Magíster en Ciencias de la Ingeniería, Mención Eléctrica. Ingeniero Civil Eléctrico. / Los sistemas cuasi-periódicos han sido estudiados en el contexto de sistemas dinámicos, como también en diversas áreas en las cuáles estos fenómenos son observables. Tal es el caso de la astronomía. El caso de estudio presentado en este trabajo corresponde a las estrellas Gamma Doradus, las que debido a sus características físicas poseen entre 1 a 5 períodos principales de pulsación, otorgándoles características periódicas y cuasi-periódicas al ser observadas en el espectro visible. En el estudio de estas estrellas, la correcta determinación de sus periodos y de la distancia entre ellos es de vital importancia, debido a que se relacionan con sus parámetros físicos, los cuales pueden llegar a ser inferidos. Por tal motivo se espera que estos modelos ayuden en la tarea de caracterización de la pulsación, mediante la descomposición de una curva de luz en señales de menor complejidad. La presente tesis se enfoca a la modelación y análisis de curvas de luz de estrellas Gamma Doradus mediante modelos de Neuropercolación. Neuropercolación es una familia de modelos estocásticos basados en la teoría de Autómata Celular Probabilístico en grillas y grafos aleatorios, inspirados en la dinámica de poblaciones neuronales. Estos modelos pueden ser utilizados para construir series de tiempo discretas, cuyos parámetros son las probabilidades que definen su dinámica. Se propone obtener tales parámetros para modelar una serie de tiempo mediante Optimización por Enjambre de Partículas (PSO), un método evolutivo de optimización basado en poblaciones. La metodología propuesta se aplicó tanto en señales sintéticas como a curvas de luz reales de estrellas Gamma Doradus. Dentro de la señales sintéticas se estudió la capacidad de modelación de una señal de Amplitud Modulada, tanto en presencia de datos perdidos como de ruido blanco aditivo en distintos niveles. Para todos los casos se obtuvieron modelos representativos de la dinámica del proceso. Posteriormente, con modelos de estrellas Gamma Doradus se observa que, con ciertos modelos, es posible recuperar todas la base de frecuencias con la que se construyen las curvas de luz. Esto entrega ventajas comparativas con la búsqueda de frecuencias directamente sobre la señal, además de mejorar la estimación del espaciamiento entre periodos. Al analizar ese método en curvas de estrellas Gamma Doradus obtenidas por el proyecto Kepler de la NASA es posible observar que si bien los modelos no obtienen ajustes perfectos de Error Cuadrático Medio, algunas de las curvas si llegan a ser modeladas con una alta precisión y bajos residuos. Otros casos, en señales con mayores componentes espectrales, la modelación no obtiene tan buenos resultados, y los residuos, aún en los mejores casos, presentan estructuras que podrían llegar a ser modeladas. Considerando la variabilidad intrínseca de resultados debido a la aleatoriedad de PSO y sus poblaciones iniciales, se concluye que es posible obtener modelos de señales cuasi-periódicas con gran exactitud, obteniendo las frecuencias principales del fenómeno. En los casos de modelos con menor ajuste la presencia de óptimos locales dificulta la convergencia hacia el óptimo global. Para los casos de estudio donde los errores fueron más altos, es posible que una mayor cantidad de datos ayude a la obtención de mejores modelos. Este trabajo presenta muchas opciones de extensiones, tales como la disminución de los tiempos de cómputo, mejoras del proceso de optimización, potencialidades en interpolación y predicción, y uso en series de tiempo con muestreos no-uniformes.

Gravity modes present in gamma Doradus stars probe the deep stellar interiors and are thus of particular interest in asteroseismology. Mode identification will improve the knowledge of these stars considerably and allow an understanding of the issues with current pulsational models. The methods used in this thesis are also applied to a low degree pressure mode pulsator as a check for their validity. A frequency analysis followed by a mode identification were done based on the high resolution spectroscopic data of one β Cephei star, PT Puppis, and two γ Doradus stars, HD 189631 and AC Lepus. Extensive spectroscopic data sets are obtained by three instruments: HARPS, FEROS and HERCULES. We obtained 161 spectra for PT Puppis, 422 spectra for HD 189631 and 248 spectra for AC Lepus. The pulsational frequencies were determined by four methods: analysis of the variations in equivalent width, radial velocity, asymmetry of the line profile and by using the pixel-by-pixel frequency analysis. The mode identification was done using the recently developed Fourier Parameter Fit method. Without achieving the same degree of confidence for all results, we report the identification of two pulsational modes in PT Puppis: (l = 0 ; m = 0) at f₁ = 6.07 d⁻¹ and (2 ; 0) or (1 ; +1) at f₂ = 5.99 d⁻¹, four modes in HD 189631: (1 ; +1) at f₁ = 1.67 d⁻¹, (3 ; -2) at f₂ = 1.42 d⁻¹, (2 ; -2) at f₃ = 0.07 d⁻¹ and (4 ; +1) at f₄ = 1.82 d⁻¹ and two modes in AC Lepus: (2 ; -1) at f₁ = 0.75 d⁻¹ and (3 ; -3) at f₂ = 1.09 d⁻¹. This study provides the first pulsational analysis based on spectroscopy of PT Puppis, HD 189631 and AC Lepus. We discuss the performance of current methods of analysis, outline the difficulties presented by γ Doradus stars, and compare our results with other published pulsational mode identifications.

This thesis has analysed spectroscopic data for three stars in detail, the β Cephei star V2052 Ophiuchus, the γ Doradus star QW Puppis and the γ Doradus candidate star HD139095. Twelve other candidate γ Doradus stars have had their Vrotsin i, binary status and, where possible, the presence of line profile variation determined. A new technique utilising scaled delta functions has been developed to allow the extraction of a single, high S/N line profile from a high resolution and large wavelength range spectrum. This procedure has performed well in the γ Doradus stars examined. The application of the new mode identification technique, the Fourier Parameter Fit method, to the three stars examined in detail has been very successful. For each of the three stars constraints have been placed on the degree (l) and the azimuthal order (m) of the non-radial pulsation modes detected.

We present the modes identified for frequencies found in spectroscopic observations of the Doradus stars HD 189631, QW Puppis, and IR Draconis. A cross-correlation tech- nique was used to create mean line profiles for HD 189631. Four frequencies and modes were identified for this star: 1.6774±0.0002 d⁻¹, 1.4174±0.0002 d⁻¹, 0.0714±0.0002 d⁻¹, and 1.8228 ± 0.0002 d⁻¹ which were identified with the modes (l,m) = (1, +1), (1, +1), (2,−2), and (1, +1) respectively. A least-squares deconvolution method was implemented for line profile generation in the study of QW Puppis and IR Draconis. Three frequen- cies were identified for QW Puppis: 0.055972 ± 0.000004 d⁻¹, 0.064846 ± 0.000004, and 5.219398±0.000002 d⁻¹. These frequencies were identified with the modes (l,m) = (1,−1), (4,−1), (4, +1). Two frequencies were identified in spectra of the rapidly rotating star IR Draconis: 0.00515 ± 0.00003 d⁻¹ and 2.35538 ± 0.00004 d⁻¹; which were identified with (l,m) = (1,−1), and (1, +1) modes respectively. These mode identifications will assist in modelling the structure and interior conditions of these main sequence, non-radially pulsating stars.

Three γ Doradus-type stars are analysed: HD139095, HD153580, and HD197541. Long-term observation campaigns have been conducted on each star, with over 300 spectra of each star being gathered for analysis using the HERCULES spectrograph at Mount John University Observatory. For each star, cross-correlation techniques were used to obtain representative line profiles for each spectrum. The analysis of these line profiles has resulted in frequency and pulsation mode identifications for these three stars. Abundance analysis has also been performed on HD139095 and HD197541, and their fundamental parameters are confirmed as being consistent with the γ Doradus class of stars. HD153580 and HD197541, previously only candidates for the class, can now be classified as bona fide γ Doradus type stars. The frequencies and modes identified in this thesis will be very useful in constraining future theoretical models, allowing us to better understand and model the interiors of γ Doradus stars.

This thesis has analysed spectroscopic data for three stars in detail, the β Cephei star V2052 Ophiuchus, the γ Doradus star QW Puppis and the γ Doradus candidate star HD139095. Twelve other candidate γ Doradus stars have had their Vrotsin i, binary status and, where possible, the presence of line profile variation determined. A new technique utilising scaled delta functions has been developed to allow the extraction of a single, high S/N line profile from a high resolution and large wavelength range spectrum. This procedure has performed well in the γ Doradus stars examined. The application of the new mode identification technique, the Fourier Parameter Fit method, to the three stars examined in detail has been very successful. For each of the three stars constraints have been placed on the degree (l) and the azimuthal order (m) of the non-radial pulsation modes detected.

The mysteries of the interior structures of stars are being tackled with asteroseismology. The observable parameters of the surface pulsations of stars inform us of the interior characteristics of numerous classes of stars. The main-sequence gamma Doradus stars, just a little hotter than the Sun, offer the potential of determining stellar structure right down to the core. To determine the structural profile of a star, the observed frequencies and a full geometric description must be determined. This is only possible with long-term spectroscopic monitoring and careful analysis of the pulsation signature in spectral lines. This work seeks to identify the pulsational geometry of several gamma Doradus stars and to identify areas of improvement for current observation, analysis and modelling techniques. More than 4500 spectra were gathered on five stars for this purpose. For three stars a successful multi-frequency and mode identification solution was determined and significant progress has been made towards the understanding of a binary system involving a gammaDoradus star. A hybrid gamma Doradus/\delta Scuti pulsator was also intensely monitored and results from this work raise important questions about the classification of this type of star. Current analysis techniques were found to be fit-for-purpose for pure gamma Doradus stars, but stars with complexities such as hybrid pulsations and/or fast rotation require future development of the current models.