4.2.4. Central Velocity Dispersions.
III. Correlation With Line Strength
The parameter correlations discussed so far suggest that the properties of elliptical galaxies are largely controlled by one parameter, the total luminosity L (e.g., Faber 1973b). Core parameters correlate closely with L; these include central velocity dispersion, core radius, central surface brightness and metallicity ^{(6)} Also correlating with L, although with larger scatter, are global parameters such as the effective radius and surface brightness (section 3.3.3) and a measure (V/)^{*} of the dynamical importance of rotation versus random motions (section 4.2.6). However, a closer examination of the log - M_{B} and Mg_{2} - M_{B} correlations suggests that a second parameter is at work. This result (Terlevich et al. 1981) is summarized in Figure 34.
Figure 34. Parameter plots from Terlevich et al. (1981) illustrating the probable two-parameter nature of elliptical galaxies. Panels (a) - (d) show correlations with absolute magnitude M_{B} of the logarithm of the velocity dispersion, log, and the metallicity index Mg_{2}. The measured parameters are shown in (a) and (b). The scatter is large compared with the estimated error bars, and is therefore real. Panel (e) shows that the deviations log and Mg_{2} from the least-squares lines shown in (a), (b) correlate with each other. Terlevich and collaborators argue that the correlation does not result from subtle measuring errors. In particular, errors in M_{B} are likely to be too small to have an effect, and would produce the wrong slope. The arrow in (e) shows the result of a 1 mag error in M_{B}. The equation of the correlation is log = 1.852( Mg_{2}) + 0.015 (straight line). The fact that the deviations correlate suggests that a single second parameter is responsible. The effect of this parameter can be removed by using the log - Mg_{2} relation to reduce (say) the observed log - M_{B} correlation (a) to the mean Mg_{2} - M_{B} relation. The result is panel (c), which shows log_{corr} = log - 1.852( Mg_{2}) - 0.015 versus M_{B}. The Mg_{2} - M_{B} correlation is similarly reduced to the mean log - M_{B} relation in panel (d). In both cases the scatter is greatly reduced and consistent with measuring errors. The straight lines in (c), (d) are new least-squares fits (equations 24, 25), with the four labeled galaxies omitted. |
The correlation of Mg_{2} and log implies that the galaxies occupy a canted surface in log - Mg_{2} - M_{B} space. A combined least-squares fit yields
(23) |
The individual relations corrected for the second parameter (Fig. 34c,d) are:
(24) |
using M_{B} and log_{corr} as independent variables, respectively;
(25) |
Figure 34 suggests that the second parameter may be related to the intrinsic axial ratio. On average, apparently rounder galaxies have higher and stronger metal lines than flatter galaxies (cf. van den Bergh's 1979 result that rounder galaxies are redder). Note that projection effects should fill in the region below the correlations in Figure 34 (f) and (g) with intrinsically flattened galaxies that are seen nearly face-on.
The above results have been criticized by Tonry and Davis (1981b), who do not confirm the correlations with axial ratio. They suggest that log and Mg_{2} do not separately correlate with M_{B}. Instead, they believe that the log - Mg_{2} relation is driven by a correlation between log and Mg_{2}. Such a correlation does exist. When plotted using parameters from Terlevich et al. (1981) the scatter is even consistent with the measuring errors, a result which supports Tonry and Davis' suggestion. In fact, the scatter is produced in part by the dispersion in M_{B} (the "second parameter" in this plot). Thus it may be that the true second parameter in ellipticals is related to Mg_{2} or log as well as being related to flattening. However, flattening does seem to be involved in the second parameter (Tonry and Davis apparently did not find any correlations with flattening because their measuring errors were too large, Davies 1982). The above discussion is consistent with Terlevich et al. (1981), who state their conclusions cautiously.
The correlations of Figure 34 contain information about the true shapes of ellipticals, although they are difficult to interpret because intrinsic correlations with flattening as well as the viewing geometry may be involved. The parameter relations also have implications for theories of galaxy formation, being generally easier to reconcile with dissipational-collapse theories than with dissipationless formation. Our understanding of these implications is very rudimentary. Besides enlarging the galaxy sample, we need to explore correlations with parameters which measure more global dynamical quantities.
Panels (f) and (g) suggest that the second parameter may be related to intrinsic axial ratio. They show correlations between the logarithm of the observed axial ratio a/b and deviations Mg_{2} and log from the corrected relations (c), (d). Only galaxies brighter than M_{B} - 20 are illustrated; fainter galaxies tend to be more heterogeneous in their stellar populations (Faber 1977) and show weaker correlations with log(a/b).
^{6} The metallicity is measured using an index Mg_{2} of the strength of Mg I "b" plus MgH at ~ 5178Å, see Faber, Burstein and Dressler (1977). The calibration of Mg_{2} (in mag) is [Fe/H] = 3.9 Mg_{2} - 0.9, where [Fe/H] is the logarithmic metal, abundance relative to the sun (Burstein 1979a; Terlevich et al. 1981). Further discussion of Mg_{2} is found in references given in Terlevich et al. (1981). The Mg_{2} - M_{B} correlation is illustrated in Fig. 1 of Faber (1977). Back.