Discovery of an equal-mass "twin" binary population reaching 1000+ AU
  separations
  We use a homogeneous catalog of 42,000 main-sequence wide binaries identified
by Gaia to measure the mass ratio distribution, p(q), of binaries with primary
masses $0.1<M_1/M_{\odot}<2.5$, mass ratios $0.1 \lesssim q<1$, and separations
$50<s/{\rm AU}<50,000$. A well-understood selection function allows us to
constrain p(q) in 35 independent bins of primary mass and separation, with
hundreds to thousands of binaries in each bin. Our investigation reveals a
sharp excess of equal-mass "twin" binaries that is statistically significant
out to separations of 1,000 to 10,000 AU, depending on primary mass. The excess
is narrow: a steep increase in p(q) at $0.95 \lesssim q<1$, with no significant
excess at $q\lesssim 0.95$. A range of tests confirm the signal is real, not a
data artifact or selection effect. Combining the Gaia constraints with those
from close binaries, we show that the twin excess decreases with increasing
separation, but its width ($q\gtrsim 0.95$) is constant over $0.01<a/{\rm
AU}<10,000$. The wide twin population would be difficult to explain if the
components of all wide binaries formed via core fragmentation, which is not
expected to produce strongly correlated component masses. We conjecture that
wide twins formed at closer separations ($a \lesssim 100$ AU), likely via
accretion from circumbinary disks, and were subsequently widened by dynamical
interactions in their birth environments. The separation-dependence of the twin
excess then constrains the efficiency of dynamical widening and disruption of
binaries in young clusters. We also constrain p(q) across $0.1 \lesssim q<1$.
Besides changes in the twin fraction, p(q) is independent of separation at
fixed primary mass over $100 \lesssim s/{\rm AU} < 50,000$. It is flatter than
expected for random pairings from the IMF but more bottom-heavy for wide
binaries than for binaries with $a\lesssim$100 AU.
