Fast Radio Burst Energetics and Detectability from High Redshifts

Abstract

We estimate the upper limit redshifts of known fast radio bursts (FRBs) using the dispersion measure (DM)-redshift ( z ) relation and derive the upper limit peak luminosity L p and energy E of FRBs within the observational band. The average z upper limits range from 0.17 to 3.10, the average L p upper limits range from 1.24 × 10 42 erg s −1 to 7.80 × 10 44 erg s −1 , and the average E upper limits range from 6.91 × 10 39 erg to 1.94 × 10 42 erg. FRB 160102 with DM = 2596.1 ± 0.3 pc cm −3 likely has a redshift greater than 3. Assuming that its intrinsic DM contribution from the host and FRB source is DM host  + DM scr  ∼ 100 pc cm −3 , such an FRB can be detected up to z  ∼ 3.6 by Parkes and the Five-hundred-meter Aperture Spherical radio Telescope (FAST) under ideal conditions up to z  ∼ 10.4. Assuming the existence of FRBs that are detectable at z  ∼ 15 by sensitive telescopes such as FAST, the upper limit DM for FRB searches may be set to ∼9000 pc cm −3 . For single-dish telescopes, those with a larger aperture tend to detect more FRBs than those with a smaller aperture if the FRB luminosity function index α L is steeper than 2, and vice versa. In any case, large-aperture telescopes such as FAST are more capable of detecting high- z FRBs, even though most of FRBs detected by them are still from relatively low redshifts.