Chemical enrichment models make specific predictions for the gas-phase abundances that can be compared to the QSO data. Hamann & Ferland 1992 and HF93a constructed one-zone models for stellar populations assembled by the infall of primordial gas. The enrichment follows standard stellar yields that compare well with observations of the Milky Way and nearby galaxies. The star formation is regulated by power-law initial mass functions (IMFs) of the form M-x, where M is the stellar mass and dM = 1. The enrichment delays caused by finite stellar lifetimes are included. We tested the calculations by constructing a simple yet viable model of the Galactic solar neighborhood, and then varied just the slope of the IMF and the timescales for star formation and infall to model the chemical history of QSO environments.
Figure 2 shows the predicted relative abundances for two cases at opposite extremes. The ``Solar Neighborhood'' model uses a 3 Gyr timescale for the infall of primordial gas and an IMF with slope x = 1.6 for M 1 M and 1.1 for M < 1 M (after Scalo 1990). The stellar birth rate is set so that Z = 1 Z at the time of the sun's formation and the fraction of mass in gas is ~ 15% at the present epoch. The ``Giant Elliptical'' model uses a stellar birth-rate 100 times faster and an infall timescale of only 0.05 Gyr so that the mass fraction in gas is ~ 15% after just 0.5 Gyr. The IMF is also flatter, with slope x = 1.1 for all masses. The shorter timescales and flatter IMF (more high-mass stars) in the Giant Elliptical case produces a rapid evolution to high Z's, reaching ~ 10 Z at ~ 1 Gyr. The star formation stops at ~ 1 Gyr because the gas is essentially exhausted; thereafter the system evolves ``passively'' and the ejecta from low-mass stars affect the abundances somewhat. See HF93a for details.
The parameters used in these calculations were based on standard one-zone infall models of the Galactic disk and massive ellipticals (Arimoto & Yoshii 1987, Matteucci & Tornambé 1987, Matteucci & Brocato 1990, Köppen & Arimoto 1990). However, the results are only illustrative and more sophisticated models would be needed to match entire galaxies.
Both models in Figure 2 exhibit the delayed rise and subsequent overabundances in N (due to secondary CNO processing in stellar envelopes) and Fe (due to the delayed enrichment by Type Ia supernova). The late increase in Fe / should be at least a factor of a few. The increase is larger in the Giant Elliptical case because, by the time SN Ia's make their Fe contribution, there is little gas left in the systems and each SN has a greater affect.
Figure 2. Logarithmic abundance ratios normalized to solar for the two evolution models discussed in the text. Two scenarios for the N enrichment are shown; one with secondary only and the other with secondary+primary (with a plateau in N/O at low Z that is forced to fit the HII region data; see Section 2.4).