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In Papers I and II, published evolutionary models of Tinsley and Gunn (1976) and empirical models of O'Connell (1976) for the central regions of bright ellipticals were compared with the infrared observations. In both cases, the best fitting models were similar in that at 2 µm, only 20% of the light was contributed by dwarf and evolving stars, while 80% was contributed by stars from the giant branch. However, the O'Connell model, with a 37% contribution from M6 giants, agreed significantly better with the data than did the Tinsley and Gunn model, with only a 12% contribution from such stars.

The model fitting work of Tinsley and Gunn (1976), O'Connell (1976b), Frogel et al. (1975a) and in Papers I and II has established that the CO and H2O indices and the V - K color provide strong constraints on both the dwarf-to-giant ratio and the shape of the giant branch luminosity function in elliptical galaxies. The data are most consistent for elliptical galaxy models with an initial mass function slope x (following the notation of Tinsley 1968, 1972) in the range 0 ltapprox x ltapprox 1, giant branches rich in late M stars, and mass-to-light ratios M / LV < 10. However, the very latest M giants - such as Miras and carbon stars - do. not appear to contribute more than about 15% to the 2 µm light (cf. Paper II). The data presented in this paper suggest that similar constraints apply to the nuclear regions of all galaxies dominated optically by populations ranging in mean spectral type from near K to near F.

While a number of empirical synthesis models for galaxies measured in this study have been published in recent years (e.g. Tifft 1963; Johnson 1966b; Wood 1966; McClure and van den Bergh 1968; Lasker 1970; Spinrad and Taylor 1971; Faber 1972; Andrillat, Souffrin, and Alloin 1972; Alloin 1973; Joly 1973, 1974; Joly and Andrillat 1976), comparison with such models is generally not instructive because either M giants were ignored completely, or they were included in only an ad hoc fashion - for instance, by lumping all stars into a single M5 bin. However, recent empirical models by Williams (1976) of mostly amorphous population galaxies, and by Turnrose (1976) of intermediate population galaxies, treat M giants in a somewhat more rigorous manner. Using the stellar-calibrations in Johnson (1966a), Papers I and II, and in Appendix A, the infrared colors of the models presented by these authors were calculated and compared with the available infrared data from Papers I and II and in this paper.

Williams (1976) has presented synthesis models for NGC 221, 224, 584, 3031, 3115, 3379, 4594, and 5194. Except for 5194, in these models the contributions from M dwarfs range from 22% to 63% of the 2 µm light, the contributions from late M giants range from 11% to 39%, and the mass-to-light ratios range from 17 to 81. Excluding NGC 5194, these models are incompatible with the data. Typically, the V - K colors are 0.5 to 1.0 mag too red, the CO indices are 0.05 to 0.10 mag too small, and the H2O indices are 0.10 to 0.15 mag too large. As an example, comparison of the observations with three of the models is made in Table 14. The model colors are quite sensitive to the V - K color adopted for Williams' late M giant bin, as apparent in Table 14. However, the discrepancies cannot be accounted for by variation in this V - K color: an increase above 7.20 drives the model V - K color, already too red, to even redder values; while a decrease below 7.20 drives the CO index, already too low, to even lower values. The major problem with the models is the excessive numbers of M dwarfs, which produce the rather high M / LV values. Only in the model for NGC 5194, which at 2 µm has a 1% contribution from late M dwarfs, a 35% contribution from late M giants (assuming V - K for this bin = 7.20), and an M / LV of 1.2, is there reasonable agreement with the data.

Table 14. Comparison with Stellar Synthesis Models of Williams

Color NGC 3031 NGC 4594 NGC 5194
  Observed Model* Observed Model* Observed Model*

U - V 1.76 1.49 1.65 1.45 1.00 1.12
V - K 3.51 3.84 - 4.09 3.54 4.42 - 4.68 3.14 3.16 - 3.68
J - H 0.72 0.67 - 0.73 0.75 0.68 - 0.73 0.71 0.76 - 0.83
H - K 0.24 0.23 - 0.26 0.19 0.26 - 0.28 0.23 0.19 - 0.25
CO 0.15 0.06 - 0.10 0.17 0.04 - 0.09 0.18 0.15 - 0.19
H2O 0.12 0.18 - 0.22 0.11 0.21 - 0.24 0.12 0.12 - 0.21
M/LV - 36 - 81 - 1.2

* The left hand values for the model infrared colors were obtained by assuming V - K = 7.20 (i.e. that for an M6 III) for Williams' late M giant bin. The right-hand values were found by assuming V - K = 8.30 (i.e. that for an M7 III) for this bin.

The galaxies modeled by Turnrose (1976) include NGC 1084, 1637, 2903, 4321, and 5194. Typically, at 2 µm the models have a ltapprox 1% contribution from late M dwarfs, a 15 - 30% contribution from late M giants, and M / LV, values < 2. In addition, these models also contain substantial numbers of upper main sequence stars and M supergiants, the contribution of the former ranging from 20 - 60% at V, and of the latter from 0 - 20% at 2 µm.

Within the uncertainties (see below), the CO and H2O indices for the Turnrose models are generally compatible with the observations. However, interpretation of the V - K color in these models is ambiguous for a number of reasons. To begin with, as usual the 2 µm luminosity is quite sensitive to the mean V - K color adopted for the M6 - M8 III bin. Now because of the large upper main sequence contribution, the intrinsic V - K colors of the models are very blue. On the other hand, Turnrose finds internal reddening values of 0.3 - 0.4 in E(B - V), which leads to corrected V - K colors about 1 mag redder. In other words, if Turnrose's internal reddening values are correct, the mean V - K colors in intermediate population spirals are deter- mined mostly by reddening effects, and not by the stellar population, as was implied in Section IV.

Adopting a V - K color of 8.3 for the M6 - M8 III bin leads to model V - K colors in the range 2.0 to 2.5, and with the Turnrose reddening corrections there is acceptable agreement with the data. However, in light of the generally large V - K color gradients in these spirals (Table 7), and of the fact that Turnrose's aperture size was 7", whereas the smallest available aperture sizes for the infrared data are typically 4 - 5 times larger, the agreement would seem to be somewhat fortuitous. It furthermore seems surprising that the intrinsic V - K colors in these galaxies should be as blue as in Magellanic irregulars, i.e., galaxies with little internal reddening (Holmberg 1975) but presumably richer upper main sequences than in the Sc's. The explanation may simply be that Turnrose's 7" data is more heavily weighted by intense star formation regions than is the much larger aperture infrared measurements. Infrared observations at Turnrose's aperture size might resolve the dilemma.

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