Broadening of universal relations at the birth and death of a neutron star

Certain relations among neutron -star observables that are insensitive to the underlying nuclear matter equation of state are known to exist. Such universal relations have been shown to be valid for cold and stationary neutron stars. Here, we study these relations in more dynamic scenarios: protoneutron stars and hypermassive neutron stars, allowing us to investigate the time evolution of these relations from the birth to the death of a neutron star. First, we study protoneutron stars. We use an effective equation of state, extracted from three-dimensional core -collapse supernova simulations, to obtain the structure of spherically symmetric protoneutron stars. We then consider nonradial oscillations to compute their f - mode frequency ( f ), as well as slow rotation and small tidal deformation, to compute their moment of inertia ( I ), spin -induced quadrupole moment ( Q ), and Love number. We find that well -established universal relations for cold neutron stars involving these observables (namely, the I - Love - Q and f - Love relations) are approximately valid for protoneutron stars, with a deviation below approximate to 10% for a postbounce time above approximate to 0.5 s, considering eight different supernova progenitors and one equation of state (SFHo). Next, we study hypermassive neutron stars. The bulk of a neutron star is defined as the region enclosed by the isodensity surface that corresponds to the maximum compactness ( C ) inside the star. We obtain a new universal relation between the f - mode frequency and the compactness of cold and nonrotating neutron stars, using bulk quantities. We show that this relation has an equation -of -state -variation of approximate to 3%, considering a set of ten equations of state. Bulk quantities of postmerger remnants can be obtained from numerical -relativity simulations. Using results from binary neutron star merger simulations, we study the evolution of hypermassive neutron stars on the f -C plane, considering two different mass ratios and one equation of state (SFHo). We find that the relation between the peak frequency of the gravitational -wave signal and the compactness from these hypermassive neutron stars deviates from the universal f -C relation by approximate to 70% -80%, when the peak frequency is taken directly as a proxy for the f - mode. As our results are limited to a single equation of state, the deviations we obtain when universal relations for cold neutron stars are used for protoneutron stars or hypermassive neutron stars can be conservatively considered as a lower limit. Finally, we discuss the reliability of the universal relations in the context of future observations of gravitational waves from remnants of core -collapse supernovae or binary neutron star mergers.