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We present a sample of 45 Damped Ly-Alpha system [DLA; H I-N is greater than or equal to 2 x 10(exp. 20) cm(exp. -2)] counterparts (33 detections, 12 upper limits) which host gamma-ray bursts (GRB-DLAs) in order to investigate star formation and metallicity within galaxies hosting DLAs. Our sample spans z is approx. 2 - 6 and is nearly three times larger than any previously detected DLA counterparts survey based on quasar line-of-sight searches (QSO-DLAs). We report star formation rates (SFRs) from rest-frame UV photometry and spectral energy distribution modeling. We find that DLA counterpart SFRs are not correlated with either redshift or H I column density. Thanks to the combination of Hubble Space Telescope and ground-based observations, we also investigate DLA host star formation efficiency. Our GRB-DLA counterpart sample spans both higher efficiency and low efficiency star formation regions compared to the local Kennicutt-Schmidt relation, local star formation laws, and z is approximately 3 cosmological simulations. We also compare the depletion times of our DLA hosts sample to other objects in the local universe; our sample appears to deviate from the star formation efficiencies measured in local spiral and dwarf galaxies. Furthermore, we find similar efficiencies as local inner disks, SMC, and Lyman-break galaxy outskirts. Finally, our enrichment time measurements show a spread of systems with under- and over-abundance of metals, which may suggest that these systems had episodic star formation and a metal enrichment/depletion as a result of strong stellar feedback and/or metal inflow/outflow.

The density of the warm ionized gas in high-redshift galaxies is known to be higher than what is typical in local galaxies on similar scales. At the same time, the mean global properties of the high- and low-redshift galaxies are quite different. Here, we present a detailed differential analysis of the ionization parameters of 14 star-forming galaxies at redshift 2.6-3.4, compiled from the literature. For each of those high-redshift galaxies, we construct a comparison sample of low-redshift galaxies closely matched in specific star formation rate (sSFR) and stellar mass, thus ensuring that their global physical conditions are similar to the high-redshift galaxy. We find that the median log [OIII] 5007/ [OII] 3727 line ratio of the high-redshift galaxies is 0.5 dex higher than their local counterparts. We construct a new calibration between the [OIII] 5007/ [OII] 3727 emission line ratio and ionization parameter to estimate the difference between the ionization parameters in the high and low-redshift samples. Using this, we show that the typical density of the warm ionized gas in star-forming regions decreases by a median factor of $7.1^{+10.2}_{-5.4}$ from z ~ 3.3 to z ~ 0 at fixed mass and sSFR. We show that metallicity differences cannot explain the observed density differences. Because the high- and low-redshift samples are comparable in size, we infer that the relationship between star formation rate density and gas density must have been significantly less efficient at z ~2-3 than what is observed in nearby galaxies with similar levels of star formation activity., 16 pages, 6 figures, accepted for publication in ApJ