Abstract
N-body simulations are employed to investigate relationships between the global properties of collisionless, self-gravitating systems (e.g., galaxies) that result from hierarchical merging. Each galaxy of mass M is assumed to form by the merging of two identical progenitors of mass 1/2 M from an interpenetrating parabolic encounter. The remnant galaxies depart strongly from homology with their progenitors at all stages in the merging hierarchy. A power-law relation between galaxy mass and central velocity dispersion results, with exponent similar to the observed luminosity-velocity dispersion relation for ellipticals. Since this relation appears to be entirely scale-free, we inspect observational data on other stellar systems supported primarily by random motions (globular clusters and dwarf elliptical galaxies). The possibily that hierarchical merging has operated over many decades in mass (10/sup 5/< or approx. =M/M/sub sun/ < or approx. =10/sup 12/) is discussed.
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