Binary pulsars as probes of a Galactic dark matter disk

As a binary pulsar moves through a wind of dark matter particles, the resulting dynamical friction modifies the binary's orbit. We study this effect for the double disk dark matter (DDDM) scenario, where a fraction of the dark matter is dissipative and settles into a thin disk. For binaries within the dark disk, this effect is enhanced due to the higher dark matter density and lower velocity dispersion of the dark disk, and due to its co-rotation with the baryonic disk.We estimate the effect and compare it with observations for two different limits in the Knudsen number ($Kn$). First, in the case where DDDM is effectively collisionless within the characteristic scale of the binary ($Kn\gg1$) and ignoring the possible interaction between the pair of dark matter wakes. Second, in the fully collisional case ($Kn\ll1$), where a fluid description can be adopted and the interaction of the pair of wakes is taken into account. We find that the change in the orbital period is of the same order of magnitude in both limits. A comparison with observations reveals good prospects to probe currently allowed DDDM models with timing data from binary pulsars in the near future. We finally comment on the possibility of extending the analysis to the intermediate (rarefied gas) case with $Kn\sim1$.