Revised LOFAR upper limits on the 21-cm signal power spectrum at z ≈ 9.1 using machine learning and gaussian process regression

The use of Gaussian Process Regression (GPR) for foregrounds mitigation in data collected by the LOw-Frequency ARray (LOFAR) to measure the high-redshift 21-cm signal power spectrum has been shown to have issues of signal loss when the 21-cm signal covariance is misestimated. To address this problem, we have recently introduced covariance kernels obtained by using a Machine Learning based Variational Auto-Encoder (VAE) algorithm in combination with simulations of the 21-cm signal. In this work, we apply this framework to 141 h (≈ 10 nights) of LOFAR data at z ≈ 9.1, and report revised upper limits of the 21-cm signal power spectrum. Overall, we agree with past results reporting a 2-σ upper limit of Δ ²₂₁ \ <\ (80)²~ mK² at k = 0.075~h~ Mpc⁻¹. Further, the VAE-based kernel has a smaller correlation with the systematic excess noise, and the overall GPR-based approach is shown to be a good model for the data. Assuming an accurate bias correction for the excess noise, we report a 2-σ upper limit of Δ ²₂₁ \ <\ (25)²~ mK² at k = 0.075~h~ Mpc⁻¹. However, we still caution to take the more conservative approach to jointly report the upper limits of the excess noise and the 21-cm signal components.