Rising Tides: Analytic Modeling of Tidal Effects in Binary Neutron Star Mergers

The gravitational waves produced by binary neutron star mergers offer a unique window into matter behavior under extreme conditions. In this context, we model analytically the effect of matter on the gravitational waves from binary neutron star mergers. We start with a binary black hole system, leveraging the post-Newtonian formalism for the inspiral and the Backwards-one-Body model for the merger. We combine the two methods to generate a baseline waveform and we validate our results against numerical relativity simulations. Next, we integrate tidal effects in phase and amplitude to account for matter and spacetime interaction, by using the NRTidal model, and test its accuracy against numerical relativity predictions, for two equations of state, finding a mismatch around the merger. Subsequently, we lift the restriction on the coefficients to be independent of the tidal deformability, and recalibrate them using the numerical relativity predictions. We obtain better fits for phase and amplitude around the merger, and are able to extend the phase modeling beyond the merger. We implement our method in a new open-source Python code, steered by a Jupyter Notebook. Our research offers new perspectives on analytically modeling the effect of tides on the gravitational waves from binary neutron star mergers.