Fast Radio Burst Energetics and Detectability from High Redshifts

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 × 10⁴² erg s^-1 to 7.80 × 10⁴⁴ erg s^-1, and the average E upper limits range from 6.91 × 10³⁹ erg to 1.94 × 10⁴² 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.