Empirical relations for post-merger GW signal and neutron star equation of state

The merger process of binary neutron stars (BNSs) is a source of gravitational waves (GWs), and the advancement of numerical relativistic simulations have allowed for deeper study of different aspects of the phenomena. GW extraction from these simulations has been shown to produce a promising potential correlation between the properties of both the emitted GWs and those of the neutron stars that could allow for principal constraints to be put on the equation of state (EoS) of nuclear matter. In particular, the relations between the properties of both the emitted GWs during post-merger such as peak frequency and those of the neutron stars: maximum mass, radius of the maximum mass star, and the ratio of radius of the half-maximum mass star and the radius of the maximum mass star. These correlations could allow us to further constrain the EoS models of neutron stars. To establish conclusive correlation results, many simulations of BNSs mergers and with varying EoSs are to be studied. In this work we employ over 400 relativistic simulations of these mergers to find whether knowledge of the peak GW frequency can be used to predict EoS quantities of neutron stars. We extract each waveform through a Fourier transform, followed by the assembling of a dataset with all applicable EoSs and their quantities. In order to identify correlation, I test different statistical approaches in analyzing the predictability of these intrinsic NS properties in regard to the post-merger GW peak frequency. I first construct a multivariate Bayesian linear model to show the predictability of peak GW frequency for each model. The predictability for a model containing no EoS quantities was compared to models that do include such quantities. We find that not only is the model's predictability better with the inclusion of EoS parameters, but it increases with the number of parameters within the model. Next steps include expanding the pool of simulations, and eventually developing machine learning (ML) techniques to fit the observed quantities with the theoretical model predictions.