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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.30 n.2 San José Jul./Dec. 2023 


On the relationship between expansión angle of earth-directed CMES and soft X-ray emission from their related flare

Sobre la relación entre el ángulo de expansión de CMES direccionados a la tierra y la emisión de rayos X blandos desde su destello inicial

Carolina Salas-Matamoros1 

Jesús Sánchez-Guevara2 

1Universidad de Costa Rica, Centro de Investigaciones Espaciales (CINESPA), Montes de Oca, San Jose, Costa Rica;

2Universidad de Costa Rica, Escuela de Matemáticas, Montes de Oca, San Jose, Costa Rica;


In space weather, to study the impact of Earth-directed coronal mass ejections (CME) in our terrestrial environment, one of the most important parameters is the propagation speed of these disturbances. We present an improvement of the 3D CME Geometrical Propagation-Expansion Description (3D-CGPED) model developed in previous work to increase the simple that we can use in CME arrival time predictions. This 3D model estimates the arrival time of Earth-directed CMEs at Earth by including a 3D geometry for the CME propagation and expansion in interplanetary space. Since the 3D-CGPED model computes the expansion of the CME based on the radial distance of the CME front, only travel times for CMEs with welldefined shapes seen by coronographs can be estimated. In the present work, we found an empirical relationship between the expansion angle of CMEs with well-defined shapes and the start-to-peak SXR fluence of their associated flares. We applied this relationship in the 3D-CGPED model to obtain the expansion angle for 8 CMEs with an irregular shape. We found similar window errors in arrival time predictions compared to the previous work. This result allows us to complement the 3D-CGPED model to include not only regular shapes but also irregular ones for CMEs observed by coronographs in future works.

Keywords: sun; coronal mass ejections; CME's; solar flare; radio waves.


En clima espacial, en el estudio de los efectos terrestres de las eyecciones de masa coronal (CME) dirigidas a la Tierra, uno de los parámetros más importantes es la rapidez de propagación de estas perturbaciones. En este artículo presentamos una mejora del modelo 3D CME Geometrical Propagation- Expansion Description (3D-CGPED) desarrollado en un trabajo anterior para aumentar la muestra que podemos usar en las predicciones de tiempo de llegada de las CMEs. Este modelo 3D estima el tiempo de llegada a la Tierra de las CMEs al incluir una geometría 3D para la propagación y expansión de la CME en el espacio interplanetario. Dado que el modelo 3DCGPED calcula la expansión de las CMEs en función de la distancia radial del frente de una CME, solo se pueden estimar los tiempos de viaje para las CME con formas bien definidas vistas por los cronógrafos. En el presente trabajo encontramos una relación empírica entre el ángulo de expansión de las CMEs con formas bien definidas y la fluencia SXR de inicio a pico de sus destellos asociados. Aplicamos esta relación en el modelo 3D-CGPED para obtener el ángulo de expansión para 8 CMEs con forma irregular. Encontramos ventanas de errores similares en las predicciones de tiempo de llegada en comparación con el trabajo anterior. Este resultado nos permite complementar el modelo 3D-CGPED en trabajos futuros, para incluir no solo formas regulares sino también irregulares, de CMEs observadas por cronógrafos.

Palabras clave: sol; eyección de masa coronal; CME's; erupción solar; ondas de radio.


Mathematics Subject Classification: Primary 85-04; Secondary 85-A35

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This study made extensive use of the CME catalogue, generated and maintained at the CDAW Data Center by NASA and The Catholic University of America in cooperation with the Naval Research Laboratory. SOHO is a project of international cooperation between ESA and NASA. GOES data were provided by NOAA and the Solar Data Analysis Center (SDAC) at NASA Goddard Space Flight Center. The data bases of WIND were also used. We would also like to thank graphic designer Nayara Ureña Sánchez for her help with Figures 1 and 2.


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Received: March 31, 2022; Accepted: May 29, 2023

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