Annu. Rev. Astron. Astrophys. 1991. 29: 239-274
Copyright © 1991 by . All rights reserved

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3.1 Global Relations

All self-consistent models can be scaled in radius and central velocity dispersion (Section 2). As the mass-to-light ratios of elliptical galaxies are not known a priori, correlations between global parameters of these galaxies provide constraints on their formation.

The first correlation that was found is the Faber-Jackson relation, between total luminosity L and central velocity dispersion sigmacen: L propto sigmacenalpha, with 3 < alpha < 5 (e.g., 96, 100, 113, 195, 328). The scatter in the relation is approx 0.m6-0.m7 for the general field, but may be lower in specific clusters (e.g., 96, 97, 328). The equivalent result for spiral galaxies is the Tully-Fisher relation L propto vcircbeta, with 3 < beta < 5, with a spread of approx 0.m3-0.m5 (1, 54, 277, 338). Both relations may deviate from pure power laws (255, 328). The origin of these relations is not well-understood. It was initially thought that they are caused entirely by the perturbation spectrum prior to galaxy formation (148), but this mechanism might produce too much scatter, so that a self-regulated process may be at work (365).

The Faber-Jackson relation has been superseded by the ``fundamental plane''. Two groups found independently that the scatter in the L vs sigmacen relation decreases if a second parameter is included: L propto sigmacen2.65 re0.65 (94, 95, 97). This implies that M / L varies systematically with luminosity and surface brightness: M / L propto L0.25 Sigma-0.05 (97). Similar relations exist for core luminosity and surface brightness (112, 207). The small scatter in the relations (approx 0.m5 in L) is a real surprise: the measured velocity dispersion is the central velocity dispersion, which is sensitive to the prevailing anisotropy in the velocity distribution. As there is a large freedom in the possible anisotropies (Section 2), the central velocity dispersion can vary considerably even when the density profile is fixed (240, 293, 320). Apparently, elliptical galaxies show a much smaller range in anisotropies than allowed by the models.

If the observed M / L values are consistent with a normal stellar population, then its systematic variation may be due to the physics of star formation (112, 149). We cannot, however, exclude the possibility that (non-baryonic) dark matter contributes significantly in the central parts of galaxies. If this is the case, the fundamental plane would have to result from a ``conspiracy'' between the luminous and dark material to produce such similar M / L values for a large variety of systems [extending from low mass ellipticals (262) to brightest cluster members].

Surprisingly, there is no conclusive evidence that any of the relations for ellipticals depend on environmental parameters (54). The residuals of the fundamental plane do not correlate with any of the other observed parameters like ellipticity, or Mg2 index (112).

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