IV. DISCUSSION OF THE GALAXY AND GLOBULAR CLUSTER DATA

The observed values of the H₂O index for the galaxies and globular clusters are presented in Tables 3 and 4, respectively. Unless noted otherwise, the 1 terrors in the photometry are ± 0.02 mag. For the values of A_v appropriate to the objects in these tables, no reddening corrections need be applied to the H₂O indices. Unlike the K-correction for the CO index where the absorption feature is shifted out of the filter bandpass for z > 0, the center of the H₂O band is shifted into the filter bandpass for z < 0.05. An analytic redshift correction based on stellar observations could not be determined, as in Paper I, because the data requires significant extrapolation past the wavelength of atmospheric cutoff. An attempt to derive the K-correction empirically as was done in Paper I for the CO index is hampered by the more limited sample of galaxies and the apparently small size of the correction. Since the indicated result was 0 K_H2O < 1.3z, and only 5 galaxies in Table 3 have redshifts z > 0.01 (the largest being z = 0.022), we have chosen to apply no redshift correction to the data.

In Figure l the data from Table 3 are plotted as a function of log A / D(0). No obvious dependence of the H₂O index on radius is seen in this diagram. As was done for the CO data of Paper I, a least squares fit to the multiaperture data for each galaxy was made, and the resulting values for the individual slopes were averaged. The mean change in the H₂O index per unit change in log A / D(0) is -0.04± 0.02 mag. Thus for our limited sample we find no significant dependence of the H₂O index on radius.

Figure 1. The H2O indices from Table 3 are plotted as a function of log A / D(0).

We have also searched for a dependence of the H₂O index on galaxian absolute magnitude. Table 5 presents a binning of the 15" aperture data into the same M_V bins as in Paper I. It is apparent that no significant dependence of H₂O index on M_V exists for M_V < - 19. Although the ordering by M_V is also an ordering by increasing z, and no redshift correction has been applied, the largest allowable correction will not significantly affect this conclusion. This result differs from that of O'Connell (1976a), who found that a Ca II + TiO index, which also increases toward late spectral type for M giants, decreases with increasing galaxian luminosity for M_V < - 19. Radial gradients in either index are not likely to affect this comparison since the aperture size used by O'Connell is close to ours. This difference remains if we restrict our sample to only those 10 galaxies observed in common with O'Connell. This and other absolute magnitude effects will be discussed further in Paper III (Persson, Frogel, and Aaronson 1977).

Table 5. Mean H₂O Indices for Galaxies with Well-Determined Distances

MV1.0 Limits	NO.	<z>	H2O Index *
MV < - 22.8	3	0.0170	0.13 (± 0.01)
-22.8 MV < - 21.8	9	0.0058	0.12 (± 0.02)
-21.8 MV < - 20.8	8	0.0037	0.115 (± 0.01)
-20.8 MV < - 19.8	8	0.0033	0.115 (± 0.02)
* Indices for an aperture diameter of 15" were averaged. The errors in parentheses are the dispersions.

Figure 2 displays the relationship between the H₂O data of Tables 3 and 4 and the corrected CO and broad-band color data from Paper I for the same or similar aperture size. Also shown are the mean relationships from Table 2. The relative location of the galaxies on the H₂O versus V-K, J-H, and H-K plots is determined by the fact that we are sampling the light of a composite stellar population. Thus, as was pointed out in Paper I, the V-K color is dominated by a hotter population of stars than is the H-K color. This accounts qualitatively for the relatively large displacement of the galaxy data from the mean relation for giants in the H₂O versus V-K plot. Now the data of Paper I showed that the 2.2 µm radiation from these galaxies is dominated by giant stars. Since the measured strength of the H₂O indices for these galaxies corresponds to that of an M5 III star, we conclude that late M giants must also make a significant contribution to the infrared light of early-type galaxies. O'Connell (1976a, b) came to a similar conclusion on the basis of his Ca II + TiO measurements.

Figure 2. The H2O indices from Tables 3 and 4 are plotted against the corrected CO indices and broad-band colors from Paper I. Mean relations shown for giant and dwarf stars are taken from Table 2 and from Paper I. The behavior of the mean relationships for dwarf stars is discussed by Persson et al. (1977), and the dependence of J-H on Teff for dwarfs is discussed by Mould and Hyland (1976). The dependences of the H2O index on colors for late-type stars (M5 and beyond) show large dispersion. Galaxy measurements from Table 3 are not plotted unless data at similar aperture sizes are available from Paper 1. In the H2O versus V-K plot, all such points lie within the ellipsoid labelled "galaxies."

In order to put this result on a more quantitative basis we compare: the predictions of the models of Tinsley and Gunn (1976, TG, model A) and O'Connell (1976b, OC, model C) with the data of Table 3. This comparison is presented in Table 6, where the mean observed values are from Table 7 of Paper I and from of the present paper. The percentage contributions to the light at 2 µm coming from three stellar "bins" were computed for the two models and the results are listed in the table. As was concluded in Paper I, the relative importance of late M giants in the OC model compared to the TG model leads to better agreement with the observations. For the H₂O index this occurs because the index increases rapidly in the latest giants.

Tinsley and Gunn (1976) have suggested that the inclusion of carbon stars could improve the fit of their model. Because of the single sideband nature of the H₂O and CO indices however, a strong temperature sensitive term is included, and the indices do not behave in carbon stars as they do in ordinary late-type giants (see Section III and Tables 1 and 2). Therefore, carbon stars alone cannot help, since the addition of any of these stars will drive the CO index, already too small in the TG model, to even lower values. Because of the large H₂O and CO absorption in Mira stars, it would appear that some contribution from these to the light at 2 µm could be present. However, we find that no combination of Mira and carbon stars added to the TG model produces as good a fit to the infrared data as does the OC model. Furthermore, the allowable contribution of these stars to the TG model cannot be greater than 15% to the light at 2 µm without producing disagreement with the data.

Finally, as was the case for the data of Paper I, we find no sharp discontinuity between the globular clusters and the galaxies in Figure 2; the globular with the strongest H₂O absorption is M69, the most metal-rich one observed. Detailed discussion of the colors and indices of globular clusters and of individual cluster stars will be presented elsewhere.

We thank our colleagues at Caltech and Harvard for their encouragement and for help in making the observations. We also thank an anonymous referee for valuable comments. This work was supported in part by NSF grant AST -74-18555A2 and NASA grant 05-002-207.