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Figure 8.4 shows as a function of age the M* / LB ratio (where M* is the stellar mass) for SSPs with solar composition, and different IMFs each with a single slope s over the whole mass range 0.1 leq M leq 100 Modot. Very large mass-to-light ratios are produced by either very flat (s = 1.35) or very steep (s = 3.35) IMFs, whereas the Salpeter's slope gives the lowest values of the M* / LB ratio. This is a result of the different stellar demography already illustrated in Figures 8.1 and 8.2, such that a steep IMF is dwarf dominated, that is, most of the mass is in low-mass stars, whereas a flat IMF is remnant dominated and most of the mass is in dead remnants.

Figure 4

Figure 8.4. The stellar mass-to-light ratio of solar metallicity SSPs as a function of age, for three different single slope IMFs, from 0.1 to 100 Modot. Also plotted are values of the dynamical M / L ratio for a sample of local elliptical galaxies with detailed dynamical modelling (source: M / L ratios for models: Maraston, C. (1998, Mon. Not. R. Astron. Soc., 300, 872); for the data: Cappellari, M. et al. (2006, Mon. Not. R. Astron. Soc., 366, 1126), van der Marel, R.P. and van Dokkum, P. (2007, Astrophys. J., 668, 756), van Dokkum, P. and van der Marel, R.P. (2007, Astrophys. J., 655, 30); ages: from Eq. (1) in Thomas, D. et al. (2010, Mon. Not. R. Astron. Soc., 404, 1775)).

Measurements of the structure (e.g., half light radius) and stellar velocity dispersion of elliptical galaxies provide estimates of their dynamical mass, hence their dynamical mass-to-light ratio can be compared to the stellar M / L ratio. This is shown in Figure 8.4 for a sample of local elliptical galaxies with detailed dynamical modelling, having adopted a relation between the luminosity-weighted   age of their   stellar populations and velocity dispersion, namely Log(Age / Gyr) = -0.11 + 0.47 Log(sigmav), consistent with Eq. (6.16). Clearly very steep (s = 3.5) and very flat (s = 1.5) slopes of the IMF appear to be excluded by the data, whereas the intermediate (Salpeter) slope is quite consistent with the data, apart from the older galaxies which have a higher M / L ratio than the SSP models. However, besides an increase of age also the average metallicity is likely to increase with sigmav, with the galaxies in Figure 8.4 spanning a range from ~ 1/2 solar to ~ 2 times solar. Thus, the same galaxies are displayed again in Figure 8.5, together with model M / L ratios for a straight Salpeter IMF and three different metallicities. The trend in M / L ratio exhibited by the data appears to be consistent with the trend resulting from the metallicity trend with sigmav, and with a straight Salpeter IMF. However, things may not be as simple as they appear. Dark matter may contribute to the dynamical M / L ratios, and the IMF may not be straight Salpeter. A Salpeter-diet IMF such as that shown in Figure 8.1 would give M* / LB ratios systematically lower by ~ 40% than shown in these figures, thus opening some room for a dark matter contribution to the dynamical mass of these galaxies. Alternatively, an IMF slightly flatter than Salpeter at high masses, with its larger contribution by stellar remnants, would reproduce the high dynamical M / L ratios of the oldest galaxies, without dark matter contribution. It is quite difficult to circumvent this dark-matter/IMF degeneracy on the dynamical M / L ratios of elliptical galaxies.

Figure 5

Figure 8.5. The M / L ratio of SSPs with a straight Salpeter IMF, for subsolar (dotted), supersolar (dashed) and solar metallicity (solid), as indicated. The two solid lines refer to two releases of the same set of SSP models (source: model M / L ratios are from Maraston, C. (1998, Mon. Not. R. Astron. Soc., 300, 872; 2005, Mon. Not. R. Astron. Soc., 362, 799); data points are the same as in Figure 8.4).

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