Chemical Enrichment at High Redshifts

We have tried to understand the recent observations related to metallicity inLy $\alpha$ forest clouds in the framework of the two component model suggestedby Chiba & Nath (1997). We find that even if the mini-halos were chemicallyenriched by an earlier generation of stars, to have [C/H] $\simeq$ -2.5, thenumber of C IV lines with column density $>10^{12} cm^{-2}$, contributed by themini-halos, at the redshift of 3, would be only about 10% of the total numberof 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. Thisis consistent with the results of numerical simulations, according to which,the chemical elements associated with the Ly $\alpha$ clouds are formed in situin clouds, rather than in an earlier generation of stars. However, the meanvalue 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 theregion in galactic halos, presumably enriched by an earlier generation ofstars. The redshift and column density distribution of C IV has been shown tobe in reasonable agreement with the observations.Comment: 23 pages, 6 figures, To appear in Astrophysical Journa