Challenging the presence of scalar charge and dipolar radiation in binary pulsars

Corrections to general relativity that introduce long-ranged scalar fields which are nonminimally coupled to curvature typically predict that neutron stars possess a nontrivial scalar field profile anchored to the star. An observer far from a star is most sensitive to the spherically symmetric piece of this profile that decays linearly with the inverse of the distance to the source, the so-called scalar monopole charge, which is related to the emission of dipolar radiation from compact binary systems. The presence of dipolar radiation has the potential to rule out or very strongly constrain extended theories of gravity. These facts may lead people to believe that gravitational theories that introduce long-ranged scalar fields have already been constrained strongly from binary pulsar observations. Here we challenge this "lore" by investigating the decoupling limit of Gauss-Bonnet gravity as an example, in which the scalar field couples linearly to the Gauss-Bonnet density in the action. We prove a theorem that neutron stars in this theory cannot possess a scalar charge, due to the topological nature of the Gauss-Bonnet density. Thus Gauss-Bonnet gravity evades the strong binary pulsar constraints on dipole radiation. We discuss the astrophysical systems which will yield the best constraints on Gauss-Bonnet gravity and related quadratic gravity theories. To achieve this we compute the scalar charge in quadratic gravity theories by performing explicit analytic and numerical matching calculations for slowly rotating neutron stars. In generic quadratic gravity theories, either neutron star-binary or neutron star-black hole systems can be used to constrain the theory, but because of the vanishing charge, Gauss-Bonnet gravity evades the neutron star-binary constraints. However, in contrast to neutron stars, black holes in Gauss-Bonnet gravity do anchor scalar charge, because of the difference in topology. The best constraints on Gauss-Bonnet gravity will thus come from accurate black hole observations, for example through gravitational waves from inspiraling binaries or the timing of pulsar-black hole binaries with radio telescopes. We estimate these constraints to be a factor of 10 better than the current estimated bound, and also include estimated constraints on generic quadratic gravity theories from pulsar timing.