The slope of the neutron star mass-radius curve, $dM/dR$, is studied to understand the information it may carry about the composition of neutron stars, particularly with regard to the presence of non-nucleonic degrees of freedom. This study uses two large sets of relativistic mean-field equations of state with either nucleonic or nucleonic and hyperonic degrees of freedom, and imposes constraints obtained from GW170817 and the pulsars PSR $\mathrm{J}0030+0451$ and PSR $\mathrm{J}0740+6620$. It is shown that: (i) some mass-radius curves are characterized by a negative slope from one solar mass up to the maximum mass; (ii) other equations of state (EoSs) have a positive slope for a given range of masses below the maximum star mass. Within the set of models considered, the first set includes only a very small number of hyperonic EoSs: fewer than 0.5% of the total number of hyperonic stars and approximately one third of the nucleonic EoS. We have also analyzed the sign of the slope for neutron star masses of 1.2, 1.4 and $1.8M_{\odot }$. Only approximately 1% of hyperonic EoSs predict a negative slope for $1.4M_{\odot }$ stars, whereas over 90% of nucleonic stars have a negative slope at this mass. Finally, almost all stars have a negative slope at $1.8M_{\odot }$. A positive slope at $1.4M_{\odot }$ may indicate the presence of non-nucleonic degrees of freedom within neutron stars. The nuclear matter property that distinguishes the different scenarios most clearly is the curvature of the symmetry energy. Nucleonic EoSs with a positive slope $dM/dR$ predict the highest values, which can exceed 100 MeV.

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• Nuclear astrophysics
• Neutron stars & pulsars