Measuring the radii of merging neutron stars with asteroseismology

The structure and dynamics of neutron stars can be used to probe the physics of extreme matter at nuclear densities and beyond. Nucleonic matter up to ~2-3 times nuclear saturation density is well-studied by nuclear experiments and theoretical modelling. Matter beyond these densities may contain non-nucleonic degrees of freedom that determine the structure of the neutron star inner core and influence bulk observables like stellar radius. Neutron star radius is a key parameter for constraining the core equation of state, but is not a direct gravitational-wave observable during neutron star mergers. Here we show that, if nucleonic physics is well constrained at low densities, the frequency of the asteroseismic crust-core interface mode in a neutron star can be used to infer its radius to within 5-10%, in a way which is notably insensitive to the details of the inner core. This frequency can be measured through multimessenger coincident timing of resonant shattering flares, or direct observation of dynamical tidal resonance with next-generation gravitational-wave detectors. We show that improved constraints on low-density nucleonic physics by nuclear experimental and theoretical efforts will substantially improve such a radius measurement, leveraging low-density efforts for an improved understanding of physics at higher densities.