Constraints on the Optical Depth to Reionization from Balloon-Borne CMB 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 mid-latitude 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 $f_{\rm sky}$ between 40% and 54%. We carry out the analysis using both parametric and blind foreground separation techniques. We compare $\sigma(\tau)$ values to those obtained with low frequency and high frequency versions of the experiment called $\tau S$-lf and $\tau S$-hf that 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 $f_{\rm sky}$=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. Exclusion of the 30 and 44 GHz data, which give information about synchrotron emission, leads to significant $\tau$ mis-estimates. Decreasing noise by an ambitious factor of 10 while keeping $f_{\rm sky}$=40% gives $\sigma(\tau) =0.0031$. The combination of $\sigma(\tau) =0.0034$, BAO data from DESI, and future CMB B-mode lensing data from CMB-S3/S4 experiments could give $\sigma(\sum m_{\nu}) = 17$ meV.