3 years ago

FRB Energetics and detectability from high redshifts.

Bing Zhang

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 an intrinsic DM contributions from the host and FRB source ${\rm DM_{host}+DM_{scr}}\sim 100 \ {\rm pc \ cm^{-3}}$, such an FRB can be detected up to $z \sim 3.61$ by Parkes with an observed DM $\sim 2947 \ {\rm pc \ cm^{-3}}$, and by FAST under ideal conditions up to $z \sim 10.4$ with an observed DM $\sim 6500 \ {\rm pc \ cm^{-3}}$. 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 $\sim 9000 \ {\rm pc \ cm^{-3}}$. Large aperture telescopes tend to detect more FRBs if the FRB luminosity function index $\alpha_{\rm L}$ is steeper than 2, and vice versa. In any case, they tend to detect more low-luminosity FRBs at regular redshifts (say, $z<3$), with a small chance of detecting high-$z$ FRBs not reachable by smaller telescopes.

Publisher URL: http://arxiv.org/abs/1808.05277

DOI: arXiv:1808.05277v1

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