DYNAMIC FRICTION IN BINARY-SYSTEMS

The Chandrasekhar formula for dynamical friction applies to an isolated body traveling uniformly through a homogeneous collisionless background, e.g., dark matter in the Galactic disk or dark halo. In a binary system interaction between the components via the background's distortion may vitiate a naive estimate with that formula of the orbital evolution through dynamical friction. We perform a full calculation of the energy loss rate using the linearized collisionless Boltzmann equation for the case that the orbital velocity is small compared with the background's velocity dispersion. Intuitively, this constraint would suggest that the binary components do not cooperate in the orbital decay, this justifying an estimate of the friction via the Chandrasekhar formula applied separately to each component. The full calculation supports this view only partially. It is found that the energy loss rate consists of a Chandrasekhar-like contribution for each binary component separately, together with a term representing the cumulative effect of all completed orbits. The latter contribution, at first negligible compared with the Chandrasekhar contribution, grows roughly logarithmically with the age of the binary until it saturates when the number of completed orbits is of the order of the square of the ratio of the background's velocity dispersion to the orbital speed. For wide binaries with separation ∼0.01-0.1 pc immersed in the Galactic disk's dark matter, the additional term eventually augments the friction by a factor of 2 over the naive prediction of Chandrasekhar's formula.