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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/sigma)* of the dynamical importance of rotation versus random motions (section 4.2.6). However, a closer examination of the logsigma - MB and Mg2 - MB correlations suggests that a second parameter is at work. This result (Terlevich et al. 1981) is summarized in Figure 34.

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 MB of the logarithm of the velocity dispersion, logsigma, and the metallicity index Mg2. 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 delta logsigma and deltaMg2 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 MB 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 MB. The equation of the correlation is delta logsigma = 1.852(delta Mg2) + 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 delta logsigma - delta Mg2 relation to reduce (say) the observed logsigma - MB correlation (a) to the mean Mg2 - MB relation. The result is panel (c), which shows logsigmacorr = logsigma - 1.852(delta Mg2) - 0.015 versus MB. The Mg2 - MB correlation is similarly reduced to the mean logsigma - MB 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 sigmaMg2 and sigma logsigma implies that the galaxies occupy a canted surface in logsigma - Mg2 - MB space. A combined least-squares fit yields

Equation 23 (23)

The individual relations corrected for the second parameter (Fig. 34c,d) are:

Equation 24 (24)

using MB and logsigmacorr as independent variables, respectively;

Equation 25 (25)

Figure 34 suggests that the second parameter may be related to the intrinsic axial ratio. On average, apparently rounder galaxies have higher sigma 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 logsigma and Mg2 do not separately correlate with MB. Instead, they believe that the delta logsigma - deltaMg2 relation is driven by a correlation between logsigma and Mg2. 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 MB (the "second parameter" in this plot). Thus it may be that the true second parameter in ellipticals is related to Mg2 or logsigma 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 Delta Mg2 and Delta logsigma from the corrected relations (c), (d). Only galaxies brighter than MB appeq - 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 Mg2 of the strength of Mg I "b" plus MgH at ~ 5178Å, see Faber, Burstein and Dressler (1977). The calibration of Mg2 (in mag) is [Fe/H] = 3.9 Mg2 - 0.9, where [Fe/H] is the logarithmic metal, abundance relative to the sun (Burstein 1979a; Terlevich et al. 1981). Further discussion of Mg2 is found in references given in Terlevich et al. (1981). The Mg2 - MB correlation is illustrated in Fig. 1 of Faber (1977). Back.

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