Title: The NICER data and a $σ$-field dependent stiffness of the hadronic equation of state

Abstract: Analyses for the NICER data indicate that there is no significant variation of the compact star radii within the mass range of 1.4 to 2.0 solar masses. Yamamoto et al. [Phys. Rev. C 108, 035811 (2023)] concluded recently that ``this feature cannot be reproduced by the hadronic matter due to the softening of the equation of state (EoS) by hyperon mixing, suggesting the possible existence of quark phases in neutron-star interiors.'' Using a collection of 162 purely nucleonic, hyperonic, and quarkish EoSs from CompOSE database and some other works, we verify that hyperons indeed lead to a significant difference in radii of stars of 1.4 and 2.0 solar masses, which diminishes in the presence of quarks. We compare the shapes of the mass-radius curves and show that hyperons and quarks in the neutron star cores prefer a particular curve shape with backbending. It is argued that the shape {is controlled by the density dependence} of the nuclear symmetry energy. We draw attention to the existence of a class of purely hadronic relativistic mean-field EoSs with scalar-field dependent hadron masses and coupling constants that satisfy the known constraints on the EoSs including the analyses of the new NICER data and the above requirement of no significant variation of the neutron star radii.