Phase-space density constraints on the formation of bulges from discs

The colours of stellar bulges and of inner stellar discs are comparable, and consistent with rather similar mean metallicities and ages. Indeed, the mean chemical abundances of the Milky Way bulge and old disc are approximately equal. Further, the scalelengths of discs and bulges are correlated. These observations imply a close relationship between discs and bulges, and may support models in which stellar bulges form from stellar discs. The present paper discusses constraints on this scenario from the stellar phase-space density of bulges and of discs. Phase-space density cannot increase in the absence of collisional processes. We show here that the maximum phase-space density of galactic bulges is higher than that of inner discs, arguing that instabilities of purely stellar discs cannot form bulges. Rather, the high densities of bulges probably reflect gaseous dissipation. Gas inflow from the disc would complicate the interpretation of the similarities in stellar colours between discs and bulges. Gas inflow from the stellar halo, if one exists, may be favoured on angular momentum grounds, but this means of formation of the bulge would provide no explanation for the relationships between disc and bulge in any one galaxy. At least in the Milky Way, the metallicity distribution of the bulge is not consistent with the bulge being built up from the dense regions of accreted satellite galaxies and/or globular clusters.