Dancing in the dark: probing Dark Matter through the dynamics of eccentric binary pulsars

We investigate the dynamics of eccentric binary pulsars embedded in dark matter environments. While previous studies have primarily focused on circular orbits in collisionless dark matter halos, we extend this framework to eccentric systems and explore their interaction with ultralight scalar fields. Adopting a perturbative approach, we compute the modifications to the orbital period induced by dark matter-driven dynamical friction. Our results show that orbital eccentricity amplifies the imprints of non-vacuum environments on binary dynamics, underscoring the potential of such systems as sensitive probes for dark matter signatures.