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.
