The Separation Distribution of Ultra-Wide Binaries across Galactic Populations

We present an extensive sample of ultra-wide binary stars in the solar neighborhood, focusing on separations of $0.01<s/{pc}<1$. Using data from Gaia DR2, we define kinematic sub-populations via the systems' tangential velocities, i.e., disk-like ($v_{\perp, tot}<40$km/s), intermediate ($v_{\perp,tot}=(40-85)$km/s), and halo-like ($v_{\perp,tot}>85$km/s) samples, presuming that these velocity cuts represent a rough ordering in the binaries' age and metallicity. Through stringent cuts on astrometric precision, we can obtain pure binary samples with thousands of binaries in each sample. For all three populations, the distribution of binary separations extends smoothly to 1pc, displaying neither strong truncation nor bimodality. Fitting a smoothly-broken power law for the separation distribution, we find that its slope at separations $s=10^{2.5-4}$AU is the same for all sub-populations, $p(s)\propto s^{\gamma}$, with $\gamma\sim-1.54$. However, the logarithmic slope of $p(s)$ steepens at $s \gtrsim 10^4$AU. We find some evidences that the degree of steepening increases with the binaries' age, with a slope-change of only $\Delta\gamma\sim0.5$ for disk-like stars, but $\Delta\gamma>1$ for halo-like stars. This trend is contrary to what might be expected if steepening at wide separations were due to gravitational perturbations by molecular clouds or stars, which would preferentially disrupt disk binaries. If we were to interpret steepening at $s\gtrsim 10^4$AU as a consequence of disruption by massive halo objects, we would have to invoke a MACHO population inconsistent with other constraints. As a more plausible alternative, we propose a simple model to predict the separation distribution of wide binaries formed in dissolving star clusters. This model generically predicts $\gamma\sim-1.5$ as observed, with steepening at larger separations due to the finite size of binaries' birth clusters.