  We analyze the effects of including $\Delta(1232)$ isobars in an equation of
state (EoS) for cold, $\beta$-stable neutron star matter, employing
relativistic nuclear mean field theory. The selected EoS reproduces the
properties of nuclear matter and finite nuclei and, in the astrophysical
context, allows for the presence of hyperons in neutron stars having masses
larger than 2$M_{\odot}$. We find that the composition and structure of neutron
stars is critically influenced by the addition of the $\Delta$ isobars, which
allows us to constrain their interaction with the meson fields taking into
account astrophysical information. Imposing that the EoS is stable and ensures
the existence of 2$M_{\odot}$ neutron stars, as well as requiring agreement
with data of $\Delta$ excitation in nuclei, we find that, in the absence of
other mechanisms stiffening the EoS at high densities, the interaction of the
$\Delta$ isobars with the sigma and omega meson fields must be at least 10\%
stronger than that of the nucleons. Moreover, the neutron star moment of
inertia turns out to be sensitive to the presence of $\Delta$ isobars, whereas
the inclusion of $\Delta$ isobars in the EoS allows for smaller stellar radii
and for a lower value of the tidal deformability consistent with the analysis
of the GW170817 merger event.
