Variations in the slope of the resolved star-forming main sequence: a
  tool for constraining the mass of star-forming regions
  The correlation between galaxies' integrated stellar masses and star
formation rates (the `star formation main sequence'; SFMS) is a
well-established scaling relation. Recently, surveys have found a relationship
between the star formation rate and stellar mass surface densities on kpc and
sub-kpc scales (the `resolved SFMS'; rSFMS). In this work, we demonstrate that
the rSFMS emerges naturally in FIRE-2 zoom-in simulations of Milky Way-mass
galaxies. We make SFR and stellar mass maps of the simulated galaxies at a
variety of spatial resolutions and star formation averaging time-scales and fit
the rSFMS using multiple methods from the literature. While the absolute value
of the SFMS slope depends on the fitting method, the slope is steeper for
longer star formation time-scales and lower spatial resolutions regardless of
the fitting method employed. We present a toy model that quantitatively
captures the dependence of the simulated galaxies' rSFMS slope on spatial
resolution and use it to illustrate how this dependence can be used to
constrain the characteristic mass of star-forming clumps.
