We construct parameter sets of the relativistic mean-field model fitted to the recent constraints on the asymmetry energy J and the slope parameter L for pure neutron matter. We find cases of unphysical behaviour, i.e. the appearance of negative pressures, for stiff parameter sets with low values of the effective mass m * /m. In some cases the equation of state of pure neutron matter turns out to be outside the allowed band given by chiral effective field theory. The mass-radius relations of neutron stars for all acceptable parameter sets shows a maximum mass in excess of 2M⊙ being compatible with pulsar mass measurements. Given the constraints on the model in the low-density regime coming from chiral effective theory, we find that the radius of a 1.4M⊙ neutron star is nearly independent on the value of L. This is in contrast to some previous claims for a strong connection of the slope parameter with the radius of a neutron star. In fact, the mass-radius relation turns out to depend only on the isoscalar parameters of symmetric matter. The constraints of GW170817 on the tidal deformability and on the radius are also discussed.

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