A Relationship Between Stellar Surface Density and Oxygen Abundance

Returning to Figure 1, we now ask the question: Is there any correlation between the azimuthally-averaged stellar surface brightness at a given radius in a galaxy, and the abundance of oxygen within the HII regions at that same radius? Such a relationship has been touched upon by McCall (1982), Webster & Smith (1983), Wevers (1984), Edmunds & Pagel (1984), and more recently, by Vila-Costas & Edmunds (1992), but never satisfactorily explained. The oxygen abundance can be determined spectroscopically to an accuracy  dex using the empirical calibration of vs. , the sum of the [OII] and [OIII] line strengths normalised to H (Edmunds & Pagel 1984; Dopita & Evans 1986).

The oxygen abundances in 97 HII regions for six of the galaxies in our sample have been measured, and plotted against the underlying stellar surface brightness in Figure 5(a)-(d). This plot re-confirms the existence of a local metallicity - surface brightness relationship in galactic disks, and offers us a second constraint on the above models.

 
Figure 5:  Observed relationship between abundance of oxygen in HII regions, and the underlying stellar surface brightness (symbols), together with the relationship predicted by our models (solid and dashed lines): (a, upper left) ``closed-box'' model, no gas infall; (b, upper right) continual (but exponentially decreasing) gas infall; (c, lower left) abandoning the Instantaneous Recycling Approximation for a given mass range; and (d, lower right) comparing the ``classical'' Schmidt Law with a star formation rate dependent also on total mass surface density.

Our first model uses the closed-box (no gas infall, each zone starts with its full quota of gas) and instantaneous recycling (high-mass stars die immediately, returning some enriched gas to the ISM; low-mass stars lock away all of their gas forever) approximations. As Figure 5(a) shows, this simple model follows almost the same slope as the observed metallicity - surface brightness relationship, but the oxygen yields are too low. Boosting the amount of oxygen present, by enhancing high-mass star formation at the expense of low-mass stars, would however violate the stellar surface brightness - star formation rate relationship.

A more realistic model with gas infall has an even more serious problem (Figure 5(b)); the dilution of enriched gas in higher density regions by the continual infall of pristine gas. This problem disappears however (Figure 5(c)) when one abandons the Instantaneous Recycling Approximation, and takes full account numerically of stellar lifetimes, and the delayed return of oxygen to the ISM by low mass stars forming planetary nebulae late in the galaxy's lifetime. Although the amount of oxygen released by each star is small, the sheer number of low-mass stars formed in each episode of star formation (relative to high-mass stars) means that they could make a significant contribution to the gas-phase oxygen abundance at late epochs.

Finally, having identified the most realistic model involving the minimum number of assumptions, we have again experimented with various combinations of the total and gas surface density indices n and m (Figure 5(d)). This time, we see that the ``classical'' Schmidt Law with m=2 falls somewhat short of satisfying the metallicity - surface brightness relationship, while the model which includes a mild dependence on the total surface mass density does slightly better. The fit could conceivably be improved further by allowing for some variations in the ratio or in the IMF. Phillipps & Edmunds (1991) also found that self-regulating star formation models which included some dependence on the total mass surface density (e.g., Dopita 1985; Matteucci et al. 1989) did a much better job at matching the observed metallicity - surface brightness/density relationships than did basic Schmidt Laws in a closed-box model. Thus, there is good evidence that a star formation law dependent on both the total and the gaseous surface densities does somewhat better than a classical Schmidt Law at simultaneously satisfying both of the relationships presented here.

© Copyright Astronomical Society of Australia 1997