Joining Bits and Pieces of Reionization History

Cosmic microwave background (CMB) temperature and polarization anisotropies from Planck have estimated a lower value of the optical depth to reionization ($\tau$) compared to WMAP. A significant period in the reionization history would then fall within $6<\text{redshift}(z)<10$, where detection of galaxies with Hubble frontier fields program and independent estimation of neutral hydrogen in the inter galactic medium by Lyman-$\alpha$ observations are also available. This overlap allows an analysis of cosmic reionization which utilizes a direct combination of CMB and these astrophysical measurements and potentially breaks degeneracies in parameters describing the physics of reionization. For the first time we reconstruct reionization histories by assuming photoionization and recombination rates to be free-form and by allowing underlying cosmological parameters to vary with CMB (temperature and polarization anisotropies and lensing) data from Planck 2018 release and a compilation of astrophysical data. We find an excellent agreement between the low-$\ell$ Planck 2018 High Frequency Instrument polarization likelihood and astrophysical data in determining the integrated optical depth. By combining both data, we report for a minimal reconstruction $\tau =0.051_{-0.0012-0.002}^{+0.001+0.002}$ at 68% and 95% C.L., which, for the errors in the current astrophysical measurements quoted in the literature, is nearly twice better than the projected cosmic variance limited CMB measurements. For the duration of reionization, redshift interval between 10%, and complete ionization, we get ${2.9}_{-0.16-0.26}^{+0.12+0.29}$ at 68% and 95% C.L., which improves significantly on the corresponding result obtained by using Planck 2015 data. By a Bayesian analysis of the combined results we do not find evidence beyond monotonic reionization histories, therefore a multiphase reionization scenario such as a first burst of reionization followed by recombination plateau and thereafter complete reionization is disfavored compared to minimal alternatives.

Figure 1

(Left to right): Results for minimal single node ($B0$), single node ($B1$), two nodes ($B2$), and three nodes ($B3$) reconstructions, respectively. Planck best fits for Tanh reionization are plotted in gray. SROLL2 refers to the independent low-$\ell E$-mode polarization likelihood based on Planck data [62]. Top: The volume filling factor as a function of redshift. Constraints are computed from the entire MCMC samples. Middle: UV luminosity density with the Ishigaki et al. [6] compiled data [also containing Bouwens et al. [57] ]. Bottom: Marginalized probability distribution function of $\tau$. It is evident from the plots that a sharp history of reionization cannot make all three datasets agree.

Figure 2

Samples of recombination timescale in Gyr as a function of redshift in minimal to three nodes cases (top to bottom) are plotted. The $2\sigma$ lower bounds are also provided in thick black curves. The volume filling factors in all samples are colored to demonstrate the progress of reionization and its dependence on $t_{\mathrm{rec}}$.

Figure 3

68.3% and 95% C.L. on $Q_{\mathrm{HII}}$ as a function of redshift in the four different cases considered. Data points and limits are also plotted. In the gray dotted, solid, and dashed lines we plot best fit Tanh model for Planck 2018, Planck 2018 with SROLL2 low-$\ell$ EE likelihood, and Planck 2015, respectively. The family of reionization histories obtained in our reconstruction address the data more efficiently compared to the Tanh model.

Figure 4

Correlations between the spectral index and the optical depth (left) and between the duration of reionization and ${\sigma }_8$ normalization (right) in single node ($B1$).