Tidal effects of a massive spheroidal halo on an inner spheroidal contracting visible body: Application to an evolutionary disk-galaxy model

The effects of the tidal interactions between two coaxial, homogeneous spheroids, one (the “Brigt Component”: B) completely embedded in the other (the “Dark Halo”: D), along a quasi-static contraction, are considered. The aim is to look how the dynamical properties and the final morphology of the B subsystem may be affected by the presence of the D component. Three initial configurations are considered: the quasi-spherical “Dark Halo” D coincides with the “Visible Component” B (case C); D is flatter than B but the two spheroids have the same semiminor axis (case N); no D component is assumed; the “visible” spheroid is single (case S). The application to an evolutionary disk-galaxy model is considered under some simple assumptions: i) in cases C and N the spheroidal halo is massive (mass ratio “dark”/“bright” about ten) and dissipationless. For a mass ratio like this, the tidal interaction of the B component over D turns to be negligible in the course of the contraction; adding to that the lack of dissipation, it appears plausible to take the D component as frozen along the evolution; ii) the degree of anisotropy and the angular momentum of B, J_B, are conserved. The conservation of J_B provides us the time-independent relationship among the key physical quantities and gives the possibility to draw the evolutionary tracks on the plane (axis ratio σ_B, semimajor axis a_B) without any explicit time-scale; iii) the global “star formation rate” is parametrized according to a simple “Schmidt power law” proportional to the square of gas density. At every step of the quasi-static contraction, the structure is determined by the tensor virial theorem extended to a double configuration. The model is very idealized, particularly because there are no available tidal gravitational terms other than for the case of two homogeneous. Nevertheless, the method based on the tensor virial appears powerful to gain insight into the correlations among the physical quantities involved and into their trend along the evolution. One of the main result is a clear indication of a leading role played by the axis ratio of the “Dark-Halo” component which might be, to the extent that this simple picture can be compared with a real galactic system, a possible new physical parameter to be added to mass and angular momentum for separating spirals from S0 galaxies.