  We use a semi-analytic model of Lyman alpha emitters (LAEs) to constrain the
reionization history. By considering two physically motivated scenarios in
which reionization ends either early (ERM, z_i ~ 7) or late (LRM, z_i ~ 6), we
fix the global value of the IGM neutral fraction (e.g. chi_{HI}=3 times
10^{-4}, 0.15 at z=6.56 for the ERM and LRM, respectively) leaving only the
star formation efficiency and the effective escape fraction of Lya photons as
free parameters. The ERM fits the observed LAE luminosity function (LF) at
z=5.7 and 6.56 requiring no redshift evolution or mass dependence of the star
formation efficiency, and LAE star formation rates (SFR) of 3-103 solar
masses/year, contributing approximately 8% of the cosmic SFR density at z=5.7.
The LRM requires a physically uncomfortable drop of approximately 4.5 times in
the SFR of the emitters from z=6.5 to 5.7. Thus, the data seem to imply that
the Universe was already highly ionized at z=6.56. The mass-dependent Lya
transmissivity is between 0.36-0.51 (ERM) and less than 0.26 (LRM) at z=6.56.
The LF data at z=4.5 imply an extra Lya line damping factor of approximately
0.25 possibly due to dust; the presence of a (clumpy) dust component with
E(B-V) ~ 0.28 is also required to reproduce the observed large Lya equivalent
widths at the same redshift. Additional useful information can be extracted
from the line profile (weighted) skewness, found to be S_W=10-17 Angstrom for
the two reionization models, which shows an interesting L_alpha-chi_{HI}
anti-correlation, holding under the model assumptions. The shortcomings of the
model and strategies to overcome them are discussed.
