Draft version May 6, 2020 Typeset using LATEX twocolumn style in AASTeX62 Consistently Simulating a Wide Range of Atmospheric Scenarios for K2-18b with a Flexible Radiative Transfer Module 1, 2, 1, 2, 2 1 3 2, 4 5 Markus Scheucher, ∗ F. Wunderlich, ∗ J.L. Grenfell, M. Godolt, F. Schreier, D. Kappel, R. Haus, K. Herbst,6 and H. Rauer1, 2, 7 1Zentrum f¨urAstronomie und Astrophysik, Technische Universit¨atBerlin, 10623 Berlin, Germany 2Institut f¨urPlanetenforschung, Deutsches Zentrum f¨urLuft- und Raumfahrt, 12489 Berlin, Germany 3Institut f¨urMethodik der Fernerkundung, Deutsches Zentrum f¨ur Luft- und Raumfahrt, 82234 Oberpfaffenhofen, Germany 4Institut f¨urPhysik und Astronomie, Universit¨atPotsdam, 14476 Potsdam, Germany 5Institut f¨urGeowissenschaften, Universit¨atPotsdam, 14476 Potsdam, Germany 6Institut f¨urExperimentelle und Angewandte Physik, Christian-Albrechts-Universit¨atzu Kiel, 24118 Kiel, Germany 7Institut f¨urGeologische Wissenschaften, Freie Universit¨atBerlin, 12249 Berlin, Germany (Accepted May 4, 2020) Submitted to ApJ ABSTRACT The atmospheres of small, potentially rocky exoplanets are expected to cover a diverse range in composition and mass. Studying such objects therefore requires flexible and wide-ranging modeling capabilities. We present in this work the essential development steps that lead to our flexible radiative transfer module, REDFOX, and validate REDFOX for the Solar system planets Earth, Venus and Mars, as well as for steam atmospheres. REDFOX is a k-distribution model using the correlated-k approach with random overlap method for the calculation of opacities used in the δ-two-stream approximation for radiative transfer. Opacity contributions from Rayleigh scattering, UV / visible cross sections and continua can be added selectively. With the improved capabilities of our new model, we calculate various atmospheric scenarios for K2-18b, a super-Earth / sub-Neptune with ∼8 M orbiting in the ⊕ temperate zone around an M-star, with recently observed H2O spectral features in the infrared. We model Earth-like, Venus-like, as well as H2-He primary atmospheres of different Solar metallicity and show resulting climates and spectral characteristics, compared to observed data. Our results suggest that K2-18b has an H2-He atmosphere with limited amounts of H2O and CH4. Results do not support the possibility of K2-18b having a water reservoir directly exposed to the atmosphere, which would reduce atmospheric scale heights, hence too the amplitudes of spectral features inconsistent with the observations. We also performed tests for H2-He atmospheres up to 50 times Solar metallicity, all compatible with the observations. Keywords: radiative transfer | methods: numerical | planets and satellites: terrestrial planets | planets and satellites: atmospheres | infrared: planetary systems arXiv:2005.02114v1 [astro-ph.EP] 5 May 2020 1. INTRODUCTION LHS1140b and c (Ment et al. 2019), K2-18b (Montet Exciting recent discoveries in exoplanetary science in- et al. 2015), and GJ1214b (Charbonneau et al. 2009). clude the TRAPPIST-1 system (Gillon et al. 2017), Exoplanet science is transitioning from detection into Proxima Centauri b (Anglada-Escud´e et al. 2016), first atmospheric characterizations from spectral obser- and potential super-Earths / warm sub-Neptunes like vations, giving us insights into their composition and possible formation and evolution. Numerous spectral observations of Jupiter-sized to warm Neptune-sized Corresponding author: Markus Scheucher planets have been reported and discussed in recent [email protected], [email protected] years (see, e.g., Sing et al. 2016; Crossfield & Kreid- ∗ Equal Contribution Authors berg 2017), but the first detection of water features in 2 Scheucher et al. INPUTS X Initial T / p Profile U r k - S - Initial Composition a r V D l s V S e a u n Stellar Spectrum l i / c I c s c o S u s i t V s t a Ion Pair Production Rate e t i c i n P r l o I t c i / s e t o b S l o l n i e a I y a t u R l o s n r M c e o c t i s - i n i t M a k o i R - s g o r e y F n B l u s h e R o n P T c rm t e io h n T r C s ea o BLAC in nt KW L in X OL ild of ua FO F u m B ste s D Sy ion E uat R Eq SW Radia tive δ Trans -Two- fer Stream T CLIMATE CHEMISTRY R EQUILIBRIUM L O A LW P C I S Eddy dT(z) - g dn ∂ ∂n T diative Transfer . dF(z) CHECKS N Ra R = . A Diffusion E = + R ( K ) P- nL V tream / T δ-Two-S . dt cp(T,z) dp(z) dt ∂z ∂z y Approx Diffusivit s tie ci C S H / H a ON IE ap AD VEC AR S Escape JU TIVE ND S t C ST BOU RIES O 2 / O ME r BOUNDA L C H a NT i e S P o H RO o 2 O v u D n s y U r CT d t r ION / i y e e D f W l e r O H a i s s c d C f e n i i c e D t e d e u s 2 t l o o p S e C i V t / a r a m t R o a L O s g h / t b o t P o u r F s i i m a D o c n e g a l 4 m s i l i c H t e u n s s o O r h i o i m a d s i 2 c o W x y r z s r e t f r n n p e A i n i H R v e n c i i a a s t i c t i g L n a w r R a g y h l C a s c e y S R s 1D-TERRA Figure 1. Schematic overview of our 1D coupled climate disequilibrium-chemistry model 1D-TERRA including the new radiative transfer module, REDFOX, and the updated chemistry scheme, BLACKWOLF. the atmosphere of the temperate (Teq ∼ 272 K) super- A main motivation for our model development is as Earth / sub-Neptune K2-18b (Benneke et al. 2019a; follows. The radiative transfer schemes, based on the k- Tsiaras et al. 2019) orbiting an early-type M-star is distribution method, implemented in previous versions especially exciting, as it offers an unprecedented possi- of our model as well as other similar models developed bility to gain insights into the atmosphere and climate for the study of terrestrial planets (e.g. Kopparapu et al. of objects in the regime between rocky and gas planets 2013; Segura et al. 2010), rely on pre-mixed k-tables for which do not exist in the Solar System. Detailed un- atmospheric conditions, such as pressure, temperature, derstanding of atmospheric processes, such as radiative and composition. Especially the latter can be a consid- transfer, convection and disequilibrium chemistry is key erable restriction for simulating atmospheres that are for the interpretation of such spectral detections. more and more different from that of Earth. Adding The atmospheres of terrestrial planets lying in the hab- radiation-absorbing constituents often requires a recal- itable zone of their respective host stars could be from culation of all k-tables. The same applies for including H2-He dominated, to H2O, CO2 and N2 dominated, or updates of line lists, for example, for one constituent. even O2 or CO dominated for warmer and cooler planets There are, however, multiple ways of treating overlap respectively (see, e.g., Madhusudhan et al. 2016; Forget of spectral absorption lines of gaseous components in k- & Leconte 2014). distribution radiative transfer calculations for more flex- ibility, assuming perfect correlation, random overlap, or disjoint lines (see, e.g., Pierrehumbert 2010). Lacis & Modeling K2-18b with 1D-TERRA 3 Oinas(1991) have described how the overlap of absorp- 2. METHODOLOGY tion by gaseous components can be treated quickly and Our 1D coupled climate-chemistry model has a long accurately, using the random overlap assumption in the heritage dating back to e.g. Kasting & Ackerman k-distribution method, which has been implemented and (1986); Pavlov et al.(2000); Segura et al.(2003) for tested for hot Jupiter studies by Amundsen et al.(2017). the study of Earth-like planets. Since then, it has Malik et al.(2017) have recently developed a GPU-based been extensively updated in our group, for example, open source radiative transfer model using the faster as- Rauer et al.(2011); Grenfell et al.(2012); Scheucher sumption of perfect correlation between spectral lines et al.(2018). von Paris et al.(2008, 2010, 2015) imple- of different molecules in the correlated-k approximation mented MRAC, a modified version of the Rapid Radia- for studying hot Jupiters and other planets with pri- tive Transfer Model (RRTM) (Mlawer et al. 1997) for mary atmospheres. This assumption, however, becomes CO2 dominated atmospheres in the climate module to less accurate the more absorbers are present. While k- study e.g. early Mars or planets at the outer edge of distribution models operate in cross section-space, Kitz- the habitable zone. Our new radiative transfer module, mann(2017) used opacity sampling in his CO 2 clouds REDFOX, is designed to operate over a wide range of studies, which can be seen as a degraded Line-By-Line stellar energy spectra, as well as diverse neutral compo- (LBL) radiative transfer model.