Context . The rate of detection of Fast Radio Bursts ( FRBs ) in recent years has increased rapidly and getting samples of sizes \mathcal { O } ( 10 ^ { 2 } ) to \mathcal { O } ( 10 ^ { 3 } ) is likely possible .
FRBs exhibit short radio bursts in order of milliseconds at frequencies of about 1 \mathrm { GHz } .
They are bright and have high dispersion measures which suggest they are of extra galactic origin .
Their extragalactic origin allows probing the electron density in the intergalactic medium .
One important consequence of this is , FRBs can help us in understanding the epoch of helium reionization . Aims . In this project , we tried to explore the possibility of identifying the epoch of Helium II ( HeII ) reionization , via the observations of early FRBs in range of z = 3 to 4 .
We constrained the HeII reionization with different number of observed early FRBs and associated redshift measurement errors to them . 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 .
We then fit our model to the ideal inter galactic medium ( IGM ) dispersion measure model to check the goodness of constraining the \ce HeII reionization via FRB measurement statistics . Conclusion . We report our findings under two categories , accuracy in detection of \ce 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 } ) \sim 0.5 from the fit model , and a detection of N \sim \mathcal { O } ( 10 ^ { 3 } ) gives an uncertainty of \sigma ( z _ { r,fit } ) \sim 0.1 .
While assuming a redshift uncertainty of level 5 - 20 \% , changes the \sigma ( z _ { r,fit } ) \sim 0.5 to 0.6 in N \sim 100 case respectively and \sigma ( z _ { r,fit } ) \sim 0.1 to 0.15 for N \sim 1000 case .