Does deuterium enable the formation of primordial brown dwarfs?

We investigate thermal and dynamical evolution of a primordial gas cloud with an updated deuterium chemistry. We consider a fragment of a postshock-cooled sheet that is expected to form by collapse of a massive cloud (greater than or equal to 10(8) M.) and by blast waves due to supernova explosions. At first we investigate molecule formation in a primordial shock. We show that almost all deuterium can be converted to HD within the age of the universe at the collapsed redshift in the case of a cloud that has a virial temperature of similar to 10(6) K and collapses at z > 1. When the postshock sheet fragments owing to gravitational instability, the fractional H-2 and HD abundances become similar to 10(-2) and similar to 10(-5), respectively, which are 10(3)-10(4) times higher than the result of molecule formation in the expanding universe after recombination. To study the subsequent evolution of a fragment, we performed one-dimensional simulations of a spherical/cylindrical cloud, of which initial conditions (e.g., fractional abundances of chemical composition, temperature) are derived from the result of the shock. It is found that, in case of a cylindrical collapse, the cooling by HD molecules keeps the temperature of the cloud less than 100 K and the cloud evolves almost isothermally. When the cloud becomes optically thick to the HD line emission (similar to 10(10) cm(-3)) and the gravitational fragmentation of the cylindrical cloud becomes effective, the Jeans mass becomes comparable to 0.1 M.. This series of processes enables the formation of primordial low-mass stars, and possibly brown dwarfs, in primordial gas clouds.