Dust Extinction Law in Nearby Star-Resolved Galaxies. II. M33 Traced by
  Supergiants
  The dust extinction curves toward individual sight lines in M33 are derived
for the first time with a sample of reddened O-type and B-type supergiants
obtained from the LGGS. The observed photometric data are obtained from the
LGGS, PS1 Survey, UKIRT, PHATTER Survey, GALEX, Swift/UVOT and XMM-SUSS. We
combine the intrinsic spectral energy distributions (SEDs) obtained from the
ATLAS9 and Tlusty stellar model atmosphere extinguished by the model extinction
curves from the silicate-graphite dust model to construct model SEDs. The
extinction traces are distributed along the arms in M33, and the derived
extinction curves cover a wide range of shapes ($R_V \approx 2-6$), indicating
the complexity of the interstellar environment and the inhomogeneous
distribution of interstellar dust in M33. The average extinction curve with
$R_V \approx 3.39$ and dust size distribution $dn/da \sim a^{-3.45}{\rm
exp}(-a/0.25)$ is similar to that of the MW but with a weaker 2175 Ang bump and
a slightly steeper rise in the far-UV band. The extinction in the $V$ band of
M33 is up to 2 mag, with a median value of $ A_V \approx 0.43$ mag. The
multiband extinction values from the UV to IR bands are also predicted for M33,
which will provide extinction corrections for future works. The method adopted
in this work is also applied to other star-resolved galaxies (NGC 6822 and
WLM), but only a few extinction curves can be derived because of the limited
observations.
