Constraining HeII reionization detection uncertainties via fast radio bursts

The rate of detection of Fast Radio Bursts (FRBs) in recent years has increased rapidly, and getting samples of sizes O(10²) to O(10³) is likely possible. FRBs exhibit short radio bursts in order of milliseconds at frequencies ∼1 GHz. The high dispersion measures (DM) of FRBs suggest it's extragalactic origin, which allows probing the electron density in the intergalactic medium (IGM). In this project, we explored the possibility of identifying the epoch of helium II (HeII) reionization, via the observations of early FRBs in the range of z=[3,4]. We constrained the HeII reionization with a different number of observed early FRBs and associated redshift measurement errors to them. We built a model of FRB DMs following the HeII reionization model, while taking into account the density fluctuation in large scale structure, host galaxy interstellar medium, and local environment of FRB contribution. Following the model, FRB DMs with redshift in range of z=[3,4] is generated. We then fit these data to the ideal IGM dispersion measure model, checking the constraint tightness of the HeII reionization epoch. We show that detection of 100 FRB gives an uncertainty of σ(z_r,fit)∼0.5 without considering additional redshift noise, which increases to σ(z_r,fit)∼0.6 when 20% of redshift noise is added. Detection of 1000 candidate gives an uncertainty of σ(z_r,fit)∼0.1 and increases to σ(z_r,fit)∼0.15 when 20% of redshift noise is added.