ETD

• General Relativity
• Gravitational Waves
• Neutron Stars

This thesis investigates the gravitational-wave emission from neutron stars affected by dynamical tidal interactions, with particular emphasis on the definition and phenomenological consequences of the dynamical Love number obtained through Post-Newtonian matching.
The first part of the work focuses on the theoretical definition of the dynamical Love number. In a binary system, the gravitational field produced by one neutron star deforms its companion, inducing a quadrupole moment which affects the gravitational wave emission. In the static or adiabatic regime, this response is described by the static Love number. In the late stage of the inspiral, the time dependence of the tidal field becomes relevant, the response becomes frequency dependent and can be described in terms of dynamical Love numbers. While the static Love number has been measured by gravitational wave detectors, the dynamical Love numbers have only recently been studied theoretically, and today they are not included in the analysis of gravitational wave observations. The definition of dynamical Love numbers considered in this thesis is obtained through a matching procedure between the metric of General Relativity and the metric describing the binary system in the Post-Newtonian approximation. This matching is performed in a region where both descriptions are valid. Particular attention is devoted to the ambiguities associated with this procedure, which arise from the non-homogeneous character of the perturbation equations.
It is possible to introduce an effective resonance frequency proportional to the ratio between the static and dynamical Love numbers. One of the original aspects of this work is the comparison between this effective frequency and the fundamental-mode frequency of neutron stars. This comparison is performed for neutron stars described by different Equations of State and with different masses. The results show that the two frequencies exhibit the same qualitative behaviour as the stellar mass varies. However, their numerical values progressively depart from each other as the mass and compactness of the star increase. It is also found that the ratio between the two frequencies appears to be independent of the Equation of State when plotted as a function of the compactness of the star.
The second part of the thesis studies the impact of dynamical tides on the gravitational waveform emitted by a compact binary system. Using the dynamical Love number obtained through Post-Newtonian (PN) matching, the waveform is calculated within the Stationary Phase Approximation. The analysis confirms that static tidal effects contribute to the gravitational-wave phase at 5PN order, consistently with previous results in the literature, while dynamical tidal effects enter at 8PN order. Although dynamical tides appear at a higher Post-Newtonian order, their contribution can become relevant because of the strong dependence of tidal deformability on the compactness of neutron stars.
Finally, the thesis investigates whether dynamical tidal effects can be detected with the Einstein Telescope. Their detectability is assessed by comparing (through the computation of the Faithfulness) two waveforms: one including only static tidal effects and another including both static and dynamical tidal effects. The results indicate that dynamical tides can become measurable for nearby, low-mass binary neutron-star systems. In particular, the effect is more significant for less massive stars and for sources at smaller distances. This study shows that neglecting dynamical tidal effects in sufficiently sensitive observations could lead to systematic shifts in the estimation of the physical parameters of the binary.
Overall, the thesis shows that dynamical tides represent a potentially important correction to the gravitational-wave signal of binary neutron stars and that their study will become increasingly relevant with the advent of next-generation detectors such as the Einstein Telescope.