Extremely Small Sizes for Faint z ∼ 2–8 Galaxies in the Hubble Frontier Fields: A Key Input for Establishing Their Volume Density and UV Emissivity

We provide the first observational constraints on the sizes of the faintest galaxies lensed by the Hubble Frontier Fields (HFF) clusters. Ionizing radiation from faint galaxies likely drives cosmic reionization, and the HFF initiative provides a key opportunity to find such galaxies. However, we cannot assess their ionizing emissivity without a robust measurement of their sizes, since this is key to quantifying both their prevalence and the faint-end slope to the UV luminosity function. Here we provide the first size constraints with two new techniques. The first utilizes the fact that the detectability of highly magnified galaxies as a function of shear is very dependent on a galaxy's size. Only the most compact galaxies remain detectable in high-shear regions (versus a larger detectable size range for low shear), a phenomenon we quantify using simulations. Remarkably, however, no correlation is found between the surface density of faint galaxies and the predicted shear, using 87 high-magnification ($\mu =10$–100) $z\sim 2$–8 galaxies seen behind the first four HFF clusters. This can only be the case if faint ($\sim -15$ mag) galaxies have significantly smaller sizes than more luminous galaxies, i.e., $\lesssim 30$ mas or 160–240 pc. As a second size probe, we rotate and stack 26 faint high-magnification sources along the major shear axis. Less elongation is found even for objects with an intrinsic half-light radius of 10 mas. Together, these results indicate that extremely faint $z\sim 2$–8 galaxies have near point-source profiles (half-light radii <30 mas and perhaps 5–10 mas). These results suggest smaller completeness corrections and hence shallower faint-end slopes for the $z\sim 2$–8 LFs than derived in some recent studies (by $\Delta \alpha \gtrsim 0.1$–0.3).