The mid-infrared Leavitt Law for Classical Cepheids in the Magellanic
  Clouds
  The Cepheid Leavitt Law (LL), also known as the Period-Luminosity relation,
is a crucial tool for assembling the cosmic distance ladder. By combining data
from the OGLE-IV catalogue with mid-infrared photometry from the Spitzer Space
Telescope, we have determined the $3.6$ $\mu$m and $4.5$ $\mu$m LLs for the
Magellanic Clouds using around 5000 fundamental-mode Classical Cepheids. Mean
magnitudes were determined using a Monte Carlo Markov Chain (MCMC) template
fitting procedure, with template light curves constructed from a subsample of
these Cepheids with fully-phased, well-sampled light curves. The dependence of
the Large Magellanic Cloud LL coefficients on various period cuts was tested,
in addition to the linearity of the relationship. The zero point of the LL was
calibrated using the parallaxes of Milky Way Cepheids from the Hubble Space
Telescope and Gaia Data Release 2. Our final calibrated relations are
$M_{[3.6]} = -3.246(\pm 0.008)(\log(P)-1.0)-5.784(\pm 0.030)$ and $M_{[4.5]} =
-3.162(\pm 0.008)(\log(P)-1.0)-5.751(\pm 0.030)$.
