  In order to understand the rates and properties of Type Ia and Type Ib/c
supernovae, X-ray binaries, gravitational wave sources, and gamma ray bursts as
a function of galactic environment and cosmic age, it is imperative that we
measure how the close binary properties of O and B-type stars vary with
metallicity. We have studied eclipsing binaries with early-B main-sequence
primaries in three galaxies with different metallicities: the Large and Small
Magellanic Clouds (LMC and SMC, respectively) as well as the Milky Way (MW).
The observed fractions of early-B stars which exhibit deep eclipses 0.25 <
Delta(m) (mag) < 0.65 and orbital periods 2 < P (days) < 20 in the MW, LMC, and
SMC span a narrow range of (0.7-1.0)%, which is a model independent result.
After correcting for geometrical selection effects and incompleteness toward
low-mass companions, we find for early-B stars in all three environments: (1) a
close binary fraction of (22+/-5)% across orbital periods 2 < P (days) < 20 and
mass ratios q = M_2/M_1 > 0.1, (2) an intrinsic orbital period distribution
slightly skewed toward shorter periods relative to a distribution that is
uniform in log P, (3) a mass-ratio distribution weighted toward low-mass
companions, and (4) a small, nearly negligible excess fraction of twins with q
> 0.9. Our fitted parameters derived for the MW eclipsing binaries match the
properties inferred from nearby, early-type spectroscopic binaries, which
further validates our results. There are no statistically significant trends
with metallicity, demonstrating that the close binary properties of massive
stars do not vary across metallicities -0.7 < log(Z/Z_sun) < 0.0 beyond the
measured uncertainties.
