Confronting a set of Skyrme and $\chi_{EFT}$ predictions for the crust of neutron stars

With the improved accuracy of neutron star observational data, it is necessary to derive new equation of state where the crust and the core are consistently calculated within a unified approach. For this purpose we describe non-uniform matter in the crust of neutron stars employing a compressible liquid-drop model, where the bulk and the neutron fluid terms are given from the same model as the one describing uniform matter present in the core. We then generate a set of fifteen unified equations of state for cold catalyzed neutron stars built on realistic modelings of the nuclear interaction, which belongs to two main groups: the first one derives from the phenomenological Skyrme interaction and the second one from $\chi_{EFT}$ Hamiltonians. The confrontation of these model predictions allows us to investigate the model dependence for the crust properties, and in particular the effect of neutron matter at low density. The new set of unified equations of state is available at the CompOSE repository.