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IP Peg is a member of a family of star systems known as cataclysmic variable stars, CVs. CVs are star systems in which a red dwarf star orbits a white dwarf and mass transfer is taking place from the red dwarf to the white dwarf. The mass ratio of the two component stars has been found the most difficult parameter to determine. Tools used in the analysis of mass-ratio included the differential photometric light curve of IP Peg, Doppler tomograms, and spectral data covering the HP emission-line. The mass ratio was found to lie in the range, q = 0.44 ± 0.14. The inclination lies in the range i = 81.5° ± 8.5°. Finally, the accretion disk radius was 0.342 times the distance between the stars. The analysis of the parameters of eclipsing CV systems like IP Peg provides a rare opportunity that helps in the understanding of other CV systems. / Department of Physics and Astronomy

M.Sc. / Just as the observations of oscillations of ordinary stars can be used to determine their composition and structure, the oscillations of neutron stars could potentially be used to determine the nature of the dense nuclear matter from which they are made. The superfluidity of the interiors of neutron stars is normally probed by observations of pulsar glitches. It turns out that the superfluidity affects the oscillations in a neutron star core. In particular, it results in a class of oscillation modes specifically associated with the superfluid core. Although these modes have not been detected from observations, it is hoped by some that gravitational wave data may be used to probe the superfluidity of neutron star cores. In this dissertation, a simple equilibrium model is used in order to calculate the superfluid modes in the context of newtonian gravity. The equilibrium model that is used is the same combination of the Serot equation of state and the Harrison-Wheeler equation of state that was used formerly by Lee and by Lindblom & Mendell. Numerical calculations of the superfluid modes are done for 20 different neutron star models ranging in mass between 0.5 and 2 solar masses. The frequencies of the oscillations for the 0.5 and 1.4 solar masses agree fairly well with Lee's results, which strongly validates the computer code written for numerical calculation in this work. In all the models, the eigenfrequencies of the super uid or s-modes are found among those of the f and p-modes. For the equation of state that is used, it is shown that the dimensionless frequencies of the p-modes increase with an increase in mass of the neutron star while those of the s-modes decrease with an increase in neutron star mass. The plan of the dissertation is as follows. Chapter 1 gives a short introduction to stellar oscillations and mentions the oscillations of neutron stars. Chapters 2 and 3 provide the general theoretical background of stellar structure and stellar oscillations respectively. Chapter 4 is a review of the equations of state of neutron star matter derived previously in the literature. Chapter 5 provides the method of calculation as well as the results. Chapter 6 provides a discussion of the results. Chapter 7 briefly gives a review of a mathematical framework for fluids that could be used in order to calculate the oscillations in a general relativistic context and then briefly describes the effects of rotation and magnetic fields. Appendix B liststhe source code for the programs used to do the calculations and also explains some of the extra numerical procedures used for the computation.

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Le but de cette thèse est de raffiner et de mieux comprendre l'utilisation de la méthode spectroscopique, qui compare des spectres visibles de naines blanches à atmosphère riche en hydrogène (DA) à des spectres synthétiques pour en déterminer les paramètres atmosphériques (température effective et gravité de surface). Notre approche repose principalement sur le développement de modèles de spectres améliorés, qui proviennent eux-mêmes de modèles d'atmosphère de naines blanches de type DA. Nous présentons une nouvelle grille de spectres synthétiques de DA avec la première implémentation cohérente de la théorie du gaz non-idéal de Hummer & Mihalas et de la théorie unifiée de l'élargissement Stark de Vidal, Cooper & Smith. Cela permet un traitement adéquat du chevauchement des raies de la série de Balmer, sans la nécessité d'un paramètre libre. Nous montrons que ces spectres améliorés prédisent des gravités de surface qui sont plus stables en fonction de la température effective. Nous étudions ensuite le problème de longue date des gravités élevées pour les DA froides. L'hypothèse de Bergeron et al., selon laquelle les atmosphères sont contaminées par de l'hélium, est confrontée aux observations. À l'aide de spectres haute résolution récoltés au télescope Keck à Hawaii, nous trouvons des limites supérieures sur la quantité d'hélium dans les atmosphères de près de 10 fois moindres que celles requises par le scénario de Bergeron et al. La grille de spectres conçue dans ces travaux est ensuite appliquée à une nouvelle analyse spectroscopique de l'échantillon de DA du SDSS. Notre approche minutieuse permet de définir un échantillon plus propre et d'identifier un nombre important de naines blanches binaires. Nous déterminons qu'une coupure à un rapport signal-sur-bruit S/N > 15 optimise la grandeur et la qualité de l'échantillon pour calculer la masse moyenne, pour laquelle nous trouvons une valeur de 0.613 masse solaire. Finalement, huit nouveaux modèles 3D de naines blanches utilisant un traitement d'hydrodynamique radiative de la convection sont présentés. Nous avons également calculé des modèles avec la même physique, mais avec une traitement standard 1D de la convection avec la théorie de la longueur de mélange. Un analyse différentielle entre ces deux séries de modèles montre que les modèles 3D prédisent des gravités considérablement plus basses. Nous concluons que le problème des gravités élevées dans les naines blanches DA froides est fort probablement causé par une faiblesse dans la théorie de la longueur de mélange. / The goal of this thesis is to refine and to understand better the spectroscopic method, which compares optical spectra of hydrogen-atmosphere white dwarfs (DA) with synthetic spectra to determine the atmospheric parameters (effective temperature and surface gravity). Our approach rests mainly on the development of improved model spectra, which come themselves from DA model atmospheres. We present a new grid of DA synthetic spectra with the first consistent implementation of the non-ideal gas theory of Hummer & Mihalas and the unified theory of Stark broadening from Vidal, Cooper & Smith. This allows for an adequate treatment of the quenching effects in Balmer lines, without the need of a free parameter. We show that these improved spectra predict surface gravities that are much more stable as a function of the effective temperature. We then study the long-standing problem that surface gravities in cool DA stars are significantly higher than those found in hotter DA white dwarfs. The hypothesis of Bergeron et al., according to which the atmospheres are contaminated by small amounts of helium, is constrained with observations. Using high-resolution spectra collected at the Keck in Hawaii, we find superior limits on the helium abundances in the atmospheres that are nearly 10 times lower than those required to sustain the Bergeron et al. scenario. The grid of spectra calculated in this work is then applied to a new spectroscopic analysis of the DA in the SDSS. Our careful analysis allows us to define a cleaner sample and to identify a large number of double degenerates. We find that a cutoff at a signal-to-noise ratio S/N > 15 optimizes the size and quality of the sample for computing the average mass, for which we find a value of 0.613 solar mass. Finally, eight new 3D white dwarf models with a radiative-hydrodynamics treatment of the convection are presented. We also calculated models with the same physics, except for a treatment of the convection with the standard mixing-length theory. A differential analysis between these two sets of models shows that the 3D models predict considerably lower surface gravities. We conclude that the high-log g problem in cool DA white dwarfs is caused by a weakness in the mixing-length theory.

Le but de cette thèse est de raffiner et de mieux comprendre l'utilisation de la méthode spectroscopique, qui compare des spectres visibles de naines blanches à atmosphère riche en hydrogène (DA) à des spectres synthétiques pour en déterminer les paramètres atmosphériques (température effective et gravité de surface). Notre approche repose principalement sur le développement de modèles de spectres améliorés, qui proviennent eux-mêmes de modèles d'atmosphère de naines blanches de type DA. Nous présentons une nouvelle grille de spectres synthétiques de DA avec la première implémentation cohérente de la théorie du gaz non-idéal de Hummer & Mihalas et de la théorie unifiée de l'élargissement Stark de Vidal, Cooper & Smith. Cela permet un traitement adéquat du chevauchement des raies de la série de Balmer, sans la nécessité d'un paramètre libre. Nous montrons que ces spectres améliorés prédisent des gravités de surface qui sont plus stables en fonction de la température effective. Nous étudions ensuite le problème de longue date des gravités élevées pour les DA froides. L'hypothèse de Bergeron et al., selon laquelle les atmosphères sont contaminées par de l'hélium, est confrontée aux observations. À l'aide de spectres haute résolution récoltés au télescope Keck à Hawaii, nous trouvons des limites supérieures sur la quantité d'hélium dans les atmosphères de près de 10 fois moindres que celles requises par le scénario de Bergeron et al. La grille de spectres conçue dans ces travaux est ensuite appliquée à une nouvelle analyse spectroscopique de l'échantillon de DA du SDSS. Notre approche minutieuse permet de définir un échantillon plus propre et d'identifier un nombre important de naines blanches binaires. Nous déterminons qu'une coupure à un rapport signal-sur-bruit S/N > 15 optimise la grandeur et la qualité de l'échantillon pour calculer la masse moyenne, pour laquelle nous trouvons une valeur de 0.613 masse solaire. Finalement, huit nouveaux modèles 3D de naines blanches utilisant un traitement d'hydrodynamique radiative de la convection sont présentés. Nous avons également calculé des modèles avec la même physique, mais avec une traitement standard 1D de la convection avec la théorie de la longueur de mélange. Un analyse différentielle entre ces deux séries de modèles montre que les modèles 3D prédisent des gravités considérablement plus basses. Nous concluons que le problème des gravités élevées dans les naines blanches DA froides est fort probablement causé par une faiblesse dans la théorie de la longueur de mélange. / The goal of this thesis is to refine and to understand better the spectroscopic method, which compares optical spectra of hydrogen-atmosphere white dwarfs (DA) with synthetic spectra to determine the atmospheric parameters (effective temperature and surface gravity). Our approach rests mainly on the development of improved model spectra, which come themselves from DA model atmospheres. We present a new grid of DA synthetic spectra with the first consistent implementation of the non-ideal gas theory of Hummer & Mihalas and the unified theory of Stark broadening from Vidal, Cooper & Smith. This allows for an adequate treatment of the quenching effects in Balmer lines, without the need of a free parameter. We show that these improved spectra predict surface gravities that are much more stable as a function of the effective temperature. We then study the long-standing problem that surface gravities in cool DA stars are significantly higher than those found in hotter DA white dwarfs. The hypothesis of Bergeron et al., according to which the atmospheres are contaminated by small amounts of helium, is constrained with observations. Using high-resolution spectra collected at the Keck in Hawaii, we find superior limits on the helium abundances in the atmospheres that are nearly 10 times lower than those required to sustain the Bergeron et al. scenario. The grid of spectra calculated in this work is then applied to a new spectroscopic analysis of the DA in the SDSS. Our careful analysis allows us to define a cleaner sample and to identify a large number of double degenerates. We find that a cutoff at a signal-to-noise ratio S/N > 15 optimizes the size and quality of the sample for computing the average mass, for which we find a value of 0.613 solar mass. Finally, eight new 3D white dwarf models with a radiative-hydrodynamics treatment of the convection are presented. We also calculated models with the same physics, except for a treatment of the convection with the standard mixing-length theory. A differential analysis between these two sets of models shows that the 3D models predict considerably lower surface gravities. We conclude that the high-log g problem in cool DA white dwarfs is caused by a weakness in the mixing-length theory.

The topic of this thesis is the study of the vertical structure of the disk galaxies and their dark matter halos through theoretical modeling and numerical calculations. The basic theoretical model of the galactic disk used involves gravitationally-coupled stars and gas under the force-field of a dark matter halo; the disk is rotationally-supported in the plane and pressure-supported perpendicular to the plane of the galaxy. The first part of the thesis involves evaluating the vertical structure of stars and gas in normal as well as dwarf spiral galaxies. The second part of the thesis deals with probing the dark matter halo density profiles of disk galaxies using both the observed rotation curve and the H i scale height data. Following is the layout of the thesis. Chapter 1 gives a general introduction to the topic of vertical structure of spiral galaxies and their dark matter halos, followed by a broad overview of the theoretical development of the topic and ends with highlighting the motivation and challenges met in this thesis. Chapters 2 & 3 deal with the vertical structure of stars and gas in galaxies, Chapters 4-6 focus on obtaining the dark matter halo density profiles of disk galaxies from the observed rotation curve and the H i scale height data whereas Chapter 7 is devoted to the summary of results and future research plans. Vertical structure of stars and gas in galaxies The vertical thickness of the stars and the gas, namely atomic hydrogen (H i) and molecular hydrogen (H2) in a spiral galaxy, is crucial in regulating the disk dynamics close to the mid-plane, especially in the inner galaxy. However, measuring it observationally is not in general practicable due to the limitations of astronomical observations, and often impossible as in the case of face-on galaxies. Therefore, it is imperative to develop a theoretical model of the galaxy which can predict the thickness of the disk components by using as input parameters the physical quantities, which are more observationally-amenable compared to the disk thickness. The vertical thickness of the disk components is determined by a trade-off between the upward kinetic pressure and the net downward gravitational pull of the galaxy. The fraction of the disk mass due to the stars is an order of magnitude higher than that of the gas in ordinary spiral galaxies, and therefore the gas contribution to the disk gravity is ignored in general. We have developed a multi-component model of gravitationally-coupled stars, HI and H2 subjected to the force-field of an external dark matter halo, and conclusively demonstrated the importance of the inclusion of gas gravity in explaining the steep vertical stellar distribution observed in galaxies. These apart, this model does not implicitly assume a flat rotation curve for the galaxy and therefore is applicable in general to obtain the thickness of stars and gas in dwarfs (with linearly rising rotation curves) as well as in ordinary spirals. In Chapter 2, we investigate the origin of the steep vertical stellar distribution in the Galactic disk. One of the direct fall outs of our above model of the galaxy, which incor¬porates the self-gravity of the gas unlike the earlier theoretical models, lies in explaining the long-standing puzzle of the steep vertical stellar density distribution of the disk galax¬ies near the mid-plane. Over the past two decades, observations revealed that the vertical density distribution of stars in galaxies near the mid-plane is substantially steeper than the sech2 function that is expected for a self-gravitating system of stars under isothermal ap¬proximation. However, the physical origin for this has not been explained so far. We have clearly demonstrated that the inclusion of the self-gravity of the gas in the dynamical model of the Galaxy solves the problem even under the purview of isothermal approximation for the disk components. Being a low dispersion component, the gas resides closer to the mid¬plane compared to the stars, and forms a thin, compact layer near the mid-plane, thereby strongly governing the local disk dynamics. This novel idea, highlighting the significance of gas gravity has produced substantial impact on the field and triggered research activities by other groups in related areas of disk dynamics. The strong effect of the gas gravity on the vertical density profile of the stellar disk indicates that it should also bear its imprint on the Milky way thick disk, as the epoch of its formation 109 years ago is marked by a value of gas fraction, almost an order of magnitude higher than its present day value. Interest-ingly, the findings of the upcoming Gaia mission can be harnessed to verify this theoretical prediction. It may also hold the clue as to the reason behind the absence of thick disk in superthin galaxies. In Chapter 3, we use the same model to theoretically determine the H i vertical scale heights in the dwarf galaxies: DDO 154, Ho II, IC 2574 & NGC 2366 for which most of the necessary input parameters are available from observations. We stress the fact that the observational determination of the gas thickness in these dwarf irregulars is not viable. Nevertheless, it is important to estimate it theoretically as it plays a crucial role in calculating the star-formation activities and other related phenomena. However, two vital aspects have to be taken care of while modeling these dwarf galaxies. Firstly, the mass fraction in gas in these galaxies is comparable to that of the stars, and hence the gas gravity cannot be ignored on any account unlike in the case of large spirals. Secondly, dwarf galaxies have a rising rotation curve over most of the disk unlike the flat rotation curves of ordinary spirals. Both these factors have been considered in developing our model of the dwarf galaxies. We find that three out of the four galaxies studied show a flaring of their H i disks with increasing radius, by a factor of a few within several disk scale lengths. The fourth galaxy (Ho II) has a thick H1 disk throughout. A comparison of the size distribution of H1 holes in the four sample galaxies reveals that of the 20 type 3 holes, all have radii that are in agreement with them being still fully contained within the gas layer. Probing the dark matter halo profiles of disk galaxies The next part of the thesis involves the dynamical study of the shapes and density profiles of galactic dark matter halos using observational constraints on our theoretical model of a spiral galaxy. The density distribution of the dark matter halo is generally modeled using the observed rotation curve of the spiral galaxies. The rotational velocity at any radius is determined by the radial component of the net gravitational force of the galaxy, which, however, is weakly dependent on the shape of the dark matter halo. Therefore, one cannot trace the dark matter halo shape by the observed rotation curve alone. The vertical thickness of the stars and gas, on the other hand, is strongly dependent on the flattening of the dark matter halo, and therefore the observed gas thickness can be used as a diagnostic to probe the halo shape. In this thesis, we have used the double constraints of the rotation curve and the H i thickness data to obtain the best-fit values of the core density, core radius and the vertical-to-planar axis ratio (or flattening) of the dark matter halos of our largest nearby galaxy Andromeda (or M31), a low-surface brightness (LSB) superthin galaxy UGC 7321 and to study the dark matter halo shape of our Galaxy. In Chapter 4, we study the dark matter halo of M31 or Andromeda, the largest nearby galaxy to the Milky Way. We find that M31 has a highly flattened isothermal dark matter halo with the vertical-to-horizontal axis ratio equal to 0.4, which interestingly lies at the most oblate end of the halo shapes found in cosmological simulations. This indicates that either M31 is a unusual galaxy, or the simulations need to include additional physics, such as the effect of the baryons, that can affect the shape of the halo. This is quite a remarkable result as it challenges the popular practice of assuming a spherical dark matter halo in the dynamical modeling of the galaxy In Chapter 5, we have applied this technique to the superthin galaxy UGC 7321. Su¬perthins are somewhat the “extreme” objects in the local Universe because of their high gas fraction and absence of a thick disk component. It is interesting to analyze their so-called extreme characteristics in the light of the physical mechanisms which determined them to understand better the properties of ordinary spirals. We find that UGC 7321 has a spher¬ical isothermal halo, with a core radius almost equal to the disk scale length. This reveals that the dark matter dominates the dynamics of this galaxy at all radii, including the inner parts of the galaxy. This is unlike the case for the large spiral galaxies, where the core radius is typically about 3-4 disk scale lengths. Interestingly, the best-fit halo core density and the core radius are consistent, with deviations of a few percent, with the dark matter fundamental plane correlations, which depict the systematic properties of the dark matter halo in late-type and dwarf spheroidal galaxies. This apart, a high value of the gas velocity dispersion is required to get a better fit to the H i scale height data, although the superthin nature of the stellar disk implies a dynamically cold dynamic galactic disk. However, it explains the low star-formation rates in these galaxies since the Toomre Q criterion (Q < 1) for instability is less likely to be satisfied, and hence the disk is liable to be more stable to star formation. In Chapter 6, we investigate the shape of the dark matter halo in the outer Galaxy. We find that the halo is prolate, with the vertical-to-planar axis ratio monotonically increasing to 2.0 at 24 kpc, or 8 radial disk scale lengths. The resulting prolate-shaped halo can explain several long-standing puzzles in galactic dynamics, for example, it permits long-lived warps thus explaining their ubiquitous nature. It also imposes novel constraints on the galaxy formation models. Finally, in Chapter 7, the thesis is concluded with a summary of the main results and a brief discussion of the scope for future work.