  We show that large, high-redshift (z>10) galaxies with virial temperature in
excess of 10^4K may be mostly comprised of cold atomic clouds which were
formerly minihalos. These clouds move at a speed of 15-30km/s and collide with
one another on a time scale of 10^7yr. The supersonic collisions result in
spatially distributed star formation with high efficiency. We then show that
most, subsequent star formation in cold atomic clouds may be triggered by
shockwaves launched from the first stars formed in collisions. Those
shockwave-compressed clouds are even more widespread spatially because of large
imparted velocities and some can possibly escape into the intergalactic medium.
More importantly, with respect to cosmological reionization, widespread star
formation would allow a much higher ionizing photon escape fraction. These
favorable conditions may form the physical basis to enable the standard
cosmological model to produce a reasonably high Thomson optical depth
\tau_e=0.10-0.14. A chain reaction of star formation in minihalos in the
intergalactic space may be triggered by explosions in the intergalactic medium,
if minihalos are strongly clustered. In this case, a still higher \tau_e would
be achievable.
