4.1. Stellar content
We have compared colors and M/L's for our sample with models of stellar population synthesis (SPS) to place constraints on age and metallicity of the average stellar content of bulges and disks. In particular we have considered Worthey's model (1994, W94 hereafter) for single stellar populations with ages from 1.5 to 17 Gyr and different metallicities, and the 1995 release of the model by Bruzual and Charlot (1993, BC95) for populations with solar metallicity and different star formation histories.
The mean colors and M/L's of bulges and disks are plotted in Fig. 3 together with the two SPS models. The average M/L for the bulges are computed excluding values below 0.2 in all bands. W94 colors and M/L's agree rather well with the observed values, whereas BC95 have both bluer colors and lower M/L's. The discrepancies between the two models have been discussed by Charlot et al. (1996). Inspection of the left panel of Fig. 3 shows that bulges are notably redder than disks, both in and in (see also Paper I). Nevertheless, the discrepancies between different SPS models, the degeneracy age/metallicity, and the possible effect of extinction make the color-color plot in Fig. 3 ambiguous as a diagnostic for distinguishing different stellar populations.
Fortunately, M/L ratios disentangle, at least partly, the ambiguity of age and metallicity. We find that bulges, on average, have lower M/L's than disks in all bands 1. Moreover, the values of M/L seen in the right panel of Fig. 3, according to the SPS predictions, suggest that bulges are younger and more metal rich than disks. We note that both W94 and BC95 models of a given abundance follow approximately the same trend with age. Hence, the displacement of the bulge and disk values relative to that trend implies that bulges are characterized by a younger age than that of the disks, independently of discrepancies between models. Except for extreme inclinations, , dust in the central regions affects the bulge more than the disk (Bianchi et al. 1996). Consequently, the noted difference between bulge and disk M/L cannot be attributed to internal extinction, since the correction would only increase the difference between the two. The possibility that the disk M/L's have been overestimated seems rather unlikely, even under the MBD hypothesis (although see Bottema 1997; Courteau & Rix 1997) since an average error greater than 30% on the estimated disk RC contribution would be required to make the disks' average age comparable to bulges'. Finally, the bulge M/L's could have been systematically underestimated. This would be the case only if all the RC's (and not just the few already noted and excluded from the mean) rose too slowly in the inner regions with respect to the true circular velocity of the galaxy. We discussed briefly this point in Sect. 3.2, concluding that most likely such underestimates, if present, are not sufficient to eliminate the observed difference in M/L between the components.
That bulges may be more metal rich than disks is not a new result (Bica & Alloin 1987; Delisle & Hardy 1991; Giovanardi & Hunt 1996; Paper I), and abundance variations are thought to be driven by variations with mass (e.g., Zaritsky et al. 1994). That bulges appear to be younger than disks is somewhat surprising; the comparison with SPS models shown in Fig. 3 implies an age difference of around 50%, or 5 Gyr. Nevertheless, such a result may be interpreted in light of recent observational and theoretical work on bulge dynamics. Many bulges show kinematic and photometric signatures usually associated with disks, including flattened distributions, exponential fall-off, dominance of the rotation velocity component, and spiral structure in the bulge-dominated region (Kormendy 1993 and references therein). Moreover, some bulges have blue colors, the result of extremely young populations (Schweizer 1990), and as noted in Paper I, at least three of the galaxies in our sample appear to be actively forming stars 2. As suggested by Kormendy and others, "bulges" may be built up over time from disk material transported to the central regions by gravitational perturbations; such bulges would appear younger than the disks from which they derive.
4.2. Correlations with mass-to-light ratios
Since, as for the photometric properties discussed in Paper I, disk characteristics are more reliably determined than those of bulges, we will concentrate on the M/L's obtained for the disks.
Several authors (see for instance Djorgovski & Santiago 1993, and references therein) have demonstrated that elliptical galaxies follow a relation which can be expressed in terms of a power law: M/L with depending on the sample and the photometric band. Kent (1986) also found that the disks of spirals follow a similar relation in the r band at fixed morphological type with an exponent . More recently Persic, Salucci, and collaborators (PSS; Salucci et al. 1991) found for a sample of late-type spirals that in B, . Burstein et al. (1997) have suggested that a relation of this kind between M/L and luminosity is common to all the self-gravitating structures in the universe, ranging from globular clusters to clusters of galaxies. Finally, models of cold dark matter halos, based on N-body simulations and adiabatic infall for disk formation, require a variation of disk M/L with B luminosity in order to accommodate observed rotation curves (Navarro et al. 1996).
We have investigated the compatibility of the values of found in the optical with our K-band data, assuming the trend of M/L with L is due to disk stars and not to DM. We can convert the index found in the B band to the K-band value using the well-established color-luminosity relation for spirals (Visvanathan 1981; Wyse 1982; Tully et al. 1982). Based on recent data, Gavazzi (1993) finds:
for early-type spirals. If we assume that is independent of luminosity (which is likely since is typically small, 0.2 mag), then we have a similar relation for with
We take 0.35 (PSS) together with the slope of the color-luminosity relation defined above, we infer a value of . If we fit our data to a regression of M/L versus disk luminosity, we obtain , consistent with the expected value of 0.15. Fig. 4 shows K-band disk luminosity plotted against disk M/L (K), together with a line having slope .
The M/L vs luminosity relation for elliptical galaxies is implicit in a more general relation, namely the one defining the fundamental plane (FP) of elliptical galaxies (see review by Kormendy & Djorgovski 1989):
where and are respectively the effective radius and surface brightness and is the observed central velocity dispersion 3. We have fitted a similar relation between disk scale lengths, central brightnesses, and peak rotation velocities of our disks, and find: and . This implies that the disks of early-type spirals also define a plane similar to that for ellipticals; the elliptical FP has and . A similar result, but for the photometric properties only, was reported in Paper I, both for bulges and disks. When we derive the M/L vs L relation from Eq. 12 and the virial theorem we obtain:
which contains a residual dependence on the central brightness . However our values for a and b yield
where, as for ellipticals, the dominant dependence is on luminosity.
As discussed by Djorgovski & Santiago (1993), a relation between M/L and luminosity (or mass) can come about in several ways. One possibility is that the disk M/L's are contaminated by a DM contribution which has a density profile similar to that of the stellar disk. The sense of the M/L vs L relation would require this DM fraction to increase with luminosity, contrary to the trend observed for the global DM fraction which increases with decreasing luminosity (e.g., PSS). Alternatively, the MBD hypothesis could be incorrect, and the stellar disk M/L constant. In this case, though, the trend in Fig. 4 would require the MBD hypothesis to be more valid in lower luminosity systems, contrary to common beliefs.
Another possibility is that disks of different luminosities harbor different stellar populations, which is also suggested by the color-luminosity relation mentioned above. W94 predicts that at fixed age, initial mass function (IMF), and star formation rate (SFR), M/L is an increasing function of metallicity in the optical, but a decreasing one in the NIR. This suggests that the M/L vs L correlation cannot be understood in terms of a metallicity variation. Alternatively, such a correlation could be driven by a change of average age or star formation history with luminosity. Again, the observed difference in the slope of the correlation at different wavelengths can be compared to the predictions of SPS models. To test this possibility we made use of the BC95 models, at fixed (solar) metallicity and IMF (Salpeter 1955), considering single burst populations at different age T, and populations with different e-folding time (exponential SFR) at fixed age (10 Gyr). We have approximated the model dependence of M/L on T and with power laws, whose index in B and K has been determined with a best fit. Assuming M/LB , in the first case the model predicts a difference in the slope of this relation of 0.17 passing to the K band, consistent with the predicted difference of 0.2. Considering the variation with the prediction is 0.2, in similarly good agreement. It, therefore, seems plausible that the variation of M/L with luminosity is driven by different star formation histories, and the consequent different stellar mixes.
4.3. Dark halos
We claim to recognize the presence of a dark halo in six of our galaxies: three of them are pseudo-isothermal and three constant-density spheres. We do not find any systematic difference between the two models, at least in terms of central densities or masses within . The statistics are sparse, but we can attempt a comparison with the general relations found by PSS in the B band for a large sample of late-type spirals. In particular, we can check that the ratios of the halo central density to the critical density, , and the dark to visible mass at the optical radius, , are consistent with the correlations with the B-band galaxy luminosity given in PSS. They find:
with . If we assume the same color-luminosity relation as in Sect. 4.2, we find in the K band after scaling to km s-1:
with g cm-3 and , the absolute magnitude corresponding to . We estimated from the color-luminosity relation, with the zero order coefficient fixed by the median values of and for our sample.
The trends shown in Fig. 5 are consistent with the anticorrelation between dark and luminous mass found in PSS. Moreover, there is no striking discrepancy between our galaxies and the behavior of later type systems, suggesting that dark halos are similar for all spirals. In the right panel of Fig. 5 our data reveal roughly the same as found in late-type galaxies with the same B luminosity.
© European Southern Observatory (ESO) 1998
Online publication: October 21, 1998