replying to R. Hills et al. Nature 564, (2018)

In our Letter1, the foreground models account for a combination of astronomical foregrounds, ionospheric effects and any residual calibration effects. We obtained best-fit parameters that absorb a degenerate combination of these effects from unconstrained fits to the models. In the accompanying Comment2, the concerns of Hills et al. arise primarily because they failed to recover physical values for two ionosphere parameters in a foreground model with three additional non-ionosphere parameters.

Ionosphere parameters are covariant with the amplitude and spectral index of the astronomical foreground. Small errors in these astronomical parameters, as well as residual effects from calibration, could bias the recovered ionosphere parameters. In ref. 3, we calculated an overall systematic uncertainty of ±0.02 on the spectral index measured by the high-band instrument, including beam correction uncertainty. We found a similar uncertainty for the low-band instrument. Errors of this level could yield deviations from the true spectrum with amplitudes and shapes comparable to those of the expected ionospheric contribution. For these reasons, we did not intend to extract ionospheric information from the measurements presented. In a previous study4, we extracted information about ionospheric variability from EDGES high-band data. We limited that analysis to differencing spectra acquired at the same local sidereal time on different nights in order to reduce the covariance with the astronomical foregrounds and mitigate any systematic effects, before fitting an ionosphere model to the differential spectra. Extracting absolute ionospheric information directly from the measured spectra would require a separate, in-depth study.

Measuring physical foreground properties requires the absolute temperature calibration of the spectrum, whereas identifying a 21-cm profile embedded in the foreground requires only relative calibration between channels in the spectrum. It is possible to recover a 21-cm feature without accurately measuring the physical foreground properties. Most global 21-cm constraints have come from this regime5,6,7,8,9. In EDGES we do aim to measure a fully absolutely calibrated spectrum. Although in our Methods section we acknowledged potential residual calibration effects, we reported tests to show that any such effects are not consistent with the reported profile. We therefore concluded that the signal is astronomical.

Hills et al.2 found that several alternative models for the foreground and signal can be fitted to the data. We broadly agree, but a general absorption profile remains the most justified a priori choice of signal model because we have disfavoured the instrument as the source of the structure and there is no known physical expectation for other shapes in either the foreground or 21-cm signal, whereas an absorption is expected. We have data that exclude some of the alternative signal models proposed by Hills et al.2 and plan to publish those results in the near future.

When using our polynomial foreground model over the full band (51–99 MHz), rather than over only the sub-band for which we used it (approximately 63–99 MHz), Hills et al.2 recovered best-fit profiles that are not consistent with our reported properties. We have shown using simulations10 that this outcome is consistent with the expected performance of that model. Therefore, their choice to use it over the full band was not justified. Other foreground models perform better than the polynomial model across the full band, including the linear physically motivated model that we used.