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

A Correction to this paper has been published: https://doi.org/10.1140/epjc/s10052-018-5537-2

It was shown in [1] that an optimal signal-to-noise ratio is obtained in the frequency band of 100-190 MHz, which allows us to lower the energy threshold of radio observations of air showers. Subsequent studies revealed a correction required to the normalisation factor of the modelled noise used in this study. A factor of 1 2 × √ N was found to be missing in the normalisation, where N is the number of samples of the time series. This resulted in the overall scale of the noise amplitude to be underestimated by a factor of ≈ 22.
While this does not change the optimal frequency band, it results in a constant scaling factor of ≈ 1 484 for all SNR values shown in [1]. To be specific, Figures 3-10 in [1] will be affected by this scaling.  Figure 1 shows the effect of the correction factor on the scale of the noise amplitudes. This is an updated version of Figure 3 in [1]. While there is no change to the time traces of the signal (from a 10 PeV gamma-ray shower with θ = 61 • ), the noise becomes significantly larger, resulting in lower values of SNR. For this particular antenna location, the SNR for the 30-80 MHz band lowers from 35 to 0.07 while that for the 50-350 MHz band lowers from 1055 to 2.07.
Another example is shown in Fig. 2 where the SNR obtained for an antenna at the Cherenkov ring at different frequency bands is shown for a 10 PeV gamma-ray shower.
In the corresponding plot in [1] all the frequency bands with SNR < 10 were set to the colour white, which is not done here for visualisation purposes. It can be clearly seen that the optimal frequency band remains 100-190 MHz as shown in [1].  The SNR for an antenna on the Cherenkov ring at various frequency bands, for a 10 PeV gamma-ray shower with θ = 61 • and α = 79 • . This is an updated version of Figure 4(b) in [1] However, the required correction to the scaling of the SNR increases the detection threshold to a higher energy value. 1 A recalculation of the SNR for the simulations used in Figure 9 of [1] allows us to estimate the new threshold energy. The updated plot is shown in Fig. 3. The new fit is given by SNR max = 0.032 ± 0.001 × E 2.03±0.02 . From the fit, it is estimated that at an energy of 16.8 PeV, for gamma rays from the direction of θ = 61 • at the South Pole, we will obtain the threshold SNR of 10. Due to the lack of simulations of air showers with energies above 10 PeV, this cannot be cross-checked. Therefore, we expect that a radio array as presented in [1] will feature a threshold energy for gamma rays above 10 PeV and the exact threshold energy needs to 1 A corresponding correction of the threshold will also apply to Figure 2 in [2], which was produced using the same wrong normalization of the noise model. be determined by a dedicated study for this higher energy range.
Acknowledgements The authors thank Alan Coleman for bringing a problem in the normalisation to our attention.

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