RELIKE: Reionization Effective Likelihood from Planck 2018 Data

Abstract: We release RELIKE (Reionization Effective Likelihood), a fast and accurate effective likelihood code based on the latest Planck 2018 data that allows one constrain any model for reionization between $6 < z < 30$ using five constraints from the CMB reionization principal components (PC). We tested the code on two example models which showed excellent agreement with sampling the exact Planck likelihoods using either a simple Gaussian PC likelihood or its full kernel density estimate. This code enables a fast and consistent means for combining Planck constraints with other reionization data sets, such as kinetic Sunyaev-Zeldovich effects, line-intensity mapping, luminosity function, star formation history, quasar spectra, etc, where the redshift dependence of the ionization history is important. Since the PC technique tests any reionization history in the given range, we also derive model-independent constraints for the total Thomson optical depth $\tau_{\rm PC} = 0.0619^{+0.0056}_{-0.0068}$ and its $15\le z \le 30$ high redshift component $\tau_{\rm PC}(15, 30) < 0.020 $ (95\% C.L.). The upper limits on the high-redshift optical depth is a factor of $\sim3$ larger than those reported in the Planck 2018 cosmological parameter paper using the FlexKnot method and we validate our results with a direct analysis of a two-step model which permits this small high-$z$ component.