Modelling uncertainties in wide binary constraints on primordial black holes

Dark matter in the form of compact objects with mass $M_{\rm co} \gtrsim 10 M_{\odot}$ can be constrained by its dynamical effects on wide binary stars. Motivated by the recent interest in Primordial Black Hole dark matter, we revisit the theoretical modelling involved in these constraints. We improve on previous studies in several ways. Specifically, we i) implement a physically motivated model for the initial wide-binary semi-major axis distribution, ii) include unbound binaries, and iii) take into account the uncertainty in the relationship between semi-major axis and observed angular separation. These effects all tend to increase the predicted number of wide binaries (for a given compact object population). Therefore the constraints on the halo fraction in compact objects, $f_{\rm co}$, are significantly weakened. For the wide binary sample used in the most recent calculation of the constraints, we find the fraction of halo dark matter in compact objects is $f_{\rm co} < 1$ for $M_{\rm co} \approx 300 \, M_{\odot}$, tightening with increasing $M_{\rm co}$ to $f_{\rm co} < 0.26$ for $M_{\rm co} \gtrsim 1000 \, M_{\odot}$.