A Precise Determination of the Mid-Infrared Interstellar Extinction Law
  Based on the APOGEE Spectroscopic Survey
  A precise measure of the mid-infrared interstellar extinction law is crucial
to the investigation of the properties of interstellar dust, especially of the
grains in the large size end. Based on the stellar parameters derived from the
SDSS-III/APOGEE spectroscopic survey, we select a large sample of G- and K-type
giants as the tracers of the Galactic mid-infrared extinction. We calculate the
intrinsic stellar color excesses from the stellar effective temperatures and
use them to determine the mid-infrared extinction for a given line of sight.
For the entire sky of the Milky Way surveyed by APOGEE, we derive the
extinction (relative to the K$_{\rm S}$ band at wavelength $\lambda=2.16\mu$m)
for the four WISE bands at 3.4, 4.6, 12 and 22$\mu$m, the four Spitzer/IRAC
bands at 3.6, 4.5, 5.8 and 8$\mu$m, the Spitzer/MIPS24 band at 23.7$\mu$m and
for the first time, the AKARI/S9W band at 8.23$\mu$m. Our results agree with
previous works in that the extinction curve is flat in the ~3--8$\mu$m
wavelength range and is generally consistent with the $R_V=5.5$ model curve
except our determination exceeds the model prediction in the WISE/W4 band.
Although some previous works found that the mid-IR extinction law appears to
vary with the extinction depth $A_{\rm{K_S}}$, no noticeable variation has been
found in this work. The uncertainties are analyzed in terms of the bootstrap
resampling method and Monte-Carlo simulation and are found to be rather small.
