We explain why the analysis in our paper [Phys. Rev. D 69, 064033 (2004), arXiv:gr-qc/0311064 ] is relevant and correct.
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 decomp
ose 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.
We use a set of semi-numerical simulations based on Zeldovich approximation, friends-of-friends algorithm and excursion set formalism to generate reionization maps of high dynamic range with a range of assumptions regarding the distribution and lumin
osity of ionizing sources and the spatial distribution of sinks for the ionizing radiation. We find that ignoring the inhomogeneous spatial distribution of regions of high gas density where recombinations are important -- as is often done in studies of this kind -- can lead to misleading conclusions regarding the topology of reionization, especially if reionization occurs in the photon-starved regime suggested by Lya forest data. The inhomogeneous spatial distribution of recombinations significantly reduces the mean free path of ionizing photons and the typical size of coherently ionized regions. Reionization proceeds then much more as an outside-in process. Low-density regions far from ionizing sources become ionized before regions of high gas density not hosting sources of ionizing radiation. The spatial distribution of sinks of ionization radiation also significantly affects shape and amplitude the power spectrum of fluctuations of 21cm emission. The slope of the 21cm power spectrum as measured by upcoming 21cm experiments should be able to distinguish to what extent the topology of reionization proceeds outside-in or inside-out while the evolution of the amplitude of the power spectrum with increasing ionized mass fraction should be sensitive to the spatial distribution and the luminosity of ionizing sources.
By means of carefully calibrated semi-analytical reionization models, we estimate the minimum mass of star-forming haloes required to match the current data. Models which do not include haloes of total mass M < 10^9 M_sun fail at reproducing the Gunn
-Peterson and electron scattering optical depths simultaneously, as they contribute too few (many) photons at high (low, z approx 6) redshift. Marginally acceptable solutions require haloes with M approx 5 times 10^7 M_sun at z approx 10, corresponding to virial temperatures (sim 10^4K) for which cooling can be ensured by atomic transitions. However, a much better match to the data is obtained if minihaloes (M sim 10^6 M_sun) are included in the analysis. We have critically examined the assumptions made in our model and conclude that reionization in the large-galaxies-only scenario can remain viable only if metal-free stars and/or some other exotic sources at z > 6 are included.
We use a semi-analytical model to study the impact of reionization, and the associated radiative feedback, on galaxy formation. Two feedback models have been considered: (i) a standard prescription, according to which star formation is totally suppre
ssed in galaxies with circular velocity below a critical threshold (model CF06) and (ii) a characterization based on the filtering scale (model G00), allowing for a gradual reduction of the gas available for star formation in low-mass galaxies. In model CF06 reionization starts at z ~ 15-20, is 85% complete by z ~ 10; at the same z, the ionized fraction is 16% in model G00. The models match SDSS constraints on the evolution of the neutral hydrogen fraction at z < 7, but predict different Thomson optical depths, tau_e = 0.1017 (CF06), and 0.0631 (G00); such values are within 1 sigma of the WMAP 3-yr determination. Both models are in remarkable good agreement with additional existing data (evolution of Lyman-limit systems, cosmic star formation history, high-z galaxy counts, IGM thermal history), which therefore cannot be used to discriminate among different feedback models. Deviations among radiative feedback prescriptions emerge when considering the expected HI 21 cm background signal, where a ~ 15 mK absorption feature in the range 75-100 MHz is present in model G00 and a global shift of the emission feature preceding reionization towards larger frequencies occurs in the same model. Single dish observations with existing or forthcoming low-frequency radio telescopes can achieve mK sensitivity, allowing the identification of these features provided that foregrounds can be accurately subtracted.
