Recently, attempts have been made by several authors (Tinsley and Gunn 1976; O'Connell 1976b; Whitford 1977) to model photometric and spectrophotometric observations of the central regions of bright elliptical galaxies. In this section, we ask how well these published models agree with our new data for bright galaxies. Detailed model fitting is deferred to a later paper.
Two models are chosen as examples: Model "A" of Tinsley and Gunn (1976, TG) in which the slope of the initial mass function x equals zero; and model "C" of O'Connell (1976b, OC) with a flat luminosity function (M dwarfs), which corresponds to an x of about 0.5. The published luminosity function of TG and unpublished values from O'Connell (1976c) were combined with the stellar calibrations of Appendix A and of Johnson (1966b), and the colors for these two models were calculated. (Johnson's J - K colors were transformed to the system of this paper as discussed in Appendix A). The results are given in Table 9, where the observed values are for the galaxies in the second group of Table 7. The OC model gives an excellent fit to the average galaxy colors, while the TG model has colors which are too blue and a CO index which is too weak. OC's model fit is probably fortuitous, however, because of the sensitivity of the infrared indices to the luminosity function of the giant branch (see Table A3) combined with the coarseness of OC's bins for giants. The origin of the difference between the two models lies in the choice of the relative shape of the giant branch luminosity function, and in the assumed values of MV for giants (which differed by up to l mag). For the OC model, about 35 percent of the light at 2 µm comes from the M6 III bin whereas these stars contribute only 12 percent of the 2 µm light in the TG model. Nevertheless, the model fitting work of TG (and references therein), OC, and Frogel et al. (1975a) has established that the V - K color and the CO index provide strong constraints on both the dwarf-to-giant ratio and the shape of the giant branch - V - K is effective for the latter and the CO index for the former. Any significant increase in the number of late-type dwarf stars beyond those already contained in the models drives the CO index to unacceptably low values and begins to make V - K too red. The J - H color is mildly sensitive to the giant-to-dwarf ratio since dwarf stars do not exhibit J - H colors greater than 0.7 (e. g., Mould and Hyland 1976). H - K provides a weak constraint on the giant branch luminosity function as can be seen from Figure 4 : stars later than M3 III must be present to provide the red H - K color.
|V - K||2.97||3.29||3.33|
|J - H||0.59||0.7||0.70|
|H - K||0.22||0.2||0.20|
|M / LV||3.0||2.4||-|