Early Low-mass Galaxies and Star-cluster Candidates at z ∼ 6-9 Identified by the Gravitational-lensing Technique and Deep Optical/Near-infrared Imaging

We present very faint dropout galaxies at z ∼ 6−9 with a stellar mass M down to that are found in deep optical/near-infrared (NIR) images of the full data sets of the Hubble Frontier Fields (HFF) program in conjunction with deep ground-based and Spitzer images and gravitational-lensing magnification effects. We investigate stellar populations of the HFF dropout galaxies with the optical/NIR photometry and BEAGLE models made of self-consistent stellar population synthesis and photoionization models, carefully including strong nebular emission impacting on the photometry. We identify 453 galaxies with . Our best-estimate function is comparable to a model of star formation duration time of 100 Myr that is assumed in Bouwens et al. We derive the galaxy stellar mass functions (GSMFs) at z ∼ 6-9 that agree with those obtained by previous studies at , and that extend to . Estimating the stellar mass densities with the GSMFs, we find a very slow evolution from z ∼ 9 to z ∼ 6-7, which is consistent with the one estimated from star formation rate density measurements. In conjunction with the estimates of the galaxy effective radii Re on the source plane, we have pinpointed four objects with low stellar masses ( ) and very compact morphologies ( pc) that are comparable with those of globular clusters (GCs) in the Milky Way today. These objects are candidates of star clusters, some of which may be related to GCs today.