  We carry out numerical-relativity simulations of coalescing binary neutron
stars in a scalar-tensor theory that admits spontaneous scalarization. We model
neutron stars with realistic equations of state. We choose the free parameters
of the theory taking into account the constraints imposed by the latest
observations of neutron-star-- white-dwarf binaries with pulsar timing. We show
that even within those severe constraints, scalarization can still affect the
evolution of the binary neutron stars not only during the late inspiral, but
also during the merger stage. We also confirm that even when both neutron stars
have quite small scalar charge at large separations, they can be strongly
scalarized dynamically during the final stages of the inspiral. In particular,
we identify the binary parameters for which scalarization occurs either during
the late inspiral or only after the onset of the merger when a remnant,
supramassive or hypermassive neutron star is formed. We also discuss how those
results can impact the extraction of physical information on gravitational
waves once they are detected.
