The Star Formation Relation for Regions in the Galactic Plane: The
  Effect of Spatial Resolution
  We examined the relations between molecular gas surface density and star
formation rate surface density in a 11 square degree region of the Galactic
Plane. Dust continuum at 1.1 mm from the Bolocam Galactic Plane Survey and 22
micron emission from the WISE All-sky survey were used as tracers of molecular
gas and star formation rate, respectively, across Galactic longitude of 31.5 >
l > 20.5 and Galactic latitude of 0.5 > b > -0.5. The relation was studied over
a range of resolutions from 33 arcsecond to 20 arcminute by convolving images
to larger scales. The pixel-by-pixel correlation between 1.1 mm and 22 micron
increases rapidly at small scales and levels off at the scale of 5 - 8
arcminute. We studied the star formation relation based on pixel-by-pixel
analysis and 1.1 mm and 22 micron peaks analysis. The star formation relation
was found to be nearly linear with no significant changes in the form of the
relation across all spatial scales and lie above the extragalactic relation
from Kennicutt (1998). The average gas depletion time is approximately 200 Myr
and does not change significantly at different scales, but the scatter in the
depletion time decreases as the scale increases.
