Identifying hyperons in neutron star matter from the slope of the mass-radius diagram

The slope of the neutron star mass radius curve $dM/dR$ determined from two large sets of relativistic mean field equations of state for nucleonic and hyperonic neutron star matter is discussed. It is shown that if the mass-radius curve always has a negative slope the probability that the star has hyperons is very small. A very small probability of the presence of hyperons can already be identified by a negative slope for low-mass stars. A positive slope at $M/M_{\odot} = 1.4$, could indicate the possible presence of hyperons. Nucleonic EoS are found to be more probable than hyperonic ones, given the GW170817 and NICER observation constraints for PSR J0030+0451 and PSR J0740+6620, and the highest probability is associated with nucleonic stars that originate a mass radius curve with positive slope. Mass-radius curves with a positive slope greater than 1.8$M_\odot$ are not expected to occur. The nuclear matter property that most distinguishes the different scenarios is the curvature of the symmetry energy, with nucleonic EoS with positive slope predicting the highest values that can go above 100 MeV.