The expected abundance of Lyman-α emitting primeval galaxies -: I.: General model predictions

We present model calculations for the expected surface density of Ly-alpha emitting primeval galaxies (PGs) at high redshifts. We assume that elliptical galaxies and bulges of spiral galaxies (=spheroids) formed early in the universe and that the Ly-alpha emitting PGs are these spheroids during their first burst of star formation at high redshift. One of the main assumptions of the models is that the Ly-alpha bright phase of this first starburst in the spheroids is confined to a short period after its onset due to rapid formation of dust. The models do not only explain the failure of early surveys for Ly-alpha emitting PGs but are also consistent with the limits of new surveys (e.g. the Calar Alto Deep Imaging Survey-CADIS). At faint detection limits S(lim)less than or equal to10(-20) W m(-2) the surface density of Ly-alpha emitters is expected to vary only weakly in the redshift range between z=3 and z=6 with values >10(3)/deg(2)/Deltaz=0.1 reaching its maximum at z(0)approximate to4. At shallower detection limits, S(lim)greater than or equal to3x10(-20) W m(-2) the surface density of high-z Ly-alpha emitters is expected to be a steep function of redshift and detection limit. This explains the low success in finding bright Ly-alpha galaxies at z>5. We demonstrate how the observed surface densities of Ly-alpha emitting PGs derived from recent surveys constrain the parameters of our models. Finally, we discuss the possibility that two Ly-alpha bright phases occur in the formation process of galaxies: An initial-primeval-phase in which dust is virtually non-existant, and a later secondary phase in which strong galactic winds as observed in some Lyman break galaxies facilitate the escape of Ly-alpha photons after dust has already been formed.