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.