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Abstract: Neutron stars are among the densest objects in the universe and are one possible end result of stellar evolution. They contain forms (phases) of matter that are not possible to create under terrestrial conditions. Therefore, we can learn about new phases of matter by studying aspects of neutron stars. In particular, the way the fluid comprising the neutron star oscillates as a result of perturbations to the pressure and density of the star can lead to a variety of interesting phenomena, including the emission of gravitational waves. These can be modeled using theory and tested by observations. In this thesis, we focus on the p-mode oscillations, which are a type of spheroidal oscillation driven by internal pressure fluctuations. These are acoustic modes with very short time periods. We have calculated, using both analytical and numerical methods, the p-mode periods in a simple model of dense relativistic stars, of which neutron stars are standard examples. In a local analysis, we found a 0.3 ms upper limit on oscillation periods analytically. We then used a numerical analysis to find exact solutions for these periods, which agreed with our upper limit calculation. Our numerical analysis demonstrated that a small spherical harmonic degree has a small effect on the oscillation spectrum, and that a larger spherical harmonic degree introduces a period doubling phenomenon.
This book presents a study of the saturation of unstable f-modes (fundamental modes) due to low-order nonlinear mode coupling. Since their theoretical prediction in 1934, neutron stars have remained among the most challenging objects in the Universe. Gravitational waves emitted by unstable neutron star oscillations can be used to obtain information about their inner structure, that is, the equation of state of dense nuclear matter. After its initial growth phase, the instability is expected to saturate due to nonlinear effects. The saturation amplitude of the unstable mode determines the detectability of the generated gravitational-wave signal, but also affects the evolution of the neutron star. The study shows that the unstable (parent) mode resonantly couples to pairs of stable (daughter) modes, which drain the parent’s energy and make it saturate via a mechanism called parametric resonance instability. Further, it calculates the saturation amplitude of the most unstable f-mode multipoles throughout their so-called instability windows.
Abstract: Currently, we lack a means of identifying the type of matter at the core of compact stars, but in the future, we may be able to use gravitational wave signals produced by fluid oscillations inside compact stars to discover new phases of dense matter. To this end, we study the fluid perturbations inside compact stars such as Neutron Stars (NS) and Strange Quark Stars (SQS), focusing on modes that couple to gravitational waves (GWs). Using a modern equation of state for quark matter that incorporates interactions at moderately high densities, we implement an efficient computational scheme to solve the oscillation equations in the framework of General Relativity, and determine the complex eigenfrequencies that describe the oscillation and damping of the non-radial fluid modes. We find that the f- mode frequency only weakly distinguishes NS from SQS. However, we do find that the p- mode has a strong discriminating signature between the two models. In addition we study the impact of parameters of the SQS equation of state on the oscillation spectra. Finally, we discuss the significance of our results for future detection of these modes through gravitational waves.
Neutron stars, whether isolated or in a binary system, display a varied and complex phenomenology, often accompanied by extreme variability of many time scales, which takes the form of pulsations due to the object rotation, quasi-periodicities associated to accretion of matter, and explosions due to matter accreted on the surface or to starquakes of highly magnetized objects. This book gives an overview of the current observational and theoretical standpoint in the research on the physics under the extreme conditions that neutron stars naturally provide. The six chapters explore three physical regions of a neutron star: the space around it, where accretion and pulsar companions allow testing of general relativity its surface, where millisecond pulsation and X-ray burts provide clues about general relativistic effects and the equation of state of neutron matter its interior, of course, inaccessible to direct observations, can nevertheless, be probed with all observational parameters related to neutron star variability.
The book gives an extended review of theoretical and observational aspects of neutron star physics. With masses comparable to that of the Sun and radii of about ten kilometres, neutron stars are the densest stars in the Universe. This book describes all layers of neutron stars, from the surface to the core, with the emphasis on their structure and equation of state. Theories of dense matter are reviewed, and used to construct neutron star models. Hypothetical strange quark stars and possible exotic phases in neutron star cores are also discussed. Also covered are the effects of strong magnetic fields in neutron star envelopes.
Neutron stars are the most compact astronomical objects in the universe which are accessible by direct observation. Studying neutron stars means studying physics in regimes unattainable in any terrestrial laboratory. Understanding their observed complex phenomena requires a wide range of scientific disciplines, including the nuclear and condensed matter physics of very dense matter in neutron star interiors, plasma physics and quantum electrodynamics of magnetospheres, and the relativistic magneto-hydrodynamics of electron-positron pulsar winds interacting with some ambient medium. Not to mention the test bed neutron stars provide for general relativity theories, and their importance as potential sources of gravitational waves. It is this variety of disciplines which, among others, makes neutron star research so fascinating, not only for those who have been working in the field for many years but also for students and young scientists. The aim of this book is to serve as a reference work which not only reviews the progress made since the early days of pulsar astronomy, but especially focuses on questions such as: "What have we learned about the subject and how did we learn it?", "What are the most important open questions in this area?" and "What new tools, telescopes, observations, and calculations are needed to answer these questions?". All authors who have contributed to this book have devoted a significant part of their scientific careers to exploring the nature of neutron stars and understanding pulsars. Everyone has paid special attention to writing educational comprehensive review articles with the needs of beginners, students and young scientists as potential readers in mind. This book will be a valuable source of information for these groups.
Abstract: The observation of gravitational waves from compact stars (neutron and quark stars) is a promising method of determining their internal composition. This research presents the details and results for calculations of some of the principal modes of compact star oscillations, by which they radiate gravitational waves. These are: the f-modes, p-modes, and g-modes. We find that for the same stellar mass, the f-modes for quark stars are higher in frequency than for neutron stars. The p-mode frequency of quark stars decrease with stellar mass, displaying an opposite trend to that of neutron stars. Two-component models were also considered. A core-ocean model was examined for a neutron star, using a polytropic equation of state (EOS), and a core-crust model for a quark star, using a bag model EOS. We find that g-mode oscillations in neutron star oceans depend on the dominant chemical species of the ocean as well as the mass of the underlying core. The addition of a solid crust onto a quark star increases the frequencies, attributable to shear stresses between the core and crust. These results pave the way to model and contrast the gravitational wave signals emitted by oscillating compact stars.
In these selections readers are treated to a rare opportunity to see the world through the eyes of one of the twentieth century's most brilliant and sensitive scientists. Conceived by Chandrasekhar as a supplement to his Selected Papers, this volume begins with eight papers he wrote with Valeria Ferrari on the non-radial oscillations of stars. It then explores some of the themes addressed in Truth and Beauty, with meditations on the aesthetics of science and the world it examines. Highlights include: "The Series Paintings of Claude Monet and the Landscape of General Relativity," "The Perception of Beauty and the Pursuit of Science," "On Reading Newton's Principia at Age Past Eighty," and personal recollections of Indira Gandhi, Jawaharlal Nehru, and others. Selected Papers, Volume 7 paints a picture of Chandra's universe, filled with stars and galaxies, but with space for poetics, paintings, and politics. The late S. Chandrasekhar was best known for his discovery of the upper limit to the mass of a white dwarf star, for which he received the Nobel Prize in Physics in 1983. He was the author of many books, including The Mathematical Theory of Black Holes and, most recently, Newton's Principia for the Common Reader.