Chemical Enrichment at High Redshifts
We have tried to understand the recent observations related to metallicity in Ly $\alpha$ forest clouds in the framework of the two component model suggested by Chiba & Nath (1997). We find that even if the mini-halos were chemically enriched by an earlier generation of stars, to have [C/H] $\simeq$ -2.5, the number of C IV lines with column density $>10^{12} cm^{-2}$, contributed by the mini-halos, at the redshift of 3, would be only about 10% of the total number of lines, for a chemical enrichment rate of $(1+z)^{-3}$ in the galaxies. Recently reported absence of heavy element lines associated with most of the Ly $\alpha$ lines with H I column density between $10^{13.5} cm^{-2}$ and $10^{14} cm^{-2}$ by Lu et al (1998), if correct, gives an upper limit on [C/H]=-3.7, not only in the mini-halos, but also in the outer parts of galactic halos. This is consistent with the results of numerical simulations, according to which, the chemical elements associated with the Ly $\alpha$ clouds are formed in situ in clouds, rather than in an earlier generation of stars. However, the mean value of $7 \times 10^{-3}$ for the column density ratio of C IV and H I, determined by Cowie and Songaila (1998) for low Lyman alpha optical depths, implies an abundance of [C/H] =-2.5 in mini-halos as well as in most of the region in galactic halos, presumably enriched by an earlier generation of stars. The redshift and column density distribution of C IV has been shown to be in reasonable agreement with the observations.