Dynamical Friction in an Ultralight Scalar Medium across Coherent and Stochastic Regimes

Abstract: We study the conservative and dissipative forces on a Newtonian binary interacting with a nonrelativistic ultralight scalar medium. We derive integral expressions for the instantaneous force and the orbit-averaged energy flux generated by wake perturbations of a general background field. For a homogeneous coherent background, the conservative force suffers from a well-known infrared divergence. We trace this divergence to the failure of perturbation theory about a constant scalar state and identify the gravitational Bohr scale at which the homogeneous approximation breaks down. In the long-wavelength regime, the leading dissipation into the medium is quadrupolar, and we obtain an explicit expression for the leading energy flux from an eccentric binary. In the short-wavelength regime, we identify a local ''hard'' region in momentum space that produces a universal Coulomb logarithm, while the nonlogarithmic contribution remains orbit dependent. We then promote the background to a stochastic ensemble with a general velocity distribution. Three independent length scales, together with a derived geometric-mean scale, produce eight distinct scale hierarchies, for which we characterize the ensemble-mean response. Finally, we derive the two-point correlation function of the orbit-averaged energy flux and evaluate it in ''coherent-response'' regimes. Wave interference produces order-unity density fluctuations, so the flux in an individual realization can differ substantially from its ensemble mean.