The Near-infrared Optimal Distances Method Applied to Galactic Classical
  Cepheids Tightly Constrains Mid-infrared Period--Luminosity Relations
  Classical Cepheids are well-known and widely used distance indicators. As
distance and extinction are usually degenerate, it is important to develop
suitable methods to robustly anchor the distance scale. Here, we introduce a
near-infrared (near-IR) optimal distance method to determine both the
extinction values of and distances to a large sample of 288 Galactic classical
Cepheids. The overall uncertainty in the derived distances is less than 4.9%.
We compare our newly determined distances to the Cepheids in our sample with
previously published distances to the same Cepheids with Hubble Space Telescope
parallax measurements and distances based on the IR surface brightness method,
Wesenheit functions, and the main-sequence fitting method. The systematic
deviations in the distances determined here with respect to those of previous
publications is less than 1-2%. Hence, we constructed Galactic mid-IR
period-luminosity (PL) relations for classical Cepheids in the four Wide-Field
Infrared Survey Explorer (WISE) bands (W1, W2, W3, and W4) and the four Spitzer
Space Telescope bands ([3.6], [4.5], [5.8] and [8.0]). Based on our sample of
hundreds of Cepheids, the WISE PL relations have been determined for the first
time; their dispersion is approximately 0.10 mag. Using the currently most
complete sample, our Spitzer PL relations represent a significant improvement
in accuracy, especially in the [3.6] band which has the smallest dispersion
(0.066 mag). In addition, the average mid-IR extinction curve for Cepheids has
been obtained: A_W1/A_Ks=0.560, A_W2/A_Ks=0.479, A_W3/A_Ks=0.507,
A_W4/A_Ks=0.406, A_[3.6]/A_Ks=0.481, A_[4.5]/A_Ks=0.469, A_[5.8]/A_Ks=0.427,
and A_[8.0]/A_Ks=0.427 mag.
