  A significant fraction of Lyman Alpha (Lya) emitting galaxies (LAEs) at z>
5.7 have rest-frame equivalent widths (EW) greater than ~100 Angstrom. However
only a small fraction of the Lya flux produced by a galaxy is transmitted
through the IGM, which implies intrinsic Lya EWs that are in excess of the
maximum allowed for a population-II stellar population having a Salpeter mass
function. In this paper we study characteristics of the sources powering Lya
emission in high redshift galaxies. We propose a simple model for Lya emitters
in which galaxies undergo a burst of very massive star formation that results
in a large intrinsic EW, followed by a phase of population-II star formation
with a lower EW. We confront this model with a range of high redshift
observations and find that the model is able to simultaneously describe the
following eight properties of the high redshift galaxy population with
plausible values for parameters like the efficiency and duration of star
formation: i-iv) the UV and Lya luminosity functions of LAEs at z=5.7 and 6.5,
v-vi) the mean and variance of the EW distribution of Lya selected galaxies at
z=5.7, vii) the EW distribution of i-drop galaxies at z~6, and viii) the
observed correlation of stellar age with EW. Our modeling suggests that the
observed anomalously large intrinsic equivalent widths require a burst of very
massive star formation lasting no more than a few to ten percent of the
galaxies star forming lifetime. This very massive star formation may indicate
the presence of population-III star formation in a few per cent of i-drop
galaxies, and in about half of the Lya selected galaxies.
