# Volatile-to-sulfur Ratios Can Recover a Gas Giant’s Accretion History

Ian J. M. Crossfield  Department of Physics and Astronomy, University of
Kansas, Lawrence, KS, USA

###### Abstract

The newfound ability to detect SO2 in exoplanet atmospheres presents an
opportunity to measure sulfur abundances and so directly test between
competing modes of planet formation. In contrast to carbon and oxygen, whose
dominant molecules are frequently observed, sulfur is much less volatile and
resides almost exclusively in solid form in protoplanetary disks. This
dichotomy leads different models of planet formation to predict different
compositions of gas giant planets. Whereas planetesimal-based models predict
roughly stellar C/S and O/S ratios, pebble accretion models more often predict
superstellar ratios. To explore the detectability of SO2 in transmission
spectra and its ability to diagnose planet formation, we present a grid of
atmospheric photochemical models and corresponding synthetic spectra for
WASP-39b (where SO2 has been detected). Our 3D grid contains $11^{3}$ models
(spanning 1–100$\times$ the solar abundance ratio of C, O, and S) for thermal
profiles corresponding to the morning and evening terminators, as well as mean
terminator transmission spectra. Our models show that for a WASP-39b-like O/H
and C/H enhancement of $\sim$10$\times$ Solar, SO2 can only be seen for C/S
and O/S $\lesssim$ 1.5$\times$ Solar, and that WASP-39b’s reported SO2
abundance of 1–10 ppm may be more consistent with planetesimal accretion than
with pebble accretion models (although some pebble models also manage to
predict similarly low ratios). More extreme C/S and O/S ratios may be
detectable in higher-metallicity atmospheres, suggesting that smaller and more
metal-rich gas and ice giants may be particularly interesting targets for
testing planet formation models. Future studies should explore the dependence
of SO2 on a wider array of planetary and stellar parameters, both for the
prototypical SO2 planet WASP-39b, as well as for other hot Jupiters and
smaller gas giants.

##  1 Introduction

###  1.1 Elemental Ratios and Planet Formation

Sulfur condenses into FeS at a condensation temperature of $T_{C}$$\sim$660 K,
far higher than that of other volatiles commonly observed in exoplanet
atmospheres (e.g. C, N, O, which all have $T_{C}$$\lesssim$180 K; Lodders,
2003; Wood et al., 2019). Exoplanetary C, N, and O abundances have therefore
been frequently proposed as probes of whether a given planet formed within or
beyond the “snow lines” of various C/N/O-bearing molecules (e.g., Öberg et
al., 2011; Ohno & Fortney, 2022b).

A longstanding example is a planet’s carbon-to-oxygen ratio (C/O; Seager et
al., 2005). These two elements, the most common in the Sun after H and He
(Lodders, 2003; Asplund et al., 2009), are expected to form many of the
dominant molecular species in gas giant atmospheres. CO, H2O, CO2, and CH4 can
all induce prominent spectral features and a planet’s C/O should strongly
affect the relative abundances of these different molecules (Seager et al.,
2005; Madhusudhan, 2012; Heng et al., 2016). C/O was also the first such ratio
proposed to hold clues to a planet’s formation and evolution (e.g., Öberg et
al., 2011), based on the idea that a gas giant’s composition should be
determined by the location(s) in its natal disk where the planet accretes most
of its mass.

However, growing evidence suggests that a planet’s formation history cannot be
interpreted simply by reading off its C/O ratio. For example, Mordasini et al.
(2016) linked a chain of planet formation, disk, and atmospheric models to
find that a planet’s C/O ratio may not uniquely correlate with its initial
formation location. Similarly, subsequent studies of planet assembly also
indicate that the C/O ratio provides, at best, limited constraints on how and
where a planet formed and accreted most of its mass (e.g., Turrini et al.,
2021; Schneider & Bitsch, 2021b; Pacetti et al., 2022; Bitsch et al., 2022).

Other axes beyond C/O may therefore be necessary if we hope to determine how
and where a given planet may have formed. Although numerous groups have
explored the dependence of atmospheric nitrogen abundance (as parameterized by
N/O) on a planet’s formation and accretion, (Turrini et al., 2021; Schneider &
Bitsch, 2021b; Ohno & Fortney, 2022a, b) measuring a planet’s N abundance is
only feasible at temperatures cooler than that of most hot Jupiters (since at
$T>$1000 K most N is tied up in N2).

###  1.2 SO2 in Gas Giant Atmospheres

Sulfur’s high $T_{C}$ implies that this species should be entirely in the
solid phase beyond $\sim$0.3 AU in protoplanetary disks (e.g., Oka et al.,
2011), where giant planet formation is thought to occur. At $T\gtrsim 1000$ K,
equilibrium chemistry predicts that most atmospheric sulfur should reside in
H2S (Zahnle et al., 2009a, 2016; Hobbs et al., 2021; Polman et al., 2023; Tsai
et al., 2023). However, the interaction of high-energy stellar photons with
the planet’s atmosphere results in the H2S abundance decreasing rapidly at
pressures $\lesssim 1$ mbar (Polman et al., 2023; Tsai et al., 2023).
Specifically, some H2S is converted to SO2 via photolysis of H2O through the
net reaction

$\mathrm{H}_{2}\mathrm{S}+2\
\mathrm{H}_{2}\mathrm{O}+\mathrm{photon}\rightarrow\mathrm{SO}_{2}+3\
\mathrm{H}_{2}.$ (1)

This SO2 resides at pressures of roughly 0.01–10 mbar, where it may be
observed via transmission spectroscopy if sufficiently abundant (Polman et
al., 2023; Tsai et al., 2023). Because SO2 contains three heavy atoms, it may
also be a useful probe of the average overall level of metal enhancement in a
planet’s atmosphere (Polman et al., 2023).

Transmission spectroscopy of hot Jupiter WASP-39b through the JWST Early
Release Science program (Program 1366; Batalha et al., 2017) revealed the
clear signatures of numerous absorbers, including SO2 (JTEC Team et al., 2023;
Rustamkulov et al., 2023; Alderson et al., 2023; Ahrer et al., 2023; Feinstein
et al., 2023). Those observations detected excess absorption from 3.95–4.15
$\mu m$ that was interpreted as roughly 1–10 ppm of SO2 at mbar pressures
(Tsai et al., 2023).

In this paper, we explore how the abundances of S, as well as C and O,
determine the atmospheric SO2 abundance and observable transmission spectra of
short-period, irradiated gas giants. Furthermore, we suggest that SO2 provides
a unique opportunity to measure volatile-to-sulfur ratios that could be a key
discriminant between competing planet formation theories.

We start by presenting a connection between planetary volatile-to-sulfur
ratios and planet formation models in Sec. 2. In Sec. 3 we then present a new
grid of photochemical models and associated synthetic transmission spectra
which we use to investigate our ability to constrain atmospheric abundances
via SO2. Finally, we conclude in Sec. 4.

##  2 Sulfur’s Connection to Planet Formation

As we describe below, the abundance ratios of volatiles to sulfur – e.g., C/S
and O/S – may provide a powerful opportunity to distinguish between competing
models of planet formation. Modern planet formation simulations frequently
track the atmospheric elemental abundances of giant planets with a range of
formation locations and migration histories, and so provide hypotheses that
can be tested via measurements of atmospheric composition. However, these
studies have not yet focused specifically on sulfur.

Sulfur is thought to be carried largely in the volatile phase in the ISM and
during the earliest stages of protoplanetary disks, but is quickly reprocessed
until $\gtrsim$90% of disk sulfur is carried in solid (refractory) species
(Kama et al., 2019; Le Gal et al., 2021; Rivière-Marichalar et al., 2022). Its
condensation temperature of $\sim$660 K (Lodders, 2003) is high enough that
sulfur remains in refractory form throughout most of the disk, in contrast to
volatile species such as C, N, and O whose dominant carriers trace “snow
lines” in the disk at distances of several AU.

Pebble accretion models of planet formation predict that gas giants may become
highly enriched in volatile elements as compared to refractories (Schneider &
Bitsch, 2021a, b, 2022). This occurs because giant planets induce pressure
extrema in the disk that inhibit the inward migration and accretion of solids.
Thus in these models less of the always-refractory S may be accreted when
compared to volatiles such as C or O (so long as the accreting planet is
exterior to the evaporation line of the dominant sulfur carrier, FeS). Fig. 1
shows the predicted C/S, O/S, and C/O ratios from the pebble accretion models
of Schneider & Bitsch (2021b); for ease of display, we present the mean and
standard deviation (in log space) of their predicted ratios over all
combinations of viscosity parameter $\alpha$ and refractory grain carbon
content. Although their models span a range of compositions, the general trend
is that when pebble accretion is the dominant mode for accreting solids, gas
giants may frequently exhibit roughly Solar C/O ratios but much higher C/S and
O/S ratios: from 3–20$\times$ Solar.

Models in which solids are accreted as planetesimals tell a different tale.
Fig. 1 shows that the planetesimal-based formation models of Pacetti et al.
(2022) predict nearly Solar C/S, O/S, and C/O ratios regardless of initial
planet location (again, for clarity we plot only the logarithmic mean and
standard deviation of their several models). These models (consistent with and
building on the initial models of Turrini et al., 2021) predict higher heavy-
element abundances (C/H, etc.) for planets that started to form closer in to
the star, similar to the absolute abundance trend predicted by pebble-
accretion models (Schneider & Bitsch, 2021b). Thus the absolute abundances of
heavy elements in a planet’s atmosphere may also be a useful proxy for planet
formation location.

Here we focus on the C/S and O/S ratios: Fig. 1 shows that these ratios could
allow a particularly powerful test of which solid accretion mode dominated a
planet’s formation history. Whereas both types of models predict that a
planet’s final atmospheric C/O ratio should be roughly stellar, pebble and
planetesimal accretion models can predict volatile-to-refractory (C/S and O/S)
ratios that are starkly different at all initial formation locations. In
reality planet formation may involve a combination of both planetesimal and
pebble accretion, in which case both these processes would shape the observed
composition of giant planets (Biazzo et al., 2022). Nonetheless Fig. 1 still
suggests that superstellar volatile-to-sulfur ratios may be a compelling
signpost of significant pebble accretion.

Refractory elements less volatile than sulfur have already been detected in
some ultra-hot planets (e.g., Lothringer et al., 2021), but these elements
will condense in most gas giant atmospheres. Since sulfur only condenses at
$\lesssim 660$ K (at 0.1 mbar; Lodders, 2003, though in planetary atmospheres
S vapor can exist at lower temperatures) its abundance – and its relation to
that of volatile elements – may thus be an especially useful tool for
constraining the dominant mechanism of planet formation.

Figure 1: Predicted atmospheric ratios of C/S, O/S, and C/O based on initial
planet location, from the planet formation models of Schneider & Bitsch
(2021b, SB21; upper, thicker curves) and Pacetti et al. (2022, P22; lower,
thinner curves). Although individual models span a range of final compositions
(only the log-mean and standard deviation of each model set are plotted here),
overall the differences suggest that volatile-to-sulfur ratios could provide a
strong test as to whether a planet formed mainly via pebble or planetesimal
accretion. The error bars at bottom-right and the shaded region show the
abundance ratios inferred for WASP-39b from Fig. 4.

##  3 Modeling

###  3.1 Modeling Details

Having shown that volatile-to-sulfur abundances may test planet formation
theories, we now explore how atmospheric S — as measured by SO2 abundances —
can reveal different atmospheric compositions. Many factors have a strong
impact on a planet’s SO2 abundance. E.g., SO2 production is predicted to drop
off steeply at $\lesssim$1000 K (Polman et al., 2023) and for FUV irradiation
considerably higher than that experienced by WASP-39b (Tsai et al., 2023); and
aerosol formation could also deplete elements that would otherwise end up in
photochemical SO2. Nonetheless, in this study we restrict our exploration to
chemical composition and leave these other axes to future studies.

We examine a three-dimensional parameter space of atmospheric elemental
abundances: $11^{3}$ combinations of a range of elemental enhancements of
carbon, oxygen, and sulfur (from solar to 100$\times$ solar), using the
VULCAN111https://github.com/exoclime/VULCAN photochemical kinetics code (Tsai
et al., 2017, 2021). For each combination of C, O, and S enhancement we
calculate atmospheric abundance profiles using VULCAN’s SNCHO chemical
network, which includes 575 chemical and photochemical reactions. We use
WASP-39b as our simulated target; based on initial analyses of its spectrum,
we hold all abundances other than C, O, and S to 10$\times$ solar (JTEC Team
et al., 2023; Rustamkulov et al., 2023; Alderson et al., 2023; Ahrer et al.,
2023; Feinstein et al., 2023; Tsai et al., 2023). The star WASP-39’s XUV flux
remains largely unknown, so we adopt the same stellar spectrum used by Tsai et
al. (2023). We compute our grid using two different, pre-determined
temperature profiles, one each for the GCM-derived morning and evening
terminator profiles presented by Tsai et al. (2023). These thermal profiles
are broadly consistent with the single profile recently retrieved by
Constantinou et al. (2023). Their retrieved, constant-with-altitude SO2
abundances are broadly consistent with (if somewhat lower than) the detailed
abundance profiles of Tsai et al. (2023) and of this work; further work is
needed to compare abundances retrieved in this way with the predictions of
photochemical codes. Finally, we also use the same $K_{zz}$ profile described
by Tsai et al. (2023), scaling with pressure as $P^{-1/2}$ (following Lindzen,
1981; Moses et al., 2022). The system parameters and abundance values we used
in our analysis are listed in Table 1. All the VULCAN outputs are available as
machine-readable supplements to this
paper222https://doi.org/10.5281/zenodo.7760360.

Table 1:  Model Parameters:  Name | Units | Description | Value | Source
---|---|---|---|---
System parameters:
$R_{*}$ | $R_{\odot}$ | Stellar radius | 0.932 | Carter & May, et al., in prep.
$R_{P}$ | $R_{J}$ | Planetary radius | 1.279 | Carter & May, et al., in prep.
$M_{P}$ | $M_{J}$ | Planetary mass | 0.281 | Carter & May, et al., in prep.
$g_{P}$ | m s-2 | Planetary surface gravity | 4.26 | Carter & May, et al., in prep.
$a$ | AU | Semimajor axis | 0.04828 | Carter & May, et al., in prep.
Modeling parameters:
He/H | – | Solar volume mixing ratio | $8.38\times 10^{-2}$ | Lodders (2020)
C/H | – | Solar volume mixing ratio | $2.95\times 10^{-4}$ | Lodders (2020)
O/H | – | Solar volume mixing ratio | $5.37\times 10^{-4}$ | Lodders (2020)
S/H | – | Solar volume mixing ratio | $1.41\times 10^{-5}$ | Lodders (2020)
$P$ | bar | Pressure range | 10–10-9
$P_{0}$ | bar | Reference pressure | 0.01
$z$ | deg | Zenith angle | 83
C | – | Abundance relative to Solar | 1, 1.8, 3, 5.6, 7.5, 10, 13, 18, 30, 56, 100
O | – | Abundance relative to Solar | 1, 1.8, 3, 5.6, 7.5, 10, 13, 18, 30, 56, 100
S | – | Abundance relative to Solar | 1, 1.8, 3, 5.6, 7.5, 10, 13, 18, 30, 56, 100

We then use the petitRadTrans333https://petitradtrans.readthedocs.io/
radiative transfer code (Mollière et al., 2019) to calculate synthetic
transmission spectra corresponding to each VULCAN run. We convert VULCAN’s
volume mixing ratios (VMRs) to petitRadTrans’ mass mixing ratios. We use
petitRadTrans’ medium-resolution, correlated-k opacity sources, giving our
synthetic spectra a resolving power of $\sim$1,000 from 1–25 $\mu m$. The
molecules and opacity sources we include are H2O, CO, CO2, SO2, CH4, HCN, H2S,
CH3, C2H2, C2H4, CN, CH, OH, and SH (Rothman et al., 2010; Polyansky et al.,
2018; Yurchenko et al., 2020; Underwood et al., 2016; Yurchenko & Tennyson,
2014; Harris et al., 2006; Barber et al., 2014; Chubb et al., 2018; Azzam et
al., 2016; Adam et al., 2019; Chubb et al., 2020; Brooke et al., 2014;
Bernath, 2020; Syme & McKemmish, 2020; Masseron et al., 2014; Brooke et al.,
2016; Yousefi et al., 2018; Gorman et al., 2019). We have three sets of
synthetic spectra: one each for the morning and evening thermal profiles, plus
a set of spectra that are the mean of the morning and evening spectra
(corresponding to the transmission spectrum that would be observed during
transit). All the petitRadTrans synthetic spectra are also available as
machine-readable supplements to this
paper444https://doi.org/10.5281/zenodo.7760360.

We note that the abundances of 15 elements (including C and O, but not S) were
measured for WASP-39 (Polanski et al., 2022), revealing a composition for
which every element is consistent with the solar values at $<1\sigma$.
Similarly, the C/O ratio of $0.46\pm 0.09$ is consistent with the solar value
of 0.55 (assuming the abundances of Lodders, 2020). Therefore, although
generally stellar (not solar) abundances are the appropriate referent for
atmospheric modeling, we elect to use abundance levels scaled from Solar
values given WASP-39’s chemical similarity to the Sun (Polanski et al., 2022).

Finally, we also note that for a nominal WASP-39b model with an atmosphere
enhanced to 10$\times$ Solar abundances, the transmission contribution
function in regions of maximal SO2 absorption span a pressure range of roughly
0.01–30 mbar. Although a weighted average of the SO2 concentration (e.g., via
weighting by atmospheric mass density) may give a somewhat more representative
view of the peak of the photochemical SO2 abundance, for simplicity (and to
facilitate direct comparison with the work of Tsai et al., 2023) here we
report the average of our modeled SO2 concentration from 0.01–10 mbar.

Figure 2: In the main panel, the dashed line shows the SO2 VMR, averaged from
0.01–10 mbar, as all elemental abundances are increased in lockstep; the gray
region shows the approximate SO2 abundance reported for WASP-39b. The inset
shows the full vertical SO2 profiles.

Figure 3: Abundance of SO2 (averaged from 0.01–10 mbar) as combinations of two
elemental abundances are varied: C vs. O (top), C vs. S (middle), and O vs. S
(bottom). The points indicate the locations of the model grid points, which we
linearly interpolate between. In each panel, all other elements are held fixed
at 10$\times$ Solar abundance.

Figure 4: Abundance of SO2 (averaged from 0.01–10 mbar) as the atmospheric
ratios of C/O (top), C/S (middle), and O/S (bottom) are varied. The gray
regions show the approximate SO2 abundance reported for WASP-39b, which
correspond here to C/S and O/S $\lesssim$1.5.  Figure 5: Synthetic spectra
showing the effect of varying the S/H ratio from 1–100$\times$ Solar while
keeping O/H and C/H at 10$\times$ Solar, as inferred for WASP-39b (equivalent
to varying C/S and O/S from 10–0.1$\times$ Solar). At 10$\times$ Solar
metallicity SO2 is detectable up to volatile-to-sulfur ratios of
$\lesssim$3$\times$ Solar. The shaded rectangles show where absorption is
dominated by SO2 (green) and by H2S (grey).

###  3.2 Differences From Previous Studies

Our modeling effort expands on previous exploration of SO2 in several ways.
The first such study presented a comprehensive examination of SO2 abundance in
hot Jupiter atmospheres (Polman et al., 2023). Their study also used the
VULCAN code to cover metallicities of 1–20$\times$ Solar, three values of
$K_{zz}$ (constant with altitude, but spanning three orders of magnitude), C/O
ratios from 0.25–0.9, several different stellar spectra, and three planetary
temperatures (spanning 400 K). More recently, Tsai et al. (2023) demonstrated
that SO2 causes the 4.2 µm absorption feature seen in JWST spectroscopy of
WASP-39b (Rustamkulov et al., 2023; Ahrer et al., 2023; Alderson et al.,
2023). That investigation used four photochemistry codes (including VULCAN) to
span three metallicities (from 5 to 20$\times$ Solar), three $K_{zz}$ profiles
(spanning two orders of magnitude), three C/O ratios (from 0.25 to 0.75),
three stellar spectra (spanning two orders of magnitude in irradiation), and a
range of temperatures (from 600 to 2000 K).

Our analysis builds upon both these works by (i) examining a more densely
sampled and fully two-dimensional grid of C and O abundances, (ii) adding a
third dimension by exploring a wide range of S abundances, and (iii) extending
the analysis up to significantly higher atmospheric metallicities.

###  3.3 Discussion and Interpretation

Fig. 2 shows how the SO2 abundance increases as all three elements (C, O, and
S) are increased in lockstep. Whereas the abundance of the triatomic CO2
(produced via equilibrium chemical processes) increases quadratically with
metallicity (Zahnle et al., 2009b), the more complicated formation pathways of
SO2 result in a more complicated metallicity dependence: much steeper than CO2
at low metallicity, and shallower at high metallicity. This suggests that if
high-metallicity ($>100\times$ Solar) ice giants also form photochemical SO2,
its VMR is unlikely to be $\gtrsim$200 ppm (as found by Tsai et al., 2021).

Fig. 3 shows three slices through our 3D abundance grid, depicting the SO2
volume mixing ratio (VMR, averaged from 0.01–10 mbar) versus C, O, and S
abundances. Fig. 4 shows 1D slices as plotted against the abundance ratios
C/O, C/S, and O/S.

Fig. 4 reveals that the SO2 abundances decreases as the atmospheric C/O ratio
increases (while the S abundance is held constant). Consistent with the
results of Polman et al. (2023), the dependence on C/O is similar regardless
of whether we increase C or decrease O (though with a slightly steeper
dependence when O is varied). In either case, when C/O increases beyond the
Solar value the SO2 abundance rapidly drops below detectable levels. The
detection of SO2 is therefore a strong sign of a C/O ratio $\lesssim$ the
Solar value.

Figure 6: Synthetic spectra showing the effect of varying C/H and O/H from
10–100$\times$ Solar while keeping the C/S and O/S ratios at 10$\times$ Solar,
as might be expected from pebble accretion (equivalent to varying S/H from
1–10$\times$ Solar). At 10$\times$ Solar C/S and O/S, SO2 is detectable down
to a volatile enhancement level of $\sim$18$\times$ Solar. The shaded
rectangles show where absorption is dominated by SO2 (green) and by H2S
(grey). Note that for volatile enrichment $\gtrsim$100$\times$ Solar the
amplitude of spectral features begins to decrease as the mean molecular weight
begins to increase.

More excitingly, Fig. 4 shows how measurements of the SO2 abundance can
distinguish between a variety of volatile-to-sulfur ratios. JWST transit
spectroscopy of WASP-39b reveal it to have an atmospheric metallicity
$\sim$10$\times$ Solar, a C/O ratio $\lesssim$ the Solar value, and a SO2 VMR
of 1–10 ppm (JTEC Team et al., 2023; Rustamkulov et al., 2023; Alderson et
al., 2023; Ahrer et al., 2023; Feinstein et al., 2023; Tsai et al., 2023).
Assuming an overall metallicity of 10$\times$ Solar, the bottom two panels of
Fig. 4 show that the SO2 measurement constrains both C/S and O/S to
$\lesssim$1.5$\times$ Solar. Reference to Fig. 1 demonstrates that such values
are rather more consistent with planetesimal accretion models (Turrini et al.,
2021; Pacetti et al., 2022) than with pebble accretion (Schneider & Bitsch,
2021b). The only pebble formation models of Schneider & Bitsch (2021b) that
can approximately reproduce these ratios assume an initial formation location
of 3 AU and $\alpha\leq 5\times 10^{-4}$.

We also show a few representative examples of our synthetic transmission
spectra. In Fig. 5 we see the effect on WASP-39b’s transmission spectra of
varying the S/H ratio from 1–100$\times$ Solar, while keeping
O/H=C/H=10$\times$ Solar (as inferred for WASP-39b); this is equivalent to
varying C/S and O/S from 10$\times$ down to 0.1$\times$ Solar. The figure
shows that at WASP-39b-like volatile enrichment levels, SO2 has a significant
impact on a planet’s transmission spectrum for S/H$\gtrsim 3\times$ Solar (C/S
or O/S $\lesssim$3$\times$ Solar).

Lest one conclude from Figs. 4 and 5 that high volatile-to-sulfur ratios
$\gtrsim$3$\times$ Solar are impossible to detect, Fig. 6 shows that SO2 is
easily discernible at C/S=O/S=10$\times$ Solar — so long as the atmospheric
volatile enrichment (i.e., O/H and C/H) is $\gtrsim$18$\times$ Solar. Since
smaller, lower-mass planets are thought to form with more metal-rich
atmospheres (e.g., Fortney et al., 2013), such planets may therefore be the
best targets to look for SO2 to reveal the extreme volatile-to-sulfur ratios
that would be a signpost of formation via pebble accretion.

##  4 Conclusions

###  4.1 Summary

In conclusion, we have shown that a planet’s formation and migration history
may imprint unique elemental abundance signatures on the planet’s atmosphere:
specifically, on the C/S and O/S ratios. In particular, Fig. 1 and Sec. 2
demonstrate how formation models in which solids are predominately accreted as
pebbles often predict much higher volatile-to-sulfur ratios (C/S and O/S) than
models in which solids are accreted as planetesimals. Although a planet’s N/S
ratio has also been proposed as a diagnostic of formation (Turrini et al.,
2021; Pacetti et al., 2022), detecting both these species in a gas giant may
be challenging: S is mostly only visible as SO2 at $T\gtrsim 1000$ K (Polman
et al., 2023) while N is mostly detectable as NH3 at $T\lesssim 1000$ K (Ohno
& Fortney, 2022b). Thus the C/S and O/S ratios may be more generally useful
(and measurable) than N/S.

We then present a grid of photochemical models and synthetic spectra for
WASP-39b in which C, O, and S abundances are varied to determine the impact on
the observable SO2 signature (Sec. 3 and Fig. 3). Consistent with previous
studies, we find that SO2 should be most prevalent at high metallicity; we
also find that it should be more abundance at higher elemental O and S
abundances but lower C abundances. By examining how the SO2 abundance varies
with C/S and O/S in our models, Fig. 4 shows that WASP-39b’s atmospheric SO2
abundance may constrain C/S and O/S to levels more consistent with
planetesimal accretion than pebble accretion – although some pebble accretion
models also predict lower volatile-to-sulfur ratios that seem more consistent
with WASP-39b.

Additional work is certainly needed to confirm this conclusion. The main
planet formation models discussed in Sec. 2 all result in planets more massive
than WASP-39b, which suggests the need for caution in linking these models to
WASP-39b’s composition. Also, relatively few planet formation studies report
the final planetary C, O, and S abundances — additional, independent models
tracking these abundances and featuring either planetesimal or pebble
accretion would be extremely useful to understand the robustness of the
dichotomy in volatile-to-sulfur ratios shown in Fig. 1.

###  4.2 Future Work

There is also considerable scope for further exploration of the planetary and
stellar parameters that impact the observed SO2 abundance. These include
bolometric irradiation, received XUV flux, aerosols, additional T-P profiles,
better high-temperature opacity data in the UV, and the observability of SO2
or other S-bearing species via thermal emission — not to mention the impact of
additional species such as nitrogen.

Regarding high-energy stellar flux, Hobbs et al. (2021) reported that
increasing UV flux by up to two orders of magnitude merely results in the SO2
abundance profile being pushed to somewhat deeper pressures, but with the
overall abundance relatively unchanged. On the other hand, Tsai et al. (2023)
instead find that increasing the NUV flux minimally changes the SO2 profile,
while increasing the FUV flux can decrease the SO2 abundance by $\sim 10^{4}$.
If the influence of UV flux could be pinned down, it would provide strong
motivation for measuring the intrinsic spectra of stars with planets expected
to exhibit SO2 (or other) photochemistry.

Also regarding WASP-39’s intrinsic stellar spectrum, we note that [S/H] has
still not been measured for this star. Although the star’s generally Solar-
like elemental abundances (Polanski et al., 2022) suggest that its sulfur
abundance may also be nearly Solar, [S/H] should be measured for WASP-39 as it
has been for many other planet-hosting stars (e.g., Costa Silva et al., 2020)
to confirm the expected, Solar-like sulfur abundance.

In this work we have not explored planetary nitrogen abundance, but it may
also be an important axis. For example, the nitrogen-to-oxygen ratio in gas
and solids should vary by several orders of magnitude from 1–100 AU (Ohno &
Fortney, 2022a). And if planet formation is dominated by planetesimal
accretion, then the sulfur-to-nitrogen ratio may be a useful probe of whether
a gas giant accreted most of its mass via solids or gas (Turrini et al.,
2021).

Further exploration is also warranted into the effect of different $K_{zz}$
values on the observable SO2 abundance. Tsai et al. (2023) found that varying
their $K_{zz}$ profile (nominally spanning $5\times 10^{7}$ to
$10^{11}\mathrm{~{}cm}^{2}\mathrm{\ s}^{-1}$) by $\pm$ an order of magnitude
had only a minor impact, consistent with the results of Hobbs et al. (2021)
from isothermal models with $K_{zz}$ spanning
$10^{6}$–$10^{12}\mathrm{~{}cm}^{2}\mathrm{\ s}^{-1}$. In contrast, other
studies report that increasing a constant-with-altitude $K_{zz}$ to
$10^{11}\mathrm{~{}cm}^{2}\mathrm{\ s}^{-1}$ sharply decreases the amount of
observable SO2 (Tsai et al., 2021; Polman et al., 2023). Although $K_{zz}$ is
a challenging quantity to empirically constrain, it would at least be useful
to understand how it quantitatively impacts the measurement of SO2 in
planetary atmospheres.

Future studies might also test the impact of self-consistently modeling the
thermal and chemical profiles in the atmospheres, thereby accounting for
thermal back-reaction of photochemical species such as SO2 on the planet’s
vertical temperature structure. Similarly, the interplay of global circulation
and atmospheric chemistry may reveal that predictions made from 1D models (as
in this work) – or even from post-processed chemistry-free global circulation
models – may lead to inaccurate interpretations of exoplanet measurements (Lee
et al., 2023).

JWST/NIRSpec may be the ideal instrument to best constrain C, O, and S and so
begin to test the connection between atmospheric SO2 and planet formation
posited in this paper. Even the G395 modes (let alone the Prism!) cover
multiple strong bands of CO2, CO, CH4, and H2O, as well as the SO2 described
by Tsai et al. (2023). The signal of SO2 may be even stronger in the MIRI/LRS
bandpass, but the overall S/N may be lower there – in addition, shorter
wavelength coverage may still be needed to provide a complete elemental assay;
the feasibility of MIRI for SO2 measurements is currently under study by
multiple groups.

Finally, although SO2 is not always the dominate sulfur carrier in
H2-dominated exoplanet atmospheres, the H2S that carries most of the sulfur is
much more difficult to detect and quantify (Polman et al., 2023). Furthermore,
since the vertical abundance profile of photochemical SO2 varies significantly
with altitude (Fig. 2), retrievals in which the abundance is assumed to be
constant with altitude may somewhat underestimate the true SO2 abundance
(which might already affect the retrieval results of Constantinou et al.,
2023). For all these reasons, physically-motivated photochemical models of
SO2in H2-dominated exoplanets should therefore remain a key tool to unraveling
the atmospheric properties of such planets.

Dedicated to E3. We heartily thank S.-M. Tsai for help with VULCAN, for
general discussions of photochemistry, and for useful comments on an early
draft of this paper. We thank B. Bitsch for several useful discussions that
improved the quality of this paper, and we thank D. Turrini for clarifying
several points regarding planet formation. Finally, we also thank the
anonymous referee for their useful comments that helped to materially improve
the quality of this work.

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