The Fundamental Plane (FP) was discovered independently and simultaneously by Djorgovski & Davis (1987) and Dressler et al. (1987b). It is a relation between , , and , and is linear in logarithmic space. Since , the FP can also be expressed as a relation between L, , and , or between , , and L.
Djorgovski & Davis (1987) found a tight correlation for elliptical galaxies
between either a radius or the luminosity on the one hand, and a
linear combination of velocity dispersion and mean surface brightness on the
other hand.
They dubbed this relation the fundamental plane.
They found the best-fitting relation involving a radius to be
(2.4) |
Dressler et al. (1987b), also known as the 7 Samurai,
found the same result, namely
that elliptical galaxies describe a plane in the 3-space of
or
.
They found the plane to be given by
(2.5) |
Dressler et al. also introduced a new photometric diameter , the diameter within which the mean surface brightness is , in Johnson B. They found to correlate as well with as any linear combination of and , and they where thus able to reformulate the FP as the - relation, . However, they noted that the correlation between and a combination of and , namely , had a small residual curvature. Phillipps (1988) demonstrated theoretically that the relation is expected for galaxies with r^{1/4} profiles and around in Johnson B. He also showed, that for the range in actually spanned by (giant) ellipticals, the FP will be seen as a curved line in the versus plot. Lucey, Bower, & Ellis (1991a) were the first to demonstrate that the residuals from the - relation were correlated with . They corrected for this by simply adding a linear term in to the - relation. JFK93 found for a sample of galaxies in the Coma cluster that the - residuals showed the dependence on that was predicted by Phillipps (1988), a dependence that has a quadratic term. They concluded that the FP is a true improvement of the - relation. In accordance with this, they found the scatter of the - relation to be larger than for the FP, namely 17% versus 11% for their sample.
In the following, we will mainly consider the FP, not the - relation.
Properties of E and S0 Galaxies in the Clusters HydraI and Coma
Master's Thesis, University of Copenhagen, July 1997
Bo Milvang-Jensen (milvang@astro.ku.dk)