  An isovector-scalar meson is incorporated self-consistently into the
quark-meson coupling description of nuclear matter and its most prominent
effects on the structure of neutron stars are investigated. The recent
measurement of GW170817 is used to constrain the strength of the
isovector-scalar channel. With the imminent measurements of the neutron star
radii in the NICER mission it is particularly notable that the inclusion of the
isovector-scalar force has a significant impact. Indeed, the effect of this
interaction on the neutron star radii and masses is larger than the
uncertainties introduced by variations in the parameters of symmetric nuclear
matter at saturation, namely the density, binding energy per nucleon and the
symmetry energy. In addition, since the analysis of GW170817 has provided
constraints on the binary tidal deformability of merging neutron stars, the
predictions for this parameter within the quark-meson coupling model are
explored, as well as the moment of inertia and the quadrupole moment of slowly
rotating neutron stars.
