Pulsation constants and period ratios are given for the first six radial pulsation modes of a set of seven polytropes with indices ranging from n = 2.25 to n = 4.00. The polytrope results are combined with published theoretical data from stellar model pulsation calculations and observational data on thirteen double mode variables in the Cepheid instability strip to obtain four interpolation formulae relating fundamental periods Po, pulsation constants Qo, and period ratios P1 /P0 and P2 /P1. The derived relations are used to obtain accurate densities for the thirteen observed variables, which include six dwarf Cepheids or AI Vel stars, one S Sct star, one RR Lyr star, and five Cepheids. Approximate masses and luminosities are obtained for some of these stars. The probable connection between mass- luminosity ratios and the existence of double mode variables is discussed.

Les Céphéides sont des étoiles pulsantes utilisées pour calculer les distances dans l'univers (notamment dans le Groupe Local). Elle font partie de la bande d’instabilité du diagramme de Hertzsprung-Russell. Le mécanisme κ (où κ désigne l’opacité du milieu), proposé par Eddington en 1917 pour expliquer ces variations périodiques de rayon et luminosité, est encore mal connu dans lecas de Céphéides froides (bord rouge de la bande d’instabilité) présentant une zone convective en surface.Cette thèse consiste à effectuer des simulations 3D de ces étoiles afin d’étudier l’interaction entre leurs pulsations radiales acoustiques et la convection de surface. On se ramène à un cas simple : l’étude de la propagation de modes acoustiques dans une boite cartésienne dont une partie est convective.Nous utilisons le code Heracles développé au CEA par Édouard Audit, que nous avons complété (ajout d’une étape de dissipation, passage à l’ordre 2 en temps pour l’étape de conduction).Pour valider notre code et notre modèle de Céphéide, nous reproduisons les résultats de Gastine & Dintrans (2011b) à 1D (cas purement radiatifs) et 2D (avec convection) : certaines simulations instables au κ-mécanisme (avec une saturation non-linéaire aux temps longs à 1D) redeviennent stables à 2D à cause de l’influence de la convection. La bande d’instabilité théorique du diagramme de Hertzsprung-Russell est donc trop étroite à 2D.L’hypothèse à vérifier était alors que ces Céphéides retrouvent une certaine instabilité et une saturation non-linéaire lors de simulations 3D. En effet, il est connu que les simulations 2D et 3D de convection différent à bas nombre de Prandtl, ce qui est notre cas. Dès lors, nous montrons que les panaches de convection sont en effet moins forts à 3D et ne perturbent pas autant les pulsations. On retrouve ainsi des simulations instables. Le bord rouge de la bande d’instabilité théorique est donc plus proche du bord observé à 3D qu’à 2D.Enfin, nous montrons que les modèles 1D de convection dépendante du temps de Stellingwerf (1982) et de Kuhfuss (1986) donnent des résultats similaires lorsqu’il s’agit de reproduire le profil de flux convectif des simulations 3D, lorsque la simulation présente des mouvements d’ensemble de type κ-mécanisme. Les deux modèles peinent cependant à reproduire les valeurs de ce flux convectif de manière convaincante. Cela justifie l’importance des simulations 3D. / Cepheids are pulsating stars used to calculate distances in the universe (more precisely in the Local Group). They are part of the Hertzsprung-Russell diagram’s instability strip. Their periodic variations (of luminosity and radius) are well explained by κ-mechanism, first suggested by Eddington (1917). But cold Cepheids (red edge of the instability strip) have a convective zone near their surface that affects their pulsation properties.Therefore, this PhD. thesis aims at performing 3D simulations of simplified Cepheids to study the interaction between surface convection and radial pulsations. We actually study the propagation of acoustic modes in a cartesian box partially convective.For this, we use Heracles, a hydrodynamical code developed in CEA, France, by Edouard Audit. We had to complete the code with a dissipation step and a second order (in time) conduction step (which was already available as a first order method).To validate the code and the Cepheid model used, we reproduce Gastine & Dintrans (2011b) results in 1D (radiative cases) and 2D (with convection): some setups that are unstable for κ-mecanism (with nonlinear saturation in 1D simulations) are stable in 2D thanks to convection. The theoretical Hertzsprung-Russell diagram’s instability strip is then too narrow in 2D.The hypothesis for this work was that those Cepheids would be unstable again (with saturation) in 3D due to the fact that convection grows weaker when convective plumes are 3D. 2D and 3D simulations are indeed different when Prandtl number is low as it is in our simulations. We show that pulsations are indeed not quenched anymore and that simulations are unstable. Theoretical 3D instability strip is then closer to the observed one than 2D strip was.Finally, we show that the 1D models of time-dependant convection from Stellingwerf (1982) and Kuhfuß (1986) give similar results for the convective flux of 3D convection with κ-mecanism. But none of them is able to give the exact values. That means that 3D simulations are indeed precious.

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Ultra-low frequency (ULF; 1 mHz - 1 Hz) waves are known to play an important role in the transfer of energy from the solar wind to Earth's magnetosphere and ionosphere. The Super Dual Auroral Radar Network (SuperDARN) is an international network consisting of 35 low-power high frequency (HF: 3-30 MHz) coherent scatter radars at middle to polar latitudes that look into Earth's upper atmosphere and ionosphere. In this study, we use Doppler velocity measurements obtained by the SuperDARN radars and coordinated spacecraft observations to investigate the occurrence statistics and driving mechanisms of ionospheric ULF waves. We begin in Chapter 2 with a case study of Pi2 pulsations which are short-duration (5-15 min) damped geomagnetic field oscillations with periods of 40-150 s. Simultaneous observations of Pi2 pulsations from THEMIS spacecraft, midlatitude SuperDARN radars, and ground magnetometers, together with analysis of their longitudinal polarization pattern and azimuthal phase propagation, confirmed that they are consistent with a plasmaspheric virtual resonance excited by a longitudinally localized source near midnight. In Chapter 3, to further investigate the overall occurrence of ionospheric ULF signatures, a comprehensive statistical study was conducted using an automated detection algorithm to identify ionospheric signatures of Pc3-4 and Pc5 waves over 7 years of high time resolution SuperDARN radar data. Specifically, we have investigated their spatial occurrence, frequency characteristics, seasonal factors, and dependence on solar wind and geomagnetic conditions. We note two particular findings: (i) an internal wave-particle interaction source is most likely responsible for Pc4 waves at high latitudes in the duskside ionosphere; and, (ii) a source associated with magnetotail dynamics during active geomagnetic times is suggested for Pc3-4/Pi2 waves at midlatitudes in the nightside ionosphere. These findings are further expanded in Chapter 4 which investigates the hypothesis that internal wave-particle interactions are an important source for generation of these waves. A case study of long-lasting poloidal waves was conducted using coordinated observations with the GOES and THEMIS satellites to examine the generation and propagation of waves observed in the dayside ionosphere by multiple SuperDARN radars. The source of wave excitation is suggested to be bump-on-tail ion distributions at 1-3 keV. Collectively, these research findings provide better constraints on where and when ionospheric ULF waves occur, their source mechanisms, and how they might affect magnetospheric and ionospheric dynamics. / Doctor of Philosophy / Earth’s magnetic field, approximates that of a bar magnet. It is an effective barrier to charged particles originating directly from the Sun and protects us against harmful space weather influences. The geomagnetic field lines can oscillate in ultra-low frequencies (ULF: 1 mHz - 1 Hz). These natural oscillations of closed magnetic field lines, analogous to vibrations on a stretched string, are also called geomagnetic pulsations or ULF waves. The interaction between matter and electromagnetic fields emitted from the Sun and the Earth’s outer atmosphere and magnetic field form a magnetic shield named the Earth’s magnetosphere. ULF waves play a key role in the transfer of energy from outside this shield to regions inside it, including Earth’s upper atmosphere and ionosphere (a region extending from about 60 km to 1000 km above the Earth’s surface). In this study, we use Doppler velocity measurements obtained by the Super Dual Auroral Radar Network (SuperDARN) radars and coordinated spacecraft observations to investigate the occurrence statistics and driving mechanisms of ionospheric ULF waves. We begin in Chapter 2 with an event study of a type of irregular pulsations (Pi2) which are short-duration (5-15 min) damped geomagnetic field oscillations with periods of 40-150 s. Simultaneous observations of Pi2 pulsations from NASA THEMIS spacecraft, midlatitude SuperDARN radars, and ground magnetometers, together with further analysis of wave spectra and propagation, confirmed their driving mechanism as a type of magnetic resonance, analogous to striking a bell. In Chapter 3, to further investigate the overall occurrence of ionospheric ULF signatures, a statistical study was conducted using an automated detection algorithm to identify ionospheric signatures of ULF waves over 7 years of high time resolution SuperDARN radar data. Specifically, we have investigated their spatial occurrence, frequency characteristics, seasonal factors, and dependence on solar and geomagnetic activity. We obtained findings regarding the different driving sources of waves observed in different regions. The findings are further expanded in Chapter 4 which investigates the generation of waves through energy exchange with charged particles. A case study of long-lasting (2-3 days) waves was conducted using coordinated observations with the GOES and THEMIS satellites to examine the generation and propagation of waves observed in the dayside ionosphere by multiple SuperDARN radars. The source of wave excitation is suggested to be unstable particle distributions in the magnetosphere. Collectively, these research findings provide better constraints on where and when ULF waves occur, their source mechanisms, and how they affect dynamics in the geospace environment.

Analyses of the light variation of the 6 Scuti star CC Andromedae and of the radial velocity variation of the ß Canis Majoris star 6 Scorpii, a single -line spectroscopic binary, indicate that the long period modulations exhibited are caused by tidal deformations induced in the hydrogen and /or helium ionization zones of each primary by a faint companion, resulting in surface zonal variations of the amplitude and phase of each primary's normal radial pulsations. The variations in the tide raising potential calculated at the center of the apparent disk of o Scorpii correlate very strongly with the observed variations in the phase zero -point of the fundamental pulsation. It is suggested that all the ß Canis Majoris and 6 Scuti stars exhibiting long period modulation, and probably also the RR Lyrae stars showing a Blazhko effect, do so because of tidal perturbations induced by faint companions.

A espectrocopia de estrelas Be realizada com alta resolução e alta relação sinal/ruído permite investigar variações temporais rápidas nos perfis de linhas de absorção, usualmente atribuidas às pulsações não radiais, entre outros mecanismos. O fenômeno Be é transitorio para esse tipo de estrelas. Com efeito, seus espectros podem apresentar as características de uma estrela B normal, ou então de uma estrela com envelope circunstelar "frio" (presença de linhas finas de emissão e absorção no espectro visível). Essas estrelas se caracterizam por apresentarem altas velocidades de rotação, entretanto insuficientes para explicar as altas taxas de perda de massa, cujos mecanismos permanecem ainda incompreendicos. Neste trabalho, adotamos o modelo de pulsações não radiais (PNR) para tentar explicar as variações temporais presentes nos perfis de linha centrados em Hel λ 667.8nm. Para este fim, foi utilizado o método CLEANEST para efetuar a determinação de periodicidades, após alguns testes de comparação prévios entre o desempenho desse método e o CLEAN. Ambos os métodos possuem grande eficiência em análises temporais, entre tanto na média o método CLEANEST se sobressaiu tanto na determinação de freqüências como de amplitudes. Além disso, foram estudados outros tipos de variabilidades também presentes nesses perfis, como as variabilidades nas intensidades relativas das asas da linha e a variabilidade na posição de um pico central em quase emissão. Os dados espectroscópicos analisados constituem quatro conjuntos de espectros obtidos nos anos 1995, 1996, 1997 e 1998 no MCT/LNA. Há ainda um conjunto de dados fotométricos proveniente do satélite HIPPARCOS relativo aos anos de 1990, 1991 e 1992. As análises dos dados espectroscópicos e fotométricos forneceram resultados que concordam com outros trabalhos sobre η Centauri. / The spectroscopy of Be stars carried out with high resolution and signal to noise relation allows to investigate quick time variations in line absorption profiles, usually due to non radial pulsations, among other mechanisms. The Be phenomenon is transitory for such stars. Indeed, their spectra may show characteristics of a normal B star, or a star with a "cold" circumstellar envelope (presence of sharp emission and absorption lines in visible spectrum). These stars are characterized by high speed rotation, however insufficient to explain high mass loss rates, whose mechanisms still remains misunderstood. In this work, we adopted the non-radial pulsation model (NRP) in order to explain the observed time series variations present in line profiles centered in HeI λ 667.8 nm. For this sake, it was used the CLEANEST method to carry out periodicity determinations, after some previous comparative tests of performance between this method and CLEAN. Both of them possess great efficiency in time analysis, however in average the CLEANEST method stood out both in determining frequencies and amplitudes. Besides, it were studied also other kinds of variability also present in these profiles, such as relative intensity variations in the wings of the profile and the variability in position of the central quasi-emission peak. The analyzed spectroscopic data constitute four sets of spectra obtained in 1995, 1996, 1997 and 1998 at the MCT/LNA. There is still one photometric data set coming from HIPPARCOS satellite spanning from 1990 to 1992. The spectroscopic and photometric data analysis have furnished results that agree with other works on η Centauri

A espectrocopia de estrelas Be realizada com alta resolução e alta relação sinal/ruído permite investigar variações temporais rápidas nos perfis de linhas de absorção, usualmente atribuidas às pulsações não radiais, entre outros mecanismos. O fenômeno Be é transitorio para esse tipo de estrelas. Com efeito, seus espectros podem apresentar as características de uma estrela B normal, ou então de uma estrela com envelope circunstelar "frio" (presença de linhas finas de emissão e absorção no espectro visível). Essas estrelas se caracterizam por apresentarem altas velocidades de rotação, entretanto insuficientes para explicar as altas taxas de perda de massa, cujos mecanismos permanecem ainda incompreendicos. Neste trabalho, adotamos o modelo de pulsações não radiais (PNR) para tentar explicar as variações temporais presentes nos perfis de linha centrados em Hel λ 667.8nm. Para este fim, foi utilizado o método CLEANEST para efetuar a determinação de periodicidades, após alguns testes de comparação prévios entre o desempenho desse método e o CLEAN. Ambos os métodos possuem grande eficiência em análises temporais, entre tanto na média o método CLEANEST se sobressaiu tanto na determinação de freqüências como de amplitudes. Além disso, foram estudados outros tipos de variabilidades também presentes nesses perfis, como as variabilidades nas intensidades relativas das asas da linha e a variabilidade na posição de um pico central em quase emissão. Os dados espectroscópicos analisados constituem quatro conjuntos de espectros obtidos nos anos 1995, 1996, 1997 e 1998 no MCT/LNA. Há ainda um conjunto de dados fotométricos proveniente do satélite HIPPARCOS relativo aos anos de 1990, 1991 e 1992. As análises dos dados espectroscópicos e fotométricos forneceram resultados que concordam com outros trabalhos sobre η Centauri. / The spectroscopy of Be stars carried out with high resolution and signal to noise relation allows to investigate quick time variations in line absorption profiles, usually due to non radial pulsations, among other mechanisms. The Be phenomenon is transitory for such stars. Indeed, their spectra may show characteristics of a normal B star, or a star with a "cold" circumstellar envelope (presence of sharp emission and absorption lines in visible spectrum). These stars are characterized by high speed rotation, however insufficient to explain high mass loss rates, whose mechanisms still remains misunderstood. In this work, we adopted the non-radial pulsation model (NRP) in order to explain the observed time series variations present in line profiles centered in HeI λ 667.8 nm. For this sake, it was used the CLEANEST method to carry out periodicity determinations, after some previous comparative tests of performance between this method and CLEAN. Both of them possess great efficiency in time analysis, however in average the CLEANEST method stood out both in determining frequencies and amplitudes. Besides, it were studied also other kinds of variability also present in these profiles, such as relative intensity variations in the wings of the profile and the variability in position of the central quasi-emission peak. The analyzed spectroscopic data constitute four sets of spectra obtained in 1995, 1996, 1997 and 1998 at the MCT/LNA. There is still one photometric data set coming from HIPPARCOS satellite spanning from 1990 to 1992. The spectroscopic and photometric data analysis have furnished results that agree with other works on η Centauri

>Magister Scientiae - MSc / This thesis reports the results of a twofold study on the recently proposed phenomenon of 'stellar pulsations' in young brown dwarfs by the seminal study of Palla and Baraffe (2005) (PB05, thereafter). The PB05 study presents results of a non-adiabatic linear stability analysis showing that young brown dwarfs should become pulsationally unstable during the deuterium burning phase of their evolution. The PB05 calculations on which this prediction is based have already been applied in a number of ground and space-based observational campaigns aimed at searching for this newly proposed putative class of potential pulsators. However, despite their significance and implications, the theoretical calculations by PB05 have not yet, to date, been subjected to independent verification in a different computational framework. To achieve this, we have generated equilibrium brown dwarf models and performed non-adiabatic linear stability calculations similar to PB05 assuming their 'frozen-in convection' approximation and the relevant input physics. The calculations performed in this thesis show, in overall, that there is a good agreement between the results from our study and those in PB05. However, there seem to be significant differences for very low mass objects as pointed out in our comparative results. We attribute this difference to our different boundary conditions. Our outer boundary condition is equivalent to the Eddington approximation in the 3-D case (e.g see Unno and Spiegel (1966)), while PB05 use a combination of different atmospheric profiles as discussed in Chabriel and Baraffe (2000). The validity of the frozen-in assumption used by PB05, which is based on the argument that the convective time scales calculated for these objects are much less than the pulsation time scales, has not been investigated. In this thesis, we have invoked a time-dependent theory of convection similar to Kuhfuss (1986) and Stellingwerf (1982) which includes turbulent pressure, turbulent diffusion and turbulent viscosity to study the pulsations. We have also investigated the effects of varying a number of free parameters in the above theoretical models. Our results show that turbulent pressure dominates in driving the pulsations in young brown dwarfs yielding growth rates much higher than in the frozen-in scenario. This is a new result that requires further analysis. The perturbation in the convective flux is found to have a damping effect on the acoustic modes. Turbulent viscosity is found to lead to damping which increases with increase in the value of the turbulent viscosity parameter and is found to have very little effect on the fundamental mode pulsation periods. Variation in the turbulent diffusion parameter has a very small effect on the fundamental mode periods and e-folding times. As a side lobe, we have determined theoretical pulsation constants for the fundamental mode and calculated the period ratios for the fundamental mode to those of the first and second harmonics. We find values of pulsation constants falling within the theoretical values calculated for variable stars shown in Cox (1980). This is explained in relation to the terms that go into the theoretical formula discussed later in this thesis. We find a correlation between the period ratios and the BDs mass and argue that such plots of the period ratios vs mass of the BDs could be useful in constraining the masses, given known periods from observations.