  We apply the phenomenological model used to explain the abundances of Fe and
r-process elements in very metal-poor stars in the Galaxy to [Fe/H] of damped
Ly alpha systems. It is assumed that the first stars formed after the Big Bang
were very massive and promptly enriched the interstellar medium to [Fe/H] ~ -3,
at which metallicity formation of normal stars took over. Subsequent Fe
enrichment was provided by Type II supernovae. The range of [Fe/H] at a given
redshift z for damped Ly alpha systems is explained by the time t* after the
Big Bang at which normal star formation started in an individual protogalactic
system. The average t* is approx 80% the age of the universe for damped Ly
alpha systems at z approx 1.5 to 4.5, indicating a long delay between the Big
Bang and the turn-on of protogalaxies. It is inferred that a substantial
fraction of the total baryonic matter may not have been aggregated into
protogalaxies where normal star formation had occurred down to z ~ 1.5. The
data near z = 2.2 suggest that the rate of turn-on of protogalaxies was
initially very low and slowly reached a maximum at ~ 3 Gyr after the Big Bang.
This may be important in understanding the rate of formation of quasars.
