Size-Mass Relations for Simulated Low-Mass Galaxies: Mock Imaging versus Intrinsic Properties

The observationally-inferred size versus stellar-mass relationship for low-mass galaxies provides an important test for galaxy formation models. However, the relationship relies on assumptions that relate observed luminosity profiles to underlying stellar mass profiles. We use the Feedback in Realistic Environments (FIRE-2) simulations of low-mass galaxies to explore how the predicted size-mass relation (SMR) changes depending on whether one uses star-particle counts directly or mock observations. We reproduce the SMR found in the ELVES survey remarkably well only when we infer stellar masses and sizes using mock surface brightness images and the same color-inferred mass-to-light ratio (CMLR) used in deriving the observed relation. However, when we use star particles to directly infer stellar masses and half-mass radii, we find that our galaxies are too large and obey a SMR with too little scatter compared to observations. The reason for this discrepancy between the "true" galaxy size and mass and those derived in the mock observation approach is twofold. First, our simulated galaxies have higher and more varied MLRs at a fixed color than those commonly-adopted because their star-formation-histories are more temporally extended and not well represented by exponential star formation models. Using a standard CMLR therefore tends to underestimate their stellar masses compared to their true, simulated values. Second, our galaxies have radially increasing MLR gradients. Using a single MLR tends to under-predict the mass in the outer regions. Similarly, the true half-mass radius is larger than the half-light radius because the light is more concentrated than the mass. If our simulations are accurate representations of the real universe, then the relationship between galaxy size and stellar mass is even tighter for low-mass galaxies than is commonly inferred from observed relations.