Spectral classification of gravitational-wave emission and equation of state constraints in binary neutron star mergers

In summer 2017 gravitational waves (GWs) from a binary neutron star (NS) merger were detected for the first time. Moreover, electromagnetic emission was observed and associated with the merger. This very first unambiguous observation of a NS coalescence has impressively advanced our understanding of the merger process and has set some first constraints on the macroscopic properties of NSs, with direct implications for the high-density equation of state. We discuss work on NS mergers focusing on the postmerger GW emission. These studies are based on numerical simulations of the merger and survey a large sample of candidate equations of state for NS matter. The goal is to connect observables with the underlying physics questions. This offers a way to constrain the properties of high-density matter through the determination of NS radii, as inferred by an empirical relation connecting the dominant GW frequency peak in the postmerger phase to the radius of nonrotating NSs of a certain mass. We clarify the physical origin of secondary peaks and discuss a spectral classification scheme, based on their relative strength. Observational prospects for the dominant and the secondary peaks are also discussed. The threshold mass to black-hole collapse is connected by another empirical relation to the maximum mass and compactness of nonrotating NSs, which can be derived semi-analytically. The observation of GW170817 then sets an absolute minimum radius for NSs of typical masses, based only on a minimal number of assumptions.