A two-parameter scheme for the evolution of symmetrical galaxies

In the present paper, a general evolutionary scheme for axisymmetrical rotationally supported equilibrium models for galaxies is considered. Its main phases are: an expansion phase of the initial protogalaxy, assumed to consist into an homogeneous gas sphere structured into clouds, from recombination to maximum expansion, during which it is surmized that angular momentum is acquired by tidal interactions by the expanding configuration; then a violent relaxation collapse phase, following maximum expansion and ending into a virialized deformed polytropic configuration; the reaching of virialization is considered as an adequate initial state for the new phase of virialized contraction of the gaseous component, due to the collisions of the constituent gas clouds, while the stellar component, due to the stars already formed according to a generalized Schmidt-type law during the early expansion and violent relaxation phases, is assumed to have reached a stabilized situation.The initial mean density and radius for both galaxy and component clouds expressed as functions of the density fluctuation spectrum at recombination, act as physical parameters determining the characteristics of the system at maximum expansion, together with the total amount of angular momentum acquired during the expansion phase. The main physical parameters at virialization are then completely specified when the initial distribution of the clouds inside the galaxy is assigned and the constants appearing in it are derived by normalization with the observed data.We find for systems of given mass that the larger the angular momentum per unit mass is: (1) the larger are the equatorial semiaxis at maximum expansion and at virialization and the lower the mean density; (2) the larger is the time elapsed up the maximum expansion and to virialization; while for systems of different mass, we obtain that to the larger mass correspond the larger time elapsed up to maximum expansion and to virialization, and the lower mean density.For the contraction phase following virialization, two limiting cases are considered: (A) either the star component already present at virialization is entirely neglected; (B) or it is thought to contract as the gas component. In such cases, it is found for systems of equal mass that lower angular momenta lead to final configurations characterized by no or small flat gaseous components (which may correspond to lenticulars and early type spirals) while the contrary is true for large angular momenta (corresponding to late type spirals and irregulars). As mass and angular momentum per unit mass decrease, according to an assumed lawj M, the allowed configurations on the late type side of the morphological sequence tend towards earlier and earlier types, until for masses low enough (10¹⁰ m ), only halo type configurations seem to exist. According to this view, the observed lack of spirals with masses below 10¹⁰ m and the wide mass range exibited by the stellar halo type galaxies might be interpreted. In general, it appears that in the limit of the approximations made, a morphological sequence of galaxies can be described by two parameters, mass and angular momentum.