THE STARS IN THE MAIN-SEQUENCE AND THEIR DYNAMIC PARAMETERS

The stars in the Main Sequence are seen as a hierarchy of objects with different masses M and effective dynamical radii R(eff) = R/alpha given by the stellar radii and the coefficients for the inner structure of the stars. As seen in a previous work (Paper I), during the lifetime in the Main Sequence R(eff)(t) remains a near invariant when compared to the variation in the time of R(t) and alpha(t). With such an effective R(eff) one obtains the amounts of action A(c)(M), the effective densities rho(eff)(M) = rho(M)alpha-3(M), the densities of action and of energy (or mean pressures in the stellar interior) a(c)(M), e(c)(M), and the potential energies E(p)(M). The amounts of action are A(c) is-proportional-to M(k) with k almost-equal-to 1.87 for the M stars, k almost-equal-to 5/3 for the KGF stars, and k almost-equal-to 1.83 for the A and earlier stars, representing very simple conditions for the other dynamical parameters. For instance k almost-equal-to 5/3 means a near invariant effective density rho(eff) for the KGF stars, while for such stars the mean densities and coefficients-alpha present the strongest variations with masses rho(M) is-proportional-to M-1.81 alpha(M) is-proportional-to M0.6. The cases for the M stars (e(c)(M) is-proportional-to M-1) and for the A and earlier stars (between a(c)(M) = constant and rho(eff)(M) is-proportional-to M-1) are also discussed. These conditions for the earlier stars also represent reasonable mean values for the whole stellar hierarchy in the range of masses 0.2 M. less-than-or-equal-to M less-than-or-equal-to 25 M.. With all this, one can build 'dynamical' HR diagrams with A(c)(M), E(p)(M), rho(eff)(M), etc., whose characteristics are analogous to these in the photometrical HR diagram. A comparison is made between A(c)(M) from the models here and the HR diagram with the best known stars of luminosity classes IV, V, and white dwarfs. The comparison of the potential energies E(p)(M) is-proportional-to M(-p) according to the stellar models used here and the observed frequency function psi(M) is-proportional-to M(-q) (number of stars in a given interval of masses) from different authors suggests the possibility that the product E(p)(M)psi(M) is a constant, but this must be confirmed with further studies of the function psi(M) and its fine structure. There are analogies between the formulation used here for the stellar hierarchy and other physical processes, for instance, in modified forms of the Kolmogorov law of turbulence and in the formulation used for the hierarchy of molecular clouds in gravitational equilibrium. Besides, the function of action A(c)(M) for the stars has analogous properties to the relations of angular momenta and masses J(M) for different types of objects. The cosmological implications of all this are discussed.