Forecasts for Helium Reionization Detection with Fast Radio Bursts in the Era of Square Kilometre Array

The observed dispersion measures (DMs) of fast radio bursts (FRBs) are a good indicator of the amount of ionized material along the propagation paths. In this work, we present a forecast of He II reionization detection using the DM and redshift measurements of FRBs from the upcoming Square Kilometre Array (SKA). Assuming a model of the Universe in which He II reionization occurred at a specific redshift $z_{\rm re}$, we analyze what extent the signal-to-noise ratio ($\mathrm{S/N}$) for the detection of the amplitude of reionization can be achieved in the era of SKA. Using $10^{6}$ mock FRB data from a one-year observation of the second phase of SKA, we find that the $\mathrm{S/N}$ for detecting He II reionization can approach the $32-50\sigma$ level and the uncertainty on the reionization redshift can be constrained to be $\sigma(z_{\rm re})\approx 0.022-0.031$, depending on the assumed FRB redshift distribution. This is the first quantitative analysis on the detection significance of He II reionization in the SKA era. We also examine the influence of different fiducial $z_{\rm re}$ values, finding that this effect has a modest impact on the forecasts. Our results demonstrate the potentially remarkable capability of SKA-era FRBs in constraining the epoch of He II reionization.