  Using a semi-analytical model developed by Choudhury & Ferrara (2005) we
study the observational constraints on reionization via a principal component
analysis (PCA). Assuming that reionization at z>6 is primarily driven by
stellar sources, we decompose the unknown function N_{ion}(z), representing the
number of photons in the IGM per baryon in collapsed objects, into its
principal components and constrain the latter using the photoionization rate
obtained from Ly-alpha forest Gunn-Peterson optical depth, the WMAP7 electron
scattering optical depth and the redshift distribution of Lyman-limit systems
at z \sim 3.5. The main findings of our analysis are: (i) It is sufficient to
model N_{ion}(z) over the redshift range 2<z<14 using 5 parameters to extract
the maximum information contained within the data. (ii) All quantities related
to reionization can be severely constrained for z<6 because of a large number
of data points whereas constraints at z>6 are relatively loose. (iii) The weak
constraints on N_{ion}(z) at z>6 do not allow to disentangle different feedback
models with present data. There is a clear indication that N_{ion}(z) must
increase at z>6, thus ruling out reionization by a single stellar population
with non-evolving IMF, and/or star-forming efficiency, and/or photon escape
fraction. The data allows for non-monotonic N_{ion}(z) which may contain sharp
features around z \sim 7. (iv) The PCA implies that reionization must be 99%
completed between 5.8<z<10.3 (95% confidence level) and is expected to be 50%
complete at z \approx 9.5-12. With future data sets, like those obtained by
Planck, the z>6 constraints will be significantly improved.
