  The system under consideration is a multi-component gas of interacting para-
and orthoexcitons confined in a three dimensional potential trap. We calculate
the spatially resolved optical emission spectrum due to interband transitions
involving weak direct and phonon mediated exciton-photon interactions. For each
component, the occurrence of a Bose-Einstein condensate changes the spectrum in
a characteristic way so that it directly reflects the constant chemical
potential of the excitons and the renormalization of the quasiparticle
excitation spectrum. Moreover, the interaction between the components leads, in
dependence on temperature and particle number, to modifications of the spectra
indicating phase separation of the subsystems. Typical examples of density
profiles and luminescence spectra of ground-state para- and orthoexcitons in
cuprous oxide are given.
