The Optical/Near-Infrared Extinction Law In Highly Reddened Regions
  A precise extinction law is a critical input when interpreting observations
of highly reddened sources such as young star clusters and the Galactic Center
(GC). We use Hubble Space Telescope observations of a region of moderate
extinction and a region of high extinction to measure the optical and
near-infrared extinction law (0.8 $\mu$m -- 2.2 $\mu$m). The moderate
extinction region is the young massive cluster Westerlund 1 (Wd1; A$_{Ks} \sim$
0.6 mag), where 453 proper motion-selected main-sequence stars are used to
measure the shape of the extinction law. To quantify the shape we define the
parameter $\mathcal{S}_{1/\lambda}$, which behaves similarly to a color excess
ratio but is continuous as a function of wavelength. The high extinction region
is the GC (A$_{Ks} \sim$ 2.5 mag), where 819 red clump stars are used to
determine the normalization of the law. The best-fit extinction law is able to
reproduce the Wd1 main sequence colors, which previous laws misestimate by
10%-30%. The law is inconsistent with a single power law, even when only the
near-infrared filters are considered, and has A$_{F125W}$/A$_{Ks}$ and
A$_{F814W}$/A$_{Ks}$ values that are 18% and 24% larger than the commonly used
\citet{Nishiyama:2009fc} law, respectively. Using the law we recalculate the
Wd1 distance to be 3896 $\pm$ 328 pc from published observations of eclipsing
binary W13. This new extinction law should be used for highly reddened
populations in the Milky Way, such as the Quintuplet cluster and Young Nuclear
Cluster. A python code is provided to generate the law for future use.
