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 ${M}_{\star }\sim {10}^{6}\,{M}_{\odot }$ 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 ${M}_{\star }\sim {10}^{6}\mbox{--}{10}^{9}\,{M}_{\odot }$ . Our best-estimate ${M}_{\star }/{L}_{\mathrm{UV}}$ 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 ${M}_{\star }\gtrsim {10}^{8}\,{M}_{\odot }$ , and that extend to ${M}_{\star }\sim {10}^{6}\,{M}_{\odot }$ . Estimating the stellar mass densities ${\rho }_{\star }$ 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 R_e on the source plane, we have pinpointed four objects with low stellar masses ( ${M}_{\star }\leqslant {10}^{7}\,{M}_{\odot }$ ) and very compact morphologies ( ${R}_{{\rm{e}}}\leqslant 40$ 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.