Erratum to: Search for PeVatrons at the Galactic Center using a radio air-shower array at the South Pole

1 Erratum to: Eur. Phys. J. C (2018) 78:111 https://doi.org/10.1140/epjc/s10052-018-5537-2

The original article contains typographic errors in the Appendix B, which deals with the process of generating a noise trace. The results presented in the article are unaffected as they were derived with the correct versions of these equations.

The correction concerns a missing square root in Eqs. (7) and (9). The corrected equations are given here. The electric field developed on the antenna arm is given by

$$\begin{aligned} \begin{aligned} |\overrightarrow{E}|=\,&\sqrt{S_{\mathrm {rec}}2Z_0} \quad [ \text {V/m}]\\ =\,&\sqrt{\frac{1}{2}2Z_0\frac{2k_\mathrm {B}\nu ^2 \delta \nu }{c^2} \int T(\theta , \phi ) \; \mathrm {d}\varOmega }. \end{aligned} \end{aligned}$$

(7)

The resulting voltage (Eq. (9) in the original article) can then be then re-written as

$$\begin{aligned} V(\nu ) = \sqrt{2Z_0\frac{k_\mathrm {B} \nu ^2 \delta \nu }{c^2} \int T(\theta ,\phi )\; |\overrightarrow{l_{\mathrm {eff}}}(\theta , \phi )|^2 \; \mathrm {d}\varOmega }. \end{aligned}$$

(9)