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Merging Rates of the First Objects and the Formation of First Mini-Filaments in Models with Massive Neutrinos

We study the effect of massive neutrinos on the formation and evolution of the first filaments containing the first star-forming halos of mass M~10^{6}M_sun at z~20. With the help of the extended Press-Schechter formalism, we evaluate analytically the rates of merging of the first star-forming halos into zero-dimensional larger halos and one-dimensional first filaments. It is shown that as the neutrino mass fraction f_ν increases, the halo-to-filament merging rate increases while the halo-to-halo merging rate decreases sharply. For f_ν<=0.04, the halo-to-filament merging rate is negligibly low at all filament mass scales, while for f_ν>=0.07 the halo-to-filament merging rate exceeds 0.1 at the characteristic filament mass scale of ~10^{9}M_sun. The distribution of the redshifts at which the first filaments ultimately collapse along their longest axes is derived and found to have a sharp maximum at z~8. We also investigate the formation and evolution of the second generation filaments which contain the first galaxies of mass 10^{9}M_sun at z=8 as the parent of the first generation filaments. A similar trend is found: For f_ν>= 0.07 the rate of clustering of the first galaxies into the second-generation filaments exceeds 0.3 at the characteristic mass scale of ~10^{11}M_sun. The longest-axis collapse of these second-generation filaments are found to occur at z~3. The implications of our results on the formation of massive high-z galaxies and the early metal enrichment of the intergalactic media by supernova-driven outflows, and possibility of constraining the neutrino mass from the mass distribution of the high-z central blackholes are discussed.