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 (SFR) 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 Feedback In Realistic Environments 2 (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 (α_MS) 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' α_MS on spatial resolution and use it to illustrate how this dependence can be used to constrain the characteristic mass of star-forming clumps.