Eccentricity dynamics of wide binaries  I. The effect of Galactic tides
Abstract
A major puzzle concerning the wide stellar binaries (semimajor axes a ≳ 10^{3} au) in the Solar neighbourhood is the origin of their observed superthermal eccentricity distribution function (DF), which is well approximated by P(e) ∝ e^{α} 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, nonsuperthermal one, under the restrictive assumptions that the eccentricity DF was initially of powerlaw form and then was rapidly phasemixed 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 nonpowerlaw DFs can be described by an effective powerlaw index α_{eff} which accurately characterizes both their initial and final states, and that a DF with initial (effective or exact) powerlaw index α_{i} is transformed by Galactic tides into another power law with index α_{f} ≈ (1 + α_{i})/2 on a timescale $\sim 4\, \mathrm{Gyr}\, (a/10^4\mathrm{AU})^{3/2}$. 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.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 September 2023
 DOI:
 10.1093/mnras/stad2073
 arXiv:
 arXiv:2303.15531
 Bibcode:
 2023MNRAS.524.3102M
 Keywords:

 celestial mechanics;
 binaries: general;
 Galaxy: kinematics and dynamics;
 Astrophysics  Astrophysics of Galaxies;
 Astrophysics  Solar and Stellar Astrophysics
 EPrint:
 Updated to accepted version: 14 pages, 9 figures. Main result in Figure 7. Comments still welcome!