The stars in the Main Sequence and their dynamical parameters

Abstract

The stars in the Main Sequence are seen as a hierarchy of objects with different massesM and effective dynamical radiiR _eff=R/α 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 SequenceR _eff(t) remains a near invariant when compared to the variation in the time ofR(t) and α(t).

With such an effectiveR _eff one obtains the amounts of actionA _c(M), the effective densities ρ_eff(M)=ρ(M)α³(M), the densities of action and of energy (or mean presures in the stellar interior)a _c(M),e _c(M), and the potential energiesE _p(M).

The amounts of action areA _c∝M ^k withk≈1.87 for the M stars,k≈5/3 for the KGF stars, andk≈1.83 for the A and earlier stars, representing very simples conditions for the other dynamical parameters. For instancek≈5/3 means a near invariant effective density α_eff for the KGF stars, while for such stars the mean densities and coefficients α present the strongest variations with masses ρ(M)∝M ^−1.81, α(M)∝M^0.6.

The cases for the M stars (e _c(M)∝M ⁻¹) and for the A and earlier stars (betweena _c(M)=constant and α_eff(M)∝M ⁻¹) and also discussed. These conditions for the earlier stars also represent reasonable mean values for the whole stellar hierarchy in the range of masses 0.2M _⊙≤M≤25M _⊙.

With all this, one can build ‘dynamical’ HR diagrams withA _c(M), E_p(M), α_eff M ^−p, etc., whose characteristics are analogous to these in the photometrical HR diagram. A comparison is made betweenA _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 energiesE _p(M)∝M ^−p according to the stellar models used here and the observed frequency function ψ(M∝M _−q (number of stars in a given interval of masses) from different authors suggests the possibility that the productE _p(M)ψ(M) is a constant, but this must be confirmed with further studies of the function ψ(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 actionA _c(M) for the stars has analogous properties to the relations of angular momenta and massesJ(M) for different types of objects. The cosmological implications of all this are discussed.