  We investigate how radiative feedback from the first stars affects the
assembly of the first dwarf galaxies. We perform cosmological zoomed SPH
simulations of a dwarf galaxy assembling inside a halo of virial mass 10^9
solar at z = 10. The simulations follow the non-equilibrium chemistry/cooling
of primordial gas and the conversion of the gas into metal-free stars. To
quantify the radiative feedback, we compare a simulation in which stars emit
both molecular hydrogen dissociating and hydrogen/helium ionizing radiation
with a simulation in which stars emit only dissociating radiation, and with a
simulation in which stars remain dark. Photodissociation and -ionization exert
a strong negative feedback on the assembly of the simulated galaxy. Gas
condensation is strongly impeded, and star formation is strongly suppressed in
comparison with the simulation in which stars remain dark. The feedback on the
gas implies a suppression of the central dark matter densities in the minihalo
progenitor by factors of up to a few, which is a significant deviation from the
singular isothermal density profile characterizing the dark matter distribution
in the absence of radiative feedback. The evolution of gas densities, star
formation rates, and the distribution of dark matter becomes insensitive to the
inclusion of dissociating radiation in the late stages of the minihalo
assembly, and it becomes insensitive to the inclusion of ionizing radiation
once the minihalo turns into an atomically cooling galaxy. The formation of an
extended disk inside the dwarf galaxy is a robust outcome not affected by the
inclusion of radiation. We estimate that dwarf galaxies such as simulated here
will be among the faintest galaxies the upcoming James Webb Space Telescope
will detect. Our conclusions are subject to our neglect of feedback from
supernovae and chemical enrichment as well as to cosmic variance. [abridged]
