  The timing of binary pulsars allows us to place some of the tightest
constraints on modified theories of gravity. Perhaps some of the most
interesting and well-motivated extensions to General Relativity are
scalar-tensor theories, in which gravity is mediated by the metric tensor and a
scalar field. These theories predict large deviations from General Relativity
in the presence of neutron stars through a phenomenon known as scalarization.
Neutron stars in scalar-tensor theories develop scalar charges, which directly
enter the timing model for binary pulsars. In this paper, we calculate and
tabulate these scalar charges in two popular, massless scalar tensor theories
for a collection of neutron star equations of state that are compatible with
constraints placed by the recent, gravitational wave observations of a binary
neutron star coalescence. We then study these scalar charges and explore
analytic scaling relations that allow us to predict their value in a large
region of parameter space. Our results allow for the quick evaluation of the
scalar charge in a large region of scalar-tensor theory parameter space, which
has applications for gravitational wave tests of scalar-tensor theories, as
well as binary pulsar experiments.
