Optical-Mid-Infrared Period-Luminosity Relations for W UMa-type Contact
  Binaries Based on Gaia DR 1: 8% Distance Accuracy
  W Ursa Majoris (W UMa)-type contact binary systems (CBs) are useful
statistical distance indicators because of their large numbers. Here, we
establish (orbital) period-luminosity relations (PLRs) in 12
optical-to-mid-infrared bands (GBV RIJHKsW1W2W3W4) based on 183 nearby W
UMa-type CBs with accurate Tycho-Gaia parallaxes. The 1{\sigma} dispersion of
the PLRs decreases from optical to near- and mid-infrared wavelengths. The
minimum scatter, 0.16 mag, implies that W UMa-type CBs can be used to recover
distances to 7% precision. Applying our newly determined PLRs to 19 open
clusters containing W UMa-type CBs demonstrates that the PLR and open cluster
CB distance scales are mutually consistent to within 1%. Adopting our PLRs as
secondary distance indicators, we compiled a catalog of 55,603 CBs candidates,
of which 80% have distance estimates based on a combination of optical, near-,
and mid-infrared photometry. Using Fourier decomposition, 27,318
high-probability W UMa-type CBs were selected. The resulting 8% distance
accuracy implies that our sam- ple encompasses the largest number of objects
with accurate distances within a local volume with a radius of 3 kpc available
to date. The distribution of W UMa-type CBs in the Galaxy suggests that in
different environments, the CB luminosity function may be different: larger
numbers of brighter (longer-period) W UMa-type CBs are found in younger
environments.
