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_{\nu} increases, the
halo-to-filament merging rate increases while the halo-to-halo merging rate
decreases sharply. For f_{\nu}<=0.04, the halo-to-filament merging rate is
negligibly low at all filament mass scales, while for f_{\nu}>=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_{\nu}>= 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.
