Spatially-unresolved SED fitting can underestimate galaxy masses: a solution to the missing mass problem

We perform spatially-resolved, pixel-by-pixel SED fitting on galaxies up to $z\sim2.5$ in the Hubble Extreme Deep Field (XDF). Comparing stellar mass estimates from spatially resolved and spatially unresolved photometry we find that unresolved masses can be systematically underestimated by factors of up to 5. The ratio of the unresolved to resolved mass measurement depends on the galaxy's specific star formation rate (sSFR): at low sSFRs the bias is small, but above sSFR$\ \sim 10^{-9.5}$ yr$^{-1}$ the discrepancy increases rapidly such that galaxies with sSFRs$\ \sim 10^{-8}$ yr$^{-1}$ have unresolved mass estimates of only one half to one fifth of the resolved value. This result indicates that stellar masses estimated from spatially-unresolved datasets need to be systematically corrected, in some cases by large amounts, and we provide an analytic prescription for applying this correction. We show that correcting stellar mass measurements for this bias changes the normalization and slope of the star-forming main sequence and reduces its intrinsic width; most dramatically, correcting for the mass bias increases the stellar mass density of the Universe at high redshift and can resolve the long-standing discrepancy between the directly-measured cosmic star formation rate density at $z\gtrsim1$ and that inferred from stellar mass densities ("the missing mass problem").