Supporting Material.
1. Modeled Spectra
This section provides additional detail to the analysis presented in section 3.6,
where measured spectra have been modeled by shifting the experimentally obtained
32SO2
spectra according to the amount of red shifting slopes calculated by ab initio
methods. This method was employed and discussed by Lyons (2008) and the energy
surfaces used in these calculations were calculated by Tokue and Nanbu (2010). The
general formulation for these calculations is as follows:
3𝑥 ∗
𝜎 (λ) =
where
3𝑥
3𝑥
32
𝜎 (𝜆) is the measured
𝑐 is the slope and
3𝑥
𝜎(λ0) − ( 3𝑥𝑐 × 32𝜎(λ0) + 3𝑥𝑏) S1
32SO2
cross section at a given wavelength 𝜆0 value,
𝑏 is the origin for 33, 34 and 36 isotopologues (data presented in
Table 1). Very simply, the calculation is not performed on the cross sections themselves
but on the wavelength axis of the measured spectra. Next wavelength-dependent
isotopic fractionations were calculated for measured (3xε) and modeled (3xε*) spectra
according to equations 4, 5 and 6. Finally, in order to estimate the ability of this
approach to model the isotope effect, the absolute difference between modeled and
calculated isotopic fractionations was compared at each wavelength λ.
𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒𝐷𝑖𝑓𝑓. = | 3𝑥𝜀 (𝜆) − 3𝑥𝜀 (𝜆)| S2
The obtained differences were compared to propagated errors from measured
values (Figs. S4 to S8). In order to make these differences clear an average of the
absolute differences presented above, averaged for 3 spectral ranges, is presented in
Table 2.
Table S1. Isotopic purity of employed S0 in the production of SO2 as reported by
manufacturer (Isoflex USA).
Sample
32
S
33
S
34
S
36
S
32
S
99.989
0.195
0.08
0.07
Isotopic composition (%)
33
34
S
S
0.005
0.001
99.795
0.005
1.08
98.80
0.05
0.064
36
S
0.005
0.005
0.04
99.24
Table S2. Reactions yields for the synthesis of SO2 samples.
Isotopologue
Yield (%)
32
SO2
88.6
33
SO2
79.6
34
SO2
63.4
36
SO2
80.5
Table S3. Calculated fractionation values for the production of SO2* state calculated at
column densities 1014, 5 x 1014, 1015, 5 x 1015, 1016, 5 x 1016 and 1017 molecules of SO2.
(All units in ‰).
33
ε
1E15
1E16
5E16
1E17
5E17
1E18
31.7
31.9
32.6
33.4
40.2
48.8
Deuterium Lamp
34
33
ε 36ε
E
41.3
41.6
42.7
44.1
55.3
68.7
10.5
10.5
10.6
10.7
11.8
13.4
-60.5
-60.7
-61.3
-62.2
-69.1
-78.0
Xenon Lamp
33
ε 36ε
E
36
33
34
31.7
31.9
32.6
33.4
40.2
48.8
27.8
28.0
28.7
29.5
36.4
44.9
34.5
34.7
35.9
37.4
49.2
63.4
E
ε
10.1
10.1
10.2
10.2
11.0
12.3
-51.0
-51.1
-51.7
-52.4
-57.9
-64.8
Solar Spectra
36
33
ε
ε
E
36
33
34
27.8
28.0
28.7
29.5
36.4
44.9
24.2
24.4
25.1
26.0
33.4
42.6
28.1
28.4
29.7
31.3
44.4
59.9
E
ε
9.8
9.8
9.8
9.9
10.5
11.7
-39.4
-39.5
-39.9
-40.5
-44.6
-49.8
36
E
24.2
24.4
25.1
26.0
33.4
42.6
Table S4. Comparison of calculated slopes from measured spectra compared to slopes in
the literature. The slopes presented here are produced by calculations at column
densities 1014, 5 x 1014, 1015, 5 x 1015, 1016, 5 x 1016 and 1017 molecules of SO2. All
values are dimensionless.
34
ε vs. 33ε slope
Xenon lamp
D2 lamp
Solar Spectrum
Calculated
0.59
0.58
0.62
Experimental
0.65a
0.58b
34
ε vs. 33E slope
Xenon lamp
D2 lamp
Solar Spectrum
Calculated
0.12
0.22
0.07
a
b
Experimental
0.13
0.11
33
E vs. 36E slope
Xenon lamp
D2 lamp
Solar Spectrum
Calculated
-6.24
-5.93
-5.27
a
b
Experimental
-1.20
-3.51
a Faquhar et al., [2001]
b Masterson et al., [2011]
Fig. S1. Measured spectra of 33SO2 in the 250-280 nm (a) and 280-320 nm (b) energy
regions compared to the measurements of Danielache et al., [2008]. The embedded
figures show the absolute residuals among the compared spectra.
Fig. S2. Measured spectra of 34SO2 in the 250-280 nm (a) and 280-320 nm (b) energy
regions compared to the measurements of Danielache et al., [2008]. The embedded
figures show the absolute residuals among the compared spectra.
Fig. S3. Relative standard deviations for measured 32SO2 (a), 33SO2 (b), 34SO2 (c) and
36
SO2 (d) cross sections. The solid black lines in panels a to c represent the relative
standard deviations of the 25 cm-1 resolution measurements by Danielache et al.,
[2008].
Figs. S4. Comparison between measured and modeled fractionation spectra (panel a),
absolute differences between measured and modeled fractionation spectra (panel b) and
propagated error (panel c) for 33ε.
Figs. S5. Comparison between measured and modeled fractionation spectra (panel a),
absolute differences between measured and modeled fractionation spectra (panel b) and
propagated error (panel c) for 34ε.
Figs. S6. Comparison between measured and modeled fractionation spectra (panel a),
absolute differences between measured and modeled fractionation spectra (panel b) and
propagated error (panel c) for 36ε.
Figs. S7. Comparison between measured and modeled mass independent fractionation
spectra (panel a), absolute differences between measured and modeled mass
independent fractionation spectra (panel b) and propagated error (panel c) for 33E.
Figs. S8. Comparison between measured and modeled mass independent fractionation
spectra (panel a), absolute differences between measured and modeled mass
independent fractionation spectra (panel b) and propagated error (panel c) for 36E.
References
Danielache, S. O., C. Eskebjerg, M. S. Johnson, Y. Ueno, and N. Yoshida (2008),
High-precision spectroscopy of S-32, S-33, and S-34 sulfur dioxide: Ultraviolet
absorption cross sections and isotope effects, Journal of Geophysical ResearchAtmospheres, 113(D17).
Farquhar, J., J. Savarino, S. Airieau, and M. H. Thiemens (2001), Observation of
wavelength-sensitive mass-independent sulfur isotope effects during SO2 photolysis:
applications to the early atmosphere, Journal of Geophysical Research - Planets,
106(E12), 32829-32839.
Masterson, A. L., J. Farquhar, and B. A. Wing (2011), Sulfur mass-independent
fractionation patterns in the broadband UV photolysis of sulfur dioxide: Pressure and
third body effects, Earth and Planetary Science Letters, 306(3-4), 253-260.