The measured orbital period decay of relativistic compact-star binaries, with characteristic orbital periods $\sim 0.1\mathrm{days}$, is explained with very high precision by the gravitational wave (GW) emission of an inspiraling binary in a vacuum predicted by general relativity. However, the binary gravitational binding energy is also affected by an usually neglected phenomenon, namely the dark matter dynamical friction (DMDF) produced by the interaction of the binary components with their respective DM gravitational wakes. Therefore, the inclusion of the DMDF might lead to a binary evolution which is different from a purely GW-driven one. The entity of this effect depends on the orbital period and on the local value of the DM density, hence on the position of the binary in the Galaxy. We evaluate the DMDF produced by three different DM profiles: the Navarro-Frenk-White (NFW) profile, the nonsingular-isothermal-sphere (NSIS) and the Ruffini-Argüelles-Rueda (RAR) DM profile based on self-gravitating keV fermions. We first show that indeed, due to their Galactic position, the GW emission dominates over the DMDF in the Neutron star (NS)-NS, NS-(White Dwarf) WD and WD-WD binaries for which measurements of the orbital decay exist. Then, we evaluate the conditions (i.e. orbital period and Galactic location) under which the effect of DMDF on the binary evolution becomes comparable to, or overcomes, the one of the GW emission. We find that, for instance for $1.3–0.2M_{\odot }$ NS-WD, $1.3–1.3M_{\odot }$ NS-NS, and $0.25–0.50M_{\odot }$ WD-WD, located at 0.1 kpc, this occurs at orbital periods around 20–30 days in a NFW profile while, in a RAR profile, it occurs at about 100 days. For closer distances to the Galactic center, the DMDF effect increases and the above critical orbital periods become interestingly shorter. Finally, we also analyze the system parameters (for all the DM profiles) for which DMDF leads to an orbital widening instead of orbital decay. All the above imply that a direct/indirect observational verification of this effect in compact-star binaries might put strong constraints on the nature of DM and its Galactic distribution.

• Received 16 June 2017

DOI:https://doi.org/10.1103/PhysRevD.96.063001