  The James Webb Space Telescope (JWST) will enable observations of galaxies at
redshifts z > 10 and hence allow to test our current understanding of structure
formation at very early times. Previous work has shown that the very first
galaxies inside halos with virial temperatures T < 10^4 K and masses M < 10^8
M_sun at z > 10 are probably too faint, by at least one order of magnitude, to
be detected even in deep exposures with JWST. The light collected with JWST may
therefore be dominated by radiation from galaxies inside ten times more massive
halos. We use cosmological zoomed smoothed particle hydrodynamics simulations
to investigate the assembly of such galaxies and assess their observability
with JWST. We compare two simulations that are identical except for the
inclusion of non-equilibrium H/D chemistry and radiative cooling by molecular
hydrogen. In both simulations a large fraction of the halo gas settles in two
nested, extended gas disks which surround a compact massive gas core. The
presence of molecular hydrogen allows the disk gas to reach low temperatures
and to develop marked spiral structure but does not qualitatively change its
stability against fragmentation. We post-process the simulated galaxies by
combining idealized models for star formation with stellar population synthesis
models to estimate the luminosities in nebular recombination lines as well as
in the ultraviolet continuum. We demonstrate that JWST will be able to
constrain the nature of the stellar populations in galaxies such as simulated
here based on the detection of the He1640 recombination line. Extrapolation of
our results to halos with masses both lower and higher than those simulated
shows that JWST may find up to a thousand star-bursting galaxies in future deep
exposures of the z > 10 universe.
