε, (B) ³³ε, (C) ³⁶ε, (D) ³³E, and (E) ³⁶E) vs. SO₂ column density, (F) ³⁴ε vs. ³³E, and (G) ³³E vs ³⁶E. Black, gray, green, gold, red, and blue lines represent the present study, Danielache et al. (2008), Endo et al. (2015), Lyons (2007), Stark et al. (1999), and Rufus et al. (2009), respectively. Cross-sections of ^33,34,36SO₂ of Stark et al. (1999) and Rufus et al. (2009) are the red shift model. We used the shifting parameters from Figure 8 of Tokue and Nanbu (2010). Cross-sections of ^33,34,36SO₂ of Lyons (2007) are also the red shift model (see text). Wavelength ranges of all plots are from 206 to 220 nm in Eq. (4). Assumed photon spectra are flat (does not depend on wavelength). Calculated SO₂ column density is from 2 × 10¹⁵ to 10¹⁹ cm^–2, and the column density range is limited in case that ³²J is larger than 2 s.d. of ³²J. Purple dashed lines in (F) and (G) represent the analytical model in the case of narrow absorption lines.

Random errors of ^33,34,36ε value (Δ^33,34,36ε) are calculated as functions of ^32,33,34,36σ_i:

  

$$\left|\text{Δ}{}^{3y}\epsilon \right|=\left|{\displaystyle {\sum }_{\text{i}=1}^{\text{n}}\left[\frac{\partial {}^{3y}\epsilon }{\partial {}^{32}\sigma {}_{\text{i}}}\text{Δ}{}^{32}\sigma {}_{\text{i}}+\frac{\partial {}^{3y}\epsilon }{\partial {}^{3x}\sigma {}_{\text{i}}}\text{Δ}{}^{3y}\sigma {}_{\text{i}}\right]}\right|$$(7)

  

$$\frac{\partial {}^{3x}\epsilon }{\partial {}^{32}\sigma {}_{\text{i}}}=-\frac{\int I\text{d}\lambda }{\int {}^{32}\sigma {}_{\text{i}}I\text{d}\lambda }$$(8)

  

$$\frac{\partial {}^{3y}\epsilon }{\partial {}^{3y}\sigma {}_{\text{i}}}=-\frac{\int I\text{d}\lambda }{\int {}^{3y}\sigma {}_{\text{i}}I\text{d}\lambda }$$(9)

where n is the number of wavelength grids, σ_i is the cross-section of the i-th wavelength step, and I (=I₀ e^–ρ32σ) is the photon spectra after shielding; shielding by ³²SO₂ spectra is assumed in this calculation. Because the number of divided wavelength steps is quite large (n = 12,791), typical random errors of ^33,34,36ε and ^33,36E values from Eqs. (7)–(9) are approximately 5‰ at an SO₂ column density (ρL) of 10¹⁹ cm^–2 or less. The random errors are not shown in Figs. 4 and 5 because they are significantly smaller than the graphs’ range. Signal drift errors (up to 4.5%, estimated in Section “Spectrometry and measurements”) were not included in the above random errors. In this calculation, drift errors are added to ^33,34,36ε and ^33,36E at all SO₂ column densities; therefore, they are not assumed to significantly contribute to ^33,34,36ε/(SO₂ column density), ^33,36E/(SO₂ column density), ³³E/³⁴ε, and ³⁶E/³³E calculations.

Fig. 4A presents a wide range of ³²J values, some of which are within plausible photolysis conditions for an Archean atmosphere. The ³²J values for column densities above 10¹⁸ cm^–2 are, in terms of kinetics, insignificant. From 10¹⁷ to 10¹⁸ cm^–2 of SO₂ column density, where ³²SO₂ is optically thick, all ^33,34,36ε values increase and significant self-shielding occurs (Fig. 4B). The capital epsilon values (^33,36E) are more complex and more sensitive to SO₂ column density than the ^33,34,36ε values (Fig. 4B). As presented in Fig. 4B and C, ³⁴ε increased, but ³³E decreased. This trend is different from the observed MIF-S in most previous SO₂ photolysis experiments (see Section “Comparison to photochemical experiments”). At ~10¹⁸ cm^–2 of SO₂ column density, the ³⁴ε, ³⁶ε, and ³³E trends changed. In particular, ³³E started increasing. This is likely due to shielding by not only ³²SO₂ but also ³⁴SO₂, as estimated by Lyons (2020).

As explained in Section “Absorption spectra measurements”, the spectral resolution in this study was lower in comparison to previously reported data (Stark et al., 1999). The lack of spectral resolution resulted in cross-sections of reduced magnitude. Additionally, the wavelength of the reported spectra was adjusted to a convolved spectrum reported by Stark et al. (1999). The lack of spectral resolution and potential errors introduced during the wavelength adjustment procedure can introduce errors in the calculation of fractionation factors. To quantify the magnitude of these errors, fractionation factors were calculated using the assumption that only the ³²SO₂ absorption spectrum was shifted (Fig. S6). The ³²SO₂ absorption spectrum was shifted by 17 wavenumber steps, 4.0984 cm^–1 (~0.0164 nm), and fractionation factors were calculated (Fig. S6, light green lines). The ³²SO₂ absorption spectrum was assumed to be the convolved spectra with 1 cm^–1 per Stark et al. (1999). Since all isotopologues were analyzed in similar ways, the displayed discrepancy represents an upper limit. The uncertainty did not change the overall trend; that is, ^33,34,36ε increased, but ³⁶E decreased and ³³E reversed from decreasing to increasing when the SO₂ column density increased. The uncertainties of the fractionation factors of ^33,34,36ε were within approximately 30‰ (Fig. S6A–C); thus, they did not contribute to significant errors in the fractionation factors. The uncertainties of the fractionation factors of ^33,36E were within approximately 25‰ (Fig. S6D and E). The uncertainties of ³³E/³⁴ε and ³⁶E/³³E were sometimes large (Fig. S6F and G).

The calculated fractionation factors were compared with those reported in previous studies (Fig. 5). Low-resolution absorption spectra of ^33,34,36SO₂ are available (~25 cm^–1, Danielache et al., 2008; Endo et al., 2015). However, because high-resolution ^33,34,36SO₂ absorption spectra have not been reported, the red-shift model (Danielache et al., 2008) was used for the natural abundance SO₂ absorption spectra per Stark et al. (1999) and Rufus et al. (2009) (details in Table 1, Rufus et al. measured at 160 K) to produce synthetic ^33,34,36SO₂ spectra. Natural abundance (³²S of 95%) SO₂ absorption spectra were assumed to be ³²SO₂ absorption spectra, and the shifted parameters were extracted from Tokue and Nanbu (2010). Additionally, we displayed fractionation factors calculated from the ^32,33,34,36SO₂ cross-sections by Lyons (2007), as shown in Fig. 5. ^33,34,36SO₂ absorption spectra from his study were also obtained from red-shifted natural abundance SO₂ absorption spectra; the natural abundance SO₂ absorption spectra were obtained from Freeman et al. (1984) (a resolution of ~0.5 cm^–1 and a temperature of 213 K) and the shifting parameters were extracted from Ran et al. (2007).

Calculations of self-shielding using synthesized absorption spectra

Isotope fractionation by self-shielding occurs under conditions in which the absorption line is narrow and ^32,33,34,36SO₂ absorbed only one wavelength, which varies on isotopologues as described in Section “Assumptions of a simple analytical self-shielding model” (Fig. 1A). An optical depth (τ) is defined here as the natural abundance SO₂ column density (ρ’) multiplied by the magnitude of the peak cross-section of each isotopologue (σ, Fig. 1) as ρ’σ. The ^3xJ values are σΔλ exp(–τ ^3xN), from Eq. (4), where ^3xN is the abundance of ^3xS of SO₂. From Eqs. (5), (6), ^3yε is 1000τ(³²N – ^3yN)σ ‰, ³³E is 1000τ(0.485 × ³²N–³³N + 0.515 × ³⁴N) ‰, and ³⁶E is 1000τ(–0.90 × ³²N–³⁶N + 1.90 × ³⁴N) ‰. The slopes of ³³E/³⁴ε and ³⁶E/³³E are functions of isotope abundance only. (These equations are the same as those in Eq. 20 in Lyons, 2020).

When the typical sulfur isotope abundance on Earth (³²S/³³S/³⁴S/³⁶S = 95.018/0.75/4.215/0.017, Farquhar, 2018) is assumed, the slopes of ³³E/³⁴ε and ³⁶E/³³E are +0.523 and –1.63; these slopes are shown in Fig. 5F and G for comparison. ³⁴ε and ³³E are +908τ ‰, and +475τ ‰, respectively. The modeled ³³E/³⁴ε (+0.52) slope is closer to the Archean slope (~+0.9; Ono et al., 2009) in comparison to the trends observed in SO₂ photolysis (≤~0.1; Ono, 2017). In addition, the optical depth for self-shielding was assumed to be ≥1 (Lyons, 2007; Claire et al., 2014), but significant self-shielding may occur even when the optical depth is ~0.1.

Additionally, we tested the sensitivity of isotope abundance. In the case of +100‰ fractionation of δ³⁴S mass-dependently (³²S/³³S/³⁴S/³⁶S = 94.558/0.789/4.636/0.017), ³³E/³⁴ε and ³⁶E/³³E were +0.528 and –1.60, respectively. Sulfur isotope abundance had insignificant effects on ³³E/³⁴ε and ³⁶E/³³E.

The linear-scale fractionation factors are suitable for considering mixing; the values of ^33,34,36ε used can be found by the following equation:

  

$${}^{3y}\epsilon =1000\times \left({}^{3y}J/{}^{32}J-1\right)‰$$(5’)

where ^33,36E values are the same as those in Eqs. 6.1 and 6.2. In the narrow absorption line scenario, ^3yε is 1000[exp(τ³²N – τ^3yN) – 1] ‰. The slopes of ³³E/³⁴ε and ³⁶E/³³E depend on the optical depth and are sometimes similar to those of the Archean slope. For example, at τ = 5, ³³E/³⁴ε and ³⁶E/³³E were 0.668 and –1.01, respectively.

Next, we calculated the clumped isotope enrichment or depletion in self-shielding in the excitation of AB molecules (AB→AB*). It was assumed that the four isotopologues absorb different wavelengths (Section “Assumptions of a simple analytical self-shielding model” and Fig. 1B). The fractionation factor of clumped isotope enrichment in kinetic reactions, ^2A,2Bγ, was defined as (see Section 3.2 of Whitehill et al., 2017):

  

$${}^{\text{2A,2B}}\gamma =\left({}^{{}^{\text{2A,2B}}}J\times {}^{{}^{\text{1A,1B}}}J\right)/\left({}^{{}^{\text{2A}}}J\times {}^{{}^{\text{2B}}}J\right)$$(10)

where ^2AJ, ^2BJ, and ^xA,xBJ represent the excitation rate constants of ²AB (weighted average considering abundance of ²A¹B and ²A²B), A²B (weighted average considering abundance of ¹A²B and ²A²B), and ^xA^xB isotopologues, respectively (Wang et al., 2016). To capture the natural abundance, assuming that the isotopologues except ¹A¹B are rare, the ^2A,2Bγ is approximately equal to e^–τ, where τ is a product of the cross-section at the peak wavelength, (σ, Fig. 1B), and column density of the AB molecule (ρ’). The deformations are described in the Supporting Information (Supporting text 1). The log scale of ^2A,2Bγ is

  

$$\ln \left({}^{\text{2A,2B}}\gamma \right)\approx -\tau$$(11)

By multiplying both sides of Eq. (11) by 1000, we obtained the clumped isotope enrichment factor in permil (‰). Consequently, the clumped isotope depletion (‰) in the product (AB*) was approximately 1000 times larger than the optical depth. Next, in a closed system, the clumped isotope compositions (Δ, the deviation from a stochastic distribution) for the reagent (AB) obey Rayleigh fractionation (in Section A.2 of Whitehill et al., 2017). Under the assumption that isotopologues are rare with the exception of ¹A¹B, the difference in the clumped isotope composition in the reagent is:

  

$$\text{Δ}-{\text{Δ}}_0\approx 1000\left(1-{\text{e}}^{\tau }\right)\times \ln f‰$$(12)

where f is the remaining fraction, Δ is the clumped isotope composition at the remaining fraction of f, and Δ₀ is the initial clumped isotope composition. The deformations are described in Supporting Information (Supporting text 1). Because ln f is negative, Δ–Δ₀ is positive. Thus, self-shielding led to clumped isotope enrichment in the reagent. In addition, the clumped isotope is a deviation in a single molecule rather than a fractionation; therefore, mass balance is not strictly conserved (net capital delta is not necessarily 0). In accordance with this, large enrichment or depletions will be recorded in major chemical species (for example, in atmospheric N₂; Yeung et al., 2017).

Discussion

We focused on self-shielding, that is, the SO₂ column density dependence. In Section “Comparing with previous SO₂ absorption spectra”, we qualitatively discuss self-shielding trends using the present and previous SO₂ spectral studies. In Section “Comparison to photochemical experiments”, the trends are discussed using both spectral studies and isotope fractionations in previous photolysis experiments, and we attempt to explain them quantitatively. Despite many efforts, the Archean MIF-S trends have not been sufficiently reproduced. In Section “Applying a self-shielding model using the synthesized absorption spectra to laboratory experiments and natural samples”, we discuss the application of the analytical self-shielding model.

Comparing with previous SO₂ absorption spectra

Owing to the fine structure of the SO₂ absorption spectra, it is believed that high wavelength resolution spectra are required to predict the self-shielding effect. The highest resolution measurements of SO₂ from 206 to 220 nm have been reported by Stark et al. (1999) at 295 K and by Rufus et al. (2009) at 160 K. Their resolutions were ~0.12 cm^–1, which does not completely resolve the Doppler width (~0.072 cm^–1). The resolutions of this study, Danielache et al. (2008), and Endo et al. (2015) were ~1, ~25, and ~25 cm^–1, respectively, which did not resolve either of the isolated rotational lines.

As illustrated in Fig. 5, the predicted fractionation factors showed a correlation with the spectral resolution between Stark et al. (1999) and the present study at a constant temperature, where the ^33,34,36ε values increased with the resolution. The absorption peak magnitudes are larger and the optical depth is apparently larger at higher resolutions, so that the effects of resolution could be qualitatively predicted. Meanwhile, the lower temperature absorption spectra at the same resolution was predictive of larger ^33,34,36ε values. The effects of temperature can also be qualitatively predicted because the magnitudes of the absorption peaks are larger at lower temperatures (Rufus et al., 2009; Wu et al., 2000). Since both the resolution (~0.5 cm^–1) and the temperature (213 K) used by Lyons (2007) were different from those used in other reports, the results cannot be compared directly with other reports. However, both the resolution and temperature were between those of this study and the one by Rufus et al. (2009). At SO₂ column densities less than 2 × 10¹⁷ cm^–2, the ^33,34,36ε values predicted by Lyons (2007) were between those obtained in this study and by Rufus et al. (2009) (Fig. 5A–C); this retains consistency with the relationships previously described.

The capital E values (^33,36E) are complex because they possess relationships with two ^3xε values. Notably, ³³E (or ³³E/³⁴ε) was sensitive to the resolution (Fig. 5F). Previous photolysis experiments have demonstrated that the isotope fractionation during SO₂ photolysis is sensitive to total pressure and, likely, the absorption line width. Additionally, ³³E was found to decrease at broad absorption lines (Endo et al., 2019; Masterson et al., 2011). This is consistent with the small or negative ³³E in the case of the low-resolution spectra discussed in Section “Comparison to photochemical experiments”.

Comparison to photochemical experiments

The isotope fractionation factors of SO₂ photolysis estimated by the absorption spectra in this study were compared with previous SO₂ photolysis experiments. Figure 6 represents the SO₂ column density dependence, and Fig. 7 represents the total pressure dependence, which was assumed to be the absorption line width dependence. The data of the photolysis experiments shown in Fig. 6 were obtained following calibrations and filtering. In laboratory experiments, the SO₂ column density depends on the distance from the window of the UV source side, thus the J value in Eq. (4) is integrated with respect to distance L (Eq. 4 in Endo et al., 2019).

Fig. 6.

Comparison between fractionation factors predicted by this study (black lines; and dashed lines are offset for comparison) and MIF-S of previous SO₂ photolysis experiments ((A, B) ³⁴ε, (C, D) ³³ε, (E, F) ³⁶ε, (G, H) ³³E and, and (I, J) ³⁶E), as functions of SO₂ column density. Panels A, C, E, G, and I present log scales of wide range of SO₂ column density, and panels B, D, F, H, and J present linear scales of narrow range. Data are from pure SO₂ of Masterson et al. (2011), DFS-3 of Whitehill and Ono (2012), front cell of Ono et al. (2013), natural abundance SO₂ of Franz et al. (2013), S⁰-1 and S⁰-2 of Whitehill et al. (2015), D2 experiments of Endo et al. (2016), and all of Endo et al. (2019). Note that we did not consider differences between UV light sources or differences born out of photolysis spectral range (cross-section in this report is from 206 to 220 nm).

Fig. 7.

Relationships between slopes of isotope fractionations/SO₂ column density (that is, (A) ³⁴ε/SO₂ column density, (B) ³³ε/SO₂ column density, (C) ³⁶ε/SO₂ column density, (D) ³³E/SO₂ column density, and (E) ³⁶ε/SO₂ column density) and SO₂ absorption line width or spectral resolution at fixed SO₂ column density. Colors represent SO₂ column density. Squares represent this study whereas circles represent previous photolysis experiments (Endo et al., 2019). Lines are calculated by revised cross-sections from Endo et al. (2019). The y-axes represent “slopes”, so that fractionation factors at each SO₂ column density subtracted by those at optically thin SO₂ (i.e., an SO₂ column density of 0 cm^–2) were divided by SO₂ column densities. For the slopes of Endo et al. (2019), fractionation factors of “D2 0 Pa (estimate)” in Endo et al. (2016) were used as the fractionation factors at the optically thin SO₂.

  

$${}^{3x}J=\int \int {}^{3x}\sigma (\lambda )\Phi (\lambda )I_0(\lambda ){\text{e}}^{-\rho L\sigma (\lambda )}\text{d}\lambda \text{d}L$$(13)

The fractionation factors (^33,34,36ε and ^33,36E) were calculated using the same equations, that is, Eqs. (5) and (6), respectively: The isotope compositions (δ^33,34,36S and Δ^33,36S) of products in photolysis experiments are sometimes significantly different from fractionation factors (^33,34,36ε and ^33,36E) owing to Rayleigh fractionation. Specifically, fractionation factors are compared with the isotope compositions of products in flow experiments; however, they are not compared with the compositions in static experiments. In static experiments, fractionation factors were estimated by Rayleigh fractionation model or were assumed to be equal to the isotope compositions in the case of small product yields (below 2%). Moreover, the photolysis experiment data were selected and filtered: self-shielding was identified as the dominant isotope fractionation and the SO₂ column densities were clearly reported; isotopic effects produced by photoexcitation or single-band photolysis were not included in the comparison.

The self-shielding trend is dependent on the total pressure, which is likely attributable to the pressure broadening of SO₂ absorption lines (Endo et al., 2019). This trend may also depend on temperature; however, this relationship remains unclear (Whitehill et al., 2015; Ignatiev et al., 2019). The room-temperature experiments are shown in Fig. 6. Experiments are divided into two groups: lower total pressure (Fig. 6, open circles; less than 0.1 bar under N₂ or CO atmosphere or less than 0.033 bar pure SO₂ atmosphere) and higher total pressure (Fig. 6, filled squares; more than 0.1 bar under N₂ or CO atmosphere or more than 0.033 bar pure SO₂ atmosphere). Fractionation factors hardly depend on total pressure when the total pressure is below 0.1 bar under N₂ or CO atmosphere. However, they demonstrate a dependent relationship with the total pressure when the total pressure is above 0.1 bar under N₂ or CO atmospheres (Endo et al., 2019). The threshold of a pure SO₂ atmosphere is unknown. The pressure broadening of individual absorption lines can explain the isotopic effect observed in the chamber experiments as summarized above. There are no reported data on the self-pressure broadening effects of SO₂ in the ultraviolet region. Using the relationship between N₂ and SO₂ of the pressure broadening coefficients in the IR region, the self-pressure broadening coefficient of SO₂ would be approximately three times as large as that of the N₂ bath gas case. A 0.033-bar (1/3 of N₂) threshold was determined. Pressure broadening coefficients and the HITRAN2016 database were used (Tasinato et al., 2010, 2013, 2014; Gordon et al., 2017; Sumpf et al., 1996a, 1996b; Sumpf, 1997; Ball et al., 1996; Kühnemann et al., 1992; Cazzoli and Puzzarini, 2012). See the Supporting Information (Supporting text 2) for further details. Lower total pressure data (Fig. 6; open circles) seems to follow the column density line, whereas higher total pressure data (Fig. 6; filled squares) seems to be scattered.

Self-shielding appears to begin at ~10¹⁶ and become fully saturated at ~5 × 10¹⁸ cm^–2 of the SO₂ column density (Fig. 6). To compare SO₂ photolysis experiments easily, fractionation factors are offset (dashed lines in Fig. 6): ³³ε, ³⁴ε, and ³⁶ε are subtracted by 26‰, 49‰, and 47‰, respectively, such that ³³E is subtracted by 1‰ and ³⁶E is added by 46‰ (from Eqs. 6.1, 6.2). The magnitude of the offsets is within the range of uncertainty: systematic errors of spectroscopy (up to 4.5%, i.e., 45‰, caused by the drift of the light source), a difference in the UV source spectra, and/or fractionations in the chamber about δ³⁴S (typically 10‰ of ³⁴ε and 0‰ of ^33,36E from the reaction of SO₂ + OH; Harris et al., 2012).

With respect to ³⁴ε (Fig. 6A and B), at <10¹⁸ cm^–2 of SO₂ column density, the ³⁴ε/SO₂ column density in this study reproduced laboratory photolysis experiments within approximately 20‰ variation of ³⁴ε, which was only weakly dependent on the total pressure. Inversely, the predicted negative ³³E/column density, which was dependent on the total pressure, did not match the results of previous experiments (Fig. 6G and H).

To date, no photolysis experiments have reported fractionation factors under experimental conditions (<10¹⁸ cm^–2 of column density and ~1 cm^–1 of line width) such that the results may be compared with this study. Thus, the total pressure and column density dependence systematically tested by Endo et al. (2019) were extrapolated for comparison with this study. Although some differences exist between spectral resolution and pressure broadened spectra, Fig. 7 shows the slopes of fractionation factors/column density with respect to the SO₂ absorption line width at a constant SO₂ column density. The absorption line width was assumed to be 1 cm^–1, which is equal to the spectral resolution. Meanwhile, the line widths were estimated from pressure broadening, namely, the total atmospheric pressures and a pressure broadening coefficient of SO₂ (0.30 ± 0.03 cm^–1 atm^–1 for N₂ atmosphere, Lyons et al., 2018).

In the photolysis experiments conducted by Endo et al. (2019), the total pressure dependence of the ³⁴ε/SO₂ column density was relatively small, suggesting that the absorption line width does not strongly affect ³⁴ε (Fig. 7A). This is consistent with the fact that this study (~1 cm^–1) reproduced the ³⁴ε/column density of photolysis experiments, despite the unresolved absorption spectra (Fig. 6A and B). On the other hand, this study’s predicted negative ³³E/SO₂ column density did not match the results of previous experiments (Fig. 6G and H). However, the ³³E/column density slope was sensitive to the total pressure and clearly decreased at high total pressure (Fig. 7D). At >0.5 cm^–1 of the estimated SO₂ absorption line width, a negative ³³E/column density was predicted (Fig. 7D, lines), which was consistent with the results of this study. With regards to ³³ε and ³⁶ε, the relationship between the SO₂ column density (Fig. 6C–F) and absorption line width (Fig. 7B and C) displayed similarities to the ³⁴ε trends; however, they are not as easily reproducible as ³⁴ε. With regard to ³⁶E, this study reproduced results within an approximately 10‰ variation below 5 × 10¹⁷ cm². However, the ³⁶E/SO₂ column density slope did not reproduce the broadening model well (Fig. 7E). Consequently, ^32,33,34,36SO₂ cross-sections may also reproduce ³³E/column density when the spectral resolution is improved; however, this is a topic requiring further research. At >10¹⁸ cm^–2 of SO₂ column density, the ³⁴ε in this study is overestimated in comparison to that of photochemical experiments (Fig. 6A). The cause for this is ultimately unclear; however, if a gas with broad absorption spectra exists, the SO₂ photolysis rate will decrease at the rear side of the chamber, and the observed fractionations will be smaller than the predicted fractionations of the column density.

Taken together, the ^32,33,34,36SO₂ absorption spectra reported by this study are likely useful for predicting ³⁴ε during SO₂ photolysis at below 10¹⁸ cm^–2 of SO₂ column density. The spectral resolution dependence of the ³⁴ε/SO₂ column density is small, and ³⁴ε/SO₂ column density of Endo et al. (2015) is similar to that of this study (Fig. 5A). Endo et al. (2015) may be more convenient to utilize than this study, given the availability of 190–220-nm wavelength cross-sections, enhanced precision, and relative ease of calculation due to its low spectral resolution and coarse wavelength steps. Since ³³E is sensitive to the SO₂ absorption line width, this study could not predict ³³E at less than ~1 bar atmospheric pressure, where the absorption line width is less than ~0.3 cm^–1 (Fig. 7D). On the contrary, at high atmospheric pressures in which the absorption line width reaches ~1 cm^–1, such as in the Venus’ atmosphere, it may be possible to predict ³³E (Fig. 7D).

Applying a self-shielding model using the synthesized absorption spectra to laboratory experiments and natural samples

As described in Section “Calculations of self-shielding using synthesized absorption spectra”, in the case of complete discrete absorption spectra of SO₂ (Fig. 1A), the self-shielding during SO₂ photolysis arises from MIF-S with ³³E/³⁴ε and ³⁶E/³³E of +0.52 and –1.63, respectively. Interestingly, the slopes are closer to the Archean MIF-S (Δ³³S/δ³⁴S ~ +0.9, Δ³⁶S/Δ³³S ~ –0.9), than the MIF-S as predicted by the SO₂ cross-section of this study (Δ³³S/δ³⁴S ~ –0.1, positive Δ³⁶S/Δ³³S) and as observed in SO₂ photolysis experiments (Δ³³S/δ³⁴S ≤ ~ +0.1, Δ³⁶S/Δ³³S ≤ ~ –2.4). The observation that the slopes are different from the ideally discrete spectra case implies that the absorption spectra of ³²SO₂ overlap with those of ³³SO₂; that is, UV attenuation by ³²SO₂ absorption decreases not only the ³²SO₂ photolysis rate constants but also the ³³SO₂ photolysis rate constants (e.g., Ono, 2017; Endo et al., 2019; Lyons, 2020). Isotope fractionation by self-shielding under the ideal conditions in which absorption lines are narrow can be tested with further laboratory experiments such as SO₂ photolysis at low temperature and low pressure and photolysis using a species with a more discrete absorption spectra (e.g., sulfur monoxide (SO), Sarka and Nanbu, 2019).

This simple model predicted that self-shielding leads to large clumped isotope depletion in products and enrichment in reagents (Section “Calculations of self-shielding using synthesized absorption spectra”). Clumped isotopes may possibly be a fingerprint of self-shielding. However, signatures related to self-shielding have not been identified. In the case of SO₂ photolysis, S–O clumped isotopes are enriched in residual SO₂ and are depleted in the product SO. To preserve the clumped isotope signatures, S–O bonds must remain in the molecules. In laboratory experiments of SO₂ photolysis (e.g., Ono et al., 2013), the S–O bonds in the residual SO₂ would remain, although the bonds in the produced SO were likely destroyed via SO photolysis. Therefore, an enrichment signature may exist in residual SO₂. However, thus far, methods for analyzing S–O clumped isotopes in SO₂ have not been developed; it follows that, to test this, sufficient analysis methods must be developed.

Conclusions

We measured the ³²SO₂, ³³SO₂, ³⁴SO₂, and ³⁶SO₂ absorption spectra from 206 to 220 nm at 296 K, set to 1 cm^–1 wavelength resolution. The resolution was 25 times higher than has been previously reported. The accuracy was approximately 10%. Compared with previous reports of high-resolution spectra for SO₂ at natural abundance, the wavelength appeared to offset from ~0.016 nm, and the magnitudes of the cross-section at the absorption peak wavelength seemed small. However, this had insignificant effects on modeling isotopic self-shielding. Using the measured absorption spectra, we estimated the sulfur isotope fractionation by self-shielding in SO₂ photolysis.

This study roughly reproduced the ³⁴ε/(SO₂ column density) slope of previous SO₂ photolysis experiments; however, the spectral resolution was insufficient to resolve the Doppler widths. This finding likely reflects the insensitivity of ³⁴ε to the absorption line width, which is supported by the total pressure effect observed in previous SO₂ photolysis experiments. The second key characteristic of the prediction was the negative ³³E/(SO₂ column density) slope. This did not match previous photolysis experiments, but was consistent with prior observations that the slopes were smaller in SO₂ photolysis experiments at higher total pressures. Under a high pSO₂ atmosphere, strong self-shielding and strong pressure broadening should occur. This provides the basis for the novel suggestion that spectroscopic research may be linked to photolysis experiments with MIF-S.

Additionally, we modeled an ideal case in which the absorption lines are narrow below the Doppler width. The produced self-shielding originates from MIF-S closer to the Archean trend than described in previous photolysis experiments and spectroscopic measurements. This suggests that self-shielding remains a major candidate for MIF-S in the Archean atmosphere.

Acknowledgments

We would like to thank Shohei Hattori and Naohiro Yoshida for sample preparation and Matthew S. Johnson for technical advice. We also thank James Lyons and an anonymous reviewer for their constructive comments. The editor, Tsubasa Otake, provided advice on the organization of the paper. Cross-sections of ^32,33,34,36SO₂ reported by Lyons (2007) were provided by James Lyons. This research was funded by JSPS KAKENHI (grant numbers JP16J06990, JP17H06105, JP20H01975, JP20K14593, and 24740364). The authors would also like to thank Editage (www.editage.com) for English language editing.

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