We study in detail the f -mode secular instability for rapidly rotating neutron stars, putting emphasis on supermassive models which do not have a stable nonrotating counterpart. Such neutron stars are thought to be the generic outcome of the merger of two standard mass neutron stars. In addition we take into account the effects of strong magnetic field and r-mode instability, that can drain a substantial amount of angular momentum. We find that the gravitational wave signal emitted by supramassive neutron stars can reach above the Advance LIGO sensitivity at distance of about 20Mpc and the detectability is substantially enhanced for the Einstein Telescope. The event rate will be of the same order as the merging rates, while the analysis of the signal will carry information for the equation of state of the post-merging neutron stars and the strength of the magnetic fields.

Theoretical models of self-interacting dark matter represent a promising answer to a series of open problems within the so-called collisionless cold dark matter (CCDM) paradigm. In case of asymmetric dark matter, self-interactions might facilitate gravitational collapse and potentially lead to formation of compact objects predominantly made of dark matter. Considering both fermionic and bosonic equations of state, we construct the equilibrium structure of rotating dark stars, focusing on their bulk properties, and comparing them with baryonic neutron stars. We also show that these dark objects admit the I-Love-Q universal relations, which link their moments of inertia, tidal deformabilities, and quadrupole moments. Finally, we prove that stars built with a dark matter equation of state are not compact enough to mimic black holes in general relativity, thus making them distinguishable in potential events of gravitational interferometers.

The basic formulation describing quadratic mode coupling in rotating Newtonian stars is presented, focusing on polar modes. Due to the Chandrasekhar-Friedman-Schutz mechanism, the f -mode (fundamental oscillation) is driven unstable by the emission of gravitational waves. If the star falls inside the so-called instability window, the mode's amplitude grows exponentially, until it is halted by nonlinear effects. Quadratic perturbations form three-mode networks inside the star, which evolve as coupled oscillators, exchanging energy. Coupling of the unstable f -mode to other (stable) modes can lead to a parametric resonance and the subsequent saturation of its amplitude, thus suppressing the instability. The saturation point determines the amplitude of the gravitationalwave signal obtained from an individual source, as well as the evolutionary path of the latter inside the instability window.

Finite size effects come into play during the late stages of neutron star binary inspiral, with the tidal deformability of the supranuclear density matter leaving an imprint on the gravitational-wave signal. As demonstrated in the case of GW170817, this leads to a constraint on the neutron star radius (and hence the equation of state). A deeper understanding of the tidal response requires an analysis of both the state and composition of matter. While these aspects may not have dramatic impact, they could lead to systematic effects that need to be kept in mind as the observational data become more precise. As a step in this direction we explore the role of the composition of matter, which is likely to remain "frozen" during the late stages of binary inspiral. We provide the first in-depth analysis of the problem, including estimates of how composition impacts on the effective tidal deformability. The results provide improved insight into how aspects of physics that tend to be "ignored" impact on binary neutron star gravitational-wave signals.

We consider the dynamical tidal response of a neutron star in an inspiralling binary, focussing on the impact of the star’s elastic crust. Within the context of Newtonian gravity, we add the elastic aspects to the theoretical formulation of the problem and quantify the dynamical excitation of different classes of oscillation modes. The results demonstrate the expectation that the fundamental mode dominates the tidal response and show how the usual tidal deformability (and the Love number) emerge in the static limit. In addition, we consider to what extent the different modes may be excited to a level where the breaking strain of the crust would be exceeded (locally). The results show that the fundamental mode may fracture the crust during the late stages of inspiral. This is also the case for the first gravity mode, which reaches the breaking threshold in strongly stratified stars. In our models with a fluid ocean, interface modes associated with the crust-ocean transition may also induce crust fracture. If this happens it does so earlier in the inspiral, at a lower orbital frequency.