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

T. K. Chatterjee^{1}, V. B. Magalinsky^{1}
^{1} Facultad de Ciencias, Fisico-Matematicas, Universidad A.

Puebla, Apartado Postal 1316, Puebla, Mexico

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).