Mitigating incoherent excess variance in high-redshift 21 cm observations with multi-output cross-Gaussian process regression

TL;DR

The paper introduces cross-GPR, a cross-covariance Gaussian process regression framework that exploits night-to-night coherence to separate the coherent high-redshift 21 cm signal from incoherent excess variance in interferometric data. By modeling multiple nights jointly and embedding cross-covariances that distinguish coherent and incoherent components, the method reduces degeneracies that arise when spectral signatures overlap and enables subtracting incoherent excess without suppressing the 21 cm signal. Across synthetic and simulated visibility cubes, cross-GPR demonstrates unbiased recovery of the 21 cm power spectrum and, in many cases, superior hyperparameter inference compared with standard single-night GPR. The approach, compatible with physics-informed kernels and learned 21 cm covariances, has the potential to improve upper-limit sensitivities for current and future 21 cm experiments and is available in the crossgp Python library for immediate integration into existing pipelines.

Abstract

Systematic effects that limit the achievable sensitivity of current low-frequency radio telescopes to the 21 cm signal are among the foremost challenges in observational 21 cm cosmology. The standard approach to retrieving the 21 cm signal from radio interferometric data separates it from bright astrophysical foregrounds by exploiting their spectrally smooth nature, in contrast to the finer spectral structure of the 21 cm signal. Contaminants exhibiting rapid frequency fluctuations, on the other hand, are difficult to separate from the 21 cm signal using standard techniques, and the power from these contaminants contributes to low-level systematics that can limit our ability to detect the 21 cm signal. Many of these low-level systematics are incoherent across multiple nights of observation, resulting in an incoherent excess variance above the thermal noise sensitivity of the instrument. In this paper, we develop a method called cross-GPR (cross covariance Gaussian process regression) that exploits the incoherence of these systematics to separate them from the 21 cm signal, which remains coherent across multiple nights of observation. We first develop and demonstrate the technique on synthetic signals in a general setting, and then apply it to gridded interferometric visibility cubes. We perform realistic simulations of visibility cubes containing foregrounds, 21 cm signal, noise, and incoherent systematics. The simulations show that the method can successfully separate and subtract incoherent contributions to the excess variance, and its advantages over standard techniques become more evident when the spectral behavior of the contaminants resembles that of the 21 cm signal. Simulations performed on a variety of 21 cm signal shapes also reveal that the cross-GPR approach can subtract incoherent contributions to the excess variance, without suppressing the 21 cm signal.

Figures (6)

• Figure 1: Impact of including cross-covariances in GPR in the separation of coherent and incoherent components demonstrated on synthetic data. The left column shows the case where the coherent and incoherent covariance kernels are distinct, while the right column shows the case of the coherent and incoherent components having similar covariances. The corner plots in the top show the posterior distribution of the hyperparameters for the block diagonal approach (in blue) and the full covariance approach (in red). The four plots at the bottom show the recovery of a single realisation of the coherent component, for the block diagonal and full covariance approaches, respectively.
• Figure 2: Cylindrical power spectra of the different input components constituting the simulated visibility cubes. The foreground and 21 cm signal components are coherent and have a common realisation for both nights. The excess and noise components are incoherent and have different realisations for the two nights.
• Figure 3: Comparison of the performance of standard and cross-GPR in recovering the input components. The standard and cross-GPR results are shown in blue and red colors, respectively. Top: Corner plot showing the posterior distribution of the GPR hyperparameters. The input hyperparameter values are indicated with black lines. Bottom: Input and recovered spherical power spectra of the different components.
• Figure 4: Power spectra of the residual data after the foregrounds and excess components have been subtracted. The standard and cross-GPR results are shown in blue and red colors, respectively.
• Figure 5: Recovery of the input hyperparameters for simulations performed for a variety of 21 cm signal shapes. The peak-normalised histograms marginalised over all signal shapes, computed after subtracting the input values, are shown. The different panels correspond to the different hyperparameters. The results from the three runs of standard GPR are shown in different shades of blue, while the cross-GPR results are shown in red. A vertical line is plotted at Recovered = Input to indicate perfect recovery.