Eccentricity dynamics of wide binaries – I. The effect of Galactic tides

Abstract

ABSTRACT A major puzzle concerning the wide stellar binaries (semimajor axes a ≳ 103 au) in the Solar neighbourhood is the origin of their observed superthermal eccentricity distribution function (DF), which is well approximated by P(e) ∝ eα with α ≈ 1.3. This DF evolves under the combined influence of (i) tidal torques from the Galactic disc and (ii) scattering by passing stars, molecular clouds, and substructure. Recently, it was demonstrated that Galactic tides alone cannot produce a superthermal eccentricity DF from an initially isotropic, non-superthermal one, under the restrictive assumptions that the eccentricity DF was initially of power-law form and then was rapidly phase-mixed toward a steady state by the tidal perturbation. In this paper, we first prove analytically that this conclusion is valid at all times, regardless of these assumptions. We then adopt a thin Galactic disc model and numerically integrate the equations of motion for several ensembles of tidally perturbed wide binaries to study the time evolution in detail. We find that even non-power-law DFs can be described by an effective power-law index αeff which accurately characterizes both their initial and final states, and that a DF with initial (effective or exact) power-law index αi is transformed by Galactic tides into another power law with index αf ≈ (1 + αi)/2 on a time-scale $\sim 4\, \mathrm{Gyr}\, (a/10^4\mathrm{AU})^{-3/2}$. In a companion paper, we investigate separately the effect of stellar scattering. As the GAIA data continues to improve, these results will place strong constraints on wide binary formation channels.