An uncertainty principle for star formation - IV. On the nature and
  filtering of diffuse emission
  Diffuse emission is observed in galaxies in many tracers across the
electromagnetic spectrum, including tracers of star formation, such as
H$\alpha$ and ultraviolet (UV), and tracers of gas mass, such as carbon
monoxide (CO) transition lines and the 21-cm line of atomic hydrogen (HI). Its
treatment is key to extracting meaningful information from observations such as
cloud-scale star formation rates. Finally, studying diffuse emission can reveal
information about the physical processes taking place in the ISM, such as
chemical transitions and the nature of stellar feedback (through the photon
escape fraction). We present a physically-motivated method for decomposing
astronomical images containing both diffuse emission and compact regions of
interest, such as HII regions or molecular clouds, into diffuse and compact
component images through filtering in Fourier space. We have previously
presented a statistical method for constraining the evolutionary timeline of
star formation and mean separation length between compact star forming regions
with galaxy-scale observations. We demonstrate how these measurements are
biased by the presence of diffuse emission in tracer maps and that by using the
mean separation length as a critical length scale to separate diffuse emission
from compact emission, we are able to filter out this diffuse emission, thus
removing its biasing effect. Furthermore, this method provides, without the
need for interferometry or ancillary spectral data, a measurement of the
diffuse emission fraction in input tracer maps and decomposed diffuse and
compact emission maps for further analysis.
