The eccentricity distribution of wide binaries and their individual measurements

Abstract

Eccentricity of wide binaries is difficult to measure due to their long orbital periods. With Gaia’s high-precision astrometric measurements, eccentricity of a wide binary can be constrained by the angle between the separation vector and the relative velocity vector (the v-r angle). In this paper, by using the v-r angles of wide binaries in Gaia Early Data Release 3, we develop a Bayesian approach to measure the eccentricity distribution as a function of binary separations. Furthermore, we infer the eccentricities of individual wide binaries and make them publicly available. Our results show that the eccentricity distribution of wide binaries at 102 AU is close to uniform and becomes superthermal at >103 AU, suggesting two formation mechanisms dominating at different separation regimes. The close binary formation, most likely disc fragmentation, results in a uniform eccentricity distribution at <102 AU. The wide binary formation that leads to highly eccentric wide binaries at >103 AU may be turbulent fragmentation and/or the dynamical unfolding of compact triples. With Gaia, measuring eccentricities is now possible for a large number of wide binaries, opening a new window to understanding binary formation and evolution.

On the Phase-mixed Eccentricity and Inclination Distributions of Wide Binaries in the Galaxy

“…These results may go some way to understanding the observed nonthermal (including superthermal) eccentricity distributions of wide binaries in the solar neighborhood (Tokovinin 2020;Hwang et al 2022). However, before strong conclusions can be drawn, both time dependence and scattering from passing stars must be incorporated into the model.…”

“…Of course there are many subtleties to be addressed before one can claim this comparison between theory and observation to be precise. To name just one, Hwang et al (2022) inferred their eccentricity DFs assuming an isotropic DF of binary orientations, whereas we have shown that the "special direction" picked out by the Galactic plane actually creates a nonisotropic DF in which e and i are correlated (and where the special values of i are easily predicted). In principle one could measure the joint e-i distribution of wide binaries and use it to distinguish the impact of Galactic tides compared to other dynamical effects/ formation channels.…”

“…Observationally, various pieces of evidence regarding metallicities (El-Badry & Rix 2018; Hwang et al 2020), mass ratios (Moe & Di Stefano 2017), and eccentricities (Tokovinin 2020; Hwang et al 2022) suggest that binaries with a  10 2 au and a  10 3 au follow separate formation channels. Let us take this literally and suppose that all binaries with a  10 3 au were formed from some channel that produced an initially superthermal DF.…”

“…However, in recent years the arrival of GAIA data has meant that statistical measurements of the distribution function (DF) of binary orbital elements are now possible. In particular, both Tokovinin (2020) and Hwang et al (2022) have analyzed the distribution of relative position and velocity vectors of binary components, which contains statistical information about binary eccentricities, and thereby claimed detection of a superthermal eccentricity distribution (P(e) ∝ e α with α > 1) for binaries with projected separations 10 3 au in the solar neighborhood. The origin of this superthermal distribution is unexplained, but is presumably affected by the birth distribution of binaries, and the subsequent dynamical perturbations those binaries experience due to (i) scattering from passing stars, molecular clouds, and so on, and (ii) the torquing effect of Galactic tides.…”

Eccentric Pairs: Analytic Gravitational Waves from Binary Black Holes in Elliptic Orbits

“…Let's look now at the predicted evolution of the eccentricity, for an equal mass binary of 50M total mass and three values for the eccentricity: e 0 = 0.5, 0.25, 0.1 at f low . We choose the highest eccentricity to be e 0 = 0.5 because is close to the average eccentricity for wide binaries [171]. Fig.…”