  The measured orbital period decay of compact-star binaries, with
characteristic orbital periods $\sim 0.1$~days, is explained with very high
precision by the gravitational wave (GW) emission of an inspiraling binary in
vacuum. 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. 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), the non-singular-isothermal-sphere (NSIS) and
the Ruffini-Arg\"uelles-Rueda (RAR) 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 NS-NS, NS-WD and WD-WD binaries for
which measurements of the orbital decay exist. Then, we evaluate the conditions
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
$1.3$--$0.2$ $M_\odot$ NS-WD, $1.3$--$1.3$~$M_\odot$ NS-NS, and
$0.25$--$0.50$~$M_\odot$ 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 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.
