Luminosity versus Phase‐Space–Density Relation of Galaxies Revisited

We reexamined the correlation between the BT magnitude and the phase-space-density parameter w = (Dvc)-1 of galaxies for the Virgo, the Coma, the Fornax, and the Perseus clusters in an effort to better understand the physical underpinning of the fundamental plane. A tight correlation (BT = a log w + b) common to different morphological types of galaxies (E, S0, S) was found for the Virgo and the Coma clusters, with a = 1.87 ± 0.10 and 1.33 ± 0.11, respectively. An investigation using only E galaxies was made for the four clusters. The results indicated that the empirical linear relation might be common among the Coma, the Fornax, and the Perseus clusters, with the Virgo Cluster showing deviation. This relation, which is another way to project the fundamental plane, has an expression insensitive to the morphology and may be suitable for treating galaxies of different morphological types collectively.