ZFIRE: Similar Stellar Growth in Hα-emitting Cluster and Field Galaxies at z~2

We compare galaxy scaling relations as a function of environment at $z\sim2$ with our ZFIRE survey where we have measured H$\alpha$ fluxes for 90 star-forming galaxies selected from a mass-limited [$\log(M_{\star}/M_{\odot})>9$] sample based on ZFOURGE. The cluster galaxies (37) are part of a confirmed system at z=2.095 and the field galaxies (53) are at $1.9<z<2.4$; all are in the COSMOS legacy field. There is no statistical difference between H$\alpha$-emitting cluster and field populations when comparing their star formation rate (SFR), stellar mass ($M_{\star}$), galaxy size ($r_{eff}$), SFR surface density [$\Sigma$(H$\alpha_{star}$)], and stellar age distributions. The only difference is that at fixed stellar mass, the H$\alpha$-emitting cluster galaxies are $\log(r_{eff})\sim0.1$ larger than in the field. Approximately 19% of the H$\alpha$-emitters in the cluster and 26% in the field are IR-luminous ($L_{IR}>2\times10^{11} L_{\odot}$). Because the LIRGs in our combined sample are $\sim5$ times more massive than the low-IR galaxies, their radii are $\sim70$% larger. To track stellar growth, we separate galaxies into those that lie above, on, and below the H$\alpha$ star-forming main sequence (SFMS) using $\Delta$SFR$(M_{\star})=\pm0.2$ dex. Galaxies above the SFMS (starbursts) tend to have higher H$\alpha$ SFR surface densities and younger light-weighted stellar ages compared to galaxies below the SFMS. Our results indicate that starbursts (+SFMS) in the cluster and field at $z\sim2$ are growing their stellar cores. Lastly, we compare to the (SFR-$M_{\star}$) relation from RHAPSODY cluster simulations and find the predicted slope is nominally consistent with the observations. However, the predicted cluster SFRs tend to be too low by a factor of $\sim2$ which seems to be a common problem for simulations across environment.