Constraining HeII Reionization Detection Uncertainties via Fast Radio Bursts

Context. The increased detection rate of Fast Radio Bursts (FRBs) makes it likely to get samples of sizes $\mathcal{O}({10}^2)$ to $\mathcal{O}({10}^3)$ in the near future. Because of their extragalactic origin can help us in understanding the epoch of helium reionization. Aims. We try to identify the epoch of Helium II (HeII) reionization, via the observations of early FRBs in range of $z=3$ to $4$. Methods. We build a model of FRB Dispersion Measure following the HeII reionization model, density fluctuation in large scale structure, host galaxy interstellar medium and local environment of FRB contribution. The model is fit to the ideal intergalactic medium (IGM) dispersion measure model to check the goodness of constraining the HeII reionization via FRB measurement statistics. Conclusion. We report our findings under two categories, accuracy in detection of HeII reionization via FRBs assuming no uncertainty in the redshift measurement and alternatively assuming a varied level of uncertainty in redshift measurement of the FRBs. We show that under the first case, a detection of $N\sim \mathcal{O}({10}^2)$ FRBs give an uncertainty of $\sigma (z_{r, fit})\sim0.5$fromthefitmodel,andadetectionof$N\sim$\mathcal{O}$ (10^3)$givesanuncertaintyof$\sigma (z_{r, fit})\sim0.1$. While assuming a redshift uncertainty of level $5-20\mathrm{\%}$, changes the $\sigma (z_{r, fit})\sim0.5$to$0.6$for$N\sim 100$and$\sigma (z_{r, fit})\sim0.1$to$0.15$for$N \sim 1000$ case.