Constraints on the Optical Depth to Reionization from Balloon-borne Cosmic Microwave Background Measurements

We assess the uncertainty with which a balloon-borne experiment, nominally called Tau Surveyor (tau S), can measure the optical depth to reionization sigma(tau) with given realistic constraints of instrument noise and foreground emissions. Using a tau S fiducial design with six frequency bands between 150 and 380 GHz, with white and uniform map noise of 7 mu K arcmin, achievable with a single midlatitude flight, and including Planck's 30 and 44 GHz data, we assess the error sigma(tau) obtained with three foreground models and as a function of sky fraction f (sky) between 40% and 54%. We carry out the analysis using both parametric and blind foreground separation techniques. We compare the sigma(tau) values to those obtained with low-frequency and high-frequency versions of the experiment called tau S-lf and tau S-hf, which have only four and up to eight frequency bands with narrower and wider frequency coverage, respectively. We find that with tau S, the lowest constraint is sigma(tau) = 0.0034, obtained for one of the foreground models with f (sky) = 54%. sigma(tau) is larger, in some cases by more than a factor of 2, for smaller sky fractions, with tau S-lf, or as a function of foreground model. The tau S-hf configuration does not lead to significantly tighter constraints. The exclusion of the 30 and 44 GHz data, which give information about synchrotron emission, leads to significant tau misestimates. Decreasing noise by an ambitious factor of 10, while keeping f (sky) = 40%, gives sigma(tau) = 0.0031. The combination of sigma(tau) = 0.0034, baryon acoustic oscillation data from DESI, and future cosmic microwave background B-mode lensing data from the CMB-S3/CMB-S4 experiments could give sigma( n-ary sumation m ( nu )) = 17 meV.