Trends in Galaxy Formation and Evolution in the Context of the Virial and Fundamental Planes

T. K. Chatterjee1, V. B. Magalinsky1
Extending the work of Magalinsky, 1972 (Azh 49,1017-Sov.Astron.-AJ 16,830), the Vlasov equation is applied to study small perturbations (considered as protogalaxies) of the exact solution corresponding to a spatially homogeneous medium in expansion. It is found that a perturbation attains a saturated size whose scale length (as a function of a reduced parameter of evolution, tau, R(tau) $\propto$ Kinetic energy / Potential energy $\propto$ (Kinetic temp.)2 / Surface density $\propto$ (Velocity dispersion)2 / Projected density $\propto$ $\sigma^2$ / I, which has the parametric form of the virial plane. The subsequest evolution is characterized principally by the variation of the energy due to gravitational interactions between stellar systems. Such that the evolution of the condensation is characterized by the inverse energy; which, we find, in this phase of the evolution, is proportional to the ratio of the square root of the kinetic energy to the potential energy. Such that the scale length of the evolved condensation is given by a relation having a parametric form, ($\tau$' corresponding to the value of $\tau$ in this epoch), R($\tau$) $\propto$ (Kinetic Energy)$^{1/2}$ / Potential Energy $\propto$ Kinetic temp. / Projected density $\propto$ $\sigma$ / I, which has the parametric form corresponding to the fundamental plane of evolved galaxies (like brightest cluster members).