The population of weak Mg II absorbers. I. A survey of 26 QSO HIRES/Keck spectra

We present a search for "weak" Mg II absorbers [those with W_r(2796) < 0.3 Å] in the HIRES/Keck spectra of 26 QSOs. We found 30, of which 23 are newly discovered. The spectra are 80% complete to W_r(2796) = 0.02 Å and have a cumulative redshift path of ∼ 17.2 for the redshift range 0.4 ≤ z ≤ 1.4. The number of absorbers per unit redshift, dN/dz, is seen to increase as the equivalent width threshold is decreased; we obtained dN/dz = 1.74 ± 0.10 for our 0.02 W_r(2796) < 0.3 Å sample. The equivalent width distribution follows a power law, N(W) ∝ W^-δ, with δ ∼ 1.0; there is no turnover down to W_r(2796) = 0.02 Å at 〈z〉 = 0.9. Weak absorbers comprise at least 65% of the total Mg II absorption population, which outnumbers Lyman limit systems (LLSs) by a factor of 3.8 ± 1.1; the majority of weak Mg II absorbers must arise in sub-LLS environments. Tentatively, we predict that ∼ 5% of the Lyα forest clouds with W_r(Lyα) ≥ 0.1 Å will have detectable Mg II absorption to W^min_r(2796) = 0.02 Å and that this is primarily a high-metallicity selection effect ([Z/Z⊙] ≥ - 1). This implies that Mg II absorbing structures figure prominently as tracers of sub-LLS environments where gas has been processed by stars. We compare the number density of W_r(2796) ≥ 0.02 Å absorbers with that of both high and low surface brightness galaxies and find a fiducial absorber size of 35 h^-1-63 h^-1 kpc, depending upon the assumed galaxy population and their absorption properties. The individual absorbing "clouds" have W_r(2796) ≤ 0.15 Å, and their narrow (often unresolved) line widths imply temperatures of ∼ 25,000 K. We measured W_r(1548) from C IV in Faint Object Spectrograph/Hubble Space Telescope archival spectra and, based upon comparisons with Fe II, found a range of ionization conditions (low, high, and multiphase) in absorbers selected by weak Mg II.