Scalar Charges and Scaling Relations in Massless Scalar-Tensor Theories

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.