  A binary system embedded in a Dark Matter (DM) background may experience a
change in its orbital period due to dynamical friction as the binary moves
through a wind of DM particles. We compute such a perturbative effect on the
binary evolution considering that DM is constituted of degenerate gas of free
fermions. The analysis point out that the secular change of the orbital period
is more sensitive, and likely measurable, to degenerate fermions with masses
$\gtrsim50$ eV, depending slightly, but still being distinguishable, on the
binary star configuration (e.g. NS-NS, NS-WD and WD-WD). Interestingly, we find
that NS-NS binary systems with large orbital periods, $P_{b}\gtrsim100$ days,
experience larger orbital period decays. We also show that this effect is
clearly increased, under the former conditions, in binaries orbiting small DM
halos, which correspond to extragalactic pulsars. This situation represents the
best astrophysical scenario to test such effects of light fermionic DM. We use
some available measurements of the orbital period time-derivative for
long-period binaries in the Milky-Way to quantify more realistically this
effect. For instance, measurements of the J1713+0747 pulsar set an upper bound
on the fermion mass of $m_{f}\lesssim 1$ keV. This bound can be considerably
improved by using pulsar timing observations of extragalactic pulsars. Under
this perspective, high precision of timing pulsar observations will reveal
whether DM dynamical friction effect may be tested with the upcoming generation
of surveys leading to the possibility of constraining more strongly the
properties of light fermionic DM.
