  In certain classes of the scalar-Gauss-Bonnet theory strong spacetime
curvature in the vicinity of neutron stars and black holes can spontaneously
trigger scalarization in the compact object if the coupling strength of the
scalar field to the Gauss-Bonnet invariant exceeds a critical value. Specifying
on neutron stars, this threshold depends on the mass and equation of state. The
presence of a companion will further influence the required coupling strength
for scalarization, and thus, a stable hair can be installed at a lower
magnitude of coupling for those neutron stars as members of binaries. Focusing
on binary neutron star mergers, we investigate this latter dynamically-driven
scalarization, and find that the reduction in the threshold coupling strength
seems to be more profound for symmetric binaries, while the threshold is only
marginally reduced for rather asymmetric binaries. The associated scalar
radiation is also discussed. We discover in addition a universal relation
between the critical coupling strength and the stellar compactness for isolated
neutron stars and perform a detailed comparison with the dynamical
scalarization threshold. In synergy with such relations, one can, at least in
principle, constrain the theory parameters regardless of the uncertainty in the
equation of state.
