Análisis de posibles compañeras en estrellas químicamente peculiares a partir de variaciones en la velocidad radial

Existe un conjunto de estrellas denominadas químicamente peculiares, cuyo enriquecimiento en elementos como nitrógeno, silicio y sodio ha despertado un gran interés en la comunidad científica. Una de las hipótesis más sólidas acerca de estos objetos sugiere que podrían tener una compañera binaria re...

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Autores:
González Troncoso, Alexander
Tipo de recurso:
Trabajo de grado de pregrado
Fecha de publicación:
2025
Institución:
Universidad de Antioquia
Repositorio:
Repositorio UdeA
Idioma:
spa
OAI Identifier:
oai:bibliotecadigital.udea.edu.co:10495/45848
Acceso en línea:
https://hdl.handle.net/10495/45848
https://github.com/AlexGTroncoso/Tesis_Astronomia_FACom/tree/main
https://github.com/AlexGTroncoso/Tesis_Astronomia_FACom/tree/main/Scientific%20production
https://alexgtroncoso.github.io/
Palabra clave:
Estrellas peculiares
Peculiar stars
Estrellas - Evolución
Stars - Evolution
Estrellas dobles - Espectros
Double stars - Spectra
Estrellas - Movimiento radial
Stars - Motion in line of sight
Método de Monte Carlo
Monte Carlo method
Astronomía - Procesamiento de datos
Astronomy - Data processing
Astrofísica
Astrophysics
http://id.loc.gov/authorities/subjects/sh87005497
http://id.loc.gov/authorities/subjects/sh85127430
http://id.loc.gov/authorities/subjects/sh92002196
http://id.loc.gov/authorities/subjects/sh85087032
http://id.loc.gov/authorities/subjects/sh88006526
http://id.loc.gov/authorities/subjects/sh85009032
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http://creativecommons.org/licenses/by-nc-sa/4.0/
id UDEA2_f499cde106b2dd5da45df453c0b1354c
oai_identifier_str oai:bibliotecadigital.udea.edu.co:10495/45848
network_acronym_str UDEA2
network_name_str Repositorio UdeA
repository_id_str
dc.title.spa.fl_str_mv Análisis de posibles compañeras en estrellas químicamente peculiares a partir de variaciones en la velocidad radial
dc.title.alternative.none.fl_str_mv Analizando los espectros de LSOM y SDSS para entender las poblaciones estelares de la galaxia
title Análisis de posibles compañeras en estrellas químicamente peculiares a partir de variaciones en la velocidad radial
spellingShingle Análisis de posibles compañeras en estrellas químicamente peculiares a partir de variaciones en la velocidad radial
Estrellas peculiares
Peculiar stars
Estrellas - Evolución
Stars - Evolution
Estrellas dobles - Espectros
Double stars - Spectra
Estrellas - Movimiento radial
Stars - Motion in line of sight
Método de Monte Carlo
Monte Carlo method
Astronomía - Procesamiento de datos
Astronomy - Data processing
Astrofísica
Astrophysics
http://id.loc.gov/authorities/subjects/sh87005497
http://id.loc.gov/authorities/subjects/sh85127430
http://id.loc.gov/authorities/subjects/sh92002196
http://id.loc.gov/authorities/subjects/sh85087032
http://id.loc.gov/authorities/subjects/sh88006526
http://id.loc.gov/authorities/subjects/sh85009032
title_short Análisis de posibles compañeras en estrellas químicamente peculiares a partir de variaciones en la velocidad radial
title_full Análisis de posibles compañeras en estrellas químicamente peculiares a partir de variaciones en la velocidad radial
title_fullStr Análisis de posibles compañeras en estrellas químicamente peculiares a partir de variaciones en la velocidad radial
title_full_unstemmed Análisis de posibles compañeras en estrellas químicamente peculiares a partir de variaciones en la velocidad radial
title_sort Análisis de posibles compañeras en estrellas químicamente peculiares a partir de variaciones en la velocidad radial
dc.creator.fl_str_mv González Troncoso, Alexander
dc.contributor.advisor.none.fl_str_mv Flor Torres, Lauren Melisa
González Díaz, Danilo
Muñoz Cuartas, Juan Carlos
dc.contributor.author.none.fl_str_mv González Troncoso, Alexander
dc.contributor.researchgroup.none.fl_str_mv Grupo de Física y Astrofísica Computacional (FACOM)
dc.contributor.jury.none.fl_str_mv Cuartas Restrepo, Pablo Andrés
Chaparro Molano, Germán
dc.subject.lcsh.none.fl_str_mv Estrellas peculiares
Peculiar stars
Estrellas - Evolución
Stars - Evolution
Estrellas dobles - Espectros
Double stars - Spectra
Estrellas - Movimiento radial
Stars - Motion in line of sight
Método de Monte Carlo
Monte Carlo method
Astronomía - Procesamiento de datos
Astronomy - Data processing
Astrofísica
Astrophysics
topic Estrellas peculiares
Peculiar stars
Estrellas - Evolución
Stars - Evolution
Estrellas dobles - Espectros
Double stars - Spectra
Estrellas - Movimiento radial
Stars - Motion in line of sight
Método de Monte Carlo
Monte Carlo method
Astronomía - Procesamiento de datos
Astronomy - Data processing
Astrofísica
Astrophysics
http://id.loc.gov/authorities/subjects/sh87005497
http://id.loc.gov/authorities/subjects/sh85127430
http://id.loc.gov/authorities/subjects/sh92002196
http://id.loc.gov/authorities/subjects/sh85087032
http://id.loc.gov/authorities/subjects/sh88006526
http://id.loc.gov/authorities/subjects/sh85009032
dc.subject.lcshuri.none.fl_str_mv http://id.loc.gov/authorities/subjects/sh87005497
http://id.loc.gov/authorities/subjects/sh85127430
http://id.loc.gov/authorities/subjects/sh92002196
http://id.loc.gov/authorities/subjects/sh85087032
http://id.loc.gov/authorities/subjects/sh88006526
http://id.loc.gov/authorities/subjects/sh85009032
description Existe un conjunto de estrellas denominadas químicamente peculiares, cuyo enriquecimiento en elementos como nitrógeno, silicio y sodio ha despertado un gran interés en la comunidad científica. Una de las hipótesis más sólidas acerca de estos objetos sugiere que podrían tener una compañera binaria responsable, al menos en parte, de dicho enriquecimiento. La caracterización de sistemas binarios con compañeras estelares o subestelares es fundamental para comprender mejor la formación y evolución estelar, siendo objetos esenciales en muchos campos de la astrofísica y en las estadísticas de multiplicidad estelar. Incluso las compañeras de masa planetaria son un observable de importancia fundamental. Para la física estelar, las binarias permiten la determinación precisa de las masas estelares, con una precisión inferior al porcentaje. Sin embargo, la identificación y clasificación precisa de estos objetos sigue siendo un desafío debido a la falta de datos informativos y a las mediciones limitadas de velocidad radial. Por esta razón, el objetivo de este trabajo es utilizar los datos del espectrógrafo FIDEOS del telescopio de 1m de La Silla, ubicado en Chile y tomados durante el año 2022, para proporcionar curvas de velocidad radial calculadas mediante el pipeline de CERES. De esta manera, se puede encontrar una posible órbita para estos objetos, utilizando el muestreador The Joker, que está especializado en el método de Monte Carlo personalizado para el problema de dos cuerpos. Este muestreador genera estimaciones en parámetros orbitales keplerianos a partir de observaciones de velocidad radial, incluso cuando los datos son escasos o muy ruidosos. Con estos parámetros, se realiza una estimación de la masa del posible compañero binario, identificando y clasificando el sistema. A través de este método, se lograron identificar ocho objetos variables, teniendo en cuenta la posible variación intrínseca que brinda el instrumento FIDEOS durante estas observaciones. De los objetos variables, se determinó que uno podría tener una posible compañera enana blanca con una masa de 0,5174+0,0021 −0,0024 M⊙, cinco podrían tener compañeras subestelares con masas en el rango de las enanas rojas y marrones, con masas entre 0,016+0,005 −0,003 y 0,12+0,12 −0,03M⊙, y dos muestran características de compañeros planetarios, específicamente con masas jovianas de 0,0078+0,0034 −0,0009 M⊙ y 0,00197+0,00014 −0,00005 M⊙. Estos hallazgos proporcionan nuevas perspectivas sobre la formación de sistemas binarios y subestelares, avanzando en el estudio de estos objetos químicamente peculiares. Además, sugieren la posibilidad de que el enriquecimiento químico específico de estos objetos esté relacionado con una gama de diferentes compañeros binarios, desde objetos estelares y subestelares hasta planetarios, destacando la necesidad de observaciones adicionales para confirmar y reforzar estos resultados.
publishDate 2025
dc.date.accessioned.none.fl_str_mv 2025-05-09T12:44:55Z
dc.date.issued.none.fl_str_mv 2025
dc.type.none.fl_str_mv Trabajo de grado - Pregrado
dc.type.coar.none.fl_str_mv http://purl.org/coar/resource_type/c_7a1f
dc.type.redcol.none.fl_str_mv http://purl.org/redcol/resource_type/TP
dc.type.content.none.fl_str_mv Text
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dc.type.driver.none.fl_str_mv info:eu-repo/semantics/bachelorThesis
dc.type.version.none.fl_str_mv info:eu-repo/semantics/draft
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dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/10495/45848
dc.identifier.url.none.fl_str_mv https://github.com/AlexGTroncoso/Tesis_Astronomia_FACom/tree/main
https://github.com/AlexGTroncoso/Tesis_Astronomia_FACom/tree/main/Scientific%20production
https://alexgtroncoso.github.io/
url https://hdl.handle.net/10495/45848
https://github.com/AlexGTroncoso/Tesis_Astronomia_FACom/tree/main
https://github.com/AlexGTroncoso/Tesis_Astronomia_FACom/tree/main/Scientific%20production
https://alexgtroncoso.github.io/
dc.language.iso.none.fl_str_mv spa
language spa
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spelling Flor Torres, Lauren MelisaGonzález Díaz, DaniloMuñoz Cuartas, Juan CarlosGonzález Troncoso, AlexanderGrupo de Física y Astrofísica Computacional (FACOM)Cuartas Restrepo, Pablo AndrésChaparro Molano, Germán2025-05-09T12:44:55Z2025https://hdl.handle.net/10495/45848https://github.com/AlexGTroncoso/Tesis_Astronomia_FACom/tree/mainhttps://github.com/AlexGTroncoso/Tesis_Astronomia_FACom/tree/main/Scientific%20productionhttps://alexgtroncoso.github.io/Existe un conjunto de estrellas denominadas químicamente peculiares, cuyo enriquecimiento en elementos como nitrógeno, silicio y sodio ha despertado un gran interés en la comunidad científica. Una de las hipótesis más sólidas acerca de estos objetos sugiere que podrían tener una compañera binaria responsable, al menos en parte, de dicho enriquecimiento. La caracterización de sistemas binarios con compañeras estelares o subestelares es fundamental para comprender mejor la formación y evolución estelar, siendo objetos esenciales en muchos campos de la astrofísica y en las estadísticas de multiplicidad estelar. Incluso las compañeras de masa planetaria son un observable de importancia fundamental. Para la física estelar, las binarias permiten la determinación precisa de las masas estelares, con una precisión inferior al porcentaje. Sin embargo, la identificación y clasificación precisa de estos objetos sigue siendo un desafío debido a la falta de datos informativos y a las mediciones limitadas de velocidad radial. Por esta razón, el objetivo de este trabajo es utilizar los datos del espectrógrafo FIDEOS del telescopio de 1m de La Silla, ubicado en Chile y tomados durante el año 2022, para proporcionar curvas de velocidad radial calculadas mediante el pipeline de CERES. De esta manera, se puede encontrar una posible órbita para estos objetos, utilizando el muestreador The Joker, que está especializado en el método de Monte Carlo personalizado para el problema de dos cuerpos. Este muestreador genera estimaciones en parámetros orbitales keplerianos a partir de observaciones de velocidad radial, incluso cuando los datos son escasos o muy ruidosos. Con estos parámetros, se realiza una estimación de la masa del posible compañero binario, identificando y clasificando el sistema. A través de este método, se lograron identificar ocho objetos variables, teniendo en cuenta la posible variación intrínseca que brinda el instrumento FIDEOS durante estas observaciones. De los objetos variables, se determinó que uno podría tener una posible compañera enana blanca con una masa de 0,5174+0,0021 −0,0024 M⊙, cinco podrían tener compañeras subestelares con masas en el rango de las enanas rojas y marrones, con masas entre 0,016+0,005 −0,003 y 0,12+0,12 −0,03M⊙, y dos muestran características de compañeros planetarios, específicamente con masas jovianas de 0,0078+0,0034 −0,0009 M⊙ y 0,00197+0,00014 −0,00005 M⊙. Estos hallazgos proporcionan nuevas perspectivas sobre la formación de sistemas binarios y subestelares, avanzando en el estudio de estos objetos químicamente peculiares. Además, sugieren la posibilidad de que el enriquecimiento químico específico de estos objetos esté relacionado con una gama de diferentes compañeros binarios, desde objetos estelares y subestelares hasta planetarios, destacando la necesidad de observaciones adicionales para confirmar y reforzar estos resultados.Astrofísica EstelarCOL0038262Trabajo de grado con distinción: Mención Especial.PregradoAstrónomo132 páginasapplication/pdfspaUniversidad 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_abf2Estrellas peculiaresPeculiar starsEstrellas - EvoluciónStars - EvolutionEstrellas dobles - EspectrosDouble stars - SpectraEstrellas - Movimiento radialStars - Motion in line of sightMétodo de Monte CarloMonte Carlo methodAstronomía - Procesamiento de datosAstronomy - Data processingAstrofísicaAstrophysicshttp://id.loc.gov/authorities/subjects/sh87005497http://id.loc.gov/authorities/subjects/sh85127430http://id.loc.gov/authorities/subjects/sh92002196http://id.loc.gov/authorities/subjects/sh85087032http://id.loc.gov/authorities/subjects/sh88006526http://id.loc.gov/authorities/subjects/sh85009032Análisis de posibles compañeras en estrellas químicamente peculiares a partir de variaciones en la velocidad radialAnalizando los espectros de LSOM y SDSS para entender las poblaciones estelares de la galaxiaTrabajo de grado - Pregradohttp://purl.org/coar/resource_type/c_7a1fhttp://purl.org/redcol/resource_type/TPTexthttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/draftAdamów, M., Niedzielski, A., Villaver, E., Nowak, G., & Wolszczan, A. 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