The SDSS Damped Lya Survey: Data Release 3

We present the results from a damped Lya survey of the Sloan Digital Sky Survey, Data Release 3 based on over 500 new damped Lya systems at z>2.2. We measure the HI column density distribution f(N) and its zeroth and first moments (the incidence l(X) and gas mass-density O_dla of damped Lya systems, respectively) as a function of redshift. The key results include: (1) the f(N) distribution is well fit by a Gamma-function with `break' column density log N_g=10^21.5 and `faint-end' slope alpha=-1.8; (2) the shape of the f(N) distributions do not show evolution with redshift; (3) l(X) and O_dla decrease by 35% and 50% during ~1Gyr between redshift z=[3.,3.5] to z=[2.2,2.5]; and (4) l(X) and O_dla in the lowest SDSS redshift bin (z=2.2) are consistent with the current values. We investigate systematic errors in damped Lya analysis and identify only one important effect: we measure 40 +/- 20% higher O_dla values toward a subset of brighter quasars than toward a faint subset. This effect runs contrary to the bias associated with dust obscuration and suggests that gravitational lensing may be important. Comparing the results against models of galaxy formation, we find all of the models significantly underpredict l(X) at z=3 and only SPH models with significant feedback may reproduce O_dla at high redshift. We argue that the Lyman limit systems contribute ~1/3 of the universe's HI atoms at all redshifts z=2 to 5 and that the f(N) distribution for N(HI)<10^20 has an inflection with slope >-1. We advocate a new mass density definition -- the mass density of predominantly neutral gas O_neut -- to be contrasted with the mass density of gas associated with HI atoms. We contend the damped Lya systems contribute >80% of O_neut at all redshifts and therefore are the main reservoirs for star formation. [abridged]