Global Relationships Among the Physical Properties of Stellar Systems.

The Κ-space three-dimensional parameter system was originally defined to examine the physical properties of dynamically hot elliptical galaxies and bulges (DRGs). The axes of Κ-space are proportional to the logarithm of galaxy mass, mass-to-light ratio, and a third quantity that is mainly surface brightness. In this paper we define self-consistent Κ parameters for disk galaxies, galaxy groups and clusters, and globular clusters and use them to project an integrated view of the major classes of self-gravitating, equilibrium stellar systems in the universe. Each type of stellar system is found to populate its own fundamental plane in Κ-space. At least six different planes are found: (1) the original fundamental plane for DRGs; (2) a nearly-parallel plane slightly offset for Sa-Sc spirals; (3) a plane with different tilt but similar zero point for Scd-Irr galaxies; (4) a plane parallel to the DRG plane but offset by a factor of 10 in mass-to-light ratio for rich galaxy clusters; (5) a plane for galaxy groups that bridges the gap between rich clusters and galaxies; and (6) a plane for Galactic globular clusters. We propose the term "cosmic metaplane" to describe this ensemble of interrelated and interconnected fundamental planes. The projection Κ1-Κ3 (M/L vs M) views all planes essentially edge-on. Planes share the common characteristic that M/L is either constant or increasing with mass. The Κ1-Κ2 projection views all of these planes close to face-on, while Κ2-Κ3 shows variable slopes for different groups owing to the slightly different tilts of the individual planes. The Tully-Fisher relation is the correct compromise projection to view the spiral-irregular planes nearly edge on, analogous to the Dπ-σ relation for DRGs. No stellar system yet violates the rule first found from the study of DRGs, namely, Κ1+Κ2 constant, here chosen to be 8. In physical terms, this says that the maximum global luminosity density of stellar systems varies as M-4/3. Galaxies march away from this "zone of exclusion" (ZOE) in Κ12 as a function of Hubble type: DRGs are closest, with Sm-Irr's being furthest away. The distribution of systems in Κ-space is generally consistent with predictions of galaxy formation via hierarchical clustering and merging. The cosmic metaplane is simply the cosmic virial plane common to all self-gravitating stellar systems, tilted and displaced in mass-to-light ratio for various types of systems due to differences in stellar population and amount of baryonic dissipation. Hierarchical clustering from an n =-1.8 power-law density fluctuation spectrum (plus dissipation) comes close to reproducing the slope of the ZOE, and the progressive displacement of Hubble types from this line is consistent with the formation of early-type galaxies from higher n-σ fluctuations than late Hubble types. The M/L values for galaxy groups containing only a few, mostly spiral galaxies, vary the strongest with M. Moreover, it is these groups that bridge the gap between the two planes defined by the brightest galaxies and the lowest mass rich clusters, giving the cosmic metaplane its striking appearance. Why this is so is but one of four key questions raised by our study. The second question is why the slopes of individual Hubble types in the Κ1-Κ2 lie plane parallel the ZOE. At face value, this appears to suggest less dissipation of massive galaxies within their dark halos compared to lower-mass galaxies of the same Hubble type. The third is why we find isotropic stellar systems only within an effective mass range of 109.5-11.75 Msun. This would seem to imply that dissipation only results in galaxy components flattened by rotation in a limited mass range. The fourth question, perhaps the most basic of all, is how does M/L vary so smoothly with M among all stellar systems so as to give the individual tilts of the various fundamental planes, yet preserve the overall appearance of a metaplane? The answer to this last question must await a more thorough knowledge of how galaxies relate to many parameters, including: their environment, structure, angular momentum acquisition, density, dark matter concentration, the physics of star formation in general, and the formation of the initial mass function in particular. The present investigation is limited by existing data to the B passband and is strongly magnitude-limited, not volume-limited. Rare or hard-to-discover galaxy types, such as R II galaxies, starburst galaxies and low-surface-brightness galaxies, are missing or are under-represented, and use of the B band over-emphasizes stellar population differences. A volume-limited Κ-space survey based on Κ-band photometry and complete to low surface brightness and faint magnitudes is highly desirable but requires data yet to be obtained.