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 A quantitative understanding the origin of sulfur isotope mass-independent fractionation (MIF) is essential to a full interpretation of the Archean sulfur geochemical record. Laboratory experiments have demonstrated that a MIF signature is present in elemental sulfur produced during SO2 photolysis, but the underlying mechanism remains unknown. Here, I report the results of atmospheric chemistry modeling of isotope-selective photodissociation of SO2 in the 1B2 − 1A1 bands from 190 to 220 nm. This band system is dominated by a bending mode progression that produces shifts in the absorption spectrum upon sulfur isotope substitution. Self-shielding in the rotationally-resolved lines of 32SO2 produces MIF signatures in SO and residual SO2. A self-shielding origin for sulfur MIF implies that the variations observed in Δ33S in Archean rocks reflect variation in atmospheric SO2 concentration, and demonstrates that MIF in terrestrial rocks can be derived from photochemistry independent of molecular symmetry.
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 The discovery of MIF of sulfur isotopes in Archean and Paleoproterozoic sedimentary sulfides and sulfates [Farquhar et al., 2000a] promises to yield both qualitative and quantitative insights into the composition of the paleoatmosphere. Photolysis experiments on SO2 and H2S, the two most abundant sulfur gases emitted during volcanism, have shown that SO2 photolysis at a variety of wavelengths produces MIF in elemental sulfur [Farquhar et al., 2001; Wing et al., 2004]. By modeling the atmospheric chemistry of sulfur compounds in the early Earth atmosphere, it has been shown that preservation of a MIF signature in reduced and oxidized sulfur (elemental sulfur and sulfate, respectively) can occur only if the partial pressure of O2 is <10−5 times the present atmospheric level (PAL) [Pavlov and Kasting, 2002] and if reducing gases are present [Zahnle et al., 2006]. Although this constraint on O2 is believed to provide the best evidence to date of an early anoxic atmosphere, it has been proposed that periods of low S-MIF in the Archean are proof of an oxidizing atmosphere [Ohmoto et al., 2006]. Determination of the mechanism responsible for S-MIF can elucidate the cause of variations in the S-MIF record.
 For relatively small isotopic fractionations, the magnitudes of sulfur MIF for the four stable isotopes of sulfur are given by the linear expressions
where and δxS = 103(xS/32S)sample/(xS/32S)ref − 1) for x = 33, 34 or 36 and for a Vienna Canyon Diablo Troilite (VCDT) reference. The values 0.515 and 1.90 are the high-temperature limit to the ratios of equilibrium partition functions for isotope exchange reactions.
 In laboratory experiments sulfur MIF has been observed during photolysis of SO2 [Farquhar et al., 2001; Wing et al., 2004] and CS2 [Zmolek et al., 1999], but only very slight MIF is seen during H2S photolysis [Farquhar et al., 2000b]. Elemental sulfur (Sel), or a CSx polymer in the case of CS2, is produced in all three photolysis experiments by a complex sequence of photolysis and association reactions. Inferring the S-MIF mechanism from laboratory photolysis experiments is difficult because only end products are analyzed. By analogy with oxygen MIF produced during O3 formation [Thiemens and Heidenreich, 1983], which is attributed to a symmetry-dependent non-statistical redistribution of internal energy in the vibrationally excited O3 [Gao and Marcus, 2001], it is likely that reactions such as S + S2S3 and S2 + S2S4 would also produce MIF signatures. However, the partial pressures of S2, S3 and S4 in a sulfur vapor are low at temperatures ∼30°C (10−16, 10−17 and 10−17 atmospheres, respectively; Sel ∼ 10−9 atmospheres [Rau et al., 1973]), suggesting that it is unlikely that S3 and S4 formed in the gas phase in the Archean atmosphere. I will discuss the atmospheric abundance of S2, S3 and S4 in future work; here my focus is on photolysis of SO2.
2. Absorption Spectra for SO2 Isotopologues
 Comparison of absorption spectra for SO2, H2S and CS2 reveals vibronic structure in SO2 and CS2 spectra but very little structure in the H2S spectrum (Figure 1), and suggests that the act of photodissociation of the parent gas could be the source of S-MIF for SO2 and CS2. In a low-O2 atmosphere with negligible O3 absorption SO2 photodissociation occurs by
Absorption by CO2 and H2O in the atmosphere limits the short wavelength photons to wavelengths greater than about 190 nm. Figure 2 shows a high-resolution spectrum for SO2 in the region 190–220 nm at 213 K [Freeman et al., 1984]. The pseudo-continuum is about a factor of 10 below the line peaks. The vibronic structure is primarily due to a (1, v2, 2) bending mode progression with an additional weaker (3, v2, 0) bending mode progression [Okazaki et al., 1997]. The spectrum from 190 to 220 nm includes bands with an upper state vibrational quantum number from v′2 = 4 to 22. Although the band assignments become progressively more ambiguous because of anharmonic coupling [Okazaki et al., 1997], I will designate bands by v2 in the (1, v2, 2) progression down to 190 nm. The rotational line structure (not shown) is resolved but very congested due to perturbation from other states. Line widths are narrow or even Doppler-limited (∼.04 cm−1 at 295 K) for wavelengths less than 220 nm [Koplow et al., 1998; Stark et al., 1999].
 I utilized medium-resolution theoretical absorption spectra for the four sulfur isotopologues of SO2 [Ran et al., 2007] to determine the shifts between the spectral vibronic features. The shifts between the 32SO2 and 36SO2 isotopologues from 190–220 nm are shown in Figure 2. The band head shifts increase with v2 in the bending mode progression. I used the theoretical spectra of Ran et al.  only to determine shifts in the vibronic features; the theoretical spectrum for 32SO2 [Ran et al., 2007] is a poor match to measured spectra for 32SO2 [e.g., Freeman et al., 1984] and would be unsuitable for photolysis calculations. At the highest resolution (<0.1 cm1) of spectral data [e.g., Freeman et al., 1984] significant variations in line positions and strengths between the various isotopologues will occur, but no attempt to account for this has been made in the present work. For this reason the results presented here must be regarded as semi-quantitative.
3. Photolysis of SO2 Isotopologues
 Radiative transfer calculations were performed in the context of modeling the photochemistry of sulfur in the early Earth atmosphere. Rather than present an in-depth discussion of the many photochemical possibilities [Zahnle et al., 2006], my emphasis here is on the dissociation rates of SO2 isotopologues. However, because absorption by CO2, H2O and other possible compounds will alter the dissociation rates of SO2, particularly at short wavelengths (<200 nm), the radiative transfer and photochemistry are necessarily linked. The photodissociation rate coefficient for the xSO2 isotopologue (x = 32, 33, 34 or 36) from 190 to 220 nm is given by
where ϕx is the photodissociation quantum yield (i.e., fraction of photoexcited SO2 that dissociates), σx is the absorption cross section for xSO2, and F0 is the photon flux at the top of the model (present-day solar spectrum is assumed). The opacity is τ(λ, z) = Ni(z)σi(λ) where Ni is the column density of absorber or scatterer i, and the sum is over all absorbers and scatterers, including all SO2 isotopologues and CO2. In equation (2)σx is as shown in Figure 2 for each isotopologue xSO2, and F0 and Ni are determined in the atmospheric model. For the (1, v2, 2) progression the fluorescence quantum yield is <0.2 in the dissociation region [Okazaki et al., 1997], and I have assumed ϕx is unity at all wavelengths and for all isotopologues.
 Atmospheric model results are shown in Figure 3 for the column densities of residual SO2 and product SO for pSO2 = 1 ppb and pCO2 = 0.02. Relatively large MD (Figure 3a) and MI (Figure 3b) effects are predicted. The MD effects arise from the shifted absorption continuum that underlie the isotopologue spectra (e.g., Figure 1), as well as from overlapping portions of the shifted vibronic features. MI effects are due to the shifted non-overlapping vibronic and rovibronic features, an effect referred to as ‘self-shielding’. Self-shielding in the most abundant isotopologue (32SO2) results in decreased photodissociation of that isotopologue relative to the rare isotopologues, and yields SO enriched in the rare S isotopes (Figure 3a). At a given wavelength the zone of 32SO2 self-shielding in the atmosphere is roughly from the height at which 32SO2 has optical depth unity to the height at which the 32SO2 absorption continuum has optical depth unity. The model also predicts Δ36S/Δ33S ∼ −3, which agrees fairly well with Antarctic ice core sulfates (ratio ∼ −3.3), but differs significantly from Archean rocks (ratio ∼ −0.9). When 32SO2 self-shielding is predominant, Δ33S and Δ36S have opposite signs. For the hypothetical case of ‘pure’ 32SO2 self-shielding in which only MIF occurs (i.e., δ33S = δ34S = δ36S), equation (1) yields Δ36S/Δ33S = −1.86.
 The Δ33S signature in photoproduct SO is a function of initial pSO2 and a weak function of pCO2 (Figure 4a). The Δ33S(SO) values in Figure 4a correspond to a 10% reduction in initial pSO2. Comparing these values to the maximum Δ33S measured in pyrites, which are ∼8–10‰ [Ono et al., 2003; Kamber and Whitehouse, 2007], and neglecting dilution by non-MIF sulfate, suggests pSO2 ∼ 10 ppb during generation of the largest S-MIF signatures, or about 100 times the present-day global SO2 concentration. The MIF signatures could also be derived from localized enhancements in SO2 concentration lasting for weeks following a volcanic eruption, although additional UV absorbers could create a more complex UV transmission environment than has been considered here. The model Δ36S/Δ33S ratios at a 10% reduction in SO2 (Figure 4b) vary with pSO2 and pCO2 for pSO2 ≤ 10 ppb, and vary strongly with pCO2 for pSO2 = 100 ppb. At the peak Δ33S(SO) at pSO2 = 10 ppb, Δ36S(SO)/Δ33S(SO) ranges from −2.7 for pCO2 = .002 to −1.2 for pCO2 = 0.2. The latter slope is close to the range measured in Archean sedimentary rocks.
 The model results in Figures 3 and 4 are for a low-O2 atmosphere in which SO does not rapidly reform SO2 by reaction with O2. For the ice core sulfate data it is unlikely that reaction R1 in the modern atmosphere is the source of the sulfur MIF. Instead, SO2 photoexcitation [Okabe, 1978], SO2 + hν(260–340 nm) → 1SO2, followed by disproportionation during self-reaction [Turco et al., 1982], 1SO2 + SO2 → SO3 + 1SO, is a more likely pathway for creating an additional sulfur reservoir (i.e., SO3) with a sulfur MI signature [Savarino et al., 2003]. The 280–320 nm region of the SO2 spectrum (Figure 1) has a rotationally-resolved band structure due to a progression of vibrational modes [Yamanouchi et al., 1995]. By the same arguments I have made above, isotope-selective photoexcitation of SO2 will occur, i.e., Δ33S(1SO2) > 0. The suggestion that SO3 photodissociation [Pavlov et al., 2005] is the source of the MI signature in ice core sulfates cannot be evaluated by the self-shielding mechanism proposed here due to a lack of sufficiently high resolution cross section data for SO3.
 Can photodissociation of SO2 isotopologues in a low-O2 atmosphere account for the measured MIF signatures in ancient pyrites and barites? The Δ36S/Δ33S results presented here are in qualitative but not quantitative agreement with the ancient rock record. Elemental S, derived from SO, is predicted to have Δ33S > 0 and Δ36S < 0, which is consistent with observations of most pyrites [Farquhar et al., 2000a], but the magnitude of the Δ36S/Δ33S ratio is a factor of 2 to 3 too high for most model cases run. This is a significant discrepancy, and may indicate that MI processes other than or in addition to SO2 photodissociation are at work. One such MI process almost certain to be important in a low-O2 atmosphere is SO photodissociation. Isotope-selective photolysis will occur in SO at wavelengths ∼190–230 nm, but rotationally-resolved spectra, either laboratory or synthetic, are needed to estimate the MI effect.
 An essential feature of self-shielding as the sulfur MI process is the dependence of the magnitude of the MI signature on the concentration of SO2 (Figure 4). It is highly likely that variability in the rates of volcanism in the Archean produced a range in atmospheric pSO2 spanning orders of magnitude. Recently, the observation of low Δ33S values (<1‰) in pyrites of various Archean ages has been attributed to either (1) very large fluctuations (factor >103) in atmospheric pO2 such that S-MIF cannot be preserved for the high pO2 conditions, or (2) a background oxic atmosphere that becomes sufficiently anoxic during an episode of massive volcanism that S-MIF can be preserved [Ohmoto et al., 2006]. However, a simpler explanation is that variations in pSO2 yield low S-MIF when pSO2 is low (e.g., ∼0.1 ppb), and high S-MIF when pSO2 is higher (e.g., ∼10 ppb). The variation seen in Δ33 S during the Archean and Paleoproterozoic is an expected consequence of the mechanism that produces the S-MIF signature, and need not reflect large variations in the oxidation state of the atmosphere.
 More broadly, a self-shielding origin for, or contribution to, S-MIF in terrestrial rocks demonstrates that MIF in rocks can be derived from purely photochemical effects independent of molecular symmetry.
 The author thanks E. Schauble at UCLA for use of and assistance with his cluster for preliminary SO2ab initio calculations, H. Guo for theoretical SO2 absorption spectra in advance of publication, J. Kasting for providing a copy of his photochemical code, and J. Farquhar and an anonymous reviewer for insightful reviews. The author gratefully acknowledges support was from the UCLA IGPP Center for Astrobiology and the NASA Astrobiology Institute, and from the NASA Exobiology and Evolutionary Biology Program (grant NNX07AK63G).