The power of binary pulsars in testing Gauss-Bonnet gravity

Context. Binary pulsars are a powerful tool for probing strong gravity that still outperform direct gravitational wave observations in a number of ways due to the remarkable accuracy of the pulsar timing. They can constrain the presence of additional charges of the orbiting neutron stars very precisely, leading to new channels of energy and angular momentum loss, such as scalar dipole radiation. Aims. In the present paper, we explore in detail the possibility of constraining different classes of scalar-Gauss-Bonnet gravity with binary pulsars. Additionally, we updated the existing constraints related to the observed maximum mass of neutron stars. Methods. Interestingly, depending on the equation of state, the resulting limits on the theory coupling parameters can outperform the constraints coming from binary merger observations by up to a factor of two, even for so-called Einstein-dilaton-Gauss-Bonnet gravity where neutron stars are often underestimated as relevant theory probes. As an additional merit, precise Bayesian methods are compared with approximate approaches, with the latter showing a very good performance despite their simplicity.