  The dynamical impact of Lyman-alpha (Ly{\alpha}) radiation pressure on galaxy
formation depends on the rate and duration of momentum transfer between
Ly{\alpha} photons and neutral hydrogen gas. Although photon trapping has the
potential to multiply the effective force, ionizing radiation from stellar
sources may relieve the Ly{\alpha} pressure before appreciably affecting the
kinematics of the host galaxy or efficiently coupling Ly{\alpha} photons to the
outflow. We present self-consistent Ly{\alpha} radiation-hydrodynamics
simulations of high-$z$ galaxy environments by coupling the Cosmic Ly{\alpha}
Transfer code (COLT) with spherically symmetric Lagrangian frame hydrodynamics.
The accurate but computationally expensive Monte-Carlo radiative transfer
calculations are feasible under the one-dimensional approximation. The initial
starburst drives an expanding shell of gas from the centre and in certain cases
Ly{\alpha} feedback significantly enhances the shell velocity. Radiative
feedback alone is capable of ejecting baryons into the intergalactic medium
(IGM) for protogalaxies with a virial mass of $M_{\rm vir} \lesssim 10^8~{\rm
M}_\odot$. We compare the Ly{\alpha} signatures of Population III stars with
$10^5$ K blackbody emission to that of direct collapse black holes with a
nonthermal Compton-thick spectrum and find substantial differences if the
Ly{\alpha} spectra are shaped by gas pushed by Ly{\alpha} radiation-driven
winds. For both sources, the flux emerging from the galaxy is reprocessed by
the IGM such that the observed Ly{\alpha} luminosity is reduced significantly
and the time-averaged velocity offset of the Ly{\alpha} peak is shifted
redward.

Astrophysics of Galaxies