Observations of transiting gas giant exoplanets have revealed a pervasive depletion of methaneSUP14SUP which has only recently been identified atmosphericallySUP56SUP. The depletion is thought to be maintained by disequilibrium processes such as photochemistry or mixing from a hotter interiorSUP79SUP. However the interiors are largely unconstrained along with the vertical mixing strength and only upper limits on the CHSUB4SUB depletion have been available. The warm Neptune WASP107b stands out among exoplanets with an unusually low density reported low core massSUP10SUP and temperatures amenable to CHSUB4SUB though previous observations have yet to find the moleculeSUP24SUP. Here we present a JWSTNIRSpec transmission spectrum of WASP107b that shows features from both SOSUB2SUB and CHSUB4SUB along with HSUB2SUBO COSUB2SUB and CO. We detect methane with 4.2 significance at an abundance of 1.0  0.5 ppm which is depleted by 3 orders of magnitude relative to equilibrium expectations. Our results are highly constraining for the atmosphere and interior which indicate the envelope has a supersolar metallicity of 43  8  solar a hot interior with an intrinsic temperature of TSUBintSUB  460  40 K and vigorous vertical mixing which depletes CHSUB4SUB with a diffusion coefficient of KSUBzzSUB  10SUP11.60.1SUP cmSUP2SUP sSUP1SUP. Photochemistry has a negligible effect on the CHSUB4SUB abundance but is needed to account for the SOSUB2SUB. We infer a core mass of 11.5SUB3.6SUBSUP3.0SUPMSUBSUB  which is much higher than previous upper limitsSUP10SUP releasing a tension with coreaccretion modelsSUP11SUP.
['Astrophysics - Earth and Planetary Astrophysics']
A warm Neptunes methane reveals core mass and vigorous atmospheric mixing
{"A warm Neptune's methane reveals core mass and vigorous atmospheric mixing": 'David K. Sing 1,2 ,  Zafar  Rustamkulov 1 ,  Daniel P. Thorngren 2 ,  Joanna K. Barstow 3 ,  Pascal Tremblin 4,5 ,  Catarina  Alves  de  Oliveira 6 ,  Tracy  L.  Beck 7 ,  Stephan  M.  Birkmann 6 ,  Ryan  C. Challener 8 , Nicolas Crouzet 9 , Néstor Espinoza 7 , Pierre Ferruit 6 , Giovanna Giardino 10 , Amélie Gressier 7 ,  Elspeth K. H. Lee 11 ,  Nikole K. Lewis 8 ,  Roberto Maiolino 12 ,  Elena Manjavacas 2,13 , Bernard J. Rauscher 14 , Marco Sirianni 15 and Jeff A. Valenti 7  \n1 Department  of  Earth  &  Planetary  Sciences,  Johns  Hopkins  University, Baltimore,  MD,  21218,  USA. 2 Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD, 21218, USA. 3 School of Physical Sciences, The Open University, Milton Keynes MK7 6AA, UK. 4 Université Paris-Saclay, UVSQ, CNRS, CEA, Maison de la Simulation, F-91191 Gif-sur-Yvette, France. 5 Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette France. 6 European Space Agency, European Space Astronomy Centre, 28692 Villanueva  de  la  Canada,  Madrid,  Spain. 7 Space  Telescope  Science  Institute,  Baltimore,  MD  21218,  USA. 8 Department of Astronomy and Carl Sagan Institute,  Cornell  University,  Ithaca,  NY,  14853,  USA. 9 Leiden Observatory,  Leiden  University,  P.O.  Box  9513,  2300  RA  Leiden,  The  Netherlands. 10 ATG  Europe  for  the European Space Agency, ESTEC, Noordwijk, The Netherlands. 11 Center for Space and Habitability, University of  Bern,  Gesellschaftsstrasse  6,  CH-3012  Bern,  Switzerland. 12 University  of  Cambridge,  The  Old  Schools, Trinity  Ln,  Cambridge  CB2  1TN,  UK. 13 AURA  for  the  European  Space  Agency  (ESA),  ESA  Ofcice,  Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD, 21218 USA. 14 NASA Goddard Space Flight Center,  Greenbelt,  MD  20771,  USA. 15 European Space Agency (ESA), ESA Ofcice, Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA. email: dsing@jhu.edu.  \nReceived:18December2023  \nAccepted:5April2024  \nObservations of transiting gas giant exoplanets have revealed a pervasive depletion of methane [1,2,3 , 4] , which  has  only  recently  been  identiRied  atmospherically [5 , 6] . The depletion  is  thought  to  be  maintained  by  disequilibrium  processes  such  as photochemistry or mixing from a hotter interior [7,8 , 9] . However, the interiors are largely unconstrained along with the vertical mixing strength and only upper limits on the CH 4 depletion  have  been  available.  The  warm  Neptune  WASP-107  b  stands  out  among exoplanets with an unusually low density, reported low core mass [10] , and temperatures amenable to CH 4 though previous observations have yet to Rind the molecule [2 , 4] .  Here we  present  a  JWST  NIRSpec  transmission  spectrum  of  WASP-107  b  which  shows features from both SO 2 and CH 4 along with H 2 O, CO 2 , and CO. We detect methane with 4.2 σ signiRicance  at  an  abundance  of  1.0±0.5  ppm,  which  is  depleted  by  3  orders  of magnitude relative to equilibrium expectations. Our results are highly constraining for the atmosphere and interior, which indicate the envelope has a super-solar metallicity of  43±8× solar,  a  hot  interior  with  an  intrinsic  temperature  of T int =460±40  K,  and vigorous vertical mixing which depletes CH 4 with a diffusion coefRicient of K zz = 10 11 . 6±0 . 1 cm 2 /s. Photochemistry has a negligible effect on the CH 4 abundance, but is needed to account for the SO 2 .  We infer a core mass of 11.5 !".$ %".& M ⊕ ,  which is much higher than previous upper limits [10] , releasing a tension with core-accretion models [11] .  \nWe observed one transit of the exoplanet WASP-107 b [12] with  JWST NIRSpec\'s G395H spectral  grating  as  part  of  Guaranteed  Time Observations (GTO)  program  1224  (P.I. Birkmann). In JWST\'s Rirst years of operation, this mode demonstrates reliable detections of H 2 O,  CO,  CO 2 and  SO 2 for  a  number  of  giant  \nexoplanets [7 , 17,18,19] . See  the  Methods  for further  details  regarding  the  observations and data analysis. The wavelength-integrated JWST  NIRSpec  time  series  photometry  of WASP-107  b  is  shown  in  Fig.  1  and  the transmission spectrum is shown in Fig. 2. The spectrum shows several molecular  \nFig.  1 The  light  curve  of  WASP-107b  observed  by  JWST  NIRSpec  G395H. ( a )  The normalized wavelength-integrated white light curves for the two detectors are shown, with the NRS1 (2.7-3.71 µm) and NRS2 (3.83-5.16 µm) detectors offset for clarity. A best-cit limbdarkenened transit model is overplotted (blue). See Extended Data Fig. 2 for additional details. ( b ) The model residuals which achieve near-photon limited precisions.  \n<!-- image -->  \nabsorption signals that are readily identiRiable. We detect a large CO 2 absorption feature at 4.3 µ m [19] (see Fig. 2) and a slopelike feature at the shortest wavelengths from H 2 O [18] .  \nWe  ran  a  series  of  model  retrievals  to provide detailed constraints on the atmospheric  composition  and  temperature (Methods).  The  H 2 O  and  CO 2 features  are detected  at  high  conRidence  (see  Extended Data  Table  2).  The  spectrum  shows  CO features between 4.5 and 5 µ m (4 σ ),  and  an SO 2 absorption feature at 4.0 µ m (5.5 σ ). SO 2 is a  known  by  product  of  photochemistry [7] , being  generated  when  stellar  UV  radiation reacts  with  H 2 S,  and  has  been  identiRied  in WASP-107  b  at  longer  wavelengths  with JWST/MIRI [4] . Finally, a narrow CH 4 feature is identiRied  at  3.32 µ m  (4.2 σ ).  While  CH 4 has been unobservable at both shorter and longer wavelengths [2 , 4] the  feature  here  is  the  Qbranch  band  head  of  CH 4 which  is  strong enough to appear above the clouds and H 2 O (see Fig. 2).  \nFor  H 2 O,  we  Rind  volume  mixing  ratio abundances  of  10 -1 . 85±0 . 22 which  indicates super-solar  abundances  near  40×  solar.  The presence of CO 2 is known to be a tracer of high metallicity [19 , 21] , and the retrieved abundances of 10 -3 . 33±0 . 27 support this, though are lower than chemical equilibrium expectations by about an order of magnitude as the  molecule  is  further  sensitive  to atmospheric mixing.  CH 4 is  also  found  to  be heavily  depleted,  with  retrieved  abundances of  10 -6 . 03±0 . 21 . These  CH 4 abundances  are consistent with previous HST and JWST upper limits [2 , 4] . At the millibar pressures probed in transmission spectra, at 40×  solar the atmosphere  in  equilibrium  would  be  about one part in a thousand CH 4 , while abundances slightly less than one part per million (ppm) are  found.  Measuring  the  amount  of  CH 4 depletion  is  highly  constraining  for  nonequilibrium models [8] , as it can be tied to the pressure  and  temperature  of  the  hotter interior  from  which  the  species  is  mixed  to higher  levels.  While  not  every  planet  is showing a CH 4 depletion [5] ,  for  those that do  \nFig.  2  WASP-107  b  transmission  spectral  measurements. Shown is the JWST NIRSpec transmission spectrum and the 1σ uncertainties. The best-cit ATMO [20] model is also plotted, as well as the individual contributions for each molecular species.  \n<!-- image -->  \nsuch  as  WASP-107  b [4] and  others [3] , only upper-limits  on  the  depletion  have  been available.  By  quantifying  the  CH 4 depletion, the non-equilibrium chemistry can be tightly constrained  and  the  depletion  mechanisms can be explored. We Rind abundances of SO 2 to be 10 -5 . 06±0 . 13 which  broadly  match  the JWST/MIRI results [4] as well as those of WASP39 b [7 , 22] indicating ongoing photochemistry in the atmosphere.  \nGiven the retrieved molecular abundances,  we  ran  a  grid  of  forward atmospheric  models  to  place  constraints  on the photochemistry, vertical mixing, metallicity  and  temperature structure of the planet. The model and includes nonequilibrium  chemistry  from  both  vertical mixing and photochemistry self consistently calculated [23 , 24] (Methods). The chemistry was computed using temperature-pressure proRiles  in  radiative-convective  equilibrium, with  a  range  of  intrinsic  temperatures, T int . The  intrinsic  temperature  is  related  to  the emitted  Rlux  generated  from  the  planet\'s interior which passes through the atmosphere,  with  Jupiter  having  a T int near 100  K.  With  vertical  mixing,  the  major molecular species detected are expected to be uniformly mixed from their quench pressures at deeper/hotter  conditions  in  chemical equilibrium to higher altitudes. We modeled  \nthe vertical mixing in a turbulent Rlow using the vertical eddy diffusion coefRicient, K zz . Our best-Rit forward  model  to  the  retrieved abundances  are  shown  in  Fig.  3  (see  also Extended Data Fig. 7).  \nWe Rind the combination of H 2 O, CO, CO 2 , CH 4 and SO 2 to be highly constraining. H 2 O and CO are insensitive to non-equilibrium chemistry in this temperature regime (see Fig. 3) helping to uniquely measure the metallicity while  the  combination  of  CO 2 and  CH 4 are jointly sensitive to K zz and T int . SO 2 also helps provide an upper bound on K zz (see Extended Data Fig. 7). With these combined constraints, the  forward  model  grid  indicates  the  planet has  a  hot  intrinsic  temperature  of T int =460±40  K,  a  high  metallicity  of Z =43±8× solar and vigorous vertical mixing with a K zz = 10 11 . 6±0 . 1 cm 2 /s.  \nTheoretical  models  have  estimated  the strength  of  vertical  mixing  and K zz [13,14,15] . However,  the  overall  uncertainty  on K zz for giant  planets  remains  large [16] ,  with  values often  ranging  from  10 4 to  10 12 cm 2 /s  in  the context  of  hot  Jupiters [8] . The  empirical constraints  on K zz for  exoplanets  currently rely on broadband Spitzer/IRAC photometry [9] ,  where  there  is  considerable planet-to-planet stochasticity and the molecular features are spectroscopically unresolved  which  gives  rise  to  modeling  \nFig. 3 Model Interpretation Figure. ATMO non-equilibrium chemistry model with vertical mixing and photochemistry. The best-cit non-equilibrium chemistry model is shown (solid lines) as well as the abundance prociles in equilibrium (dot-dashed lines). The retrieved JWST abundances are shown (data points) with the model grid indicating the planet has hot interior  temperatures  (T int =458±38  K),  a  super-solar  metallicity  (Z/Z ⊙ =43±8)  with vigorous vertical mixing (K zz = 10 11.6±0.1 cm 2 /s).  \n<!-- image -->  \ndegeneracies. The K zz measurement in WASP107 b here is a substantial improvement over the order of magnitude estimates previously explored using either the upper limits on CH 4 from JWST/MIRI [4] or population-level results [9] .  The measurement is best evidence to-date that non-equilibrium chemistry from vertical  mixing  is  an  important  physical process  in  exoplanetary  atmospheres,  a mechanism long known to be important for Jupiter [25] .  The K zz value for WASP-107 b at 1 bar is about 1,000 to 10,000× higher than the typical  estimates  used [7 , 26] which  are  largely based  on  3D  GCM  modeling [13] .  This  could indicate  the  planet  has  anomalously  high vertical  mixing,  perhaps  due  to  the  high T int resulting in a convective region which reaches lower than expected pressures. Alternatively, the GCM  models  may  be  inadequately capturing  the  eddy  dissipation  with  the artiRicial viscosity parameters used [27] .  \nThe high T int is a direct constraint on the energy stored in the deep atmosphere, which can  help  us  understand  the  mechanism responsible  for  the  inRlated  radius  of  the planet. The  anomalously  large  radii  of irradiated  warm  Neptunes/hot  Jupiters  are one of the most intriguing and long-standing problems in our understanding of extrasolar giant planets with several proposed mechanisms including: tidal heating [28] ,  \ndownward  transport  of  kinetic  energy [29] , enhanced opacities [30] , ongoing layered convection [31] , ohmic dissipation [32] , and more recently the advection of potential temperature [20 , 33] . The potential temperature mechanism has been recently demonstrated in  the  hot  Jupiter  WASP-76b  using  Rirst principle  radiative  GCM  simulations [34] .  The hot  interior  temperature  can  explain  the higher vertical mixing rates found, as hotter temperatures and lower surface gravities are expected  to  both  increase K zz . These  high vertical mixing rates with supersolar metallicities and hot intrinsic temperatures in turn also explain the cloud properties observed, where silicate cloud particles were surprisingly  found  with  JWST/MIRI [4] . For planets  like  WASP-107  b  with  equilibrium temperatures near 770 K, the condensation of silicate  clouds  should  be  occurring  at  high unobservable pressures if T int was low (∼100 K) [8] .  However,  with  a  high T int of  460  K  the silicate cloud base is moved to ∼bar pressures (see  Extended  Data  Fig.  6)  and  the  high K zz values found here are more than sufRicient to aloft  the  cloud  particles  to  mbar  pressures where they are observed in transmission.  \nThe mass, radius, and T int alone constrain the overall bulk metallicity of the planet to be Z p = 63.5 !\'.( %)&.* %. A precise atmospheric metallicity  and T int allows  us  to  place  better  \nconstraints  on  the  planet\'s  overall  metal content and estimate the planet\'s core mass (Methods). To date, no gas giant exoplanet has had  the  presence  of  a  core  signiRicantly detected, with upper limits reported for HATP-13 b [35] and WASP-107 b [10] . Any metals seen in the bulk but not in the atmosphere must be hidden in the interior in a core or composition layers. Assuming a uniform composition core, an  isothermal  50-50%  mixture  of  rock  and water,  gives  us M c = 11.5 !".$ %".& M ⊕ -  which  is  a third  the  mass  of  the  planet  and  the  Rirst statistically-signiRicant  core  detection  for  a giant  exoplanet.  This  value  is  much  higher than previous estimates limiting the core to < 4 . 6 M ⊕ [10] ,  which  had  assumed  the  planet followed  a  standard  cooling  track  with  no tidal  heating.  These  low  core-mass  values were in tension with standard core-accretion models [11] which  do  not  predict  such  a  light core could accrete the massive H/He envelope observed. In contrast, our core mass estimate matches  the  ∼10 M ⊕ prediction  needed  to elicit runaway gas accretion within the disks lifetime. It\'s worth noting that the structure of the interior may not be exactly an envelopeon-core model, but may be more like Neptune and Uranus with a rocky core and an icy water mantle [36] or the core may be diffuse and/or similar to Jupiter [37 , 38] .  The core mass result should be understood as the total excess nonH/He heavy elements in the interior, irrespective  of  exactly  how  it  is  structured. With the proof-of-concept demonstrated here,  using  CH 4 -depletion  as  a  thermometer of  the  deep  atmosphere  for  other  gas  giant exoplanets could help provide constraints at the  population  level  about  how  planetary cores  might  differ  with  planet  or  host  star mass and metallicities.  \nWASP-107 b is one of the lowest density planets known, which has led to speculation that  the  planet  have  formed  substantially different than the solar system, with dust-free accretion  or  in-situ  scenarios  explored [10] . However, the important bulk properties found here line up well with the solar-system (SS) planets  indicating  a  similar  core-accretion  \nscenario.  In  particular,  with  a  metallicity  of 43±8× solar, WASP-107 b is close to the massmetallicity trend of the gas giant SS planets [39] . In  addition,  with  an  estimated  core  mass  of 11.5 !".$ %".& M ⊕ , WASP-107 b is also intermediate between Neptune and Saturn, falling reasonably along their lines of formation [40 , 41] . The major difference for WASP-107 b appears to be its much hotter interior, resulting in an extremely puffy planet.', 'References': "- [1] Stevenson, K. B. et al. Possible thermochemical disequilibrium in the atmosphere of the exoplanet GJ 436b. Nature 464 , 1161-1164 (2010).\n- [2] Kreidberg,  L.,  Line,  M.  R.,  Thorngren,  D., Morley, C.  V.  &  Stevenson,  K.  B.  Water,  Highaltitude  Condensates,  and  Possible  Methane Depletion  in  the  Atmosphere  of  the  Warm Super-Neptune  WASP-107b. Astrophys.  J.  L. 858 , L6 (2018).\n- [3] Fu, G. et al. Water and an Escaping Helium Tail Detected  in  the  Hazy  and  Methane-depleted Atmosphere of HAT-P-18b from JWST NIRISS/SOSS. Astrophys. J. L. 940 , L35 (2022).\n- [4] Dyrek, A. et al. SO 2 , silicate clouds, but no CH 4 detected in a warm Neptune. Nature 625 , 5154 (2024).\n- [5] Bell,  T.  J. et  al. Methane  throughout  the atmosphere  of  the  warm  exoplanet  WASP80b. Nature 623 , 709-712 (2023).\n- [6] Madhusudhan,  N. et al. Carbon-bearing Molecules in a Possible Hycean Atmosphere. Astrophys. J. L. 956 , L13 (2023).\n- [7] Tsai, S.-M. et al. Photochemically produced SO 2 in the atmosphere of WASP-39b. Nature 617 , 483-487 (2023).\n- [8] Fortney, J. J. et al. Beyond  Equilibrium Temperature:  How  the  Atmosphere/Interior Connection  Affects  the  Onset  of  Methane, Ammonia,  and  Clouds  in  Warm  Transiting Giant Planets. Astron. J. 160 , 288 (2020).\n- [9] Baxter,  C. et  al. Evidence  for  disequilibrium chemistry from vertical mixing in hot Jupiter atmospheres.  A  comprehensive  survey  of transiting  close-in  gas  giant  exoplanets  with warm-Spitzer/IRAC. Astron.  Astrophys. 648 , A127 (2021).\n- [10] Piaulet, C. et al. WASP-107b's Density Is Even Lower:  A  Case  Study  for  the  Physics  of Planetary Gas Envelope Accretion and Orbital Migration. Astron. J. 161 , 70 (2021).\n- [11] Pollack,  J.  B. et  al. Formation  of  the  Giant Planets by Concurrent Accretion of Solids and Gas. Icarus 124 , 62-85 (1996).\n- [12] Anderson, D. R. et al. The discoveries of WASP91b, WASP-105b and WASP-107b: Two warm Jupiters and a planet in the transition region between  ice  giants  and  gas  giants. Astron. Astrophys. 604 , A110 (2017).\n- [13] Parmentier,  V.,  Showman,  A.  P.  &  Lian,  Y.  3D mixing in hot Jupiters atmospheres. I. Application to the day/night cold trap in HD 209458b. Astron. Astrophys. 558 , A91 (2013).\n- [14] Zhang,  X.  &  Showman,  A.  P.  Global-mean Vertical Tracer Mixing in Planetary Atmospheres.  I.  Theory  and  Fast-rotating Planets. Astrophys. J. 866 , 1 (2018).\n- [15] Menou,  K.  Turbulent  vertical  mixing  in  hot exoplanet  atmospheres. Mon.  Not.  R.  Astron. Soc. 485 , L98-L103 (2019).\n- [16] Mukherjee,  S. et  al. Probing  the  Extent  of Vertical Mixing in Brown Dwarf Atmospheres with  Disequilibrium  Chemistry. Astrophys.  J. 938 , 107 (2022).\n- [17] Birkmann,  S.  M. et  al. The  Near-Infrared Spectrograph  (NIRSpec)  on  the  James  Webb Space Telescope IV. Capabilities and predicted performance  for  exoplanet  characterization. Astron. Astrophys. 661 , A83 (2022).\n- [18] Alderson, L. et al. Early Release Science of the exoplanet  WASP-39b  with  JWST  NIRSpec G395H. Nature 614 , 664-669 (2023).\n- [19] The  JWST  Transiting  Exoplanet  Community Early Release Science Team et al. Identicication of carbon dioxide in an exoplanet atmosphere. Nature 614 ,  649-652 (2023).\n- [20] Tremblin,  P. et  al. Advection  of  Potential Temperature in the Atmosphere of Irradiated Exoplanets:  A  Robust  Mechanism  to  Explain Radius Inclation. Astrophys. J. 841 , 30 (2017).\n- [21] Moses,  J.  I.,  Madhusudhan,  N.,  Visscher,  C.  & Freedman, R. S. Chemical Consequences of the C/O  Ratio  on  Hot  Jupiters:  Examples  from WASP12b, CoRoT-2b, XO-1b, and HD 189733b. Astrophys. J. 763 , 25 (2013).\n- [22] Rustamkulov, Z. et al. Early Release Science of the exoplanet WASP-39b with JWST NIRSpec PRISM. Nature 614 , 659-663 (2023).\n- [23] Drummond, B. et al. The effects of consistent chemical kinetics calculations on the pressure-temperature  prociles  and  emission spectra of hot Jupiters. Astron. Astrophys. 594 , A69 (2016).\n- [24] Nicholls, H., H'ebrard, E., Venot, O., Drummond,  B.  &  Evans,  E.  Temperaturechemistry  coupling  in  the  evolution  of  gas giant  atmospheres  driven  by  stellar  clares. Mon.  Not.  R.  Astron.  Soc. 523 , 5681-5702 (2023).\n- [25] Prinn, R. G. & Barshay, S. S. Carbon Monoxide on Jupiter and Implications for Atmospheric Convection. Science 198 , 1031-1034 (1977).\n- [26] Moses, J. I., Tremblin, P., Venot, O. & Miguel, Y. Chemical variation with altitude and longitude  on  exo-Neptunes:  Predictions  for Ariel phase-curve observations. Experimental Astronomy 53 , 279-322 (2022).\n- [27] Mayne, N. J. et al. The unicied model, a fullycompressible, nonhydrostatic, deep atmosphere global circulation model, applied to  hot  Jupiters.  ENDGame for a HD 209458b test case. Astron. Astrophys. 561 , A1 (2014).\n- [28] Bodenheimer, P., Lin, D. N. C. & Mardling, R. A. On  the Tidal Inclation of Short-Period Extrasolar Planets. Astrophys. J. 548 , 466-472 (2001).\n- [29] Showman,  A.  P.  &  Guillot,  T.  Atmospheric circulation  and  tides  of  '51  Pegasus  b-like' planets. Astron.  Astrophys. 385 , 166-180 (2002).\n- [30] Burrows, A., Hubeny, I., Budaj, J. & Hubbard, W. B. Possible Solutions to the Radius Anomalies of Transiting Giant Planets. Astrophys. J. 661 , 502-514 (2007).\n- [31] Chabrier,  G.  &  Baraffe,  I.  Heat  Transport  in Giant (Exo)planets: A New  Perspective. Astrophys. J. L. 661 , L81-L84 (2007).\n- [32] Batygin, K., Stevenson, D. J. & Bodenheimer, P. H. Evolution of Ohmically Heated Hot Jupiters. Astrophys. J. 738 , 1 (2011).\n- [33] Sainsbury-Martinez, F. et al. Idealised simulations  of  the  deep  atmosphere  of  hot Jupiters.  Deep,  hot  adiabats  as  a  robust solution  to  the  radius  inclation  problem. Astron. Astrophys. 632 , A114 (2019).\n- [34] Sainsbury-Martinez,  F. et al. Evidence  of radius  inclation  in  radiative  GCM  models  of WASP-76b due to  the  advection  of  potential temperature. Mon.  Not.  R.  Astron.  Soc. 524 , 1316-1325 (2023).\n- [35] Buhler,  P.  B. et  al. Dynamical Constraints  on the  Core  Mass  of  Hot  Jupiter  HAT-P-13b. Astrophys. J. 821 , 26 (2016).\n- [36] Cavalié ,  T. et  al. The  Deep  Composition  of Uranus and Neptune from In Situ Exploration and Thermochemical Modeling. Space Sci. Rev. 216 , 58 (2020).\n- [37] Vazan,  A.,  Helled,  R.  &  Guillot,  T.  Jupiter's evolution with primordial composition gradients. Astron. Astrophys. 610 , L14 (2018).\n- [38] Debras, F. & Chabrier, G. New Models of Jupiter in the Context of Juno and Galileo. Astrophys. J. 872 , 100 (2019).\n- [39] Thorngren, D. P., Fortney, J. J., Murray-Clay, R. A. & Lopez, E. D. The Mass-Metallicity Relation for Giant Planets. Astrophys. J. 831 , 64 (2016).\n- [40] Guillot, T. et al. Giant Planets from the InsideOut. arXiv e-prints arXiv:2205.04100 (2022).\n- [41] Mankovich, C. R. & Fuller, J. A diffuse core in Saturn  revealed  by  ring  seismology. Nature Astronomy 5 , 1103-1109 (2021).  \nExtended Data Figure 1 FIREFLy transit  light  curve  spectrophotometry.  Shown  is  the relative clux as a function of wavelength and time for NIRSpec detectors ( a ) NRS1 and ( b ) NRS2.  \n<!-- image -->  \nExtended  Data  Table  1  Orbital  parameters. Best-cit  orbital  parameters  as  \nmeasured from the FIREFLy JWST white light curve.", 'Data Reduction': 'One transit of WASP-107 b was observed on 2023 June 23 with JWST for 6.5 hours using the  NIRSpec  instrument  with  the  G395H grating.  This  setup  gives  a  wavelength  range from 2. 7 to 5.18 µ m with the corresponding resolving  power  ranging  between  1828  to 3600.  The  instrument  used  the  NRSRAPID readout pattern and SUB2048 subarray with 20  groups  per  integration,  resulting  in  1230 integrations over the 6.5 hour observation.', 'FIREFLy': 'We  reduce  the  data  using  the  Fast InfraRed Exoplanet Fitting Lyghtcurve ( FIREFLy ) [22 , 42] reduction  suite,  which  starts with a customized reduction using the STScI pipeline  and  the  uncalibrated  images.  Our custom  reduction  includes  1/ f destriping  at the  group  level  before  the  ramp  is  Rit.  The jump-step  and  dark-current  stages  of  the STScI pipeline were skipped. We then use the custom-run pipeline 2D images after the gain  \nscale  step,  and  perform  customized  cleaning of bad pixels, cosmic rays and hot pixels. Using cross-correlation, we measured the positional shift of the spectral trace across the detector and  shift-stabilized  the  images  with  Rluxconserving interpolation. This procedure has been  found  to  reduce  the  amplitude  of position-dependent trends [22 , 42] , as the underlying  stellar  spectra  is  not  shifting  in wavelength  across  a  pixel  through  the  time series. We note nearly identical results can be found if the data is not shift-stabilized and the extraction window is moved instead. Further position-dependent  trends  can  be  expected from intrapixel sensitivity variations [17] , though their magnitude on-sky has been very small as JWST generally has excellent pointing with the detector shifts found in this dataset to be  on  the  order  of  ∼1/1000  of  a  pixel.  We optimized  the  width  of  our  Rlux  extraction aperture to minimize the standard deviation of  the  white  light  curve  photometry  and extracted the spectrophotometric time series. The 2D extracted spectral time series can be seen in Extended Data Fig. 1. We extracted the  \nExtended  Data  Figure  2  Stellar  spot-crossing. Shown  is  the  residual  white-light  \n<!-- image -->  \ncurve photometry from NRS1 when citting for the non-spotted data (black dots). The suspected  occulted  spot  (red  crosses)  is  shown,  with  a  Gaussian  smoothed  cilter overplotted (blue line).  \ntransmission spectra with a range of different wavelength bin sizes, reporting an extraction with a resolution near R =950.  \nWe  Rit  the  transit  light  curves  using  a quadratic  function  to  model  stellar  limb darkening given as,  \n. (1)  \nwhere I (1) is the intensity at the center of the stellar  disk, µ = cos ( θ )  where θ is  the  angle between  the  line  of  sight  and  the  emergent intensity, and a and b are the limb darkening coefRicients. In practice, we remap a and b and Rit instead for q 1 and q 2 which has shown to be less degenerate [43] . The resulting limbdarkening coefRicients can be seen in Extended Data Fig. 3.  \nModel limb darkening coefRicients calculated  from  3D  models [44] capture  the wavelength  dependence  of  limb-darkening well,  but  we  Rind  an  overall  offset  in  the coefRicients of -0.0378 and +0.175 for q 1 and q 2 respectively.  We  applied  these  offsets  to  the wavelength dependent model limb-darkening  \ncoefRicients and re-Rit the transmission spectra with Rixed limb-darkening. This iterative  procedure  reduces  the  bin-to-bin scatter  of  the  transmission  spectra  as  the limb-darkening is Rixed, but allows for overall differences  between  the  transit  data  and stellar  model  limb-darkening.  We  bin  the spectrophotometry into 576 wavelength bins, providing a spectral resolution of R∼950 for the planet.', 'Stellar Spot Crossing': 'A stellar spot crossing event is observed in  our  transit  light  curve  data,  appearing  in both NRS1 and NRS2 shortly after mid-transit, which  we  decontaminated  from  the  light curves  and  the  transmission  spectrum.  The host  star  is  known  to  be  modestly  active [12] , with  optical  photometric  modulations  of ∼0.4%  on  a  period  of  about  17  days.  We modeled this spot empirically, Rirst Ritting the non-spotted region with a transit light curve and using the overall residual in the spotted region to deRine the photometric shape of the spot  (see  Extended  Data  Fig.  2.)  A  Gaussian Rilter was then applied to the spot-shape and  \n<!-- image -->  \nExtended Data Figure 3 LimbDarkening. Shown  are  the  resulting stellar  limbdarkening  coefcicients q 1 ( a ) and q 2 ( b )  derived  from  the  transit  light curves  using  a  quadratic  law.  The  limbdarkening  coefcicients  derived  from  a stellar model are also shown, along with the models with an offset derived from the difference between the data and model.  \nsubsequently  used  to  model  the  full  transit light curves, Ritting for a scaling factor. As the spot  is  low  in  amplitude  and  only  covers  a small portion of the data, our overall transmission  spectrum  is  insensitive  to  the occulted  spot.  We  found  equivalent  results between masking the region for all the transit light curve Rits and Ritting for the spot shape in the light curves.', 'TEATRO': "An  independent  data  reduction  was performed  using  the  Transiting  Exoplanet Atmosphere Tool for Reduction of Observations ( TEATRO ) pipeline.  \nThe  data  were  processed  using  the jwst calibration  software  package  version  1.10.2, CRDS version 11.16.19, CRDS context 1147 [115 , 116] , starting from the 'uncal' Riles. For stage 1, a jump rejection threshold of 6 was used and the  'jump.Rlag  4  neighbors'  parameter  was turned  off.  For  stage  2,  the  Rlat  Rield  and photometric  calibration  steps  were  skipped. Bad  pixels  and  missing  pixels  were  then corrected for in each integration. The center of the spectral trace in the spatial direction was computed  by  Ritting  a  Gaussian  function  to each  column  and  Ritting  a  third  order polynomial to their maxima. For each integration, the background was computed on a column-by-column basis using pixels above and below the spectral trace (or only one of them at the short and long wavelength edges of NRS2).  \nAn  aperture  half-width  of  2.73  and  3 pixels  and  background  regions  starting  6.5 and 6 pixels further away were used for nrs1 and nrs2, respectively. The background subtraction  and  spectral  extraction  were performed using the 'extract 1d' routine with the corresponding polynomial coefRicients as parameters. The whitelight Rlux was computed using  the  'white  light'  step  routine.  For  the spectroscopic analysis, we binned the spectra in  86  and  136  wavelength  bins  of  0.01 µ m width,  covering  the  2 . 86  -  3 . 72 µ m  and 3 . 82-5 . 18 µ m  ranges  with  nrs1  and  nrs2, respectively. The lightcurves were normalized  \nby the out of transit Rlux and a 5-iteration 3.5 sigma-clipping was applied to remove outliers.  \nLightcurve Rits were performed using the exoplanet [117 , 118] package with a quadratically limb darkened transit lightcurve model and a second order polynomial to account for long term  trends.  A  Rit  to  the  whitelight  curve obtained from NRS1 only was Rirst performed to  derive  system  parameters  (mid-transit time, impact parameter, planet to star radius ratio, stellar density). These parameters were then Rixed for the spectroscopic lightcurve Rits, leaving only the radius ratio and polynomial trend  as  free  parameters.  Limb-darkening coefRicients were obtained from ExoTETHyS [119] , they were  free  for the whitelight curve Rit and Rixed for the spectroscopic  lightcurve  Rits.  The  median  of the  posterior  distribution  of  the  radius  ratio was used to  derive  the  transit  depth  in  each wavelength bin. The uncertainties were computed  by  summing  quadratically  the standard  deviations  of  the  in-  and  -out-oftransit parts of the lightcurve divided by the square  root  of  their  respective  number  of points  (this  gave  a  better  estimate  than  the standard deviation of the posterior distributions).  \nComparing  the TEATRO reduction  to FIREFLy ,  we  Rind  good  consistency  with  the spectra agreeing at the point-to-point level at better than 1σ for both NRS1 and NRS2.", 'Resolution-linked Bias': "We have adjusted the retrieved abundance  to  account  for  the  resolutionlinked bias (RLB) effect [46] , in which planetary absorption  signatures  are  diluted  within stellar absorption lines. For G395H data, this in particular dilutes the transmission spectral signatures of CO, as the molecule is found in both  the  star  and  planet's  atmosphere.  We followed  the  method  in  Ref.  [42],  estimating the  magnitude  of  the  effect  using  highresolution  models.  Compared  to  WASP-39A, WASP-107A is a cooler later-type star which enhances  the  RLB  effect  as  the  stellar  CO  is  \nstronger.  However,  within  the  CO  lines,  the planet's  atmosphere  is  cloudier  than  WASP39b,  which  somewhat  reduces  the  effect.  In total, we Rind the RLB reduces the inferred CO abundance by 0.2 dex, which is about half of the uncertainty in the CO abundance.", 'Atmospheric Models ATMO Setup': 'We use ATMO , a 1D-2D  radiativeconvective  equilibrium  model  for  planetary atmospheres to generate models of WASP-107 b.  More  comprehensive  descriptions  of  the model can be found in Refs. [20, 47,48,49,50], and [51]. The ATMO model is used here as both a  forward  physical  model  in  radiative  and chemical  (dis-)equilibrium  and  a  retrieval model where the abundances and temperature-pressure proRile are let free to Rit the  data.  By  comparing  the  retrieved  and forward  model  abundances  within  a  single model  suite, model-to-model  systematics from such sources as differences in opacites can  be  avoided. ATMO has  been  validated against  the  publicly  available  MET  ofRice radiative transfer code SOCRATES [52] , and has been  benchmarked  against  Exo-REM [53] and petitCODE [54] in the context of JWST observations [55] .  \nATMO solves the radiative transfer equation with isotropic scattering in 1D planeparallel  geometry  for  the  irradiation  and thermal emission, Rinding a pressuretemperature (P-T) proRile that satisRies hydrostatic  equilibrium  and  conservation  of energy  and  is  also  self-consistent  with  the atmospheric chemistry and opacities, given a set of elemental abundances. The total opacity of  the  gas  mixture  is  computed  using  the correlatedk approximation using the random overlap method with resorting and rebinning [47 , 56] . The k -coefRicients are calculated  \'on  the  Rly\'  for  each  atmospheric layer, spectral band and iteration such that the derived opacities are physically selfconsistent  with  the  T-P  proRile  and  chemical composition. ATMO can be also used as a full line-by  line  code  at  high  spectral  resolution,  \nthough  that  is  not  used  here  as  it  is  too computationally  heavy  for  spectral  retrieval purposes. The spectrally active species currently  include  H 2 -H 2 and  H 2 He  collision induced absorption (CIA) opacities, as well as H 2 O,  CO 2 ,  CO, CH 4 ,  NH 3 ,  Na, K, Li, Rb, Cs, TiO, VO, Fe, FeH, CrH, PH 3 , HCN, C 2 H 2 , H 2 S, SO 2 and H- (see Refs. [57, 58] full description). Multigas Rayleigh scattering contributions from the different species are also included.  \nThe chemical abundances in equilibrium are determined by minimizing the Gibbs free energy following the method of Ref.[59], and using the thermochemical data from Ref. [60]. Solar elemental abundances are set from Refs. [61, 62], with the chemistry fully Rlexible for any mix of input elemental abundances. This method  also  allows  for  the  depletion  of  gas phase species due to condensation as well as thermal ionization and dissociation. ATMO has as  several  different  chemical  schemes  which can  be  chosen,  and  by  default  calculates  the abundances  for  175  neutral,  9  ionic,  and  93 condensate  species.  Condensation  can  be treated  locally,  or  with  rainout.  Rainout  is treated  by  calculating  the  chemistry  at  the highest pressure initially, then following the TP proRile towards lower pressures. Condensed elements are removed locally, as well as for all lower  pressures [63] , allowing  for  opacity changes  which  can  alter  the  radiativeconvective balance and P-T proRile.  \nFor  non-equilibrium C-H-N-O chemistry, ATMO uses  a  chemical  kinetics  scheme  from Ref. [64] as described in Ref. [50]. As done in Ref.  [7]  to  model  the  S  photochemistry  of WASP-39  b  with ATMO , we  used  the thermochemical network from Ref. [65] along with the photochemical scheme from Ref. [66] including  71  photolysis  reactions  of  H 2 S,  S 2 , SO 2 , SO, SO 2 , CH 3 SH, SH, H 2 SO and COS.  \nATMO includes a relatively simple treatment of clouds and hazes [57] and does not consider the  distribution  of  aerosol  particles.  An aerosol  \'haze\'  scattering  is  implemented  as enhanced Rayleigh-like scattering [67], presented as  \nσ (𝜆) haze = δ haze 𝜎 & (𝜆/𝜆0) !+ !"#$ , (2)  \nwhere σ (𝜆) is  the  total  scattering  crosssection  of  the  material, δ haze is  an  empirical enhancement  factor,  and σ 0 is  the  scattering cross  section  of  molecular  hydrogen  at  0.35 µ m,  and α haze is  a  factor  determining  the wavelength dependence  with α haze = 4 corresponding to Rayleigh scattering. Condensate \'cloud\' absorption is assumed to have  a  grey  wavelength  dependence,  and  is calculated as  \nκ (𝜆) ,-./0 = δ cloud 𝜅 12 , (3)  \nwhere κ (𝜆) ,-./0 is  the  \'cloud\'  absorption opacity, δ cloud is an empirical factor governing the strength of the grey scattering, and κ H2 is the  scattering  opacity  due  to  H 2 at  0.35 µ m. σ (𝜆) haze and κ (𝜆) ,-./0 are  added  to  the  total gaseous scattering and absorption respectively.  \nFor  spectra  retrievals,  we  coupled  the forward ATMO model  to  a  nested  sampling statistical algorithm to marginalize the posterior distribution and measure the model evidence [68,69,70] . The  retrieval  aspects  of ATMO were developed to Rit transit and eclipse data,  with  results  published for a number of transiting planets (e.g. Refs [3, 71, 72, 73, 74, 75]).  A  main  difference  compared  to  the forward  models  is  the  retrieval  does  not converge the TP proRile to radiativeconvective equilibrium, but rather parameterizes  the  proRile  which  is  then  Rit against  the  planetary  spectrum.  With  the retrieval  model,  the k -coefRicients  are  still calculated  \'on  the  Rly\'  in  the  same  way  as described in the forward model (and', 'Extended Data Table 2 Model Results .': 'The retrieval results from the ATMO and NEMESIS codes are given, with the bestcit  parameter  values  shown  along  with their 1σ uncertainties. T int refers to the intrinsic temperature, which is related to the  clux, F , emitted  from  the  planet\'s interior by F = 𝜎 ! 𝑇 "#$ % , where 𝜎 ! the StefanBoltzmann  constant.  VMR  refers  to  the Volume Mixing Ratio.  \nequilibrium  chemistry  if  speciRied)  for  every likelihood evaluation step to maximize accuracy and consistency. To parameterize the T-P  proRile,  we  use  the  three  channel  (two optical, one infrared) analytic radiative equilibrium  model  as  described  in  Ref.  [76], which is based on the derivations by Ref. [77].', 'ATMO WASP-107b Retrievals': "For  the  NIRSpec  WASP-107  b  data,  we found  the  Rlexible  parameterized  P-T  proRile simply Rit to a simple isotherm, so we instead Rit for a single isothermal temperature for the atmosphere. Given the planet's atmosphere is far out of equilibrium, we Rit a constant VMR for each molecule. In addition to the cloud, we included the spectrally active species of H 2 H 2 , H 2 -He  (CIA)  opacities,  H 2 O[78],  CO 2 [79], CO[80], CH 4 [81], NH 3 [82], H 2 S[83], and SO 2 [84].  \nWe searched the G395H data for H 2 S, and can marginally improve the model Rits to the data,  but  its  inclusion  is  not  supported  with conRidence by the Bayesian evidence. Considerable  opacity  from  aerosols  are  also needed  to  Rit  the  spectrum,  which  is  in-line with previous HST results where H 2 O and He features are observed between 0.9 and 1.6 µ m peaking above the clouds [2 , 73] . We Rit the data with  a  grey  cloud  and  a  scattering  haze,  but found only a grey cloud was needed to Rit the data (see Extended Data Table 3). In addition, we found the choice of cloud parameterization did  not  have  a  strong  inRluence  on  the retrieved  abundances.  Fitting  the  grey  cloud with either a single uniform opacity or for a cloud-top pressure also gave similar results. A  \nnarrow feature of NH 3 is potentially found in the data at 3.0 microns, but similar to H 2 S, its identiRication  is  not  supported  with  high conRidence by the Bayesian evidence. NH 3 has been marginally detected at longer wavelengths  with  JWST/MIRI,  indicating  the molecule could be conRidently identiRied with a dedicated multi-wavelength study.  \nThe  retrieval  constraints  are  given  in Extended  Data  Table  2.  CO  is  found  to  have abundances of 10 -2 . 7±0 . 4 ,  which is slightly low relative to 40× solar values derived from H 2 O. While  low, the uncertainty on the CO abundance is large as the feature is subtle in the  data  and  H 2 O  and  clouds  help  mask  the signature. A confounding factor regarding CO is  a  resolution-linked-bias  (RLB)  effect [22 , 46] , where CO present in the stellar spectra dilutes the strong  molecular  line  cores  in  the planetary  transmission  spectrum.  This  does not affect H 2 O, CH 4 or CO 2 as those molecules  \nExtended  Data  Figure  4 WASP-107  b  retrieval posteriors. Shown is the distribution for the ATMO free-retrieval.  VMR  refers  to  the  Volume  Mixing Ratio  of  the  molecular  species.  1,  1.5,  and  2σ equivalent contours are shown. The 1D histograms show the marginalized parameter median value and 1σ range (red).  \n<!-- image -->  \nare not present in the stellar photosphere.  In  this  work,  we  applied  a correction to the CO abundance to account for the RLB effect.  \nOverall, we Rind a good Rit to the data with a 𝜒 3 2 =1.1 for 566 DOF and 10 free parameters. Our  retrieval  results  are  given  in  Extended Data  Table  2  and  Extended  Data  Fig.  4.  To estimate  the  detection  conRidence  of  each molecule  identiRied,  we  re-ran  the  retrieval leaving  out  the  molecule  in  question  and computed the detection signiRicance using the Bayesian evidence between the models with and  without  the  molecule.  We  report  the results where H 2 S and NH 3 are included in the model,  though  the  G395H  data  are  not sufRicient to conRidently detect either species. We  report  the  abundances  and  detection signiRicances  from  the ATMO results,  as  they can  be  directly  used  to  compare  against  the non-equilibrium  models  presented  in  the main text.", 'ATMO WASP-107b Forward nonequilibrium chemistry Models': "It is computationally infeasible to currently run the ATMO retrieval with the full non-equilibrium photochemistry selfconsistently computed at every model evaluation 'on the Rly'. Instead, we adopt a twostep grid-retrieval approach, Rirst computing a grid  of  non-equilibrium  chemistry  values which are then Rit against the retrieved VMR abundances. As we use the same ATMO model setup  for  both  the  forward  and  retrieval modeling, the abundances computed between them can be self-consistently compared.  \nOur  use  of  a  1D  atmospheric  model  to interpret  the  non-equilibrium  chemistry  has several  assumptions.  The  Rirst  is  that  the atmosphere  can  be  considered  1D  and  is independent  of  both  latitude  and  longitude.  \n<!-- image -->  \nExtended Data Figure 5 Equilibrium chemistry estimation .  Shown  is  a  posterior  distribution  of metallicity, temperature, pressure and C/O equilibrium chemistry [88] values that are simultaneously  compatible  with  the  retrieved abundances of H 2 O, CO, CO 2 .  \n<!-- image -->  \nHot  and  ultra-hot  Jupiters  show  large  daynight temperature gradients [85] . Spitzer phase curves  show  these  differences  decrease  at lower T eq [86] . Thus, the latitude and longitude temperature  differences  for  warm  ∼750K planets  like  WASP-107b  are  expected  to  be modest. Another important assumption is that the parameters of T int and K zz are constant and assumed to be uniform with depth. Our model contains  a  single  convective  region  (see Extended Data Fig. 6), though the possibility of a  separate low-pressure convective zone has been  studied [87] .  Multiple  convective  regions would affect our interpretation of T int and the link between atmospheric and interior constraints.  In  addition,  our  modeling  also assumes a single K zz value  which  is  constant with altitude. Theoretical studies have predicted  that  K zz increases  with  altitude [13] . Higher K zz values at higher altitudes would not greatly  affect  our  results,  as  the  quench pressures  for  the  molecular  features  probed here  are  similar  (see  Extended  Data  Fig.  6). However,  if  multiple  convective  zones  are present, the use of a single K zz value may have to be re-visited.  \nTo  estimate  the  parameter  space  needed for the grid, we  Rirst  used  a  chemical  \nExtended  Data  Figure  6  Pressure-Temperature ProWiles . Shown  are  P-T  prociles  in  radiativeconvective equilibrium with T int values ranging from 100 to 500 K (grey). The T-P with the best-cit T int is shown (blue), with a shaded region showing where the model is dominated by convection. The quench pressures  for  CO 2 and  CH 4 are  also  depicted  along with Mg-Si condensation curves (dashed, dot dashed lines).  The  equilibrium  CH 4 =CO  equal  abundance curve  is  also  shown  (dotted  line),  with  the  CH 4 abundance dropping at increased temperatures. The brightness  temperatures  measured  from  Spitzer secondary  eclipse  observations  are  shown  from Ref.[91]. The corresponding pressures and ranges are derived from the best-cit model  contribution function, with the y-axis range encapsulating 80% of the  total  emitted  clux.  The  Spitzer  brightness temperatures are consistent with the best-citting T int = 450 K T-P procile.  \nequilibrium  model [88] and  assumed  a  single quench  pressure  to  estimate  the  posterior distribution of temperature, pressure, metallicity, and C/O ratio parameters that are consistent with the retrieved abundances (see Extended Data Fig. 5). This equilibrium model indicated  metallicites  near  50×  solar,  C/O ratios near 0.5 and temperatures near 1000 K at pressures just below a bar are needed to Rit the  observed  molecular  abundances.  These temperatures are reached at 1 bar only if the planet  has  an  intrinsic  temperature  greater than about 300 K with super-solar metalicities (see Extended Data Fig. 6). Intrinsic temperatures lower than 300 K are ruled out as CH 4 becomes be too abundant in the deep atmosphere,  such  that  no  amount  of  mixing could  sufRiciently  deplete  the  molecule.  We also  estimate  a  limit  on K zz to  be  less  than 10 13 . 5 cm 2 /s  based  on  requiring  velocities  to  \nExtended Data Figure 7 WASP-107b forward non-equilibrium chemistry model grid results. ( a ) Shown are the best-citting chemical abundances (within 1σ ) from the nonequilibrium chemistry models along with the retrieved values from the JWST transmission spectrum (datapoints). ( b ) The corner plot depicts the forward model grid points (red squares) along with the constraints in atmospheric metallicity ( Z/Z ⊙ ), intrinsic temperature (T int ), and eddy diffusion coefcicient (K zz ).  \n<!-- image -->  \nbe  less  than  the  local  sound  speed.  The presence  of  clouds  near  millibar  pressures also places a lower limit on K zz of ∼ 10 9 cm 2 /s, as signiRicant vertical mixing is needed to keep the aerosol particles aloft [13] .  \nWe  input  pressure-temperature  proRiles in radiative-convective  equilibrium,  using intrinsic temperatures ( T int ) of 300 to 500 K in steps of 50 K along with a T int of 425 K. With these  T-P  proRiles,  we  computed  the  nonequilibrium  chemistry  as  described  in  Ref. [50],  using  metallicities  ( Z )  between  20  and 50×  solar  in  steps  of  5×,  and  ten  log 10 [ K zz (cm 2 /s)] values ranging from 11 to 13. A K6V star was used for our input to the photochemical model [89] . Each nonequilibrium  model  was  integrated  to  1×10 8 sec, which we found was sufRicient such that the  abundances  did  not  evolve  further.  We assumed  a  solar  C/O  ratio,  which  is  also consistent  with  WASP-107A  from  Ref.  [90] who found values of C/O=0.5±0.1. We Rind the C/O  ratio  does  not  differ  substantially  from the  solar  or  host-star  value  (see  Extended Data Fig. 5) and we subsequently ran low (0.1 & 0.2) and high (0.7) non-equilibrium chemistry  cases  which  did  not  improve  the Rits.  \nFor this grid of models, we then calculated the χ 2 for each grid-model, using the retrieved  abundances  for  H 2 O,  CO,  CO 2 ,  CH 4 and SO 2 in Extended Data Table 2. We did not use the H 2 S or NH 3 abundances, as they are not  \nfully supported by the data and the errors in any  case  are  large.  The  best-Rit  model  has  a good χ 2 of 4.1 when Ritting the 5 abundances with  3  grid-parameters  (see  Fig.  3  and Extended Data Fig. 7). The grid-posterior can be seen in Extended Data Fig. 7, where each model was given a weight proportional to it's probability, P , calculated with P = 𝑒 !4 % /2 . From the  marginalized  grid-posterior,  we  Rit  a Gaussian  to  the  distributions  and  report  the Ritted Z/Z ⊙ , T int and K zz values  in  Extended Data Table 2.  \nWe  Rind  the  molecular  constraints  to  be highly constraining for both T int and K zz . Lower vertical mixing rates generally require higher intrinsic  temperatures  to  deplete  CH 4 to similar  values.  However,  if T int becomes  too high  it  over-depletes  CH 4 relative  to  CO 2 .  In addition, SO 2 helps provide an upper bound on K zz as SO 2 is sensitive to both the photochemistry, needed  to produce the species at low pressures, and vertical mixing. Higher  values  of K zz mix  the  species  from deeper pressures where the abundances are lower,  while  lower K zz values  allow  the photochemistry to build up the species near 0.1 mbar pressures.", 'NEMESIS free retrievals': 'NEMESIS is  a  free-chemistry  radiative transfer and retrieval code, initially developed for  solar  system  applications [92] .  It  couples  a  \nExtended Data Figure 8 Interior structure modeling constraints. A corner plot of the posterior mass ( M J )), radius ( R J ), envelope metallicity (unitless), core mass ( M ⊕ ), and intrinsic temperature (K). The model inputs (from observations) are shown in the upper-right, and the priors were weakly-informative. The overall bulk metallicity is set by M , R , and T int , and can be seen as an arc in Z e -M c space. Our atmospheric constraint restricts us to a section of this arc; without it, the two parameters would be fully degenerate, running from M c = 0 on one side to Z e = 0 on the other, though the effect on Z p would be much more limited. The intrinsic temperature is signicicantly higher than unheated evolution models would produce and is thus evidence of tidal heating (see text).  \n<!-- image -->  \ncorrelated-k  [56]  radiative  transfer  scheme with  the PyMul5Nest [68-70,  93]  Nested Sampling algorithm [94]. It has been extensively  applied  to  spectra  of  hot  Jupiter exoplanets (e.g. [95-97]).  \nThe retrievals for WASP-107b incorporate abundances of the gases H 2 O (line data: [98]), CO 2 [99], CO [100], CH 4 [101], SO 2 [84], NH 3 [102], HCN [103] and H 2 S [104]. For each of the gas abundances, we specify a loguniform  prior  spanning  10 -12 to  10 -0 . 5 .  The rest of the atmosphere is composed of H 2 and He  with  a  ratio  of  0.8547:0.1453.  Collisioninduced  absorption  for  H 2 and  He  is  taken from [105] and [106].  \nOther retrieved properties are an isothermal temperature with a uniform prior and a range of 300 - 1000 K, and a grey cloud top  pressure  with  a  log-uniform  prior  and  a range of 10 -8 - 100 bars. We also retrieve the planetary  radius  at  a  reference  pressure  of  \n100 bars. The retrieved abundances are given in Extended Data Table 2. Additional retrievals were run which had a more Rlexible T-P proRile in  addition  to  retrievals  with  patchy-clouds and enstatite clouds, though were not favored statistically over the simpler model.', 'Interior Structure Models': 'The constraints we found for the intrinsic temperature  of  WASP-107  b  have  important implications  for  the  interior  structure  of  the planet.  To  investigate  these,  we  use  the interior structure models of Ref. [39], updated to use the H/He EOS [107] and parameterize the amount of metal in the core vs mixed into the envelope. As in Ref. [39], we assume the metal is a 50-50 mixture of rock and ice.  \nTo  match our models to WASP-107 b, we use  a  Bayesian  retrieval  approach  similar  to the  one  used  in  Ref.  [108].  However,  our measurement  of T int determines  the  thermal  \nstate of the  plane  rather  than  thermal evolution.  The  parameters  of  the  statistical model were therefore the mass of the planet M ,  the  metallicity  of  the  envelope Z e (a  mass fraction),  the  core  mass M c ,  and  the  speciRic entropy  of  the  envelope s .  From  these,  our forward model calculates the radius and T int of the planet. The model was constrained by four normally-distributed observations: the mass, the  radius,  the  atmospheric  metallicity,  and T int .  These  are  constraining  enough  that  we can choose very uninformative priors just to keep the parameters inside model bounds: a uniform  mass  prior  from  0.01  to  30 M J ,  a uniform Z env from 0 to 1, a uniform core mass from 0 to M J (thus conditional on M but still proper), and a uniform entropy prior from 5 to 11 k b / baryon. We sampled from the posterior using the Metropolis-Hastings MCMC algorithm and veriRied convergence with the auto-correlation plots and the Gelman-Rubin statistic [109] .  \nOur interior model retrievals (See Extended  Data  Fig.  8)  Rind  a  planet  that contains similar amounts of H/He vs heavier elements, with Z p = 0 . 608 ± 0 . 046. This seems reasonable  for  a  planet  of  this  mass:  it accreted  a  substantial  amount  of  material from the disk, but never reached the runaway gas  accretion  stage.  However,  this  is  in  stark contrast to previous estimates of the planet\'s composition, which saw it as having substantially larger quantities of H/He: > 85% H/He from Ref.  [10]!  The  reason  is  that  our measured T int is much hotter than a standard thermal  evolution  model  would  suggest;  we would expect the planet to have cooled below our 2 σ lower bound of 300 K within tens of Myr. of formation. Instead, it is clear that the planet is being inRlated by an extra heat source despite  being  too  cool  to  experience  hot Jupiter-type inRlation [110] . Instead, a mechanism  such  as  tidal  heating [111,112,113] , previously  suspected  to  be  operating  on WASP-107  b [10 , 114] ,  is  warming  the  interior. These models propose that the eccentricity of WASP-107  b  is  excited  by  WASP-107  c,  but then  damped  out  through  tidal  interaction  \nwith the star; the resulting energy is deposited in  the  interior  of  the  planet.  Our  large measured T int is  evidence  that  this  process could be occurring, with a precise eccentricity further capable of constraining the mechanism.  \nAnother interesting result of our interior structure models is that it puts constraints on the mass of the planet\'s core. The mass, radius, and T int already constrain the overall metallicity of the planet (more metal means a smaller planet) to Z p = 63.5 !\'.( %)&.* %, but we also have  a  measurement  of  the  atmospheric metallicity  of  the  planet.  This  allows  us  to make a modestly better constraint on Z (see previous paragraph); more importantly, metal seen  in  the  bulk  but  not  in  the  atmosphere must  be  hidden  in  the  interior  in  a  core  or composition  layers  [see  Ref  108,  for  further discussion]. Assuming a uniform composition core  gives  us 𝑀 6 = 11.5 !".$ %".& M ⊕ .  Importantly, this  range  excludes  zero,  meaning  that  we have  detected  the  presence  of  a  core!  The exact  structure  of  the  interior  may  not  be exactly  an  envelope-on-core  model,  but  may be more like Neptune and Uranus with a rocky core, water envelope, then a H/He envelope [36] .  Alternatively,  the  core  may  be diffuse and/or layered as Jupiter\'s is thought to be [37 , 38] . Nevertheless, our result that a core exists is not affected by these possibilities: one cannot propose a layered core without a core in the Rirst place.', 'Data availability': 'The data used in this paper are associated with JWST program GO 1224 (PI Birkmann) and are publicly available from the Mikulski Archive for Space Telescopes (https://mast.stsci.edu) from 23 June 2024. The data products in Figures 1, 2, 3 are available here:  \nhttps://doi.org/10.5281/zenodo.10891400.', 'Code availability': 'The codes used in this publication to extract, reduce, and analyze the data are as follows; STScI JWST Calibration pipeline  \n(https://github.com/spacetelescope/jwst),  \nFIREFLy  \n[22, 42] And TEATRO  \n(https://github.com/ncrouzet/TEATRO). In  \naddition,  these made use ExoTiC-LD [120] (https://exotic-ld.readthedocs.io/en/latest/), Emcee (https://emcee.readthedocs.io/en/stable/) [121] , which uses the python libraries scipy[122] numpy[123] astropy[124] and matplotlib[125] . Model and retrievals were generated using ATMO , a proprietary code extensively described in Refs. [20, 47, 48, 49, 50, 51], and NEMESIS [92]  \n(https://github.com/nemesiscode/radtrancode).  \nAcknowledgments This work is based on observations made with the NASA/ESA/CSA JWST. The data were obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Institute,  which  is  operated  by  the  Association  of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127 for JWST.  \nAuthors contributions D.K.S. led the data analysis and  modeling.  Z.R.,  N.E.  and  N.C.  provided  data analysis and input. J.B., Z.R. provided atmospheric models.  D.T.  provided  planetary  interior  models. S.M.B. led the observational setup and execution of the program. R.C.C., N.K.L., E.K.H.L provided support interpreting  the  results.  C.A.O.,  T.L.B.,  S.M.B.,  P. F. , G.G.,  R.M.,  E.M.,  B.R.,  M.S,  J.A.V.  contributed  to  the NIRSpec instrument and GTO team. The manuscript was written by D.K.S. along with D.T. J.B. and P.T.  \nCompeting  interests The  authors  declare  no competing interests.', 'Correspondence and requests for materials': "should be addressed to David K. Sing (dsing@jhu.edu).  \nReprints and permissions information is available at http://nature.com/reprints  \n- [42] Rustamkulov, Z., Sing, D. K., Liu, R. & Wang, A. Analysis of a JWST NIRSpec Lab Time Series: Characterizing Systematics, Recovering Exoplanet Transit Spectroscopy, and Constraining a Noise Floor. Astrophys. J. L. 928 , L7 (2022).\n- [43] Kipping, D. M. Efcicient, uninformative sampling  of  limb  darkening  coefcicients  for two-parameter laws. Mon. Not. R. Astron. Soc. 435 , 2152-2160 (2013).\n- [44] Magic, Z., Chiavassa, A., Collet, R. & Asplund, M. The  Stagger-grid: A grid of 3D  stellar atmosphere  models.  IV. Limb  darkening coefcicients. Astron. Astrophys. 573 , A90 (2015).\n- [45] Dai, F. & Winn, J. N. The Oblique Orbit of WASP107b from K2 Photometry. Astron. J. 153 , 205 (2017).\n- [46] Deming, D. & Sheppard, K. Spectral Resolutionlinked Bias in Transit Spectroscopy of Extrasolar  Planets. Astrophys.  J.  L. 841 , L3 (2017).\n- [47] Amundsen,  D.  S. et  al. Accuracy  tests  of radiation  schemes  used  in  hot  Jupiter  global circulation models. Astron. Astrophys. 564 , A59 (2014).\n- [48] Tremblin,  P. et  al. Fingering  Convection  and Cloudless  Models  for  Cool  Brown  Dwarf Atmospheres. Astrophys. J. L. 804 , L17 (2015).\n- [49] Tremblin,  P. et  al. Cloudless Atmospheres for L/T  Dwarfs  and  Extrasolar  Giant  Planets. Astrophys. J. L. 817 , L19 (2016).\n- [50] Drummond, B. et al. The effects of consistent chemical kinetics calculations on the pressuretemperature prociles and emission spectra of hot  Jupiters. Astron.  Astrophys. 594 , A69 (2016).\n- [51] Goyal,  J.  M. et  al. A  library  of  ATMO  forward model  transmission  spectra  for  hot  Jupiter exoplanets. Mon.  Not.  R.  Astron.  Soc. 474 , 5158-5185 (2018).\n- [52] Edwards,  J.  M.  &  Slingo,  A.  Studies  with  a clexible  new  radiation  code.  I:  Choosing  a conciguration for a large-scale model. Quarterly  Journal  of  the  Royal  Meteorological Society 122 , 689-719 (1996).\n- [53] Baudino, J. L. et al. Interpreting the photometry and spectroscopy of directly imaged planets: a new atmospheric model applied to β Pictoris b and  SPHERE  observations. Astron.  Astrophys. 582 , A83 (2015).\n- [54] Molliè re,  P.,  van  Boekel,  R.,  Dullemond,  C., Henning, T. & Mordasini, C. Model Atmospheres  of  Irradiated  Exoplanets:  The Incluence  of  Stellar  Parameters,  Metallicity, and the C/O Ratio. Astrophys. J. 813 , 47 (2015).\n- [55] Baudino,  J.-L. et  al. Toward  the  Analysis  of JWST Exoplanet Spectra: Identifying Troublesome  Model  Parameters. Astrophys.  J. 850 , 150 (2017).\n- [56] Lacis,  A.  A.  &  Oinas,  V.  A  description  of  the correlated-k distribution method for modelling nongray gaseous absorption, thermal  emission,  and  multiple  scattering  in vertically inhomogeneous  atmospheres. J. Geophys. Res. 96 , 9027-9064 (1991).\n- [57] Goyal,  J.  M. et  al. A  library  of  ATMO  forward model  transmission  spectra  for  hot  Jupiter\n- exoplanets. Mon.  Not.  R.  Astron.  Soc. 474 , 5158-5185 (2018).\n- [58] Goyal,  J.  M. et  al. A  library  of  self-consistent simulated exoplanet atmospheres. Mon. Not. R. Astron. Soc. 498 , 4680-4704 (2020).\n- [59] Gordon, S. & McBride, B. J. Computer program for calculation of complex chemical equilibrium  compositions  and  applications. part  1:  Analysis. NASA  Reference  Publication 1311 (1994) .\n- [60] McBride,  B.  J.  Coefcicients  for  calculating thermodynamic  and  transport  properties  of individual  species. National  Aeronautics  and Space  Administration,  OfPice  of  Management, ScientiPic  and  Technical  Information  Program 4513 (1993) .\n- [61] Asplund, M., Grevesse, N., Sauval, A. J. & Scott, P.   T h e   C h e m i c a l   C o m p o s i t i o n   o f   t h e   S u n . Annu. Rev. Astron. 47 , 481-522 (2009).\n- [62] Caffau, E., Ludwig, H. G., Steffen, M., Freytag, B. &  Bonifacio,  P.  Solar  Chemical  Abundances Determined  with  a  CO5BOLD  3D  Model Atmosphere. Sol. Phys. 268 , 255-269 (2011).\n- [63] Goyal, J. M. et al. Fully scalable forward model grid  of  exoplanet  transmission  spectra. Mon. Not. R. Astron. Soc. 482 , 4503-4513 (2019).\n- [64] Venot,  O. et  al. A  chemical  model  for  the atmosphere of hot Jupiters. Astron. Astrophys. 546 , A43 (2012).\n- [65] Tsai,  S.-M. et  al. A  Comparative  Study  of Atmospheric Chemistry with VULCAN. Astrophys. J. 923 , 264 (2021).\n- [66] Venot, O. et al. New chemical scheme for giant planet thermochemistry. Update of the methanol chemistry and new reduced chemical scheme. Astron. Astrophys. 634 ,  A78 (2020).\n- [67] Lecavelier  Des  Etangs,  A.,  Pont,  F.,  VidalMadjar, A. & Sing, D. Rayleigh scattering in the transit  spectrum  of  HD  189733b. Astron. Astrophys. 481 , L83-L86 (2008).\n- [68] Feroz,  F.  &  Hobson,  M.  P.  Multimodal  nested sampling: an efcicient and robust alternative to Markov  Chain  Monte  Carlo  methods  for astronomical data analyses. MNRAS 384 , 449463 (2008).\n- [69] Feroz, F., Hobson,  M.  P. & Bridges, M. MULTINEST: an efcicient and robust Bayesian inference  tool  for  cosmology  and  particle physics. MNRAS 398 , 1601-1614 (2009).\n- [70] Feroz, F., Hobson, M. P., Cameron, E. & Pettitt, A. N. Importance  Nested  Sampling  and  the MultiNest Algorithm. Open J. of Astrophysics 2 , 10 (2019).\n- [71] Evans,  T.  M. et  al. An  ultrahot  gas-giant exoplanet  with  a  stratosphere. Nature 548 , 58-61 (2017).\n- [72] Wakeford,  H.  R. et  al. HAT-P-26b: A Neptunemass exoplanet with a well-constrained heavy element  abundance. Science 356 , 628-631 (2017).\n- [73] Spake,  J.  J. et  al. Helium  in  the  eroding atmosphere of an exoplanet. Nature 557 ,  6870 (2018).\n- [74] Nikolov, N. et al. An absolute sodium abundance  for  a  cloud-free  'hot  Saturn' exoplanet. Nature 557 , 526-529 (2018).\n- [75] Carter, A. L. et al. Detection of Na, K, and H 2 O in the hazy atmosphere of WASP-6b. Mon. Not. R. Astron. Soc. 494 , 5449-5472 (2020).\n- [76] Line,  M.  R. et  al. Information  Content  of Exoplanetary Transit Spectra: An Initial Look. Astrophys. J. 749 , 93 (2012).\n- [77] Guillot,  T.  On  the  radiative  equilibrium  of irradiated planetary atmospheres. Astron. Astrophys. 520 , A27 (2010).\n- [78] Barber,  R.  J.,  Tennyson,  J.,  Harris,  G.  J.  & Tolchenov,  R.  N.  A  highaccuracy  computed water  line  list. Mon. Not.  R.  Astron.  Soc. 368 , 1087- 1094 (2006).\n- [79] Tashkun,  S.  &  Perevalov,  V.  Cdsd-4000:  Highresolution,  hightemperature  carbon  dioxide spectroscopic databank. Journal of Quantitative Spectroscopy and Radiative Transfer 112 , 1403-1410 (2011).\n- [80] Rothman, L. et al. Hitemp, the hightemperature molecular spectroscopic database. Journal of Quantitative Spectroscopy and Radiative Transfer 111 , 2139-2150 (2010). xVIth Symposium on High Resolution Molecular Spectroscopy (HighRus-2009) .\n- [81] Yurchenko, S. N. & Tennyson, J. ExoMol line lists -  IV.  The  rotation-vibration  spectrum  of methane up to 1500 K. Monthly Notices of the Royal  Astronomical  Society 440 ,  1649-1661 (2014).\n- [82] Yurchenko, S. N., Barber, R. J. & Tennyson, J. A variationally  computed  line  list  for  hot  NH 3 . Mon.  Not.  R.  Astron.  Soc. 413 , 1828-1834 (2011).\n- [83] Rothman,  L. et  al. The  hitran2012  molecular spectroscopic database. Journal of Quantitative Spectroscopy and Radiative Transfer 130 , 4-50 (2013).\n- [84] Underwood, D. S. et al. ExoMol molecular line lists  -  XIV.  The  rotationvibration  spectrum  of hot SO 2 . Mon. Not. R. Astron. Soc. 459 ,  38903899 (2016).\n- [85] Mikal-Evans, T. et al. Diurnal variations in the stratosphere  of  the  ultrahot  giant  exoplanet WASP-121b. Nature  Astronomy 6 , 471-479 (2022).\n- [86] Bell, T. J. et al. A comprehensive reanalysis of Spitzer's 4.5 µ m phase curves, and the phase variations of the ultra-hot Jupiters MASCARA1b and KELT-16b. Mon. Not. R. Astron. Soc. 504 , 3316-3337 (2021).\n- [87] Guillot,  T.  &  Showman,  A.  P.  Evolution  of  '51 Pegasus b-like' planets. Astron. Astrophys. 385 , 156-165 (2002).\n- [88] Cubillos, P., Blecic, J. & Fossati, L. Radiative and Chemical Equilibrium Calculations with Application to Exoplanets. journal (2022) .\n- [89] France, K. et al. The MUSCLES Treasury Survey. I.  Motivation and Overview. Astrophys. J. 820 , 89 (2016).\n- [90] Hejazi, N. et  al. Elemental Abundances of the Super-Neptune  WASP107b's  Host  Star  Using High-resolution,  Near-infrared  Spectroscopy. Astrophys. J. 949 , 79 (2023).\n- [91] Deming, D. et al. Emergent Spectral Fluxes of Hot  Jupiters:  An  Abrupt  Rise  in  Dayside Brightness Temperature Under Strong Irradiation. Astron. J. 165 , 104 (2023).\n- [92] Irwin,  P.  G.  J. et  al. The  NEMESIS  planetary atmosphere  radiative  transfer  and  retrieval tool. JQSRT 109 , 1136-1150 (2008).\n- [93] Buchner, J. et al. X-ray spectral modelling of the AGN obscuring  region  in  the  CDFS:  Bayesian model selection and catalogue. Astron. Astrophys. 564 , A125 (2014).\n- [94] Krissansen-Totton,  J.,  Garland,  R.,  Irwin,  P.  & Catling, D. C. Detectability of Biosignatures in Anoxic  Atmospheres  with  the  James  Webb Space Telescope: A TRAPPIST-1e Case Study. AJ 156 , 114 (2018).\n- [95] Barstow, J. K., Aigrain, S., Irwin, P. G. J. & Sing, D. K.  A  Consistent  Retrieval  Analysis  of  10  Hot Jupiters Observed in Transmission. Astrophys. J. 834 , 50 (2017).\n- [96] Lewis, N. K. et al. Into the UV: The Atmosphere of  the  Hot  Jupiter  HAT-P-41b  Revealed. ApJL 902 , L19 (2020).\n- [97] Rathcke,  A.  D. et  al. HST PanCET Program: A Complete  Near-UV  to  Infrared  Transmission Spectrum  for  the  Hot  Jupiter  WASP-79b. AJ 162 , 138 (2021).\n- [98] Polyansky,  O.  L. et  al. ExoMol  molecular  line lists XXX: a complete highaccuracy line list for water. Mon.  Not.  R.  Astron.  Soc. 480 ,  25972608 (2018).\n- [99] Yurchenko, S. N., Mellor, T. M., Freedman, R. S. &  Tennyson,  J.  ExoMol  line  lists  -  XXXIX.  Rovibrational molecular line list for CO 2 . MNRAS 496 , 5282-5291 (2020).  \n[100] Li,  G. et  al. Rovibrational  Line  Lists  for Nine Isotopologues of the CO Molecule in the X 1 Σ + Ground Electronic State. Astrophys. J. S. 216 , 15 (2015).  \n- [101] Yurchenko, S. N., Amundsen,  D.  S., Tennyson, J. & Waldmann, I. P. A hybrid line list for  CH 4 and  hot  methane  continuum. Astron. Astrophys. 605 , A95 (2017).\n- [102] Coles, P. A., Yurchenko, S. N. & Tennyson, J. ExoMol  molecular  line  lists  -  XXXV.  A rotation-vibration  line  list  for  hot  ammonia. Mon.  Not.  R.  Astron.  Soc. 490 , 4638-4647 (2019).  \n[103] Barber, R. J. et al. ExoMol line lists - III. An improved  hot  rotationvibration  line  list  for HCN  and  HNC. MNRAS 437 , 1828-1835 (2014).  \n[104] Azzam, A. A. A., Tennyson, J., Yurchenko, S. N.  &  Naumenko,  O.  V.  ExoMol  molecular  line lists - XVI. The rotation-vibration spectrum of hot H2S. Monthly  Notices of the Royal Astronomical Society 460 , 4063-4074 (2016).  \n- [105] Borysow, A., Jorgensen, U. G. & Fu, Y. Hightemperature (1000-7000 K) collision-induced absorption  of  H'2  pairs  computed  from  the cirst  principles,  with  application  to  cool  and dense stellar atmospheres. J. Quant. Spectrosc. Radiat. Transf. 68 , 235-255 (2001).  \n[106] Borysow, A. Collision-induced absorption coefcicients  of  H 2 pairs  at  temperatures  from 60 K to 1000 K. A&A 390 , 779-782 (2002).  \n[107] Chabrier, G., Mazevet, S. & Soubiran, F. A New  Equation  of  State  for  Dense  HydrogenHelium Mixtures. Astrophys. J. 872 , 51 (2019).  \n[108] Thorngren, D. & Fortney, J. J. Connecting Giant Planet Atmosphere and Interior Modeling:  Constraints  on  Atmospheric  Metal Enrichment. Astrophys. J. L. 874 , L31 (2019).  \n[109] Gelman, A. & Rubin, D. B. Inference from Iterative Simulation Using Multiple Sequences. Statistical Science 7 , 457-472 (1992).  \n- [110] Miller,  N.  &  Fortney,  J.  J.  The  Heavyelement  Masses  of  Extrasolar  Giant  Planets, Revealed. Astrophys. J. L. 736 , L29 (2011).  \n[111] Bodenheimer, P. & Lin, D. N. C. Implications of Extrasolar Planets for Understanding Planet Formation. Annual Review  of  Earth  and  Planetary  Sciences 30 , 113-148 (2002).  \n[112] Jackson,  B.,  Greenberg,  R.  &  Barnes,  R. Tidal Heating of Extrasolar Planets. Astrophys. J. 681 , 1631-1638 (2008).  \n[113] Millholland,  S.  Tidally  Induced  Radius Inclation of Sub-Neptunes. Astrophys. J. 886 , 72 (2019).  \n[114] Millholland, S., Petigura, E. & Batygin, K. Tidal  Inclation  Reconciles  Low-density  SubSaturns with Core Accretion. Astrophys. J. 897 , 7 (2020).  \n[115] JWST  calibration  pipeline  developers. jwst:  Python  library  for  science  observations from the James Webb Space Telescope (2022). URL https:  \n//github.com/spacetelescope/jwst.  \n[116] CRDS  developers. CRDS: Calibration Reference  Data  System  for  HST  and  JWST (2022). URL  \nhttps://github.com/spacetelescope/crds.  \n[117] Foreman-Mackey,  D. et  al. exoplanet: Gradient-based  probabilistic  inference  for exoplanet  data  &  other  astronomical  time series. arXiv e-prints arXiv:2105.01994 (2021).  \n[118] Foreman-Mackey,  D. et  al. exoplanetdev/exoplanet v0.5.1 Zenodo (2021).  \n[119] Morello, G. et al. The ExoTETHyS Package:  Tools  for  Exoplanetary  Transits around Host Stars. Astron. J. 159 , 75 (2020).  \n[120] Grant, D. &  Wakeford,  H.  R.  ExoTiC/ExoTiC-LD:  ExoTiC-LD  v3.0.0.  Zenodo (2022).  \n[121] Foreman-Mackey, D., Hogg, D. W., Lang, D. &  Goodman,  J.  emcee:  The  MCMC  Hammer. Publ. Astron. Soc. Pacif. 125 , 306 (2013).  \n[122] Virtanen, P. et al. SciPy 1.0: Fundamental Algorithms for Scienticic Computing in Python. Nature Methods 17 , 261-272 (2020).  \n[123] Harris,  C.  R. et  al. Array  programming with NumPy. Nature 585 , 357-362 (2020).  \n[124] Astropy Collaboration et al. The Astropy Project: Building an Open science Project and Status of the v2.0 Core Package. Astron. J. 156 , 123 (2018).  \n[125] Hunter,  J.  D.  Matplotlib:  A  2d  graphics environment. Computing in Science & Engineering 9 , 90-95 (2007)."}