Sensitivity of binary pulsar timing to spin-0 and spin-1 ultralight dark matter

Abstract: If dark matter consists of ultralight bosons, on galactic scales it can be effectively described as a coherent classical field experiencing oscillations. Such a field could perturb the dynamics of celestial bodies via a direct coupling to ordinary matter, introducing signatures detectable through high-precision pulsar timing analysis. In this work, we extend a two-step Bayesian inference framework, originally developed for linearly coupled scalar ultralight dark matter (ULDM), to probe a quadratic scalar coupling and spin-1 vector dark matter. By explicitly marginalising over nuisance orbital parameters, our approach provides robust sensitivity limits that avoid the artificial overestimation often associated with direct fitting techniques. For quadratic scalar ULDM, we establish new constraints on the coupling $β$ in the range between $2 \times 10^{-22}$ eV and $2 \times 10^{-21}$ eV inaccessible to other experiments, while identifying mass regimes where the sensitivity is dominated by the orbital phase $Ψ'$ or the projected semi-major axis $x$. For vector ULDM, we characterize resonant signatures present even in circular orbits and obtain bounds on the coupling $g$ within the $10^{-23}$ eV to $10^{-18}$ eV range, yielding results within the same orders of magnitude as current laboratory and space-based experiments.