MNRAS 000,1–15 (2020) Preprint 28 June 2021 Compiled using MNRAS LATEX style file v3.0 Sulfur Chemistry in the Atmospheres of Warm and Hot Jupiters Richard Hobbs,1¢ Paul B. Rimmer2,3,4 Oliver Shorttle,1,2 and Nikku Madhusudhan1 1Institute of Astronomy, University of Cambridge, Cambridge, CB3 0HA, UK 2Cambridge Earth Sciences, University of Cambridge, Cambridge CB2 3EQ, UK 3MRC Laboratory of Molecular Biology, Cambridge, CB2 OQH, UK 4Cavendish Astrophysics, University of Cambridge, Cambridge, CB3 0HE, UK Accepted XXX. Received YYY; in original form ZZZ ABSTRACT We present and validate a new network of atmospheric thermo-chemical and photo-chemical sulfur reactions. We use a 1-D chemical kinetics model to investigate these reactions as part of a broader HCNO chemical network in a series of hot and warm Jupiters. We find that temperatures approaching 1400 K are favourable for the production of H2S and HS around 10−3 bar at mixing ratios of around 10−5, an atmospheric level where detection by transit spectroscopy may be possible. At 10−3 bar and at lower temperatures, down to 1000 K, mixing −5 ratios of S2 can be up to 10 , at the expense of H2S and HS, which are depleted down to a mixing ratio of 10−7. We also investigate how the inclusion of sulfur can manifest in an atmosphere indirectly, by its effect on the abundance of non-sulfur-bearing species. We find that in a model of the atmosphere of HD 209458 b, the inclusion of sulfur can lower the −3 abundance of NH3, CH4 and HCN by up to two orders of magnitude around 10 bar. In the atmosphere of the warm Jupiter 51 Eri b, we additionally find the inclusion of sulphur depletes the peak abundance of CO2 by a factor of five, qualitatively consistent with prior models. We note that many of the reactions used in the network have poorly determined rate constants, especially at higher temperatures. To obtain an accurate idea of the impact of sulfur chemistry in hot and warm Jupiter atmospheres, experimental measurements of these reaction rates must take place. Key words: planets and satellites: gaseous planets – planets and satellites: atmospheres – planets and satellites: composition – planets and satellites: individual (HD 209458b, 51 Eri b) 1 INTRODUCTION molecule is responsible for the absorption feature seen. The warm Jupiter 51 Eri b has also been an excellent example of the importance Sulfur chemistry is known to play an important role in the atmo- of sulfur chemistry. Two groups have produced models of 51 Eri spheric chemistry of planets in our solar system. In Earth’s past, b’s atmosphere, one study did not include sulfur chemistry (Moses it may have lead to the first Snowball Earth event (Macdonald & et al. 2016) and the other did include sulfur chemistry (Zahnle et al. Wordsworth 2017), and sulfur isotope ratios can be used as a tracer 2016). Significant differences were found between the two models, of Earth’s Great Oxidation Event (Hodgskiss et al. 2019). Sulfur in particular in the modelled abundance of CO , but it was unknown photochemistry is thought to influence the production of hazes and 2 whether this was due to sulfur chemistry or other differences in the arXiv:2101.08327v2 [astro-ph.EP] 25 Jun 2021 clouds in the upper atmospheres of solar system planets such as models. Thus, we believe that including sulfur chemistry in models Earth (Malin 1997), Venus (Zhang et al. 2012; Titov et al. 2018), of exoplanets, both terrestrial and gas-giant, would be valuable in Jupiter (Moses et al. 1995) and the moon Io (Irwin 1999). Similar obtaining more accurate pictures of their atmospheric composition. hazes, expected to appear in the atmospheres of exoplanets (He et al. 2020), would greatly affect their observed spectra. This would limit There are several works that include sulfur chemistry for exo- our ability to examine their atmosphere, and make assessments of planet atmospheres. We highlight a subset of these relevant for the their habitability challenging (Gao et al. 2017). atmospheric chemistry of gas giants. Hu et al.(2013) investigate the Sulfur has also recently been of interest in the field of Jupiter- photochemistry of H2S and SO2 in terrestrial planet and conclude like exoplanets. A tentative detection of the mercapto radical, HS, in that their direct detection is unlikely due to rapid photochemical the atmosphere of the hot Jupiter WASP-121 b has been made (Evans conversion to elemental sulfur and sulfuric acid. Visscher et al. et al. 2018). However, it is still uncertain whether HS or another (2006) examine thermo-chemical sulfur chemistry for the hot, deep atmospheres of sub-stellar objects and find H2S to be the dominant sulfur bearing gas. However, due to the high temperatures and pres- ¢ E-mail: [email protected] sures of the atmospheres they are studying, disequilibrium effects © 2020 The Authors 2 R. Hobbs et al. such as diffusion or photochemistry are not considered. Zahnle et al. 2 MODEL DETAILS (2009) investigate whether sulfur photochemistry could explain the To investigate sulfur chemistry in the atmospheres of hot Jupiters, hot stratospheres of hot Jupiters, and find that UV absorption of we chose to use Levi, a one-dimensional photo-kinetics code, orig- HS and S may provide an explanation. Zahnle et al.(2016) also 2 inally described in Hobbs et al.(2019). This code was previously investigate whether sulfur could form photochemical hazes in the developed to model carbon, oxygen and nitrogen chemistry in hot atmosphere of 51 Eri b, and under what conditions they could be Jupiter atmospheres. It was validated against several other photo- formed. They find that sulfur clouds should appear on many planets chemical models of hot Jupiters. where UV irradiation is weak. Wang et al.(2017) create synthetic In this work, Levi, is being used to model the atmospheres of spectra of their hot Jupiter atmospheric models to determine whether Jupiter-like planets. It does so via calculations of: H2S and PH3 could be detected by JWST, and find that H2S features should be observable for Teq ¡ 1500K. Gao et al.(2017) examine • The interactions between chemical species the effects of sulfur hazes on the reflected light from giant planets • The effects of vertical mixing due to eddy-diffusion molecular and find that the hazes would mask the presence of CH4 and H2O. diffusion and thermal diffusion We need models to be able to investigate the effects of sulfur • Photochemical dissociation due to an incoming UV flux. on exoplanet atmospheres. One way of modelling the atmosphere And uses the input parameters of: of planets is through the use of chemical kinetics models. These exist in the form of 1-D (e.g., Moses et al. 2011; Venot et al. 2012; • The pressure-temperature (P-T) profile of the atmosphere Rimmer & Helling 2016; Tsai et al. 2017), 2-D (e.g., Agúndez et al. • The eddy-diffusion ( II) profile of the atmosphere 2014) and 3-D (e.g. Drummond et al. 2018) models. The 1-D models • The profiles of the UV stellar spectrum take a network of possible chemical reactions within an atmosphere • The metallicity of the atmosphere and a temperature profile of the atmosphere to produce abundance • The gravity of the planet. profiles of chemical species. These models are frequently combined It uses the assumptions of: with prescriptions for diffusion and include a UV flux applied to the top of the model, to allow a full disequilibrium model to be created. • hydrostatic equilibrium Atmospheric models are obtained by computing these models until • The atmosphere being an ideal gas they reach a converged steady-state condition. • The atmosphere is small compared to the planet, such that Throughout the last few decades, chemical models of exoplane- gravity is constant throughout the atmospheric range being mod- tary atmospheres have grown more detailed and complex. What had elled. begun as equilibrium models containing limited molecular species By combining all of these factors, abundance profiles of the made of only a few elements in small chemical networks (e.g., atmosphere are computed. Lodders & Fegley 2002; Liang et al. 2003; Zahnle et al. 2009) As is typical for codes of this type, Levi finds steady-state have evolved into large photo-kinetic models containing hundreds solutions for species in the atmosphere by solving the coupled one- of molecular species made of many elements in chemical networks dimensional continuity equation: with thousands of reactions (Moses et al. 2011; Venot et al. 2012; Rimmer & Helling 2016). The focus of this work is to continue this m=8 mΦ8 evolution. We do so by introducing a new element, sulfur, to the = P − L − , (1) mC 8 8 mI model and to the network described in our previous paper (Hobbs −3 et al. 2019). In this way we can produce a tested and validated net- where =8 (m ) is the number density of species 8, with 8 = 1, ..., #, −3 −1 work of sulfur chemistry. In this work we apply the network to hot with # being the total number of species. P8 (m s ) and L8 and warm Jupiters. By doing so, we can investigate the importance (m−3 s−1) are the production and loss rates of the species 8. mC of sulfur in the atmospheres of exoplanets in both the context of (s) and mI (m) are the infinitesimal time step and altitude step −2 −1 sulfur itself and the way it impacts carbon and oxygen chemistry. respectively. Φ8 (m s ) is the upward vertical flux of the species, It was found in the work of Zahnle et al.(2016) that sulfur photo- given by, chemistry in the atmosphere of the warm Jupiter 51 Eri b was the m-8 1 1 U) ,8 3) source of a large number of radicals that went on to catalyse other Φ8 = −¹ II ¸ 퐷8º=C ¸ 퐷8=8 − − , (2) chemistry.