QUANTUM SELF-GRAVITATING SYSTEMS OF BOSONS AND FERMIONS

We examine self-gravitating systems made of a mixture of condensed bosons and degenerate fermions in the Newtonian regime. We develop a numerical approach to determine the relevant quantities of the equilibrium configurations. An analytical treatment is also obtained in the limits in which the central density of one component is dominant. For the case in which the fermions are neutrons and the boson mass is greater than 10(-7) eV c-2, we find: 1) for those configurations in which the central density of fermions dominates, the gravitational field confines the boson component to a region smaller than that occupied by the corresponding pure boson configuration. The size of such region (R(B) approximately (h/m(B) square-root G rho-F (0))) 1/2 is independent of the boson number and relates to the fermion density; 2) both in the cases of a boson density smaller or larger than the fermion density, the bosons do not perturb significantly the fermions, which distribute according to the usual solution of Chandrasekhar.