Exploring the High-Mass End of the Stellar Mass Function of Star Forming Galaxies at Cosmic Noon

We present the high-mass end of the galaxy stellar mass function using the largest sample to date (5,352) of star-forming galaxies with $M_{\star} > 10^{11} M_{\odot}$ at cosmic noon, $1.5 < z < 3.5$. This sample is uniformly selected across 17.2 deg$^2$ ($\sim$0.44 Gpc$^3$ comoving volume from $1.5 < z < 3.5$), mitigating the effects of cosmic variance and encompassing a wide range of environments. This area, a factor of 10 larger than previous studies, provides robust statistics at the high-mass end. Using multi-wavelength data in the Spitzer/HETDEX Exploratory Large Area (SHELA) footprint we find that the SHELA footprint star-forming galaxy stellar mass function is steeply declining at the high-mass end probing values as high as $\sim$$10^{-4}$ Mpc$^3$/dex and as low as $\sim$5$\times$$10^{-8}$ Mpc$^3$/dex across a stellar mass range of log($M_\star$/$M_\odot$) $\sim$ 11 - 12. We compare our empirical star-forming galaxy stellar mass function at the high mass end to three types of numerical models: hydrodynamical models from IllustrisTNG, abundance matching from the UniverseMachine, and three different semi-analytic models (SAMs; SAG, SAGE, GALACTICUS). At redshifts $1.5 < z < 3.5$ we find that results from IllustrisTNG and abundance matching models agree within a factor of $\sim$2 to 10, however the three SAMs strongly underestimate (up to a factor of 1,000) the number density of massive galaxies. We discuss the implications of these results for our understanding of galaxy evolution.