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.