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Constraining the Neutral Hydrogen Fraction from SKA Simulated Observation using a Double-Gaussian Decomposition Technique

Jiajun Zhang, Huanyuan Shan

TL;DR

Problem: estimate the global neutral hydrogen fraction $x_{HI}$ during the Epoch of Reionization from noisy SKA imaging data. Approach: model the pixel-value histogram as a two-component Gaussian mixture with a zero-centered noise/ionized component and an offset Gaussian for the $21$ cm signal, then infer $x_{HI}$ per redshift bin and apply Gaussian Process regression to enforce a smooth evolution. Contributions: a fast, interpretable, model-independent method that yields $x_{HI}$ values across three redshift bins in agreement with the simulations. Significance: enables robust reconstruction of the reionization history from imaging data and provides a practical framework for future SKA analyses.

Abstract

The Epoch of Reionization (EoR) is a unique phase in cosmic history, marked by the ionization of neutral hydrogen by the first luminous sources. The global neutral hydrogen fraction (x_HI) is a key observable for probing this era. This paper presents a novel, statistically robust method to extract the evolution of x_HI from the challenging noise-dominated data from the Square Kilometre Array (SKA) Data Challenge 3b. Our approach is based on a key physical insight: the pixel value distribution in SKA intensity maps is a mixture of signals from ionized and neutral regions. We model this distribution as a superposition of two Gaussian components-one fixed at zero representing noise and ionized bubbles, and a second, offset Gaussian tracing the neutral hydrogen signal. We perform this decomposition on data grouped into three redshift bins. The double-Gaussian model provides an excellent fit to the pixel histogram data. The derived x_HI values show a clear decreasing trend across the three redshift bins, consistent with a progressing reionization process. And the results are consistent with the provided simulation data. This method offers a powerful, model-independent, and fully interpretable way for measuring x_HI from 21 cm data, demonstrating significant potential for application to future SKA observations.

Constraining the Neutral Hydrogen Fraction from SKA Simulated Observation using a Double-Gaussian Decomposition Technique

TL;DR

Problem: estimate the global neutral hydrogen fraction during the Epoch of Reionization from noisy SKA imaging data. Approach: model the pixel-value histogram as a two-component Gaussian mixture with a zero-centered noise/ionized component and an offset Gaussian for the cm signal, then infer per redshift bin and apply Gaussian Process regression to enforce a smooth evolution. Contributions: a fast, interpretable, model-independent method that yields values across three redshift bins in agreement with the simulations. Significance: enables robust reconstruction of the reionization history from imaging data and provides a practical framework for future SKA analyses.

Abstract

The Epoch of Reionization (EoR) is a unique phase in cosmic history, marked by the ionization of neutral hydrogen by the first luminous sources. The global neutral hydrogen fraction (x_HI) is a key observable for probing this era. This paper presents a novel, statistically robust method to extract the evolution of x_HI from the challenging noise-dominated data from the Square Kilometre Array (SKA) Data Challenge 3b. Our approach is based on a key physical insight: the pixel value distribution in SKA intensity maps is a mixture of signals from ionized and neutral regions. We model this distribution as a superposition of two Gaussian components-one fixed at zero representing noise and ionized bubbles, and a second, offset Gaussian tracing the neutral hydrogen signal. We perform this decomposition on data grouped into three redshift bins. The double-Gaussian model provides an excellent fit to the pixel histogram data. The derived x_HI values show a clear decreasing trend across the three redshift bins, consistent with a progressing reionization process. And the results are consistent with the provided simulation data. This method offers a powerful, model-independent, and fully interpretable way for measuring x_HI from 21 cm data, demonstrating significant potential for application to future SKA observations.

Paper Structure

This paper contains 9 sections, 2 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Data and Methodology
  3. SKA Data Challenge 3b Data
  4. Data Pre-processing
  5. The Physical Basis for the Double-Gaussian Model
  6. Analysis Pipeline
  7. Results
  8. Conclusion and Discussion
  9. Acknowledgments

Figures (3)

  • Figure 1: Three example images from SDC3b, showing the luminosity distribution in the unit of Jy/beam, at 161MHz, 176MHz, and 191MHz. Structured patterns can be seen in the central region.
  • Figure 2: The histogram and double-Gaussian model fitting results for the pixel values in the images. Group 1 contains 151MHz-166MHz, Group 2 contains 166MHz-181MHz, Group 3 contains 181MHz-196MHz. The green dashed line represents the contribution from foreground removal residual and thermal noise. The blue dashed line represents the contribution from 21cm signal.
  • Figure 3: The top panels show the two-dimensional joint probability for 3 groups of frequency bins. The bottom panels show the one-dimensional probability inference results using our method. The red dashed line is the central value answer, and the shaded red region is the $1\sigma$ range, obtained from the SDC3b website.