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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.