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 x 10(42) erg s(-1) to 7.80 x 10(44) erg s(-1), and the average E upper limits range from 6.91 x 10(39) erg to 1.94 x 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 DMhost + DMscr similar to 100 pc cm(-3), such an FRB can be detected up to z similar to 3.6 by Parkes and the Five-hundred-meter Aperture Spherical radio Telescope (FAST) under ideal conditions up to z similar to 10.4. Assuming the existence of FRBs that are detectable at z similar to 15 by sensitive telescopes such as FAST, the upper limit DM for FRB searches may be set to similar 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 alpha(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.