In this research, we study how a finite-temperature nuclear equation of state suitable for astrophysical simulations impacts the oscillation modes of neutron stars. We chose the Shen equation of state (EOS) because it accurately describes both stable and unstable nuclei as well as nuclear incompressibilities. I modified the existing MHD code at BYU, the HAD code, to call a lookup table for the Shen EOS for use at run time, and added a Newton-Raphson method algorithm to convert conserved variables to primitive variables. The algorithm was tested and verified by evolving a stable neutron star for several dynamical times and evolving the same star at different resolutions. The normal mode frequency of the neutron star with the Shen EOS was measured and compared to those for neutron stars with an ideal gas EOS found by Font et. al. We found that the fundamental mode of the neutron star using the Shen EOS was slightly larger than that of the ideal gas EOS. This difference is due to the Shen EOS producing stars that are stiffer, increasing the sound speed.

<p> An expression is obtained for the energy per particle in neutron star matter. The energy per particle is expressed as a function of, y, the ratio of protons to the total number of nucleons in the system. Minimizing the energy with respect to y gives the optimum proton ratio at a given density. Using an effective nuclear force, the results were extrapolated to a density of p = 6pNM. The proton ratio is rather sensitive to the force used, but all forces used indicated a peak in the proton concentration at p (approximately equal to) 2pNM. The expression for the energy as a function of y was also used to interpolate the energy per particle between the nuclear matter and neutron . gas limits. The form of this interpolation is important in determining the stability of neutron-rich nuclei. </p> / Thesis / Master of Science (MSc)

We will consider the scenario of the co-rotation of a fluid star (in specific, a neutron star) and a black hole. The neutron star (or primary)is assumed to have constant angular velocity. The tidal effects on the primary are investigated. First, the centrally condensed approximation is applied, where both bodies are considered as point sources. In the second treatment, the primary is treated as an incompressible and homogeneous fluid mass, which in addition to its own gravity is subject to centrifugal and Coriolis forces, derived from fluid motions. The black hole (or secondary) is treated as a rigid sphere and can be regarded as a point mass. The equilibrium figure is derived. The problem is then adapted to include vorticity and a pseudo-Newtonian potential. The coalescence of neutron star - black hole binaries and their importance to gravitational wave detection is also discussed. / Mathematical Sciences / M. Sc. (Applied Mathematics)

In this thesis, we construct a new hydrodynamical algorithm able of handling general compressible reactive flow problems, based on a finite-volume method inspired by the original MUSCL scheme of van Leer (1979). The algorithm is of second-order in the smooth part of the flow and avoids dimensional splitting. It uses MPI to achieve parallelism, and includes an astrophysical equation of state and a nuclear reaction network. It proves to be robust to tests cases. In particular it reproduces quite well the reactive and non-reactive results obtained with two different numerical methods (Fryxell & al. 1989, Busegnies & al. 2007). Moreover the time-dependent results are in agreement with the corresponding steady state solution. This gives us confidence in applying it to an astrophysical situation which has never been studied, the propagation of a detonation in conditions relevant to superbursts. The algorithm is described in (Noel & al. 2007). In a firt step we obtain the detonation profiles in pure carbon and in a mixture of carbon and iron. In both cases we underline the large difference between the total reaction length and the length on which some species burn. This difference leads to enormous numerical difficulties because all the length scales cannot be resolved at the same time in a single simulation. We show that the carbon detonation might be studied in a partial resolution approach like the one of Gamezo & al. (1999). In a second step we construct a new reduced nuclear reaction network able to reproduce the energy production due to the photo-disintegrations of heavy elements, like ruthenium, which are thought to occur during superbursts in mixed H/He accreting systems. Using this new nuclear network we simulate detonations in mixture of carbon and ruthenium. An interesting feature is that, in this case, all the reaction lengths can be resolved in the same simulation. This makes the C/Ru detonations easier to study in future multi-dimensional simulations than the pure carbon ones (Noel & al. 2007b). Finally we perform some numerical experiments which show that our algorithm is able to deal with initially inhomogeneous medium, and that the multi-dimensional simulations are attainable even if they are quite computational time consuming. - B. Van Leer, J. Comp. Phys., 21, 101, 1979 - Fryxell, B.A., Muller, E., and Arnett, W.D., Technical report MPA 449, 1989 - Busegnies, Y., Francois, J. and Paulus, G., Shock Waves, 11, 2007 - Gamezo, V.N., Wheeler, J.C., Khokhlov, A.M., and Oran, E.S., ApJ, 512, 827, 1999 - Noël, C., Busegnies, Y., Papalexandris, M.V. & al., A&A, 470, 653, 2007 - Noël, C., Goriely, S., Busegnies, Y. & Papalexandris, M.V., submitted to A&A, 2007b / Un algorithme parallèle basé sur une méthode aux volumes finis inspirée du schéma MUSCL de Van Leer (1979) a été construit. Il a été développé sur base de la méthode de Lappas & al. (1999) qui permet de résoudre simultanément toutes les dimensions spatiales. Cette méthode se base sur la construction de surfaces appropriées dans l'espace-temps, le long desquelles les équations de bilan se découplent en équations plus simples à intégrer. Cet algorithme est actuellement le seul à éviter le "splitting" des dimensions spatiales. Dans les modèles conventionnels (PPM, FCT, etc.), l'intégration spatiale des équations est réalisée de manière unidimensionnelle pour chaque direction. Un réseau de réactions nucléaires ainsi qu'une équation d'état astrophysique ont été inclus dans l'algorithme et celui-ci a ensuite été soumis à une grande variété de cas tests réactifs et non réactifs. Il a été comparé à d'autres codes généralement utilisés en astrophysique (Fryxell & al. 1989, Fryxell & al. 2000, Busegnies & al. 2007) et il reproduit correctement leurs résultats. L'algorithme est décrit dans Noël & al. (2007). Sur base de cet algorithme, les premières simulations de détonation dans des conditions thermodynamiques représentatives des Superbursts ont été réalisées. Différentes compositions du milieu ont été envisagées (carbone pur, mélange de carbone et de fer, mélange de carbone et de cendres du processus rp). Dans la plupart des systèmes où des Superbursts ont été observés, la matière accrétée est un mélange d'hydrogène et d'hélium. Dans ce cas, des phases de combustion précédant le Superburst produisent des nucléides plus lourd que le fer (Schatz & al. 2003). Ces nucléides peuvent être photodésintégrés durant le Superburst. Pour prendre en compte ces réactions endothermiques de photodésintégration, nous avons construit un nouveau réseau réduit de réactions nucléaires qui a été incorporé dans l'algorithme hydrodynamique (Noël & al. 2007b). Ce réseau réduit reproduit globalement l'énergétique d'un réseau complet et a permis de faire la première simulation numérique de détonation dans des conditions caractéristiques de systèmes accréteurs d'un mélange hydrogène-hélium. Finallement quelques simulations multidimensionelles préliminaires ont éte réalisées. - Busegnies, Y., Francois, J. and Paulus, G., Shock Waves, 11, 2007 - Fryxell, B.A., Muller, E., and Arnett, W.D., Technical report MPA 449, 1989 - Fryxell, B.A., Olson, K., Ricker, P. & al., ApJS, 131, 273, 2000 - Lappas, T., Leonard, A. and Dimotakis, P.E., SIAM J. Sci. Comput., 20, 1064, 1999 - Noël, C., Busegnies, Y., Papalexandris, M.V. & al., A&A, 470, 653, 2007 - Noël, C., Goriely, S., Busegnies, Y. & Papalexandris, M.V., submitted to A&A, 2007b - Röpke, F. K. PhD thesis, Technischen Universitat Munchen, 2003 - Schatz, H., Bildsten, L., Cumming, A. and Ouellette, M., Nuclear Physics A, 718, 247, 2003 - Van Leer, B. Comp. Phys., 21, 101, 1979 - Weinberg, N.N. and Bildsten, L., ArXiv e-prints, 0706.3062, 2007

Nesta dissertação, estuda-se estrelas compactas constituídas por uma forma estável do plasma ultra-relativístico de {\\it quarks} e glúons, a {\\it strange quark matter} ou matéria estranha, com pequena fração de elétrons para manter a neutralidade de carga. São abordadas, aqui, soluções matemáticas razoáveis que descrevem com simplicidade e agilidade certas propriedade dessas estrelas, a começar pela importantíssima relação massa-raio. Um perfil gaussiano para a densidade de energia foi escolhido como ponto de partida para contruir uma solução matemática para o problema e são apresentadas as motivações para tal escolha. Prova-se que o perfil escolhido não soluciona as Equações de Einstein exatamente e uma solução aproximada é fornecida. A seguir, as conhecidas soluções Tolman IV e Buchdahl I foram utilizadas para modelar uma estrela estranha com base no estudo de Alcock, Farhi e Olinto. Discute-se, ainda, como foi redescoberta a solução exata de Finch e Skea e discute-se, também, a solução exata para uma estrela de {\\it quarks} de Komathiraj e Maharaj, construída para um problema ligeiramente diferente, que incluía a existência de um campo elétrico. Conclui-se o trabalho comparando os resultados numéricos de Alcock, Farhi e Olinto com a solução aproximada aqui desenvolvida, apresentando o intervalo de validade desta solução. Além disso, são feitas comparações entre as diferentes soluções exatas e as características que cada uma delas exibe, e discute-se qual delas deve-se utilizar, tendo em mente que característica da estrela estranha se quer estudar. Os caminhos existentes para solucionar as Equações de Einstein, quando se quer modelar um objeto compacto, são discutidos e apontam-se quais os problemas que alguém encontrará ao seguir cada caminho. Por fim, relaciona-se a construção da relação massa-raio com a diferenciação dos tipos de objetos compactos que podem, em princípio, existir. / In this dissertation we study compact stars constituted by a stable form of ultra-relativistic quark-gluon plasma, the strange matter, with a small fraction of electrons to keep the neutrality of charge. We address here reasonable mathematical solutions that describe with simplicity and agility some properties of these stars, beginning by the important mass-radius relationship. A gaussian energy density profile was chosen as the starting point for the construction of a mathematical solution for this problem and the motivations for this choice was presented. We prove that this profile is not an exact solution for the Einstein Field Equations and an approximated solution is presented. Following, the previous known solutions of Tolman IV and Buchdahl I were used to model a strange star, based on the work of Alcock, Farhi and Olinto. We discuss the rediscovery of the exact solution of Finch and Skea and also the exact solution for a quark star by Komathiraj and Maharaj, constructed to a problem slightly different, that includes the existence of an electric field. We conclude this work comparing the numerical results of Alcock, Farhi and Olinto with the approximated solution here developed, presenting the range of validity of this solution. Furthermore, comparisons were made between the different exact solutions and the features displayed by each one and we discuss which solution must be used when one have in mind which features of the strange star one wants to study. The existent ways for solving the Einstein Equations when we want to model a compact star are discussed and we point out the problems that one will find in following each way. At last, we make a relation between the mass-radius relationship and the differentiation of the many types of compact objects that could, in principle, exist.

Les pulsars sont des étoiles à neutron hautement magnétisées en rotation rapide produisant un rayonnement pulsé. Cette thèse est dédiée à leur magnétosphère, c'est à dire la zone proche de l'étoile à neutron, remplie d'un plasma entraîné par la rotation rapide de celle-ci. Il a été montré dès 1969 que la magnétosphère doit avoir des zones très peu denses arborant des champs électriques intenses capables d'accélérer le plasma raréfié de ces régions à des énergies très élevée le long du champ magnétique. La courbure des lignes de champ, couplé avec la rotation d'une particule autour du champ, cause un rayonnement dit de « synchro-courbure ». L'énergie est rayonnée essentiellement en photons gamma (g). Ces photons peuvent ensuite être convertis par interaction quantique photon γ-champ magnétique ou γ-γ en une paire électron-positron e+e- dont chaque composante rayonne à son tour, résultant en une cascade qui alimente la magnétosphère en plasma. Cette thèse traite particulièrement de deux phénomènes clefs de ces cascades : le rayonnement de synchro-courbure et la création de paires par interaction γγ.La théorie quantique du rayonnement de synchro-courbure est développée pour la première fois à partir des principes de base de l'électrodynamique quantique. Les paramètres compatibles avec les approximations du calcul correspondent à une large gamme de conditions physiques typiques des magnétosphères de pulsars. Les transitions quantiques sont considérées dans l'approximation continue lorsqu'elles impliquent un saut de l'impulsion de la particule dans la direction parallèle au champ, et discrète dans la direction perpendiculaire. Il en résulte un spectre tendant asymptotiquement vers les descriptions classiques des rayonnement de courbure et de synchro-courbure mais présentant des déviations très importantes lorsque les transitions discrètes dominent le rayonnement.L’interaction γγ→e+e- a été étudiée dans le cas où un gamma réagit sur un fond de photons de basse énergie. Ce mécanisme est considéré comme potentiellement important lorsque le champ magnétique n'est pas assez fort pour produire des paires par le mécanisme γ-champ magnétique. Tout indique que le fond est anisotrope, c'est pourquoi nous avons développé un formalisme permettant de prendre en compte arbitrairement les anisotropies et de produire les spectres des particules produites. Appliqué à un modèle simple d'étoile rayonnant thermiquement en X, il en résulte une dépendance forte du taux de réaction sur la direction du photon gamma.Cette thèse comprend également un modèle de chronométrage du pulsar milliseconde dans un système triple J0337+1715. Ce pulsar orbite avec deux étoiles naines blanches dont les interactions mutuelles ne sont pas négligeables. Une intégration numérique, à l'ordre newtonien et post-newtonien, a été développée pour déterminer les orbites. Un modèle complet incluant le calcul des retards du système du pulsars au télescope a été réalisé. Le modèle s'ajuste aux données de chronométrage provenant du radiotélescope de Nançay avec des résidus d'écart-type inférieur à 2 µs. Un tel système permet en principe le test du principe d'équivalence fort gravitationnel par une technique similaire à celle employée lors des expériences de laser-lune, mais avec une précision sans précédent en régime de champ fort. Ce test requiert une évaluation rigoureuse des incertitudes sur chaque paramètre, échantillonnées grâce à un code MCMC. La validation du code et l'évaluation des incertitudes sont en cours. / Pulsars are highly magnetized fast rotating neutron stars producing a pulsed radiation. This thesis is dedicated to their magnetosphere, namely the zone surrounding the star and filled with a plasma dragged by the rotation of the star. It was shown as soon as 1969 that the magnetosphere must have vacuum gaps, where intense electric fields develop that are capable of accelerating the rarefied plasma to very high energies along the magnetic field. The curvature of the field lines, together with the rotation around the magnetic field, results in the so-called «  synchrocurvature » radiation. The energy is mostly radiated in gamma photons (γ). These photons may then be converted by the quantum processes γ photon-magnetic field or γ-γ in an electron-positron pair e+e-, each component of which then radiates at its turn which results in a cascade that provides plasma to the magnetosphere. This thesis particularly deals with two key phenomena of these cascades : synchrocurvature radiation and γγ pairs.The quantum theory of synchrocurvature radiation is developed for the first time from the first principles of quantum electrodynamics. The range of parameters compatible with the approximations of the derivation covers a wide range of physical conditions typical of pulsar magnetospheres. Quantum transitions are considered in the continuous limit when they imply a jump of the particle impulsion parallel to the magnetic field, and discrete when the jump is in the perpendicular direction. It results in a spectrum that asymptotically tends to the classical descriptions of curvature and synchrocurvature radiations but that presents very important deviations when the discrete transitions dominate the radiation.The γγ→e+e- process was studied in the case of the reaction of a gamma photon on a soft photon background. This mechanism is considered as potentially important when the magnetic field is nopt strong enough for the γ-magnetic field process to efficiently produce pairs. The soft background is most likely anisotropic, and that is why we developed a formalism allowing to arbitrarily take into account anisotropies, as well as produce the spectra of the outgoing particles so as to be able to feed the subsequent cascade consistently. Applied to a simple model of a star radiating thermal X rays, it results in a strong dependence of the reaction rate on the direction of the gamma photon.This thesis also includes a timing model of the millisecond pulsar in a triple system J0337+1715. This pulsar orbits with two white-dwarf stars, and their mutual interactions are not negligible. It follows that a numerical integration of the orbits was developed at Newtonian and first post-Newtonian orders. A complete model including the computation of delays from the star to the telescope was realized. This model is able to fit the timing data from the Nançay (France) radiotelecope with a standard deviation of less than 2µs. In principle, such a system allows to test the strong equivalence principle by a technique similar to that employed in Lunar-laser-ranging experiments, but with an unprecedented accuracy in the strong-field regime. This test demands a careful estimate of the uncertainties on each parameter, which we sample using a MCMC code. The validation of the code and the evaluation of the uncertainties are ongoing.

This dissertation describes the current version of GenASiS and reports recent progress in its development. GenASiS is a new computational astrophysics code built for large-scale and multi-dimensional computer simulations of astrophysical phenomena, with primary emphasis on the simulations of neutron star mergers and core-collapse supernovae. Neutron star mergers are of high interest to the astrophysics community because they should be the prodigious source of gravitation waves and the most promising candidates for gravitational wave detection. Neutron star mergers are also thought to be associated with the production of short-duration, hard-spectral gamma-ray bursts, though the mechanism is not well understood. In contrast, core-collapse supernovae with massive progenitors are associated with long-duration, soft-spectral gamma-ray bursts, with the `collapsar' hypothesis as the favored mechanism. Of equal interest is the mechanism of core-collapse supernovae themselves, which has been in the forefront of many research efforts for the better half of a century but remains a partially-solved mystery. In addition supernovae, and possibly neutron star mergers, are thought to be sites for the emph{r}-process nucleosynthesis responsible for producing many of the heavy elements. Until we have a proper understanding of these events, we will have only a limited understanding of the origin of the elements. These questions provide some of the scientific motivations and guidelines for the development of GenASiS. In this document the equations and numerical scheme for Newtonian and relativistic magnetohydrodynamics are presented. A new FFT-based parallel solver for Poisson's equation in GenASiS are described. Adaptive mesh refinement in GenASiS, and a novel way to solve Poisson's equation on a mesh with refinement based on a multigrid algorithm, are also presented. Following these descriptions, results of simulations of neutron star mergers with GenASiS such as their evolution and the gravitational wave signals and spectra that they generate are shown. In the context of core-collapse supernovae, we explore the capacity of the stationary shock instability to generate magnetic fields starting from a weak, stationary, and radial magnetic field in an initially spherically symmetric fluid configuration that models the stalled shock in the post-bounce supernova environment. Our results show that the magnetic energy can be amplified by almost 4 orders of magnitude. The amplification mechanisms for the magnetic fields are then explained.

We will consider the scenario of the co-rotation of a fluid star (in specific, a neutron star) and a black hole. The neutron star (or primary)is assumed to have constant angular velocity. The tidal effects on the primary are investigated. First, the centrally condensed approximation is applied, where both bodies are considered as point sources. In the second treatment, the primary is treated as an incompressible and homogeneous fluid mass, which in addition to its own gravity is subject to centrifugal and Coriolis forces, derived from fluid motions. The black hole (or secondary) is treated as a rigid sphere and can be regarded as a point mass. The equilibrium figure is derived. The problem is then adapted to include vorticity and a pseudo-Newtonian potential. The coalescence of neutron star - black hole binaries and their importance to gravitational wave detection is also discussed. / Mathematical Sciences / M. Sc. (Applied Mathematics)

Nesta dissertação, estuda-se estrelas compactas constituídas por uma forma estável do plasma ultra-relativístico de {\\it quarks} e glúons, a {\\it strange quark matter} ou matéria estranha, com pequena fração de elétrons para manter a neutralidade de carga. São abordadas, aqui, soluções matemáticas razoáveis que descrevem com simplicidade e agilidade certas propriedade dessas estrelas, a começar pela importantíssima relação massa-raio. Um perfil gaussiano para a densidade de energia foi escolhido como ponto de partida para contruir uma solução matemática para o problema e são apresentadas as motivações para tal escolha. Prova-se que o perfil escolhido não soluciona as Equações de Einstein exatamente e uma solução aproximada é fornecida. A seguir, as conhecidas soluções Tolman IV e Buchdahl I foram utilizadas para modelar uma estrela estranha com base no estudo de Alcock, Farhi e Olinto. Discute-se, ainda, como foi redescoberta a solução exata de Finch e Skea e discute-se, também, a solução exata para uma estrela de {\\it quarks} de Komathiraj e Maharaj, construída para um problema ligeiramente diferente, que incluía a existência de um campo elétrico. Conclui-se o trabalho comparando os resultados numéricos de Alcock, Farhi e Olinto com a solução aproximada aqui desenvolvida, apresentando o intervalo de validade desta solução. Além disso, são feitas comparações entre as diferentes soluções exatas e as características que cada uma delas exibe, e discute-se qual delas deve-se utilizar, tendo em mente que característica da estrela estranha se quer estudar. Os caminhos existentes para solucionar as Equações de Einstein, quando se quer modelar um objeto compacto, são discutidos e apontam-se quais os problemas que alguém encontrará ao seguir cada caminho. Por fim, relaciona-se a construção da relação massa-raio com a diferenciação dos tipos de objetos compactos que podem, em princípio, existir. / In this dissertation we study compact stars constituted by a stable form of ultra-relativistic quark-gluon plasma, the strange matter, with a small fraction of electrons to keep the neutrality of charge. We address here reasonable mathematical solutions that describe with simplicity and agility some properties of these stars, beginning by the important mass-radius relationship. A gaussian energy density profile was chosen as the starting point for the construction of a mathematical solution for this problem and the motivations for this choice was presented. We prove that this profile is not an exact solution for the Einstein Field Equations and an approximated solution is presented. Following, the previous known solutions of Tolman IV and Buchdahl I were used to model a strange star, based on the work of Alcock, Farhi and Olinto. We discuss the rediscovery of the exact solution of Finch and Skea and also the exact solution for a quark star by Komathiraj and Maharaj, constructed to a problem slightly different, that includes the existence of an electric field. We conclude this work comparing the numerical results of Alcock, Farhi and Olinto with the approximated solution here developed, presenting the range of validity of this solution. Furthermore, comparisons were made between the different exact solutions and the features displayed by each one and we discuss which solution must be used when one have in mind which features of the strange star one wants to study. The existent ways for solving the Einstein Equations when we want to model a compact star are discussed and we point out the problems that one will find in following each way. At last, we make a relation between the mass-radius relationship and the differentiation of the many types of compact objects that could, in principle, exist.

Besides being sources of gravitational waves, there has been evidence that neutron starmergers release neutron-rich material suitable for the production of heavy r-process nuclei.The radioactive decay of these freshly synthesised elements powers a rapidly evolvingthermal transient, the “macronova” (also known as “kilonova”). Its spectral propertiesstrongly depend on the ejecta composition, since neutron rich material synthesises heavyr-process elements that can efficiently trap radiation inside the ejecta producing a longlasting signal peaking in the red part of the spectrum. The first detection of a binaryneutron star merger was also accompanied by the evidence of a relativistic jet. Despitebeing ascertained the presence of these two dynamical components, neutron-rich ejectaand ultra-relativistic jet, the observational consequences of the interplay between the twois still unclear. In the paper we investigate such interaction through dedicated specialrelativistic hydrodynamic simulations, starting from a realistic environment obtained byprevious works. Light curves are then constructed up to the time scale of days by postprocessing the hydrodynamic results adopting proper radiative transfer. I show thatjet propagation within such environment can significantly affect the observation of theradioactive transient. A relativistic outflow can in fact “punch-away” a fraction of highopacity material before the brightening of the macronova, resulting in the transient beingbrighter and bluer for on-axis observers in the first few days. In this way the jet impactsboth time scale and luminosity of the macronova peak, that are the two main observablesallowing the estimate of the ejecta properties.