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Direct reconstruction of the Reionization history from 21cm 2D Power Spectra

Yannic Pietschke, Caroline Heneka, Tom Schlenker, Ayodele Ore, Benedikt Schosser

TL;DR

The paper tackles reconstructing the Epoch of Reionization history from non-Gaussian 21cm signals by bypassing explicit likelihoods through simulation-based inference. It presents EoRFlow, a conditional invertible neural network that uses 2D power spectra as the conditioning statistic to infer the global neutral fraction $x_{ m HI}(z)$ across 15 redshift slices, validated on realistic SKA-Low mock data. The approach yields fast, well-calibrated posteriors, robust to observational noise and foreground assumptions, and capable of reconstructing complex reionization histories across early to late scenarios. This work provides a scalable, likelihood-free pathway for extracting reionization timelines from upcoming 21cm observations, with direct relevance to SKA-era 21cm cosmology and cross-validation with Ly$\alpha$ forest and CMB constraints.

Abstract

The 21cm line from the spin-flip transition of neutral hydrogen (HI) provides a unique window into the Epoch of Reionization (EoR), the final phase transition of our Universe. The Square Kilometre Array (SKA) enables precise measurements of 21cm fluctuations that trace ionization, temperature, and density fluctuations of the intergalactic medium (IGM). Nevertheless, a direct reconstruction of the timeline of the EoR in terms of the progress of ionization remains an ongoing challenge due to the highly non-Gaussian nature and thus intractable likelihood of the 21cm signal. Here, we present EoRFlow, a simulation-based inference (SBI) framework for reconstructing the global neutral hydrogen fraction $x_{\mathrm{HI}}(z)$ directly from 2D cylindrically averaged power spectra (2DPS) of the 21cm signal. We validate our method on realistic mock datasets for SKA-Low. Bypassing the need for explicit likelihood formulations, our approach enables fast, unbiased posterior estimation of the $x_{\mathrm{HI}}$ evolution in narrow redshift slices, allowing for piecewise reconstruction of the global reionization history. By directly inferring the reionization history from 21cm power spectra, our framework provides a scalable and robust path forward for 21cm cosmology in the SKA era.

Direct reconstruction of the Reionization history from 21cm 2D Power Spectra

TL;DR

The paper tackles reconstructing the Epoch of Reionization history from non-Gaussian 21cm signals by bypassing explicit likelihoods through simulation-based inference. It presents EoRFlow, a conditional invertible neural network that uses 2D power spectra as the conditioning statistic to infer the global neutral fraction across 15 redshift slices, validated on realistic SKA-Low mock data. The approach yields fast, well-calibrated posteriors, robust to observational noise and foreground assumptions, and capable of reconstructing complex reionization histories across early to late scenarios. This work provides a scalable, likelihood-free pathway for extracting reionization timelines from upcoming 21cm observations, with direct relevance to SKA-era 21cm cosmology and cross-validation with Ly forest and CMB constraints.

Abstract

The 21cm line from the spin-flip transition of neutral hydrogen (HI) provides a unique window into the Epoch of Reionization (EoR), the final phase transition of our Universe. The Square Kilometre Array (SKA) enables precise measurements of 21cm fluctuations that trace ionization, temperature, and density fluctuations of the intergalactic medium (IGM). Nevertheless, a direct reconstruction of the timeline of the EoR in terms of the progress of ionization remains an ongoing challenge due to the highly non-Gaussian nature and thus intractable likelihood of the 21cm signal. Here, we present EoRFlow, a simulation-based inference (SBI) framework for reconstructing the global neutral hydrogen fraction directly from 2D cylindrically averaged power spectra (2DPS) of the 21cm signal. We validate our method on realistic mock datasets for SKA-Low. Bypassing the need for explicit likelihood formulations, our approach enables fast, unbiased posterior estimation of the evolution in narrow redshift slices, allowing for piecewise reconstruction of the global reionization history. By directly inferring the reionization history from 21cm power spectra, our framework provides a scalable and robust path forward for 21cm cosmology in the SKA era.

Paper Structure

This paper contains 12 sections, 4 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. 21cm simulations and 2D power spectra
  3. EoRFlow for reconstruction of the EoR history
  4. Training and preprocessing
  5. Results
  6. Inferring posteriors for the neutral fraction $x_\mathrm{HI}$
  7. Calibration
  8. Reconstructing the EoR history
  9. Conclusion
  10. Further posterior examples
  11. Network architecture and training loss
  12. Impact of noise on network training and inference results

Figures (10)

  • Figure 1: 2DPS at redshifts $z=7$ (left) and $z=10$ (right) with corresponding neutral fractions $x_\mathrm{HI}$ for a fiducial light-cone with $\Omega_\mathrm{m}=0.31$, $m_\mathrm{WDM} =2 \, \mathrm{keV}$, $T_\mathrm{vir} =10^{5.2}$, $\zeta= 97.46$, $E_\mathrm{0} = 1143.21 \, \mathrm{eV}$ and $L_\mathrm{X} =10^{41.29} \, \mathrm{erg \, s^{-1}M^{-1}_\odot yr}$; shown are the 2DPS without noise (upper panels), for AA4 opt noise (center panels), and AA$^*$ mod noise (lower panels).
  • Figure 2: The 15000 simulated reionization histories of the dataset. The majority of models start and finish reionization entirely within the redshift regime $z\in[5,12]$, but some begin earlier or stop later. We retain these extreme models to ensure that our database remains as versatile as possible. The fiducial models used for analysis in Section \ref{['sec:Results']} are highlighted in green (see Figure \ref{['fig:inferred_timelines']}).
  • Figure 3: Illustration of the EoRFlow inference framework developed in this work. A set of 2DPS at 15 different redshift bins from $z=5.2$ to $z=12.0$ (see Section \ref{['sec:data']} for a description of the data) is fed into EoRFlow for posterior estimation and reconstruction of the EoR history, see Section \ref{['sec:data']} for a description of the 2DPS as well as noise and array configurations, AA$^\star$ mod and AA4 opt, and Section \ref{['sec:NN']} for a detailed description of the EoRFlow model.
  • Figure 4: Marginalised posteriors for neutral fractions $x_\mathrm{HI}(z)$ for a randomly chosen set of parameters, $\Omega_\mathrm{m}=0.31$, $m_\mathrm{WDM} =2 \, \mathrm{keV}$, $T_\mathrm{vir} =10^{5.2}$, $\zeta= 97.46$, $E_\mathrm{0} = 1143.21 \, \mathrm{eV}$ and $L_\mathrm{X} =10^{41.29} \, \mathrm{erg \, s^{-1}M^{-1}_\odot yr}$. The shadings indicate 68$\%$ and 95$\%$ CI. Red shows the posterior derived from mock 2DPS including AA4 opt noise, blue corresponds to AA$^*$ mod noise and grey to the noiseless case for comparison; the black dot denotes the fiducial values. The zoom-in panel (upper right) shows for improved clarity a selection of contours with the same axis scaling as the scaling of the corresponding panel in the full triangle plot.
  • Figure 5: Empirical coverage of the posteriors for the model trained with AA4 opt noise (red), AA$^*$ mod noise (blue) and without noise (grey). Error bands are estimated based on a binomial distribution. The ideal coverage is represented by the black diagonal line.
  • ...and 5 more figures