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*~10^6Mo 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 357 galaxies with
M*~10^6-10^9Mo, and find that a stellar mass to UV luminosity L_UV ratio
M*/L_UV is nearly constant at M*~10^6-10^9Mo. Our best-estimate M*/L_UV
function is comparable to a model of star-formation duration time of 100 Myr,
but 2-7 times higher than the one of 10 Myr assumed in a previous study (at the
5sigma level) that would probably underestimate M* of faint galaxies. We derive
the galaxy stellar mass functions (GSMFs) at z~6-9 that agree with those
obtained by previous studies with no M*/L_UV assumptions at M*>~10^8Mo, and
that extends to M*~10^6Mo. Estimating the stellar mass densities rho* with the
GSMFs, we find that rho* smoothly increases from log(rho*/[Mo Mpc^(-3)])=5.91
+0.75/-0.65 at z~9 to 6.21 +0.39/-0.37 at 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 two objects with low stellar masses (M*<=10^7Mo) and very
compact morphologies (R_e<=40 physical pc) that are comparable with those of
globular clusters (GCs) in the Milky Way today. These objects are candidates of
star clusters that should be a part or a dominant component of high-redshift
low-mass galaxy, some of which may be related to GCs today.
