Opportunities For Observing Fast Radio Bursts With Wide-field Telescopes Based On Monte Carlo Simulations

Fast radio bursts are one of the fastest growing astronomy disciplines in recent years.Fast radio bursts may theoretically have optical counterparts with millisecond to hour time scales,but so far,no definitive optical counterparts of fast radio bursts have been found.This is both an opportunity and a challenge,and it is of great significance to study the detectability of fast radio burst optical counterparts in China’s future large-field telescopes,including the China Space Station Space Survey Space Telescope（CSST）,the 2.5-meter Large Field Survey Telescope（WFST）and Earth 2.0（ET）in cooperation between the University of Science and Technology of China and the Purple Mountain Observatory.The urgent problem is that there are few samples of fast radio bursts,and there is no simple relationship between the duration of optical afterglow radiation of fast radio bursts for research and the total energyoutflow,which needs to be carried out by Monte Carlo simulation.In this paper,the statistical characteristics of the main parameters of fast radio bursts are discussed,which are consistent with the common Gaussian distribution.The data were dimensionally reduced by principal component analysis.The k-Means clustering method was used to briefly discuss the classification of fast radio bursts.Finally,multiple sets of fast radio burst data based on different probability distributions are generated by Monte Carlo simulation.As for the optical counterpart of fast radio burst,it can be divided into three categories:millisecond timescale optical counterpart,hourly timescale optical counterpart and optical afterglow.The first two can be generated by high-energy epitaxy of fast radio bursts or inverse Compton scattering with high-energy electrons,and the detection rate is greatly dependent on the optical-radio flux ratio.We find that for millisecond timescale optical counterparts,the detection rate of WFST,CSST and ET can reach hundreds per year.If～10^-3,the corresponding annual detection rates of WFST and CSST are in the order of 1,and the annual detection rate of ET is 19.5.For the hourly duration optical counterparts,if the age of the supernova remnant is 5 years,is about10^-6,and the annual detection rates are above 100.The X-ray counterpart of FRB 200428indicates that FRBs may produce relativistic outflow,which will interact with the interstellar medium and produce optical afterglows.We simulate FRBs according to the energy and redshift distribution from the literature and study the detectability with the standard afterglow model.Similar to FRB 200428,when the total energy-radio energy ratio is=10⁵,the detection rates of fast radio burst optical afterglow of WFST,CSST and ET based on the Chime-FRB catalog are 5.0,4.2 and 118.2 per year,respectively.Based on SFRD and energy function,the annual detection rates of CSST,WFST and ET are 1.3,1.0 and 67.4,respectively.