Lyman-$\alpha$ polarization from cosmological ionization fronts: II. Implications for intensity mapping

This is the second paper in a series whose aim is to predict the power spectrum of intensity and polarized intensity from cosmic reionization fronts. After building the analytic models for intensity and polarized intensity calculations in paper I, here we apply these models to simulations of reionization. We construct a geometric model for identifying front boundaries, calculate the intensity and polarized intensity for each front, and compute a power spectrum of these results. This method was applied to different simulation sizes and resolutions, so we ensure that our results are convergent. We find that the power spectrum of fluctuations at $z=8$ in a bin of width $\Delta z=0.5$ ($\lambda/\Delta\lambda=18$) is $\Delta_\ell \equiv [\ell(\ell+1)C_\ell/2\pi]^{1/2}$ is $3.2\times 10^{-11}$ erg s$^{-1}$ cm$^{-2}$ sr$^{-1}$ for the intensity $I$, $7.6\times10^{-13}$ erg s$^{-1}$ cm$^{-2}$ sr$^{-1}$ for the $E$-mode polarization, and $5.8\times10^{-13}$ erg s$^{-1}$ cm$^{-2}$ sr$^{-1}$ for the $B$-mode polarization at $\ell=1.5\times10^4$. After computing the power spectrum, we compare results to detectable scales and discuss implications for observing this signal based on a proposed experiment. We find that, while fundamental physics does not exclude this kind of mapping from being attainable, an experiment would need to be highly ambitious and require significant advances to make mapping Lyman-$\alpha$ polarization from cosmic reionization fronts a feasible goal.