The Red Supergiant Binary Fraction of the Large Magellanic Cloud
  The binary fraction of unevolved massive stars is thought to be 70-100% but
there are few observational constraints on the binary fraction of the evolved
version of a subset of these stars, the red supergiants (RSGs). Here we
identify a complete sample of RSGs in the Large Magellanic Cloud (LMC) using
new spectroscopic observations and archival UV, IR and broadband optical
photometry. We find 4090 RSGs with log L/Lo > 3.5 with 1820 of them having log
L/Lo > 4, which we believe is our completeness limit. We additionally
spectroscopically confirmed 38 new RSG+B star binaries in the LMC, bringing the
total known up to 55. We then estimated the binary fraction using a k-nearest
neighbors algorithm that classifies stars as single or binary based on
photometry with a spectroscopic sample as a training set. We take into account
observational biases such as line-of-sight stars and binaries in eclipse while
also calculating model-dependent corrections for RSGs with companions that our
observations were not designed to detect. Based on our data, we find an initial
result of 13.5 +7.56/-6.67% for RSGs with O or B-type companions. Using the
Binary Population and Spectral Synthesis (BPASS) models to correct for
unobserved systems, this corresponds to a total RSG binary fraction of 19.5
+7.6/-6.7%. This number is in broad agreement with what we would expect given
an initial OB binary distribution of 70%, a predicted merger fraction of 20-30%
and a binary interaction fraction of 40-50%.
