  The critical densities and impact of forming \D resonances in neutron stars
are investigated within an extended nonlinear relativistic mean-field (RMF)
model. The critical densities for the formation of four different charge states
of \D are found to depend differently on the separate kinetic and potential
parts of nuclear symmetry energy, the first example of a microphysical property
of neutron stars to do so. Moreover, they are sensitive to the in-medium Delta
mass $m_{\Delta}$ and the completely unknown $\Delta$-$\rho$ coupling strength
$g_{\rho\Delta}$. In the universal baryon-meson coupling scheme where the
respective $\Delta$-meson and nucleon-meson coupling constants are assumed to
be the same, the critical density for the first $\Delta^-(1232)$ to appear is
found to be \rc=$(2.08\pm0.02)\rho_0$ using RMF model parameters consistent
with current constraints on all seven macroscopic parameters usually used to
characterize the equation of state (EoS) of isospin-asymmetric nuclear matter
(ANM) at saturation density $\rho_0$. Moreover, the composition and the
mass-radius relation of neutron stars are found to depend significantly on the
values of the $g_{\rho\Delta}$ and $m_{\Delta}$.
