  We study the effect of the relative velocity of dark matter and baryonic
fluids after the epoch of recombination on the evolution of the first bound
objects in the early universe. Recent work has shown that, although relative
motion of the two fluids is formally a second order effect in density, it has a
dramatic impact on the formation and distribution of the first cosmic
structures. Focusing on the gas content, we analyze the effect of relative
velocity on the properties of halos over a wide range of halo masses and
redshifts. We calculate accurately the linear evolution of the baryon and dark
matter fluctuations, and quantify the resulting effect on halos based on an
analytical formalism that has been carefully checked with simulations in the
case with no relative velocity. We estimate the effect on the abundance of and
gas fraction in early halos. We find that the relative velocity effect causes
several changes: (i) the characteristic mass that divides gas-rich and gas-poor
halos is increased by roughly an order of magnitude, from 2 10^4 Msun to about
2 10^5 Msun; (ii) this characteristic mass has a large scatter (full width at
half maximum is ~ 1.5 10^5 Msun at z=20); (iii) the fraction of baryons in
star-less gas minihalos is suppressed by a factor of 4 at z=20; (iv) the
fraction of baryons in halos that can cool and form stars is suppressed by a
factor of 1.5 at z=20; and (v) there are enhanced spatial variations of these
various fractions.
