Abstract
Dark matter (DM) can consist of very light bosons behaving as a classical scalar field that experiences coherent oscillations. The presence of this DM field would perturb the dynamics of celestial bodies, either because the (oscillating) DM stress tensor modifies the gravitational potentials of the galaxy, or if DM is directly coupled to the constituents of the body. We study secular variations of the orbital parameters of binary systems induced by such perturbations. Two classes of effects are identified. Effects of the first class appear if the frequency of DM oscillations is in resonance with the orbital motion; these exist for general DM couplings including the case of purely gravitational interaction. Effects of the second class arise if DM is coupled quadratically to the masses of the binary system members and do not require any resonant condition. The exquisite precision of binary pulsar timing can be used to constrain these effects. Current observations are not sensitive to oscillations in the galactic gravitational field, though a discovery of pulsars in regions of high DM density may improve the situation. For DM with direct coupling to ordinary matter, the current timing data are already competitive with other existing constraints in the range of DM masses $\sim 10^{-22}-10^{-18}\,{\rm eV}$. Future observations are expected to increase the sensitivity and probe new regions of parameters.
Highlights
Dark matter (DM), a key ingredient in the success of the standard cosmological model, remains a mysterious component of our Universe
In our previous work [35] we showed that competitive constraints on ultralight dark matter (ULDM) in the mass range 10−22 eV ≲ mΦ ≲ 10−18 eV are obtained from the timing of millisecond binary pulsars
In this paper we have made a detailed study of the influence of ULDM candidates on the evolution of binary systems and have identified potentially observable signatures in high-precision timing measurements of binary pulsars
Summary
Dark matter (DM), a key ingredient in the success of the standard cosmological model, remains a mysterious component of our Universe. In this paper we extend the analysis of [35] by including the possibility of nonuniversal couplings and studying the secular effect of ULDM on all orbital parameters appearing in the pulsar timing model [39,40,41]. It is worth stressing that the couplings of ULDM to the two components of the binary pulsar system are naturally expected to be different even if at the fundamental level ULDM couples to the SM fields universally This is a consequence of the SEP violation and large gravitational binding energy of the pulsar constituting a few tens of percent of its mass. Appendix B contains the osculating orbit equations for a binary interacting with ULDM prior to extraction of secular contributions
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