Annu. Rev. Astron. Astrophys. 1992. 30: 613-52
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2.6 Statistics of Emission Lines in Galaxies

The emission line [OII] 3727 is present in regions of active star formation and appears commonly in the integrated spectra of galaxies (indeed, redshifts for faint galaxies are often based solely on a single line attributed to [OII] 3727, e.g. Minkowski 1961). Unlike Halpha which is redshifted into the forest of bright OH sky lines, [OII] remains in a good spectral region up to z ~ 0.8. Since emission lines are relatively easy to detect, a measure of the frequency with which this line appears above some specified strength, as a function of redshift, is a natural relationship to explore. Such a test for evolution is in the same category as the distribution of broad-band colors as a function of redshift, except that since the strength of [OII] 3727 depends on the excitation and the oxygen abundance, it is a less direct measure of current star formation.

The statistics of [OII] emission at zmed ~ 0.2 were discussed by Broadhurst, Ellis, and Shanks (1988, hereafter BES), who used these data to support their picture for enhanced bursts of star formation at z > 0.1 that were preferentially in galaxies of lower luminosity. Specifically, they found twice as high a fraction of galaxies with an equivalent width of [OII] 3727 (W3727) greater than 20 Å as they would have expected had there been no evolution. This result was reconsidered by Colless et al. (1990) in the deeper sampling of the Low Dispersion Survey Spectrograph (LDSS) survey. Colless et al. found an excess of only about 40% of galaxies with strong W3727. In both cases the comparison was with respect to the scaled statistics of the B ~ 17 sample of Peterson et al. (1986). These results were amplified by Broadhurst, Ellis, and Glazebrook (1992) who showed W3727 versus magnitude for all of these surveys, plus a new survey by Broadhurst and Ellis (BE) that fills in the gap 18 < B < 20 (Figure 2 of Broadhurst, Ellis, and Glazebrook 1992). This diagram shows that within each of the magnitude-limited surveys, the median W3727 increases with apparent B magnitude. Taking the surveys together, there is no trend from B = 16 to B = 19.5, and no trend from B = 19.5 to B = 22.5. In the regions of overlap (B ~ 20.25 for BES and BE, B ~ 21.25 for BES and LDSS), the deeper survey of the pair has lower median W3727. The fainter galaxies will naturally have greater random errors in W3727, and it is possible that some of the effect may be due to an asymmetry in the measurement error.

Figure
6
Figure 6. Equivalent width of [OII] 3727 versus redshift for the field galaxy samples of Broadhurst, Ellis, and Shanks (1988) and Colless et al. (1990). To ensure that galaxies of similar luminosity are represented at each redshift, only galaxies satisfying -19.0 < B - 5logz - 43.9 < -20.5 have been plotted, which is why there are so few galaxies with z < 0.15. Broadhurst, Ellis, and Shanks (1988) report non-detections of [OII] 3727 (the zero values in the Figure), but for Colless et al. (1990) the lack of a recorded measurement may or may not mean that the line has W3727 = 0. Hence as plotted the Colless et al. data are biased with respect to the Broadhurst data.

Comparing histograms of W3727 for different samples cannot provide a compelling case for evolution without some check that the samples contain galaxies that are otherwise similar. In fact, if W3727 is plotted against redshift, a very different picture is apparent (Figure 6). In the BES sample, there is in fact an anti-correlation with redshift, such that galaxies at z ~ 0.15 have stronger W3727 than galaxies at z ~ 0.3. This behavior can be understood if lower-luminosity galaxies tend to have larger W3727, since in the BES sample the narrow range of apparent magnitude results in a strong correlation between redshift and absolute magnitude. In the same way, a dependence of W3727 on absolute magnitude would explain why there is an increase in median W3727 with apparent magnitude, since in these surveys the apparently fainter galaxies tend to be of lower luminosity.

That lower-luminosity galaxies might have larger W3727 is plausible on the basis of the tendency of lower-luminosity galaxies to have bluer U - B colors (Huchra 1977). Although Huchra's (1977) sample of Markarian galaxies included by definition predominantly blue galaxies, the trends of W5007 versus MB and U - B in his sample are likely to be qualitatively relevant. Figure 7 shows W5007 versus MB, indicating that there is indeed a strong correlation between these quantities in the sense needed to explain the BES result.

Figure
7
Figure 7. Estimates of the [OIII] 5007 equivalent width versus MB (H0 = 50 km sec-1 Mpc-1) from Huchra's (1977) survey of Markarian galaxies. (The distribution of equivalent widths of Hbeta, also measured by Huchra, is qualitatively similar.)

Dressler and Gunn (1982) published W3727 for 21 nearby field galaxies and showed that for even the bluest galaxies W3727 did not exceed 30 Å. This result has been used by others to argue that the high fraction of strong-lined galaxies in faint samples is unexpected and therefore indicative of evolution. There was however no effort by Dressler and Gunn to ensure that their sample was representative of field galaxies. On the contrary, they state that ``the sample was heavily weighted toward Sb and Sc galaxies, since it was realized that these were the only luminous galaxies to have colors much bluer than ellipticals.''

In summary, the Broadhurst, Ellis, and Shanks (1988) argument for the increasing prevalence of bursts of star formation at z > 0.1 is based partly on the claim that W3727 > 20 Å is uncommon in local samples, but we have argued that it has not been shown that local samples have been selected in the same way and contain comparable galaxies. Direct evidence in the form of showing an increase in median W3727 as a function of redshift is lacking, if one discounts the median W3727 at z ~ 0. Figure 6 shows W3727 for both the BES and the LDSS as a function of redshift, with only galaxies in the range -19 < MB < -20.5 being plotted in order to ensure that the galaxies are comparable, and no trend is apparent. (Had a fainter luminosity interval been chosen, there would have been more galaxies of higher line strength, but the range of redshifts would not have extended as high.)

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