  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 $2M_\odot$ 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 $1.4M_\odot$
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.
