Joint QSO-CMB constraints on reionization history
  Based on the work by Mitra, Choudhury & Ferrara (2010), we obtain
model-independent constraints on reionization from cosmic microwave background
(CMB) and QSO absorption line data by decomposing the function N_{ion}(z) (the
number of photons entering the IGM per baryon in collapsed objects) into its
principal components. The main addition in this work is that for the CMB data
set, we explicitly include the angular power spectra C_l for TT, TE and EE
modes in our analysis which seem to contain somewhat more information than
taking the electron scattering optical depth tau_{el} as a single data point.
Using Markov Chain Monte Carlo methods, we find that all the quantities related
to reionization can be severely constrained at z < 6 whereas a broad range of
reionization histories at z > 6 are still permitted by the current data sets.
With currently available data from WMAP7, we constrain 0.080 < tau_{el} < 0.112
(95% CL) and also conclude that reionization is 50% complete between 9.0 <
z(Q_{HII} = 0.5) < 11.8 (95% CL) and is 99% complete between 5.8 < z(Q_{HII} =
0.99) < 10.4 (95% CL). With the forthcoming PLANCK data on large-scale
polarization (ignoring effect of foregrounds), the z > 6 constraints will be
improved considerably, e.g., the 2-sigma error on tau_{el} will be reduced to
0.009 and the uncertainties on z(Q_{HII} = 0.5) and z(Q_{HII} = 0.99) would be
\sim 1 and 3 (95% CL), respectively. For more stringent constraints on
reionization at z > 6, one has to rely on data sets other than CMB. Our method
will be useful in such case since it can be used for non-parametric
reconstruction of reionization history with arbitrary data sets.
