Double gravitational bound system in virial equilibrium: tidal scale length induced on one subsystem by another

摘要

When a gravitational bound system of two components, one completely inside the other, is considered, and virial equilibrium holds, Clausius' virial generalization of each subcomponent, defined as that which balances twice the kinetic energy of the corresponding virial equation, does not, in general, match the total potential energy of the same subsystem. When the substructures are modeled as two concentric homothetic and oblate spheroids of spheroidal, similar and coaxial strata mass distributions, the conditions for the existence of a minimum in Clausius' virial function, related to the inner component, are searched and discussed as a function of both the two power-law density profiles. The semimajor axis at which the minimum appears leads to the definition of a tidal scale length induced from the outer subsystem, assumed frozen in size and shape, on the the inner one. The special case of two homogeneous spheroidal subsystems is also considered in order to highlight the effect of different eccentricities between the inner and outer component. The tidal interaction term between the two matter distributions is taken into account, by using tensor virial theorem. Applications to the world of galaxies are considered and some possible consequences for galaxy dynamics are taken into account.