Robust statistics towards detection of the 21 cm signal from the Epoch of Reionization

Abstract

We explore methods for robust estimation of the 21 cm signal from the Epoch of Reionisation (EoR). A Kernel Density Estimator (KDE) is introduced for measuring the spatial temperature fluctuation power spectrum from the EoR. The KDE estimates the underlying probability distribution function of fluctuations as a function of spatial scale, and contains different systematic biases and errors to the typical approach to estimating the fluctuation power spectrum. Extraction of histograms of visibilities allows moments analysis to be used to discriminate foregrounds from 21 cm signal and thermal noise. We use the information available in the histograms, along with the statistical dis-similarity of foregrounds from two independent observing fields, to robustly separate foregrounds from cosmological signal, while making no assumptions about the Gaussianity of the signal. Using two independent observing fields to robustly discriminate signal from foregrounds is crucial for the analysis presented in this paper. We apply the techniques to 13 hours of Murchison Widefield Array (MWA) EoR data over two observing fields. We compare the output to that obtained with a comparative power spectrum estimation method, and demonstrate the reduced foreground contamination using this approach. Using the second moment obtained directly from the KDE distribution functions yields a factor of 2-3 improvement in power for k < 0.3h Mpc −1 compared with a matched delay space power estimator, while weighting data by additional statistics does not offer significant improvement beyond that available for thermal noise-only weights.

Snowmass2021 Cosmic Frontier White Paper: 21cm Radiation as a Probe of Physics Across Cosmic Ages

“…True to its broad science case, the tile layout of the MWA is a hybrid between a spread out non-regular configuration and two closely packed, hexagonal grids of 36 tiles each [215]. The MWA has published a number of upper limits over a broad range of redshifts in recent years ranging from Cosmic Dawn redshifts to reionization redshifts [216][217][218][219][220][221][222][223][224].…”

Two-point statistics without bins: A continuous-function generalization of the correlation function estimator for large-scale structure

“…This is useful when we want to reconstruct a distribution without making many assumptions about the data, as is required in parametric methods. KDEs have found use in many areas of astrophyics, for example to measure the 21cm power spectrum with reduced foreground contamination (Trott et al 2019), and to estimate luminosity functions with superior performance compared to binned methods (Yuan et al 2020). Hatfield et al (2016) uses a KDE approach to estimate the angular correlation function, in order to address the issues of information loss and arbitrary bin choice inherent to binning; they optimize for the kernel choice, and find a correlation function consistant with that of the binned method.…”

Probing the Epoch or Reionisation with the MWA

“…Beyond new analyses the extract cosmological information, the large systematic impediments presented currently by foreground signals demands careful attention. In [15], the EoR group used a kernel density estimator to study the distribution of data in different wavemodes from two different observing fields. This work showed that foregrounds differed between locations on the sky, potentially offering an avenue for future use of such estimators to discriminate isotropic cosmological signal from local foreground contamination.…”