Influence of the crust on the neutron star macrophysical quantities and universal relations

Measurements of neutron-star macrophysical properties thanks to multimessenger observations offer the possibility to constrain the properties of nuclear matter. Indeed cold and dense matter as found inside neutron stars, in particular in their core, is not accessible to terrestrial laboratories.We investigate the consequences of using equations of state that employ models for the core and the crust that are not calculated consistently on the neutron-star macrophysical properties, on some of the so-called universal relations and on the constraints obtained from gravitational-wave observations. We use various treatments found in the literature to connect together nonconsistent core and crust equations of state. We then compute the mass, the radius, the tidal deformability, and the moment of inertia for each model. Finally, we assess the discrepancies in the neutron-star macrophysical properties obtained when consistent models for the whole star and nonconsistent ones are employed. The use of crust models nonconsistent with the core introduces an error on the macrophysical parameters which can be as large as the estimated accuracy of current and next generation telescopes. The precision of some of the universal relations reported in the literature is found to be overestimated. We confirm that the equation of the crust has limited influence on the macrophysical properties. The discrepancy between results obtained for a fully consistent equation of state and a nonconsistent one can be reduced if one connects the core and the crust models at baryon densities around 0.08-0.1 fm$^{-3}$. The equation of the crust cannot be probed with current multimessenger observations and near-future ones.