Atmospheric Characterization of the Sub-Neptune Exoplanet K2-18b : a Bayesian Analysis of its Possible Structure and Composition

K2-18b is a temperate habitable-zone Sub-Neptune that has attracted significant interest due to its potential to host a H/He-rich envelope and to contain H2O traces in its atmosphere. Transmission spectroscopy with JWST has revealed the presence of the carbon-bearing molecules CH4 and CO2 along with...

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Autores:
Zapata Marín, Juan Esteban
Tipo de recurso:
Trabajo de grado de pregrado
Fecha de publicación:
2025
Institución:
Universidad de Antioquia
Repositorio:
Repositorio UdeA
Idioma:
eng
OAI Identifier:
oai:bibliotecadigital.udea.edu.co:10495/46043
Acceso en línea:
https://hdl.handle.net/10495/46043
Palabra clave:
Extrasolar planets
Planetas extrasolares
Planets - Atmospheres
Planetas - Atmósferas
Bayesian statistical decision theory
Teoría bayesiana de decisiones estadísticas
Spectrum analysis
Análisis espectral
Atmospheric retrievals
http://id.loc.gov/authorities/subjects/sh96011308
http://id.loc.gov/authorities/subjects/sh85102654
http://id.loc.gov/authorities/subjects/sh85012506
http://id.loc.gov/authorities/subjects/sh85126423
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openAccess
License
http://creativecommons.org/licenses/by-nc-sa/4.0/
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network_name_str Repositorio UdeA
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dc.title.eng.fl_str_mv Atmospheric Characterization of the Sub-Neptune Exoplanet K2-18b : a Bayesian Analysis of its Possible Structure and Composition
title Atmospheric Characterization of the Sub-Neptune Exoplanet K2-18b : a Bayesian Analysis of its Possible Structure and Composition
spellingShingle Atmospheric Characterization of the Sub-Neptune Exoplanet K2-18b : a Bayesian Analysis of its Possible Structure and Composition
Extrasolar planets
Planetas extrasolares
Planets - Atmospheres
Planetas - Atmósferas
Bayesian statistical decision theory
Teoría bayesiana de decisiones estadísticas
Spectrum analysis
Análisis espectral
Atmospheric retrievals
http://id.loc.gov/authorities/subjects/sh96011308
http://id.loc.gov/authorities/subjects/sh85102654
http://id.loc.gov/authorities/subjects/sh85012506
http://id.loc.gov/authorities/subjects/sh85126423
title_short Atmospheric Characterization of the Sub-Neptune Exoplanet K2-18b : a Bayesian Analysis of its Possible Structure and Composition
title_full Atmospheric Characterization of the Sub-Neptune Exoplanet K2-18b : a Bayesian Analysis of its Possible Structure and Composition
title_fullStr Atmospheric Characterization of the Sub-Neptune Exoplanet K2-18b : a Bayesian Analysis of its Possible Structure and Composition
title_full_unstemmed Atmospheric Characterization of the Sub-Neptune Exoplanet K2-18b : a Bayesian Analysis of its Possible Structure and Composition
title_sort Atmospheric Characterization of the Sub-Neptune Exoplanet K2-18b : a Bayesian Analysis of its Possible Structure and Composition
dc.creator.fl_str_mv Zapata Marín, Juan Esteban
dc.contributor.advisor.none.fl_str_mv Cuartas Restrepo, Pablo Andrés
dc.contributor.author.none.fl_str_mv Zapata Marín, Juan Esteban
dc.contributor.researchgroup.none.fl_str_mv Grupo de Física y Astrofísica Computacional (FACOM)
dc.subject.lcsh.none.fl_str_mv Extrasolar planets
Planetas extrasolares
Planets - Atmospheres
Planetas - Atmósferas
Bayesian statistical decision theory
Teoría bayesiana de decisiones estadísticas
Spectrum analysis
Análisis espectral
topic Extrasolar planets
Planetas extrasolares
Planets - Atmospheres
Planetas - Atmósferas
Bayesian statistical decision theory
Teoría bayesiana de decisiones estadísticas
Spectrum analysis
Análisis espectral
Atmospheric retrievals
http://id.loc.gov/authorities/subjects/sh96011308
http://id.loc.gov/authorities/subjects/sh85102654
http://id.loc.gov/authorities/subjects/sh85012506
http://id.loc.gov/authorities/subjects/sh85126423
dc.subject.proposal.eng.fl_str_mv Atmospheric retrievals
dc.subject.lcshuri.none.fl_str_mv http://id.loc.gov/authorities/subjects/sh96011308
http://id.loc.gov/authorities/subjects/sh85102654
http://id.loc.gov/authorities/subjects/sh85012506
http://id.loc.gov/authorities/subjects/sh85126423
description K2-18b is a temperate habitable-zone Sub-Neptune that has attracted significant interest due to its potential to host a H/He-rich envelope and to contain H2O traces in its atmosphere. Transmission spectroscopy with JWST has revealed the presence of the carbon-bearing molecules CH4 and CO2 along with the non-detection of NH3, aligning with the "Hycean" world scenario, which consists of a shallow H2-dominated atmosphere overlaying a potentially liquid water surface ocean, creating optimal conditions that favour habitability. Recent studies have proposed alternative scenarios compatible with observations, including a mini-Neptune scenario with a deep atmosphere and no well-defined surface, or a lava world scenario consisting of a molten magma ocean on its surface. Here, we report a Bayesian retrieval analysis of K2-18b’s transmission spectrum, exploring several models for its chemical composition, temperature profile, and cloud properties. We evaluate a set of not self-consistent atmospheric retrievals aiming to constrain the atmospheric properties, examining the detection significance of key molecular species and investigating how grey and non-grey cloud treatments impact the inferred structure and composition. For both cloud treatments, we find detection significances for CH4 and CO2 of 5 σ and 3 respectively, while finding no significant evidence for H2O and NH3, in agreement with previous studies. Additionally, we find that a cloud-free atmosphere for K2-18b is strongly ruled out by observations. Our results suggest that a model consisting of non-grey cloud treatment and following a semi-ideal temperature-pressure profile provides the best fit to the observed spectrum.
publishDate 2025
dc.date.accessioned.none.fl_str_mv 2025-05-21T19:10:08Z
dc.date.issued.none.fl_str_mv 2025
dc.type.none.fl_str_mv Trabajo de grado - Pregrado
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dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/10495/46043
url https://hdl.handle.net/10495/46043
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.references.none.fl_str_mv Ackerman A. S., Marley M. S., 2001, The Astrophysical Journal, 556, 872–884
Batalha N. M., 2014, Proceedings of the National Academy of Sciences, 111, 12647
Benneke B., et al., 2019, The Astrophysical Journal Letters, 887, L14
Borysow J., Frommhold L., Birnbaum G., 1988, Astrophys. J.; (United States), 326
Borysow A., Jørgensen U. G., Fu Y., 2001, Journal of Quantitative Spectroscopy and Radiative Transfer, 68, 235
Coles P. A., Yurchenko S. N., Tennyson J., 2019, Monthly Notices of the Royal Astronomical Society, 490, 4638
Feroz F., Hobson M. P., Bridges M., 2009, Monthly Notices of the Royal Astronomical Society, 398, 1601–1614
Guillot T., 2010, arXiv: Earth and Planetary Astrophysics
Lueber, Anna Novais, Aline Fisher, Chloe Heng, Kevin 2024, A&A, 687, A110
Madhusudhan N., Seager S., 2009, The Astrophysical Journal, 707, 24–39
Madhusudhan N., Piette A., Constantinou S., 2021, The Astrophysical Journal, 918, 1
Madhusudhan N., Sarkar S., Constantinou S., Holmberg M., Piette A., Moses J., 2023, The Astrophysical Journal Letters, 956, L13
Mollière P., Wardenier J. P., van Boekel R., Henning T., Molaverdikhani K., Snellen I. A. G., 2019, Astronomy & Astrophysics, 627, A67
Polyansky O. L., Kyuberis A. A., Zobov N. F., Tennyson J., Yurchenko S. N., Lodi L., 2018, Monthly Notices of the Royal Astronomical Society, 480, 2597
Trotta R., 2008, Contemporary Physics, 49
Wogan N., Batalha N., Zahnle K., Krissansen-Totton J., Tsai S.-M., 2024, in AAS/Division for Extreme Solar Systems Abstracts. p. 625.15
Yurchenko, Sergei N. Amundsen, David S. Tennyson, Jonathan Waldmann, Ingo P. 2017, A&A, 605, A95
Yurchenko S. N., Mellor T. M., Freedman R. S., Tennyson J., 2020, Monthly Notices of the Royal Astronomical Society, 496, 5282
dc.rights.uri.none.fl_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
dc.rights.accessrights.none.fl_str_mv info:eu-repo/semantics/openAccess
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dc.format.extent.none.fl_str_mv 10 páginas
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dc.publisher.none.fl_str_mv Universidad de Antioquia
dc.publisher.program.none.fl_str_mv Astronomía
dc.publisher.department.none.fl_str_mv Instituto de Física
dc.publisher.place.none.fl_str_mv Medellín, Colombia
dc.publisher.faculty.none.fl_str_mv Facultad de Ciencias Exactas y Naturales
dc.publisher.branch.none.fl_str_mv Campus Medellín - Ciudad Universitaria
publisher.none.fl_str_mv Universidad de Antioquia
institution Universidad de Antioquia
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spelling Cuartas Restrepo, Pablo AndrésZapata Marín, Juan EstebanGrupo de Física y Astrofísica Computacional (FACOM)2025-05-21T19:10:08Z2025https://hdl.handle.net/10495/46043K2-18b is a temperate habitable-zone Sub-Neptune that has attracted significant interest due to its potential to host a H/He-rich envelope and to contain H2O traces in its atmosphere. Transmission spectroscopy with JWST has revealed the presence of the carbon-bearing molecules CH4 and CO2 along with the non-detection of NH3, aligning with the "Hycean" world scenario, which consists of a shallow H2-dominated atmosphere overlaying a potentially liquid water surface ocean, creating optimal conditions that favour habitability. Recent studies have proposed alternative scenarios compatible with observations, including a mini-Neptune scenario with a deep atmosphere and no well-defined surface, or a lava world scenario consisting of a molten magma ocean on its surface. Here, we report a Bayesian retrieval analysis of K2-18b’s transmission spectrum, exploring several models for its chemical composition, temperature profile, and cloud properties. We evaluate a set of not self-consistent atmospheric retrievals aiming to constrain the atmospheric properties, examining the detection significance of key molecular species and investigating how grey and non-grey cloud treatments impact the inferred structure and composition. For both cloud treatments, we find detection significances for CH4 and CO2 of 5 σ and 3 respectively, while finding no significant evidence for H2O and NH3, in agreement with previous studies. Additionally, we find that a cloud-free atmosphere for K2-18b is strongly ruled out by observations. Our results suggest that a model consisting of non-grey cloud treatment and following a semi-ideal temperature-pressure profile provides the best fit to the observed spectrum.Ciencias PlanetariasCOL0038262PregradoAstrónomo10 páginasapplication/pdfengUniversidad de AntioquiaAstronomíaInstituto de FísicaMedellín, ColombiaFacultad de Ciencias Exactas y NaturalesCampus Medellín - Ciudad Universitariahttp://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccessAttribution-NonCommercial-ShareAlike 4.0 Internationalhttp://purl.org/coar/access_right/c_abf2Extrasolar planetsPlanetas extrasolaresPlanets - AtmospheresPlanetas - AtmósferasBayesian statistical decision theoryTeoría bayesiana de decisiones estadísticasSpectrum analysisAnálisis espectralAtmospheric retrievalshttp://id.loc.gov/authorities/subjects/sh96011308http://id.loc.gov/authorities/subjects/sh85102654http://id.loc.gov/authorities/subjects/sh85012506http://id.loc.gov/authorities/subjects/sh85126423Atmospheric Characterization of the Sub-Neptune Exoplanet K2-18b : a Bayesian Analysis of its Possible Structure and CompositionTrabajo de grado - Pregradohttp://purl.org/coar/resource_type/c_7a1fhttp://purl.org/redcol/resource_type/TPTexthttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/publishedVersionAckerman A. S., Marley M. S., 2001, The Astrophysical Journal, 556, 872–884Batalha N. M., 2014, Proceedings of the National Academy of Sciences, 111, 12647Benneke B., et al., 2019, The Astrophysical Journal Letters, 887, L14Borysow J., Frommhold L., Birnbaum G., 1988, Astrophys. J.; (United States), 326Borysow A., Jørgensen U. G., Fu Y., 2001, Journal of Quantitative Spectroscopy and Radiative Transfer, 68, 235Coles P. A., Yurchenko S. N., Tennyson J., 2019, Monthly Notices of the Royal Astronomical Society, 490, 4638Feroz F., Hobson M. P., Bridges M., 2009, Monthly Notices of the Royal Astronomical Society, 398, 1601–1614Guillot T., 2010, arXiv: Earth and Planetary AstrophysicsLueber, Anna Novais, Aline Fisher, Chloe Heng, Kevin 2024, A&A, 687, A110Madhusudhan N., Seager S., 2009, The Astrophysical Journal, 707, 24–39Madhusudhan N., Piette A., Constantinou S., 2021, The Astrophysical Journal, 918, 1Madhusudhan N., Sarkar S., Constantinou S., Holmberg M., Piette A., Moses J., 2023, The Astrophysical Journal Letters, 956, L13Mollière P., Wardenier J. P., van Boekel R., Henning T., Molaverdikhani K., Snellen I. A. G., 2019, Astronomy & Astrophysics, 627, A67Polyansky O. L., Kyuberis A. A., Zobov N. F., Tennyson J., Yurchenko S. N., Lodi L., 2018, Monthly Notices of the Royal Astronomical Society, 480, 2597Trotta R., 2008, Contemporary Physics, 49Wogan N., Batalha N., Zahnle K., Krissansen-Totton J., Tsai S.-M., 2024, in AAS/Division for Extreme Solar Systems Abstracts. p. 625.15Yurchenko, Sergei N. Amundsen, David S. Tennyson, Jonathan Waldmann, Ingo P. 2017, A&A, 605, A95Yurchenko S. N., Mellor T. M., Freedman R. 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