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Dynamical tidal deformations play a crucial role in the gravitational waves emitted by binary neutron-star systems during their late inspiral. In this work, we systematically explore how relativistic (dynamical and dissipative) tidal deformations depend on the internal structure of a neutron star using two analytic classes of equations of state. The first class is a nucleonic model that is parametrized by nuclear-physics observables, such as the symmetry energy coefficients and saturation properties. The second class is a toy model of quark matter, the MIT bag model. To model tidal dissipation, we self-consistently include contributions from weak-interaction-driven bulk-viscous effects while considering both the nucleonic and the quark-matter equations of state. The dissipative tide is sensitive to frequency and temperature, but its magnitude, as predicted by weak-interaction-driven bulk-viscous effects, is too small (within the equation-of-state models studied here) to be detectable by current or future observations. However, we find that the (conservative) dynamical tidal response function depends strongly on the slope of the symmetry energy and on higher-order coefficients of the symmetry energy. This indicates that the (conservative) dynamical tide is sensitive to higher-order coefficients, motivating a dedicated parameter-estimation study to assess how well they can be constrained.

We analyse the gravitational-wave emission from 60 two-dimensional core-collapse supernova simulations. The models cover a range of progenitors and equations of state. We focus on the narrow frequency interval in the gravitational-wave spectrum where the emitted power is strongly suppressed (the power gap) and how its central frequency relates to the physical properties of the simulations. We find that the power-gap frequency exhibits strong and systematic correlations with the properties of the inner core of the forming neutron star, for example the sound speed, suggesting that the gap encodes information about the behaviour of matter at extreme densities. We further examine how well several mechanisms proposed in the literature account for the presence and evolution of the gap in our simulations. Finally, we explore a scenario in which the gap arises from destructive interference between a narrow oscillation mode and a broadband background signal, demonstrating that such an interaction can produce a sharp minimum in the emitted gravitational-wave power.