4.3. Metallicity versus Galaxy Luminosity/Mass

One well established correlation is the relation between metallicity and galaxy luminosity or (Garnett & Shields 1987, Lequeux et al. 1979). This is shown in the top panel of Figure 9, where I plot O/H determined at the half-light radius of the disc (R_eff) versus B-band magnitude M_B. This is the usual way of plotting the relation. [Note that the choice of what value of metallicity to use for spiral disks, where the metallicity is not constant, is somewhat arbitrary. I have used the value at one disk scale length in the past on the grounds that the disk scale length is a structural parameter determined by galaxy physics, whereas the photometric radius can be biased by observational considerations. The actual "mean" abundance in the disk ISM would be determined by convolving the abundance gradient with the gas distribution. As a simple compromise I have used the disk half-light radius, which is 1.685 times the disk scale length (de Vaucoleurs & Pence 1978), and so is still connected to galaxy structure. It should be noted also that a O/H - M_B correlation is derived whether one uses the central abundance, the abundance at one disk scale length, or some other fractional radius.] ZKH noted the remarkable uniformity of this correlation over 11 magnitudes in galaxy luminosity, for ellipticals and star-forming spiral and irregular galaxies.

Figure 9. Top: The correlation of spiral galaxy abundance (O/H) at the half-light radius of disk from the galaxy nucleus vs. galaxy blue luminosity. Bottom: abundance versus maximum rotational speed Vrot.

To the extent that blue luminosity reflects the mass of a system, the metallicity-luminosity correlation suggests a common mechanism regulating the global metallicity of galaxies. What the mechanism might be is not very well understood at present. The most commonly invoked mechanism is selective loss of heavy elements in galactic winds (e.g., Dekel & Silk 1986). However, the metallicity-luminosity correlation for star-forming galaxies by itself does not imply that lower-luminosity galaxies are losing metals. Such a correlation could occur if there is a systematic variation in gas fraction across the luminosity sequence, either because the bigger galaxies have evolved more rapidly, or because the smaller galaxies are younger. In fact, there is evidence that both of these may be true. There is also evidence for fast outflows of hot X-ray gas from starburst galaxies such as M82 (Bregman, Schulman, & Tomisaka 1995). However, the question of whether this hot gas is escaping into the IGM or will be retained by any given galaxy depends not just on the gravitational potential, but also on details such as the vertical distribution of ambient gas and the radiative cooling which are not so well understood.

The question of loss of metals from galaxies is profound because of the existence of metals in low column density Lyman- forest systems (Ellison et al. 1999), which are probably gas clouds residing outside of galaxies. Where the heavy elements came from in these systems is still a mystery; it is possible that they were seeded with elements from a generation of pre-galactic stars or with elements expelled in starbursts during galaxy formation. In the dense environments of galaxy clusters, ram pressure stripping by intracluster gas, tidal interactions, and galaxy mergers may also liberate material to the intracluster medium (Mihos 2001). It is therefore a useful exercise to investigate what kinds of galaxies are potential candidates for ejecting heavy elements into the IGM.

I begin by looking at the metallicity-luminosity relation in a different way. It is often argued that the B-band luminosity is not a very good surrogate for mass, since the B-band light can be affected by recent star formation and dust. Therefore, in Figure 9(b) I plot the mean O/H for the galaxies in Fig. 9(a) versus rotation speed (obtained from resolved velocity maps [e.g., Casertano & van Gorkum 1991, Broeils 1992], not single-dish line widths), where for the spirals the rotation speed is taken to be the value on the flat part of the rotation curve. Interestingly, the Z-V_rot correlation turns over and flattens out for V_rot 150 km s-1, suggesting that spirals with rotation speeds higher than this have essentially the same average metallicity. Does this indicate a transition from galaxies that are likely to be losing metals to the IGM to galaxies that essentially retain the metals they produce?

This question can be examined further by studying metallicity as a function of gas fraction. In the context of the simple, closed box, chemical evolution, Edmunds (1990) derived a few simple theorems that show that outflows of gas and inflows of metal-poor gas cause galactic systems to deviate from the closed box model in similar ways. Specifically, defining the effective yield y_eff

(4.6)

outflows of any kind and inflows of metal-poor gas tend to make the effective yield smaller than the true yield of the closed box model. y_eff defined this way is an observable quantity, and provides a tool for studying gas flows in galaxies. Although the true yield is relatively uncertain, comparing effective yields for a sample of galaxies can provide information on the relative importance of gas flows from one galaxy to another.

Such a comparison is presented in Figure 10 (Garnett 2002), where I show data compiled on abundances, atomic and molecular gas, and photometry for 22 spiral and 10 nearby irregular galaxies. Figure 10 plots the effective yields derived for each galaxy using equation 3.1 and the global gas mass fraction versus galaxy rotation speed. The plot shows a very strong systematic variation in y_eff with V_rot in the dwarf irregular galaxies, with y_eff increasing asymptotically to a roughly constant value for the most massive galaxies. The uncertainties in the individual y_eff values are relatively large, because of relatively large uncertainties in M/L ratios for the stellar component and the CO - H₂ conversion for the molecular gas component; individual values of y_eff are probably not known to better than a factor of two. Nevertheless, the data show a factor of 30 systematic increase in y_eff from the least massive irregulars to the most massive spirals.

Figure 10. Effective yields yeff for nearby spiral and irregular galaxies versus rotation speed Vrot (Garnett 2002). Filled squares represent the data for spirals while the crosses show the data for irregulars.

This result is striking verification that the yields derived for dwarf irregulars are significantly lower than in spiral galaxies, and shows that the variation is a systematic function of the galaxy potential. In strict terms, the trend in Figure 10 does not distinguish between infall of unenriched gas and outflows as the cause. However, the trend toward small y_eff in the least massive galaxies suggests that it is the loss of metals in galactic winds that drives the correlation. It would be of interest to use this correlation to estimate the total amount of gas lost in the small systems, and to determine the manner in which supernova energy feeds back into the ISM of the host galaxies.

Although not quite certain yet where one can say that galaxies are losing significant quantities of metals and which ones retain essentially all their metals, it appears likely that this boundary point is somewhere near V_rot 150 km s^-1. Given this, one can surmise that the outflow of hot gas seen in the starburst galaxy M82 (V_rot 100 km s^-1) may contribute significantly to enrichment of the IGM, while the hot gas flow seen in NGC 253 (V_rot 210 km s^-1) is likely to remain confined to the galaxy.