The leading-order effect of small perturbations - such as tidal interactions or environmental effects (EEs) - on GW signals is the accumulated phase shift over long observation times. However, the existing literature on these effects is scattered and occasionally inconsistent. I therefore began by surveying the various perturbations that can dephase GW signals, including external potentials, additional energy fluxes, and observational effects such as Doppler delays. This resulted in an overview that synthesizes insights from the literature into a unified conceptual narrative, complemented by a curated reference of key formulas, illustrative examples, and methodological guidelines.
Although most of the relevant formulas existed in some form for circular binaries, I extended the discussion to finite eccentricities, which are expected for binaries formed in dynamical environments where EEs are especially relevant. This extension is also essential for characterizing how non-zero eccentricities influence dynamical tides. I derived new analytic expressions for the direct and indirect effects of energy and angular momentum perturbations on eccentric binaries, and demonstrated that the higher harmonics present in eccentric waveforms substantially enhance the detectability of tidal interactions and EEs.
For eccentric binaries, tidal modes do not just resonate at a single orbital frequency but instead with all the higher harmonics at different stages of the evolution. The energy deposited into the modes across these repeated resonances can accumulate, producing a larger overall dephasing, making them easier to detect. However, these resonances also require that the mode excitation remain coherent over multiple orbits. Incorporating this coherence condition, I developed an analytic framework for the expected dephasing of eccentric binaries due to dynamical g-mode tides. I further showed that observing mildly eccentric binary NSs (with e~0.2–0.4 at a GW frequency of 10 Hz) could improve current constraints on g-mode properties by nearly an order of magnitude.
The effect of DM on NS observables has been the focus of many recent studies, yet the expected DM fraction inside NSs located in dense DM environments is rarely discussed. While DM capture by isolated NSs has been thoroughly explored, the accumulation of DM in NSs within binary systems had not previously been studied. To address this gap and to see if further investigation of DM admixed NSs was justified, I developed a Monte Carlo simulation that tracks the trajectories of test-particles (DM particles) around a compact binary. I found that DM capture can be enhanced in binaries by a factor of ~5 relative to isolated NSs, depending on the ambient DM velocity and the binary hardness. However, I also showed that dynamical friction from the same DM particles accelerates the inspiral, placing an upper limit on the capturable DM fraction even in extremely dense environments.
