We examine the assembly process and the observability of a first galaxy (M_vir~10^9 solar mass at z~8) with cosmological zoom-in, hydrodynamic simulations, including the radiative, mechanical, and chemical feedback exerted by the first generations of stars. To assess the detectability of such dwarf systems with the upcoming James Webb Space Telescope (JWST), we construct the spectral energy distribution for the simulated galaxy in a post-processing fashion. We find that while the non-ionizing UV continuum emitted by the simulated galaxy is expected to be below the JWST detection limit, the galaxy might be detectable using its nebular emission, specifically in the H-alpha recombination line. This requires that the galaxy experiences an active starburst with a star formation rate of Mdot_star > 0.1 Msun/yr at z~9. Due to the bursty nature of star formation in the first galaxies, the time interval for strong nebular emission is short, less than 2-3 Myr. The probability of capturing such primordial dwarf galaxies during the observable part of their duty cycle is thus low, resulting in number densities of order one source in a single pointing with MIRI onboard the JWST, for very deep exposures. Gravitational lensing, however, will boost their observability beyond this conservative baseline. The first sources of light will thus come firmly within our reach.
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