We estimate the upper limit redshifts of known 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 $1.24 \times 10^{ 42} \rm erg \ s^{ -1}$ to $7.80 \times 10^{ 44} \rm erg \ s^{ -1}$, and the average $E$ upper limits range from $6.91 \times 10^{ 39}$ erg to $1.94 \times 10^{ 42}$ erg. FRB 160102 with DM $=2596.1 \pm 0.3 \ { \rm pc \ cm^{ -3}}$ likely has a redshift greater than 3. Assuming that its intrinsic DM contribution from the host and FRB source is ${ \rm DM_{ host}+DM_{ scr}}\sim 100 \ { \rm pc \ cm^{ -3}}$, such an FRB can be detected up to $z \sim 3.6$ by Parkes and by FAST under ideal conditions up to $z \sim 10.4$. Assuming that there exist FRBs detectable at $z\sim 15$ by sensitive telescopes such as FAST, the upper limit DM for FRB searches may be set to $\sim 9000 \ { \rm pc \ cm^{ -3}}$. 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 $\alpha_{ \rm L}$ 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.
Categories: astro-ph.HE