Piecewise polytropic meshing and refinement method for the reconstruction of the neutron star equation of state using tidal deformabilities and constraints in the piecewise polytropic parameters given by the GW170817 event

In this paper we present a new approach to the inverse problem for relativistic stars using the piecewise polytropic parametrization of the equation of state. The algorithm is a piecewise polytropic meshing and refinement method that reconstructs the neutron star equation of state from experimental data of the mass and the tidal Love parameter. We use an initial mesh of 65536 equations of state in a 4-volume of piecewise polytropic parameters that contains most of the candidate equations of state used today. The refinement process drives us to the reconstruction of the equation of state with a certain precision. Using the reconstructed equation of state, we calculate predictions for quasinormal modes and slow rotation parameters. In order to check the meshing and refinement method, we use as input data a few (6) configurations of a given equation of state. We reconstruct the equation of state in a quite good approximation, and then we compare the curves of physical parameters from the original equation of state and the reconstructed one. We obtain a relative difference for all the parameters smaller than 7.5%. We also study the constraints that impose the GW170817 event on the piecewise polytropic parameters $\{{\log_{10}p_1},{\Gamma_1},{\Gamma_2},{\Gamma_3}\}$. We use the waveform model TaylorF2 for the low-spin scenario, and see that the EOSs that lie outside the 90% credible region when ${\bar{\lambda}^{tid}_1}={\bar{\lambda}^{tid}_2}$ define a zone of polytropic parameters that does not depend on ${\Gamma_3}$.