Probing Fundamental Physics and Astrophysics With Tides and Deformations of Compact Stars

Compact stars are the stellar evolution remnants no longer supported by thermal and radiation pressure. Since these objects have high densities and strong surface gravity, they provide a unique environment to study fundamental physics like nuclear interactions and gravity theory. Moreover, binary compact objects serve as strong gravitational wave sources, complementing the electromagnetic observations and offering new methods to probe new physics within the compact star environment. This thesis delves into several aspects of astrophysics, gravitation, and nuclear physics related to compact stars including white dwarfs and neutron stars. In astrophysics, we consider the prospects of measuring the tidal properties of white dwarfs using the precession of periastron of eccentric binaries. This provides an alternative method to measure tides within white dwarf binaries using gravitational waves. Additionally, we examine the stability of individual compact stars by relaxing the conventional assumption of isotropic stress, accounting for realistic astrophysical conditions that cause anisotropy. There, we find a new type of instability which is caused by the spontaneous growth of the non-radial oscillation modes as the star emits gravitational waves. In gravitation, we explore the potential of utilizing gravitational wave signals from galactic compact binaries to constrain the theory of gravity with future space-based detectors. We demonstrate that proper modeling of the astrophysical factors governing the orbital motion, like the tidal deformations or the influence of magnetic field, is essential for placing meaningful constraints on alternative gravity theories with gravitational waves. Lastly, we also explore probing the deconfinement of quarks in the neutron star core by measuring the resonance effect of tides in a binary neutron star from the gravitational wave signals. We find that even the current generation of detectors can measure the effect of the quark stellar core given that the quarks are in a crystallized state with extreme rigidity. These studies demonstrate the utilization of gravitational wave observations from compact stars to push the boundaries of fundamental physics and astrophysics.