Revised LOFAR upper limits on the 21-cm signal power spectrum at $\mathbf{z\approx9.1}$ using Machine Learning and Gaussian Process Regression

TL;DR

This paper introduces a machine learning-enhanced Gaussian Process Regression method to improve foreground mitigation in LOFAR data, leading to revised upper limits on the high-redshift 21-cm signal power spectrum at z≈9.1.

Contribution

The study applies a novel VAE-based covariance kernel within GPR to reduce signal loss and systematically improve upper limit estimates for the 21-cm power spectrum.

Findings

Revised 2-sigma upper limit of Δ²₁₋₂ < (25)^2 mK² at k=0.075 h Mpc⁻¹.

VAE-based kernel shows smaller correlation with excess noise.

GPR approach effectively models LOFAR data for 21-cm signal constraints.

Abstract

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 hours ($\approx 10$ nights) of LOFAR data at $z \approx 9.1$, and report revised upper limits of the 21-cm signal power spectrum. Overall, we agree with past results reporting a 2-$\sigma$ upper limit of $\Delta^2_{21} < (80)^2~\rm mK^2$ at $k = 0.075~h~\rm Mpc^{-1}$. 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-$\sigma$ upper limit of $\Delta^2_{21} < (25)^2~\rm mK^2$ at $k = 0.075~h~\rm Mpc^{-1}$. 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.